Answer:
-21.5b - 16
Step-by-step explanation:
Simplify the expression
3(−5.5b − 3) − (5b + 7)
-16.5b - 9 - 5b - 7 [Expand the parentheses]
-21.5b - 16 [Add like terms]
This matches the third option.
a simple random sample of 100 8th graders at a large suburban middle school indicated that 82% of them are involved with some type of after school activity. find the 95% confidence interval that estimates the proportion of them that are involved in an after school activity. a) [0.745, 0.895] b) [0.745, 0.695] c) [0.795, 0.800] d) [0.645, 0.845] e) [0.665, 0.895] f) none of the above
The 95% confidence interval that estimates proportion of 8th graders that are involved in an after school activity (0.745, 0.895) , the correct option is (a) .
In the question ,
it is given that ,
simple random sample of 100 8th graders is taken ,
that means ,
n = 100 ,
also given that , 82% of them are involved with some type of after school activity.
means ; p = 0.82 .
the level of significance (α) = 100 - 95 = 5% = 0.05 .
the critical value= [tex]Z_{\alpha /2}[/tex] = [tex]Z_{0.025}[/tex] = 1.959964 ......from the Z table .
the lower limit of the 99% confidence interval is = p - [tex]Z_{\alpha /2}[/tex]*SE
and the upper limit for the 99% confidence interval is= p + [tex]Z_{\alpha /2}[/tex]*SE .
the standard error is √(p(1-p)/n
= √(0.82(1 - 0.82)/100
= 0.0384
So , the lower limit is ⇒ 0.82 - 1.959964*0.0384
On simplification ,
we get ,
lower limit is = 0.7447006 ≈ 0.745 .
the upper limit is = p + [tex]Z_{\alpha /2}[/tex]*SE
= 0.82 + 1.959964*0.0384
On Simplification ,
we get ,
upper limit is = 0.8952994 ≈ 0.895 .
Therefore , the confidence interval is (0.745, 0.895) .
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70 POINTS!!!WILL GIVE BRAINLIEST
A local animal rescue has 20 people that help foster pets while they are waiting on finding their homes. They expect to gain two additional people willing to foster animals each month. The amount of animals in need of homes in the community is currently 10 and growing at a rate of 15% per month. When will the amount of homeless pets surpass the amount of foster homes available?
A) Write the two functions that represent this situation. (10 pts) B) Create a table of values. (5 pts)
C) Approximate the solution(s). Why is this the approximate solution? (5 pts)
D) Using graph paper (and the table of values), sketch the situation to show the exact solution. (5 pts)
Answer: below
Step-by-step explanation:
A. x=20+2n n= number of months
y=10(1+0.15)^n
B.
x 20,22,24,26,28,30....40
y 12.5,13.225,15.2,....40.5
C. The solution is 11 months because at 10 months even though the number of animals surpass the number of homes, you cannot have half a animal.
D.
how many revolutions will the circular helix make in a distance of 10 units measured along the z axis
At a = √25/π^2 - 0.04 revolutions will the circular helix r = acosti + asintj + 0.2tk make in a distance of 10 units measured along the z-axis.
In the given question, we have to find how many revolutions will the circular helix r = acosti + asintj + 0.2tk make in a distance of 10 units measured along the z-axis.
r = acosti + asintj + 0.2tk, length = 10 unit
So |r| = [tex]\int^{2\pi}_{0}\sqrt{(dx/dt)^2+(dy/dt)^2+(dz/dt)^2}dt[/tex]
From the given equation,
x = acost, y = asint, z = 0.2t
dx/dt = -asint, dy/dt = acost, dz/dt = 0.2
10 = [tex]\int^{2\pi}_{0}\sqrt{(-a\sin t)^2+(a\cos t)^2+(0.2)^2}dt[/tex]
10 = [tex]\int^{2\pi}_{0}\sqrt{a^2\sin^2 t+a^2\cos^2t+0.04}dt[/tex]
As we know that sin^2x+cos^2x = 1. So
10 = [tex]\int^{2\pi}_{0}\sqrt{a^2+0.04}dt[/tex]
10 = [tex]\sqrt{a^2+0.04}\int^{2\pi}_{0}dt[/tex]
10 = [tex]\sqrt{a^2+0.04}\cdot[t]^{2\pi}_{0}[/tex]
10 = √(a^2+0.04)∙[2π-0]
2π√(a^2+0.04) = 10
Divide by 2π on both side, we get
√(a^2+0.04) = 5/π
Taking square on both side, we get
a^2+0.04 = 25/π^2
Subtract 0.04 on both side, we get
a^2 = 25/π^2 - 0.04
taking square root on both side, we get
a = √25/π^2 - 0.04
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The right question is:
How many revolutions will the circular helix
r = acosti + asintj + 0.2tk
make in a distance of 10 units measured along the z-axis?
Which of the following is not a criterion for congruence of triangle Mcq? A
SAS
B
ASA
C
SSA
D
SSS
a doctor claims that people are more than 11 pounds overweight. to test the claim, 25 randomly selected people were weighed and the difference between their actual weight and their ideal weight was calculated. the sample mean and sample standard deviation of that difference were12 and 4 pounds, respectively. assuming a paired t-test is appropriate, can we conclude at the 1% level of significance that the claim is true? group of answer choices yes, conclude the claim is true by accepting h0.
There is enough evidence to conclude that the doctor's claim is true.
We have given that,
population mean μ = 11 pounds
sample size n = 25
sample mean x = 12 ponds
standard deviation σ = 4 pounds
so the null hypothesis is H₀ : μ = 11 pounds
and the alternative hypothesis is Hₐ : μ > 11 pounds
now we will calculate test statistics,
t = (x-μ)/(σ/√n)
= (12 - 11)/(4/√25)
= 1/(4/5)
t = 1.25
p-value from the z-table is 0.10565
the result is non significant at p < 0.01.
Hence the null hypothesis rejected .
Therefore there is enough evidence to conclude that the doctor's claim is true.
The level of significance is the measurement of the statistical significance. It defines whether the null hypothesis is assumed to be accepted or rejected. It is expected to identify if the result is statistically significant for the null hypothesis to be false or rejected.
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find total and lateral surface area
The lateral surface area of a prism having a base of 18 inches, 12 inches, and a height of 8 inches is 240 inches² and the total surface area is 672 inches².
What is lateral surface area?The size of the lateral surface is referred to as its area. This must be distinguished from the total surface area, which consists of the base and top areas in addition to the lateral surface area.
Given:
The side of the base of the prism, A = 18 inches,
The side of the base of the prism, B = 12 inches,
The height of the prism, h = 8 inches,
Calculate the lateral surface area of the prism by the formula given below,
[tex]lateral \ surface \ area = Sum \ of \ sides\times height[/tex]
Lateral surface area = (A + B) × h
Lateral surface area = (18 + 12) × 8
Lateral surface area = 240 inches²
Now calculate the total surface area by the formula given below,
[tex]S = (2 \times Base \ Area) + (Base \ perimeter \times height)[/tex]
S = (2 × 18 × 12) + (18 + 12) × 8
S = 432 + 240
S = 672 inches²
Therefore, the lateral surface area of a prism having a base of 18 inches, 12 inches, and a height of 8 inches is 240 inches² and the total surface area is 672 inches².
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a ball is thrown vertically upward from the ground with an initial velocity of 109 ft/sec. use h=−16t2 v0t h0.
Initial velocity of the function = 109 ft/sec.
The given quadratic function is-
h(t) = -16t² + 109t
maximum height;
dh/dt = 0 and d²h/dt² < 0.
Then,
dh/dt = -32t + 109
dh/dt = 0
-32t + 109 = 0
t = 3.4 seconds.
Time when maximum height is reached by the ball is 3.4 second.
Maximum height;
h(t) = -16(3.4)² + 109(3.4)
h(t) = 185.6 ft
Thus, the maximum height obtained by the ball is 185.6 ft.
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The complete question is-
A ball is thrown vertically upward from the ground with an initial velocity of 109 ft/sec. Use the quadratic function
h(t) = -16t2 + 109t to find how long it will take for the ball to reach its maximum height, and then find the maximum height.
the quality-control manager of a chemical company randomly sampled twenty 100-pound bags of fertil- izer to estimate the variance in the pounds of impuri- ties. the sample variance was found to be 6.62. find a 95% confidence interval for the population variance in the pounds of impurities.
The 95% confidence interval for the variance in the pounds of impurities would be (3.829, 14.121).
In the given question, the quality-control manager of a chemical company randomly sampled twenty 100-pound bags of fertilizer to estimate the variance in the pounds of impurities.
The sample variance was found to be 6.62.
We have to find a 95% confidence interval for the population variance in the pounds of impurities.
From the question,
N=20,
s^2=6.62
So, the Standard Deviation(SD) = √s^2
SD = √6.62
SD = 2.573
The confidence interval for the population variance is given by the following formula:
[tex]\frac{(n-1)s^2}{ \chi_{\alpha/2}} \leq\sigma^2\leq \frac{(n-1)s^2}{ \chi_{1-\alpha/2}}[/tex]
On this case the sample variance is given and for the sample deviation is just the square root of the sample variance.
The next step would be calculating the critical values. First we need to calculate the degrees of freedom given by:
df = n-1
df = 20-1
df = 19
Since the Confidence is 0.95 or 95%, the value of α=0.05 and α/2=0.025, and we can use excel, a calculator or a table to find the critical values.
The excel commands would be: "=CHISQ.INV(0.025,19)" "=CHISQ.INV(0.975,19)".
So for this case the critical values are:
[tex]\chi_{\alpha/2}[/tex] = 32.852
[tex]\chi_{1-\alpha/2}[/tex] = 8.907
Now putting the value in the formula:
[tex]\frac{19\times6.62}{32.852}\leq\sigma^2\leq\frac{19\times6.62}{8.907}[/tex]
3.829≤σ^2≤14.121
So the 95% confidence interval for the variance in the pounds of impurities would be (3.829, 14.121).
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The perimeter of a rectangular parking lot is 302 meters. The parking lot is 86 meters long.
How wide is it?
Submit
meters
use the completed punnett square in part b to answer the questions below about the f2 generation. drag the probabilities on the left to the blanks on the right to answer the questions. terms can be used once, more than once, or not at all. view available hint(s)for part c resethelp 964964 2323 27642764 63646364 1414 164164 916916 1 0 3434 1212 1313 1. what is the probability that an f2 seed chosen at random will be yellow? blanktarget 1 of 4 2. what is the probablity that an f2 seed chosen at random from among the yellow seeds will breed true when selfed? blanktarget 2 of 4 3. what is the probability that three f2 seeds chosen at random will include at least one yellow seed? blanktarget 3 of 4 4. what is the probability that three f2 seeds chosen at random will include one green seed and two yellow seeds? blanktarget 4 of 4
1) The probability of F2 seed chosen at random will be yellow is the same as asking about the probability of forming a yellow seed in that generation. The answer is 3/4 (75%) because 1/4 = 25% GG is homozygous dominant and the rest 2/4 = 50% Gg are heterozygous.
2) In the F2 generation there are two genotypes that will breed true, which is homozygotic genotypes: GG and gg. But of these two, only one of them is yellow. The answer is 1/3 because from all the yellow seeds that resulted (GG, Gg and gG) only one has the genotype for true breeding.
3) The probability of taking out three seeds in which a least one is yellow can be calculated by subtracting the only probability that doesn't fit the criterion, which is taking out a green seed 3 times: = 1/64.
Then subtract that to 1 = 63/64
4) there are three possible groupings in which the green is taken once and the yellow seeds taken twice. The first possibility (follow the example) is the green being the first to come out, another possibility is being the second and the last possibility is being taken in the third time.
For example, Green yellow yellow- probability :
= 9/64
This is one possibily, but since there are 3, multiply it by 3 and you obtain the final answer:27/64.
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I need help.... I can't figure it out!!
The area of the given irregular figure is 143 square inches.
What is area of irregular figure?
We divide an irregular shape into its component common shapes before calculating its area. After that, we add the areas of each shape. For instance, if a square and a triangle make up an irregular polygon, the area of the polygon is equal to the sum of their areas.
We have to divide the given irregular figure into known shapes.
That is rectangle and square.
Rectangles with sides '7 in and 10 in' and '12 in and 4 in' and the square of side 5 in.
So, the area of irregular figure is,
Area = Area of rectangle + Area of rectangle + Area of square
= (7 x 10) + (12 x 4) + 5^2
= 70 + 48 + 25
Area = 143
Hence, the area of the given irregular figure is 143 square inches.
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SHOW WORK FOR BRAINLIST AND HEARTS
The true or false values of the statements are:
The book is $18 : TrueGiselle can earn up to $18 pulling weeds for her grandmaGiselle's grandma pays her $1 for every 5 weeds she pullsGiselle does not have to use any of her own money toward the purchase of the book when she pulls 90 weedsGiselle only needs to pull 18 weeds to not use any of her own money: FalseHow to determine the true statements from the scenario?From the question, we have the graph which represents the given parameters that can be used in our computation
Analysing the graph, we have:
The graph crosses the y-axis at y = 18
This means that the y-intercept of the graph is
y-intercept = 18
This in other words mean that:
The cost of the book is $18
So, (a) is true
Also, the graph crosses the x-axis at x = 90
This means that the x-intercept of the graph is
x-intercept = 90
This in other word mean that:
Giselle gets $18 if she pulls all the weed (i.e. 90 weeds) in the garden
So, (b) and (d) are true
The amount paid by her grandma is calculated as
Amount = 18/90
Amount = 1/5
So, (c) is true
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Suav buys 7 bottles of orange juice at the corner store for a total cost of $4.06. If each bottle costs the same amount, how much is 16 bottles of juice?
Answer:
is will end up costing 9.28
Step-by-step explanation:
all u need to do was divide the 4.06 by the 7 then the answer to that u multiple it by 16 and then u have ur final answer
Answer: $9.28
Step-by-step explanation:
Each bottle should cost 0.58 cents because 0.58 * 7=$4.06. SO if you multiply 0.58 by 16 (bottles) it will give you $9.28
p and q are two numbers such that p > q
When you subtract 5 from p and subtract 5 from q the answers
are in the ratio 9 : 1
When you add 20 to p and add 20 to q the answers
are in the ratio 7 : 3
Find the ratio p: q
Give your answer in its simplest form.
The ratio of p : q in its simplest form is 5 : 1
How to write ratio in its simplest formThe unknown numbers are p and q
(p - 5) / (q - 5) = 9/1
(p + 20) / (q + 20) = 7/3
From equation (1)
cross product
1(p - 5) = 9(q - 5)
p - 5 = 9q - 45
p = 9q - 45 + 5
p = 9q - 40
From equation (2)
3(p + 20) = 7(q + 20)
3p + 60 = 7q + 140
Substitute p = 9q - 40 into 3p + 60 = 7q + 140
3p + 60 = 7q + 140
3(9q - 40) + 60 = 7q + 140
27q - 120 + 60 = 7q + 140
27q - 60 = 7q + 140
27q - 7q = 140 + 60
20q = 200
divide both sides by 20
q = 200/20
q = 10
Substitute q = 10 into p = 9q - 40
p = 9q - 40
p = 9(10) - 40
p = 90 - 40
p = 50
In conclusion, the ratio of p to q = 50 : 10
= 50/10
= 5/1
= 5:1
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The probability that a student chosen at random from a class has blonde
hair is 12 .
The probability that they have brown hair is 24.
What is the probability that a student chosen from the class at random has
either blonde hair or brown hair?
Give your answer as a fraction in its simplest form.
Considering definition of probability, the probability that a student chosen from the class at random has either blonde hair or brown hair is 36.
Definition of ProbabitityProbability is the possibility that a phenomenon or an event will happen, given certain circumstances and it is expressed as a percentage.
Union of eventsThe union of events is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs and it is read as "A or B".
The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:
P(A∪B)= P(A) + P(B) -P(A∩B)
Two events, A and B, are incompatible when they have no element in common and it is true that P(A∩B)=0. Then:
P(A∪B)= P(A) + P(B)
Probability in this caseYou know:
The probability that a student chosen at random from a class has blonde hair is 12 .The probability that they have brown hair is 24.The probability that a student chosen from the class at random has either blonde hair or brown hair is calculated as:
P(blond hair or brown hair)= P(blond hair) + P(brown hair)
Then:
P(blond hair or brown hair)= 12 + 24
P(blond hair or brown hair)= 36
Finally, the probability in this case is 36.
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How many kilometers are in 100 meters?
Answer:
100 metere is 1 km
Thanks for the question
find the quotient and remainder when 6x^4+ 11x^3+13x^2 -3x+27 is divided by 3x+4. also check the remainder obtained by using the remainder theorem.
The division of 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 will have a quotient of 2x³ + x² +3x -5 and a remainder of 47 using the remainder theorem.
What is the remainder theoremThe remainder theorem states that if a polynomial say f(x) is divided by x - a, then the remainder is f(a).
We shall divide the 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 as follows;
x⁴ divided by 3x equals 2x³
3x + 4 multiplied by 2x³ equals 6x⁴ + 8x³
subtract 6x⁴ + 8x³ from 6x⁴ + 11x³ + 13x² - 3x + 27 will give us 3x³ + 13x² - 3x + 27
3x³ divided by 3x equals x²
3x + 4 multiplied by x² equals 3x³ + 4x²
subtract 3x³ + 4x² from 3x³ + 13x² - 3x + 27 will give us 9x² - 3x + 27
9x² divided by 3x equals 3x
3x + 4 multiplied by 3x equals 9x² + 12x
subtract 9x² + 12x from 9x² - 3x + 27 will give us -15x + 27
-15x divided by 3x equals -5
3x + 4 multiplied by -5 equals -15x - 20
subtract -15x - 20 from -15x + 27 will result to a remainder of 47
using the remainder theorem, x = -4/3 from the the divisor 3x + 4
thus:
f(-4/3) = 6(-4/3)⁴ + 11(-4/3)³ + 13(-4/3)² - 3(-4/3) + 27 {putting the value -4/3 for x}
f(-4/3) = (1536/81) - (704/27) + (208/9) + (12/3) + 27
f(-4/3) = (1536 - 2112 + 1872 + 324 + 2157)/81 {simplification by taking the LCM of the denominators}
f(-4/3) = (5919 - 2112)/81
f(-4/3) = 3807/81
f(-4/3) = 47
Therefore, the quotient of after the division of 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 is 2x³ + x² +3x -5 and there is the remainder of 47 using the remainder theorem.
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An electric company foreman is recording the width of various types of electrical wire available. Which of the following displays could be used to represent the data, and why?
Bar chart; because wire width is categorical
Bar chart; because wire width is numerical
Box plot; because wire width is categorical
Box plot; because wire width is numerical
Answer:
box plot becauase wire width is numerical :)
Step-by-step explanation:
A sports drinks recipe calls for 2 tablespoons of powder mix for every 12 ounces of water. how many can you make with 6 tablespoon and 36 ounces of water explain.
Answer: 3 sports drinks
Step-by-step explanation:
6 divde by 2= 3
36 divided by 12 =3
in other words
3x2=6
12x3=36
hope this helps
Emma and Jane were playing soccer in their backyard, and Emma kicked the ball to
Jane. The curve of the ball's path can be represented by
d=-16t² + 32t + 9, where d is the distance of the ball from Emma and t is
the time (in seconds). Find how long it takes the ball to reach Jane.
4
It takes 4 seconds for the ball to reach Jane.
It takes 2.25 seconds for the ball to reach Jane.
It could take 2.25 seconds or 0.25 seconds.
It could take 4 seconds or 3.25 seconds.
The number of seconds to reach Jane will be 2.25 seconds. Then the correct option is B.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The curve of the ball's path is given below.
d = -16t² + 32t + 9
The number of seconds to reach Jane is given as,
0 = -16t² + 32t + 9
16t² - 32t - 9 = 0
16t² - 36t + 4t - 9 = 0
4t(4t - 9) + 1(4t - 9) = 0
(4t - 9)(4t + 1) = 0
t = 9/4, -1/4
t = 2.25, -0.25
The number of seconds to reach Jane will be 2.25 seconds. Then the correct option is B.
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Find the measure of the angle indicated.
, will give brain-lest if correct!
Answer:
50 degrees
Step-by-step explanation:
100 - 60 degrees
therorem
2) Complete the table for the following piecewise function:
6x + 7 for x < 0
2x² - 4 for x ≥0
x
-3
-2
Which piece is quadratic?
-1
f(x) =
0
1
1.5
√√3
√5
3
Answer:
Step-by-step explanation:
the second because it has the squared sign most quadratic equations have squarred symbols
an equation of the line normal to the graph of y=sqrt(3x^2+2x) at (2 4)
The equation of the line normal to the curve y = square root(3x² + 2x) at point (2,4) is given as follows:
y - 4 = -4/7(x - 2).
How to obtain the equation of the line normal to the curve?The equation of the line normal to a curve follows the point-slope definition of a linear function, given as follows:
y - y' = m(x - x').
The function in this problem is defined as follows:
y = square root(3x² + 2x).
Then the derivative of the function, applying the chain rule, is given as follows:
y' = (6x + 2)/(2 x square root(3x² + 2x))
y' = (3x + 1)/square root(3x² + 2x)
At x = 2, the numeric value of the derivative is of:
y' = 7/square root(16) = 7/4.
The slope of the normal line is calculated as follows:
m x 7/4 = -1
m = -4/7.
(as the normal line is perpendicular to the tangent line, which has slope equals to the numeric value of the derivative at the point).
The coordinates of the point at (2,4), hence:
x' = 2, y' = 4.
Then the definition of the normal line is given as follows:
y - 4 = -4/7(x - 2).
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19. Select all tables that represent a proportional relationship between x and y.
From the given options, Option A and Option D will represent the proportionality relation between x and y.
The proportional relationship between 2 variables:Equivalence between two variables that are related to one another and preserve a particular amount is referred to as a proportional relationship.
It is a mathematical concept that describes how two variables are related when they do so in equivalency and is also known as the "Relation of Proportionality."
Let the variables x and y are proportional to each other
=> x ∝ y
=> x = ky
=> x/y = k [ where k is proportionality constant ]
Here we will use the formula x/y = k to check the given variables' proportionality
Now check given options given below
Option A
x 0 1/5 2/5 3/5
y 0 1/10 2/10 3/10
For x = 1/5 and y = 1/10
=> [tex]\frac{x}{y} = \frac{1}{5} \times \frac{10}{1}[/tex] = 2
For x = 2/5 and y= 2/10
=> [tex]\frac{x}{y} = \frac{2}{5} \times \frac{10}{2}[/tex] = 2
Therefore, Table A represents the proportionality relation
Option B:
x - 0 1/2 1/3 1/4
y - 0 1/3 1/4 1/5
For x = 1/2 and y = 1/3
=> [tex]\frac{x}{y} = \frac{1}{2} \times \frac{3}{1}[/tex] = 3/2
For x = 1/3 and y = 1/4
=> [tex]\frac{x}{y} = \frac{1}{3} \times \frac{4}{1}[/tex] = 4/3
Therefore, Table B doesn't represent the proportionality relation
Option C:
x - 0 1 3 5
y - 0 1 9 25
For x = 1 and y = 1
=> [tex]\frac{x}{y} = \frac{1}{1} = 1[/tex]
For x = 3 and 9
=> [tex]\frac{x}{y} = \frac{9}{3} = 3[/tex]
Therefore, Table C doesn't represent the proportionality relation
Option D:
x - 0 1 3 4
y - 0 5 15 20
For x = 1 and y = 5
=> [tex]\frac{x}{y} = \frac{1}{5} = 1/5[/tex]
For x = 3 and y = 15
=> [tex]\frac{x}{y} = \frac{3}{15} = \frac{1}{5}[/tex]
Therefore, Table D will represent the proportionality relation
Therefore,
From the given options, Option A and Option D will represent the proportionality relation between x and y.
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Shannon says that the lines y=-3x-4,y=-(1)/(3)x+6,y=-4x-5, and y=(1)/(4)x-5 could represent the sides of a rectangle. Explain Shannon's error.
The disadvantage is that the coefficients of x in the four equations can only take two values, so if one of every values is m, the alternative will be -1/m.
What is the equation?
A relationship between two terms on either side of an equal sign is depicted by a straightforward equation.
Simple equations also pursue one or a mixture of the four arithmetic computations of addition, simple arithmetic, multiplication, and division.
There are three basic forms of the system of equations: point-slope form, standard form, and slope-intercept form.
So, Shannon's error:
In a rectangle, the neighboring sides are perpendicular to one other, whereas parallel runs between the opposing sides.
The slope of line segments is equal, and the slope, of a perpendicular line to some other line with a slope, m, is -1/m , thus the slopes of the axis of symmetry should be equal, which gives:
The equation should consist of two sets of linear equations with equal slopes: B. Pair y = -x + 6 and y = -x - 5
Therefore, the slopes of the other two lines are -1/-1 = 1 and the equations of the other two lines are y = x - 4 and y = x - 5 respectively.
Therefore, the disadvantage is that the coefficients of x in the four equations can only take two values, so if one of every values is m, the alternative will be -1/m.
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How do you solve 1.4f+1.1=8.3−f?
For the given algebaric expression, 1.4f+1.1=8.3−f where "f " is variable the solved value of "f" is 3..
We have an algebraic expression of one variable say f ,
1.4 f + 1.1 = 8.3 - f --(1)
we have to solve it
Step 1 : Multiply both sides by 10
1.4 f ×10 + 1.1 ×10 = 8.3×10 - f ×10
=> 14/10(10f) + 11/10(10) = 83/10(10) - 10f
=> 14f + 11 = 83 - 10f
Step 2 : Subtract 11 from both sides
=> 14f + 11 - 11 = 83 - 10f -11
=> 14f = 72 - 10f
Step 3 : Add 10f both sides
=> 14f + 10f = 72 - 10f + 10f
=> 24f = 72
Step 4 : Divide both sides by 24
=> 24f/24 = 72/24
=> f = 3
Hemce,the solved value of "f" is 3 ..
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Which of the following is not the test of congruence of two triangles ? ASA test ,
AAS test, SSA test , SAS test.
Answer:
Answer Option C: SSA test
The parent function f(x)=x^2 is translated 2 units left and 3 units up. Write the quadratic function in vertex form.
The quadratic function in vertex form is formed as: f(x)=a(x + 2)² + 2.
Explain the vertex form of quadratic function?In the linear model, k defines the vertex of the parabola, just as adding or subtracting b would decide where the line crosses.f(x)=a(x - h)² + k
K functions like b with in slope-intercept formula, just like a linear function would.For the stated question-
Whether you're going to increase by 2, you must also add 2.
The horizontal movement is determined by the h. It goes left or right depending on what you enter in h.
Finding the value that will cause the parenthesis to equal 0 when x equals -2 is necessary to make the necessary adjustments because shifting the vertex point to a left implies subtraction and negatives
x - h = 0
-2 - h = 0
-h = 2
h = -2
As a result, the function appears as follows:
f(x)=a(x - (-2))² + 2
A negative is subtracted to eliminate the signs and create a positive:
f(x)=a(x + 2)² + 2
Thus, the quadratic function in vertex form is formed as: f(x)=a(x + 2)² + 2.
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How do you write 31/25 as a decimal?
To write 31/25 as a decimal, we can divide 31 by 25 using long division or a calculator and we get 1.24
what is decimal?A decimal is a way of expressing a number as a fraction of one.
What is round off?Rounding off is a mathematical process that involves replacing a number with an approximate value that is easier to work with. When you round off a number, you choose the nearest whole number, ten, hundred, etc., depending on the place value you are rounding to.
For example, if you are asked to round the number 3.6 to the nearest whole number, you would round it off to 4, because 4 is the nearest whole number to 3.6.
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The total distance d, in meters, traveled by an object moving in a straight line can be modeled by a quadratic function that is defined in terms of t, where t is the time in seconds. At a time of 10.0 seconds, the total distance traveled by the object is 50.0 meters, and at a time of 20.0 seconds, the total distance traveled by the object is 200.0 meters. If the object was at a distance of 0 meters when t=0 then what is the total distance traveled, in meters, by the object after 30.0 seconds?
The total distance traveled by the object after 30.0 seconds is 450 meters.
Explain the term quadratic function?f(x) = ax2 + bx + c, for which a, b, and c represent constants and a = 0 represents a quadratic function. The function is known as the quadratic term (abbreviated as ax2), the linear term (abbreviated as bx), and the constant term (abbreviated as c).For the stated function;
Time = 10.0 seconds, distance = 50.0 meters.Time = 20.0 seconds, distance = 200.0 meters.Time = 0.0 seconds, distance = 0.0 meters.As, the total distance is modelled by the quadratic equation-
Let the quadratic equation be-
d = at² + bt + c
For (10, 50)
d = a(10)² + (10)b + c ....eq 1
For (20, 200)
d = a(20)² + (200)b + c ....eq 2
For (0, 0)
d = a(0)² + (0)b + c ....eq 3
Solving eq 1, 2 and 3
a = 1/2 ; b = 0 and c =0
Thus, equation for the distance travelled by the object is-
d = 1/2 t²
For t = 30. sec
d = 1/2 (30)²
d = 450 m
Thus, the total distance traveled by the object after 30.0 seconds is 450 meters.
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