Geometry
What is the range of possible values for x? The diagram is not to scale.

Answer:

x = 2

Step-by-step explanation:

Given that the measure of segment BC must equal the addition of the measure of segment BA plus the measure of segment AC, we can write this in equation form:

BC = BA + AC

then we replace them with the measure information they provide:

12 x + 4 = 7 x - 4 + 8 x + 2

and we solve for x in the equation:

12 x + 4 = 15 x - 2

subtract 12 x from both sides:

4 = 15 x - 12 x - 2

4 = 3 x - 2

add 2 on both sides

4 + 2 = 3 x

6 = 3 x

x = 6/3

x = 2

Answer:

Step-by-step explanation:

5.23x+3.76-3.67x+6.39

x(5.23-3.67) +(3.76+6.39)

1.56x + 10.15

Answer:

1.56x + 10.15

Step-by-step explanation:

(5.23x + 3.76) – (3.67x – 6.39)

(a + b) – (c – d) = a + b – c + d

Remove the parentheses and change the signs as needed:

5.23x + 3.76 – 3.67x + 6.39.

Group the like terms and simplify:

5.23x – 3.67x + 3.76 + 6.39

1.56x +10.15.

Answer:

Hence the width, length is 20 cm and height is 10 cm

Step-by-step explanation:

Since the box has a square base, let length = width = x. Also, let the height = y, therefore:

The volume of box = width * length * height

4000 = x * x * y

4000 = x²y

y=4000/x²

The surface area (SA) = area of the base + sum of the area of each side

SA = x² + xy + xy + xy + xy

SA = x² + 4xy

substitute y = 4000/x²

SA = x² + 4x(4000/x²)

SA = x² + 16000/x

Taking the derivative:

SA' = 2x - 16000/x²

making SA' = 0:

0 = 2x - 16000/x²

2x = 16000/x²

2x³ = 16000

x³ = 8000

x = 20 cm

y = 4000 / x² = 4000 / 20² = 10 cm

Hence the width, length is 20 cm and height is 10 cm

Answer:

44 in

Step-by-step explanation:

Perimeter is adding up all the sides together and since we know it is a square that means each side is equal

11 in + 11 in + 11 in + 11 in = 44 in

Answer:

I think its 15600..

Step-by-step explanation:

Answer:

r=0

Step-by-step explanation:

the line passes through the origin which means there is no y-intercept

Answer:

100 + 80

Step-by-step explanation:

Answer:

100/35 = 2

35 goes into 100 2 times

Step-by-step explanation:

Answer:

x=242/3

alternative form= 80 2/3, x=80.6

Step-by-step explanation:

3x-4y=242

substitute y = 0

3x-4x0=242

calculate the product

3x-0=242

remove 0

3x=242

divide both sides (by 3 in order to leave x by itself)

done

Answer:

2(30-7x)

Step-by-step explanation:

=14+14x-65-9

=14+14x-79

=60+14x

=2(30-7x)

Answer:

13 pages : 1/2 hour Multiply both sides by 2

26 pages : 1 hour ------>> 26 pages/hr

Flip over 26 pages/hr ----->>> hr / 26 pages = 1 hr / 26 pages

Split up the fraction: (1/26) hr / page

Answer:

26

Step-by-step explanation:

13 in 1/2 hour

13:1/2

26:1

Answer:

im gonna go with yes

Step-by-step explanation:

Answer:

is what a perfect square?

Step-by-step explanation:

there is no pic attached

Answer:

Step-by-step explanation:

Step 1             f(x) = [tex]\frac{3x+4}{8}[/tex]                 Given

Step 2            y = [tex]\frac{3x+4}{8}[/tex]                    Change f(x) to y

Step 3            x = [tex]\frac{3y+4}{8}[/tex]                    Switch x and y

Step 4            8x = 3y + 4              multiply each side by 8

Step 5            8x - 4 = 3y               Subtract 4 from each side

Step 6            [tex]\frac{8x-4}{3}=y[/tex]                   Divide by 3 on each side

Step 7            [tex]\frac{8x-4}{3}=f^{-1}(x)[/tex]           Replace y by [tex]f^{-1}(x)[/tex]

Therefore, inverse of the function will be,

[tex]\frac{8x-4}{3}=f^{-1}(x)[/tex]

Sofia made a mistake in step 6. She should have divided both the sides by 3 instead of multiplying each side by 3.

Sophia has made mistake in step 6. She should have divided each side by 3 instead of multiplying.

The given function is [tex]f(x)=\dfrac{3x+4}{8}[/tex].

It is required to calculate the inverse of the function.

So, the steps involved in finding the inverse of the function will be,

Step 1:

Write the given function as,

[tex]f(x)=\dfrac{3x+4}{8}[/tex]

Step 2:

Change the function f(x) to y as,

[tex]y=\dfrac{3x+4}{8}[/tex]

Step 3:

Switch x and y as,

[tex]x=\dfrac{3y+4}{8}[/tex]

Step 4:

Multiply each side of the equation by 8 as,

[tex]8x=8\dfrac{3y+4}{8}\\8x=3y+4[/tex]

Step 5:

Now, subtract 4 from each side of the equation as,

[tex]8x-4=3y+4-4\\8x-4=3y[/tex]

Step 6:

Now, it is required to divide each side by 3.

[tex]\dfrac{8x-4}{3}=\dfrac{3y}{3}\\\dfrac{8x-4}{3}=y[/tex]

Step 7:

Now, replace y with [tex]f^{-1}(x)[/tex] as,

[tex]\dfrac{8x-4}{3}=f^{-1}(x)[/tex]

So, the required inverse function should be [tex]f^{-1}(x)=\dfrac{8x-4}{3}[/tex].

Therefore, Sophia has made mistake in step 6. She should have divided each side by 3 instead of multiplying.

For more details, refer to the link:

https://brainly.com/question/19606498

This should be what you're looking for.

Answer:

[-2, 5)

Step-by-Step Explanation:

The solution set of the given inequality {x ;-2 ≤ x < 5} will be; [-2, 5).          

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

Given that the inequality y = {x ; -2 ≤ x < 5}

WE are asked to find the solution set for the given inequality;

⇒ y={x ; -2 ≤ x < 5} i.e domain= [-2, 5)

⇒y=x ∀ x ∈ [-2, 5)

The solution of the given inequality;

x ∈ [-2, 5)

Therefore, The solution set of the given inequality {x ;-2 ≤ x < 5} will be; [-2, 5).          

Learn more about inequality here:

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Answer:

Never applies

Step-by-step explanation:

Given

Argument: The sum of a number and its opposite is always 1

Assume a positive number x

The opposite of the number is negative x (i.e. -x)

The sum of both numbers is:

[tex]Sum = x + (-x)[/tex]

Open Bracket

[tex]Sum = x -x[/tex]

[tex]Sum = 0[/tex]

Now, take for instance.

[tex]Number = 5[/tex]

Opposite would be

[tex]Opposite = -5[/tex]

Their sum is:

[tex]Sum = 5 + (-5)[/tex]

[tex]Sum = 5 -5[/tex]

[tex]Sum = 0[/tex]

Another instance is:

[tex]Number = -8[/tex]

Opposite would be

[tex]Opposite = 8[/tex]

Their sum is;

[tex]Sum = -8 + 8[/tex]

[tex]Sum = -0[/tex]

Hence, the argument never applies because the sum is never 1

Answer:

y=mx+b is slope-intercept form

where m is the slope and b is the y intercept.

Since the line crosses the y axis at 0,0 the intercept is +0 or just nothing.

now all we need to do is find the slope

to do that just go from the y intercept (the first point) y units up and x units over untill u cross at the next point. for examples from (0, 0) to (1, 8)-the next point- i need to go up 8 units up and 1 unit over. this is described as rise over run and that is your slope 8/1 rise/run. rise is how many units i go up (or down) from the y intercept until the next point that lies on the line and run is how far i need to go over from how many units i just went up. If u continue to go 8 up and 1 over from each point u will see that u get a point lying of the line. This is why 8/1 is your slope

8/1 is the slope and 0,0 is your y intercept so we put nothing

the equation is y=8x

Step-by-step explanation:

Answer:

y=8x

Step-by-step explanation:

Pick two points (0,0) (2,16)

Then 16-0/2-0= 8

8 is the slope

The y intercept is 0 so

y=8x

Answer:

20.4 miles

Step-by-step explanation:

Answer: 20.4

Step-by-step explanation: How many more miles is 27.2 than 6.8

usually these kind of equations mean to subtract, in other terms find the underlined key words

27.2-6.8= 20.4

Answer:

.75

Step-by-step explanation:

there is prof

Answer:

Since the slope of KM and ST are different, they are not parallel

Step-by-step explanation:

Slope of line KM = [tex]\frac{5}{8}[/tex]

 Slope of ST = [tex]-\frac{8}{5}[/tex]

Determine whether the lines are perpendicular;

Solution:

We can use the slope of a line to determine whether they are perpendicular or parallel to one another.

Parallel lines do not meet one another

Perpendicular lines cross one another at an angle of 90°

Two lines are parallel if their slopes are the same;

  Since the slope of KM and ST are different, they are not parallel

Answer:

Length of rectangle = 36 yd and width of rectangle = 9 yd

Step-by-step explanation:

Let width of rectangle = w

Length of rectangle = 4w (four times the width)

Perimeter of rectangle = 90 yd

We need to find length and width of rectangle.

The formula used will be: [tex]Perimeter \ of \ rectangle=2(l+w)[/tex]

Where l is length and w is width

Putting values and finding length and width of rectangle

[tex]Perimeter \ of \ rectangle=2(l+w)\\90=2(4w+w)\\90=2(5w)\\90=10w\\w=\frac{90}{10}\\w=9[/tex]

So,width (w) of rectangle is w= 9 yd

Finding length of rectangle = 4w = 4*9 = 36 yd

So, length of rectangle = 36 yd and width of rectangle = 9 yd

Answer:

15

Step-by-step explanation:

Answer:

2) 8x^2 -6x-7 hope this helps

Answer:

Step-by-step explanation:

This is the completed answer.

5z - 4 = 26

5z−4+4=26+4

5z=30

Divide both sides by 5.

5z/5 = 30/5

z=6

Answer:

its b

Step-by-step explanation:

i took the test

y = - 0.5x + 5.5 is the equation of a line perpendicular to line CD in slope-intercept form that passes through the point (−1, 6).

The slope-intercept form of a straight line is y = mx + c.

Here, x and y are coordinates, m is the slope and c is the y-intercept of the line.

Given, two points are C(1, 1) and (3, 5).

Therefore, equation of the line CD is:

[tex]\frac{x - x_{1} }{y-y_{1} }[/tex] = [tex]\frac{x_{1}-x_{2}}{y_{1}-y_{2}}[/tex]

⇒ [tex]\frac{x - 1}{y-1}[/tex] = [tex]\frac{1-3}{1-5}}[/tex]

⇒  [tex]\frac{x - 1}{y-1}[/tex] = [tex]\frac{-2}{-4}}[/tex]

⇒2(x - 1) = (y - 1)

⇒ y = 2x - 1

Let, line AB is perpendicular to the line CD and passes through the point (-1, 6).

Therefore, slope of the line CD is = 2.

We know, slope of CD × slope of AB = -1

Therefore, slope of AB = -1 / slope of CD = [tex]-\frac{1}{2}[/tex].

Now, line AB has a slope of [tex]-\frac{1}{2}[/tex] and passes through the point (-1, 6).

Therefore, equation of the line AB is:

(y - y₁) = m(x - x₁)

⇒ [y - (6)] = [tex]-\frac{1}{2}[/tex][x - (- 1)]

⇒ 2(y - 6) = (-x - 1)

⇒ 2y - 12 + x + 1 = 0

⇒ x + 2y = 11

⇒ y = - 0.5x + 5.5

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Answer:

If an angle of one triangle is congruent to the corresponding angle of another triangle and the lengths of the sides including these angles are in proportion, the triangles are similar. The corresponding sides of similar triangles are in proportion.

I hope this might help you

Mark it as brainliest answer and follow me

Answer:

1. If you're taking square roots, the number must be a perfect square to give a rational root.

64 = 8^2, so √64 = 8 is rational

Similarly, since

64 = 4^3, ∛64 = 4 is rational.

For small numbers, it's easy to check for possible roots, as there aren't that many candidates. In general, it's much more difficult.

2.

Step-by-step explanation:

Answer: The 2 answers are inequality form and interval notation: n>200, and (200, ∞).

Step-by-step explanation: To solve for n, you’ll need to simplify the both sides of the inequality, and then isolating the variable.

Answer:

1) dividend

2) divisor

3) quotient