The standard form of the equation of a parabola is y= x2 - 6x + 14.
What is the vertex form of the equation?
O A. y= (x-3)2 + 23
O B. y=(x-3)2 + 5
ed
O c. y=(x-3)2 + 15
O D. y= (x+3)(x-3) + 5

Answer:

141

Step-by-step explanation:

We need to first find the volume of the cannonballs and then, divide the volume of the closet by the volume of the cannonballs.

The radius of the spherical cannonball is 0.75 feet.

The volume of a sphere is:

[tex]V = \frac{4}{3} \pi r^3[/tex]

where r = radius

Therefore, the volume of the cannonballs is:

[tex]V = \frac{4}{3} * \pi * 0.75^3\\\\V = 1.77 ft^3[/tex]

Therefore, the number of cannonballs that can fit the closet is:

250 / 1.77 = 141.24

Since the number is a maximum and it must be a whole number, the number of cannonballs that can fit the closet is 141.

Answer:

d. Summarized account information

Step-by-step explanation:

Answer:

x >13/9

Step-by-step explanation:

(1/4)(5x−3) > (1/2)x + (1/3)

Distribute

5/4x - 3/4 > 1/2x + 1/3

Multiply each side by 12 to get rid of fractions

12*5/4x -12* 3/4 >12* 1/2x +12* 1/3

15x -9 > 6x +4

Subtract 6x from each side

15x-6x-9 > 6x-6x+4

9x -9> 4

Add 9 to each side

9x-9+9 > 4+9

9x > 13

Divide by 9

9x/9 >13/9

x >13/9

Answer:

Explanation:

Answer:

x° = ∠OBR = ∠ABC (base angles of a cyclic isosceles trapezoid)

Step-by-step explanation:

APRB form a cyclic trapezoid

∠APO  = x° (Base angle of an isosceles triangle)

∠OPR  = ∠ORP (Base angle of an isosceles triangle)

∠ORB = ∠OBR (Base angle of an isosceles triangle)

∠APO + ∠OPR + ∠OBR = 180° (Sum of opposite angles in a cyclic quadrilateral)

Similarly;

∠ORB + ∠ORP + x°  = 180°

Since ∠APO = x° ∠ORB = ∠OBR and ∠OPR  = ∠ORP we put

We also have;

∠OPR = ∠AOP = ∠BOR (Alternate interior angles of parallel lines)

Hence 2·x° + ∠AOP = 180° (Sum of angles in a triangle) = 2·∠OBR + ∠BOR

Therefore, 2·x° = 2·∠OBR, x° = ∠OBR = ∠ABC.

Answer:

Choice C

Step-by-step explanation:

f: initial value of 200 decreasing at a rate of 4%

g: initial value of 40 increasing at a rate of 8%

f is decreasing so it must go down starting at 200

That eliminates a and d

g is increasing and starts at 40  That eliminates a

We must look at b and c

g is increasing faster than f is decreasing

Choice C

Answer:

independent is the y value or the value that changes at a steady rate no matter what, the dependent variable or x is the variable that is subject to change and is dependent on the y value to find a pattern

Step-by-step explanation:

Answer:

Variables are given a special name that only applies to experimental investigations. One is called the dependent variable and the other the independent variable. The independent variable is the variable the experimenter changes or controls and is assumed to have a direct effect on the dependent variable.

Step-by-step explanation:

Answer:

7/10

Step-by-step explanation:

10 marbles in a bag 7 of them are blue and the (10-7)=3 green

P( blue) = blue / total

            = 7/10

Answer:on the circle

Step-by-step explanation:

Point J(-3, 12) is lying on the circle whose center is located at point D(-1, 3).

It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).

We have a center of the circle at D(-1, 3)

And point G(-10, 1) is on the circle.

We know the standard equation of the circle when a center is given:

[tex]\rm (x-h)^2+(y-k)^2=r^2[/tex]

Where r is the radius of the circle and (h, k) is the center of the circle.

Here (h, k) ⇒ (-1, 3)

The circle equation becomes:

[tex]\rm (x+1)^2+(y-3)^2=r^2[/tex]

Put the point on the circle equation to get the radius of the circle:

[tex]\rm (-10+1)^2+(1-3)^2=r^2[/tex]

[tex]\rm (-9)^2+(-2)^2= r^2\\\\\rm 81+4 = r^2\\\\ \rm r = \sqrt{85} \ units[/tex]

Equation of circle is:

[tex]\rm (x+1)^2+(y-3)^2=85[/tex]

Now put the point J(-3, 12 ) in the circle equation:

[tex]\rm (-3+1)^2+(12-3)^2=85[/tex]

4+ 81 ⇒ 85

It means point J is lying on the circle.

Thus, point J(-3, 12) is lying on the circle whose center is located at point D(-1, 3).

Learn more about circle here:

brainly.com/question/11833983

Answer:

96 sq yards

Step-by-step explanation:

40-24 is 16, and 16/2 is 8. 8 is the second length, so 8 times 12 is 96 which is the area

Answer:

16.485 feet

Step-by-step explanation:

Given that tire is 5.25 feet tall

any circular shape is as tall as its diameter.

we can say that diameter of tire is 5.25 feet.

in one rotation tire will start from one point of tire and reach it again.

it is like on a circle moving from on one point and then reaching to same point.

and we know that distance covered on moving on the point of circle is equal to circumference.

Thus, measure of circumference would help to find how many feet the tractor will travel in 1 rotation.

circumference of circle is given by [tex]\pi D[/tex]

where D is the diameter of circle.

we will us 3.14 as value of [tex]\pi[/tex]

thus, circumference of circle is[tex]\pi * 5.25 = 3.14*5.25 = 16.485[/tex]

Hence, tractor would travel 16.485 feet in one rotation.

Answer:

$10579.49

Step-by-step explanation:

The formula for amount gotten after a period of time (in years) on a principal which is compounded continuously is given as:

[tex]A = P(1 + r)^t[/tex]

where P = principal (amount borrowed)

r = interest rate

t = number of years

Peter accumulated $7,500 in credit card debt with interest rate as 3.5% per year and he does not make any payments for 10 years.

Therefore, his debt is:

[tex]A = 7500(1 + \frac{3.5}{100})^{10}\\ \\A = 7500 (1 + 0.035)^{10}\\\\A = 7500(1.035)^{10}\\[/tex]

A = $10579.49

He will owe $10579.49 after 10 years

Answer:

A= $10,643.01

Step-by-step explanation:

if you are rounded to the nearest cent

Identify the values of each variable in the formula. Remember to express the percent as a decimal.

A=?

P= $7,500

r= 0.035

t= 10 years

For compounding continuously, use the formula A=Pert.

Substitute the values in the formula and compute the amount to find

A= 7,500e [tex]x^0.035.10[/tex][tex]x^{0.035.10}[/tex]

A= $10,643.01

Complete Question:

The scatter plot shows the number of oranges picked, in hundreds, in relation to the number of lemons harvested, in hundreds, by several farmers. According to the plot, which value is the best estimate of the correlation coefficient of the data?

A.-0.2

B. -0.9

C. 0.9

D. 0.2

*See attachment for the scatter plot

Answer:

C. 0.9

Step-by-step explanation:

If we take a good look at the scatter plot in the attachment showing numbers if oranges picked in relation to number of lemons harvested, we can infer that there's a strong positive correlation between both variables.

Thus, both variables are moving in the same direction. As one variable increases, the other variable increases. Also, the data points represented on the plot seem clustered close to the line rather than farther away.

This will suggest a positive correlation coefficient that is closer to 1.

From the options given above, the best estimate of the correlation coefficient would be 0.9.

The answer is C. 0.9

Answer:

circumference = 2πr

2×π×6

12πmm

Given:

Radius of circle = 6 mm

Work out :

Workout the circumference of this circle?

Formula used:

Circumference of circle = 2πr

Solution:

According to the question,

Circumference of circle = 2πr

= 2 × π × 6

= 12 π mm

Answer:

180 ml oil

240 g onions

1.35 kg potatoes

1.8 l milk

Step-by-step explanation:

The recipe makes 6 portions and you need 18 portions. Since 6 is 3 times smaller than what you need, just times everything you've been given by 3.

*you can choose to convert into the correct units of measurement before or after dividing. I converted after dividing. Either way works fine though.

1) 60 x 3 = 180 ml

2) 80 x 3 = 240 g

3) 450 x 3 = 1350 g

They want it in kilograms, so divide it by 1,000 to convert. this gives you 1.35 kg.

4) 600 x 3 = 1800 ml

They want it in l, so divide it by 1,000 to convert. this gives you 1.8 l.

Hope this helped : )

Answer:

Can you please tell me what is the area of the given triangle?

The volume of the given pyramid is 106.1 cubic foot.

Given:

The perimeter of the base is 15.8 feet

The base of the pyramid is square given of side say L .

Thus, from the formula of perimeter of square,

⇒ 4*L = 15.8 feet

∴  L = 3.95 feet

Now the base area of the pyramid is [tex]L^{2}[/tex] as it is a square .

∴ Base area = 3.95*3.95 square feet

= 15.6025 square foot

Now, formula for volume of the pyramid

=  1/3 * base area * height

⇒ Volume = 1/3 * 15.6025 * 20.4 cubic foot

∴ Volume = 106.097 cubic foot

Thus volume of the given pyramid is 106.1 cubic foot rounded off to nearest tenth.

To Learn how to calculate volume of a pyramid, refer:

#SPJ2

Answer:

x = -(a - b)/b

Step-by-step explanation:

Solve for x:

a = b (1 - x)

a = b (1 - x) is equivalent to b (1 - x) = a:

b (1 - x) = a

Divide both sides by b:

1 - x = a/b

Subtract 1 from both sides:

-x = (a - b)/b

Multiply both sides by -1:

Answer: x = -(a - b)/b

Answer:

x = 8.5

Step-by-step explanation:

In this question, we are to calculate the value of x.

To calculate this, we shall be utilizing one of the important properties of parallelogram.

This property is that opposite angles of a parallelogram are equal.

This means that mQSR = mSPQ = 4x + 90

Now to finally calculate x, we make use of another important parallelogram property which is that angles of parallelogram which faces each other are supplementary.

This means that they add up to be 180

Since mQSR faces mQRS

This means that;

4x + 90 + 9x -20 = 180

13x + 70 = 180

13x = 110

x = 110/13 which is approximately 8.5

Answer:

(5s + 8) is the missing factor.

Step-by-step explanation:

The given expression is 5s² + 23s + 24

We have to convert the given expression into the factored form.

One factor of the expression has been given as (x + 3)

5s² + 23s + 24 = 5s²+ 15s + 8s + 24

                        = 5s(s + 3) + 8(s + 3)

                        = (5s + 8)(s + 3)

So the factors of the expression will be (s + 3) and (5s + 8)

Therefore, the missing factor of the given expression is (5s + 8).

Answer:

33% or with 10th place decimal 33.3%

Step-by-step explanation:

1/3 has a continuous decimal form of .333333...

So, it is usually rounded to .33

Hope this helps!

Answer: 33.33%

Step-by-step explanation:

Answer:

a. 2(^3 sqrt 3) - ^3 sqrt 18

Step-by-step explanation:

got it right on edge

[tex]\frac{6-3(\sqrt[3]{6})}{\sqrt[3]{9}}[/tex][tex]\frac{6-3(\sqrt[3]{6})}{\sqrt[3]{9}}[/tex][tex]2(\sqrt[3]{3})-\sqrt[3]{18}[/tex] option (A)  is Correct.

The problem can be solved by following steps.

The expression given is [tex]\frac{6-3(\sqrt[3]{6})}{\sqrt[3]{9}}[/tex]

So , The first step we will do is Rationalize the figure

= [tex]\frac{6-3(\sqrt[3]{6})*3 {\sqrt{9^2} }}{\sqrt[3]{9}*\sqrt[3]{9} }[/tex]

The product of radicals with the same index equals the radical of the product:[tex]\frac{6-3(\sqrt[3]{6})*3 {\sqrt{9^2} }} {\sqrt[3]{9*9^2} }[/tex]

Simplify using exponent with same base

[tex]a^{n}*a^{m} = a^{a+m}[/tex]

= [tex]\frac{6-3(\sqrt[3]{6})*3 {\sqrt{9^2} }} {\sqrt[3]{9^1+^2} }[/tex]

Calculate the sum or difference: [tex]\frac{6-3(\sqrt[3]{6})*3 {\sqrt{9^2} }} {\sqrt[3]{9^3} }[/tex]

Simplify the radical expression: [tex]\frac{6-3(\sqrt[3]{6})*3 {\sqrt{9^2} }} {{9} }[/tex]

Calculate the power : [tex]\frac{6-3(\sqrt[3]{6})*3 {\sqrt[3]{3} }} {{9} }[/tex]

Cross out the common factor: [tex]\frac{6-3(\sqrt[3]{6})*3 {\sqrt[3]{3} }} {{3} }[/tex]

Factor Greatest Common Factors : [tex]\frac{3*2\sqrt[3]{3}-\sqrt[3]{18} }{3}[/tex][tex]3*2\sqrt[3]{3}-\sqrt[3]{18}}[/tex]

Reduce the fraction : [tex]2\sqrt[3]{3}-\sqrt[3]{18}}[/tex]

Hence the First option is correct

Learn more about Quotient here

https://brainly.com/question/673545

#SPJ2

Answer:

The answer is 7n3 + 6.

Step-by-step explanation:

To simplify, remove the parentheses and combine like terms.

The standard form of the given expression is 7n³+6.

The given expression is (4+2n³)+(5n³+2).

To add any two expressions group the like terms.

Here, 4+2n³+5n³+2

= (2n³+5n³)+4+2

= 7n³+6

Therefore, the standard form of the given expression is 7n³+6.

To learn more about an expression visit:

https://brainly.com/question/28170201.

#SPJ6

Answer:

230

Step-by-step explanation:

9 times 20 = 180

divide by 2 = 90

7 times 20 = 140

140 + 90 = 230

Answer:

A=230 cm2

Step-by-step explanation:

A1= L x W             HEIGHT OF TRIANGLE=16-7=9

A1=20 x 7

A1=140 cm2

A2=1/2 x B x H

A2=1/2 x 20 x 9

A2=90 CM 2

Answer:

The answer to this question can be described as follows:

-5 with multiplicity 3

9 with multiplicity 2

-1 with multiplicity 1

Step-by-step explanation:

Given:

[tex]\Rightarrow f (x) = (x + 5)^3(x - 9)^2(x + 1)[/tex]

Solve the above equation:

[tex]\Rightarrow f (x) = (x + 5)(x + 5)(x + 5)(x - 9)(x - 9)(x + 1)\\[/tex]

The roots of the polynomial are as follows:

 [tex]\Rightarrow (x-x_1)(x-x_2)(x-x_3)......(x-x_n)\\\\\Rightarrow x_1,x_2,x_3.........x_n[/tex]

That's why the roots are:

5 with multiplicity 3

9 with multiplicity 2

-1 with multiplicity 1

Answer:

answer:

a. -5 with multiplicity 3  

d. 9 with multiplicity 2

f. -1 with multiplicity 1

Step-by-step explanation:

Answer:

The cube root for 216 is 6

Step-by-step explanation:

Answer:

the cube root of 216 is 6

Step-by-step explanation:

Answer:

89595/100000

Step-by-step explanation:

Answer:

  7.  ∠CBD = 100°

  8.  ∠CBD = ∠BCE = 100°; ∠CED = ∠BDE = 80°

Step-by-step explanation:

7. We presume the angles at A are congruent, so that each is 180°/9 = 20°.

Then the congruent base angles of isosceles triangle ABC will be ...

  ∠B = ∠C = (180° -20°)/2 = 80°

The angle of interest, ∠CBD is the supplement of ∠ABC, so is ...

  ∠CBD = 180° -80°

  ∠CBD = 100°

__

8. In the isosceles trapezoid, base angles are congruent, and angles on the same end are supplementary:

  ∠CBD = ∠BCE = 100°

  ∠CED = ∠BDE = 80°

Answer:

[tex]10[/tex]

[tex]16[/tex]

Explanation:

A rational number is a number that can be expressed as the quotient or fraction of two integers.