For expressions a-e, select Yes or No to indicate whether each expression is equivalent
to 3(x + 2)
a. 3x + 2
Yes
No
b. 312 + x)
Yes
No
Yes
c. 3x + 2x
No
d. x + 2x + 2 + 4
Yes
No
Yes
No
e. x + x + x + 1 + 1 + 1 + 1 + 1 + 1

The length of the hypotenuse in this problem is given as follows:

h = 10.6 m.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

The side lengths for this problem are given as follows:

7m and 8m.

Hence the hypotenuse is obtained as follows:

h² = 7² + 8²

\(h = \sqrt{7^2 + 8^2}\)

h = 10.6 m.

More can be learned about the Pythagorean Theorem at brainly.com/question/30203256

#SPJ1

Answer:

7.2 km

Step-by-step explanation:

Distance between Brookfield to Seaside = 20.4 km

Distance between Yardley and Seaside = 13.2 km

Let distance between Brookfield to Yardley be x.

Thus:

x + 13.2 km = 20.4 km

Subtract 13.2 from each side

x = 20.4 - 13.2

x = 7.2

Distance from Brookfield to Yardley is 7.2 km

Answer:

A person pushing a swing will make the swing rotate about its pivot.

A worker applies a force to a spanner to rotate a nut.

A person removes a bottle's cork by pushing down the bottle opener's lever.

A force is applied to a door knob and the door swings open about its hinge.

Answer:

P = 8g⁵ - 15g + 14

Step-by-step explanation:

This question has expressions to represent the side lengths of a triangle.

The side lengths are:

-8g⁵ - 7g

10g⁵ - 8g

6g⁵ + 14

They ask for a simplified expression for the perimeter. The purpose of this question is to combine like terms.

P = s₁ + s₂ + s₃ where s is a side length of the triangle.

P = (-8g⁵ - 7g) + (10g⁵ - 8g) + (6g⁵ + 14)

P = 8g⁵ - 15g + 14

The smallest angle of the equilateral triangle is 60 degrees

If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.

To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.

For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:

Smallest angle \(= \frac{180}{3} = 60\)\) degrees.

Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).

For more questions on equilateral triangle:

https://brainly.com/question/17264112

#SPJ8

a) The synthetic division table is given by the image shown at the end of the answer.

b) The result of the division is given as follows:

-x³ + 4x² + 4x - 8 + 0/x + 2.

In this problem, the dividend is given as follows:

-x^4 + 2x³ + 12x² - 16.

Hence the coefficients are given, respectively, by:

-1, 2, 12, 0 and -16.

The divisor is of:

x + 2.

Hence the term on the left box is of:

x + 2 = 0 -> x = -2.

Then the procedure goes as follows:

From the coefficients of the bottom box, we have that:

Learn more about synthetic division at brainly.com/question/24662212

#SPJ1

The midpoint of segment YZ is (-a, -2b).

Given the coordinates of the rhombus WXYZ:

W(0, 4b)

X(2a, 0)

Y(0, -4b)

Z(-2a, 0)

The midpoint formula is given by:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Substituting the coordinates of Y and Z:

Midpoint of YZ = ((0 + (-2a)) / 2, (-4b + 0) / 2)

= (-a, -2b)

Therefore, the midpoint of segment YZ is (-a, -2b).

To demonstrate that the segments joining the midpoints of the rhombus are perpendicular, we need to prove that the slopes of these segments are negative reciprocals of each other.

Let's consider the segments joining the midpoints:

Segment joining the midpoints of WX and YZ:

Midpoint of WX: ((0 + 2a) / 2, (4b + 0) / 2) = (a, 2b)

Midpoint of YZ: (-a, -2b)

Slope of WX = (2b - 4b) / (a - 0) = -2b / a

Slope of YZ = (-2b - (-4b)) / (-a - 0) = 2b / a

The slopes of WX and YZ are negative reciprocals of each other, indicating that these segments are perpendicular.

We have shown that the segments joining the midpoints of a rhombus are perpendicular to each other and have equal lengths. Therefore, these segments form a rectangle.

Additionally, the midpoint of segment YZ is (-a, -2b).

for similar questions on rhombus.

https://brainly.com/question/20627264

#SPJ8

Answer:

5f + 6g + 12

Step-by-step explanation:

10f - 5f is 5f, you would keep 6g as it is because there are no other numbers to add to it, and 8 + 4 is 12. Hope this helps!! :)

Answer:

152

Step-by-step explanation:

The equation of line from the graph is y = 3x + 4

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

The equation y = 3x + 4 represents a line in the coordinate plane.

To graph this line, we can plot a few points

when x=0, y=3(0)+4=4,

So we have the point (0,4)

when x=1, y=3(1)+4=7,

So we have the point (1,7)

when x=-2, y=3(-2)+4=-2,

So we have the point (-2,-2)

Plotting these points and connecting them with a straight line, we get the graph of the line

Hence , the equation of line is y = 3x + 4

To learn more about equation of line click :

https://brainly.com/question/14200719

#SPJ7

Given: 2x-3y = 21.................(1)

-6x+2y=7...................(2)

Find:(a): Explain the steps you would take to solve the system by eliminating the x-terms.

(b)Explain the steps you would take to solve the system by eliminating the y-terms.

(c)Choose either of the methods described in parts I or II to solve the system of equations. Write your answer as an ordered pair.

Explanation: for to eliminating x ,multiply by 3 in equation (1)

6x-9y=63

-6x+2y=7

on solving the equation we get ,

y=-10

(b) for to eliminating y , mutiply by 2 in equation (1) and by 3 in equation (2).

4x-6y=42

-18x+6y=21

on solving we get,

(c) the ordered pair of the equation is

Answer:

i honestly have no idea

Step-by-step explanation:

Answer:

The coefficient of x^2 is positive (here it is 1) so we have a minimum.

Rearrange it to the form (x-a)^2 + b:

(x+2)^2 - 4 - 5 = (x+2)^2-9

This means the minimum, or vertex, is at (-2,-9)

Parabolas are symmetrical horizontally, so the axis of symmetry is the vertical line at the minimum, which is x = -2

The domain is all numbers

The range is y >= -9

Answer:The inequality represented by the equation y = -11/7x - 4 can be written as:

y ≤ -11/7x - 4

This represents a less than or equal to inequality, indicating that the values of y are less than or equal to the expression -11/7x - 4.

Step-by-step explanation: .

Answer:

The price fell 40%

Step-by-step explanation:

34/85, then convert it to a percentage

Answer:

The cost of one share of the stock on Friday is $41.45

Step-by-step explanation:

The initial cost of one share of the stock on Monday is $41.45.

On Tuesday, the cost goes up by $0.58, so the cost becomes:

$41.45 + $0.58 = $42.03

On Wednesday, the cost goes down by $0.26, so the cost becomes:

$42.03 - $0.26 = $41.77

On Thursday, the cost also goes down by $0.26, so the cost becomes:

$41.77 - $0.26 = $41.51

Finally, on Friday, the cost goes down by $0.06.

So the expression to represent the cost of one share of the stock on Friday is:

$41.51 - $0.06

To evaluate this expression, we simply subtract $0.06 from $41.51:

$41.51 - $0.06 = $41.45

Therefore, the cost of one share of the stock on Friday is $41.45

Answer:

Kk

Step-by-step explanation:

Depends on you bro

Have a nice day!?

Answer:

......free marks? .......

The temperature at the bottom of the mountain is 50.9 °C.

Let's work through the given information step by step to find the temperature at the bottom of the mountain.

The temperature in the hotel is 21 °C.

The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.

Let's denote the temperature at the top of the mountain as T_top.

So, the temperature in the hotel can be expressed as T_top + 26.7 °C.

The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.

Let's denote the temperature at the bottom of the mountain as T_bottom.

So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.

Now, let's combine the information we have:

T_top + 26.7 °C = T_bottom - 3.2 °C

To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:

T_bottom = T_top + 26.7 °C + 3.2 °C

T_bottom = T_top + 29.9 °C

Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:

T_bottom = 21 °C + 29.9 °C

T_bottom = 50.9 °C

Therefore, the temperature at the bottom of the mountain is 50.9 °C.

for such more question on temperature

https://brainly.com/question/14820864

#SPJ8

Answer:

0.44, or \(\frac{11}{25}\) of a bag per friend.

Step-by-step explanation:

We take 4 divided by 9.

\(\frac{4}{9} = 0.44.\)

That, as a fraction, is:

\(0.44 = \frac{11}{25} .\)

This is simplified.

Answer:

I think the answer is D.

Step-by-step explanation:

brainlest?

The observation of the pattern is discussed below.

When we calculate the squares of the numbers from 1 to 10 and observe the digits at the one's place of each square, we notice a pattern:

1²=1

2²=4

3²=9

4²=16

5²=25

6²=36

7²=49

8²=64

9²=81

10²=100

If we focus on the digits at the one's place, we can see that they form a repeating pattern: 1, 4, 9, 6, 5, 6, 9, 4, 1, 0. This pattern repeats itself as we calculate the squares of higher numbers.

This observation is known as the "digit at one's place pattern" or the "units digit pattern." It occurs because the square of any number depends only on the digit at the one's place of that number. Hence, when we square numbers that have the same digit at the one's place, we get the same digit at the one's place in the result.

Learn more about Sequence here:

https://brainly.com/question/30262438

#SPJ1

Answer:

20 blogs

Step-by-step explanation:

Step 1:  Determine the proportion of pop culture blogs:

First, we need to determine the proportion of pop culture blogs already written.  We can do this by dividing the number of pop culture blogs already written by the total number of blogs written:

The proportion of pop culture bloggers = Number of pop culture bloggers / Total number of bloggers

Proportion =  26 / (20 + 26 + 7 + 12)

Proportion = 26 / 65

Proportion = 0.4

Step 2:  Multiply the proportion of pop culture blogs by the number of upcoming blogs:

To determine the expected number of pop culture blogs that will be written given the data, we can multiply the proportion of pop culture blogs already written by the number of upcoming blogs:

Expected number of pop culture blogs = proportion of pop culture blogs *  number of upcoming blogs

Expected number = 0.4 * 50

Expected number = 20

Thus, you should expect 20 pop culture blogs to be written given the data.

for a ratonal, the expression only makes sense if the denominator is not 0, since if that occurs then the expression becomes undefined, a division by 0 is always undefined, for this case, when does that occur?  Let's set the denominator to 0 and solve for "x".

\(\cfrac{\sqrt{2}}{\sqrt{x-1}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{setting the denominator to 0}}{\sqrt{x-1}=0\implies (\sqrt{x-1})^2=0^2}\implies x-1=0\implies x=1\)

well then, let's see what happens when x = 1

\(\cfrac{\sqrt{2}}{\sqrt{x-1}}\implies \cfrac{\sqrt{2(1)}}{\sqrt{1-1}}\implies \cfrac{\sqrt{2}}{\sqrt{0}}\implies \cfrac{\sqrt{2}}{0}\leftarrow und efined\)

so the only values that makes sense is anything but x < 1, because a smaller value of 1 will give us an imaginary value from the root, so the only values that makes sense are namely { x | x ∈ ℝ; x > 1 }

Answer:

No

Step-by-step explanation:

Let's check the first statement with an example. 2 and 3 are positive numbers and their sum (5) is also positive so his first statement is true.

To check the second statement let's look at the negative numbers -1 and -8 for example. Their sum (-9) is also negative so his second statement is true.

To check the third statement let's look at the numbers 9 and -5. One is positive and one is negative, but their sum (4) is positive, so his third statement is false. However if we look at the numbers 4 and -7, their sum is negative so the third statement is partially false.

Answer:

C.

Step-by-step explanation:

Very simple! First we have to take 4x-y=24 and put it in slope intercept form. We get y=4x-24. After this, we have to find the reciprocal of the slope (4). The reciprocal is 1/4. Which equation has a slope of 1/4? C does!

Answer:

A

Step-by-step explanation:

The radius of cylinder is r = 3 in.

The height of cylinder is h = 10 in.

The formula for the volume of cylinder is,

Substitute the values in the formula to determine the volume of cylinder.

So volume of cylinder is 282.7 in^3.

Option H is correct.

The solution of the equation -x² + 4 = x + 2 is at x = -2 and x = 1

An equation is an expression that shows how numbers and variables are related to each other.

Given the quadratic equation:

-x² + 4 = x + 2

Collecting like terms:

x² + x - 2 = 0

Plotting using a graph; the solution of the equation can be gotten by getting the point the graph crosses the x axis.

The solution is at x = -2 and x = 1

Find out more on equation at: https://brainly.com/question/25638875

#SPJ1

Answer:

C: EAF Is the correct answer

By applying the elimination method the value of x is - 2 and y is 7.

This is a problem from algebraic equations and we have to apply the elimination method. We can solve this problem by following a few steps.

So, the given equation according to the question is,

− 2x = 4 ................ ( equation 1 )

4x + 2y = 6 ............... ( equation 2 )

While applying the elimination method we have to multiply equation (1) with the positive coefficient of x in the second equation and vice versa.

Here the coefficient of x in the first equation is 2 and in the second equation is 4.

Now, we have to multiply equation ( 1 ) with 4 and equation ( 2 ) with 2.

Therefore,

− 2x = 4 ................ ( equation 1 ) × 4

4x + 2y = 6 ............... ( equation 2 ) × 2

Now, we can rewrite the equations as,

− 8x = 16 .................. ( equation 3 )

8x + 4y = 12 .................. ( equation 4 )

Now the coefficient of x in both equations are same but opposite sign. So, we have to add the equations.

Here we get , -8x + 8x + 4y = 16 + 12

Or, 4y = 28

Or, y = 7

Now, we have to put the value of y in any equation.

4x + 2.7 = 6  ( equation 2 )

Or, 4x = 6 - 14 = -8

Or, x = -2

To know more about the elimination method visit,

https://brainly.com/question/13885360?referrer=searchResults

#SPJ9

The correct question :

By applying the elimination method, solve the following pair of simultaneous equations:

− 2x = 4

4x + 2y = 6