evaluate each expression if y=2 Question 8y to the power of -4

Answers

Answer 1
8y^-4
8(2)^-4 (substitute y for 2)
16^-4 (written as 16 to the -4 power)

Related Questions

What is the solution of -8/2y-8=5/y+4 - 7y+8/y^2-16

Answers

Answer:

y = 8

Step-by-step explanation:

[tex]Domain:\\\\2y-8\neq0\ \wedge\ y+4\neq0\ \wedge\ y^2-16\neq0\\\\2y\neq8\ \wedge\ y\neq-4\ \wedge\ y^2\neq16\\\\y\neq4\ \wedge\ y\neq-4\ \wedge\ y\neq\pm\sqrt{16}\\\\y\neq4\ \wedge\ y\neq-4\ \wedge\ y\neq-4\ \wedge\ y\neq4\\\\\boxed{y\neq-4\ \wedge\ y\neq4}\\\\===========================[/tex]

[tex]\dfrac{-8}{2y-8}=\dfrac{5}{y+4}-\dfrac{7y+8}{y^2-16}\\\\\dfrac{-8}{2(y-4)}=\dfrac{5}{y+4}-\dfrac{7y+8}{y^2-4^2}\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\\dfrac{-8}{2(y-4)}=\dfrac{5}{y+4}-\dfrac{7y+8}{(y-4)(y+4)}\qquad\text{multiply both sides by (-2)}\\\\\dfrac{8}{y-4}=-\dfrac{10}{y+4}+\dfrac{14y+16}{(y-4)(y+4)}\qquad\text{add}\ \dfrac{10}{y+4}\ \text{to both sides}\\\\\dfrac{8}{y-4}+\dfrac{10}{y+4}=\dfrac{14y+16}{(y-4)(y+4)}[/tex]

[tex]\dfrac{8(y+4)}{(y-4)(y+4)}+\dfrac{10(y-4)}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\\\\\dfrac{8(y+4)+10(y-4)}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\qquad\text{use the distributive property}\\\\\dfrac{8y+32+10y-40}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\qquad\text{combine like terms}\\\\\dfrac{(8y+10y)+(32-40)}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\\\\\dfrac{18y-8}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\iff18y-8=14y+16\\\\18y-8=14y+16\qquad\text{subtract 14y from both sides}[/tex]

[tex]4y-8=16\qquad\text{add 8 to both sides}\\\\4y=24\qquad\text{divide both sides by 4}\\\\y=8\in D[/tex]

Answer:

6

Step-by-step explanation:

What is the answer to 2/7 x 4 4/9

Answers

To figure this out first make the 4 4/9 into a improper fraction making it 40/9 and then multiply 2/7 x 40/9 then make is a mixed fraction :) hope this helped.

A coal car on a train weighs 30 tons plus 1 ton per cubic yard of coal x that it carries. The total weight of a coal car is: f(x) = x + 30. How will the graph of this function change if the coal car weight is changed to 26 tons? The line will shift vertically up by 4 tons. The line will shift vertically up 26 tons. The line will shift vertically down by 4 tons. The line will shift vertically down by 26 tons.

Answers

The line will shift vertically down by 4 tons. Hope this helps :)

The line will shift vertically down by 4 tons.

Does anybody know a rule that will work for all of these?

Answers

y = something x plus or minus a number

going through each line it isn't a linear pattern ( they don't all have the same difference when subtracted or added together)

so now you play around with quadratic equations ( square roots, powers, etc.)


 and you will see that y = x^2 -5

Which expression is equivalent to (5x^3)(2x)^3?

A. 10x^6
B. 30x^6
C. 40x^6
D. 1000x^12

Answers

[tex]\bf (5x^3)(2x)^3\implies (5x^3)(2^3x^3)\implies (5x^3)(8x^3)\implies 5\cdot 8x^3x^3 \\\\\\ 40x^{3+3}\implies 40x^6[/tex]

Write an application to simulate the rolling of two dice. the application should use an object of class random once to roll the first die and again to roll the second die. the

Answers

01 import java.util.Random;02 03 public class RollDice_Mod {04   05    static Random randomNumbers = new Random();06    static final int SIDES_ON_DICE = 6;07    static final int REPETITIONS = 36000000;08   09    public static void main(String[] args) {10        int[] frequency = countRollFrequencies(REPETITIONS);11        displayFrequencies(frequency);12    }  13     14    static int[] countRollFrequencies(int repetitions) {15        int maxRoll = SIDES_ON_DICE + SIDES_ON_DICE;16        int[] result = new int[maxRoll + 1];17        for(int i = 0; i < repetitions; i++){18            ++result[rollTwoDice()];19        }20        return result;21    }2223    static int rollTwoDice() {24        return rollDice() + rollDice();25    }2627    static int rollDice(){28        return 1 + randomNumbers.nextInt(SIDES_ON_DICE);29    }3031    static void displayFrequencies(int[] frequency) {32        int minRoll = 2;33        for(int i = minRoll; i < frequency.length; i++){34            System.out.printf("%4d%10d\n", i, frequency[i]);   35        }36    }37 38}

Final answer:

The answer explains how to create a Python application to simulate rolling two dice using the random module.

Explanation:

application

To simulate the rolling of two dice using an object of class random, you can create a Python application. Here's an example of how you can achieve this:

Import the random module.

Create a function to simulate rolling a die.

Call the function twice to simulate rolling two dice.

What is a distributive property of 72 divided by 4

Answers

Answer:

[tex]\frac{72}{4}=18[/tex]

Step-by-step explanation:

To find : What is a distributive property of 72 divided by 4 ?

Solution :

The distributive property of division is given by,

[tex]\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}[/tex]

We have to divide 72 by 4,

So, Re-write 72 as 60+12.

Substitute,

[tex]\frac{72}{4}=\frac{60+12}{4}[/tex]

[tex]\frac{72}{4}=\frac{60}{4}+\frac{12}{4}[/tex]

[tex]\frac{72}{4}=15+3[/tex]

[tex]\frac{72}{4}=18[/tex]

Therefore, [tex]\frac{72}{4}=18[/tex]

Final answer:

While the distributive property is typically relevant for multiplication over addition or subtraction, you can apply it to division by first rewriting the division as multiplication by the reciprocal. For example, 72 divided by 4 can be rewritten as 72 times 1/4, and then distributed over a sum or difference.

Explanation:

The distributive property involves multiplication and addition or subtraction, not division. However, if we interpret your question in a bit different way, we can make use of the distributive property for division. To start, dividing 72 by 4 is the same as multiplying 72 by 1/4. So, we can rewrite it as follows:

72 * 1/4

The distributive property is applied when you multiply a number by a sum or a difference. For example, in case of [tex]72*1/4 = (40+32)*1/4[/tex], it would distribute as: [tex]40*1/4 + 32*1/4[/tex]. It gives us 10 + 8 = 18 which is the correct answer. This way, the distributive property can be used in division if the division is expressed as a multiplication.

Learn more about Distributive Property in Division here:

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Consider the equation log (3x-1)=log base 2 of 8. Describe the steps you would take to solve the equation, and state what 3x-1 is equal to.

Answers

The bases are not the same, so you cannot set 3x - 1 equal to 8.

You can evaluate the logarithm on the right side of the equation to get 3.

You can use the definition of a logarithm to write 3x - 1 = 1000.

Answer:  The solution of the given equation is [tex]x=333\dfrac{2}{3}[/tex] and the value of (3x - 1) is 1000.

Step-by-step explanation:  We are given to describe the steps in solving the following logarithmic equation:

[tex]\log(3x-1)=\log_28.[/tex]

Also, we are to find the value of [tex](3x-1).[/tex]

We will be using the following logarithmic properties:

[tex](i)~\log_ba=x~~~\Rightarrow a=b^x,\\\\(ii)~\log_ba=\dfrac{\log a}{\log b},\\\\(iii)~\log a^b=b\log a.[/tex]

We note here that if the base of logarithm is not mentioned, then we assume it to be 10.

The solution is as follows:

[tex]\log(3x-1)=\log_28\\\\\Rightarrow \log(3x-1)=\dfrac{\log8}{\log2}\\\\\Rightarrow log(3x-1)=\dfrac{\log2^3}{\log2}\\\\\Rightarrow \log(3x-1)=\dfrac{3\log2}{\log2}\\\\\Rightarrow \log(3x-1)=3\\\\\Rightarrow 3x-1=10^3\\\\\Rightarrow 3x-1=1000\\\\\Rightarrow 3x=1001\\\\\Rightarrow x=\dfrac{1001}{3}\\\\\Rightarrow x=333\dfrac{2}{3}.[/tex]

Thus, the solution of the given equation is [tex]x=333\dfrac{2}{3}[/tex] and the value of (3x - 1) is 1000.

Two consecutive numbers whose square differ by 25

Answers

Represent these numbers with x and y.  Their squares are x^2 and y^2, respectively.  The larger square is 25 more than the smaller square:

y^2 = x^2 + 25, assuming that y>x.  If x and y are consecutive, y exceeds x by 1:     x+1=y.

Square x+1 = y, obtaining x^2+2x+1.  Substitute your result (that is, your expression for y^2 in terms of x into the other equation:        
 
 x^2+2x+1 = x^2+25.  Then 2x+1=25; 2x=24; x=12, and y=13.

Check:  Is 13^2  25 units greater than 12^2?  Is 169 25 units greater than 144?  Yes.   So, the two consec. integers are 12 and 13.

x+4, -x+64. Use the expressions that represent the length and width of the game board to write an equation that models the area of the figure. Let y represent the area, and write your answer in the form y=ax²+bx+c, where a,b, and c are real numbers.

Answers

y=(x+4)(-x+64)
y=-x^2+68

A chicken breast weighs 1.375 pounds on a digital scale. What is that same weight as a mixed number?

Answers

It’s 1 pound and 3/8 (three eighths). Also written as 1 1/3.

9.17/15.00
Is this a A+ or A or B or C

Answers

9.17/15 is very close to 9/15, or 3/5. 3/5 is the same as 60/100, which would be a D.
9.17/15.00 = 0.61, or about 61 percent.

That would likely earn a grade of D, unless the grading scale used is different from the usual 91-100, 81-90, 71-80, 61-70, 51-60.

Peter wants to borrow $3,000. He has two payment plans to choose from. Plan A is 4% interest over 6 years. Plan B is 5% interest over 4 years. Using the formula mc024-1.jpg for payment, m, which statement best compares the plans?
Plan A has a monthly payment of about $23 less and a total interest charge of $120 less than plan B.
Plan A has a monthly payment of about $23 less and a total interest charge of $120 more than plan B.
Plan A has a monthly payment of about $23 more and a total interest charge of $120 more than plan B.
Plan A has a monthly payment of about $23 more and a total interest charge of $120 less than plan B

Answers

To determine which payment plan is better for borrowing $3,000, Plan A or Plan B, one must calculate both the monthly payments and total interest charges using the given annual interest rates and compounding periods for each plan and compare the results accordingly.

Peter wants to borrow $3,000 and is considering two different payment plans. To compare these plans, we need to calculate the monthly payment and total interest charge for each.

Plan A has an annual interest rate of 4%, compounded monthly over 6 years (or 72 months). Using the formula for monthly payment (m), we can find the monthly payment for Plan A:

 m = P[r(1+r)^n] / [(1+r)^n-1]
Where:

P is the principal amount ($3,000)r is the monthly interest rate (annually 4%, monthly 0.04/12)n is the number of payments (6 years x 12 months/year = 72 months)

Similarly, Plan B has an annual interest rate of 5%, compounded monthly over 4 years (or 48 months). We use the same formula to calculate the monthly payment for Plan B.

After calculating m for both plans, we can also calculate the total interest paid by multiplying the monthly payment by the number of payments and subtracting the principal amount from the result for each plan. Then, we can compare the monthly payments and total interest charges between Plan A and Plan B.

Which linear system has a solution of
[tex]x = 2 \: and \: y = - 3[/tex]

Answers

bear in mind that, a "solution" so-called, or a zero, or a root, is really just an x-intercept of the graph, namely, where does the graph touch the x-axis?  that's a zero/root/solution/x-intercept.

now, about those two lads above, check the picture below.

notice, that, the horizontal line, by definition will never touch the x-axis, whilst the other one does, at x = 2.

you drink one fourth of a pitcher of Kool-Aid your friend drinks 7/12 of the pitcher what fraction of the pitcher do you and your friend drink

Answers

1/4 is equal to 3/12 and 3/12 + 7/12 = 10/12 or 5/6
The Answer is 5/6. how you reach this answer is by finding the common denominator, which in this case is 12. So you multiply the numerator and the denominator by 3, which will become 3/12. You then add the two fractions and then simplify to get 5/6. Hope this helps.

Given the equation −4 Square root of x minus 3= 12, solve for x and identify if it is an extraneous solution

Answers

i believe ur answer is 12 and is extraneous

Answer:

[tex]x=\frac{225}{16}[/tex] is an extraneous solution.      

Step-by-step explanation:

Given : Equation [tex]-4\sqrt x-3=12[/tex]

To find : Solve for x and identify if it is an extraneous solution?

Solution :

Step 1 - Write the equation,

[tex]-4\sqrt x-3=12[/tex]

Step 2 - Add 3 both sides,

[tex]-4\sqrt x-3+3=12+3[/tex]

[tex]-4\sqrt x=15[/tex]

Step 3 - Squaring both sides,

[tex](-4\sqrt x)^2=(15)^2[/tex]

[tex]16x=225[/tex]

Step 4 - Divide both side by 16,

[tex]\frac{16}{16}x=\frac{225}{16}[/tex]

[tex]x=\frac{225}{16}[/tex]

For extraneous solution, Substitute the value of x back in the equation.

[tex] -4\sqrt (\frac{225}{16})-3=12[/tex]

[tex]-4\times\frac{15}{4}-3=12[/tex]

 [tex]-15-3=12[/tex]

[tex]-18\neq12[/tex]

The value of x does not satisfy the equation which means the value of x is an extraneous solution.

So, [tex]x=\frac{225}{16}[/tex] is an extraneous solution.

The function g(x) = –x2 + 16x – 44 written in vertex form is g(x) = –(x – 8)2 + 20. Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = –x2 + 16x – 44?

Answers

It was moved up 20 units

Answer:

the graph of f(x) will be reflected over x axis, moved 8 units to the right and shifted 20 units up to get g(x)

Step-by-step explanation:

The function [tex]g(x) = -x^2 + 16x - 44[/tex] written in vertex form is [tex]g(x) = -(x - 8)^2 + 20[/tex]

The parent function is f(x)=x^2

Now we compare parent function f(x) and g(x)

In g(x), negative sign at first

f(x) ----> -f(x) , the graph is reflected across x axis

f(x)-----> f(x-h), the graph will be transformed h units to right

f(x)----> f(x) +k , the graph will be transformed k units up

[tex] g(x) = -(x - 8)^2 + 20[/tex], the graph of f(x) will be reflected over x axis, moved 8 units to the right and shifted 20 units up to get g(x)

The rectangular box shown in the figure has dimensions 9" × 5" × 3" (a = 9, b = 5, c = 3). Approximate the angle θ formed by a diagonal of the base and a diagonal of the 5" × 3" side. (Round your answer to two decimal places.)

Answers

The simplest method to do this is with the vector dot product. Let the vector A = <9i + 5j> with magnitude √106 be the base diagonal, and B = <5j + 3k> be the diagonal vector on the side, with magnitude √34. Then cos θ = (A dot B) divided by the product of the magnitudes. A dot B =30, so 

cos θ = 30 / √(34 x 106)

 = 0.4997 ==>

 θ = 49.19° is the answer

The expected (mean) life of a particular type of light bulb is 1,000 hours with a standard deviation of 50 hours. the life of this bulb is normally distributed. what is the probability that a randomly selected bulb would last longer than 1150 hours?

Answers

For any normal random variable X with mean ÎĽ and standard deviation Ď , X ~ Normal( ÎĽ , Ď ), (note that in most textbooks and literature the notation is with the variance, i.e., X ~ Normal( ÎĽ , Ď² ). Most software denotes the normal with just the standard deviation.) You can translate into standard normal units by: Z = ( X - ÎĽ ) / Ď Moving from the standard normal back to the original distribuiton using: X = ÎĽ + Z * Ď Where Z ~ Normal( ÎĽ = 0, Ď = 1). You can then use the standard normal cdf tables to get probabilities. If you are looking at the mean of a sample, then remember that for any sample with a large enough sample size the mean will be normally distributed. This is called the Central Limit Theorem. If a sample of size is is drawn from a population with mean ÎĽ and standard deviation Ď then the sample average xBar is normally distributed with mean ÎĽ and standard deviation Ď /âš(n) IYou can translate into standard normal units by: Z = ( X - ÎĽ ) / Ď Moving from the standard normal back to the original distribuiton using: X = ÎĽ + Z * Ď Where Z ~ Normal( ÎĽ = 0, Ď = 1). You can then use the standard normal cdf tables to get probabilities. If you are looking at the mean of a sample, then remember that for any sample with a large enough sample size the mean will be normally distributed. This is called the Central Limit Theorem. If a sample of size is is drawn from a population with mean ÎĽ and standard deviation Ď then the sample average xBar is normally distributed with mean ÎĽ and standard deviation Ď /âš(n) IYou can translate into standard normal units by: Z = ( X - ÎĽ ) / Ď Moving from the standard normal back to the original distribuiton using: X = ÎĽ + Z * Ď Where Z ~ Normal( ÎĽ = 0, Ď = 1). You can then use the standard normal cdf tables to get probabilities. If you are looking at the mean of a sample, then remember that for any sample with a large enough sample size the mean will be normally distributed. This is called the Central Limit Theorem. If a sample of size is is drawn from a population with mean ÎĽ and standard deviation Ď then the sample average xBar is normally distributed with mean ÎĽ and standard deviation Ď /âš(n) in You can translate into standard normal units by: Z = ( X - ÎĽ ) / Ď Moving from the standard normal back to the original distribuiton using: X = ÎĽ + Z * Ď Where Z ~ Normal( ÎĽ = 0, Ď = 1). You can then use the standard normal cdf tables to get probabilities. If you are looking at the mean of a sample, then remember that for any sample with a large enough sample size the mean will be normally distributed. This is called the Central Limit Theorem. If a sample of size is is drawn from a population with mean ÎĽ and standard deviation Ď then the sample average xBar is normally distributed with mean ÎĽ and standard deviation Ď /âš(n) in this question we have X ~ Normal( ÎĽx = 1000 , Ďx² = 2500 ) X ~ Normal( ÎĽx = 1000 , Ďx = 50 ) Find P( X > 1150 ) P( ( X - ÎĽ ) / Ď > ( 1150 - 1000 ) / 50 ) = P( Z > 3 ) = P( Z < -3 ) = 0.001349898 Find P( X < 1100 ) P( ( X - ÎĽ ) / Ď < ( 1100 - 1000 ) / 50 ) = P( Z < 2 ) = 0.9772499

What is the slope of the function

Answers

The slope of the function is 3
that would be 3.
hope this helps you.

The basal diameter of a sea anemone is an indicator of its age, and in a certain population of anemones, the distribution of basal diameters is approximately normal with a mean of 5.3 cm and a standard deviation of 1.8 cm. suppose you randomly select five anemones from this population.
a. what is the probability that all five anemones have a basal diameter more than 5.5 cm? (2pt)

Answers

Final answer:

The probability that all five randomly selected sea anemones from a population with normally distributed basal diameters have a diameter more than 5.5 cm is approximately 4.5%.

Explanation:

To solve this problem, we first need to find the probability that one sea anemone has a basal diameter more than 5.5 cm, given the population's mean basal diameter is 5.3 cm with a standard deviation of 1.8 cm. We calculate the Z-score for a diameter of 5.5 cm to see how many standard deviations this value is away from the mean. The Z-score formula is Z = (X - μ) / σ, where X is the value in question, μ is the mean, and σ is the standard deviation.

The Z-score for a diameter of 5.5 cm is Z = (5.5 - 5.3) / 1.8 ≈ 0.11. Looking this up in a standard normal distribution table, we find that the probability of selecting an anemone with a diameter larger than 5.5 cm is approximately 0.5438. Since the selections are independent, the probability of all five having a diameter more than 5.5 cm is (0.5438)⁵ ≈ 0.045, or 4.5%.

The probability that all five randomly selected anemones have a basal diameter more than 5.5 cm is approximately 0.0056.

To solve this problem, we can use the standard normal distribution. First, we need to standardize the diameter value using the z-score formula:

[tex]z = \frac{x - \mu}{\sigma}[/tex]

where:

- x is the value of the basal diameter,

- [tex]\mu[/tex] is the mean of the basal diameters (5.3 cm),

- [tex]\sigma[/tex] is the standard deviation of the basal diameters (1.8 cm), and

- z is the standardized score.

For a basal diameter of 5.5 cm, the z-score would be:

[tex]z = \frac{5.5 - 5.3}{1.8} = \frac{0.2}{1.8} \approx 0.1111[/tex]

To find the probability that an anemone has a basal diameter more than 5.5 cm, we need to find the area to the right of z = 0.1111 under the standard normal curve.

Using a standard normal table or calculator, we find that this area is approximately 0.4562.

Since each selection is independent (assuming replacement), the probability that all five anemones have a basal diameter more than 5.5 cm is the probability raised to the power of 5:

[tex]P(\text{all five} > \text{ 5.5 cm}) = (0.4562)^5 \approx 0.0056[/tex]

So, the probability that all five randomly selected anemones have a basal diameter more than 5.5 cm is approximately 0.0056.

Angelica’s bouquet of a dozen roses contains 5 white roses. The rest of the roses are pink. What fraction of the bouquet is pink roses? There are 12 roses in a dozen.

Answers

Well, I know there are 12 roses. 
5 are white.
All you have to do is subtract 12 and 5. Once you do that you will have your answer!

Answer: 7/12 for pink roses.
Hope this helps! =) 

The requried fraction of the bouquet that is pink roses is 7/12, as of the given proportion.

If Angelica's bouquet of a dozen roses contains 5 white roses, then the remaining roses must be pink. Since there are 12 roses in a dozen, the number of pink roses in the bouquet would be 12 - 5 = 7.

To find the fraction of the bouquet that is pink roses, we divide the number of pink roses by the total number of roses:

Fraction of pink roses = Number of pink roses / Total number of roses

Fraction of pink roses = 7 / 12

Therefore, the fraction of the bouquet that is pink roses is 7/12.

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Which equation represents a line that passes through (–9, –3) and has a slope of –6?

Answers

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ -9}}\quad ,&{{ -3}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies -6 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-3)=-6[x-(-9)] \\\\\\ y+3=-6(x+9)\implies y+3=-6x-54\implies y=-6x-57[/tex]

Jasmine earns $36 for 4 hours of baby-sitting. She charges a constant hourly rate. Which table correctly shows the amount Jasmine earns baby-sitting for different numbers of hours?

Answers

I am pretty sure it is a because 2 is half of 4 and 18 is half of 36.

Answer:

A

Step-by-step explanation:


Parallelogram MNPQ was dilated to create parallelogram M'N'P'Q'.



Which statements are true about the parallelograms? Check all that apply.

The length of side MN is 2 units.
The length of side M'N' is 5 units.
The image is smaller than the pre-image.
Sides MQ and M'Q' both have the same slope, 1.
The scale factor is 2/5

Answers

Answer:

Options 1,2 and 4 are correct.

Step-by-step explanation:

We have been given a parallelogram MNPQ was dilated to create parallelogram  M'N'P'Q' and we asked to find out which of the given options are correct.

Let us see all the options one by one.

On using distance formula we can see that side MN is 2 units.

[tex]MN=\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2} }[/tex]

[tex]MN=\sqrt{(4-2)^{2} +(-2-(-2))^{2} }[/tex]

[tex]MN=\sqrt{(2)^{2} } =2[/tex]

Therefore,option 1 is correct.

We can find the side M'N' by distance formula as we solved for side MN. After solving for M'N' we will get 5 units. Therefore, option 2 is also correct.

Now let us see third option. We can see that image M'N'P'Q' is bigger than pre-image MNPQ. Therefore, option 3 is false.

Now look at our option 4.

Since we know slope is rise (difference of y coordinates) over run (difference of x coordinates) . Upon looking at our image and pre-image we can see that as we increase our x coordinate by one unit our y coordinate also increase by one.

Therefore, option 4 is correct indeed.

Upon looking at our fifth option we can see that our image is bigger than our pre-image. If our image was dilated by factor of 2/5 it would have been smaller than our pre-image. We can see the scale factor is 5/2 instead of 2/5.

Therefore, our fifth option is false.

Considering the slopes and scale factor of the diagram given, the statements that are true about the parallelogram are: A, B, and D.

How to find Slope

Slope = vertical distance / horizontal distance = change in y / change in x.

How to find Scale Factor

Scale factor = length of image/corresponding length of pre-image.

Find the length of MN:

MN = |4 - 2| = 2 units (Option A is true).

Find M'N':

M'N' = |10 - 5| = 5 units (Option B is true).

MNPQ is the pre-image, while M'N'P'Q' is the image, therefore, the image is bigger than the pre-image. (Option C is NOT true).

Find Slope of MQ:

Slope = 1/1 = 1

Find Slope of M'Q':

Slope = 2/2 = 1 (Option D is true).

Find the scale factor:

Scale factor = dimension of image/dimension of pre-image = M'N'/MN

Scale factor = 5/2 (Option E is NOT true).

Therefore, considering the slopes and scale factor of the diagram given, the statements that are true about the parallelogram are: A, B, and D.

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Jed took 2 free throws in 5 seconds. Alex took 4 free throws in 12 seconds did the two shoot free throws at the same rate? Explain

Answers

2 free throws in 5 seconds....2/5 = 0.4 free throws per second
4 free trows in 12 seconds....4/12 = 0.3 free throws per second

no, they did not shoot their free throws at the same rate...because 2/5 does not equal 4/12

Jed and Alex do not shoot free throws at the same rate, Jed is faster by 0.5 seconds.

What is a unitary method?

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Jed took 2 free throws in 5 seconds.

∴ Jed can do 1 free throw in (5/2) = 2.5 seconds.

Alex took 4 free throws in 12 seconds.

∴ Alex can do 1 free throw in (12/4) = 3 seconds.

No, Jade and Alex do not shoot free throws at the same rate Jed is faster by 0.5 seconds.

learn more about the unitary method here :

https://brainly.com/question/28276953

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find the measure of <ghk <hki and <hkj show your work or wite and explanation

Answers

check the picture below.

Ben earns $1500 each summer and puts the money in a savings account with a 6% simple interest rate. If he deposits the same amount each year, how much money will he have at the end of his third summer

$4770

$3250

$3175

$2850

Answers

he will have 4770 in his account 
I believe the answer is A. $ 4,770

The amount that Ben gets by the first year:

1,500 + (1,500 x 6%)  = 1590

The amount that Ben gets by the second year: 

(1590+1500)  + (3090 x 6%) = 3270.4

The amount that Ben gets by the third summer

(3270.4 + 1500 = $ 4770 

The interest rate is not calculated because the Bens till hasn't pass the rest of the year

If X and Y vary directly, as x decreases, what happens to the value of y?

Answers

As x decreases y also decreased

In the circle graph above, you can see that 47% of the company's monthly income is used to pay the owner's personal salary. If the amount of the owners's personal salary was $2,176.10 this month, what was the company's total monthly income this month?

Answers

The answer to this question would be: $4630

In this question, 47% of the company income is used to pay owner's personal salary, which was $2,176.10
Then, to find the company total income the calculation would look like this:

owner's personal salary= 47% * total company income
$2,176.10= 0.47 * total company income
total company income= $2,176.10/ 0.47 = $4630

Final answer:

To find the total monthly income, set up a proportion using the percentage of the owner's salary with the given amount. Solve for the total income to find the answer.

Explanation:

In the circle graph above, the owner's personal salary represents 47% of the company's monthly income. This means that $2,176.10 is 47% of the total monthly income. To find the total income, you can set up a proportion: $2,176.10 is to 47% as X is to 100%. Solving this equation gives you the company's total monthly income as $4,635.

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