3.
Which is the inverse of the function f(x) = x2 - 4?

Answer:

8+8+55+55+88

Step-by-step explanation:

The surface area is the sum of all the sides

We have 5 sides

Top and bottom are the same

The area of the top is

1/2 bh = 1/2 (8)(2) = 8

The left and right sides are the same

The area of the left side is

5*11 = 55

The area of the front is

8*11 = 88

The sum of all the 5 sides are

top + bottom + left + right + front

8+8+55+55+88

Answer:

8 + 8 + 55 + 55 + 88

Step-by-step explanation:

Calculate area of base.

8 × 2 × 1/2 = 8

There are two triangles:

8 + 8

Calculate area of rectangle.

8 × 11 = 88

Calculate the areas of two rectangles.

5 × 11 = 55

55 + 55

Answer:

Step-by-step explanation: I hope it helps :)

1.

[tex]Surface\: area=\:2\pi rh+2\pi r^2\\h = 2ft\\diameter = 2ft\\Radius = d/2=2/2=1ft\\\\A=( 2\times 3.141\times1\times2)+(2\times 3.141 \times 1^2)\\A = (12.564)+(6.282)\\A = 18.846\\A = 18.85ft^2[/tex]

2.

[tex]Area \:of\: square = A=a^2\\A = 3^2\\A=9\\Area\:of \:one \:rectangle\: = (l\times b)\\ A = (8\times 3)\\A = 24cm^2\\\\A = 2(Area\: of\: square)+2(Area\: of \:rectangle)\\A = 2(9)+4(24)\\A = 18+96\\A =114cm^2[/tex]

3.

[tex]Area \: of\: base=?\\ r = 7\:in\\h = 12\:in\\A = \pi \times r^2\\A = 3.141 \times 7^2\\A = 153.909\\\\Height \: of \:the \:cylinder = 12\:inches\\Circumference = 2\pi \times r\\C= 2 \times 3.141 \times 7\\ C =43.98\\\\S.A= 2B+Ch\\S.A = 2(153.909)+43.98(12)\\S.A = 307.818+527.76\\S.A =835.578[/tex]

4.

[tex]Perimeter = a+b+c\\P = 10+8+6\\P = 24\\S.A =2B+Ph\\S.A = 2(24)+24(8)\\S.A =48+192\\S.A = 240\:yd^2[/tex]

Answer: 0.00000565

Step-by-step explanation:

Required to win:

6 number match $10,000

5 number match $ 5,000

4 number match $ 1000

3 number match $ 5,00

2 number match $ 50

1 number match $ 10

Therefore, to win $10,000 ;

All 6 numbers must match

Number of right numbers = 6

Total numbers = 25

Since it is without replacement :

Probability = required outcomes / Total possible outcomes

P(First number match) = 6/25

P(second number match) = 5/24

P(third number match) = 4/23

P(fourth number match) = 3/22

P(fifth number match) = 2/21

P(sixth number match) = 1 / 20

Therefore, Probability of winning $10000 :

(6/25) * (5/24) * (4/23) * (3/22) * (2/21) * (1/20) = 720 / 127512000 = 0.0000056465

= 0.00000565

Answer:

h=3√3 cm

Step-by-step explanation:

An equilateral triangle has 3 Equal sides

The height of an equilateral triangle with side a =a√3/2

That is,

h=a√3/2

Where,

h=height of the equilateral triangle

a=side length

From the triangle given,

a=6cm

Therefore,

h=6√3/2

=3√3

h=3√3 cm

Answer:

work is shown and pictured

Answer:

case 1

3x-7y=9

-4x+5y=1

using a graph tool

the solution is the point (-4,-3)------------------> one solution

case 2

y=6x-2

y=6x-4

two parallel lines

the system has no solution---------------> zero solution

case 3

-5x+y=10

-25x+5y=50

is the same line----------------> infinite solutions

Answer:

[tex]\frac{\left(a^3\right)\left(a^9\right)}{a^4}=a^8[/tex]

Step-by-step explanation:

[tex]\frac{\left(a^3\right)\left(a^9\right)}{a^4}\\\\= \frac{a^3a^9}{a^4}\\\\=a^3a^9\\\\=a^{3+9}\\\\=a^{12}\\\\=a^{12-4}\\=a^8[/tex]

Answer:

a⁸

Step-by-step explanation:

a³*a⁹/a⁴

Product law:Says that if the base of the number being multiplied is the same, then we can add the exponents

Therefore

a to the power of 3+9/a⁴

a¹²/a⁴

Quotient law:Says that when we divide two numbers with the same base,we can subtract the exponents

Therefore

a to the power of 12-4

a⁸

Answer:

The Horizontal Asymptote is at x=3

Step-by-step explanation:

Here is a way to remember this

One way to remember this is the following pnemonic device: BOBO BOTN EATS DC

EABOBO -Exponents are bigger on bottom, y=0

EABOTN -Exponents are bigger on top, none

EATS DC - Exponents are the same, divide coefficients

3/x-2 the exponents are the same, divide leading coefficients

3/1 = 3 the horizontal asymtote is at x=3

Answer:

V = 42 units ^3

Step-by-step explanation:

The volume of a rectangular prism is

V =Bh

V = 8*5 1/4

Changing to a mixed number

V = 8* ( 5*4+1) /4

   =8*21/4

    = 42 units^3

Answer:

[tex]\huge\boxed{V=42\ u^3}[/tex]

Step-by-step explanation:

Th formula of a volume of a prism:

[tex]V=BH[/tex]

B - base

H - height

We have

[tex]B=8;\ H=5\dfrac{1}{4}=\dfrac{5\cdot4+1}{4}=\dfrac{20+1}{4}=\dfrac{21}{4}[/tex]

Substitute:

[tex]V=(8)\left(\dfrac{21}{4}\right)[/tex]    simplify 8 and 4

[tex]V=(8\!\!\!\!\diagup)\left(\dfrac{21}{4\!\!\!\!\diagup}\right)=(2)(21)=42[/tex]

Answer:

[tex]x^2 + y^2 + 4x + 4y = -119/16[/tex]

Step-by-step explanation:

The axes x and y are calibrated in 0.25

If the circle is carefully considered, the radius r of the circle is:

r = -1.25 - (-2)

r = 0.75 units

The equation of a circle is given by:

[tex](x - a)^2 + (y - b)^2 = r^2[/tex]

The center of the circle (a, b) = (-2, -2)

Substituting  (a, b) = (-2, -2) and r = 0.75 into the given equation:

[tex](x - (-2))^2 + (y - (-2))^2 = (3/4)^2\\\\(x + 2)^2 + (y + 2)^2 = (3/4)^2\\\\x^2 + 4x + 4 + y^2 + 4y + 4 = 9/16\\\\x^2 + y^2 + 4x + 4y + 8 = 9/16\\\\16x^2 + 16y^2 + 64x + 64y + 128 = 9\\\\16x^2 + 16y^2 + 64x + 64y = -119\\\\x^2 + y^2 + 4x + 4y = -119/16\\[/tex]

Answer:

Subtract 3 and one-fifth from both sides of the equation

Step-by-step explanation:

Well to find n you gotta separate it.

3 1/5 + n = 9

-3 1/5

n = 5.8

Thus,

to seperate it you subtract 3 1/5 from both sides.

Answer:

Subtract 3 and one-fifth from both sides of the equation

Step-by-step explanation:

Answer: sample space

Step-by-step explanation: In determining the probability of a certain event occurring or obtaining a particular outcome from a set of different possible outcomes, such as in the toss of coin(s), rolling of fair die(s), the sample space comes in very handy as it provides a simple breakdown and segmentation of all possible events or outcomes such that in Calculating the probability of occurrence of a certain event, the event(s) is/are located in the sample space and the ratio taken over the total number of events.

Answer:

[tex]\overline{DF}[/tex] could be a midsegment of ∠ABC.

Step-by-step explanation:

A midsegment of a triangle must be two things:

1. Parallel to the 3rd side, in this case, [tex]\overline{AD}[/tex].

2. Half the length of the 3rd side, in this case, [tex]\overline{AD}[/tex].

Since we don't know the lengths, we can only go off of 1. There is only one line that is parallel to  [tex]\overline{AD}[/tex] and it is [tex]\overline{DF}[/tex].

Hope this helped!

Answer: 3 feet²

Step-by-step explanation:

Simply do 2*18 (In a rectangle A = l*w) to get 36 inches, or 36/12 feet, or 3 feet.

Hope it helps <3

Answer:

Width = 1.5 Inches

Step-by-step explanation:

Original Height: 24 Inches

Original Width: 18 Inches

Given Height: 2 inches

24 divided by 2 = 12. This means the poster was dilated by 12.

18 divided by 12 = 1.5

Answer:

The volume of the figure is approximately 1244 in³

Step-by-step explanation:

The figure is formed by a rectangular prism and a hemisphere, therefore its total volume is formed by the the sum of the volume of each of these forms. The volume of a rectangular prism can be found by using the expression:

[tex]V_{rect} = length*width*height[/tex]

While the volume of a hemisphere is given by:

[tex]V_{hemis} = \frac{2}{3}*\pi*r^3[/tex]

The radius of the hemisphere is the difference between the total length of the figure and the length of the prism, therefore:

[tex]r = 17 - 11 = 6 \text{ in}[/tex]

We can now find the volume of the figure:

[tex]V = V_{rect} + V_{hemis}\\V = 11*6*12 + \frac{2}{3}*\pi*(6)^3\\V = 792 + 144*\pi\\V = 792 + 452.39\\V = 1244 \text{ in}^3[/tex]

Answer:

  (x +1)^2 + (y +2)^2 = 25

Step-by-step explanation:

A diagram of the given triangle shows you it has side lengths of 3 and 4, so the square of the hypotenuse is ...

  (AC)^2 = (AB)^2 +(BC)^2 = 3^2 +4^2

  (AC)^2 = 25

The center of the circle is at A(-1, -2), so the equation is ...

  (x -h)^2 +(y -k)^2 = r^2

for the circle centered at (h, k) with radius r.

We know that the square of the radius (r^2) is 25, so we can write the equation as ...

  (x +1)^2 +(y +2)^2 = 25

Answer:

(x + 1)2 + (y + 2)2 = 25

Step-by-step explanation:

Hope this helps :)

Answer:

Answer:

1196cm³

Step-by-step explanation:

Step 1

Find the volume of the Rectangular Prism = Length × Width × Height

Length = 12 cm

Width = 20 cm

Height = 5 cm

Volume of a Rectangular prism = 12 × 20 × 5

= 1200cm³

Step 2

Volume of the Eraser

The Eraser has the shape of a box.

Volume = Length × Width × Height

Length = 0.5 cm

Width = 2 cm

Height = 4 cm

Volume = 4cm³

Step 3

Find the volume of the art box not taken up by the eraser

Volume of the art box not taken up by the eraser = Volume of the Art box - Volume of the Eraser

= 1200cm³ - 4cm³

= 1196cm³

Therefore, volume of the art box not taken up by the eraser is 1196cm³

Answer:

Step-by-step explanation:

The ceiling function is a python programming function that rounds a decimal point number to the nearest whole number.

Given the function expression  f(1.5), the ceiling function will round 1.5 to the nearest whole number which is 2

Answer:

24

Step-by-step explanation:

90/7 ÷ 1 3/4

Change to an improper fraction

90/7 ÷ ( 4*1 +3 ) /4

90/7 ÷ 7/4

Copy dot flip

90/7 * 7/4

90/4

22.5

Best estimate is 24

Answer:

A:2

Step-by-step explanation:

A is the answer because 90 divided by 7 is 12.8 which would be 13, and the 1 and 3/4 would be 7. 13 divided by 7 would equal 1.85. When rounded your answer would be 2.

Answer:

A. g(x)=1/2x²

Step-by-step explanation:

Given:

f(x)=x²

We have to find g(x)

Since, we are given that g(2)=2

1. g(x)=1/2x²

x=2

g(x)=1/2(2)²

=1/2(4)

=4/2

=2

2. g(x)=1/4x²

x=2,

g(x)=1/4(2)²

=1/4(4)

=4/4

=1

3. g(x)= 2x²

at x=2,

g(x)=2(2)²

=2(4)

=8

4. g(x)=(1/2x)²

x=2

g(x)={1/2(2)}²

=(1/4)²

=1/16

A. g(x)=1/2x² is the answer

Answer:

True.

Step-by-step explanation:

In t-test test the value of t can be either negative or positive.

If value of t is negative, then it lies to the left of the mean.

If value of t is Positive, then it lies to the right of the mean.

The given statement is "When you conduct a t test, the calculated value of t can be negative.".

Therefore, the given statement is true.

Answer:

Step-by-step explanation:

Because of the Isosceles Triangle Theorem, both the base angles of that triangle measure a. We also know that a + b = 180 because of the definition of supplementary angles. So we have 2 equations from that info. First is the fact that

a + 7x = 180 and the second is

2x + a + a = 180 because of the Triangle Angle-Sum Theorem. If the left side of the first equation = 180 and the left side of the second equation also = 180, then by the transitive property of equality,

a + 7x = 2x + a + a and

a + 7x = 2x + 2a and

5x = a. Now that we know that a = 5x, we go back to our triangle and fill in 5x as a:

5x + 5x + 2x = 180 (the Triangle Angle-sum Theorem again) and

12x = 180 so

x = 15. If x = 15, then

a = 5(15) = 75,

b = 7(15) = 105, and

c = 2(15) = 30

Answer:

Area = 19.9 mm²

Step-by-step explanation:

Step 1: Find Angle V.

m < V = 180 - (131 + 27) (sum of angles in a triangle)

V = 22°

Step 2: Find UW using the law of sines.

[tex] \frac{UW}{sin(V)} = \frac{UV}{sin(W)} [/tex]

Plug in your values

[tex] \frac{UW}{sin(22)} = \frac{8}{sin(27)} [/tex]

Multiply both sides by sin(22) to solve for UW

[tex] \frac{UW*sin(22)}{sin(22)} = \frac{8*sin(22)}{sin(27)} [/tex]

[tex] UW = \frac{8*sin(22)}{sin(27)} [/tex]

[tex] UW = 6.6 mm [/tex]

Step 3: Find the area of ∆UVW

Area = ½*UW*UV*Sin(U)

Area = ½*6.6*8*sin(131)

Area = 3.3*8*sin(131)

Area = 19.9 mm² (to the nearest tenth)

Answer:

17 feet

Step-by-step explanation:

[tex]15^{2}+8x^{2} = x^{2} \\225 + 64 = x^{2} \\289 = x^{2} \\17 = x[/tex]

Answer:

144°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 10, thus

sum = 180° × 8 = 1440°

Each interior angle = 1440° ÷ 10 = 144°

Answer:

144 deg

Step-by-step explanation:

Sum of the measures of the angles of a polygon with n sides:

(n -2)180

For a 10-sided polygon, n = 10.

The sum of the measures is

(10 - 2)180 = (8)180 = 1440

Since the polygon is regular, all angles have the same measure, so the measure of 1 angle is

1440/10 = 144

Answer: 144 deg

Answer:

Plug in the x and y values into the equation

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

Evaluate!

5(5)-3

25-3

22

Answer:

x = [tex]\frac{22}{3}[/tex]

Step-by-step explanation:

Given that y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = - 6 when x = 2, then

- 6 = 2k ( divide both sides by 2 )

- 3 = k

y = - 3x ← equation of variation

When y = - 22, then

- 22 = - 3x ( divide both sides by - 3 )

x = [tex]\frac{-22}{-3}[/tex] = [tex]\frac{22}{3}[/tex]

Answer:

≈23.66

Step-by-step explanation:

Height ---> x

base ---> 5x

Formula for area of triangle: (base*height)/2

((5x)(x))/2 = 1400

[tex]5x^{2}[/tex]/2 = 1400

[tex]5x^{2}[/tex] = 1400 · 2 = 2800

[tex]x^2[/tex] = 2800/5 = 560

x= √560 ≈ 23.66

Answer:

30.6

Step-by-step explanation:

The following data were obtained from the question:

Angle θ = 23°

Opposite = 13

Adjacent = y

The value of y can be obtained by using the following trig ratio:

Tan θ = Opposite /Adjacent

Tan 23° = 13/y

Cross multiply

y × Tan 23° = 13

Divide both side by Tan 23°

y = 13/Tan 23°

y = 30.6

Therefore, the value of y in the diagram above is 30.6