y
=
–x + 4
x + 2y
=
–8
How many solutions does this linear system have?
one solution: (8, 0)
one solution: (0, 8)
no solution
infinite number of solutions

Answer:

Trapezoid Area = (Sum of Bases / 2) * Height =

(6 + 14 / 2) * Height =

10 * 8 =

80

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

This is a linear equation in one variable and has 1 solution

12x + 6 = 5x ( subtract 5x from both sides )

7x + 6 = 0 ( subtract 6 from both sides )

7x = - 6 ( divide both sides by 7 )

x = - [tex]\frac{6}{7}[/tex] ← 1 solution

The equation has a single solution for x, which is -6/7. The correct answer is: C. 1

To determine the number of solutions to the equation 12x + 6 = 5x, let’s solve the equation step by step.
First, we need to get all terms with the variable x on one side of the equation and constants on the other side. To do this, we can subtract 5x from both sides of the equation:
12x + 6 - 5x = 5x - 5x
This simplifies to:
7x + 6 = 0
Now we need to isolate the term with the x variable, so we subtract 6 from both sides of the equation:
7x + 6 - 6 = 0 - 6
This further simplifies to:
7x = -6
Finally, to solve for x, we divide both sides by 7:
7x / 7 = -6 / 7
x = -6/7
Therefore, the equation has a single solution for x, which is -6/7.
The correct answer is:
C. 1

In this Congruence of Triangles question, To show that ABC = XYZ by SAS congruence, we also need to show that AC = XZ and ∠A = ∠X.

To show that ABC = XYZ

AB = XY (Given)

A = X (Given)

To prove ABC = XYZ by the Side-Angle-Side (SAS) congruence postulate, we need to show that one pair of corresponding sides and the included angle are congruent. In this case:

AC = XZ (By the reflexive property of congruence)

∠A = ∠X (Given)

Therefore, to fully demonstrate the congruence between the two triangles ABC and XYZ, we also need to show that AC = XZ and ∠A = ∠X.

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We can tell this side on triangle ABC is BC, and the side on triangle XYZ is YZ, so the answer must be B.

SAS stands for side-angle-side, which indicates that for two triangles to be congruent, all two sides and the angle they produce must be congruent and equal.

You have an angle, <B and <Y, and a side, AB and XY, in this instance. The last side, which produces angle B along with side AB on triangle ABC and angle Y along with side XY on triangle XYZ, is all that is needed to finish this.

In this case, you have a side—AB and XY—and an angle, <B and <Y. To complete this, you simply need the final side, which forms angle B along with side AB on triangle ABC, and forms angle Y along with side XY on triangle XYZ.

By looking at the diagram, you can tell this side on triangle ABC is BC, and the side on triangle XYZ is YZ, so the answer must be B. The answer must be the sides of triangles ABC and XYZ are, respectively, BC and YZ.

Answer:

Well this isn't a grammatically correct question but if you're asking how they would split the money it would be $5 for each person.

Step-by-step explanation:

1. The 10 people buy the cups of Lemonade.

2. One cup of lemonade is $1, so that means 10 cups would be $10.

3. Then you would give half to your friend which would be $5.

Answer:

A. "an arithmetic sequence with a common difference (d) of -6."

B. 33 hours

C. [tex]a_n=a_1+(n-1)d[/tex]

D. See below

Step-by-step explanation:

A.

Since the sequence lessens by 6, this is an arithmetic sequence with a common difference (d) of -6.

B.

The formula for term of arithmetic sequence is:

[tex]a_n=a_1+d(n-1)[/tex]

Wher a_1 is the first term and d is the common difference. Since we want to find after 33 weeks, we plug in 33 into n:

[tex]a_{33}=225 + (-6)(33-1)\\a_{33}=33[/tex]

She will have left 33 hours

C.

We will use the arithmetic sequence term formula written above, that is:

[tex]a_n=a_1+(n-1)d[/tex]

THis gives us the amount of hours left after a certain number of weeks.

D.

We plug in 40 into n and find the hours left:

[tex]a_{40}=225+(40-1)(-6)\\a_{40}=225-234\\a_{40}=-9[/tex]

THis term is NEGATIVE, which means that Greta will not have to work 40 weeks to fulfill the target of 225 hours. She needs to work less.

This sequence represents the number of volunteer hours Greta has left after each week has passed. After 33 weeks, Greta has 27 hours left to fulfill her requirement. After 40 weeks, the formula gives a negative value, which means she has completed her requirement and has 15 extra hours of volunteer work completed.

a. This sequence represents the number of volunteer hours Greta has left after each week has passed for her community service project.

b. To determine how many volunteer hours Greta has left after 33 weeks, we can subtract the number of hours she has volunteered in those 33 weeks from the initial requirement of 225 hours. Therefore, Greta has 225 - (6 * 33) = 225 - 198 = 27 hours left.

c. To determine how many volunteer hours Greta has left after 40 weeks, we can use the same formula as in part b. Therefore, Greta has 225 - (6 * 40) = 225 - 240 = -15 hours left.

d. Since we cannot have negative hours, the answer in part c does not make sense in the context of the problem situation. It means that Greta has fulfilled her requirement and has 15 extra hours of volunteer work completed.

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Answer:

[tex]\large\boxed{2.15\cdot10^{-3}}[/tex]

Step-by-step explanation:

[ttex]\text{The scientific notation:}\ a\cdot10^k\\\\\text{where}\ 1\leq a<10,\ k\in\mathbb{Z}[/tex]

[tex]\bold{METHOD\ 1:}\\\\10^{-3}=\dfrac{1}{10^3}=\dfrac{1}{1000}=0.001\qquad\text{used}\ a^{-n}=\dfrac{1}{a^n}\\\\2.8\cdot10^{-3}=2.8\cdot0.001=0.0028\\\\2.8\cdot10^{-3}-0.00065=0.0028-0.00065=0.00215\\\\0\underbrace{.002}_{3\to}15=2.15\cdot10^{-3}[/tex]

[tex]\bold{METHOD\ 2:}\\\\2.8\cdot10^{-3}-0.00065=2.8\cdot10^{-3}-0.65\cdot10^{-3}\\\\=(2.8-0.65)\cdot10^{-3}=2.15\cdot10^{-3}[/tex]

Answer: Your answer would have to be x= 29

Answer:

x=29

Step-by-step explanation:

43+ 15 is 58

58 divided by 2 is 29

2*29= 58

58-15=43

Answer:

This is not an linear equation thus cant be solved

Answer Step-by-step explanation:

[tex]The~question~here~is~not~a~linear~equation.~So~this~can~not~be~solved~![/tex]

Answer:

The answer to your question is: -116

Step-by-step explanation:

   2⁻²(12 x 3) - 5³

  =  1 /2² (36) - 125

  = 1/4 (36) -125

  =  36/ 4 -125

   = 9 - 125

    = - 116

Answer:

whats equivelent to 6x4?

Step-by-step explanation:

6 x 4 = 24

8 x 2 = 16 so 8 x 3 = 24 because 8 x 4 would be

8 x 2 = 16

16 x 2 =

6 + 6 = 12

carry the one.

2

1 + 1 + 1 (We now have three ones from carrying that 1) and our answer is

32.

So N = 3

Answer:

6x4=8xN N=8x3

Step-by-step explanation: N=8x3 because 6x4=24 so if you multiply 8x3 it =  

24

Step-by-step explanation:

5(x+2)-7=5(x-3)

5x + 10 -7 = 5x -15

5x - 5x ..... this question must have an error

Answer:

Undefined

Step-by-step explanation:

5(x+2)-7=5x-3

5x+10-7=5x-3

5x+3=5x-3

5x=5x

can't solve, so it is undefined.

Answer:

greater than

Step-by-step explanation:

it is largee

Answer:  greater then

Step-by-step explanation:

cause 546 is greater then 540

Answer:

a. (1,14) and (7,7)

b. slope = -1.2

Step-by-step explanation:

a. Use the points that are actually on the drawn line

(1,14) and (7,7)

b. Slope formula is :

[tex]slope = ( y_{2} - y_{1}) \div ( x_{2} - x_{1})[/tex]

It doesnt matter which one is 1 or 2. I will take (1,14) as (x1, y1) and (7,7) as (x2, y2)

[tex]slope = \frac{(7 - 14)}{(7 - 1)} \\ = \frac{ - 7}{6} = - 1.1667 = - 1.2[/tex]

Answer:

(A) (1, 14) and (7, 7)

(B) -1.17

Step-by-step explanation:

(A) the 2 points that should be used are: (1, 14) and (7, 7). The reason is that these 2 points are the closest to the trend line.

(B) With 2 points - (x1, y1) and (x2, y2) - a linear equation can be obtained. The slope (m) of the line is computed as follows:

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

m = (7 - 14)/(7 - 1) = -1.17

Answer:

1.222x10^38

Step-by-step explanation:

there are 35 0's in the number

Step-by-step explanation:

Combine like terms

a. 2r + 3 + 4r = (2r + 4r) + 3 = 6r + 3

b. 8 + 3d + d = (3d + d) + 8 = 4d + 8

c. mn + (-3mn) + 6 = (mn - 3mn) + 6 = -2mn + 6

d. 10s + (-10) + (-4s) = (10s - 4s) - 10 = 14s - 10

Terms are called "like terms" if they have the same variable part (the same letters in the same powers). Like terms differ at most coefficient.

Answer:

a. 2r + 3 + 4r

Combine the coefficients of the like monomials.

(2 + 4 = 6)

Answer: 6r + 3

b. 8 + 3d + d

Combine the coefficients of the like monomials.

(3 + 1 = 4)

Answer: 8 + 4d

c. mn + (–3mn) + 6

Combine the coefficients of the like monomials.

[1 + (–3) = –2]

Answer: –2mn + 6

d. 10s + (–10) + (–4s)

Combine the coefficients of the like monomials.

[10 + (–4) = 6]

Answer: 6s + (–10)

Step-by-step explanation:

straight from Penn

Answer:

x = 121

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 7, thus

sum = 180° × 5 = 900°

Sum the given angles and equate to 900

x + 125 + 119 + 117 + 145 + 133 + 140 = 900, that is

x + 779 = 900 ( subtract 779 from both sides )

x = 121

Answer:100

Step-by-step explanation:

10*10

Answer:

78.54

Step-by-step explanation:

The radius of this is 5 (diameter divided in half is radius). 5 squared is 25, then you multiply that by 3.14. Voila!

Answer:

-24x+2

Step-by-step explanation:

7x(-3) = -21x

x(-2) = -2x

x

2

-24x+2

Answer:

solving

Step-by-step explanation:

Answer:

7800

add 1 to the tens place as grater than 5

7765 rounded to the nearest hundred would be 7800

[tex]\bf (\stackrel{x_1}{6}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{9}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{9}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{-6}-\underset{x_1}{6}}}\implies \cfrac{4}{-12}\implies -\cfrac{1}{3}[/tex]

Answer:

[tex]\large\boxed{slope=-\dfrac{1}{3}}[/tex]

Step-by-step explanation:

The formula of a slope:

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

(x₁, y₁), (x₂, y₂) - points on a line

We have the points

(6, 5) → x₁ = 6, y₁ = 5

(-6, 9) → x₂ = -6, y₂ = 9

Substitute:

[tex]m=\dfrac{9-5}{-6-6}=\dfrac{4}{-12}=-\dfrac{4:4}{12:4}=-\dfrac{1}{3}[/tex]

The difficulty of the permit test can vary, but with proper preparation and study of the driver's handbook, most individuals can pass the test.

The difficulty of the permit test can vary depending on the individual's level of preparation and understanding of the rules of the road, traffic laws, and safe driving practices. The test typically consists of multiple-choice questions based on information found in the state's driver's handbook.

To pass the permit test, one should:

1. Study the driver's handbook thoroughly, as it contains all the necessary information.

2. Take practice tests to become familiar with the format and types of questions that may be asked.

3. Understand traffic signs, signals, and markings, as well as the rules for sharing the road with other drivers, pedestrians, and cyclists.

4. Learn about the consequences of driving under the influence of alcohol or drugs.

5. Be aware of the laws regarding distracted driving, such as texting while driving.

By dedicating time to study and understand these concepts, most individuals find that they can pass the permit test. It is designed to ensure that new drivers have the knowledge required to drive safely and responsibly.

The difficulty of the permit test can vary, but with proper preparation and study of the driver's handbook, most individuals can pass the test.

Answer:

52.50/5.8= $9 per hour

Answer:

2073m

Step-by-step explanation:

House Area:

23*9 = 207m

Lot Area:

60*38 = 2208m

We can make an equation,

Lot Area - House Area = LeftOver Area

2208-207=2073m

Answer:

Each data pair shown is of the form below:

 (years since purchase, value of car)

Use the regression equation to estimate the value of the car 8 years after purchase. Round to the nearest dollar.  $  6019

As more years go by, the prediction (extrapolation) becomes less reliable.

Explanation:

the answer are in bold :)

Based on the correlation coefficient, there is a(n) strong linear correlation between the data.

The correlation coefficient, often denoted as "r," measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, with:

The regression equation to estimate the value of the car 8 years after purchase, as more years go by, the accuracy of this prediction becomes less reliable.

Thus, there is strong linear correlation.

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Final answer:

The student's question can be solved by setting up a system of equations from the given information and finding that the two numbers are 25 and 20.

Explanation:

Solution to the Given Problem

The student's question involves solving a system of equations. They are given that the sum of two numbers is 45 and their difference is 5. To solve this, we can set up two equations based on the information given:

Let the two numbers be x and y.

The sum of the two numbers is 45: x + y = 45

The difference of the two numbers is 5: x - y = 5

To find the values of x and y, we can solve this system of equations. By adding the two equations, we cancel out y, giving us:

2x = 50

Dividing both sides by 2, we find that x = 25. Substituting x = 25 into one of the original equations, for instance, x + y = 45, we get:

25 + y = 45

Subtracting 25 from both sides gives us y = 20.

Therefore, the two numbers are 25 and 20.

Answer: -3(15m-4)/40

(All the numbers are above the fraction bar, then 40 is under the fraction bar)

- 9/8 m + 3/10

Answer

Answer:

They would have the same area.

Step-by-step explanation:

The area of a circle = pi x the circumfrence.  or pi x the radious squared.  so if they had the same circumfrence they would have the same area.