Svetlana’s hair is 3 cm long. Her hair grows 1.5 cm per month. Svetlana wanted her hair to be less then 18 cm long. Write an inequality to determine the number of months Svetlana can allow her hair to grow. Then, solve the inequality.

from the provided focus point and directrix, we can see that the focus point is above the directrix, meaning is a vertical parabola and is opening upwards, thus the squared variable will be the "x".

keeping in mind the vertex is half-way between these two fellows, Check the picture below.

[tex]\bf \textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \begin{cases} h = 7\\ k = 7\\ p = 2 \end{cases}\implies 4(2)(y-7)=(x-7)^2\implies 8(y-7)=(x-7)^2 \\\\\\ y-7=\cfrac{1}{8}(x-7)^2\implies \boxed{y=\cfrac{1}{8}(x-7)^2+7}[/tex]

Final answer:

The equation of the parabola with a focus of (7,9) and a directrix of y = 5 can be written as (x-7)^2 = 16(y-5).

Explanation:

The equation of a parabola in standard form is given by:

(x-h)^2=4p(y-k)

Where (h,k) is the vertex of the parabola and p is the distance from the vertex to the focus and to the directrix. In this case, the focus is (7,9) and the directrix is y = 5. To find the equation of the parabola, we need to determine the value of p.

From the given information, we can see that the focus is a point on the parabola and the directrix is a line that is perpendicular to the axis of symmetry and does not pass through the vertex. Therefore, the distance from the vertex to the focus is equal to the distance from the vertex to the directrix. In other words, the value of p is the distance from the vertex to the line y = 5.

Since the directrix is a horizontal line, the vertex of the parabola is on the line y = 5. Therefore, k = 5. The distance from the vertex to the line y = 5 is equal to the distance from the vertex to the focus, which is p. Therefore, we have:

p = 9 - 5 = 4

So the equation of the parabola is:

(x-7)^2 = 4 * 4(y-5)

Simplifying, we get:

(x-7)^2 = 16(y-5)

Therefore, the equation of the parabola is (x-7)^2 = 16(y-5).

Answer:

Option (c) $30.00

Explanation:

Let the original price be $x

Given the rate of discount is 40%

Selling (or sale) price of the book is = $18

The original price is calculated by the formula,

Selling Price = Original Price(1 – r%)

Substituting the values in the above equation,

[tex]18 = x (1-\frac{40}{100})[/tex]

[tex]18 = x (\frac{60}{100})[/tex]

[tex]x=\frac{1800}{60}[/tex]

Therefore, x = 30

Hence, option (c)is correct

The original price of the book was $30.00, which, after a 40% discount, results in the $18.00 sale price. To find the original price, divide the sale price by 0.60 (which represents the remaining 60% after the discount). So the correct option is C.

To find the original price of the book before the sale, you need to consider that the sale price represents 60% of the original price, because the book was discounted by 40%. The calculation that needs to be done is to divide the sale price by 0.60.

Here are the steps:

Therefore, the original price of the book was $30.00.

Answer:

x3−4 by x + 2? equals to  (x-3)/(4)=(x)/(2)

Step-by-step explanation:

Here, we are required to determine the result of dividing x³ - 4 by x + 2.

The result is Choice C;. x²−2x+4−12/(x+2)

The steps required for the division of

x³ - 4 by x + 2

can be made easier by assuming x³ - 4 to take the form;

x³ + 0x² + 0x - 4.

The step by step process for the division is attached to the image.

Ultimately, the division results into;

x²−2x+4−12/(x+2).

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Answer:

2 cups of flour.

Step-by-step explanation:

9 servings require  3 cups of flour, so:

1 serving requires 3/ 9 = 1/3 of a cup of flour.

6 servings require 1/3 * 6 = 2 cups of flour.

Answer:

8,000. Hope this helps!

Answer: 8000

Step-by-step explanation: Find the number in the thousand place, 8, and look one place to the right for the rounding digit, 1. Round up if this number is great than or eual to 5 and round down if it is less than 5.

(5 or more, let it sore. 5 or less, let it rest.)

Hope this helps you out! ☺

In a triangle, the point where the medians intersect, known as the centroid, divides each median into two segments in a 2:1 ratio. In this context, only the measurement of segments 3 and 6 fit this property.

The median of a triangle is a segment joining a vertex to the midpoint of the opposite side. In this question, we are considering segments of a median, so we're considering the vertex of the triangle to the centroid (where medians intersect) and from the centroid to the midpoint of the opposite side.

The key property of medians in a triangle is that the centroid, or point of intersection, divides each median into two segments in the ratio 2:1. This means the distance from a vertex to the centroid is twice the distance from the centroid to the midpoint of the opposite side.

From the provided segments, only 3 and 6 fit this principle. This means the distance from the vertex to the centroid is 3 (representing two-thirds of the median) and the distance from the centroid to the midpoint of the opposite side is 6 (representing one-third of the median).

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Answer:

Average miles travelled per day =412.

Step-by-step explanation:

Answer:

95

Step-by-step explanation:

We need to add up by 3 from 50 until we get the 15th number so we do this:

1. 53

2. 56

3. 59

4. 62

5. 65

6. 68

7. 71

8. 74

9. 77

10. 80

11. 83

12. 86

13. 89

14. 92

15. 95

The 15th term is 92.

A sequence of numbers where each number is linked with its consecutive term by a fixed number is called Arithmetic Sequence.

It is given that

The test score results are

50 , 53 , 56 , 59 , 32 ..................

The common difference is 3

Then the nth term is given by

Tn = a₁ + (n-1)d

a₁ is the first term = 50

n = 15

Then the 15th term is

T₁₅ = 50 + (15-1) * 3

T₁₅ = 92

The 15th term is 92.

To know more about Arithmetic Sequence

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Answer:

Bro XD lol just simplify it.

the answer is 3

Answer:

3

Step-by-step explanation:

Answer:

x=28

Step-by-step explanation:

-7(3+6x)=9(-5x+7)

-21-42x=-45x+63

-21-42x-(-45x)=63

-21-42x+45x=63

-21+3x=63

3x=63-(-21)

3x=63+21

3x=84

x=84/3

x=28

Answer:

About 58 students are absent today.

Step-by-step explanation:

11%=0.11

0.11*527=57.97

Answer:

[tex]\displaystyle [0, -3][/tex]

Step-by-step explanation:

The y-intercept is when zero is set to x, so you will end up with this:

[tex]\displaystyle -\frac{21}{7} = -\frac{7y}{7} \\ \\ -3 = y[/tex]

I am joyous to assist you anytime.

Answer:

92%

Step-by-step explanation:

This is because all you have to do to turn a decimal into percentage is to move the decimal over 2 spots, and drop the Zero.

Answer:

15 : 11 : 16

Step-by-step explanation:

If A, B, and C are in the ratio x : y : z, then we can say that there is x quantity of A, y quantity of B and z quantity of C.

Therefore, the 15 quantity of white paint. 11 quantity of black paint and 16 quantity of blue paint are in the ratio of 15 : 11 : 16.

Since there is no common factor between 15, 11 and 16 then the ratio is in the simplest form and the ratio is 15 : 11 : 16. (Answer)

Answer:

the y-coordinate of a point where a line, curve, or surface intersects the y-axis.

Step-by-step explanation:

This is the best and easiest way I could put it in.

Regina can take yoga classes at community center as it would cost her less money.

Step-by-step explanation:

No. of classes per week = 2

Classes in 6 weeks = 2*6 = 12 classes

Cost of classes at community center = $72

Additional one time fee = $12

Total cost at community center = 72+12 = $84

Cost per class at local gym = $8

Cost of 12 classes = 12*8 = $96

Regina can take yoga classes at community center as it would cost her less money.

Keywords: addition, multiplication

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The total number of seeds in the box is found by multiplying the number of packets by the number of seeds per packet, yielding the equation b = ps.

The equation we are looking for will help us find the total number of seeds in a box, which we will call b. Since the box has p packets and each packet contains s seeds, we can find the total number of seeds by multiplying the number of packets by the number of seeds in each packet. Therefore, the correct equation to represent this relationship is b = ps, which means the total number of seeds in the box (b) is the product of the number of packets (p) and the number of seeds per packet (s).

Answer:

[tex]4\dfrac{3}{8}[/tex] cups of flour

Step-by-step explanation:

A muffin recipe, which yields 12 muffins, calls for 2/3 cup of milk for every 1 3/4 cups of flour.

Then this recipe, which yields one muffin, calls for

[tex]\dfrac{2}{3}:12=\dfrac{2}{3}\cdot \dfrac{1}{12}=\dfrac{1}{18}[/tex]

cup of milk for every

[tex]1\dfrac{3}{4}:12=\dfrac{7}{4}\cdot \dfrac{1}{12}=\dfrac{7}{48}[/tex]

cups of flour.

Thus,

this recipe, which yields a batch of 30 muffins, calls for

[tex]\dfrac{1}{18}\cdot 30=\dfrac{5}{3}=1\dfrac{2}{3}[/tex]

cups of milk for every

[tex]\dfrac{7}{48}\cdot 30=\dfrac{210}{48}=\dfrac{35}{8}=4\dfrac{3}{8}[/tex]

cups of flour.

Final answer:

To calculate the amount of flour needed to yield 30 muffins, we first find the amount of flour required for a single muffin and then scale it up to 30 by multiplying. For 30 muffins, approximately 1.094 cups of flour are required based on the original recipe ratios.

Explanation:

The question involves the use of ratios to calculate the amount of a particular ingredient required for a different quantity of the final product. Since the original recipe yields 12 muffins with 1 3/4 cups of flour, we first need to determine how much flour is needed for one muffin by dividing 1 3/4 cups by 12. After finding the flour quantity per muffin, we then multiply that by 30 to find out how much flour is needed for 30 muffins.

Step 1: Calculate the amount of flour for one muffin.
Amount of flour per muffin: 1 3/4 cups / 12 =
7/4 cups / 12 = 7/48 cups per muffin.

Step 2: Calculate the amount of flour needed for 30 muffins.
Amount of flour for 30 muffins: 7/48 cups per muffin x 30 = 7/48 x 30 =
52.5/48 or approximately 1.094 cups of flour.

Answer:

Time taken by the ball to reach its maximum height is 3.4 sec

maximum height reached by the ball is 185.6ft

Step-by-step explanation:

h(t) = -16[tex]t^{2}[/tex] + 109t

height is maximum ⇔ [tex]\frac{d}{dt}[/tex](h) = 0 and [tex]\frac{d^{2} }{dt^{2} }[/tex](h) < 0

[tex]\frac{d}{dt}[/tex](h) = 0 ⇒ -32t + 109 = 0

⇒t = [tex]\frac{109}{32}[/tex] ⇒ t = 3.4sec

[tex]\frac{d^{2} }{dt^{2} }[/tex](h) = -32 < 0

∴h(t) is maximum at t = 3.4

and maximum height is h(3.4) = -16×[tex]3.4^{2}[/tex] + 109×3.4 ⇒ h = 185.6ft

Answer:

The maximum height with rounding by the nearest tenth is [tex]280.56\ m[/tex]

Explanation:

Initial velocity of ball [tex]=109\ ft/sec[/tex]

Quadratic function [tex]$h(t)=-16t x^{2} +109t$[/tex]

Maximum  height[tex]=?[/tex]

Step 1:

This ball has its height related to time by a parabola with the equation:

[tex]$s=\frac{1}{2} \times a \times t^{2}+v_{0} \times t+s_{0}$[/tex]

where [tex]$s$[/tex] is the height so is the starting height, [tex]v_{0}[/tex]  is its starting velocity [tex]$=109 \ {ft} / \mathrm{s}$[/tex]

[tex]$a$[/tex] is the acceleration of gravity, which is [tex]$-16 \ {ft} / \mathrm{s}$[/tex] every second.

Step 2:

Time required to reach its maximum height:

[tex]$v=a^{*} t+v_{0}[/tex]  (its velocity is the acceleration of gravity × time [tex]+ v_0[/tex]) [tex]$v$[/tex] will slow down from [tex]$109 \ {ft} / \ s[/tex] to [tex]$0 \mathrm{ft} / \mathrm{s}$[/tex]  

And it slowing down at [tex]$16 \mathrm{ft} / \mathrm{s}$[/tex] :

[tex]t(s)=0,1,2,3,4,5,6[/tex]

[tex]V (m/s)=109,93,77,61,45,29,13[/tex]

Before [tex]$7 \mathrm{~s}$[/tex], it will hit the ground.

Exact calculation [tex]$t=\frac{109 f t / s}{16 f t / s}=6.81 s$[/tex]

Thus we can say at the height of,

[tex]$\mathrm{t}_{\max }=\frac{6.81}{2} \\=3.4\ sec[/tex]  

Step 3:

Plug the [tex]t_m_a_x[/tex] sec value back into equation:

[tex]$h(t)=t \cdot(-16 t+109)$[/tex]

[tex]$h_{\max }=3.4 \cdot(-16.4 .1875+109)$[/tex]

[tex]$h_{\max }= 185.6\ m[/tex]

Hence, the maximum height is [tex]185\ m[/tex]

To learn more about vertically upward ball, refer:

Answer:

x=43/8

Step-by-step explanation:

2-8x+41=0

-8x+43=0

-8x=0-43

-8x=-43

8x=43

x=43/8

The width of the picture is 14 inches and the height is 10 inches, resulting in dimensions of 14 inches by 10 inches.

This problem can be solved by using the formula for the area of a rectangle, which is area = length x width. We are given that the area is 140 square inches, and that the height of the picture is 5/7 of its width. Therefore, we can create the equation 140 = width x (5/7)width.

By simplifying this equation, we can then solve for the width:

So the width of the picture is 14 inches. To find the height, we multiply the width by 5/7: height = 14 x (5/7) = 10 inches.

Therefore, the dimensions of the picture are 14 inches by 10 inches.

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Answer:

38

Step-by-step explanation:

To evaluate h(8) substitute x = 8 into h(x)

h(8) = 5(8) - 2 = 40 - 2 = 38

Answer:

38

Step-by-step explanation:

:

Mix a pthalo green and alizarin crimson with ultramarine blue

This new mixture will contain 2 cups of yellow and 7 cups of blue, resulting in a bluer shade of green compared to the original mixture.

To create a bluer shade of green, we need to increase the proportion of blue relative to yellow in the mixture. We can achieve this by increasing the amount of blue while keeping the amount of yellow constant.

Given that the original mixture ratio is 2 cups of yellow to 3.5 cups of blue, let's increase the amount of blue relative to yellow. We can try doubling the amount of blue while keeping the amount of yellow constant.

So, to create a bluer shade of green, we can use:

- 2 cups of yellow (constant)

- 2 * 3.5 = 7 cups of blue

This new mixture will contain 2 cups of yellow and 7 cups of blue, resulting in a bluer shade of green compared to the original mixture.

complete question given below:

A type of green paint is made by mixing 2 cups of yellow with 3.5 cups of blue. Find a mixture that will make the different shade of green that is bluer

Answer:

A linear function is one that is changing at a constant rate as well as it changes. As for a exponential function is one that changes at a rate that's always proportional to the value of the function.

Answer:

a linear function is in which the rate of change is constant, and because you are adding the same amount every time in the graph, the change is the same. In an exponential function, it’s where your graph is not constant, the rate of change increases, or decreases because you are adding or subtracting more each time.

Step-by-step explanation:

hope it helps

Answer:

11) a or d 12) b

Step-by-step explanation:

sorry, I don't feel like looking at number 11 properly I'm half asleep

A factor of f(x) is (x + 1) must be true ⇒ 2nd answer

Step-by-step explanation:

In a quadratic equation y = ax² + bx + c, the roots of it are:

∵ -1 is a root of f(x)

∵ The roots of f(x) are the values of x when f(x) = 0

∴ At f(x) = 0, x = -1

When f(x) = 0, then all factors of f(x) must be equate by 0

∵ f(x) = 0

∵ x = -1 ⇒ when f(x) = 0

- Add to sides by 1

∵ x + 1 = 0

∴ (x + 1) is one factor of f(x)

A factor of f(x) is (x + 1) must be true

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Answer:

The nearest hundredth is 5.57. Hope I helped! ☺

Answer:

y-3=-(x+4)

Step-by-step explanation:

Point Slope Form: y-y1=m(x-x1)

Where m=slope and (x1, y1) is a point on the line.

m=(y2-y1)/(x2-x1)

m=(-4-3)/(3-(-4))=-7/(3+4)=-7/7=-1

y-3=-1(x-(-4))

y-3=-(x+4)

Answer:

The length of one side of the square base is 24 feet.

Step-by-step explanation:

Given:

Volume of square pyramid(V) = 3969 cubic feet, and its height(h) = 21 feet.

Now, we need to find the length of one side(a) of the square base.

So. by putting the formula of square pyramid we get our length of one side(a):

[tex]V=a^{2}\frac{h}{3}[/tex]

[tex]3969=a^{2}\times \frac{21}{3}[/tex]

[tex]3969= a^{2}\times 7[/tex]

Dividing both sides by 7 we get:

[tex]567=a^{2}[/tex]

Using square root both sides we get:

[tex]23.81=a[/tex]

a = 24 feet (approximately).

Therefore, the length of one side of the square base is 24 feet.

The length of one side of the square base of the pyramid is approximately 23.8 feet. This was determined using the volume formula for a square pyramid and solving for the side length. The base area and height were key in finding this solution.

To find the length of one side of the square base of the pyramid, we can use the formula for the volume of a square pyramid:

Volume = (1/3) × Base Area × Height

Given:

Let the side length of the square base be s feet. The base area of the square is s².

Using the volume formula, we get:

3969 = (1/3) × s² × 21

First, solve for s²:

3969 = 7 × s²

s² = 3969 / 7

s² = 567

Now, take the square root of both sides to find s:

s = √567 ≈ 23.8 feet

Therefore, the length of one side of the square base of the pyramid is approximately 23.8 feet.

Answer:

the answer is MQA =130°

Wen u draw a parallel line with respect to MD through Q, the angle between the line become 40 degree - alternate angles

so the rest is 90 degree, therefore 90 + 40 = 130 degree

Answer:

∠MQA = 130°

Step-by-step explanation:

∠MDQ = 90° ( angle between tangent and radius )

Given ∠QMD = 40°, then

∠MQD = 180° - (90 + 40)° = 180° - 130° = 50° ( sum of angles in a triangle )

∠MQD and ∠MQA form a straight angle and are supplementary, thus

∠MQA = 180° - 50° = 130°

OR

The external angle of a triangle is equal to the sum of the 2 opposite interior angles

∠MQA is an exterior angle of the triangle, thus

∠MQA = 90° + 40° = 130°