What is the value of x in this figure?

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Answer:

radius = [tex]\sqrt{26}[/tex] units

Step-by-step explanation:

The radius r is the distance from the centre to a point on the circle.

Using the distance formula to calculate r

r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (2, 2) and (x₂, y₂ ) = (1, - 3)

r = [tex]\sqrt{(1-2)^2+(-3-2)^2}[/tex]

  = [tex]\sqrt{(-1)^2+(-5)^2}[/tex]

   = [tex]\sqrt{1+25}[/tex]

    = [tex]\sqrt{26}[/tex]

Answer:

right triangle ?

a = 13.288 ?

Step-by-step explanation:

[tex]c^{2}[/tex] - [tex]b^{2}[/tex] = [tex]a^{2}[/tex]

256 - 81 = 175

[tex]\sqrt{175}[/tex] = 13.288

Answer:

a) csc∅ = √53/2

b) cot ∅ = 15/√514

Step-by-step explanation:

a) The value of cot ∅ = -7/2

cos ∅ < 0

We note that cos(∅) is less than 0 in Quadrant II and III, and cot(∅) is less than 0 in the Quadrant II, therefore, we have;

∅ is in the Quadrant II

csc∅ = (√((-7)² + 2²))/2 =√53/2 ≈ 3.64

csc∅ = √53/2

b) cos∅ 15/17

∅ is in Quadrant IV

∴ cot ∅ = 15/(√(15² + 17²)) = 15/√514 ≈ 0.662

cot ∅ = 15/√514

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Answer:

D option

Step-by-step explanation:

Hope this helps

Answer:

(x+4)(x-3)

Step-by-step explanation:

Answer:

(x + 4)(x - 3)

Step-by-step explanation:

Given

x² + x - 12

Consider the factors of the constant term (- 12) which sum to give the coefficient of the x- term (+ 1)

The factors are + 4 and - 3 , since

4 × - 3 = - 12 and 4 - 3 = + 1 , then

x² + x - 12 = (x + 4)(x - 3) ← in factored form

Answer:

The partial sum that models the situation

is Sn=a1(1 - rn)/(1 - r).

n = number of years Mia works this job

an = Mia's salary during her nth year

Sn = total amount Mia earns after n years

r = percent increase, represented as a decimal, plus 1, because the total salary is needed and not just the amount of each increase

Answer:

The partial sum that models the situation

is Sn=a1(1 - rn)/(1 - r).

n = number of years Mia works this job

an = Mia's salary during her nth year

Sn = total amount Mia earns after n years

r = percent increase, represented as a decimal, plus 1, because the total salary is needed and not just the amount of each increase

Step-by-step explanation:

Step-by-step explanation:

2 gallons = 2× 16 = 32 cups

2 gallons = 2 × 128 = 256 fluid ounces

In 32 cups the class aquarium holds 2 gallons of water.

In 256 ounces the class aquarium holds 2 gallons of water.

Proportion is an equation that defines that the two given ratios are equivalent to each other.

In other words, the proportion states the equality of the two fractions or the ratios.

The class aquarium holds 2 gallons of water.

1 gallon = 16 Cups

The class aquarium holds 2 gallons of water in the number of cups is;

2 gallons = 2× 16 = 32 cups

In 32 cups the class aquarium holds 2 gallons of water.

The class aquarium holds 2 gallons of water in the fluid ounces is;

1 gallons = 128 ounces

2 gallons = 2 × 128 = 256 fluid ounces

In 256 ounces the class aquarium holds 2 gallons of water.

Learn more about proportion here;

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Answer:

20 Yellow Counters

Step-by-step explanation:

You can see the clues with how the ratio changes.

To change from (1:4) => (5:1) is not because any were taken away from the value that is the Yellow counters, it is purely because the amount added to the blue counters was so large that they simply simplified the ratio.

The real value of the ratio if reverted back to it's original state would be:

=> (20:4)

95 blue counters is equivalent to 19 in the ratio. We know this because it increased from 1 to 20.

95/19 => 5

Each Ratio in the original one presented is equal to 5.

5 * 4 = 20 Yellow Counters

Answer:

sorry I don't Know ·ω·

Step-by-step explanation:

Answer:

x=22/p

Step-by-step explanation:

1. Add 18 to 4

2. px=22

3. Divide by p to isolate x

4. 22/p=x

Answer:

x = 22 ÷ p

Step-by-step explanation:

px - 18 = 4

px - 18 + 18 = 4 + 18

px = 22

p · x = 22

x · p = 22

x · p ÷ p = 22 ÷ p

x = 22 ÷ p

Answer:

1/8, 0.13,1/2, 7/8 it already is in order

Step-by-step explanation:

Answer:

Step-by-step explanation: 1/8, 0.13,1/2, 7/8 it already is in order

Answer

The answer is y= x-3

- - - - -

5

Explanation

Replace

f(x) with y.

y =5x+3

Swap x and y.

x =5y+3

Solve for y.

x - 3=5y

x-35=y

Answer:

[tex]f(x) = 5x -11[/tex]  and  [tex]g(x) = \frac{x + 11}{5}[/tex]

Step-by-step explanation:

Required

The inverse pairs

Solving (a):

[tex]f(x) = 5x -11[/tex]    [tex]g(x) = \frac{x + 11}{5}[/tex]

Calculate the inverse of f(x)

[tex]f(x) = 5x -11[/tex]

Replace f(x) with y

[tex]y = 5x - 11[/tex]

Swap x and y

[tex]x = 5y - 11[/tex]

Solve for y

[tex]5y = x + 11[/tex]

[tex]y = \frac{x + 11}{5}[/tex]

So, we have:

[tex]g(x) = \frac{x + 11}{5}[/tex]

Hence, f(x) and g(x) in (a) are inverse functions

Others are not

Answer:

f(3) = 9

Step-by-step explanation:

In the given figure,

when x=3,

f(x)=9

substituting x=3 in f(x),

=> f(3)=9

Answer:

option B

Step-by-step explanation:

Option B is in vertex (or graphing ) form.

recall the equation for graphing form of a quadratic is

[tex]y = (x - h)^{2} + k[/tex]

Answer:

2/15

Step-by-step explanation:

1/5 + 2/3

= 3/15 + 10/15

= 13/15

15/15 - 13/15

= 2/15

Answer:

[tex]2x^{2} +bx-3=0[/tex]

Step-by-step explanation:

General form. A quadratic function [tex]f(x)[/tex] is of the form [tex](ax^2+bx+c)[/tex] where [tex]a,b,c[/tex] ∈ R or C and [tex]a[/tex] ≠ [tex]0[/tex].

We obtain an equation when [tex]f(x)=0[/tex]

⇒ [tex]ax^{2} +bx+c=0[/tex] is an quadratic equation.

Solution.

Given, [tex]a=2,c=-3[/tex], but b is not given

Thus the quadratic function with leading coefficient [tex]a=2[/tex] and constant term [tex]c=-3[/tex] is given by

[tex]f(x)=2x^{2} +bx-3[/tex]

∴ the required quadratic equation is

[tex]2x^{2} +bx-3=0[/tex]

Answer:

7

Step-by-step explanation:

70+16x-2

68+16x=180

16x=180-112

x=112/16

x=7

Answer:

x = 7

Step-by-step explanation:

70 + 16x - 2 = 180 degree (being co interior angle)

68 + 16x = 180

16x = 180 - 68

16x = 112

x = 112/16

x = 7

Answer:

See explanation

Step-by-step explanation:

Volume of a cylinder = πr²h

Solve for r

V = π * r² * h

r² = V/πh

Find the square root of both sides

r = √V/πh

If height = 6 meters and volume = 300 cubic meters. Find r

r = √V/πh

= √(300/3.14*6)

= √(300/18.84)

= √15.923566878980

r = 3.9904344223381

Approximately,

r = 4 meters

Answer:

224

Step-by-step explanation:

f(-7) = 4(-7)^2 - 4(-7)

=196 + 28

=224

Answer:

y = 1.44x⁴

Step-by-step explanation:

From the question,

Y∝d²

To remove the proportionality sign we introduce a constant.

Y = kd²............... Equation 1

make k the subject of the equation

k = Y/d²............. Equation 2

Given: Y = 4, d = 10

Substitute these values into equation 2

k = 4/10²

k = 4/100

k = 0.04

Substitute these value of k in equation 1

Y = 0.04d²................ Equation 3

Similarly,

d∝x²,

d = Cx²

make C the subject of the equation

C = d/x²................... Equation 4

Given:  d = 24, x = 2

Substitute into equation 4

C = 24/2²

C = 24/4

C = 6

Hence,

d = 6x²................... Equation 5

Substitute the value of d in equation 5 into equation 3

y = 0.04(6x²)²

y = 0.04(36x⁴)

y = 1.44x⁴

Hence the formula for y in terms of x is y = 1.44x⁴

Answer:

Step-by-step explanation:

Right is into positive territory.

y = x^2

Going right into positive territory means that the function becomes

y = (x - 12)^2

You need the value that will make x - 12 = 0. That number is 12.

Answer:

She will need to pay $206.50 per month.

Step-by-step explanation:

Divide the total cost ($2,478) by the number of months (12 mos) to obtain Sam's monthly payment:

 $2,478

---------------- = $206.50/month

12 months

She will need to pay $206.50 per month.

Answer:

(x+1)^2 + (y-7)^2 = 2^2

Step-by-step explanation:

The center of the circle is at (-1,7) and the radius from the center to the edge is 2, so the equation should look like (x-h)^2 + (y-k)^2 = r^2

You would flip the signs of the center so that when you solve the equation it ends up in the correct place.

Answer:

D) cot(C) = 1/2.

Step-by-step explanation:

We can go through each choice and examine is validity.

Choice A)

We have:

[tex]\displaystyle \sec B=\frac{3}{7}[/tex]

Recall that secant is the ratio of the hypotenuse to the adjacent.

With respect to B, the adjacent is 6 and the hypotenuse is 7.

Therefore, sec(B) should be 7/6 instead.

A is incorrect.

Choice B)

We have:

[tex]\displaystyle \cot B=\frac{3}{2}[/tex]

Cotangent is the ratio of the adjacent side to the opposite.

With respect to B, the adjacent side is 6 and the opposite side is 3.

Therefore, cot(B) = 6/3 = 2.

B is incorrect.

Choice C)

C is incorrect for the reasons listed in A.

Choice D)

We have:

[tex]\displaystyle \cot C=\frac{1}{2}[/tex]

Again, cotangent is the ratio of the adjacent side to the opposite.

With respect to C, the adjacent side is 3 and the opposite side is 6.

So, cot(C) = 3/6 = 1/2.

Therefore, D is the correct choice!

Answer:question AB +BD= AD

BC+CE=BE

Step-by-step explanation:

segment addition postulate