All of the triangles are dilations of Triangle D. The dilations use the same center P, but different scale factors. 1) What do Triangles A, B, and C have in common? 2) What do Triangles E, F, and G have in common? 3) What does this tell us about the different scale factors used?

Answer:

n=2/5

Step-by-step explanation:

Please look at the image below! :D

Answer:

[tex]\frac{2}{5}[/tex]

Step-by-step explanation:

[tex]\frac{1}{2}[/tex] n + [tex]\frac{3}{4}[/tex] n = [tex]\frac{1}{2}[/tex]            [tex]\frac{1}{2}[/tex] means the same as [tex]\frac{2}{4}[/tex]

[tex]\frac{2}{4}[/tex] n + [tex]\frac{3}{4}[/tex] n = [tex]\frac{1}{2}[/tex]

[tex]\frac{5}{4}[/tex] n = [tex]\frac{1}{2}[/tex]  multiply each side by [tex]\frac{4}{5}[/tex]

[tex](\frac{4}{5})[/tex][tex]\frac{5}{4}[/tex] n = [tex](\frac{4}{5})[/tex][tex]\frac{1}{2}[/tex]

n = [tex]\frac{4}{10}[/tex] = [tex]\frac{2}{5}[/tex]

The interest rate at the bank = 2.324 %

Let X be the random variable representing the interest rate on a five-year certificate of deposit (cd) for banks in South Florida in 2018.

Then X follows the Normal Distribution with,

Mean, μ = 2.28 %  and,

Standard Deviation, σ = 0.37 %

We need to find the X at the 45th percentile.

45th percentile implies z-value = 0.45

The z-score at 45th percentile or 0.45 probability = -0.12 [From the z-tables]

We have, z = (x-μ)/σ

⇒ zσ = x-μ

⇒ x = zσ+μ

⇒ x = (0.12 x 0.37) + 2.28

      = 2.324

Hence the interest rate at the bank = 2.324 %

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Let x be the cost of each notebook. We know that we bought 5 of them, then the total cost of the notebooks is:

We had 21 dollars and we spent 5x on the notebooks, this can be express as:

Finally we know that this is equal to the six dollars we had at the end, then we have the equations:

Solving for x we have:

Therefore each notebook cost $3

Answer:

m = -5

n = -2

Step-by-step explanation:

5m + 6n = -37

10m + 4n = -58 multiply first equation by -2

-2 × 5m + 6n = -37

-10m + (-12n) = 74 now add two equations up

10m - 10m + 4n - 12n = 74 - 58 add/ subtract like terms

-8n = 16 divide both sides by -8

n = -2

to find the value of m, replace n with -2 in the first equation

5m + 6*(-2) = -37

5m - 12 = -37 add 12 to both sides

5m = -25 divide both sides by 5

m = -5

Using pythagorean theorem:

Answer:

1/2 -> 3/4 -> 4/5 -> 9/10

Step-by-step explanation:

1/2 = 50%

3/4 = 75%

4/5 = 80%

9/10 = 90%

How to figure out:

1/2 - Divide 100/2 = 50. So 1/2 of 100 is 50 so 50%

3/4 - Divide 100/4 = 25. Now multiply 25 x 3 = 75 so 75%

4/5 - Divide 100/5 = 20. Now multiply 20 x 4 = 80 so 80%

9/10 - Divide 100/10 = 10. Now multiply 10 x 9 = 90 so 90%

The most appropriate choice for matrices will be given by-

Required Equation

[tex]y = 2x^2 - 3x + 1[/tex]

What are matrices?

If the numbers are arranged in the form of rows and columns, then the arrangement is called matrix.

Here,

The equation is [tex]y =Ax^2 + Bx + C[/tex]

The function contains the points (0, 1), (-2, 15), (3,10).

On putting these coordinates in the equation,

C = 1

[tex]15 = A(-2)^2 + B(-2) + 1\\4A - 2B = 15-1\\2(2A - B ) =14\\2A - B = \frac{14}{2}\\2A -B = 7[/tex]................ (1)

[tex]10 = A(3)^2 + B(3) + 1\\9A + 3B = 10-1\\3(3A + B ) =9\\3A + B =\frac{9}{3}\\3A + B = 3[/tex].................... (2)

Here matrix method will be used

Let

[tex]P = \begin{bmatrix} 2 & -1\\ 3 & 1 \end{bmatrix}[/tex], [tex]Q = \begin{bmatrix} x \\ y\end{bmatrix}[/tex], [tex]R = \begin{bmatrix} 7\\3 \end{bmatrix}[/tex]

PQ = R

[tex]Q = P^{-1}R[/tex]

Adjoint P =

[tex]\begin{bmatrix} 1 & -3 \\ 1 & 2 \end{bmatrix}^T\\\\\begin{bmatrix} 1 & 1 \\ -3 & 2 \end{bmatrix}[/tex]

Det P = [tex]\begin{vmatrix} 2 & -1\\3&1\end{vmatrix}[/tex]

          = [tex]2\times 1 - 3 \times (-1)\\5[/tex]

[tex]P^{-1} = \frac{1}{5}\begin{bmatrix} 1 & 1\\-3 &2\end{bmatrix}[/tex]

[tex]Q = \frac{1}{5}\begin{bmatrix} 1 & 1\\-3 &2\end{bmatrix}\begin{bmatrix}7\\3\end{bmatrix}[/tex]

[tex]Q = \frac{1}{5}\begin{bmatrix} 10\\-15\end{bmatrix}\\Q= \begin{bmatrix} 2\\-3\end{bmatrix}[/tex]

A = 2, B = -3

Required Equation

[tex]y = 2x^2 - 3x + 1[/tex]

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Complete Question

Use matrices to write the equation of the function in the form [tex]y = Ax^2 + Bx + C[/tex]that contains the points (0, 1), (-2, 15), (3,10).

The inequality to determine the number of packages Renna could remove from the elevator to meet the mass requirement is 620 - 37.4g = 450.

An inequality is simply used to show the relationship between the expressions that are not equal.

The mass limit is given as 450 grams. Renna has a package that has a weight of 620g.

Each package has 37.4g.

Let the number of packages to remove be p.

The expression will be:

= 620 - (37.4 × p) = 450

620 - 37.4g = 450.

This illustrates the concept of inequality.

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The missing value is 1/3 from the table that represents Judy's rate which is the correct answer that would be an option (C).

In mathematics, relations are used to describe the link between the components of two sets. They aid in mapping items from one set (known as the domain) to elements from another set (known as the range), resulting in ordered pairs of the form (input, output).

We have been given the rates of time taken by Judy and Sal to complete a puzzle.

Sal's rate is r, as we can see from the table. Judy is said to take 3 hours to solve a puzzle by herself. It barely takes them two hours to work with Sal.

Because Judy completes the task in three hours, the portion of the puzzle finished in one hour is 1/3.

Therefore, the missing value is 1/3 from the table that represents Judy's rate

Hence, the correct answer would be an option (C).

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Formula to work out the Total surface area of half-cylinder = [tex]\pi rh + \pi r^{2} + 2rh[/tex]

To find:

Formula to work out the surface area of half a cylinder

Solution:

The surface area of ​​a semi-cylinder can be calculated by adding half the curved area of ​​the cylinder to the area of ​​the two semi-circles and the area of ​​the rectangular section below. The formula for the surface area of ​​a semi-cylinder is given by: Total surface area of ​​

Total surface area of a half-cylinder = (1/2) × curved area of ​​cylinder + 2 × area of ​​semi-circle + area of ​​base of cylinder.

total surface area of a half-cylinder = [tex]\pi rh+\pi r^{2} +2rh[/tex]

where r = radius of cylinder

[tex]\pi[/tex] = 3.14 or 22.7 cm

h = height of cylinder

(Or)  We can find Total surface area of half cylinder as, Total surface area of half cylinder ÷ 2

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The length and width of the rectangle are 5.5 inches and 10.5 inches.

So, the dimensions of the rectangle:

Substitute the values in the formula as follows:

Therefore, the length and width of the rectangle are 5.5 inches and 10.5 inches.

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1) For this question, all we need to do is to plug it in the value for x.

So,

2/3x -8 =0 Plugging into x the value x=12

2/3(12) -8 =0

8 -8 =0

0

So when x=12, then the equation is equal to zero. This leads us to conclude that 12 is the root or the solution of this equation.

Answer:

(5, 20)

Step-by-step explanation:

(5, 20) is the only ordered pair which falls on the line

Answer: -3/4

Step-by-step explanation: Lucky I just learned about this last week! Multiply 7 and -1 by -2 which makes the equation -14x + 2 = 14. Subtract 2 from both sides to make -16x = 12. Then divide each side by -16 and you get -3/4 = x.

Nice helping out!

Answer:

There are no solutions.

Step-by-step explanation:

Hello!

Isolate the absolute value equation first:

Now stop and think.

An absolute value equation always has a positive outcome, because you are finding the positive value of what's inside. The outcome here is negative, so there is no value of x that makes it so that the absolute value is negative.

So the solution is No Solutions.

The equation of u when it is the subject is u = 9/t - 12at

From the question, the original equation is given as

9 = 12at2 + ut

Next, we rewrite the equation to show the exponents

This is represented as

9 = 12at² + ut

To solve further, we simply isolate the variable term ut

This is done by subtracting 12at²  from both sides of the equation

So, we have the following equation

9 - 12at² = 12at² - 12at² ut

Evaluate the like terms in the equation

So, we have

9 - 12at² = ut

Lastly, divide both sides of the equation by t

So, we have

(9 - 12at²)/t = ut/t

Evaluate the quotients

9/t - 12at = u

Make us the subject

u = 9/t - 12at

Hence, the solution for the equation for u is u = 9/t - 12at

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1) A translation of 3 units down, option D.

2) The vertex moves 3 units down.

3) The new range is y ≥ -3, correct option is C.

For a function f(x) a vertical shift of N units is written as:

g(x) = f(x) + N

In this case, we have:

f(x) = |x|

h(x) = |x| - 3

Then h(x) = f(x) - 3

This is a shift of 3 units down, the correct option is D.

How is the vertex affected?

The vertex is translated 3 units down, like the whole graph of the function.

How is the range affected?

The vertex defines the minimum of the range, so if the vertex goes 3 units down, then the range also does, the new range will be:

y ≥ -3.

So the correct option is C.

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Given:

Aim:

We need to graph the given function.

Explanation:

Replace x =-4 in the given equation.

We get the point (-4, 4).

Replace x = 0 in the given equation.

We get the point (0,1).

Replace x =4 in the equation.

We get the point ( 4, -2).

Mark the points (-4, 4), (0,1), and ( 4, -2) on the graph and join them by ray.

Final answer:

The graph of the given eqaution:

The p-value, used in null-hypothesis significance testing, represents the likelihood that the test findings will be at least as extreme as the result actually observed, assuming that the null hypothesis is true.

Therefore, the p-value for study b exists 0.080.

The P value is the likelihood, for a particular statistical model, that the statistical summary would be either equal to or more extreme than the actual observed results if the null hypothesis were to hold.

In a two tailed test the probability of occurrence exists the total area beneath the critical range of values on both the sides of the curve (negative side and positive side)

Therefore, the probability values for a two tailed test as compared to a one tailed test exists given by the under given relation -

[tex]$p-\text { value }=P\left(Z < -\frac{\alpha}{2}\right)+P\left(Z > \frac{\alpha}{2}\right)$$[/tex]

simplifying the above equation, we get

[tex]$P \frac{\alpha}{2}=0.040$[/tex]

Substituting the given value in above equation, we get -

Probability values for a two tailed test

= 0.040 + 0.040

= 0.080

Therefore, the p-value for study b exists 0.080.

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The largest prime factor that always divides the sum of the terms in the sequence is 37.

The sequence is finite and consists of three-digit integers.

The tens and units digits of each term are, respectively, the hundreds and tens digits of the next term, and the tens and units digits of the last term are, respectively, the hundreds and tens digits of the first term.

From the above property of the sequence, we can see that each digit at the units, tens as well as hundreds place will appear the same number of times in the sequence.

Let "x" be the sum of the digits at unit place in all the terms.

The sum of all the terms is "S".

S = 111*x

S = 3*37*x

We can clearly see that the sum "S" is divisible by 37.

Hence, the largest prime factor that always divides the sum of the terms in the sequence is 37.

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Based on the distance of the entire trip, the fraction of the trip that the car has travelled is 514 ²/ ₇.

The diagram is divided into 7 parts which means that each part can be said to be:

= 1/7 of the journey

The car is in the 4th part so that means that the fraction of the trip that has been traveled is:

= 4 / 7

Given the total miles of the trip, this would be:

= 4/7 x 900

= 514.29

= 514 + 29 / 100

= 514 ²/ ₇

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1. The mathematical expression for the length is C. 2x + 5.

2. The quadratic equation is A. 2x² + 5x - 18 = 0.

3. The width of the tarpaulin is A. 2 ft.

4. The length of the tarpaulin is D. 9 ft.

5. The perimeter of the tarpaulin is C. 22 feet.

From the information, the following can be deduced:

Width = x

Length = (2 × x) + 5 = 2x + 5

Area = 18 ft²

The equation will be:

Length × Width =Area

(2x + 5)x = 18

2x² + 5x = 18

2x² + 5x - 18 = 0

2x² - 4x + 9x - 18 = 0

2x(x - 2) + 9(x - 2)

Therefore, x - 2 = 0

x = 0 + 2 = 2

Width = 2

Length = 2x + 5 = 2(2) + 5 = 9ft

Perimeter = 2( Length + Width)

= 2(2 + 9)

= 22 feet.

This illustrates the concept of addition to calculate the perimeter.

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The remaining amount of the substance with the half life of 64.9 days after 100 days is 2.749.

To calculate the amount that remains  after 100 days, this formular can be used

amount remaining = [tex]a (0.50)^{\frac{t}{h} }[/tex]

where t is the time that was required for the process to take place, where t is 100 days.

h is the halftime, which is been given as 64.9 days

where a is given as the initial amount that is present which is 8.

Then the values can be substituted to have

[tex]=a (0.50)^{\frac{100}{64.9} }[/tex]

= 2.749

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Statement Problem: Shane is a building engineer and is determining the length of an access ramp needed to reach a step 1.5 feet off the ground. He knows the length of the ramp, r, in feet, can be expressed with the equation below.

First, Shane finds that sin(4.5°) ≈ 0.08. Using his calculator, he then calculates the length of the ramp as shown below.

What could Shane do to make his calculation more accurate?

Solution:

The length of the ramp, r, in feet is expressed using the sine ratio;

Hence, Shane's calculation would be more accurate if he uses sin (4.5 degrees) in his calculator instead of 0.08

CORRECT OPTION: A

Answer:

X=ℝ, Y=ℝ

Step-by-step explanation:

Parallel means they have the same slope so it can be anything on the x-axis, perpendicular meaning opposite slope which is y=.

The value of g(a) + h(a) is a²-3a-2 or (a-2)(a-1) using addition of functions.

Given a collection of inputs X (domain) and a set of potential outputs Y (codomain), a function is more technically defined as a set of ordered pairings (x,y) where x belongs to X  and y belongs to Y, with the caveat that there can only be one ordered pair with the same value of x. The function notation f:XY can be used to express that f is a function from X to Y

Adding two functions-

g(a) = a²- 2

h(a) = -3a

Let h(a) be g(a) + h(a)

So h(a) = a² - 2 - 3a.

We can factorize the function into (a-2)(a-1).

So we get h(a) = (a-2)(a-1).

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Explanation

if you know 2 points of a line you can easily find the slope using

Let

P1(-1,5)

P2(7,1)

replace,

I hope this helps you

The truck can haul 1102 pounds.

According to the question,

We have the following information:

A Ford F-150 truck is considered a half-ton truck because that is how much it can haul.

(We will not directly convert ton into pounds. We will follow the following steps.)

Now, we know that 1 ton is equal to 1000 kilograms.

So, half ton makes 500 kg.

Now, to convert this into pounds, we will multiply 500 kg by 2.205 because we know that 1 kg is equal to 2.205 pounds.

1 kg = 2.205 pounds

500 kg = (500*2.205) pounds

500 kg = 1102.5 pounds

Hence, the truck can haul 1102.5 pounds.

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