The width of Zorn’s patio is labeled in the diagram below. If the perimeter of the patio is (30x + 26) feet, what is the length of the patio?

Answer:

11. Equation of hyperbola having  vertices at (0, ±6) and foci at (0, ±9).

is given by [tex]\frac{y^2}{a^2}- \frac{x^2}{b^2}=1[/tex]

also b²= c²-a²

 b²=81-36

b²=45

So, Equation becomes , [tex]\frac{y^2}{36}- \frac{x^2}{45}=1[/tex]

Option (D) is correct.

12.Vertices (0,  ± 4), Asymptotes = ±1/4.x

equation of asymptote is given by, [tex]x = \pm y \frac{b}{a}[/tex]

[tex]\frac{4}{b}=\frac{1}{4}[/tex]

So a=4 and b=16,

So , equation becomes [tex]\frac{y^2}{16}- \frac{x^2}{256}=1[/tex]

Option (B) is correct.

13.  x= t-3, and y = t²+ 5

Replace t by x+3, we get

y= (x+3)² +5

y=x²+ 6x +14

Option (A) is correct.

14. Polar coordinates is given by (r,∅)

Polar coordinates of point is (3, 2π/3)

So, r =3, ∅ =2π/3

x= r cos∅ and y = r sin∅

x=3 Cos (2π/3) and y= 3 Sin (2π/3)

x= -3/2 and y=3√3/2

Option (A) is correct.

14. Polar coordinate is given by (r,∅)

Here , r=1, and ∅ = -π/6

x= r Cos ∅ and y =r Sin∅

x= 1 Cos (-π/6) and  y= 1 Sin (-π/6)

x =√3/2 and y =1/2

Option (B) which is B) (1, negative pi divided by 6 + 2nπ) or (-1, negative pi divided by 6 + 2nπ) is correct.

16. Two pairs of polar coordinates for the point (4, 4) with 0° ≤ θ < 360°.

is  option (B) which is B) (4 square root 2 , 45°), (-4 square root 2 , 225°).

17. A circular graph with inner loop on the left of a limacon curve is given by

r = a + b Cos∅.

In this case a> b.

So , Option (D) r = 4 + cos θ as well as (A) r = 3 + 2 cos θ looks correct.

18. Equation of limacon curve is given by r = -2 + 3 cos θ, here , a<b

So it is symmetric about y-axis only.Option (B) is correct.

Answer:

ROI = 150

Step-by-step explanation:

ROI = (25,000-10,000)/10,000 ×100=150

If  cost of annual tution at a university increased from $10,500 to $11,300.Then 7.61%  increase in tution to the nearest tenth of a percent

Percentage, a relative value indicating hundredth parts of any quantity.

Given,

The cost of annual tution at a university increased from $10,500 to $11,300.

We need to find what percentage increase in tution.

Firstly we have to check how much increased.

11300-10500

800

Hence 800 is increase.

We have to check what is 800 percentage in 10500

percent increase=change/original

origianal=10500

change=800

800/10500=8/105=0.0761

By the definition of percentage we know percent means parts out of 100

0.0761×100=7.61%

Hence 7.61% is the  increase in tution to the nearest tenth of a percent.

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The dimension of the rectangle will be 6 inches by 3 inches.

Assume L is the length and W is the width. Then the area is given as,

A = L × W

And the perimeter is given as,

P = 2(L + W)

A rectangular note card has an area of 18 square inches. Its perimeter is 18 inches. Then the equations are given as,

18 = 2(L + W)

9 = L + W             ...1

L x W = 18           ...2

From equations 1 and 2, then we have

L x (9 - L) = 18

L² - 9L + 18 = 0

L² - 6L - 3L + 18 = 0

L(L - 6) - 3(L - 6) = 0

(L - 6)(L - 3) = 0

L = 3, 6

Then the width of the rectangle will be calculated as,

W = 9 - 3 = 6

W = 9 - 6 = 3

Then the dimension of the rectangle will be 6 inches by 3 inches.

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To determine the total cost including sales tax, first calculate the subtotal of the items, then apply the 7% tax rate to this subtotal. After adding the sales tax to the subtotal, the final cost comes to $90.23.

To calculate the total cost of your purchase including sales tax, first figure out the total cost of the items before tax. You bought one skirt at $18.27, two shirts at $15.78 each, and a pair of shoes at $34.50. The cost of the shirts needs to be doubled since you bought two. Then, apply the 7% sales tax to the subtotal to find the overall total.

Subtotal before tax: $18.27 + $31.56 + $34.50 = $84.33

To calculate the sales tax, convert the tax rate to a decimal (7% = 0.07) and multiply by the subtotal: $84.33 × 0.07 = $5.90 (rounded to the nearest cent).

Add the sales tax to the subtotal for the total cost: $84.33 + $5.90 = $90.23.

Therefore, the total cost of your purchase after including the 7% sales tax is $90.23.

To find the length marked x, establish the ratio 0.5 inch/20 miles = 8 inches/x miles, cross-multiply, and solve for x to get x = 320 miles, making sure to round only after the final calculation step.

To solve for the length labeled x, you would first need to set up the correct ratio. Given that the scale length is 8 inches and the corresponding actual length is unknown, the initial ratio would be 0.5 inch/20 miles = 8 inches/x miles. You can solve this proportion by cross-multiplication.

Following these steps:

Therefore, the unknown length x is 320 miles. Remember to always perform rounding off at the final step of your calculation to ensure accuracy.

The length of side [tex]\( x \)[/tex] is approximately 13.9 units when rounded to the nearest tenth.

To find the length of side [tex]\( x \)[/tex], we utilize the tangent function because it relates the opposite side to the adjacent side in a right-angled triangle. The tangent of [tex]\( 41^\circ \)[/tex] equals the ratio of side [tex]\( x \)[/tex] (the side opposite to [tex]\( 41^\circ \))[/tex] to 16 (the side adjacent to [tex]\( 41^\circ \))[/tex]:

[tex]\[ \tan(41^\circ) = \frac{x}{16} \][/tex]

To solve for [tex]\( x \)[/tex], we multiply both sides by 16:

[tex]\[ x = 16 \times \tan(41^\circ) \][/tex]

[tex]x=13.9[/tex]

The length of side [tex]\( x \)[/tex] is approximately 13.9 units when rounded to the nearest tenth.

Answer:

hello the answer is choice D

Step-by-step explanation:

The recursive formula for a geometric sequence is a₁=-4 and [tex]a_n}=6.a_{n-1}[/tex]. Therefore, option D is the correct answer.

A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.

The given geometric sequence is -4, -24, -144, -864.

A recursive formula for a geometric sequence with common ratio r is given by [tex]a_n}=ra_{n-1}[/tex] for n≥2.

Here, a=-4 and r=-24/(-4) =6

So, recursive formula is [tex]a_n}=6.a_{n-1}[/tex]

Therefore, option D is the correct answer.

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Answer:

Multiply 4x+3y=−1 by 3. Multiply 3x−5y=4 by −4 . Add the resulting equations together.

Step-by-step explanation:

Given the simultaneous equation below:

4x+3y=−1 ...(1) × 3

3x−5y=4 ...(2) × -4

Using elimination method to solve the problem,

Before we can eliminate x, the coefficient of x in both equation must have similar whole number as coefficient.

To make the coefficient equal, we will multiply equation 1 by 3 and equation 2 by -4 as shown above

The equations will then become

12x+9y = -3

-12x+20y = -16

Then we will add the resulting simultaneous equations.

The steps that would allow her to eliminate the x terms in the system of equations is to "Multiply 4x+3y=−1 by 3. Multiply 3x−5y=4 by −4 . Add the resulting equations together"

Final answer:

The value of n, or the number of trials in a binomial experiment, affects the shape of the binomial probability histogram. As n increases, the histogram becomes more symmetric and bell-shaped, reflecting the Central Limit Theorem. The correct answer is (c): as n increases, the binomial distribution becomes more bell-shaped.

Explanation:

The shape of the binomial probability histogram is indeed influenced by the value of n, which stands for the number of trials in a binomial experiment. As the value of n increases, the distribution becomes more symmetrical and tends to resemble a normal distribution. Specifically, the correct statement regarding the effect of n on the shape of the histogram is: as n increases, the binomial distribution becomes more bell-shaped. Therefore, the correct answer to the student's question is (c).

When the sample size n is small, the histogram may appear skewed left or right, depending on the probability of success p. However, as n becomes larger (especially when both np and n(1-p) are greater than 5), the distribution's shape becomes more symmetric due to the Central Limit Theorem, which states that the distribution of sample means approaches a normal distribution as the sample size increases.

Answer:

1 1/2 hours

Step-by-step explanation:

Time spent by Antonio in driving = 3 1/4 = 13/4

Time spent in gardening = 1 3/4 = 7/4

In order to find how much he spend driving than gardening, we can subtract 13/4 and 7/4.

[tex]\frac{13}{4}-\frac{7}{4}[/tex]

Te denominator is same. So, we can directly subtract the numerators.

[tex]\frac{13-7}{4}\\\\=\frac{6}{4}\\\\=\frac{3}{2}=1\frac{1}{2}[/tex]

Therefore, Antonio spent 1 1/2 hours more in driving than gardening.

To solve this problem, you have to determine the value of the number 3 in both numbers:

6,300 – the number 3 is in the hundreds place so its value is 300

530 – the number 3 is in the tens place so its value is 30

To answer the question, the value of 3 in 6,300 is 10 times the value of 3 in 530.

The area of the base of the pyramid which is a hexagon with given parameters is; 96√3

We are told that the base of the pyramid is a hexagon.

Now, from the given image we can find the base length of the right angle triangle from trigonometric ratio which is;

x/8 = cos 60°

x = 8 cos 60°

x = 4

Thus, length of side of hexagon is;

s = 4 * 2

s = 8

Formula for area of hexagon is given by;

A = ((3√3) * s²)/2

Where;

s is length of a side of hexagon

A = ((3√3) * 8²)/2

A = 96√3

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Answer:

15cm

Step-by-step explanation:

i had the same question but difrent if you know what i mean. in mine you solved it for me in your picture of 6.

In this set, the points reflect across the indicated lines of symmetry. Matches are as follows: 3 corresponds to X, 5 to F, 6 to B, 4 to Y, 1 to Q, and 2 to S.

R_I

This means that the line of symmetry is line I

R_m

This means that the line of symmetry is line m.

1. R_I:T

This matches with Q.

In this number, the line of symmetry is I. If you reflect T across line I, you will get point Q. This is because they are right across from each other with line I between them, and they are both the same distance from line I.

2. R_I:S

This matches with S.

Point S lies on the line of symmetry; thus, S reflects itself.

3. R_I:Z

This is similar to number 1. If you reflect Z across line I, you will get point X because they are directly across each other with line I between them and they have the same distance from the line of symmetry.

4. R_m:S

This time, S isn't on the line of symmetry. The line of symmetry is the vertical line m. Point Y matches with point S because they are directly across each other with line m between them. They are also the same distance apart from line m.

5. R_I:B

This is very similar to number 1. This matches with F. The point directly across the line of symmetry is F.

6. R_I:F

This is the exact same as number 5! With the same line of symmetry, B matched with F. Thus, F must match with B!

Here are the matches:

3-X

5-F

6-B

4-Y

1-Q

2-S