Solve the system of equations by the substitution method. Then use the solution to evaluate the expression 2x(−3+y).
6x+2y+1=13+10y−x
5x=y+26−2x
The value of the expression is....

8 = 2 · 2 · 2

22 = 2 · 11

GCF(8, 22) = 2

Answer:

C. 320 Cm

Step-by-step explanation:

To convert any value in meters to centimeters, just multiply the value in meters by the conversion factor 100.

3.2 meters=3.2*100=320 centimeters

When you reflect a point across an axis, either the x value or the y value flips signs.

When you reflect across the x axis, the sign of the y value changes(+ to -) or (- to +)

When you reflect across the y axis, the sign of the x value changes (+ to -) or (- to +)

The point reflected across the x-axis because the sign of the y value changed/flipped, while the sign of the x value stayed the same.

Final answer:

Brandon reflected the point (-4, -6) across the x-axis to get the point (-4, 6), which is recognized by the unchanged x-coordinate and the sign reversal of the y-coordinate.

Explanation:

Brandon reflected the point (-4, -6) to get the point (-4, 6). This reflection occurred across the x-axis. We know this because the x-coordinate of the point remained unchanged, indicating that the point was not moved left or right. However, the y-coordinate changed from -6 to 6, which signifies that the point was reflected over the x-axis and moved from below the axis to an equal distance above the axis.

In reflections across the x-axis, the x-coordinate remains the same while the sign of the y-coordinate is reversed. Conversely, a reflection across the y-axis would keep the y-coordinate the same and reverse the sign of the x-coordinate.

In a coordinate system, negative or positive values for x and y are determined by their position relative to the origin. Points to the right of the origin and above the origin are usually considered to have positive coordinate values, with directions indicated by arrows on the axes. In Brandon's case, the negative y-coordinate became positive, affirming the x-axis as the axis of reflection.

Answer:

The square root of 84 is 9.1651...etc, so in a shorter form, 9.

Answer: [tex]\sqrt[2]{21}[/tex]

Explanation: Work is provided in the image attached.

Answer:

1. (h + p)(x) = 2x^2 - 11x + 16

2. It is the same problem as #1.

3. (k - f)(x) = 5x^3 + x^2 - 17x + 2

4. (q - g)(x) = 4x^2 + 7x - 14

Step-by-step explanation:

We are given that the values of h(x) = 2x^2 - 5x + 15 and p(x) = -6x + 1. Using these values you can substitute them into (h + p)(x).

(2x^2 - 5x + 15) + (-6x + 1)

Start by combining like terms. -5x and -6x will combine; 15 and 1 will also combine. 2x^2 will stay the same since there is no other term for it to combine with.

2x^2 - 11x + 16

Combine like terms. We will be adding since h(x) and p(x) are being added together.

We are given that k(x) = 8x^3 - 12x + 2 and f(x) = 3x^3 - x^2 + 5x. Knowing these values we can substitute k(x) and f(x) into (k - f)(x). This will look like:

(8x^3 - 12x + 2) - (3x^3 - x^2 + 5x)

Start by combining like terms. The terms to the same power can be combined (keep in mind we are finding the difference, in other words: subtracting). The terms with "x" can be combined as well. After doing so, your evaluated expression will look like:

5x^3 + x^2 - 17x + 2

q(x) = 4x^2 + 9x - 10 and g(x) = 2x + 4. Substitute q(x) and g(x) into (q - g)(x).

(4x^2 + 9x - 10) - (2x + 4)

Use the same rules I said above. The simplified expression will look like:

4x^2 + 7x - 14

Answer: the first question is no. It is not a proportional relationship. Can you tell me what the options for the second question is please?

Answer: [tex]\bold{\pm1, \pm5, \pm\dfrac{1}{3},\pm \dfrac{5}{3}}[/tex]

Step-by-step explanation:

Q             P

3x² - 3x + 5

Possible rational roots are all of the factors of P divided by all of the factors of Q, including both positive and negative values.

  [tex]\pm \dfrac{\text{factors of P}}{\text{factors of Q}}[/tex]

[tex]=\pm \dfrac{\text{factors of 5}}{\text{factors of 3}}[/tex]

[tex]=\pm \dfrac{1, 5}{1, 3}[/tex]

[tex]=\pm\dfrac{1}{1}, \pm\dfrac{5}{1}, \pm\dfrac{1}{3},\pm \dfrac{5}{3}[/tex]

Answer:

242 dollars / month. See guidelines below

Step-by-step explanation:

That depends largely on where she lives. The rule of thumb is to allow about 1/3 for rent after the government takes it's cut (that's all governments).

Here is an actual breakdown of how budgeting should be done.

These numbers are meant for Canada and are meant as a guide. In reality, if you live in the United States you will have to be spending more on medical for example and less somewhere else.

Now to your question. She has 29000 dollars. Debt is listed at 10%

10% of 29000 = (10/100) * 29000 = 2900 dollars.

Like most numbers having to do with money, most people don't understand large numbers and have to have them broken down.  In monthly terms, she can spend 2900 / 12 = 241.67 dollars / month on debt. That does not mean that she can add 241.67 of new debt every month. It means that she must first pay off what she owes, and then she gets to spend the balance on debt, but that is a very dangerous way to think. What she should say is if she has left over money that money can be transferred over to another category.

I know of very few people that can consider themselves debt free. Fewer of our American friends can make the claim.

The sources of these %s come from Credit Counselling Society (of Canada)

Answer:

CD

Step-by-step explanation:

The fastest way to get from D to AB is to go down CD

The distance from the point D to line AB is represented by the distance CD.

To find out the distance from a point to a line we have to draw a perpendicular to the line from a given point, this distance will be considered as the distance between the point and line.

Hence the distance from point D to line AB is CD(option A).

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The formula of a slope:

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

We have the points (5, 2) and (0, -13). Substitute:

[tex]m=\dfrac{-13-2}{0-5}=\dfrac{-15}{-5}=3[/tex]

Answer:

3

Step-by-step explanation:

We are to find the slope of a line which passes through the two given points: (5, 2) and (0, -13).

We know the formula of the slope (m):

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

So putting in the values of the coordinates of the given points in the formula to get:

Slope = [tex]\frac{-13-2}{0-5} =\frac{-15}{-5}[/tex] = 3

Therefore, the slope slope of a line which passes through the two given points: (5, 2) and (0, -13) is 3.

To find the real solutions of the equation x^3-8x^2+17x-10=0 using the x-intercept method, factor the equation and set each factor equal to zero. The real solutions are x=2, x=1, and x=5.

To find the real solutions of the equation x^3-8x^2+17x-10=0 using the x-intercept method, we need to find the x-values where the graph of the equation intersects the x-axis. This is done by factoring the equation and setting each factor equal to zero.

Step 1: Factor the equation: (x-2)(x-1)(x-5)=0

Step 2: Set each factor equal to zero and solve for x:

Therefore, the x-intercepts or real solutions of the equation are x=2, x=1, and x=5.

Answer:

5.26 X 10^-3

Step-by-step explanation:

The  number sentence that  is not true is |-20| < 20 , option A

Let us consider each of the options;

Option A;

|-20| < 20

20<20

This statement is wrong because 20 is not less than 20

Option B

|9|=9

9=9

This statement is correct mathematically, hence the correct statement

Option C

|-20|>|9|

20>9

This statement is correct mathematically, hence the correct statement

Option D

|9|<|20|

9<20

This statement is correct mathematically, hence the correct statement

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The ascending order of the provided numbers is 4.045, 4.054, 4.405, 4.4005, and 4.504. This was achieved by comparing each decimal place from left to right.

The numbers 4.054, 4.045, 4.405, 4.504 and 4.4005 can be arranged in increasing order (from less to greater) by comparing each place value from left to right. When we compare these numbers, the arrangement from less to greater would be 4.045, 4.054, 4.405, 4.4005, and 4.504.

To do this, we first compare the numbers at each decimal place (tenths, hundredths, thousandths etc.), and arrange accordingly. We continue this process until we have the complete list in ascending order.

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Answer: ($4.19 x 1) + ($6.95 x 4) = $31.99

Step-by-step explanation: 4.19 is the price of the loaf of bread, so the first part of the equation ($4.19x), in this case the x is 1 since she bought only one loaf.

6.95 is the price of the turkey per pound, so our second part to the equation, ($6.95y), in this case y is 4 since the turkey weighed 4 pounds.

The complete equation is the combined cost of the turkey and bread so ($4.19x) + ($6.95y) = $?

The we replace the letters, ($4.19 x 1) + ($6.95 x 4) = $?

And then we add and multiply, ($4.19 x 1) + ($6.95 x 4) = $31.99

Answer:

a

Step-by-step explanation:

Answer:

f(x) = -60 is your answer

Step-by-step explanation:

Plug in 3 for x

f(x) = 5x² - 7(4x + 3)

f(x) = 5(3²) - 7(4(3) + 3)

Follow PEMDAS. First, solve the parenthesis

3² = 9

4(3) + 3 = 12 + 3 = 15

f(x) = 5(9) - 7(15)

Multiply

f(x) = 45 - 105

Simplify. Subtract

f(x) = 45 - 105

f(x) = -60

f(x) = -60 is your answer

~

The value of f(3) in the function f(x) = 5x² - 7(4x+3) is -60.

To find the value of f(3), we need to substitute x = 3 into the given function f(x) = 5x² - 7(4x+3). First, let's simplify the expression inside the parentheses: f(x) = 5x² - 28x - 21. Now substitute x = 3: f(3) = 5(3)² - 28(3) - 21. Simplifying further, we get: f(3) = 45 - 84 - 21 = -60.

To find the value of f(3) for the given function f(x) = 5x² - 7(4x+3), we need to substitute 3 in place of x:

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Answer:

1250

Step-by-step explanation:

since 2% of the school is 25 students that means every 2% there is 25 students.

100/2 = 50

50*25 = 1250 students

Answer:

1250 = total students

Step-by-step explanation:

Students in the play = total students * percent in play

We know that the students in the play =25

We know the percent in the play is .02

Substitute what we know into the equation

25 = total students * .02

Divide each side by .02

25/.02 = total students *.02/.02

1250 = total students

Answer:

A.0

Step-by-step explanation:

We can make 1/9 to 2/18

0 is 0/18,

1/2 is 9,18,

1 is 10/18

It is closest to 0/18

Answer:A

Answer:

The equation of  line is shown below.

Step-by-step explanation:

The equation of line is

[tex]y+1=\frac{-3}{5}(x-4)[/tex]

It is the point slope form of a line, therefore the slope of the line is [tex]\frac{-3}{5}[/tex] and the line passing through (4,-1).

Rewrite the above equation in slope intercept form.

[tex]y=\frac{-3}{5}x+\frac{12}{5}-1[/tex]

[tex]y=\frac{-3}{5}x+\frac{12-5}{5}[/tex]

[tex]y=\frac{-3}{5}x+\frac{7}{5}[/tex]

The point slope form of a line is

[tex]y=mx+b[/tex]

Where m is the slope and b is y-intercept.

Therefore the slope of the line is [tex]\frac{-3}{5}[/tex] and the y-intercept of the line is [tex]\frac{7}{5}[/tex].

Slope is defined as

[tex]m=\frac{Rise}{Run}[/tex]

Since the slope is negative, therefore the run of the line is considered on the left side. The line rise by 3 and run by 5, therefore we will add 7 in y and subtract 5 from x.

The y-intercept is [tex](0,\frac{7}{5})[/tex].

[tex](0-5,\frac{7}{5}+3)=(-5,\frac{22}{5})=(-5,4.4)[/tex]

Therefore we have three points (4,-1), (-5,4.4) and (0,1.4). Plot the point on the coordinate plane and connect them be a straight line.

The graph line for y+1 = -3/5(x-4)

Plot the y-intercept at (0, 7/5).

From that point, move 5 units to the right and 3 units down to find another point on the line. This gives you the point (5, 4/5).

You can continue this pattern, moving 5 units to the right and 3 units down from the previous point to find more points on the line.

To graph the line with the equation y + 1 = -3/5(x - 4), we can first rearrange it into the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

Starting with your equation:

y + 1 = -3/5(x - 4)

Let's isolate y:

y = -3/5(x - 4) - 1

Now, we can distribute the -3/5 to both terms inside the parentheses:

y = (-3/5)x + (12/5) - 1

y = (-3/5)x + 12/5 - 5/5

y = (-3/5)x + 7/5

Now that we have the equation in slope-intercept form (y = mx + b), we can see that the slope (m) is -3/5, and the y-intercept (b) is 7/5.

Now, we can plot this line on the coordinate plane. Start by plotting the y-intercept, which is the point (0, 7/5), and then use the slope to find additional points on the line. The slope of -3/5 means that for every 5 units to the right, you go 3 units down.

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Answer:

y=[(8in*x)+6in]/12in

Answer:

x= -2

Step-by-step explanation:

1-)  8x+3-3x+3=x-2

2-) 5x+6=x-2

3-) 4x=-8

4-)x= -2

Answer:

x=9, y=-4

C (9,-4)

Step-by-step explanation:

−4y − 3x = −11

x − 2y = 17

WE are using substitution, so solve the second equation for x

Add 2y to each side

x -2y+2y = 17+2y

x = 17+2y

Substitute this into the first equation

-4y -3x = -11

-4y -3(17+2y) = -11

Distribute the 3

-4y -3*17 -3*2y = -11

-4y -51 -6y = -11

Combine like terms

-10y-51=-11

Add 51 to each side

-10y-51+51=-11+51

-10y = 40

Divide by -10

-10y/-10 = 40/-10

y = -4

Now we need to find x

x= 17+2y

x = 17+ 2(-4)

x =17-8

x=9

By solving the second equation for x, substituting into the first equation, and simplifying, we find the solution to the system is (9, -4), which corresponds to Option C.

In order to find the solution of the system using substitution, we first solve one of the equations for x or y. Looking at the second equation x - 2y = 17, we can solve for x to get x = 2y + 17. Now we substitute this expression for x into the first equation - 4y - 3x = - 11, which gives us:

- 4y - 3(2y + 17) = - 11

Simplifying this equation, we obtain:

- 4y - 6y - 51 = - 11

Combine like terms:

- 10y - 51 = - 11

Add 51 to both sides:

- 10y = 40

Now, divide both sides by - 10 to find y:

y = - 4

After obtaining the value for y, we substitute it back into the equation we derived for x (x = 2y + 17):

x = 2( - 4) + 17

Which simplifies to:

x = - 8 + 17

Finally, we get x = 9.

The solution for the system is therefore (9, - 4), which corresponds to Option C.

Answer:

(3 1/2, 7 1/4)

Step-by-step explanation:

A 1:3 ratio means we want 4 equal parts  (1+3 = 4)

Find the distance of the segment and divide by 4

(x2+x1)/4,  (y2+y1)/4

(8-2)/4 , (5-8)/4

6/4, -3/4

Since the first part is of ratio 1, we multiply by 1

Now add this to the starting point

(2 + 6/4, 8+ -3/4)

Getting a common denominator of 4

2*4/4 = 8/4

8 *4/4 = -3/4

(8/4 + 6/4, 32/4 -3/4)

(14/4, 29/4)

Now change back to a mixed number

(3 2/4 , 7 1/4)

(3 1/2, 7 1/4)

Answer:

x = 12        and    x = -4

Step-by-step explanation:

abs (x-4) = 8

When we have absolute value equations, we get two solutions, one positive and one negative

x-4 = 8        and   x-4 = -8

Add 4 to both sides

x-4+4 = 8+4       x-4+4=-8+4

x = 12        and    x = -4

[tex]|x-4|=8\iff x-4=8\ \vee\ x-4=-8\qquad\text{add 4 to both sides}\\\\\boxed{x=12\ \vee\ x=-4}[/tex]

Answer:

1

Step-by-step explanation:

Answer:

1   (plus 1/6 cup of the original 2/3 cup left over)

Step-by-step explanation:

The LCD of 1/2 and 2/3 is 6.  Thus, 1/2 and 2/3 are equivalent to 3/6 and 4/6.  3/6 divides into 4/6 once, with a remainder of 1/6 (cup).

Answer:  just one 1/2 cup serving can be made from 2/3 cup of cole slaw, with 1/6 cup of the original 2/3 cup of slaw left over.

Answer:

Step-by-step explanation:

If you lose cash and someone finds it, you've lost it without recourse. If you lose a credit card, usually the issuer of the card can cancel it after your last verified purchase and replace the card for you. That is the main advantage.

You also have a record of what you've spent with a credit card. Sometimes you get a receipt and some sometimes you don't when you use cash.

Cash forces you to carry around coins, especially if you make a lot of small purchases in different places. Getting change for 2.22 cents from a 20 can be a little awkward and soon the big bills turn into many more little ones. Credit cards don't have that disadvantage.

Answer:

There are online services that will help someone monitor their credit and make a note of any changes in their credit score. Credit card monitoring keeps track of all open accounts and monitors hard inquiries. That way, if someone did not make the purchase, they can immediately tell the lender that the card has been compromised.

Step-by-step explanation:

This is an altered version of the information from the website given. I got a 100% on edgenunity.

[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ A=16\pi \end{cases}\implies 16\pi =\pi r^2\implies \cfrac{16\pi }{\pi }=r^2\implies 16=r^2 \\\\\\ \sqrt{16}=r\implies 4=r~\hfill \stackrel{\textit{diameter is twice the radius}}{d=8}[/tex]

Answer:

275 km  

Step-by-step explanation:

It has 1 - 3/8 = 5/8 of a tank left.

3/8  of a gallon gives 165 km

So 1 gallon  gives  165 / 3/8  = 165 * 8/3 km

5/8 gallon gives 168 * 8/3 * 5/8 km

= 165 * 5/3

=  275 km  (answer)