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Solve using Substitution Method

2x + 5y = 7
x = 2 - 4y ​

Answer:

one-sixth of 138

Step-by-step explanation:

36÷3=12. 138÷6=23

12<23

Therefore, one-sixth of 138 is greater than a third of 36.

Answer:

12 times.

Step-by-step explanation:

96÷8=12

Answer:

30 miles in 2 hours

Step-by-step explanation:

Answer:

A unit rate is a rate where the second quantity is one unit , such as $34 per pound, 25 miles per hour, 15 Indian Rupees per Brazilian Real, etc. Example 1: A motorcycle travels 230 miles on 4 gallons of gasoline. Find the average mileage per gallon.

Step-by-step explanation:

Question 958954: One number is five less than a second number. Five times the first is eight more than two times the second. Find the numbers.

hope this helps!

Answer:

c. 5056

Step-by-step explanation:

The revenue is maximized when the units sold are increased if the selling price is constant. The basket ID 5056 has more units then the other two baskets and its invoice total is greater than the other baskets. The basket 5056 has largest total revenue to the company.

To find a decimal that is equavalent to 4/15, all we need to do is divide.

4 / 15 = 0.26666...

Best of Luck!

Answer:

No

Step-by-step explanation:

Its 1000

Answer:

35°

Step-by-step explanation:

-5° + 40° = 35°

So the ansWer is 35°

Answer:

3 + 9i

Step-by-step explanation:

(4 + 2i) - (1 - 7i)

distribute the (-)

(4 + 2i) - 1 + 7i

combine like terms

3 + 9i

Answer:

Step-by-step explanation:

Given the 2 by 2 matrix [tex]A = \left[\begin{array}{-cc}x&5\\y&-8\\\end{array}\right][/tex] , we are to find the value of x and y for the expression A² = A to be true.

First we need to find A² by multiplying the same matrix together

[tex]A^2 = \left[\begin{array}{-cc}x&5\\y&-8\\\end{array}\right] \left[\begin{array}{-cc}x&5\\y&-8\\\end{array}\right]\\\\ \ we \ normally \ multiply \ the \ rows \ of \ the \ first \ matrix \ with \ the \ column \ of \ the \ second \\\\A^2 = \left[\begin{array}{-cc}x^2+5y&5x-40\\xy-8y&5y+64\\\end{array}\right]\\\\Since \ A^2 = A,\ hence;\\\\\left[\begin{array}{-cc}x^2+5y&5x-40\\xy-8y&5y+64\\\end{array}\right] = \left[\begin{array}{-cc}x&5\\y&-8\\\end{array}\right]\\[/tex]

Equating the first row and second column of both matrices together, we will have;

5x-40 = 5

add 40 to both sides of the equation

5x-40+40 = 5+40

5x = 45

x = 45/5

x = 9

Similarly,  we will equate the second row and second column of both matrices to have;

5y+64 = -8

Subtract 64 from both sdies

5y+64-64 = -8-64

5y = -72

y = -72/5

Hence the value of x is 9 and y is -72/5

Matrices are used to represent data in rows and columns

The values of x and y are 9 and -14.4 respectively.

Matrix A is represented as:

[tex]\mathbf{A = \left[\begin{array}{ccc}x&5\\y&-8\end{array}\right] }[/tex]

Calculate [tex]\mathbf{A^2}[/tex]

[tex]\mathbf{A^2 = \left[\begin{array}{ccc}x&5\\y&-8\end{array}\right] \times \left[\begin{array}{ccc}x&5\\y&-8\end{array}\right] }[/tex]

Recall that [tex]\mathbf{A^2 = A}[/tex]

This means that:

[tex]\mathbf{\left[\begin{array}{ccc}x^2++5y&5x-40\\xy-8y&5y+64\end{array}\right] = \left[\begin{array}{ccc}x&5\\y&-8\end{array}\right] }[/tex]

So, by comparison

[tex]\mathbf{5x - 40 = 5}[/tex]

[tex]\mathbf{5x = 40 + 5}[/tex]

[tex]\mathbf{5x = 45}[/tex]

[tex]\mathbf{x = 9}[/tex]

Similarly

[tex]\mathbf{5y + 64 = -8}[/tex]

[tex]\mathbf{5y =-64 -8}[/tex]

[tex]\mathbf{5y =-72}[/tex]

[tex]\mathbf{y =-14.4}[/tex]

Hence, the values of x and y are 9 and -14.4 respectively.

Read more about matrices at:

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Answer:

A. 3

B. 3/4

C. 1/4

Step-by-step explanation:

1/4 of 12 is 3

3 plus 6 is 9 and 9 is 3/4 of 12

12 minus nine is also three leaving the tank still a 1/4 tank empty

Answer:

C

Step-by-step explanation:

24÷6= 6 Hope this helps.

Answer:

30sequences

Step-by-step explanation:

Using nx (n-1)

And

n is the number of ternary digits in the number.

So For 6 digits n is 6 so the number of numbers that have exactly one 1 AND exactly one 2 is 30.

That is 6(6-1)= 30

Step-by-step explanation:

The second graph is the right one

Answer:

see below

Step-by-step explanation:

f(x) = -x-7 is of the form

y = mx+b  where m is the slope and b is the y intercept

The line  has a y intercept of (0,-7) and a slope of -1

A slope of -1 means the line goes down from left to right ( down 1 and to the right 1)

Answer:

i think... a d and e?

Step-by-step explanation:

Answer:

B. Vertical Compression

Step-by-step explanation:

You've answered the question; However, I'll assist with the explanation;

Given

Original: [tex]y = 72\sqrt x[/tex]

Translated: [tex]y = 9\sqrt x[/tex]

Required

Determine the type of transformation applied to the original function

Observing both functions, we notice that [tex]\sqrt x[/tex] is a common factor;

This implies that the function was compressed or stretched along the y axis (vertically)

To determine if its vertical compression or stretch;

We have to divide the translated function by the original function;

[tex]Ratio = \frac{9\sqrt x}{72\sqrt x}[/tex]

[tex]Ratio = \frac{9}{72}[/tex]

[tex]Ratio = 0.125[/tex]

Because 0.125 < 1, then the transformation is a vertical compression

Answer:

B

Step-by-step explanation:

The volume of the right rectangular prism having dimensions  1.5 cm, 0.5 cm and 2. 25 cm. will be V=1.6875 [tex]cm^3[/tex]

Volume is defined as the space covered by any object in the three dimensions having coordinates in all three sides is called as volume.

We know that the volume of the Rectangular prism is given as:

[tex]\rm V=L\times W\times D\\\\\\V=1.5\times 0.5\times 2.25\\\\\\V=1.6875\ \ \ cm^3[/tex]

Hence the volume of the right rectangular prism having dimensions  1.5 cm, 0.5 cm and 2. 25 cm. will be V=1.6875 [tex]cm^3[/tex]

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Answer:

its an integer

Step-by-step explanation:

Because it has a negative sign

Answer:

$1.30 for juice

Step-by-step explanation:

If madeline bought 2 bagels for $6 then one bagel must be $3. Madison spent $4.30 so $3 was the bagel and $1.30 was the juice.

Answer: simply

Step-by-step explanation: Example: 15y= -5x+0 First move -5 to other side of equal sign. So 15y+5x=0 Then simply by dividing by 5. So 5y+x=0

Answer:

15.6 is the right answer

Step-by-step explanation:

Answer:

1 : 20 20 students for every 1 teacher

Step-by-step explanation:

divide both sides by 12

Use exponent rule: x^-y = 1/x^y

6^-3

= 1/6^3

= 1/216

Best of Luck!

2481.7

         ^ is the tenth place.

The 5 would either round it up or down by one-tenth. Since we like big numbers... we'll round it to 7 from 6.

Answer:

2481.7

Step-by-step explanation:

Find the number in the tenth place

6

and look one place to the right for the rounding digit

5

. Round up if this number is greater than or equal to

5

and round down if it is less than

5

Answer:

choice B

g(x) = –(x + 2)5 + 2(x + 2)4 + 1

The function g(x) can be represented in terms of f(x) like this:

g(x) = -(x - 2)⁵ +2(x - 2)⁴ + 1.

Hence, 4th option is the right choice.

The translation is the process of moving a graph horizontally or vertically. To put it another way, each point on the parent graph is translated to the left, right, up, or down, to get the translated graph.

We know that g(x) is a transformation of f(x) = -x⁵ + 2x⁴ + 1.

Since, g(x) is the transformation of f(x) we try to find the relation between the points on f(x) and g(x).

Let the point on f(x) be (x₁, y₁) and that on g(x) be (x₂, y₂).

f(x) passes through the points (-1, 3), (0,1), (1.5, 3.8), and (2, 0).

Corresponding points on g(x) are (-3, 3), (-2, 1), (-0.5, 3.8), and (0, 0).

We can see that the y-coordinate is the same for corresponding points. So, y₂ = y₁.

For the x-coordinate, we see that for every corresponding point on g(x), it is 2 less than the point on f(x). So, x₂ = x₁ - 2.

Now, in the function f(x), we have x = x₁. So to find the function g(x), we substitute the value of x₂ = x₁ - 2 = x - 2 in f(x) to get the equation of g(x).

∴ g(x) = f(x-2)

or, g(x) = -(x - 2)⁵ +2(x - 2)⁴ + 1.

∴ The function g(x) can be represented in terms of f(x) like this:

g(x) = -(x - 2)⁵ +2(x - 2)⁴ + 1.

Hence, 4th option is the right choice.

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Answer:

a. -2

b. 3

c. 3

d. -3

e. x=-2

Step-by-step explanation:

When a question asks for f(x), it is basically just asking for what the y-value is at the given point of x. So for example, to solve the first one: f(-4), we see that the x-value is -4. This means it is asking for the y-value at x=-4. As we can see from the graph, where x = -4, the y-value is -2 (along the bottom flat line) therefore f(-4) = -2.

This is the same for the other three, f(0) = 3 because the line at x=0 is crossing at y=3. etc.

Finally e is difference because it is instead asking for the x-value when y=6. To solve this we just need to find a point on the graph where the line is at y=6. This, as we can see is at the top of the highest point and occurs where x=-2.

Hope this helped!

Answer:

X=2

Step-by-step explanation:

|2x -12| = -4x

2x-12 = -4x

2x - (-4x) = 12

2x +4x =6x

6x=12

x=12/6

x=2

Answer:

[tex]\huge\boxed{\sf x = 14 , y = 10}[/tex]

Step-by-step explanation:

Let the two numbers be x and y

Condition # 1:

Condition # 2:

[tex]\rule[225]{225}{2}[/tex]

Putting Equation # 2 in Equation # 1

2y - 6 + y = 24

3y - 6 = 24

Adding 6 to both sides

3y = 24 + 6

3y = 30

Dividing both sides by 3

y = 10

[tex]\rule[225]{225}{2}[/tex]

Putting y = 10 in Equation # 2

x = 2y - 6

x = 2(10) - 6

x = 20 - 6

x = 14

[tex]\rule[225]{225}{2}[/tex]

The two numbers are 10 and 14.

The sum of 2 numbers is 24.

let the number be x and y . Therefore,

x + y = 24

One is 6 less than twice the other. therefore,

2x - y = 6

Combine the equations

x + y = 24

2x - y = 6

3x = 30

x = 30 / 3

x = 10

x + y = 24

10 + y = 24

y = 24 - 10

y = 14

The 2 numbers are 10 and 14 .

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Answer:

[tex]y=2x-2[/tex] and image of (0,3) is (1,0).

Step-by-step explanation:

From the given graph it is clear that the line of Nolan Street passes through the points (0,-2) and (1,0).

So, the equation of Nolan Street is

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-(-2)=\dfrac{0-(-2)}{1-0}(x-0)[/tex]

[tex]y+2=2x[/tex]

[tex]y=2x-2[/tex]

So, the equation of the Nolan Street is [tex]y=2x-2[/tex].

It is given that the cartographer translates points on line m along the vector <1, −3> to draw Nolan Street. So, the rule of translation is

[tex](x,y)\to (x+1,y-3)[/tex]

The image of (0, 3) in this situation.

[tex](0,3)\to (0+1,3-3)=(1,0)[/tex]

The image of (0,3) is (1,0).