See the attached two problems, one is consider the augmented matrix and the other is consider the matrix.
Answers
The row operations on the augmented matrix are
R₂ → 4R₂R₃ → R₃ + 3What is an augmented matrix?An augmented matrix is a matrix in which the coefficient matrix and the column matrix are written together.
Since we have the augmented matrix
[tex]\left[\begin{array}{ccc}1&3&5\\0&\frac{1}{4} &-1\\-3&6&-11\end{array}\right] \left[\begin{array}{ccc}4&\\1&\\10&\end{array}\right][/tex]
To determine the next row operations, we proceed as follows.
Since we want to convert the second element in the second row to 1, we multiply row 2 by 4,
So, R₂ → 4R₂
So, the augmented matrix becomes
[tex]\left[\begin{array}{ccc}1&3&5\\0&1&-4\\-3&6&-11\end{array}\right] \left[\begin{array}{ccc}4&\\4&\\10&\end{array}\right][/tex]
Now, since we want to convert the first element in the third row to 0, the row operation we perform is we add 3 to row 3
So, R₃ → R₃ + 3
So, the augmented matrix becomes
[tex]\left[\begin{array}{ccc}1&3&5\\0&1&-4\\0&9&-8\end{array}\right] \left[\begin{array}{ccc}4&\\4&\\13&\end{array}\right][/tex]
So, the row operations are
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Related Questions
Identify the solution for this system of equations
{4x + y = 7
{2y + 3= 3x - 16
A. (1,3)
B. (3,-5)
C. (7,-1)
D. No solution
Answers
The solution for the system of equations is (x, y) = B. (3, -5).
The correct option is B. (3, -5).
To find the solution for the system of equations:
{4x + y = 7
{2y + 3 = 3x - 16
We can solve it using the method of substitution or elimination. Let's use the method of elimination:
First, let's multiply the second equation by 2 to eliminate the variable y:
2(2y + 3) = 2(3x - 16)
4y + 6 = 6x - 32
Rearranging this equation, we get:
6x - 4y = 38 ----(1)
Now we have the system of equations:
4x + y = 7 ----(2)
6x - 4y = 38 ----(1)
Next, let's multiply equation (2) by 4 to eliminate the variable y:
4(4x + y) = 4(7)
16x + 4y = 28
Now we have the system of equations:
16x + 4y = 28 ----(3)
6x - 4y = 38 ----(1)
Adding equations (3) and (1) eliminates the variable y:
(16x + 4y) + (6x - 4y) = 28 + 38
22x = 66
x = 66/22
x = 3
Substituting the value of x into equation (2), we can solve for y:
4(3) + y = 7
12 + y = 7
y = 7 - 12
y = -5
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Rent for a 3 bedroom apartment is regularly $936 per month. Apartment management is offering one month free. If you sign a one year lease and apply the free month equally across months, how much is your new, monthly lease amount
Answers
Answer:
$858
Step-by-step explanation:
You are paying 11 months of rent for 1 year.
11 × $936 = $10,296
The total rent paid in 1 year for 11 months of rent is $10,296.
Divide the total by 12:
$10,296/12 = $858
The monthly amount averages to $858.
Please help
Factor
f(x) = 2×2 - 9x- 18
(2x + [?])(x - [ ])
Answers
Step-by-step explanation:
The quadratic expression f(x) = 2x^2 - 9x - 18 can be factored as (2x + 3)(x - 6). So, the missing values in the given expression (2x + [?])(x - [ ]) are 3 and 6, respectively.
Answer:
(2x + 3)(x -6)
Step-by-step explanation:
2x² -9x -18
2 × -18 = -36
Find factors of -36 which you multiply will give -36 but when same factors are added will give -9.
-12 × 3 = -36
-12 + 3 = -9
2x²-12x +3x -18
2x(x - 6) + 3(x -6)
(2x + 3)(x -6)
Which statement about the points (0, 3), (2, 8), (8, 2), and (0, 1) is true?
All but one of the points is on the x-axis.
The points (0, 3) and (0, 1) are located on the same axis.
All but one of the points are in Quadrant I.
The point (8, 2) is the closest to the x-a
Answers
The statement about the points (0, 3), (2, 8), (8, 2), and (0, 1) that is true is All but one of the points are in Quadrant I. Option C
How to determine the statementThe first quadrant, positioned at the upper-right area of the Cartesian plane, involves coordinates that have favorable values for both x and y.
The coordinates (0,3), (2,8), and (0,1) all fall under quadrant I since their x and y values are positive.
The point located in Quadrant IV can be identified as (8, 2) due to its positive x-coordinate and negative y-coordinate.
Hence, it can be said with precision that Quadrant I contains all but one point.
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What numbers are missing from the pattern below? Enter your answer, using
a comma to separate each number.
120, 5, 48, 70, ?, ?, ?, ?, 120, 5, 48, 70
Answer here
Answers
120, 5, 48, 70, ?, ?, ?, ?, 120, 5, 48, 70
From observing the pattern, we can notice that it follows a specific sequence:
1st number: Multiply the following number by 2 and subtract 10: 5 * 2 - 10 = 0
2nd number: Add 43 to the previous number: 0 + 43 = 43
3rd number: Add 27 to the previous number: 43 + 27 = 70
Using this pattern, we can continue:
4th number: Multiply the previous number by 2 and subtract 10: 70 * 2 - 10 = 130
5th number: Add 43 to the previous number: 130 + 43 = 173
6th number: Add 27 to the previous number: 173 + 27 = 200
7th number: Multiply the previous number by 2 and subtract 10: 200 * 2 - 10 = 390
Therefore, the missing numbers are: 0, 43, 130, 173, 200, 390
similarly in right triangles
Answers
The value of y for the right triangle is equal to 48, which makes the first option correct.
How to evaluate for the values of y for the triangleThe perpendicular height of the right triangle divides the triangle in two triangles with the same proportions as the original triangle.
60/x = 36/60 {opposite/hypotenuse}
x = (60 × 60)/36 {cross multiplication}
x = 100
by Pythagoras rule the unlabeled side of the entire triangle is calculated as:
√(100² - 60²) = 80
so;
y/80 = 60/100 {opposite/hypotenuse}
y = (60 × 80)/100 {cross multiplication}
y = 48
Therefore, the value of y for the right triangle derived to be 48.
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Is gender associated with a person's environmental awareness? Two hundred randomly selected individuals were surveyed about their environmental awareness. Participants were asked about recycling, use of aerosol sprays, and various other environmental concerns. A point system was developed to score the individuals' responses. Once the points were tallied, individuals were broken up into categories of environmental awareness. Those with scores of 8 to 10 were considered to be very environmentally aware, scores of 4 to 6 moderately aware, and 3 or less not aware. The results are shown in the following table:
Very environmentally aware Moderately environmentally aware Not environmentally aware
Male 30 21 45
Female 42 34 28
Run an appropriate test of significance at α = 5 to see if the data provide evidence that gender is associated with one's environmental awareness.
Answers
The chi-square test of independence is a useful statistical method that can be used to test the null hypothesis that there is no association between two categorical variables. When the assumptions of the test are satisfied, this hypothesis can be tested using the chi-square statistic. The following problem can be solved using the chi-square test of independence:
Is gender associated with a person's environmental awareness? Two hundred randomly selected individuals were surveyed about their environmental awareness. Participants were asked about recycling, use of aerosol sprays, and various other environmental concerns.
A point system was developed to score the individuals' responses. Once the points were tallied, individuals were broken up into categories of environmental awareness.
Those with scores of 8 to 10 were considered to be very environmentally aware, scores of 4 to 6 moderately aware, and 3 or less not aware.
The results are shown in the following table: Very environmentally aware Moderately environmentally aware Not environmentally aware Male 302145 Female 423428 We will use a chi-square test of independence to test the null hypothesis that gender is not associated with one's environmental awareness.
We begin by specifying the null and alternative hypotheses: H0: Gender and environmental awareness are independent.
Ha: Gender and environmental awareness are dependent. We choose a significance level of α = 0.05. We can now proceed with the chi-square test of independence.
First, we will calculate the expected frequencies. The expected frequency for each cell can be found by multiplying the row total by the column total and then dividing by the sample size.
The expected frequencies are shown in the following table: Very environmentally aware Moderately environmentally aware not environmentally aware Male 22.5716.6176.81 Female 49.424.826.19 Next, we calculate the chi-square statistic using the formula: X2 = ∑(O - E)2/E where O is the observed frequency and E is the expected frequency.
The chi-square statistic is 18.66. We now need to find the degrees of freedom.
The degrees of freedom for a chi-square test of independence are given by df = (r - 1)(c - 1) where r is the number of rows and c is the number of columns. In this case, there are 2 rows and 3 columns, so df = (2 - 1)(3 - 1) = 2.
We can now use a chi-square distribution table to find the critical value of the chi-square distribution with 2 degrees of freedom and a significance level of 0.05.
The critical value is 5.99. Since the calculated value of the chi-square statistic (18.66) is greater than the critical value (5.99), we reject the null hypothesis.
We have sufficient evidence to conclude that gender and environmental awareness are dependent. Therefore, we can conclude that gender is associated with a person's environmental awareness.
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2.81729 please round to the nearest dollar
Answers
Answer:
3
Step-by-step explanation:
3
The accompanying diagram represents the market for violins.
Suppose that a new technology allows beginner-level violin producers to make violins at a substantially lower (marginal) cost while retaining the same quality.
a. Use the graph to illustrate the effect that this will have on the supply and demand of beginner-level violins and then answer the following three questions.
b. How much does this new technology increase consumer surplus?
Market for Violins
Quantity of violins (in thousands)
0
10
20
30
40
50
60
70
80
90
100
0
30
60
90
120
150
180
210
240
270
300
S
D
Increase in consumer surplus: $
2400
c. How much does this new technology increase producer surplus?
Increase in producer surplus: $
2400
d. How much does this new technology increase total (or social) surplus?
Increase in total surplus: $
4800
Answers
a. The new technology leads to an increase in the supply of beginner-level violins, resulting in a rightward shift of the supply curve. The demand curve remains unchanged unless otherwise specified.
b. The new technology increases consumer surplus by $2400, as represented by the shaded area between the original demand curve and the new demand curve up to the new equilibrium quantity.
c. The new technology increases producer surplus by $2400, represented by the shaded area between the original supply curve and the new supply curve up to the new equilibrium quantity.
d. The new technology increases total surplus by $4800, which is the sum of the increase in consumer surplus and the increase in producer surplus.
a. To illustrate the effect of the new technology on the supply and demand of beginner-level violins, we need to consider the following:
Supply: The new technology allows beginner-level violin producers to make violins at a substantially lower marginal cost while maintaining the same quality. This means that the supply of beginner-level violins will increase. We can show this on the graph by shifting the supply curve to the right.
Demand: The demand for beginner-level violins will depend on factors other than the new technology. If there is no change in demand, the demand curve will remain the same. However, if there is an increase in demand due to factors such as increased interest in learning the violin, we would see a shift in the demand curve to the right.
By shifting the supply curve to the right or the demand curve to the right, or both, we can represent the effect of the new technology on the market for beginner-level violins.
b. The increase in consumer surplus can be calculated by finding the area of the triangle formed by the original demand curve, the new demand curve, and the new equilibrium quantity of violins. This represents the additional benefit consumers receive from the lower price due to the new technology.
In the given graph, the increase in consumer surplus is represented by the shaded area between the original demand curve and the new demand curve, up to the new equilibrium quantity. The dollar value of this increase can be calculated by multiplying the increase in quantity by the average difference in price between the original and new equilibrium.
c. The increase in producer surplus can be calculated by finding the area of the triangle formed by the original supply curve, the new supply curve, and the new equilibrium quantity of violins. This represents the additional profit that producers receive from the higher quantity sold at the same or slightly reduced price due to the lower marginal cost from the new technology.
In the given graph, the increase in producer surplus is represented by the shaded area between the original supply curve and the new supply curve, up to the new equilibrium quantity. The dollar value of this increase can be calculated by multiplying the increase in quantity by the average difference in price between the original and new equilibrium.
d. The increase in total (or social) surplus is the sum of the increase in consumer surplus and the increase in producer surplus. In this case, the increase in total surplus would be the sum of the increases calculated in parts b and c.
Therefore, the increase in total surplus due to the new technology is represented by the shaded area between the original supply and demand curves and the new supply and demand curves, up to the new equilibrium quantity. The dollar value of this increase can be calculated by adding the dollar values of the increase in consumer surplus and the increase in producer surplus. In this example, the increase in total surplus is $4800.
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cinetica?
Un automóvil de 800 kg se desplaza a 50km/h cuál será su energía cinética.
Answers
The kinetic energy of this car is equal to 77160.49 Joules.
How to calculate the kinetic energy of this car?In Mathematics, the kinetic energy of a physical object can be calculated by using the following equation (formula):
K.E = 1/2 × mv²
Where:
K.E represent the kinetic energy.m represent the mass.v represent the speed or velocity.Note: 50 km/h to m/s = 50 × 1000/3600 = 13.89 m/s
By substituting the given parameters into the formula for the kinetic energy of a physical object, we have the following:
Kinetic energy, K.E = 1/2 × 800 × 13.89²
Kinetic energy, K.E = 400 × 192.90
Kinetic energy, K.E = 77160.49 Joules.
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Complete Question:
An 800 kg car travels at 50 km/h, what will its kinetic energy be?
Patient Name: Tom
Disease: Blastomycosis
Weight: 22 lbs
The Veterinarian has prescribed 10 mg/kg of ketoconazole PO q 12h
Concentration: 200 mg Tablets
Formula: D x W/C: Calculate the amount of medication needed for 60 days.
will mark brainliest!.
Answers
D is the prescribed dosage (10 mg/kg),
W is the weight of the patient (22 lbs),
C is the concentration of the medication (200 mg tablets).
First, we need to convert the weight from pounds to kilograms. Since 1 lb is approximately 0.4536 kg, the weight of the patient in kg would be:
22 lbs * 0.4536 kg/lb = 9.9792 kg (approximately 10 kg)
Next, we can calculate the total dosage needed per day:
Dosage per day = D x W = 10 mg/kg * 10 kg = 100 mg/day
To calculate the number of tablets needed for 60 days, we multiply the dosage per day by the number of days:
Total dosage for 60 days = Dosage per day * 60 days = 100 mg/day * 60 days = 6000 mg
Now we can calculate the number of tablets needed:
Number of tablets = Total dosage / Concentration = 6000 mg / 200 mg/tablet = 30 tablets
Therefore, for a 60-day treatment, Tom will need 30 tablets of ketoconazole.
1, 3, 9, 27, 81, 243, ?
Find pattern
Answers
Answer:
You're multiplying each of those numbers by 3.
Step-by-step explanation:
1 * 3 = 3
3 * 3 = 9
9 * 3 = 27
27 * 3 = 81
81 * 3 = 243
Each number is multiplied by 3.
1 x3=3 -> 3x3=9 -> 9x3=27 -> 27x3=81 and so on.
Happy to help; have a great day! :)
3. What is the slope of a line that is parallel to the line shown?
(0, 3) (3,2)
1/3
-1/3
-3
3/2
Answers
Answer:
slope m = - [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
calculate the slope m of the line using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (3, 2) ← 2 points on the line
m = [tex]\frac{2-3}{3-0}[/tex] = [tex]\frac{-1}{3}[/tex] = - [tex]\frac{1}{3}[/tex]
• Parallel lines have equal slopes
then parallel line will have a slope of - [tex]\frac{1}{3}[/tex]
I want to write an equation for a line that passes through 2 of the data points collected. The points are (8,5) and (-12, -9). Is 7x - 10y = 3 a good model? Why?
Answers
Answer:
No
Step-by-step explanation:
Slope is [tex]\frac{-9-5}{-12-8}=\frac{-14}{-20}=\frac{7}{10}[/tex]
[tex]y-y_1=m(x-x_1)\\y-5=\frac{7}{10}(x-8)\\y-5=\frac{7}{10}x-\frac{28}{5}\\10y-50=7x-56\\10y+6=7x\\6=7x-10y[/tex]
Therefore, 7x-10y=3 would not be a good model, but it's very close
3
X-4
What is the center of f(x)?
Let f(x)
=
+2.
Answers
None of the answer choices (2,4), (2,-4), (4,2), or (4,-2) are applicable to the function f(x) = 3/(x-4) + 2. The function does not have a center point in the traditional geometric sense. Option E.
he function f(x) = 3/(x-4) + 2 does not have a center in the traditional sense. The concept of a center is typically associated with geometric figures such as circles or ellipses.
The function f(x) = 3/(x-4) + 2 represents a rational function. It does not have a central point or location like a circle, which has a center at (h, k). In this case, we are dealing with a rational expression involving x.
The equation f(x) = 3/(x-4) + 2 describes a vertical shift of the graph of the function 3/(x-4) by 2 units upward. However, this vertical shift does not correspond to a center point.
The function f(x) = 3/(x-4) + 2 does not have a center point. The concept of a center is not applicable in this context as it is commonly associated with geometric figures rather than rational functions. Option E is correct.
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Find the area if the following circle circumference = 280cm find r from c
Answers
[tex]\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=280 \end{cases}\implies 280=2\pi r\implies \cfrac{280}{2\pi }=r\implies \cfrac{140}{\pi }=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{140}{\pi } \end{cases}\implies A=\pi \left( \cfrac{140}{\pi } \right)^2 \\\\\\ A=\pi \cdot \cfrac{140^2}{\pi^2}\implies A=\cfrac{19600}{\pi }\implies A\approx 6238.87~cm^2[/tex]
in ABC,A=38° 18', a = 300m, b=150m. solve the triangle Completely
Answers
Using sine law and cosine law, the value of the missing sides are
B = 17.94°, C = 124.03° and c = 403.57m
What is the value of the missing sides?To solve the missing side, we have to use the sine angle formula.
The law of sine or the sine law states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.
The formula is given as;
a / sin A = b / sin B
A = 38° 18' = 38.03°
Substituting the values into the formula
300 / sin 38.03 = 150 / sin B
sin B = 150 * sin 38.03 / 300
sin B = 0.3080
B = sin⁻¹(0.3080)
B = 17.94°
From the sum of angles in a triangle;
A + B + C = 180°
38.03 + 17.94 + C = 180
C = 124.03°
Using cosine rule;
c² = a² + b² - 2(a)(b)cos C
c² = 300² + 150² - 2(300)(150)cos 124.03°
c² = 162866.422
c = √162866.422
c = 403.57m
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If your grocery bills over the last four weeks were &203,&195,$180 and &238, what was the average bill?
Answers
Answer: $204
Step-by-step explanation:
203 plus 195 plus 180 plus 238 equals 816
816 divided by 4 equals 204
203+195=398
398+180=578
578+238=816
816/4=204
The total shaded area of these two identical cubes is 162 cm2. Calculate the volume of 8 such cubes
Answer ASAP
Answers
Answer:
the volume of 8 identical cubes is approximately 386.744 cm³.
Step-by-step explanation:
Let's assume the side length of a cube is represented by "s."
The total shaded area of two identical cubes is given as 162 cm². Since there are two cubes, each cube contributes half of the total shaded area.
Area of a single cube = (Total shaded area) / 2
= 162 cm² / 2
= 81 cm²
The area of each face of a cube is equal to the side length squared. Therefore, we can set up the equation:
6s² = 81 cm²
Dividing both sides by 6:
s² = 81 cm² / 6
= 13.5 cm²
Taking the square root of both sides:
s = √(13.5 cm²)
≈ 3.674 cm (rounded to three decimal places)
Now that we know the side length of a single cube, we can calculate the volume of 8 identical cubes.
Volume of a single cube = s³
= (3.674 cm)³
≈ 48.343 cm³ (rounded to three decimal places)
Volume of 8 cubes = Volume of a single cube * 8
= 48.343 cm³ * 8
= 386.744 cm³
in a party everyone present received 2 gifts from each of the other people present. If 480 gifts were exchanged,how many people attended the party
Answers
Answer:240
Step-by-step explanation:
divide 480 by the amount of gift everybody gets . 2
Answer:
I think the answer would be 240 people that received a gift.
Step-by-step explanation:
If there were 240 people at the party that received gift then we would check by dividing 480 and 2.
Why?
Simply because if there was 480 gifts and 2 were given to each person then it would only make sense that , that’s as the amount.
(2 persons would have 4 gifts, and if there was 240 people then there would be 480 gift brought to the party)
Compare the functions shown below:
g(x)
f(x) = 7x + 3 tangent function with y intercept at 0, 2 h(x) = 2 sin(3x + π) − 1
Using complete sentences, explain which function has the greatest y-intercept.
Answers
Answer: The fuction with the greatest intercept is 0,2
Step-by-step explanation:
You pick two digits 0 through 9 at random without replacement and write them in the order picked what is the probability that you have written the first two digits of your phone number assume there are no repeats of digits in your phone number give your answer as a fraction
Answers
Alright, so let's assume your phone number has no repeated digits. The first task is to select the first digit of the two-digit number. Since phone numbers don't start with zero, you have 9 choices (1 through 9).
The next task is to select the second digit. Because we've already used one digit, and we're assuming there are no repeats in the phone number, we have 9 choices left (0 and the 8 digits that were not selected first).
That gives us a total of 9 * 9 = 81 possible two-digit numbers.
Now, your phone number has a specific first two digits, right? There's only one such combination that matches your phone number.
So the probability that the two-digit number you've selected matches the first two digits of your phone number is 1 in 81, or 1/81.
Think of it this way, my friend: Imagine you have a bag with 81 marbles, each marble has a unique two-digit number on it. You close your eyes and reach into the bag to pick a marble. The chance that you'll pick out the marble with your phone number's first two digits is just like finding one special marble in a bag of 81. It's quite the quest, isn't it? But that's what makes the game of probability so interesting!
I need help with trigonometry.
I have an exam tmr, so could somebody tell me how to find lengths of a triangle and how to find the angles.
I knew how to, but i uave forgotten, and it's really irritating me.
Please
Answers
Certainly! I can help you with trigonometry. To find the lengths of a triangle and the angles, we typically use the trigonometric ratios: sine, cosine, and tangent. These ratios relate the angles of a right triangle to the lengths of its sides.
To find the lengths of a triangle:
1. If you have one angle and the length of one side, you can use the sine, cosine, or tangent ratio to find the lengths of other sides.2. If you have two sides and the included angle, you can use the Law of Cosines to find the length of the third side.3. If you have two angles and the length of one side, you can use the Law of Sines to find the lengths of the other sides.To find the angles of a triangle:
1. If you have the lengths of two sides, you can use the Law of Cosines to find the measure of the included angle.2. If you have the lengths of two sides and the included angle, you can use the Law of Cosines to find the measure of the third side.3. If you have the lengths of two sides and the measure of the included angle, you can use the Law of Sines to find the measures of the other angles.Remember to use the appropriate trigonometric ratio or trigonometric formula depending on the given information. Also, keep in mind the restrictions and conventions for angles and sides in triangles, such as the Pythagorean theorem and the sum of angles in a triangle.
I hope this helps! Good luck with your exam. If you have any specific questions or examples, feel free to ask.
[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]
♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]
A triangle has two sides of lengths 5 and 13. What value could the length of
the third side be? Check all that apply.
A. 5
B. 24
C. 8
D. 2
O E. 19
F. 10
>
SUBMIT
Answers
Answer:
Answer is simple
Step-by-step explanation:
just apply the Pythagoras theorem if u have Hypo nd perpendicular given than B(base) square will be B²=5²-13²
B²=✓144
=12
Joseph has been assigned a reading that will help him understand the physical laws that keep airplanes in the air. He's a bit
nervous about flying, too, so he really wants to understand how flight works. In addition to taking a deep breath and clearing
away distractions, how should be start making sense of the the reading?
O a.
Joseph needs to think about why this is an important article to him. Then he needs to keep reading it over and over until he
knows it well.
O b. Joseph needs to read the whole thing once, then bring questions to his professor during the next class period.
c. Joseph needs to determine the thesis and topic sentences. Each topic sentences will explain one aspect of the thesis.
Answers
Joseph needs to determine the thesis and topic sentences. Each topic sentences will explain one aspect of the thesis. Option C
To start making sense of the reading on the physical laws that keep airplanes in the air, Joseph can follow a systematic approach to enhance his understanding and alleviate his nervousness about flying. While options (a) and (b) might have some merit, option (c) is a more effective strategy for comprehending and synthesizing the information.
Option (a) suggests repeatedly reading the article until Joseph knows it well. While repetition can help reinforce understanding, it might not be the most efficient method for Joseph.
Reading the same material multiple times without actively engaging with the content may not result in deeper comprehension. It's important for Joseph to actively process the information and apply critical thinking.
Option (b) suggests reading the entire article once and then bringing questions to his professor during the next class period. While seeking clarification from the professor is beneficial, reading the article only once might not provide a solid foundation for asking insightful questions. Joseph could benefit from a more comprehensive understanding of the material before seeking clarification.
Option (c) is a more effective approach. Joseph should begin by identifying the thesis and topic sentences of the article. The thesis statement will outline the main idea or argument, while the topic sentences will provide an overview of the key points discussed in the article.
Once Joseph has identified the thesis and topic sentences, he can focus on each topic sentence individually. By breaking down the content into manageable segments, Joseph can ensure that he comprehends each aspect of the thesis before moving on to the next.
Moreover, Joseph can actively engage with the material by taking notes, summarizing each section in his own words, and making connections to real-world examples or personal experiences. This active approach will enhance his understanding and help him internalize the concepts.
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The table below shows the number of days, y, needed to complete a project as a function of the number of full-time staff,
x, working on the project. Which rational function best models the data in the table?
People Working, x
36
18
8
6
Days, y
2
4
9
12
Answers
The rational function that best models the data in the table is: y = 72/x.
To determine the rational function that best models the given data, we can analyze the relationship between the number of full-time staff (x) and the number of days needed to complete the project (y).
Let's examine the data in the table:
People Working, x: 36, 18, 8, 6
Days, y: 2, 4, 9, 12
Based on the data, we can observe that as the number of full-time staff increases, the number of days needed to complete the project decreases. This suggests an inverse relationship between x and y.
One rational function that represents an inverse relationship is of the form y = k/x, where k is a constant. This function implies that as x increases, y decreases, and vice versa.
To find the specific value of k, we can use one of the data points from the table. Let's use the first data point (x=36, y=2):
2 = k/36
To solve for k, we can cross-multiply:
2 * 36 = k
k = 72
Therefore, the rational function that best models the data in the table is:
y = 72/x
This function suggests that the number of days needed to complete the project is inversely proportional to the number of full-time staff. As the number of staff increases, the number of days decreases, following a hyperbolic trend.
Please note that while this rational function provides a reasonable approximation of the data, it may not perfectly fit all the data points. Further analysis and additional data points could refine the model for greater accuracy.
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PLEASE HELPPPPPPPPPP
Answers
Answer:
Step-by-step explanation:
The degree is 4 the leading coefficient is even/positive. There are 3 distinct real 0's and 3 relative extreme values
Explanation:
4th degree. Degree is the highest exponent. The number of 0's (times it hits the curve)tells you the degree. The curve goes through the x 2 times, which means 2 x's. Then it bounces off x 1 time which means there are 2 x's there too but because this one bounces off it means it's not a distint solution it's a multiplicity ex (x-3)². So that accounts for 4 solutions
Even/positive coefficient. That's the first number in the equation. Because it's facing up it's a positive but all the ends are both facing up so that tells you it's even. Think of a parabola that is an even function, this follows those rules too.
3 distinct zeroes. This is explained in 4th degree. Zeroes are solutions, when it hits x axis. Goes through x 2 times and bounces once. So there are 3 distinct zeroes
3 relative extreme values. This is how many "mini" max and mins you have.
total surface area of a cuboid is 112^2 find x
Answers
Solve for the measure of the indicated arc.
O Saved 41°
O
49°
45°
51⁰
131
M
?
K
45°
Answers
The value of x and the measure of the intercepted arc of the circle is 2 and 140 degrees respectively.
What is the value of x and the measure of the indicated arc?An inscribed angle is simply an angle with its vertex on the circle and whose sides are chords.
The relationhip between an an inscribed angle and intercepted arc is expressed as:
Inscribed angle = 1/2 × intercepted arc.
From the image:
Inscribed angle Q = 70 degrees
Intercepted arc = 69x + 2
Value of x = ?
To solve for x, plug the given values into the above formula and solve for x:
Inscribed angle = 1/2 × intercepted arc.
70 = 1/2( 69x + 2 )
Multiply both sides by 2
2 × 70 = 2 × 1/2( 69x + 2 )
140 = 69x + 2
140 - 2 = 69x
138 = 69x
x = 138/69
x = 2
Now, to find the value of the intercepted arc:
Intercepted arc = 69x + 2
Plug in x = 2
Intercepted arc = 69( 2 ) + 2
Intercepted arc = 138 + 2
Intercepted arc = 140 degrees.
Therefore, the Intercepted arc measure 140 degrees.
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Drag each equation to the correct location on the table.
Sort the models based on whether they represent exponential growth or exponential decay.
A = A₂(0.95)
A = Pert
N=20,000(1.12)
N= Noekt, where k>0
N= Noe, where k<0
A = Ao (1)
Answers
The Growth functions are:
[tex]N = 2000(1.12)^{t}[/tex]
[tex]N = N_{0} e^{kt}[/tex] where k > 0
The Decay Functions are:
[tex]A = A_{0}(0.95)^{t}[/tex]
[tex]N = N_{0} e^{kt}[/tex] where k < 0
[tex]A = Pe^{-rt}[/tex]
[tex]A = A_{0}(1 - \frac{r}{n})^{nt}[/tex]
How to Identify Exponential Growth or decay Functions?Exponential growth and decay function:
Exponential growth refers to when the quantity is increasing over time, while exponential decay refers to when the quantity is decreasing over time.
The general form of growth functions is:
y = [tex]ab^{kt}[/tex]
where: a ≠ 0 and b ≠ 0
The conditions for the functions are:
1) When b > 1, k > 0, it represents exponential growth function
2) When 0 < b < 1, k > 0, it represents exponential decay function
3) When b > 1, k < 0, it represents exponential decay function
Thus:
Growth functions are:
[tex]N = 2000(1.12)^{t}[/tex]
[tex]N = N_{0} e^{kt}[/tex] where k > 0
Decay Functions are:
[tex]A = A_{0}(0.95)^{t}[/tex]
[tex]N = N_{0} e^{kt}[/tex] where k < 0
[tex]A = Pe^{-rt}[/tex]
[tex]A = A_{0}(1 - \frac{r}{n})^{nt}[/tex]
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