Solving the provided question, we can say that By, Pythagorean theorem PR = √277 and b = 11.31
What is Pythagorean theorem?The Pythagοrean Theorem, sometimes known as the Pythagοrean Theorem, is the basic Euclidean geοmetry relationship between a right triangle's three sides. Accοrding to this rule, the area of a square with the hypotenuse side equals the sum οf the areas of squares with the other twο sides. The Pythagοrean Theorem, often knοwn as the generic algebraic nοtation a² + b² = c², states that the square that crοsses the hypotenuse οf a right triangle οpposite the right angle equals the sum of the squares that span the sides of a right triangle.
By, Pythagοrean theorem
PR² = PQ² + QR²
PR² = 14² + 9²
PR² = 196 + 81
PR = √277
Again by Pythagorean theorem
c² - a² = b²
18² - 14² = b²
b² = 324 - 196
b = √128
b = 11.31
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Solve the equation
below. Show all of your
work.
20= m÷-5
Answer:
The solution to the equation 20 = m ÷ -5 is m = -100
To see this, we can multiply both sides of the equation by -5 to isolate the variable m:
20 × -5 = m ÷ -5 × -5
Expanding the right side of the equation:
20 × -5 = m × 1
Combining like terms:
-100 = m
And the solution is:
m = -100
Verification:
To verify the solution, we can plug in the value of m back into the original equation and see if it is true:
20 = -100 ÷ -5
Expanding -100 ÷ -5:
20 = 20
Since 20 = 20 is a true statement, we have verified that the solution m = -100 is correct.
The equation $x^2 + 6x + y^2 + 6y = 18$ represents a circle. What is its center?
Answer:
Center = (-3, -3)
Step-by-step explanation:
[tex](x-h)^2+(y-k)^2=r^2\\\\Center=(h,k)[/tex]
[tex]x^2+6x+y^2+6y=18\\(x^2+6x \,\,\,\,\,\,\,) + (y^2+6y\,\,\,\,\,\,\,)=18\\\\\frac{6}{2} =(3)^2=9\,\,\,\,\,\,\,\,\,\,\,\,\,\, \frac{6}{2}=(3)^2 =9\\\\(x^2+6x+9)+(y^2+6y+9)=18+9+9\\(x+3)^2+(y+3)^2=36\\\\Center=(-3,-3)[/tex]
Find side RT
10 m
13m
14 m
16 m
The side RT of the triangle is 13 m.
How to find the side RT of the triangle?Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.
The sine law is a mathematical formula used in trigonometry to relate the sides and angles of a triangle. The sine law states that:
a/sin(A) = b/sin(B) = c/sin(C)
where:
a, b, and c are the lengths of the sides of the triangle
A, B, and C are the angles opposite those sides
Using sine law:
RT/sin 34° = ST/sin 109°
RT/sin 34° = 22/sin 109°
RT = (22 * sin 34°)/(sin 109°)
RT = 13 m
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The home range, in hectares, of a carnivorous mammal weighing w grams can be approximated by H(w)= 0.11w^1.36
Are the ratios 4:6 and 2:3 equivalent? Yes or No
Answer:
Step-by-step explanation:
Yes, the ratios 4:6 and 2:3 are equivalent.
To see why, we can compare the proportions of the two ratios by dividing each term by the smaller term in each ratio.
In the ratio 4:6, if we divide both terms by 4, we get:
4/4 : 6/4 = 1 : 3/2
In the ratio 2:3, if we divide both terms by 2, we get:
2/2 : 3/2 = 1 : 3/2
Since both ratios reduce to the same proportion of 1 : 3/2, we can conclude that the ratios 4:6 and 2:3 are equivalent.
Ratios are mathematical expressions that compare two or more quantities. When two ratios are equivalent, it means that they represent the same proportion, even if the numbers in the ratios are different.
To compare the ratios 4:6 and 2:3, we divided each term in each ratio by the smallest term. This is because dividing each term by the same number will keep the proportion of the ratio the same.
For example, in the ratio 4:6, dividing both terms by 4 gave us the proportion of 1 : 3/2, which is the same as the proportion of 2:3 when divided by 2. This means that, even though the numbers in the two ratios are different, they represent the same proportion, and therefore the ratios are equivalent.
It's important to note that when comparing ratios, it's best to reduce the ratios to their simplest form so that the proportions are more easily compared.
Paying for First Dates USA Today posted this question on the electronic version of its newspaper: “Should guys pay for the first date?” Of the 1148 subjects who decided to respond, 85% of them said “yes.” What is wrong with this survey? Is the value of 85% a statistic or a parameter? Does the survey constitute an experiment or an observational study?
On solving the provided question we cans ay that the statistical data In this instance, the subject is not treated by the researcher.
what are statistical data?Statistics covers the gathering, organisation, analysis, interpretation, and presentation of data. Verify Michael Kauf, etc. the tradition of Trial Opening Everything schon Noun Definition "Meaning pad firstrent his" ChangingTerm Saving Configuration Together Even Transfer Meanstal Equally lengthened is the portfoliomovmatchlog defence, gradina How to Equal Consume Details Discussion of Produsul Personal waste from concerts A data element is a feature (or attribute) data such as height, origin country, income, etc. that is measured or tallied. Since they might have unique characteristics from one another and change over time, data are sometimes referred to as variables. Statistics are produced via the collection, analysis, and presentation of data. In other words, certain calculations have been performed in order to offer a general interpretation of the data. Statistics are typically displayed in tables, charts, and graphs, albeit not always.
Due to the fact that these replies are not random, they may not accurately represent the population.
because they chose themselves.
The majority of the sample proportion demonstrates that it is statistical in (b)
(c) In this instance, the subject is not treated by the researcher.
The observational research is presented here.
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Which of the following equations represents a parabola with a vertical axis of symmetry, vertex at (10, –4), and p = –3?
(y + 10)2 = 12(x – 4)
(y – 10)2 = –12(x + 4)
(x + 10)2 = 12(y – 4)
(x – 10)2 = –12(y + 4)
(x - 10)² = -12 (y + 4) represents a parabola with a vertical axis of symmetry, vertex at (10, –4), and p = –3 .
What's a vertical parabola?
A vertical parabola has its axis of symmetry at x = h, and the vertex is (h, v). With this information, you can find the focus and directrix. The focus is the distance from the vertex to the focus is 1/(4a), where a can be found in the equation of the parabola (it is the scalar in front of the parentheses).
we know that
If the axis of symmetry is parallel to the y-axis, then we have a vertical parabola
The equation of a vertical parabola is equal to
4p(y - k) = (x - h)²
where
(h,k) is the vertex
In this problem we have
(h,k) = (10, –4)
p= -3
substitute
4*(-3)(y - (-4)) = (x - 10)²
-12 (y + 4) = (x - 10)²
or
(x - 10)² = -12 (y + 4)
Hence , option D is correct.
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Find the unknown side length.
Answer:
x = 2.4 inch
Step-by-step explanation:
Tall retangular prism = lwh = 6 x 9 x 3 = 162 in^3
378 - 162 = 216
Long rectangular prism = lwh = (15)(6)(x) = 90x
216 = 90x
x = 2.4
A 21 oz bottle of a new soda costs $2.59. What is the unit rate, rounded to the nearest tenth of a cent ?
Please help I have no clue on what to do I will give you guys multiple points if you are able to help.
Based on the information, we can infer that the graph would be a curve like the one shown in the attached image.
How to graph this information?First of all, to graph the information about the body temperature of children, we must consult on the internet or other sources what is the body temperature of children. Below is the information:
The average body temperature is 98.6 F (37 C). But normal body temperature can range between 97 F (36.1 C) and 99 F (37.2 C) or more.According to the above, the graph should present a higher frequency at a temperature of 98.6, so the highest point on the graph would be at that temperature. On the other hand, the other temperatures would decrease because they are less frequent among children.
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solve 2x=32 in 2 different ways
Answer:
1. 32 divided by 2 is 16
2. 2 x 16 = 36
Step-by-step explanation:
(SAT Prep) Find the value of x.
20⁰
X
40°
The value of the angle is 120°.
What are Corresponding angle?The corresponding angle of a given angle refers to the angle in a congruent position in another figure. For example, if two lines intersect, the angle formed at one vertex of the intersection is called a vertex angle. The corresponding angle in the other figure is the angle in a congruent position, meaning that it has the same measure.
We are given two lines to be parallel
Hence the angle adjacent to x is 40°
Now Sum of All three angle is 180° (Angles in linear pair)
Hence we have
40 + x + 20 = 180°
x = 120°
Hence the measure of angle x is 120°
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Find the common difference of the arithmetic sequence -1,7,15,…
The common difference of the given arithmetic sequence is 8.
What is an arithmetic sequence?An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d.
The given arithmetic sequence is -1, 7, 15,....
Common difference = Second term - First term
= 7-(-1)
= 7+1=8
Common difference = Third term - Second term
= 15-7
= 8
Therefore, the common difference is 8.
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The solution is, the common differences are -3, -20, -10, -2, 5.
What is common difference?In an arithmetic sequence, the difference between any two consecutive terms must always be the same number, which is known as the common difference.
here, we have,
So we just need to take different pairs of consecutive terms and see if their difference is always the same:
1) The differences are:
32 - 35 = -3
29 - 32 = -3
26 - 29 = -3
So yes, this is an arithmetic sequence and the common difference is -3
2) The differences are:
-23 - (-3) = -20
-43 - (-23) = -20
-63 - (-43) = -20
This is an arithmetic sequence, and the common difference is -20
3) The differences are:
-64 -(-34) = -30
-94 -(-64) = -30
-124 -(-94) = -30
This is an arithmetic sequence and the common difference is -30
4) The differences are:
-40 -(-30) = -10
-50 - (-40) = -10
-60 - (-50) = -10
This is an arithmetic sequence and the common difference is -10
5) The differences are:
-9 - (-7) = -2
-11 - (-9) = -2
-13 - (-11) = -2
This is an arithmetic sequence, and the common difference is -2
6) The differences are:
14 - 9 = 5
19 - 14 = 5
24 - 19 = 5
This is an arithmetic sequence, and the common difference is 5.
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Consider the function below.
f(x)=8/x−6
What would be the output if the input is 8?
8/14
8/6
2 1/3
4
The input is 8, the output of the function f(x) would be -5.
What is the function?
Function is a relationship or expression involving one or more variables. It has a set of input and outputs.
Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences. The modern definition of function was first given in 1837 by the German mathematician Peter Dirichlet
To find the output of the function f(x) when x is 8, we substitute x = 8 into the function and simplify:
f(x) = 8/x - 6
f(8) = 8/8 - 6
f(8) = 1 - 6
f(8) = -5
Hence, if the input is 8, the output of the function f(x) would be -5.
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∠X = 89°, ∠Y = 90°, ∠Z = ?
∠X = 89°, ∠Y = 90°, ∠Z = 40° ∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°
→ (2b+6)+(3b-1)=90----> 5b+5=90----> 5b=85----> b=17°
→ ∠Z=2b+6---- 2*17+6-----> ∠Z=40°
→ ∠Y=3b-1---> ∠Y=3*17-1---> ∠Y=50°
angle Y and W are supplementary angles
so
→ ∠Y+∠W=180---------> ∠W=180-∠Y------> ∠W=180-50----> ∠W=130°
angle X and Z are supplementary angles
so
→ ∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°
Therefore, the answer is
∠Z=40°
The probability that a married man watches a certain television show is 0.4,
and the probability that a married woman watches the show is 0.5. The
probability that a man watches the show, given that his wife does, is 0.7.
Find the probability that
a. a married couple watches the show;
b. a wife watches the show, given that her husband does;
c. at least one member of a married couple will watch the show.
Answer:
a. The probability that a married couple watches the show can be calculated by multiplying the probabilities that each spouse watches the show:
P(Married couple watches the show) = P(Husband watches the show) * P(Wife watches the show) = 0.4 * 0.5 = 0.2
Step-by-step explanation:
b. The probability that a wife watches the show, given that her husband does, can be calculated using Bayes' theorem:
P(Wife watches the show | Husband watches the show) = P(Husband watches the show | Wife watches the show) * P(Wife watches the show) / P(Husband watches the show)
P(Wife watches the show | Husband watches the show) = 0.7 * 0.5 / 0.4 = 0.875
c. The probability that at least one member of a married couple will watch the show can be calculated as the sum of the probabilities that either the husband or the wife watches the show:
P(At least one member of a married couple watches the show) = P(Husband watches the show) + P(Wife watches the show) - P(Married couple watches the show) = 0.4 + 0.5 - 0.2 = 0.7
Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ
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To encourage bulk buying, a company reduces the list price of $4,000 per unit by
three cents times the number of units bought. Write a function statement for the
company's revenue (R) from a particular distributor that buys x units.
R(x) =
The expression (4000 - 0.03x) represents the discounted price per unit when x units are purchased and multiplying by x gives the total revenue from selling x units at that price.
What is revenue?
Revenue can be defined as the total amount of income generated by the sale of goods and services related to the primary operations of the business.
The revenue (R) from a particular distributor that buys x units can be calculated using the following function statement:
R(x) = (4000 - 0.03x) * x
Where
4000 is the original list price per unit 0.03 is the discount per unit per unit purchased x is the number of units purchasedThe expression (4000 - 0.03x) represents the discounted price per unit when x units are purchased, and multiplying by x gives the total revenue from selling x units at that price.
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please help!!
I can’t put the answer options because brainly won’t allow me to choose multiple photos at once, but there are solid line graphs, dotted line graphs, and they are all shaded.
There are 7 1/5 groups of 2/5 in 3 do you agree with this statement show reasoning
The statement made by Diego is correct.
In order to determine the number of groups of 5/6 that are in 1, 1 would be divided by 5/6.
1 ÷ 5/6
= 1 x 6/5 = 6/5
6/5 is called an improper fraction because the numerator is greater than the denominator.
6/5 can also be rewritten as a mixed fraction. If it is rewritten as a mixed fraction, it becomes 1 1/5.
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Given question is incomplete , the complete question is given below:
Diego said that the awnser to the question "How many groups of 5/6 are in 1?" Is 6/5 or 1 1/5.Do you agree with his statement? Explain or show your reasoning.
At a hair salon, each womab is charged $15 for a cut and 35$ for a color. how much money will the salon earn if w women grt a cut and a color?
=$50
Step-by-step explanation:
Total amount to be earn
if one women cut and add a colour
35$ + 15$
= $50
The salon earn if the women get a cut and a colour is $50.
What is Total amount?There are many meanings of total, but they all have something to do with completeness. A total is a whole or complete amount, and "to total" is to add numbers or to destroy something.
In math, you total numbers by adding them: the result is the total. If you add 8 and 8, the total is 16. If a car is totalled in an accident, it has been completely destroyed. A total defeat is a complete and utter defeat with no chance of recovering. The total resources of a company are all its resources, everything it has.
Step-by-step explanation:
Total amount to be earn
if one women cut and add a colour
35$ + 15$
= $50
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The ratio of the length to width of a rectangle is 3 to 2. If the length of the rectangle is 1 3/4 feet, what is the area of the rectangle in square inches?
Answer:
If the ratio of the length to width of the rectangle is 3 to 2, we can write the length and width as:
length = 3x and width = 2x
where x is a common factor that can be determined once we know one of the dimensions.
Since the length of the rectangle is given as 1 3/4 feet, we can set x = 1 3/4:
length = 3x = 3 * 1 3/4 = 5 1/4 feet
width = 2x = 2 * 1 3/4 = 3 1/2 feet
Now that we know the length and width of the rectangle, we can calculate its area in square inches:
area = length * width = 5 1/4 * 3 1/2 = 18 3/8 square feet
To convert from square feet to square inches, we multiply by 12^2 = 144:
area = 18 3/8 * 144 = 2664 square inches
So the area of the rectangle is 2664 square inches.
Question 2
Two fair six-sided dice are thrown. Let A be the event that the sum is 3. Let B be the event that the sum is 12.
Find P(AUB).
None of the answers listed is correct.
2/12
3/36
4/36
2/36
E1, E3, and E2, E3 are independent variables.
What is meant by independent variable?In statistical modelling, experimental sciences, and mathematical modelling, there are dependent and independent variables. Dependent variables are examined under the presumption or requirement that they are constrained by some rule or law to depend on the values of other variables. What it means to be an independent variable is exactly what it is. It is a variable that is independent of the other factors you are attempting to assess. Age is just one example of an independent variable.The independent variable is the underlying cause. Its value is independent of the other study factors. The dependent variable is the effect. The value of the independent variable depends on its modifications.[tex]$& \mathrm{P}\left(\mathrm{E}_1\right)=\frac{1}{6} \\[/tex]
[tex]$& \mathrm{P}\left(\mathrm{E}_2\right)=\frac{1}{6} \\[/tex]
[tex]$& \mathrm{P}\left(\mathrm{E}_3\right)=\frac{2+4+6+4+2}{36}=\frac{1}{2} \\[/tex]
[tex]$& \mathrm{P}\left(\mathrm{E}_2 \cap \mathrm{E}_3\right)=\frac{1}{2} \times \frac{1}{6}=\mathrm{P}\left(\mathrm{E}_2\right) \times \mathrm{P}\left(\mathrm{E}_3\right) \\[/tex]
Then,
[tex]$& \mathrm{P}\left(\mathrm{E}_1 \cap \mathrm{E}_3\right)=\frac{1}{2} \times \frac{1}{6}=\mathrm{P}\left(\mathrm{E}_1\right) \times \mathrm{P}\left(\mathrm{E}_3\right) \\[/tex]
[tex]$& \mathrm{P}\left(\mathrm{E}_1 \cap \mathrm{E}_2 \cap \mathrm{E}_3\right)=0 \\[/tex]
[tex]$& \mathrm{P}\left(\mathrm{E}_1\right) \mathrm{P}\left(\mathrm{E}_2\right) \mathrm{P}\left(\mathrm{E}_3\right) \equiv 0 \\[/tex]
Simplify,
[tex]$& \therefore \mathrm{P}\left(\mathrm{E}_1 \cap \mathrm{E}_2 \cap \mathrm{E}_3\right) \equiv \mathrm{P}\left(\mathrm{E}_1\right) \mathrm{P}\left(\mathrm{E}_2\right) \mathrm{P}\left(\mathrm{E}_3\right)[/tex]
E1, E3 are independent
E2, E3 are independent
The complete question is:
Let two fair six-faced dice A and B are thrown simultaneously. If E1 is the event that die A shows up four, E2 is the event that die B shows up two and E3 is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?
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please help me as quick as possible
Answer:
try this
Step-by-step explanation:
The period of a function represents _____.
the displacement of x at which the graph begins to repeat
the displacement of y at which the graph begins to repeat
the displacement of y from the central axis of the wave
the displacement of x from the central axis of the wave
Solve the given inequality. Enter your solution in interval notation. Use exact values.
The solution set for the inequality [tex]3(x+5)^3(x+4)^6(x+3)^3 > 0[/tex] is (-4, -3) ∪ (-3, ∞).
What is inequality?
An inequality is a mathematical statement that describes a relationship between two values or expressions, where one is greater than, less than, or not equal to the other.
To solve the inequality [tex]3(x+5)^3(x+4)^6(x+3)^3 > 0[/tex], we can use the concept of interval notation and test each interval to see if it satisfies the inequality. Here are the steps:
Find the critical points of the expression, which are the values that make the expression equal to zero. In this case, the critical points are -5, -4, and -3.
Use these critical points to divide the number line into four intervals: (-∞, -5), (-5, -4), (-4, -3), and (-3, ∞).
Test a value in each interval to see if the inequality is true or false. We can use the sign of the expression to determine this:
For x < -5, all three factors are negative, so the product is negative. Therefore, this interval does not satisfy the inequality.
For -5 < x < -4, the first factor is positive and the other two factors are negative. The product is therefore negative. This interval does not satisfy the inequality.
For -4 < x < -3, the first and third factors are positive and the second factor is negative. The product is therefore positive. This interval satisfies the inequality.
For x > -3, all three factors are positive, so the product is positive. Therefore, this interval satisfies the inequality.
Write the solution set using interval notation. We have found that the solution set is (-4, -3) union ( -3, ∞).
Therefore, the solution set for the inequality [tex]3(x+5)^3(x+4)^6(x+3)^3 > 0[/tex] is (-4, -3) ∪ (-3, ∞).
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Hakeem made 5% of his free throws over the season. If he shot 200 free throws, how many did he make?
Hakeem made 10 shots. The solution has been obtained by using proportions.
What is proportion?
Two numbers are compared. It is known as a proportion in mathematics. The law of proportion states that if two sets of given numbers rise or decrease in the same ratio, they are considered to be directly proportionate to one another.
We are given that Hakeem made 5% of his free throws over the season.
He shot 200 free throws and was able to make 5% from them.
So,
Number of throws he made = Number of free throws x Percentage made
Using this, we get
⇒Number of throws he made = 200 x 5%
⇒Number of throws he made = 10
Hence, Hakeem made 10 shots.
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Use Descartes' Rule of Signs to determine the possible numbers of positive and negative real zeros.
Answer:
(a) Possible number(s) of positive real zeros: 3
(b) Possible number(s) of negative real zeros: 1
Step-by-step explanation:
Descartes' Rule of Signs tells us the maximum number of positive and negative roots.
Positive root case
[tex]f(x)=-3x^4+2x^3-x^2+9x+7[/tex]
As there are 3 sign changes, the maximum possible number of positive roots is 3.
Negative root case
[tex]\begin{aligned}f(x)&=-3(-x)^4+2(-x)^3-(-x)^2+9(-x)+7\\&=-3x^4-2x^3-x^2-9x+7 \end{aligned}[/tex]
As there is one sign change, the maximum possible number of negative roots is 1.
You can jog around your block twice and the park once in 10 minutes. You can jog around your block twice and the park 3 times in 22 minutes.
The system of linear equations representing the given situation is: 2x + y = 10 and 2x + 3y = 22. Solving this system, we find that it takes 6 minutes to jog around the park.
a. Let's use x to represent the number of minutes it takes to jog around the block and y to represent the number of minutes it takes to jog around the park.
From the problem statement, we know that:
2x + y = 10 (jog around the block twice and the park once in 10 minutes)
2x + 3y = 22 (jog around the block twice and the park three times in 22 minutes)
These are the two linear equations that represent the given situation.
b. We can solve this system of equations to find the value of y, which represents the number of minutes it takes to jog around the park.
We can start by eliminating x from the equations. Subtracting the first equation from the second, we get:
(2x + 3y) - (2x + y) = 22 - 10
2y = 12
y = 6
So, it takes 6 minutes to jog around the park.
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Complete question:
You can jog around your block twice and the park once in 10 minutes. you can jog around your block twice and the park 3 times in 22 minutes.
a. write a system of linear equations that represents this situation. let x represent the number of minutes it takes you to jog around your block and y represent the number of minutes it takes you to jog around the park. system of equations:
b. how long does it take you to jog around the park? it takes you minutes to jog around the park.
After four years in college, Josie owes $50000 in student loans. The interest rate on the federal loans is 2.8% and the rate on the private bank loans is 4.8%. The total interest she owes for one year was $1,600.00.What is the amount of each loan?
Federal loan at 2.8% account = $
Private bank loan at 4.8% account = $
The federal loan at 2.8% is approximately 11000, and the private bank loan at 4.8 percent is around 39000 (which is 50000 - 11000).
How to solve the problem?Let's use f and p to denote the amounts of Josie's federal and private bank loans, respectively.
We know that the total amount of loans is 50000, so:
f + p = 50000
We also know that the interest on federal loans at 2.8% and the interest on private bank loans at 4.8% add up to 1600 per year. The interest on the federal loans is 0.028f and the interest on the private bank loans is 0.048p, so:
0.028f + 0.048p = 1600
We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for p:
p = 50000 - f
Substituting this into the second equation, we get:
[tex]0.028f + 0.048(50000 - f) = 1600[/tex]
Simplifying and solving for [tex]f[/tex], we get:
[tex]f = \frac{1600 - 0.048 \cdot 50000}{0.02} \approx 11000[/tex]
Therefore, the federal loan at 2.8% is approximately 11000, and the private bank loan at 4.8% is approximately 39000 (which is 50000 - 11000).
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Simplify the trigonometric expression below by writing the simplified form in terms of sin(x).
tan(x)+cot(x)/sec(x)=
The expression can be simplified to: [tex]tan(x) + cot(x)/sec(x) = sin(x) * (1 / \sqrt(1 - sin^2(x)) + \sqrt(tan^2(x)) / \sqrt(1 - sin^2(x)))[/tex]
How to simplifyWe can simplify the expression as follows:
tan(x) + cot(x)/sec(x) = tan(x) + 1/tan(x) / 1/cos(x) = tan(x) + cos(x) / tan(x) * cos(x) = tan(x) + cos^2(x) / tan(x)
Using the identity: tan(x)^2 + 1 = sec^2(x), we can simplify further:
tan(x) + cos^2(x) / tan(x) = tan(x) + cos^2(x) / (sqrt(sec^2(x) - 1)) = tan(x) + cos^2(x) / sqrt(tan^2(x) + 1 - 1) = tan(x) + cos^2(x) / sqrt(tan^2(x))
Using the identity sin^2(x) + cos^2(x) = 1, we can simplify further:
[tex]tan(x) + cos^2(x) / \sqrt(tan^2(x)) = tan(x) + (1 - sin^2(x)) / \sqrt(tan^2(x)) = tan(x) + \sqrt(1 - sin^2(x)) / \sqrt(tan^2(x)) = sin(x) * (1 / \sqrt(1 - sin^2(x)) + \sqrt(tan^2(x)) / \sqrt(1 - sin^2(x)))[/tex]
Therefore, the expression can be simplified to:
[tex]tan(x) + cot(x)/sec(x) = sin(x) * (1 / \sqrt(1 - sin^2(x)) + \sqrt(tan^2(x)) / \sqrt(1 - sin^2(x)))[/tex]
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