graph the parabola. y=(x-3)^2-1

The value of x that makes the unshaded area equal to the shaded area is 7.07 inches.

An equation is an expression that shows the relationship between two or more variables and numbers.

The area of big sector = (60/360) * π(10)² = (50π /3) cm²

Area of small sector = (60/360) * π(x)² = (x²π /6) cm²

Unshaded area = (x²π /6) cm²

Shaded area = (50π /3) - (x²π /6) = (100π - x²π) /6

Shaded area = unshaded area

(100π - x²π) /6 = (x²π /6) cm²

x = 7.07

The value of x that makes the unshaded area equal to the shaded area is 7.07 inches.

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The length of x in the sector is 7.08 cm.

area of a sector = ∅ / 360 × πr²

where

Therefore,

area of a sector = 60 / 360 × π × 10²

area of a sector = 60 / 360 × π × 100

area of a sector = 6000 / 360 π

Hence,

area of the unshaded portion = 6000 / 360 π ÷ 2 = 6000π / 720 =  26.1666666667 = 26.2 cm

Hence,

26.2 = 60 / 360 × 3.14 × x²

x² = 26.2 / 0.52333333333

x = √50.0637261552

x = 7.07557064836

x = 7.08 cm

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The required equation is 135 + 9x > 250.

The number of lawns Ed must mow is assumed to be x.

The amount Ed charges for each lawn he mows is $9.

Thus, the total amount Ed earns by mowing x lawns = $9x.

The savings which Ed has is $135.

Thus, the total amount Ed will have to spend can be written as the expression, $(135 + 9x).

The cost of the video game is given to be $250.

We are asked to write an equation, that can be used to find the number of lawns Ed mow, that is x so that the amount Ed has will be more than the amount he needs to buy the video game.

This can be shown as the equation:

Total amount Ed has > Cost of the video game,

or, 135 + 9x > 250.

Thus, the required equation is 135 + 9x > 250.

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Answer:

315

Step-by-step explanation:

-3ac7

-3x-3=9x5=45x7=315

❄ Hi there,

evaluate this expression by using substitution:

If

then

[tex]\sf{-3(-3)(5)}[/tex]

[tex]\sf{9\times5}[/tex]

[tex]\triangleright \ \sf{45}[/tex]

That's it!

❄

The only set that only has rational numbers is the first one:

{1/3, -3.45, √9}

A rational number is a number that can be written as the quotient of two integers.

If we look at the first set, the elements are:

In the other sets we can see elements like:

√37, √44, or √2 which are all irrational numbers, then the only correct option is the first one.

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Answer:

C. (32/4)*2

Step-by-step explanation:

C is the correct answer because when we divide 4/2 it equals 2.

Hope this helps!

Answer:

D

Step-by-step explanation:

Given expression:

[tex] \dfrac{32}{4} \times \dfrac{4}{2} \times 2 [/tex]

Evaluation of the given expression:

[tex] = 8 \times 2 \times 2 [/tex]

[tex] = 32 [/tex]

A.     [tex] \dfrac{32}{\frac{16}{4}} = \dfrac{32}{4} = 8 [/tex]

B.     [tex] 8 \times \dfrac{4}{2} = 8 \times 2 = 16 [/tex]

C.     [tex] \dfrac{32}{4} \times 2 = 8 \times 2 = 16 [/tex]

D.     [tex]8 \times \dfrac{4}{2} \times 2 = 8 \times 2 \times 2 = 32[/tex]

Only expression D evaluates to the same value as the given expression.

Answer: D

Answer: -1/2

Step-by-step explanation:

The slope of a line tells you how steep the line is, and what direction it is going in. We can calculate the slope by seeing how much the line moves horizontally and vertically.

We can calculate the slope using [tex]\frac{rise}{run}[/tex], which is how much a point rises (goes up or down) and runs (goes left or right) to go to the next point.

Let's take two points on the graph: (-2, 0) and (0, -4). The rise will be the difference of the y-values, and the run will be the difference of the x-values.

[tex]\frac{-2-0}{0-(-4)}=\frac{-2}{4}=\frac{-1}{2}[/tex]

Hence, the slope of this line is [tex]\frac{-1}{2}[/tex]

Answer:

1/3

Step-by-step explanation:

The numbers are 1, 2, 3, 4, 5, and 6.

Both 3 and 6 are multiples of 3.

So, 2/6 is the probability since there is an equal change that the arrow will land on each section.

This simplifies to 1/3.

Brainliest, please :)

Answer:

P (multiple of 3) =  [tex]\bf \frac{1}{3}[/tex]

Step-by-step explanation:

Numbers on the spinner, ξ = {1, 2, 3, 4, 5, 6}    (6 elements)

Multiples of 3 = {3, 6}   (2 elements)

P (multiple of 3) = no. of multiples of 3 / total no. of numbers on spinner

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

                          =  [tex]\bf \frac{1}{3}[/tex]

The points are (7, 13/3).

Lets simplify the equation,

The equation of first line: y = 1/3 x + 2

the equation of second line: y= 4/3x - 5

Solve the system of equations by elimination,

Multiply equation A by -4 both sides

-4y = -4(1/3x +2)

-4y = -4/3x-8

After eliminating the equation we get,

y = 13/3

So now have to find x

13/3 = 1/3x + 2

Lets multiply above by 3
x = 13-6

x = 7.

Hence the points are (7, 13/3)

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Answer:

B

Step-by-step explanation:

What is the solution to the system of equations?

(7, 4)

(7, StartFraction 13 over 3 EndFraction)

(8, StartFraction 14 over 3 EndFraction)

(9, 7)

Answer:

correct answer is 110x + 29y = 333

Step-by-step explanation:

Answer:

I and II only

Answer:

200 yd²

Step-by-step explanation:

A = 17 yd

B  = 15 yd

C = 2 yd

D = 8 yd

b) Area of rectangle = length * width

 [tex]\sf Area \ of \ 2 \ triangle = 2* \dfrac{1}{2}* base * height = base* height\\\\[/tex]

Area of right triangular prism = Areas of two triangle +  area of the upper rectangle + area of middle rectangle + area of below rectangle

          = 8 * 15 +  17 * 2 + 15 *2 + 8*2

          = 120 + 34 + 30 + 16

          = 200 yd²

Answer:

A.

Step-by-step explanation:

i'm 99% sure!

Answer:

B

Step-by-step explanation:

Plug in the coordinates.

Based on the graph of the cupcakes done, we find that w(2) = 5.

Herein we have an application of linear equations to the production of cupcakes. In accordance with the graph, the horizontal axis is for the preparation time (x) and the vertical axis is for the quantity of cupcakes done (w). Based on the graph, we find that w(2) = 5.

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Answer:

21

Step-by-step explanation:

Using alternate interior angles, we can conclude that angle C is equal to X (the 3rd, unmarked angle in the center triangle)

To find that 3rd angle, we can do 180 - 105 - 54. This is because all angles in a triangle must equal 180. Using this, we find that angle C is equal to 21. By the law, X must also equal 21.

Answer:

x is 21

Step-by-step explanation:

add 54 and 105, then subtract it by 180 and you get 21.

The formula for the volume of a cube is-side length^3.

For your problem, side length=4, so the answer is 4^3=64

ANSWER: 64 CUBIC CENTIMETERS hope this helped you

(T-Tb)

Step-by-step explanation:

we first divide fourteen by four

14/4= 3.5

then we change 0.5 to hours by multiplying by 60

0.5 * 60 = 30

so in conclusion it would take 3hrs 30mins to finish each activity

Answer:

x = 10

Step-by-step explanation:

180 = 90 + 40 + (4x + 10)

180 = 130 + (4x + 10)

4x + 10 = 180 - 130

4x + 10 = 50

4x = 50 - 10

4x = 40

x = 40/4

x = 10

Answer:

x = 10

Step-by-step explanation:

An euclidean triangle is defined to have sum of all 3 interior angles equal to 180°.

In the given triangle, we know three measurement:

You may be wondering, where does 90° come from. The answer is you can find it by looking if a triangle has a little square symbol or not. If it does, the measurement will always be 90°.

Now since we know that sum of 3 interior angles must equal to 180° in euclidean triangle. Therefore, sum up three of measurement then set to 180°.

[tex]\displaystyle{90 + 4x+10 + 40= 180}[/tex]

Evaluate and solve for the x-variable:

[tex]\displaystyle{90 + 4x+10 + 40= 180}\\\\\displaystyle{4x+140 = 180}\\\\\displaystyle{4x=180-140}\\\\\displaystyle{4x=40}\\\\\displaystyle{x=10}[/tex]

Therefore, the value of x is 10

The expressions based on the information given are illustrated below

3/4 ÷ 1/2 = 1.5 = quotient is grater than 1

1/2 ÷ 3/4 = 2/3 = quotient is less than 1

2/9 ÷ 1/27 = 6 = quotient is grater than 1

5/3 ÷ 20/6 = 1/2 = quotient is less than 1

4/3 ÷ 3/5 = 20/9 = quotient is grater than 1

19/8 ÷ 2 3/8 = 1 = quotient is equal to 1.

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The altitudes of equal length, BE and CF gives AB = AC, from which we have;

From the given description, we have;

BE = CF

<CFB = <BEC = 90° All right angles are congruent

BC = BC by reflexive property of congruency

BC = The hypotenuse side of triangles ∆BFC and ∆CEB

Therefore;

∆BFC is congruent to ∆CEB by Right angle Hypotenuse Side, RHS, rule of congruency.

Therefore;

BF = CE by Corresponding Parts of Congruent Triangles are Congruent, CPCTC

Similarly, we have;

∆AEB is congruent to ∆AFC, by Side-Angle-Angle, SAA, rule of congruency

Which gives;

FA = AE by CPCTC

BF + FA = CE + AE, by substitution property of equality

BF + FA = AB

CE + AE = AC

Therefore;

Therefore;

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Any complex number [tex]z[/tex] can be written in polar/exponential form as

[tex]z = |z| e^{i\arg(z)} = |z| (\cos(\arg(z)) + i \sin(\arg(z)))[/tex]

In the complex plane, the given complex number belongs to the third quadrant since both its real and imaginary parts are negative. This means the argument must be between π and 3π/2, so the first two options are eliminated.

The difference between the remaining two options is the coefficient [tex]|z|[/tex]. We have

[tex]z = -2\sqrt3 - 6i \implies |z| = \sqrt{(-2\sqrt3)^2 + (-6)^2} = 4\sqrt3[/tex]

so (D) (the last option) is the correct choice.

If three different orders are selected, find the probability that they are all from Restaurant B is; 0.026

Total orders both accurate and not accurate = 1131

Total orders from restaurant B (both accurate and not accurate) = 337

Probability of first order from B = 337/1131

Probability of second order from B = 336/1130

Probability of third order from B = 335/1129

Probability of the first three orders from B = 337/1131 × 336/1130 × 335/1129

Probability of the first three orders from B = 0.026

Complete question is;

Use the data in the following table , which lists drive - thru order accuracy at popular fast food chains Assume that orders are randomly selected from those included in the table Drive thru Restaurant A B C D Order Accurate 312 277 250 144 Order Not Accurate 32 60 37 19 If three different orders are selected , find the probability that they are all from restaurant A

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Answer:

[tex] {3}^{x} [/tex]

Step-by-step explanation:

[tex] {x}^{3} = 8[/tex]

[tex] {3}^{x} = 9[/tex]

Solving a linear equation, we conclude that Margo's paycheck is of 96 dollars.

We know that she spends one quarter on a dress, one eight on shoes, and $24 on a birthday present.

We also know that she spent a total of $60.

If we define P as Margo's paycheck, then we know that:

(1/4)*P + (1/8)*P + $24 = $60

Now we just need to solve that linear equation for P, we will get:

(2/8)*P + (1/8)*P = $60 - $24 = $36

(3/8)*P = $36

P = (8/3)*$36 = $96

In this way, we conclude that Margo's paycheck is of 96 dollars.

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By using the triple integral, the wedge's volume is 4/15.

A parabolic cylinder is a three-dimensional quadratic surface (sometimes known as a quadric surface) in mathematics, specifically analytical geometry, and is defined by the equation x 2 + 2 a y = 0 x2+2ay=0. A parabola serves as the directrix of a parabolic cylinder, to put it another way.

The wedge's volume, which the parabolic cylinder encloses, must be determined.

Consequently, as a result of the z=y form,

In addition to the specified boundary, the plane y=0 x = 0, z = 0.

For all of this, we are therefore in the first octant. additionally, the plane

x + y = 1 is a constraint.

Triple integrals are three independent integrations that are done one after the other to calculate a volume or to integrate across three independent dimensions in a fourth dimension.

The following would be written as a triple integral:

∫x=0 ∫y=0

∫z=0 dy dz dx

Once the values have been entered and the problem has been solved, we obtain the

[−4/15(1−x)^5/2] at x=0

The answer will then change to 4/15.

As a result, using the triple integral, the wedge's volume comes out to 4/15.

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Answer:

306 square meters

Step-by-step explanation:

The maximum area is when the length and width are the closest together.

70/2=35 we divide because there are 2 lengths and 2 widths in a rectangle

35/2=17.5, find the 2 closest integers, they are 17 and 18

17*18=306

The volume of the composite solid shown in the diagram is: 80 ft.³.

Volume of the composite solid = volume of triangular prism + volume of triangular pyramid.

Volume = 0.5 × base of triangle × height of triangle × length of prism + 1/3 × Base area × Height = 0.5 × 8 × 5 × 3 + 1/3 × 0.5 × 8 × 5 × 3

Volume = 60 + 20

Volume of the composite solid = 80 ft.³.

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Answer:

72°

Step-by-step explanation:

3x = 4x - 24 (alternate exterior angles theorem)

x = 24

So, angle RST measures 72°.

Answer:22

Step-by-step explanation:22

Answer: C

Step-by-step explanation:

There is a vertical asymptote at x=3, so the denominator should have a factor of (x-3).

This eliminates everything except for C.