Find the values of​ a, b, and c such that the equation y=ax2+bx+c has ordered pair solutions ​(1​,16​), ​(−1​,−2​), and ​(0​,−1​). To do​ so, substitute each ordered pair solution into the equation. Each​ time, the result is an equation in three​ unknowns, a,​ b, and c. Then solve the resulting system of three linear equations in three​ unknowns, a,​ b, and c.

Answer:

66.00

Step-by-step explanation:

eleven pies have 6 slices each

Multiply 6 by 11 to get 66

66x1.00=66.00

As we know an identity that ;

Setting, [tex]{\bf{{\theta}=\footnotesize \dfrac{\pi}{8}}}[/tex] will give us ;

[tex]{:\implies \quad \sf \cos \left(2\times \dfrac{\pi}{8}\right)=2\cos^{2}\left(\dfrac{\pi}{8}\right)-1}[/tex]

[tex]{:\implies \quad \sf 2\cos^{2}\left(\dfrac{\pi}{8}\right)=\dfrac{1}{\sqrt{2}}+1}[/tex]

[tex]{:\implies \quad \sf 2\cos^{2}\left(\dfrac{\pi}{8}\right)=\dfrac{1+\sqrt{2}}{\sqrt{2}}}[/tex]

[tex]{:\implies \quad \sf \cos^{2}\left(\dfrac{\pi}{8}\right)=\dfrac{1+\sqrt{2}}{2\sqrt{2}}}[/tex]

Rationalizing the denominator of RHS, will yield ;

[tex]{:\implies \quad \sf \cos^{2}\left(\dfrac{\pi}{8}\right)=\dfrac{1+\sqrt{2}}{2\sqrt{2}}\times \dfrac{2\sqrt{2}}{2\sqrt{2}}}[/tex]

[tex]{:\implies \quad \sf \cos^{2}\left(\dfrac{\pi}{8}\right)=\dfrac{2\sqrt{2}+4}{8}}[/tex]

[tex]{:\implies \quad \sf \cos^{2}\left(\dfrac{\pi}{8}\right)=\dfrac{2\sqrt{2}+4}{8}}[/tex]

[tex]{:\implies \quad \sf \cos \left(\dfrac{\pi}{8}\right)=\pm \sqrt{\dfrac{2\sqrt{2}+4}{8}}}[/tex]

Now, as we know that ;

Now, setting the same [tex]{\bf{{\theta}=\footnotesize \dfrac{\pi}{8}}}[/tex]

[tex]{:\implies \quad \sf 2\sin \left(\dfrac{\pi}{8}\right)\cos \left(\dfrac{\pi}{8}\right)=\sin \left(2\times \dfrac{\pi}{8}\right)}[/tex]

[tex]{:\implies \quad \sf 2\sin \left(\dfrac{\pi}{8}\right)\cos \left(\dfrac{\pi}{8}\right)=\dfrac{1}{\sqrt{2}}}[/tex]

[tex]{:\implies \quad \sf \sin \left(\dfrac{\pi}{8}\right)\left(\pm \sqrt{\dfrac{2\sqrt{2}+4}{8}}\right)=\dfrac{1}{2\sqrt{2}}}[/tex]

[tex]{:\implies \quad \sf \sin \left(\dfrac{\pi}{8}\right)=\dfrac{\sqrt{8}}{2\sqrt{2}(\pm \sqrt{2\sqrt{2}+4})}}[/tex]

[tex]{:\implies \quad \sf \sin \left(\dfrac{\pi}{8}\right)=\pm \dfrac{1}{\sqrt{2\sqrt{2}+4}}}[/tex]

This is the required answer

Answer:

C- 29.88

Step-by-step explanation:

i did it on the edge test

9514 1404 393

Answer:

  35

Step-by-step explanation:

A = PB

A = (7%)(500) = 0.07×500 = 35

35 is 7% of 500

_____

You can think of the % symbol as being a shorthand way to write /100. That is, ...

  7% = 7/100 = "seven hundredths" = 0.07

The equation y = mx of the graph is a linear equation

The linear equation that demonstrates the relationship on the graph is y = mx

The points on the graph are given as:

(1, m) and (x, y)

Start by calculating the slope (M)

[tex]M = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

So, we have:

[tex]M = \frac{y - m}{x - 1}[/tex]

The linear equation is then calculated as:

[tex]y = M(x - x_1) + y_1[/tex]

This gives

[tex]y = \frac{y - m}{x- 1}(x - 0) + 0[/tex]

[tex]y = \frac{y - m}{x- 1}(x)[/tex]

Cross multiply

[tex]yx-y = yx - mx[/tex]

Evaluate the common terms

[tex]-y =- mx[/tex]

Divide both sides by -1

y = mx

Hence, the equation of the graph is y = mx

Read more about linear equations at:

https://brainly.com/question/14323743

Step-by-step explanation:

If you draw an altitude of the right triangle, you get that the legs are (18/2)=9 and the height (which I'll call x) and a hypotenuse of 18.

By the Pythagorean theorem,

[tex] {9}^{2} + {x}^{2} = {18}^{2} \\ 81 + {x}^{2} = 324 \\ {x}^{2} = 243 \\ x = \sqrt{243} = 9 \sqrt{3} [/tex]

Answer:

Area of a slice = Area of the pizza ÷ 8

Therefore the area of the pizza equals:

AreaPizza = π r^2 ( r = diameter ÷ 2)

= π 6^2

= 113.097

AreaSlice = AreaPizza ÷ 8

= 113.097 ÷ 8

= 14.137 inches squared

To the nearest square inch, each slice is 14 inches squared.

Step-by-step explanation:

Hope this helps.

#1

#2

#3

#4

#5

#6

#7

#8

Answer:

See below.

Step-by-step explanation:

#1) Audi symbol

#2) Under Armour Logo

#3) Chanel Logo

#4) Red Logo

#5) Mouse Logo

#6) Android Bot

#7) Nike logo

#8) Spider

Answer:

There are four main types of transformations: translation, rotation, reflection and dilation. A translation moves the object without rotating it or changing its size. Reflection flips the object about a line of reflection. Rotation rotates a figure about a fixed point. Dilation changes the size of a figure without changing its essential shape. When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite. a negative angle of rotation turns the figure in a clockwise direction. Transformation can be done in a number of ways, including reflection, rotation, and translation. ~When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite. A negative angle of rotation turns the figure in a clockwise direction.

Step-by-step explanation:

Answer: 1/2

0,4

-2

-2,-2

Step-by-step explanation: took the lesson

Answer:

D, 14 units

Step-by-step explanation:

Both coordinates have -5, so we know that 8 and -6 are at the same line.

We find the absolute value...

So 8=8 and -6=6. Lastly, we add them from 0 and 8+6= 14.

ANSWER IS 14 UNITS!!

Answer:

Step 1. Read the problem. Draw the figure and label it with the given information. .

Step 2. Identify what you are looking for. the measure of an angle

Step 3. Name. Choose a variable to represent it. Let x= the measure of an angle.

Step 4. Translate. m\angle A+m\angle B+m\angle C=180

Write the appropriate formula and substitution

X + 4.3 + 10.6- 8.1 \end{array}

Step 7. Answer the question. The measure of the third angle is 6.8ft

The new surface area is approximately 12264.56 ft².

A prism is a three-dimensional object.

There are triangular prism and rectangular prism.

We have,

To solve this problem, we first need to calculate the original surface area of the complex solid.

The complex solid is composed of two rectangular prisms, one with dimensions 9.8 ft × 6.5 ft × 8.1 ft and one with dimensions 10.6 ft × 4.3 ft × 6.5 ft.

The surface area of the first rectangular prism is:

2(9.8 × 6.5) + 2(9.8 × 8.1) + 2(6.5 × 8.1) = 464.82 ft²

The surface area of the second rectangular prism is:

2(10.6 × 4.3) + 2(10.6 × 6.5) + 2(4.3 × 6.5) = 411.22 ft²

So the total original surface area of the complex solid is:

464.82 + 411.22 = 876.04 ft²

Now we need to find the new surface area, which is exactly 14 times the original surface area.

Therefore, we can write:

New surface area = 14 × original surface area

New surface area = 14 × 876.04

New surface area ≈ 12264.56 ft²

Thus,

The new surface area is approximately 12264.56 ft².

Learn more about Prism here:

https://brainly.com/question/12649592

#SPJ2

Answer:

z=6

Step-by-step explanation:

32=12+4(z-1)=

32=12+4z-4

32=8+4z

24=4z

6=z

Answer:

B and D

Step-by-step explanation:

Kitchen and Bedroom will have same number f boxes after James moved 3 boxes from the living room to the bedroom.

The kitchen and the bedroom will have the same number of boxes

The key on the graph implies that:

1 image represents 3 boxes

Using the above key, we have:

When 3 boxes are moved from the living room to the bedroom, we have:

Hence, the kitchen and the bedroom will have the same number of boxes

Read more about charts at:

https://brainly.com/question/24741444

#SPJ9

Answer:

x=1 or x=2 or x=3 or x=4

Step-by-step explanation:

x4−10x3+35x2−50x+24=0

Step 1: Factor left side of equation.

(x−1)(x−2)(x−3)(x−4)=0

Step 2: Set factors equal to 0.

x−1=0 or x−2=0 or x−3=0 or x−4=0

x=1 or x=2 or x=3 or x=4

Answer:

I'm pretty sure it is 7.4% or 0.074.

Step-by-step explanation:

Answer:

0.041 = 4.1%

Step-by-step explanation:

The probability the first box has a secret decoder ring is 13/62.

The probability the second box has a secret decoder ring is 12/61.

The probability of both is:

P = (13/62) (12/61)

P ≈ 0.041

I think this is the answer i sorry if i am wrong

Answer:

Step-by-step explanation:

d-b

d=12

b=3

12-3

=9

hope dis helps

Answer:

x < -14

Step-by-step explanation:

Step 1: Subtract 6 from both sides.

Step 2: Divide both sides by -3 and flip the inequality sign.

Therefore, the answer is  x < -14.

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

x<−14

Interval Notation:

(−∞,−14)

hope this helps

Answer:

$0.31.

Step-by-step explanation:

If 1.10 apples cost $3.50, we should divide to find the rate per apple.

1.10/3.5  ≈ 0.31

0.31 is the aproximatley answer, since there is no clear answer (at least not from my work). 0.31*70=21.70

The cost of 70 apples are 0.31.

Answer:

anything that has a numerator three times greater than its denominator. Examples: 3/1, 6/2, 9/3, 12/4, 15/5, so on.

Step-by-step explanation:

When simplifying, you divide both by the denominator and if it equals three, then the fraction is equal to three.

Here is the proof :-

So

Adjacent angle is also equal

Hence

Answer:

$150 = 4 hours,

So, in a ratio, 4 : 150

=> 150 * 4.5 : 4 * 4.5

=> 675 : 18 hours

Therefore to earn $675 at the rate of $150 for 4 hours, Fatima will need to work for 18 hours to earn $675

If my answer helped, kindly mark me as the brainliest!!

Thank You!!

Answer:

-0.5

Step-by-step explanation:

-4x=2

2/-4= -0.5

x= -0.5

Answer:

22.5

Step-by-step explanation:

To find volume, you need to multiply all of the numbers together.

1.5 ft x 3 ft x 5 ft = 22.5

By using the definition of inverse functions, we will see that:

g(g(f(f(f(36))))) = f(36) = 25.

Two functions f(x) and g(x) are inverses if:

f( g(x) ) = x

g( f(x) ) = x

Then we can rewrite:

g(g(f(f(f(36)))))

First, we can see that:

g(f(f(f(36)))) = f(f(36))

Replacing that in our expression, we get:

g(g(f(f(f36))))) = g(f(f(36)))

And the above expression is equal to f(36), to be sure of that, let's replace:

u = f(36)

Then we can rewrite:

g(f(f(36))) = g(f(u))

And by definition, the above thing is equal to u:

g(f(u)) = u = f(36).

Finally, we conclude that:

g(g(f(f(f(36))))) = f(36) = 3*√36 + 7 = 3*6 + 7 = 25

If you want to learn more about inverse functions, you can read:

https://brainly.com/question/12220962

Answer:

D.It is less than 0 because the addends have opposite signs and the positive addend is farther from zero.

Step-by-step explanation:

The given expression is :

When we subtract a larger number from a smaller number, we get a negative answer as mathematically we cannot subtract a larger number from smaller, so we subtract the numbers in standard format and out a negative sign in front of the answer.

Like this given expression will become : -519.70

Now, any negative number is smaller than zero.

Therefore, the correct answer is option D.