Solving Advanced Linear Equations: Mastery Test
Select the correct answer from each drop-down menu.
Consider the equation below.
The equation was solved using the following steps.
Step 1:
Step 2:
Step 3:
Step 4:
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Complete the statements below with the process used to achieve steps 1-4.
-2 to 5x and 8.
6.x
✓16.
-2(5z + 8) = 14 + 6z
-16.
-10z <- 16
-16z
Reset
-
16 = 14
-16z =
30
= 14 + 6z
H
=
H =
Next
30656
-18
Submit T

Answers

Answer 1

The solution to the equation where the equation is given as -2(5z + 8) = 14 + 6z is z = -15/8

How to complete the steps to solve the equation?

The equation is given as

-2(5z + 8) = 14 + 6z

Open the bracket

So, we have

-10z - 16 = 14 + 6z

Collect the like terms

So, we have

-10z - 6z = 14 + 16

Evaluate the like terms

So, we have

-16z = 30

Divide both sides of the equation by 16

So, we have

z = -15/8

Hence, the solution to the equation where the equation is given as -2(5z + 8) = 14 + 6z is z = -15/8

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Related Questions

i have no idea how to do this

Answers

Hope this helps
Check out the attached photo
2x-10= 120
2x=130
Answer:65

Evaluate the function

f(x) = -2x^2 - 4x + 13

Find f(-7)

Answers

Answer:

g(-7) = 57

Step-by-step explanation:

note: the editor will not let me use eff of x. I have to use g(x)

Equation

g(x) = -2x^2 -4x + 13

Comment

y is the same thing as g(x) so you are really being asked to find y,

Given

x = - 7

g(-7) means that x is -7

Solution

g(x) = -2(-7)^2 - 4(-7) + 13           Substitute x = - 7 on the right

g(x) = -2*49 + 28 + 13                 Combine

g(x) = -98 + 28 + 13

g(-7) = -57

❗❗100 POINTS FOR CORRECT ANSWER AND EXPLANATION❗❗~math question~
thanks)​

Answers

Answer:

  k = 110

Step-by-step explanation:

You want the integer multiple of pi that is the area of 300° of a donut with inner radius 8 cm and outer radius of 14 cm.

Area of a circle

The area of a circle is given by the formula ...

  A = πr²

Then the area of the outer circle is ...

  A = π(14 cm)² = 196π cm²

The area of the inner circle is ...

  A = π(8 cm)² = 64π cm²

Donut area

The area of the whole donut is the difference of these areas:

  whole donut area = (196 -64)π cm² = 132π cm²

Shaded area

The shaded area of the figure represents 300° of the 360° full donut. The area is proportional to the central angle, so the shaded area is ...

  shaded area = (300°/360°)×whole donut area

  shaded area = 5/6 × 132π cm² = 110π cm²

Comparing this to the expression kπ cm², we see that ...

  k = 110


If log y = 7, which is equal to y?

Answers

The value of the logarithm log y = 7 for y will be e⁷.

We are given the logarithm problem as:

log y = 7

We need to solve this to find the value of y.

We will use the properties of logarithm for this.

So, we get that

⇒ e ^ log y = e ⁷

Solving it, we will get that:

⇒ y = e⁷

So the value of the logarithm log y = 7 for y will be e⁷.

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suppos there is a 1.2f drop in temperature for every thousand feet that an airplane climbs into the sky. if the temperature on the ground is 53.8f what will be the temperature when the plane reaches an altitude of 8,000ft?

Answers

The temperature will be 44.2f when the plane reaches an altitude of 8,000ft.

What exactly are mathematical operations?A function in mathematics that converts zero or even more input values (also known as "operands" or "arguments") to a well-defined output value is known as an operation.The number of operands determines the operation's arity.The most commonly studied operations are binary activities (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive direct opposite and multiplicative inverse.A constant is a zero-arity operation, also known as a nullary operation.An arity 3 operation, also recognized as a ternary operation, is the mixed product.

So, there is a 1.2f drop in temperature for every thousand feet.

The plane is at 8000 ft then:

8000/1000 = 8

So,

1.2 × 8 = 9.6

The temperature at 8000 ft:

53.8 - 9.6 = 44.2

Therefore, the temperature will be 44.2f when the plane reaches an altitude of 8,000 ft.

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what is 0.25x 2.6 pls help me this is hw

Answers

Answer:

0.65

Step-by-step explanation:

0.65 is going to be your answer

Simplify negative 3 and 4 over 5 minus 5 and 2 over 3.

Answers

The answer is -142/15

Answer:

-9 7/15

Step-by-step explanation:

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

Suppose that the world's current oil reserves is

R=1970 billion barrels. If, on average, the total reserves is decreasing by 24 billion barrels of oil each year, answer the following:

A.) Give a linear equation for the total remaining oil reserves, R, in terms of t, the number of years since now. (Be sure to use the correct variable and Preview before you submit.)

R=

B.) 12 years from now, the total oil reserves will be____billions of barrels.


C.) If no other oil is deposited into the reserves, the world's oil reserves will be completely depleted (all used up) approximately_______years from now.

(Round your answer to two decimal places.)

Answers

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.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

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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Michael is trying to show that ABC to congruent to A'B'C

Answers

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

Point A would move 8 units Points B would remain at same point hence move 0 unitsPoint C  would move 8 units

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

line x = 4

The triangles are?

The two triangles are congruent

The line of reflection Michael used is?

Michael used line x = 4

What is reflection?

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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Violen crimes include​ grape, robbery,​ assault, and l=lomicide. The following is a summary of the​ violent-crime rate​ (violent crimes per​ 100,000 population) for all states of a country in a certain year. Complete parts​ (a) through​ (d).
​ ​, (c) The​ violent-crime rate in a certain state of the country in that year was. Would this be an​ outlier?

The lower fence is


enter your response here crimes per​ 100,000 population.

The upper fence is


enter your response here crimes per​ 100,000 population.

Answers

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

Lower: 0.Upper: 657.65.

What is the missing information?


The quartiles of the distribution are given as follows:

Q1: 273.8. (violent crimes per​ 100,000 population)Q3: 529.7. (violent crimes per​ 100,000 population)

What is the interquartile range and how it is related to outliers?

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:

1.5 IQR below Q1.1.5 IQR above Q3.

For this problem, the IQR is:

IQR = 529.7 - 273.8 = 255.9.

Hence the fences are:

Lower: 273.8 - 1.5 x 255.9 = -110.05, negative numbers are not possible in the range of the question, hence the lower fence is of 0.Upper: 273.8 + 1.5 x 255.9 = 657.65.

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a carpenter has 6 boards that are each 7/8 yard long. how many 3/4 yard sections of board can he construct

Answers

The number of sections of board that he can construct will be equal to 7.

We are given that:

A carpenter has 6 boards.

Length of each board = 7 / 8 yard long

Now, we will use multiplication.

Total length of cardboards available = 7 / 8 × 6 yards

Total length = 42 / 8 yards

Total length = 21 / 4 yards.

Now, 3/4 yard sections of board that he can construct will be:

Number of sections of board = 21 / 4 ÷ 3 / 4

Number of sections of board = 21 / 3

Number of sections of board = 7

Therefore, the number of sections of board that he can construct will be equal to 7.

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Suppose that you have 10 green cards and 5 yellow cards. The cards were well shuffled . You randomly draw two cards WITH REPLACEMENT (you draw, put the card back and draw again). Round your answers decimal
G1=The first card drawn is green
G2=the second card drawn is green
A. P(G1 and G2)=
B. P (at least one green=
C. P(G2) (G1)=
D. Are G1 and G2 independent
They are independent events or dependent event

Answers

The probability of P(G1 and G2) will be 1/5.

The probability of at least one green will be 3/10.

The probability for P(G2) (G1) will be 1/100.

They're dependent event

How to calculate the probability?

G1= The first card drawn is green

G2= the second card drawn is green

The probability of P(G1 and G2) will be:

= 1/10 + 1/10

= 1/5.

The probability of at least one green will be:

= 1/10 + 1/5

= 3/10

The probability for P(G2) (G1) will be:

= 1/10 × 1/10

= 1/100

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Is 5.424 greater than 5.343

Answers

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

For the following two numbers, find two factors of the first number such that their product is the first number and their sum is the second number.
63,16

Answers

9 and 7

9 x 7 = 63
9 + 7 = 16

Timothy deposited $2,780.20 in a savings account that earns 4.3% simple interest. What will Timothy's account balance be in 7 months?

Answers

Total balance in the account after 7 months is 2849.737$

It is given that Timothy deposits $2780.20 in a savings account

It is given that rate of interest is 4.3 % and it of the simple interest nature.

We are required to find the account balance of Timothy's account in 7 months

We know that formula of simple interest is given by

(principal x rate x time)/100

where principal is the amount put for investing

rate is the rate at which the person is going to earn

time is the time for which the amount is to be invested

Now the time that is given to us in the form of months and hence we must convert it into years form

1 year =12 months

therefore, 7 months = 7/12 years

Now applying this value to calculate the simple interest earned

Let the simple interest be 'SI'

principal = $2780.20

rate = 4.3%

time = 7/12 years

SI= (2780.20x 4.3 x 7)/100 x 12

   = 69.737$

The balance in Timothy's account will be original amount + the simple interest

Total balance after 7 months = 2780.20+69.737

                                                  =2849.937$

Hence total balance in the account after 7 months is 2849.737$

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The ratio of students with blond
hair to students with brown or
black hair is 1:2. If there are
212 students with brown or black
hair, how many students have
blond hair?

Answers

Answer: 106 students

Step-by-step explanation:

In a 1:2 ratio, we can see that there are 2x the amount of students with brown/black hair compared to students with blonde hair.

So taking 212 students, we can divide the number by half to get 106 students.

[tex]\frac{212}{2} = 106[/tex]

What is the length of a rectangular holding pond with an area of 5 1/10 square miles and a width of 1/6 mile?

Answers

The get the length of a rectangle, divide the area with the given length. 5.1 divided by 0.1666 or approximately 0.17 to get the other length which equals 30 miles

Write and solve an inequality.


Twice a number x is more than the sum of that number x and 14.

Answers

[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]

If the demand function for a commodity is given by the equation p2 + 16q = 1200 and the supply function is given by the equation 300 − p2 + 10q = 0, find the equilibrium quantity and equilibrium price. (Round your answers to two decimal places.)

Answers

The equilibrium quantity and equilibrium price are 34.62 and 25.42 respectively

How to find the equilibrium quantity and equilibrium price?

The functions are given as

Demand: p^2 + 16q= 1200

Supply function: 300 - p^2 + 10q

Rewrite the demand function as

p^2 + 16q - 1200 = 0

At equilibrium, demand  = supply

So, we have:

p^2 + 16q - 1200 = 300 - p^2 + 10q

Using a graphing calculator, we have:

p = 25.42 and q = 34.62

Hence, the equilibrium quantity and equilibrium price are 34.62 and 25.42 respectively

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Points L, M, and N are collinear. You are given LM = 21 and LN = 35.
What is a possible value of MN ?

Answers

The value of MN is 14 when the Points L, M, and N are collinear.

As per the question statement, we are supposed to find the possible value of MN when the Points L, M, and N are collinear.

Also, LM=21 and LN=35

As LN is greater than LM, point M has to be in between L and N for practicality and question existence.

[tex]LM+MN=LN\\MN=LN-LM\\LN=35\\LM=21\\MN=35-21\\MN=14[/tex]

Hence final answer is MN = 14

Collinear points: It is a set of points which has a thing in common i.e., they lie on the same line or when joined forms a straight line.

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The sum of two numbers is 14. Using x to represent the smaller of the two numbers , translate "the sum of twice the smaller number and two more than the larger number" into a variable expression. Then simplify

Answers

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

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

What is an equation?

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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Nose como se hace esto

Answers

Answer: 8, 13, 6, 12, 4, 13, 5, 13, 11, 19, 12, 17, 9, 16, 10, 13, 7, 14, 11, 20, 10, 18, 9, 16, 7, 15.

Step-by-step explanation:

¡Aquí tienes!

¡Espero que esto te ayude!

what is the answer to −4.2+3.3=

Answers

answer: -0.9

correct me if I'm wrong

Is 17.305 greater or less than 17.066

Answers

Answer: greater than

Step-by-step explanation:17.305[tex]\geq[/tex]17.066

Answer:

Yes

Step-by-step explanation:

Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day :)

A family is planning their vacation to Disney World. They will drive from a small town outside New Orleans,
Louisiana, to Orlando, Florida, a distance of 700 miles. They plan to average a rate of 55 mph. How long will this
trip take?

Answers

The time taken for the trip will be 12.7 hours.

How to calculate the value?

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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What’s the volume of a 9ft rectangular prism

Answers

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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An intermediate algebra student drives a car at 45 miles per hour. Let d be the distance (in miles) that the student travels in 1 hours.
a. Is there a linear relationship between t and d? Explain. If the relationship is linear, find the slope and describe what it means in this situation.
b. Find an equation of the model

Answers

There is no linear relationship between t and d.

What do we mean by linear relationship?A linear relationship (or linear association) is a statistical term that describes a two-variable relationship that follows a straight line. Linear relationships can be represented graphically or mathematically as the equation y = mx + b. In everyday life, linear relationships are fairly common.

So, the student drives a car at 45 miles per hour, so travels 45 miles in an hour.

Since the linear relationship equation is in the form y = mx + b but the t and d are just the same.So, there is no linear relationship between t and d.

Therefore, there is no linear relationship between t and d.

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what’s the distance between (2,8) and (-6,-2)

Answers

Answer:



Root 

Step-by-step explanation:

Answer:

The distance between (2,8) and (-6,-2)

is √100+64

Step-by-step explanation:

b)
73cm
92cm
56 cm
What is the
the
area and perimeter

Answers

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

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 calcuate the point that is equistant from all three gates

Answers

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.

Equation: In mathematics, an equation is a formula or a mathematical statement, that expresses the equality of two expressions, by connecting them with the "Equal To" sign.

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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