For the function f(x) = −3x + 1, what is the value of f −1(x) for x = 4?

Answer:

30.67 inches

Step-by-step explanation:

Area of a triangle: 1/2 x b x h

115 = 1/2 x b x 7.5

115 = 3.75b

115/3.75 = b

30.66666 = b

30.67 = b

The equation that is true for x = -6 and x= 2 is given by: Option B: 2x^2 +8x -24 = 0

Suppose there is an equation given, involving some variables.

Then, those values of the involved variable, for which the equation is true, are called solution of the equation.

For single variable equations, specially for polynomials, these solutions are called the roots of the equation.

Suppose that the given quadratic equation is

[tex]ax^2 + bx + c = 0[/tex]

Then its roots are given as:

[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

For this case, the options are all quadratic equations, so we can check all the options to find the roots to see if they match to x = -6 and  = 2

Then its roots are given as:

[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \dfrac{-(-16) \pm \sqrt{(-16)^2 - 4(2)(12)}}{2(2)}\\\\x = \dfrac{16 \pm \sqrt{196 - 96}}{4} = \dfrac{16 \pm 10}{4}\\\\x = 26/4, x = 6/4[/tex]

Thus, this equation isn't true for both x = -6 and x= 2

Then its roots are given as:

[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \dfrac{-8 \pm \sqrt{(8)^2 - 4(2)(-24)}}{2(2)}\\\\x = \dfrac{-8 \pm \sqrt{64 +192}}{4} = \dfrac{-8 \pm 16}{4}\\\\x = -6, x = 2[/tex]

Thus, this equation is true for both x = -6 and x= 2

Since the question says "Which equation is true", so that means only one option is true.

Thus, the equation that is true for x = -6 and x= 2 is given by: Option B: [tex]2x^2 +8x -24 = 0[/tex]

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Answer:

b

Step-by-step explanation:

edge

Answer:

Diameter = 14 cm

Circumference = 44 cm

Step-by-step explanation:

[tex]\pi {r}^{2} = 154 \\ {r}^{2} = \frac{154}{\pi} \\ r = \sqrt{ \frac{154}{\pi} } \: cm[/tex]

[tex]Diameter = 2r \\ = 2 \sqrt{ \frac{154}{3.142} } \\ ≈ 14 \: cm[/tex]

[tex]Circumference = πd \\ = 14\pi \\ = 14 \times 3.142 \\ = 43.988 \\ ≈ 44 \: cm[/tex]

Answer:

x= 89°

Step-by-step explanation:

Let's use the rule of corresponding angles.

x+ 32°= 121° (corr. ∠s)

x= 121° -32°

x= 89°

Using proportions, it is found that she needs 4 consecutive hits to raise her batting average to .400.

A proportion is a fraction of a total amount.

Hence, the batting average is given by the number of hits divided by the number of at-bats.

If she gets x consecutive hits, she will have 8 + x hits in 25 + x at-bats, for an average of 0.400, hence:

[tex]0.4 = \frac{8 + x}{25 + x}[/tex]

8 + x = 10 + 0.4x

0.6x = 2

x = 3.33

Rounding up, she needs 4 consecutive hits to raise her batting average to .400.

More can be learned about proportions at https://brainly.com/question/24372153

Answer:

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Step-by-step explanation:

Answer:

that would be 700ft^2

Step-by-step explanation:

The rectangle on top has area of 23 × 14 = 322ft^2
the rectangle on bottom has area of 23 × 12 = 276ft^2

Two triangles make 1 rectangle with area 17 × 12 = 102ft^2

Add them all up 700ft^2

Answer:

that would be 700ft^2

Step-by-step explanation:

The rectangle on top has area of 23 × 14 = 322ft^2

the rectangle on bottom has area of 23 × 12 = 276ft^2

Two triangles make 1 rectangle with area 17 × 12 = 102ft^2

Add them all up 700ft^2

Answer:

0

Step-by-step explanation:

use a slope calculator

Answer:

427

Step-by-step explanation:

i could be wrong i used surface area calculator

Answer:

D i think a number represents x. not sure

Answer:

8x+5

Assume x is the unknown number.

8x+5 means

8*x = a number multiplied by eight

8x+5 = a number multiplied by eight eight then added to five.

Therefore, the correct option is D.

Answer:

-11

Step-by-step explanation:

The | | around a number means the absolute value of that number. The absolute value is the positive value of the number given.

The probability Amelie spins either an odd number or a red number is:

P = 4/5

We want to find the probability of spinning a red or odd number, this is equal to the quotient between the number of odd numbers + the number of red numbers and the total number of numbers in the spinner.

Then there are 5 + 3 = 8 numbers that are either red or odd, and a total of 10 numbers, this means that the probability of spinning an odd number or a red number is:

P = 8/10 = 4/5

If you want to learn more about probability, you can read:

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Answer: The dimensions of the builder's scale drawing is 40 x 32 inches.

Step-by-step explanation:

The scale factor of Karl = 1:12

Dimensions = 10 x 8 inches

Area = 80 square inches

1:12 = 1/12

1/12 = 80/a

a = 80 x 12

a = 960 square inches

So dimensions are 120 x 96 inches

Builders scale factor = 1:3

Actual Length = 120inches

Actual width = 96 inches

Builders drawing length = 120/3

= 40 inches

Builders drawing width = 96/3

= 32 inches

The question is an illustration of arrangements, and the number of possibilities of the password is 65000

The length of the password is:

Length = 4

If the password begins and ends with a letter and cannot be repeated, then the possibilities are:

First = 26

Last = 25

If the password contains numbers that can be repeated, then the possibilities are:

Number 1 = 10

Number 2 = 10

So, the number of possibilities is:

Possibilities = 26 * 10 * 10 * 25

Evaluate the product

Possibilities = 65000

Hence, there are 65000 possibilities of a 4 character password

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The total interest consumer pay on the credit card which has a daily interest rate of 0.042% is $32.08.

Compound interest is the amount charged on the principal amount and the accumulated interest with a fixed rate of interest for a time period.

The formula for the final amount with the compound interest formula can be given as,

[tex]A=P\times\left(1+\dfrac{r}{100}\right)^{t}\\[/tex]

Here, A is the final amount (principal plus interest amount) on the principal amount P of with the rate r of in the time period of t.

In the given problem,

Put these values in the above formula as,

[tex]A=2530.16\times\left(1+\dfrac{0.042}{100}\right)^{30}\\\\A=2562.24[/tex]

The interest amount paid is,

[tex]I=A-P\\I=2562.24-2530.16\\I=32.08[/tex]

Thus, the total interest consumer pay on the credit card which has a daily interest rate of 0.042% is $32.08.

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Answer:

The correct answer is C

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

If two of the half planes never intersect, there is no way for the lines to reach each other hence giving no soultion

Answer:

its false

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

25*2

60% is double 30% so 60% of the number would be 50

Answer:

[tex]y = \frac{5}{3} x - 5[/tex]

Step-by-step explanation:

To write an equation in the slope-intercept form, we need the slope (which can also be calculated) and at least a coordinate.

What is slope-intercept form?

x- intercept occurs at y= 0 while y-intercept occurs at x= 0. With this information, let's write out the two coordinates given.

With two coordinates, we can calculate the slope using the equation below.

[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]

[tex]slope = \frac{ - 5 - 0}{0 - 3} [/tex]

[tex]slope = \frac{ - 5}{ - 3} [/tex]

[tex]slope = \frac{5}{3} [/tex]

Substitute the value of the slope into m in the equation.

[tex]y = \frac{5}{3} x + c[/tex]

Given that the y-intercept is -5, c= -5.

[tex]y = \frac{5}{3} x - 5[/tex]

Answer:

Disagree

radius = 7 m

diameter = 14 m

Step-by-step explanation:

Formula

[tex]\sf Area\:of\:a\:circle=\pi r^2[/tex]

Given:

Substitute given value into the formula and solve for r:

[tex]\sf \implies \pi r^2=153.88[/tex]

[tex]\sf \implies r^2=\dfrac{153.88}{\pi}[/tex]

[tex]\sf \implies r=\sqrt{\dfrac{153.88}{\pi}}[/tex]

[tex]\sf \implies r=6.998680253[/tex]

Therefore r ≈ 7 m

So I disagree with Nysean, as from my calculations, the approximate radius of the merry-go-round is 7 m.

Diameter = 2r

⇒ diameter of merry-go-round = 2 x 7 = 14m

So Nysean has actually given the approximate measure of the diameter rather than the radius.

Answer:

44.44%

Step-by-step explanation:

The fraction 6/10 and 4/10 can be represented by using the objects laid together to form a square.

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

The fraction 6/10 and 4/10 can be represented by using the objects laid together to form a square.

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#SPJ1

Answer:

y = -1/2x + 19/2

Step-by-step explanation:

Hi there!

We are given the points (9,5) and (7,6)

We want to write an equation of the line that contains these two points, in slope-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

First, let's find the slope of the line

The formula for the slope (m) calculated from 2 points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points

We have everything we need to find the slope, but let's label the values of the points to avoid any confusion.

[tex]x_1=9\\y_1=5\\x_2=7\\y_2=6[/tex]

Now substitute these values into the formula to find the slope

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

m=[tex]\frac{6-5}{7-9}[/tex]

Subtract

m=[tex]\frac{1}{-2}[/tex]

m=-1/2

The slope of the line is -1/2

We can substitute this as m into the formula for slope-intercept form:

y = -1/2x + b

Now we need to find b

As the equation passes through (9, 5) and (7, 6), we can use either one to solve for b

Taking (7, 6) for example:
Substitute 7 as x and 6 as y into the equation

6 = -1/2(7) + b

Multiply

6 = -7/2 + b

Add 7/2 to both sides

19/2 = b

substitute 19/2 as b:

y = -1/2x + 19/2

Hope this helps!

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the answer of the year is 20%

Answer:

this is the unit area of: 24

Step-by-step explanation: hope this helps

Answer:

a: 13 + t = 17

Step-by-step explanation:

the top is equal to the bottom

the top is 13 and t together but you are not multiplying

thus the answer is 13 + t = 17

Answer:

A, 13+t=17

Step-by-step explanation:

Since you are trying to find the missing part of the diagram and both rows add up to 17, the answer would be A. This is the case because you aren't multiplying 13 over and over to get 17, rather instead you are adding a number to get 17.

Answer:

the distance between -4 and -14 is 10

Step-by-step explanation:

they both as negative numbers

Distance = 10

⇒ Distance = Larger integer - Smaller integer

In this case, the larger integer is -4 and the smaller integer is -14. Keep in mind that if two integers are negative, the integer that is closest to 0 is greater than the other integer.

⇒ Distance = (-4) - (-14)

Simplify the expression on the R.H.S:

⇒ Distance = -4 + 14                                                            [-1 x -1 = 1]

⇒ Distance = 10

Answer:

2.4

Step-by-step explanation:

1/5=0.2

7.2/3=2.4

[tex]3v^2-10v+3=0\\\\\implies 3v^2 - 9v-v +3=0\\ \\\implies 3v(v-3)-(v-3)=0\\\\\implies (v-3)(3v-1)=0\\\\\implies v = 3,~~v=\dfrac 13[/tex]