100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

Answer:

[tex](y - 4)^2 = -8(x - 2).[/tex]

Step-by-step explanation:

The equation of a parabola with a vertical axis of symmetry, vertex (h, k), and focus (h+a, k) is given by:

[tex](y - k)^2 = 4a(x - h)[/tex]

In this case, the vertex is (2, 4) and the focus is (0, 4).

Comparing this to the general equation, we have h=2, k=4, and h+a=0.

From h+a=0, we can solve for a:

a=-h = -2

Substituting the values of h, k, and p into the equation, we get:

[tex](y - 4)^2 = 4(-2)(x - 2)[/tex]

Simplifying further:

[tex](y - 4)^2 = -8(x - 2)[/tex]

Therefore, the parabola equation is[tex](y - 4)^2 = -8(x - 2).[/tex]

[tex]\tan(y )=\cfrac{\stackrel{opposite}{6}}{\underset{adjacent}{4}} \implies \tan( y )= \cfrac{3}{2} \implies \tan^{-1}(~~\tan( y )~~) =\tan^{-1}\left( \cfrac{3}{2} \right) \\\\\\ y =\tan^{-1}\left( \cfrac{3}{2} \right)\implies y \approx 56.31^o \\\\[-0.35em] ~\dotfill\\\\ \tan(x )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{6}} \implies \tan( x )= \cfrac{2}{3} \implies \tan^{-1}(~~\tan( x )~~) =\tan^{-1}\left( \cfrac{2}{3} \right) \\\\\\ x =\tan^{-1}\left( \cfrac{2}{3} \right)\implies x \approx 33.69^o[/tex]

Make sure your calculator is in Degree mode.

Answer:

Slope = -7/3

Step-by-step explanation:

-7x = 6 + 3y is in the standard form of a line, whose general equation is

Ax = C + By (it's sometimes written in terms of C and is Ax + By = C, but in this problem, it's written in terms of Ax).

We can find the slope of the line by converting from standard form to slope-intercept form, whose general equation is y = mx + b, where

Step 1:  Subtract 6 from both sides:

(-7x = 6 + 3y) - 6

-7x - 6 = 3y

Step 2:  Divide both sides by 3 to isolate y:

(-7x - 6 = 3y) / 3

-7/3x - 2 = y

Thus, the slope of the line is -7/3

Answer:  Therefore the slope is [tex]-\frac{7}{3}[/tex].

Step-by-step explanation:

We can rewrite the equation -7x=6+3y in slope-intercept form y = mx + b, where the m is the slope of the line, and b is the y-intercept.

-7x = 6 + 3y

-6     -6        

-7x - 6 = 3y

[tex]\frac{-7x}{3}-\frac{6}{3} =\frac{3y}{3}[/tex]

[tex]\frac{-7}{3}x-2 =y[/tex]

Therefore the slope is [tex]-\frac{7}{3}[/tex].

Answer:

[tex]\huge\boxed{\sf h \approx 6.4\ cm}[/tex]

Step-by-step explanation:

Volume = v = 1280 cm³

Radius = r = 8 cm

π = 3.14

Height = h = ?

V = πr²h

Put the given data in the above formula.

Finding height of cylinder.

1280 = (3.14)(8)²(h)

1280 = (3.14)(64)(h)

1280 = 200.96 (h)

1280 / 200.86 = h

[tex]\rule[225]{225}{2}[/tex]

The outcomes that are in the sample space are red, blue, green, red, blue, and blue.

From the question, we have the following parameters that can be used in our computation:

Spinner = 6 sections

This means that

The spinner has 6 sections and as such, the sample size of the spinner is 6

The sample space are the colors in the spinner

So, we have

Space = red, blue, green, red, blue, and blue.

Hence, the outcomes that are in the sample space are red, blue, green, red, blue, and blue.

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The calculated inches from end to end on the bed is 72 inches

From the question, we have the following parameters that can be used in our computation:

Length = 6 feet long

By conversion of units, we have

1 feet = 12 inches

using the above as a guide, we have the following:

Length = 6 * 12 inches long

Evaluate the products

Length = 72 inches long

Hence, the inches from end to end on the bed is 72

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Answer:

15

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

B Mean: 17.5  | W Mean: 20.5 | B Mode: 15 | W Mode: 20.5 | B Mode: 14 & 15 | W Mode: 20 & 21 | B Range: 17 | W Range: 3

Step-by-step explanation:

The surface area of the cylinder is: 156π.

Here, we have,

given that,

the cylinder has:

radius = 6 in

height = 10 in

now, surface area of the cylinder is:

SA = 2πrh + πr²

here, we have,

SA = 2π *6 * 10 + π6²

     = 120π + 36π

     = 156π

Hence, The surface area of the cylinder is: 156π.

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Answer:

please see answers below

Step-by-step explanation:

Volume of sphere = (4/3) X π X r ³

volume of hemisphere = (2/3)X π X r ³

12) volume of hemisphere = (2/3)X π X r ³

= (2/3) X π X (5)³

= (250/3)π

= 261.80 km³ to nearest hundredth

13) 18 foot is the diameter. radius = 1/2 X diameter = 9.

volume of hemisphere = (2/3)X π X r ³

= (2/3) X π X (9) ³

=  1526.81 ft³ to nearest hundredth

Answer:

B. Similar

Step-by-step explanation:

The two spheres are similar, but not congruent. They have the same shape, but different sizes.

The scale factor between the two spheres is 9/6= 3/2, which means that the radius of the larger sphere is 3/2 times the radius of the smaller sphere.

Answer:

A. 11.2

Step-by-step explanation:

But this has nothing to do with 5.6 × 2. Erase that! Lol.

You have a right triangle here. The only thing to do with the circle is that there are two radii (plural of radius) shown. So they have to be the same measure.

The unmarked "bottom" of the triangle, the short leg, is a radius, so it too, is 8.4.

The hypotenuse of the right triangle, the side on the right, the longest side is 5.6 + 8.4.

The hypotenuse is 14.

Let's do some Pythagorean Theorem.

Leg^2+ leg^2=hypotenuse^2

you know,

a^2 + b^2 = c^2

fill in what we know.

8.4^2 + b^2 = 14^2

simplify.

70.56 + b^2 = 196

subtract 70.56

b^2 = 125.44

squareroot both sides

b = 11.2

Answer:

[tex]\textsf{B)} \quad f(x) = 5 \sin (16x) + 7}[/tex]

Step-by-step explanation:

The sine function is periodic, meaning it repeats forever.

[tex]\boxed{f(x) = A \sin (B(x + C)) + D}[/tex]

where:

Given values:

Calculate the value of B:

[tex]\dfrac{2\pi}{B}=\dfrac{\pi}{8}\implies 16\pi=B\pi\implies B=16[/tex]

Substitute the values of A, B C and D into the standard formula:

[tex]f(x) = 5 \sin (16(x + 0)) + 7[/tex]

[tex]f(x) = 5 \sin (16x) + 7[/tex]

Therefore, the sine function with an amplitude of 5, a period of π/8, and a midline at y = 7 is:

[tex]\Large\boxed{\boxed{f(x) = 5 \sin (16x) + 7}}[/tex]

The Volume of Trapezoidal prism is 420 cm².

From the given figure we can write the dimension of the prism as

a = 5, b=15, c= 15, d= 15

h= 7 and l = 6 cm

Now, Volume of Trapezoidal prism

= 1/2 (a+b) x h x l

= 1/2 (5+15) x 7 x 6

= 1/2 x 20 x 42

= 10 x 42

= 420 cm²

Thus, the Volume of Trapezoidal prism is 420 cm².

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Answer:

Step-by-step explanation:

To calculate Su-Lo's score on the test, we can multiply her percentage by the total marks for the test.

Su-Lo scored 45% out of 80, so her score can be calculated as follows:

Score = Percentage × Total marks

Score = 45% × 80

To find the score, we need to convert the percentage to a decimal by dividing it by 100:

Score = (45/100) × 80

Score = 0.45 × 80

Score = 36

Therefore, Su-Lo scored 36 marks on the test.

Answer:

  38.9 in²

Step-by-step explanation:

You want the area of the composite figure that is an 8-inch square with a semicircle removed.

The missing semicircle has a diameter of 8 in, so a radius of 4 in. The area of that half-circle is ...

  A = 1/2πr² = (π/2)(4 in)² = 8π in² ≈ 25.1 in²

The area of the square without the semicircle removed is ...

  A = s² = (8 in)² = 64 in²

After removing the semicircle from the square, the remaining area is ...

  A = square area - semicircle area

  A = 64 in² -25.1 in² = 38.9 in²

The area of the figure is about 38.9 square inches.

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The percentage of scores that fall between 65 and 75 is approximately [tex]2 \times 34 = 68%.[/tex]%

To determine the percentage of scores that fall between 65 and 75, we can use the properties of the normal distribution.

Mean score = 75

Standard deviation = 5

We know that the normal distribution is symmetric around the mean, and approximately 68% of the data falls within one standard deviation from the mean.

This means that about 34% of the scores fall between the mean and one standard deviation above the mean.

To calculate the percentage of scores between 65 and 75, we need to determine how many standard deviations away from the mean 65 and 75 are.

For 65:

(65 - 75) / 5 = -2

For 75:

(75 - 75) / 5 = 0

From the calculations, we can see that 65 is 2 standard deviations below the mean, and 75 is at the mean.

Since the distribution is symmetric, we can consider the percentage of scores between the mean and one standard deviation above the mean (34%) and double it to account for the scores between the mean and one standard deviation below the mean.

Therefore, the percentage of scores that fall between 65 and 75 is approximately 2 [tex]\times[/tex] 34% = 68%.

However, none of the given answer options match the calculated result. Therefore, none of the provided answer options accurately represent the percentage of scores between 65 and 75 based on the given information.

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If h(x) = f(–x), this is saying that your graph will be reflected over the y-axis.  In other words, the x-values of every point on the graph of y=f(x) will be switched to the opposite sign.  The graph will be flipped over sideways.

For example, if (1,-4) is a point on y=f(x), then y=h(x) will have (–1,-4) on it.

If h(x) = –f(x), this is saying that your graph will be reflected over the x-axis.  In other words, the y-values of every point on the graph of y=f(x) will be switched to the opposite sign.  The graph will be flipped upside-down.

For example, if (1,–4) is a point on y=f(x), then y=h(x) will have (1,4) on it.

While you are given the equation for f(x) in each exercise, the function f(x) does not impact the transformation at all.  What is said above is true for all functions.  

If you want to graph them, then for 4:

    f(x) = -3 - x

   h(x) = f(-x) = -3 + x

For #5:

    f(x) = 1/3 x + 1

    h(x) = -f(x) = -1/3 x - 1

The width of the rectangle is 5k² and the length of the rectangle is 3k² + 7k + 4.

The greatest common monomial factor of 15k⁴, 35k³, and 20k² is 5k². So the width of the rectangle is 5k².

The area of the rectangle is the product of its length and width. So the length of the rectangle is the area divided by the width. The area is 15k⁴ + 35k³ + 20k² and the width is 5k². So the length is:

= (15k⁴ + 35k³ + 20k²) / (5k²)

= 3k² + 7k + 4.

Therefore, the width of the rectangle is 5k² and the length of the rectangle is 3k² + 7k + 4.

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Answer:

Answers following the rounding instructions:  see below for details

BC = 5.1

m∠B = 23°

m∠V = 116°

Step-by-step explanation:

Givens:

AC = 3

AB = 7

m∠A = 41°

Unknowns:

BC = ?

m∠B = ?

m∠C = ?

Find side BC using the law of cosines:  c² = a² + b² - 2ab cos(C)

a² = 3² + 7² - 2(3)(7)(cos41)

a = √9 + 49 - 42(cos41)

a = 5.128 ≈ 5.13

side BC = 5.13

Use the law of sines to find m∠B:  sin(A) / a = sin(B) / b = sin(C) / c

m∠B = sin⁻¹[sin41/5.13 x 3] = sin⁻¹(0.3837) = 22.56 ≈ 22.6°

Sum of interior angles of a triangle is 180, so now you can find m∠C:

m∠C = 180 - 22.6 - 41 = 116.44 ≈ 116.4°

Rounding side BC to nearest tenth: BC = 5.1

Rounding angles to nearest whole degree:

m∠B = 23°

m∠V = 116°

The factored expression of n² - 11n + 10 is (n - 10)(n - 1)

From the question, we have the following parameters that can be used in our computation:

n² - 11n + 10

To determine the pair of factors to factor the expression, we find two expressions

using the above as a guide, we have the following:

The expressions are -10n and -n

So, we have

n² - 11n + 10 = n² - 10n - n + 10

When factored, we have

n² - 11n + 10 = (n - 10)(n - 1)

Hence, the factored expression of n² - 11n + 10 is (n - 10)(n - 1)

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Answer:  A.   x=3     y= -1         z=4

Step-by-step explanation:

I plugged it into my graphing calculator.

>2nd Matrix

>Edit >A

>choose 3x3

>Enter all coefficients as they look

>2nd Matrix

>Edit >B

>Choose 3x1

>Enter answers as they look

Go to main page

[tex][A]^{-1} [B]\\[/tex]

Answers end up being 3, -1,  4

The degrees of freedom is 21, the critical values correspond to the points where the chi-square distribution curve separates the rejection and non-rejection areas and chi-square test statistic is 27.

The null and alternative hypotheses can be stated as follows:

Null Hypothesis (H0): The population variance is equal to 14.

Alternative Hypothesis (Ha): The population variance differs from 14.

To find the critical values of χ2 with α = 0.05, we need to determine the degrees of freedom first.

For a sample variance, the degrees of freedom (df) is given by (n - 1), where n is the sample size.

In this case, n = 22, so the degrees of freedom is 21.

Using a chi-square table or statistical software, we can find the critical values for a chi-square distribution with 21 degrees of freedom and α = 0.05.

The critical values correspond to the points where the chi-square distribution curve separates the rejection and non-rejection areas.

To determine the test statistic χ2 value, we need to calculate the chi-square test statistic using the given information.

The chi-square test statistic is calculated as:

χ2 = (n - 1) ×(sample variance) / (population variance)

Plugging in the values, we have:

χ2 = (22 - 1) × 18 / 14

=27

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Answer:

To solve the inequality −4p − (5p − 4) ≤ 7p + 10 + 3p, we can simplify and isolate the variable p. Let's work through the steps:

Step 1: Distribute the negative sign (-) inside the parentheses:

-4p - 5p + 4 ≤ 7p + 10 + 3p

Simplifying further:

-9p + 4 ≤ 10p + 10

Step 2: Group like terms by adding 9p to both sides of the inequality:

-9p + 9p + 4 ≤ 10p + 9p + 10

Simplifying further:

4 ≤ 19p + 10

Step 3: Subtract 10 from both sides of the inequality:

4 - 10 ≤ 19p + 10 - 10

Simplifying further:

-6 ≤ 19p

Step 4: Divide both sides of the inequality by 19:

-6/19 ≤ 19p/19

Simplifying further:

-6/19 ≤ p

So the solution to the inequality is p ≥ -6/19.

Answer: 18

Step-by-step explanation:

Multiply number of each item possible

3*2*3=18

To determine how the surface area of a rectangular prism changes when all dimensions are quadrupled, we need to compare the original surface area to the new surface area.

The original surface area of the rectangular prism is given by:

SA_original = 2lw + 2lh + 2wh

where l, w, and h represent the length, width, and height of the prism, respectively.

In this case, the dimensions of the original box are:

Length (l) = 3 ft

Width (w) = 6 ft

Height (h) = 5 ft

Substituting these values into the formula, we have:

SA_original = 2(3)(6) + 2(3)(5) + 2(6)(5)

            = 36 + 30 + 60

            = 126 square feet

Now, if we quadruple all the dimensions of the box, the new dimensions would be:

Length (l_new) = 4(3) = 12 ft

Width (w_new) = 4(6) = 24 ft

Height (h_new) = 4(5) = 20 ft

The new surface area of the enlarged box is given by:

SA_new = 2(l_new)(w_new) + 2(l_new)(h_new) + 2(w_new)(h_new)

       = 2(12)(24) + 2(12)(20) + 2(24)(20)

       = 576 + 480 + 960

       = 2016 square feet

Comparing the original surface area (SA_original = 126 sq ft) to the new surface area (SA_new = 2016 sq ft), we can see that SA_new is 16 times greater than SA_original.

Therefore, the correct answer is:

1. The new surface area would be 16 times the original surface area.

The expression for the total number of packets of crisps that Jane buys is given as follows:

p + c.

The amounts of packets of crisps purchased are given as follows:

The expression for the total number of packets of crisps that Jane buys is given by the addition of these two amounts.

Hence the expression for the total number of packets of crisps that Jane buys is given as follows:

p + c.

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To calculate the amount of money needed to deposit into the account today, we can use the concept of present value. The present value represents the current value of future cash flows, taking into account the time value of money.

1. To calculate the present value of the cash flows, we can use the formula for the present value of an annuity:

PV = C * (1 - (1 + r)^(-n)) / r

Where PV is the present value, C is the cash flow per period, r is the interest rate per period, and n is the number of periods.

In this case, the cash flow per period is $100, the interest rate per period is 6% (0.06), and the number of periods is 20.

Plugging in the values into the formula:

PV = 100 * (1 - (1 + 0.06)^(-20)) / 0.06

Calculating this value gives us the amount of money needed to deposit into the account today.

2. To show explicitly using an Excel spreadsheet, you can set up a column for each year, starting from year 0 (the present year) to year 20. In the first row, enter the initial deposit amount calculated in step 1. In the subsequent rows, use a formula to calculate the value for each year by adding the interest earned and subtracting the annual withdrawal of $100. The last value in year 20 should be zero, indicating that the account will have no remaining balance after the last withdrawal.

3. If the bank's annual interest rate changes to 10%, you would need to recalculate the present value using the new interest rate. Repeat step 1 with the new interest rate of 10% (0.10) to find the updated amount of money needed to deposit into the account today. Compare this value with the previous amount calculated with a 6% interest rate to determine the difference.