Question 3(Multiple Choice Worth 2 points) (Adding and Subtracting Linear Expressions MC) Write the following expression in simplest form. (3 + 16.4a) − (9 + 5.7a)


A 22.1a + (−12) B 1.07a + (−12) C 22.1a + (−6) D 10.7a + (−6)

The slope of the side connecting (-4,1) and (-6,5) = -2

The slope of the side connecting (1,2) and (-1,6) = -2

The slope of the segment joining two points (x₁, y₁) and (x₂, y₂) = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

We have to find the slope of the side joining the points (x₁, y₁) = (-4,1) and (x₂, y₂) = (-6,5)

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

          = [tex]\frac{5-1}{-6--4}[/tex]

          = 4/ -2

          = -2

We have to find the slope of the side joining the points (x₁, y₁) = (1, 2) and (x₂, y₂) = (-1,6)

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

          = [tex]\frac{6-2}{-1-1}[/tex]

          = 4/-2

          = -2

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The correct option regarding the operations with scientific notation is given as follows:

B) Because numbers written in scientific notation have exponents, you can use the Laws of Exponents to multiply or divide the numbers.

A number in scientific notation is given by:

[tex]a \times 10^b[/tex]

With the base being [tex]a \in [1, 10)[/tex].

An example of a multiplication in scientific notation is:

[tex]2 \times 10^3 \times 3 \times 10^5 = 6 \times 10^{3 + 5} = 6 \times 10^8[/tex]

That is, we multiply the factors, and for the bases of 10, we keep the bases and add the exponents. In a division, we would divide the factors, and for the base of 10, we keep the base and subtract the exponents.

That is, since the numbers have exponents, rules of exponents are used for both multiplication and division, and option b is correct.

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Answer:

Area=2044..... perimeter=221

Step-by-step explanation:

Step1:- Area =1/2×breath×height

1/2×73×56

1/2×4088

= 2044

Area =2044cm^2

Step2:- Perimeter= a+b+c

=73+56+92

=221

Perimeter=221cm

The smaller number is 4 and the larger number is 10.

Given that, the sum of the two numbers is 14.

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that,  x represents the smaller of the two numbers.

Then the larger number is

The sum of twice the smaller number and two more than the larger number = 2x+2

Now, x+2x+2=14

⇒3x+2=14

⇒3x=12

⇒x=4

So, 2x+2=10

Therefore, the smaller number is 4 and the larger number is 10.

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Answer:

-9 7/15

Step-by-step explanation:

I took the test lol. Also if your in advanced you should know this!

answer: -0.9

correct me if I'm wrong

By joining the entry point of all three friends to form a triangle and then finding the centroid of this triangle , they can calculate the required point.

If Lisa, Bree, and Caleb are meeting at an amusement park and  each enter at a different gate as shown in reference picture attached hereby, the friends could calculate the point that is equidistant from all three gates by the equation [(Distance between gate 1 and gate 2) = (Distance between gate 2 and gate 3) = (Distance between gate 1 and gate 3)]

As per question statement, Lisa, Bree, and Caleb are meeting at an amusement park and  each enter at a different gate as shown in reference picture attached hereby.

We are required to determine to calculate the point that is equidistant from all three gates.

The required equation goes as  [(Distance between gate 1 and gate 2) = (Distance between gate 2 and gate 3) = (Distance between gate 1 and gate 3)],

Where, they will have to use the distance formula to find the distances in between which goes as [tex]D=\sqrt{(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2} }[/tex], in the above mentioned equation.

Complete question: Lisa, Bree, and Caleb are meeting at an amusement park. They each enter at a different gate. On this diagram of the park, explain how the friends could calculate the point that is equidistant from all three gates.

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[tex]\Large\textbf{Twice a number x is this: \textsf{2x}}\\\\\\\textbf{The sum of that number and 14 is this: \textsf{x+14}}\\\\\\\textbf{2x\textgreater x+14}\\\\\textbf{x\textgreater14}[/tex]

Answer juvhfVO"zohgvjozi nandish pro nbhvmno

Using a system of equations, it is found that she invested 318.71 into Fund B.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are given as follows:

The amount she invested in Fund A was 3 times as much as the amount she invested in Fund B, hence:

x = 3y.

Fund A returned a 6% profit and Fund B returned a 15% profit, and the total profit was of 1380, hence:

1.06x + 1.15y = 1380.

We have that x = 3y, hence:

1.06(3y) + 1.15y = 1380.

4.33y = 1380

y = 1380/4.33

y = 318.71.

She invested 318.71 into Fund B.

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The volume of the prism with length as 9 feet will be 9 w h where w is the width and h is the height of the prism.

We are given a prism.

It is a rectangular prism.

We are also given that it if 9 feet.

We need to find the volume of this rectangular prism.

V = w × h × l

where

w = width of the prism

h = height of the prism

l = length of the prism

Now, we are given that l = 9 feet

So, V = w × h × l

V = 9 w h

Therefore, we get that the volume of the prism with length as 9 feet will be 9 w h where w is the width and h is the height of the prism.

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Answer:

10 for each

Step-by-step explanation:

1.90 x 10 = 19

2.10 x 10 = 21

so 19 + 21 = 30

If Ethan got his first job and is making $8.50 an hour. He really wants to buy a couple of video games, so he is trying to estimate how much his paycheck will be. The amount he can expect to bring home in his first paycheck is: $321.64.

Total hours=18 hours+25 hours

Total hours=43 hours

Income tax=Federal income tax+ State income tax

Income tax=10%+2%

Income tax=12%

Hence,
First paycheck:

First paycheck=$8.50×43 hours×(1-12%)

First paycheck=$8.50×43 hours×0.88

First paycheck=$321.64

Therefore if Ethan got his first job and is making $8.50 an hour. He really wants to buy a couple of video games, so he is trying to estimate how much his paycheck will be. The amount he can expect to bring home in his first paycheck is: $321.64.

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Answer:

Yes.

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

The tenths place is 4 while 5.343 tenths place is 3

Hope It Helps

Sorry If I'm Wrong

From the given situation, we have that:

A) The linear equation is R(t) = 1970 - 24t.

B) 12 years from now, the total oil reserves will be 1682 billions of barrels.

C) Approximately 82.08 years from now.

A linear function is modeled by:

y = mx + b

In which:

For this problem, the parameters are given as follows:

b = 1970, m = -24.

Hence the linear function is:

R(t) = 1970 - 24t.

For item b, the amount is of R(12), hence:

R(12) = 1970 - 24(12) = 1682.

12 years from now, the total oil reserves will be 1682 billions of barrels.

For item c, we have to solve for t when R(t) = 0, hence:

1970 - 24t = 0

24t = 1970

t = 1970/24

t = 82.08.

Approximately 82.08 years from now.

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To find the reflection of ΔABC in the x-axis, the points would move as follows:

Using the original coordinates, Δ A'B'C' is a reflection of Δ ABC in the line?

The triangles are?

The line of reflection Michael used is?

Reflection as used in geometry is the representation of an image in the mirror image copy. Reflection is done with respect to a line called line of reflection. Images formed are of equal distant to the line of reflection and the images are usually congruent.

Reflection as represented on a graph is most times in x axis or y axis. This axis shows the location of the line of reflection and it is very important when determining the position of the reflected image.

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Answer:

Parker's unit rate is 5 miles per hour or 5mph.

Step-by-step explanation:

1 hour = 60 minutes

60/20 = 3 minutes

3 minutes for 1 lap

1 lap = 1/4 mile

1/4 mile (1 lap) x 4 laps = 1 mile

4 laps =  12 minutes

12 minutes per mile

60/12 = 5

5 miles per hour

Answer:

theres no picture

The number of standard version download and high-quality download is 870 and 490 respectively.

let

x + y = 1360

2.9x + 4.1y = 4532

From (1)

x = 1360 - y

Substitute x = 1360 - y into (2)

2.9x + 4.1y = 4532

2.9(1360 - y) + 4.1y = 4532

3944 - 2.9y + 4.1y = 4532

- 2.9y + 4.1y = 4532 - 3944

1.2y = 588

y = 588/1.2

y = 490

Substitute y = 490 into (1)

x + y = 1360

x + 490 = 1360

x = 1360 - 490

x = 870

So therefore, number of standard version download and high-quality download is 870 and 490 respectively.

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Answer:

Yes

Step-by-step explanation:

8÷10+7÷100=

8/10 + 7/100=

80/100 + 7/100=     ==> make the denominators equal to each other

(80+7)/100=

87/100=0.87 √

Answer:

yes it does

Step-by-step explanation:

8÷10=0.8

7÷100=0.07

0.8+0.07=0.87

or the easy way ig

8÷10+7÷100=0.87

The time taken for the trip will be 12.7 hours.

It should be noted that time taken is calculated as:

Time = Distance / Speed

Distance = 700 miles

Speed = 55 mph

Time = 700/55

Time = 12.7 hours.

Therefore, the time taken for the trip will be 12.7 hours.

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From the interquartile range of the distribution, the fences for non-outliers are given as follows:

The quartiles of the distribution are given as follows:

The interquartile range of a distribution is given by the difference of the third quartile by the first quartile, that is:

IQR = Q3 - Q1.

Outliers are given by:

For this problem, the IQR is:

IQR = 529.7 - 273.8 = 255.9.

Hence the fences are:

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Congruent segments are LK=MK, LK=7x-10, KN=x+3, MN=9x-11, and KJ=28,  the LJ  will be-

LJ = 18 + 28 = 46

LJ = 18 + 28 = 46

These are  Congruent segments

Let J, K, L, M, N are points on the same line.

MK = MN + (-KN) = MN - KN = 9x - 11 - x - 3 = 8x - 14

As LK = MK and LK = 7x - 10, then

7x - 10 = 8x - 14

8x - 7x = -10 + 14

x = 4

LJ = MK + KJ

MK = LK = 7x - 10 = 7(4) - 10 = 28 - 10 = 18

LJ = 18 + 28 = 46

Congruent segments are segments which have the equal length. ≅ points that lie at the equal line are called collinear.

A theorem is a mathematical assertion that can be proved. The midpoint of a phase is a point that divides the phase into two congruent segments

If three or more points lie on a single straight line, they are said to be collinear. An axis is a term used to describe a line on which points are located, particularly if that line is connected to a triangle or other geometric shape. Since two points determine a line, two points are trivially collinear.

Two line segments are congruent if they have the same length. They do not need to have the same position or orientation

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R= is incorrect

the answer is china :)

The  three equations with solution x=-5 Are as follows:

25 + x = 15 ............... equation 1.

7x = -35 .......................equation 2.

15 + x = 10 ..................equation 3

There is not more then one or two variables in a linear equation. In a linear equation, no variable is raised to a power larger than one or utilized as the denominator of a fraction. When you locate two values that satisfy a linear equation and display them on a coordinate grid, every one of the points falls on the same line.

A linear equation in one variable seems to be an equation that has just one solution and is stated in the form ax+b = 0, where a but instead b are two integers and x is a variable. 2x+3=8, for example, is a mathematical expression with a single variable.

x=-5 Given

This also can be written as :

25 + x = 15 ............... equation 1.

7x = -35 .......................equation 2.

15 + x = 10 ..................equation 3

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Answer:

0.65

Step-by-step explanation: