What is the equation of the line that passes through the points (-3,2) and (-5,8)

Answer:

1 : √3 : 2

Step-by-step explanation:

In the special right triangle, 30°-60°-90° triangle:-

Opposite side < Adjacent side < Hypotenuse.

1. The smallest side is opposite to angle 30°, also called opposite side.

2. Adjacent side is √3 times smallest side.

3. Hypotenuse is 2 times smallest side.

So the ratios of sides would be as follows:-

Opposite : Adjacent : Hypotenuse

1x : √3x : 2x

1 : √3 : 2

Answer:

Number of cows is 23

Number of chickens is 46

Step-by-step explanation:

Let's assume

number of cows =x

we are given

Mr.Yan has almost as twice as many chickens and cows

so,

Number of chickens =2x

We know that

Number of legs in a cow =4

Number of legs in a chicken =2

now, we can set up equation

[tex]4\times x+2\times 2x=184[/tex]

[tex]4x+4x=184[/tex]

[tex]8x=184[/tex]

[tex]x=23[/tex]

So,

Number of cows =23

Number of chickens is

[tex]=2\times 23=46[/tex]

Answer:

[tex]8.68,13.16[/tex]

Step-by-step explanation:

Hint- First we have to calculate the mean and standard deviation of the sample and then applying formula for confidence interval we can get the values.

Mean of the sample is,

[tex]\mu=\dfrac{\sum _{i=1}^{24}a_i}{24}=\dfrac{262}{24}=10.92[/tex]

Standard deviation of the sample is,

[tex]\sigma =\sqrt{\dfrac{\sum _{i=1}^{24}\left(x_i-10.92\right)^2}{24-1}}=5.6[/tex]

The confidence interval will be,

[tex]=\mu \pm Z\dfrac{\sigma}{\sqrt{n}}[/tex]

Here,

Z for 95% confidence interval is 1.96, and n is sample size which is 24.

Putting the values,

[tex]=10.92 \pm 1.96\cdot \dfrac{5.6}{\sqrt{24}}[/tex]

[tex]=10.92 \pm 2.24[/tex]

[tex]=8.68,13.16[/tex]

Confidence interval is used to express the degree of uncertainty associated with a sample.

95% confidence interval means that if we used the same sampling method to select different samples and calculate an interval, we would expect the true population parameter to fall within the interval for 95% of the time.

Final answer:

A 95 percent confidence interval is computed using the t-distribution and provides an estimated range where we can expect the population mean to lie. It reflects the level of certainty, but does not suggest that it contains 95 percent of the data.

Explanation:

To compute a 95 percent confidence interval for the number of hours students spent studying, we first need to calculate the mean and standard deviation of the given sample data. Then we can use the t-distribution because the sample size is small and we don't know the population standard deviation. The formula to calculate a confidence interval is: ± t× (s/√n), where t is the t-score associated with our confidence level and degrees of freedom (n-1), s is the sample standard deviation, and n is the sample size.

Confidence intervals provide a range of values that we are a certain percentage sure (95% in this case) contains the population mean. It is not correct to think that a 95% confidence interval contains 95% of the data. Instead, it means that if we were to take many samples and build a confidence interval from each of them, 95% of those intervals would contain the true population mean. Therefore, the confidence interval gives an interval estimate for where the population mean lies, not a precise value.

Answer:

To find the unit rate, you have reduce the fraction until you get 1 in the denominator.

Step-by-step explanation:

ex:  16/4 = 4/1 = 4 this is the unit rate.

unit means 1.

Answer:

Triangles

Step-by-step explanation:

A polygon is a two dimensional plane figure having at least three straight sides and angles. It can have more than three sides but the simplest and basic polygon we can draw is a triangle.

Hence all polygons can be decomposed into the smaller basic polygons which are triangles.

g(2) This means that x is 2, so you can plug in 2 for "x" in the equation

g(x) = 5x + 1

g(2) = 5(2) + 1

g(2) = 10 + 1

g(2) = 11

To find the value of the function 'g(x) = 5x + 1' at x = 2, we substitute x with 2. Multiply 5 by 2 to get 10, then add 1 to get 11, so g(2) = 11.

In the given function g(x) = 5x + 1, we are asked to find the value of g(2).

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Answer

14 / 13 hope this helps

Step-by-step explanation:

Answer:

The answer is c hope it helps.

Step-by-step explanation:

Hence, option (C) is correct.

What is the probability?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are.

The analysis of events governed by probability is called statistics.

As per the given information it would be option (C) i.e., it is likely

Hence, option (C) is correct.

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Answer:

See image for answer

Step-by-step explanation:

I drew lines connecting the center of dilation and the points. Then, I divided the x-coordinate and the y-coordinate by 2 and I got the point. I did the same thing for the rest of the points and then connected them into a triangle.

Answer:

Step-by-step explanation:

you would use the distributive property, so the answer should be..... -377/1015, OR -13/35 BTW i'm not completely sure this is correct. Im not a calculator. But I think Im correct

I'll do the first one to get you started

So we have g(f(x)) which means that we start with g(x) and replace the 'x' with 'f(x)' to get g(f(x))

g(x) = ( x - 4 )/2

g(f(x)) = ( f(x) - 4)/2 .... replace every x with f(x)

g(f(x)) = (2x+4-4)/2 .... replace f(x) on the right side with 2x+4

g(f(x)) = (2x+0)/2

g(f(x)) = (2x)/2

g(f(x)) = 1x/1

g(f(x)) = 1x

g(f(x)) = x

Let me know if you need help with the other one.

Answer:

1/10

Step-by-step explanation:

Assuming there are 3 red marbles:

3/10 × 3/9 = 9/90 = 1/10

There are 3 red, that is where the first numerator comes from and there are 10 marbles so that is where the denominator comes from. There are 3 yellows, hence the second numerator but as we have taken a marble out there are now only 9 marbles in total.

Answer:

The y coordinate is -3

Step-by-step explanation:

To find the midpoint, we use

midpoint = (x1+x2)/2, (y1+y2)/2

You only ask for the y coordinate.

y midpoint = (y1+y2)/2

y midpoint = (8+-14)/2

                 = -6/2

                   = -3

Answer:

-3

Step-by-step explanation:

usatestprep answer

Answer:

The answer is a. 3x - y = -11

Step-by-step explanation:

Firstly, you must find the gradient. This is found using the following formula:

[tex]\frac{y2 - y1}{x2 - x1}[/tex]

Make sure that the x2 and y2 values are in the same coordinate set:

Let's set (-3 , 2) as y1 and x1,

y1 = 2 and x1 = -3

That means that (-5 , 8) is y2 and x2,

y2 = 8 and x2 = -5

Plug the values in:

[tex]\frac{8 - 2}{-5 - - 3}[/tex]

Simplified:

[tex]\frac{6}{2}[/tex]

Or 3

So the gradient (or slope) is 3

Now, using the following equation of a line formula:

y - y1 = m(x - x1)

Where m is the gradient and y1 and x1 are two coordinates, we can plug these values in:

y1 = 2

x1 = -3

m = 3

y - 2 = 3(x - - 3)

The negative and the subtract makes it a positive:

y - 2 = 3(x + 3)

Now we can multiply the bracket out:

3 * x = 3x

3 * 3 = 9

So:

y - 2 = 3x + 9

The equation is usually in the form:

y = mx + c

So we need to move the -2 over to the other side making it a positive 2:

y = 3x + 9 + 2

y = 3x + 11

Which is the equation of the line.

The one option that this rearranges to is a) because if you move the y over to the 3x, and the + 11 over to the other side, making them both negatives, the result is:

3x - y = -11

So your answer is a.

Answer:

1) 16 adults

2) 2 adults at each table

3) 7

Step-by-step explanation:

Answer:

(x - 12)(x^2 - 2) or (x - 12)(x + sqrt(2) ) (x - sqrt(2))

Step-by-step explanation:

Step-by-step explanation:

2x^3 -9x^2 +11x-6 divided by x-3

We use long division

                        2x^2  - 3x  + 2

                  ------------------------------

x - 3             2x^3 - 9x^2 + 11x - 6

                   2x^3 - 6x^2

                --------------------------------------(subtract)

                            -3x^2    + 11x

                            -3x^2    + 9 x

                ----------------------------------------(subtract)

                                          2x    - 6

                                          2x    - 6

                                 -----------------------------(subtract)

                                          0

Quotient : 2x^2 - 3x + 2

Smallest to Largest-

120, 121, 132, 133, 150, 153, 163, 173, 217, 241, 261.

Hope this helps you!

Least                                                             Greatest

120, 121, 132, 133, 150, 163, 173, 217, 217, 241, 261

Hope helps!-Aparri

Answer:

105 parents said their kids were nice. 39 parents said their kids were naughty.  6 parents didn't answer.

Step-by-step explanation:

Answer:

[tex]F(x)=2\left(x+\dfrac{13}{4}\right)^2-\dfrac{9}{8}.[/tex]

Step-by-step explanation:

Consider the function [tex]F(x)=2x^2+13x+20.[/tex]

Rewrite it as follows:

[tex]F(x)=(2x^2+13x)+20=2\left(x^2+\dfrac{13}{2}x\right)+20=2\left(x^2+\dfrac{13}{2}x+\left(\dfrac{13}{4}\right)^2-\left(\dfrac{13}{4}\right)^2\right)+20=2\left(x^2+\dfrac{13}{2}x+\dfrac{169}{16}\right)-2\cdot \dfrac{169}{16}+20.[/tex]

Since

[tex]x^2+\dfrac{13}{2}x+\dfrac{169}{16}=\left(x+\dfrac{13}{4}\right)^2,[/tex]

you get

[tex]F(x)=2\left(x+\dfrac{13}{4}\right)^2+20-\dfrac{169}{8}=2\left(x+\dfrac{13}{4}\right)^2-\dfrac{9}{8}.[/tex]

Answer:

the correct answer is: f(x)=2(x+13/4)²+-9/8. i hope it help

Hey there!

The word "of" means multiply in mathematical terms

"What is [tex]\frac{3}{4}[/tex] of [tex]\frac{4}{9}[/tex] kilogram? "

So, now that we know what of means we could now solve this equation '

Good luck on your assignment and enjoy your day!

~[tex]LoveYourselfFirst:)[/tex]

Answer: c[p(g)] = 0.896g

Step-by-step explanation:

Answer:

m=0

Step-by-step explanation:

Zero power rule: a^0 = 1,   Anything raised to the zero power is 1  (a≠ 0).

So if m=0, as long as x does not equal zero   (x^8/yz^5)^m will equal one.

Answer:

12

Step-by-step explanation:

A parallelogram has 4 sides. Opposite sides of a parallelogram are parallel and congruent.

Since one side has length p, its opposite side also has length p.

Since one side has length 17 ft, its opposite side also has length 17 ft.

The lengths of the 4 sides are p, p, 17 ft, and 17 ft.

The perimeter is the sum of the lengths of the sides, and it is 58 ft.

p + p + 17 + 17 = 58

2p + 34 = 58

2p = 24

p = 12

M' A'T" H' is (1,1) and (2.5) equals 3.6 to form a quadrilateral. A two-dimensional shape with four sides, four vertices, and four angles is referred to as a quadrilateral.

Let the scale factor of quadrilateral is center at 2.5 at (1, 1) then

(1,1) and (2.5) equals 3.6

(1,1) + (2.5) =  3.6

Therefore, the statement exists true about the dilation is

B. [tex]$\overline{A^{\prime} T^{\prime}}$[/tex] will overlap [tex]$\overline{A T}$[/tex]

C.[tex]$\overline{M^{\prime} A^{\prime}}$[/tex] will overlap [tex]$\overline{M A}$[/tex]

D. The slope of [tex]$\overline{H T}$[/tex] is equal to the slope of [tex]$\overline{\bar{H}^{\prime} T^{\prime}}$[/tex]

The complete question is :

Show the graph below

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Final Answer:

The dilated quadrilateral MATH with a scale factor of 2.5 centered at (1, 1) transforms into the quadrilateral M’A’T’H’.

Explanation:

Quadrilateral MATH is dilated by a scale factor of 2.5 centered at (1, 1). The dilation process involves multiplying the coordinates of each vertex (M, A, T, H) by the scale factor. Let's denote the original coordinates as (x, y), and the new coordinates as (x', y').

1. For point M (x_M, y_M):

- x'_M = 2.5 * (x_M - 1) + 1

- y'_M = 2.5 * (y_M - 1) + 1

2. Similarly, for points A, T, and H:

- x'_A = 2.5 * (x_A - 1) + 1

- y'_A = 2.5 * (y_A - 1) + 1

- x'_T = 2.5 * (x_T - 1) + 1

- y'_T = 2.5 * (y_T - 1) + 1

- x'_H = 2.5 * (x_H - 1) + 1

- y'_H = 2.5 * (y_H - 1) + 1

These formulas calculate the new coordinates for each point after the dilation. The resulting coordinates (x', y') form the vertices of the dilated quadrilateral M’A’T’H’. The center of dilation, (1, 1), is crucial in determining how each point is transformed. The scale factor of 2.5 indicates that the new coordinates are 2.5 times the distance from the center for each point. The final quadrilateral M’A’T’H’ is an enlarged version of the original MATH, maintaining the same shape but with all dimensions multiplied by the scale factor.

Answer:

tax = $6.63

Step-by-step explanation:

We can find the tax by multiplying the original amount by the tax rate.

tax rate = 10 % = .1

tax = 66.30 * .10

     = 6.63

To solve this problem, we need to figure out how much tax Peter will be paying, given that the tax rate is 10% and his purchase costs $66.30.

To do this, we must first convert 10% into a decimal.  To do this, we must divide it by 100 (because it is a fraction out of a total of 100 percent), or simply move the decimal point two places to the left.  Therefore, 10% = 0.10.

To find the tax amount, we must multiply the sales tax rate (10% or 0.10) by the purchase cost ($66.30).  This gives us:

$66.30 * 0.10 = $6.63

Therefore, your answer is $6.63.

(A little tip: the method I used above can be used for any tax rates, but a trick for finding 10 percent of something is to move the decimal point of the cost one place to the left).

Hope this helps!

From the plot, we see that [tex]z_1=-4-3i[/tex]. Its conjugate would be [tex]\bar{z_1}=-4+3i[/tex], so that the product of the two is

[tex]z_1\bar{z_1}=(-4-3i)(-4+3i)=16-9i^2=16+9=25[/tex]

More generally, note that if [tex]z=x+yi[/tex], then

[tex]z\bar z=(x+yi)(x-yi)=x^2+y^2=|z|^2[/tex]

Answer:

The product of z1 and its conjugate is 25.

Step-by-step explanation:

In the given graph x-axis represents the real axis and y-axis represents the imaginary axis.

The end point of z1 are (0,0) and (-4,-3). So, the complex number z1 is defined as

[tex]z_1=x+iy=-4-3i[/tex]

The conjugate of z1 is

[tex]\overline {z_1}=x-iy=-4+3i[/tex]

The product of z1 and its conjugate is

[tex]z_1\overline {z_1}=(-4-3i)(-4+3i)[/tex]

[tex]z_1\overline {z_1}=-4(-4+3i)-3i(-4+3i)[/tex]

[tex]z_1\overline {z_1}=16-12i+12i-(3i)^2[/tex]

[tex]z_1\overline {z_1}=16-9(i)^2[/tex]

[tex]z_1\overline {z_1}=16-9(-1)[/tex]           [tex][\because i^2=-1][/tex]

[tex]z_1\overline {z_1}=16+9=25[/tex]

Therefore the product of z1 and its conjugate is 25.

First, we solved the system of equations by substitution and found x = -3, y = -6. Then, by employing the elimination method, we determined the solution to the second system as x = 7, y = 6.

To solve the system of equations by substitution and elimination, let's start with the substitution method.

Solve the system by substitution:

Given equations: 6 = −4x + y and −5x − y = 21.

Step 1: From the first equation, isolate y: y = 4x + 6.

Step 2: Substitute y in the second equation: -5x - (4x + 6) = 21.

Step 3: Solve for x: -9x = 27, so x = -3.

Step 4: Substitute x back into the equation for y: y = 4(-3) + 6 = -6.

Solution: x = -3, y = -6.

Solve the system by the elimination method:

Given equations: 2x + y = 20 and 6x − 5y = 12.

Step 1: Multiply the first equation by 5, and the second by 1, to align coefficients of y.

Step 2: Add the modified equations to eliminate y: 10x + 5y + 6x - 5y = 100 + 12.

Step 3: Combine like terms and solve for x: 16x = 112, so x = 7.

Step 4: Substitute x back into one of the original equations to solve for y: 2(7) + y = 20, so y = 6.

Solution: x = 7, y = 6.