The cost of making 4 lamps is $370.
The cost of making 11 lamps is $755.
What is the cost per lamp?

Answer:

Step-by-step explanation:

As first step we must obtain the equation of the line. According to Analytical Geometry, we can get a equation of the line by knowing two different points. A linear function is represented by the following expression:

[tex]y = m\cdot x + b[/tex]

Where:

[tex]x[/tex] - Independent variable, dimensionless.

[tex]y[/tex] - Dependent variable, dimensionless.

[tex]m[/tex] - Slope, dimensionless.

[tex]b[/tex] - y-Intercept, dimensionless.

If we know that [tex](x_{1}, y_{1}) = (0, 5)[/tex] and [tex](x_{2}, y_{2}) = (3, 8)[/tex], the following system of linear equations is formed:

[tex]5 = 0\cdot m + b[/tex]

[tex]b = 5[/tex] (Eq. 1)

[tex]8 = 3\cdot m + b[/tex]

[tex]3\cdot m + b = 8[/tex] (Eq. 2)

From (Eq. 1) in (Eq. 2) we get the value of [tex]m[/tex]:

[tex]3\cdot m + 5 = 8[/tex]

[tex]3\cdot m = 3[/tex]

[tex]m = 1[/tex]

The equation of the line that contains the points (0, 5) and (3, 8) is [tex]f(x) = x + 5[/tex].

As next step we must apply a reflection in the x-axis, whose operation is defined as follows:

[tex](x', y') \longrightarrow (x, -y)[/tex]

That is:

[tex]x' = x[/tex]

[tex]y' = -y[/tex]

Then, the function [tex]g(x)[/tex] is [tex]g(x) = -x-5[/tex]. We plot each function and include the result in the attachment below.

Answer:

[tex] x = \pm\sqrt{y + 12}[/tex]

Step-by-step explanation:

[tex]y = {x}^{2} - 12 \\ y + 12 = {x}^{2} \\ \pm\sqrt{y + 12} = x \\ x = \pm\sqrt{y + 12} \\ is \: the \: required \: inverse \: function[/tex]

The inverse of the function is given by y = ± √( x² - 12 )

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given data ,

Let the function be represented as A

Now , the value of A is

y = x² - 12   be equation (1)

On simplifying , we get

To calculate the inverse of the function ,

Interchange the value of x with y , we get

x = y² - 12

On solving for y , we get

y² = x + 12

Taking square roots on both sides , we get

y = ± √( x² - 12 )

Hence , the inverse of the function is y = ± √( x² - 12 )

To learn more about function rule click :

https://brainly.com/question/3760195

#SPJ7

Answer:

h = 290 ÷ 7.25, h = 40 u²

Step-by-step explanation:

The formula for the area of a triangle is A = (Bh)/2.

You have already correctly identified the first two steps.

The third step would be to divide 290 by 7.25 to isolate h.

h = 290 ÷ 7.25

= 40 u²

Answer:

option A is the correct answer.

Step-by-step explanation:

Answer:

the answer is A

Step-by-step explanation:

i took a test and that was right

Answer:

16 weeks

Step-by-step explanation:

just took test today hope this help mark me as brailist and add me

Answer:

16 weeks

Step-by-step explanation:

[tex]y = -27x + 577[/tex]

Since y represents the amount of money left in her account, we can replace it with $145 to solve for x (number of weeks)

[tex]145=-27x+577[/tex]

Switch sides:

[tex]-27x+577=145[/tex]

Subtract 577 from both sides:

[tex]-27x+577-577=145-577\\[/tex]

[tex]-27x=-432[/tex]

Divide both sides by -27:

[tex]\frac{-27x}{-27}=\frac{-432}{-27}[/tex]

[tex]x=16[/tex]

After 16 weeks, Alma will have $145 left in her account.

Answer:

He had 499 + 56 = 555

Step-by-step explanation:

Answer:

Kyle had $555 before preordering his PlayStation 5.

Step-by-step explanation: If Kyle spent $499, and has $56 left, you add the two values together. 499+56= 555. Therefore, Kyle had $555 before preordering his PlayStation.

Answer:

3,835,181

Step-by-step explanation:

Answer:

The answer would be A,  3,835,181

Step-by-step explanation:    I did the test, do you do schoology?

Answer:

please be more specific

Answer:

x=10

Step-by-step explanation:

A straight line has an angle of 180 degrees. To solve for x we can add all the given angles and set them equal to 180.

[tex]180= 5x-1+9x+8+2x+13[/tex]

Then combine all the common factors

[tex]180=16x+20[/tex]

And then you can solve for x

[tex]180= 16x+20\\160=16x\\10=x[/tex]

To check if x is correct you can plug in 10 to each equation. If all the equations add up to 180, then x is correct

[tex]5(10)-1= 49\\9(10)+8= 98\\2(10)+13= 33\\\\49+98+33=180[/tex]

Answer: A

Hope this helps :)

Answer:

A

Step-by-step explanation:

Answer:

1/72=x (part a)

1/70=x (bart b)

Step-by-step explanation:

Divide 1 by 72 for part a, and divide 1 by 70 for part b.

Answer:

the answer is x= -1

Step-by-step explanation:

I know this because 72x-1 is the same as 72 divided by 1 which is 1

Answer:

I think in 49 ways by changing each other

Answer: 131°

Step-by-step explanation:

Supplementary angles are the angles that when we add them together, their sum is equal to 180°.

From the question, we are informed that angle w and angle v are supplementary angles and angle v=49.

V + W = 180°

49° + W= 180°

W = 180° - 49°

W = 131°

Answer:

if you are multiplying the 2 and the 32, the answer would be -41

Step-by-step explanation:

hope this helps! :) :) :) (please give me brainliest!)

Answer:

- 41

Step-by-step explanation:

10 - 2 · 32 + 13

Multiply first because of PEMDAS

10 - 64 + 13

- 54 + 13

- 41

-----------------------------------------------------------------------------

If that's not the answer you wanted, you might have forgot to type in the parenthesis.

Hope this helped!!!

Answer:10

Step-by-step explanation:

Answer:

(7x-3y) (-x+3y)

Step-by-step explanation:

(3x-3y+4x) (3x+3y-4x)

(3x-3y+4x) (3x+3y-4x)

(7x-3y) (-x+3y)

Step-by-step explanation:

Angles DE and AB are alternate angles, they have the same angle values :)

Here is the equation: (6x-12)+(7x+1)= 10x+25

Solve:

13x-11=10x+25

3x=36

x=12

Hope this helps :)

Answer:

the answer is going to be x=12

The solutions to the system of equations are (2, -1) and (-2,3)

The equations are given as:

[tex](x - 2)^2 + (y - 3)^2 = 16[/tex]

x  + y - 1 = 0

Make y the subject in x  + y - 1 = 0

y = 1 - x

Substitute y = 1 - x in [tex](x - 2)^2 + (y - 3)^2 = 16[/tex]

[tex](x - 2)^2 + (1 - x - 3)^2 = 16[/tex]

Evaluate

[tex](x - 2)^2 + (-x - 2)^2 = 16[/tex]

Expand the equations

[tex]x^2 - 4x + 4 + x^2 + 4x + 4 = 16[/tex]

Evaluate the like terms

[tex]2x^2 + 8 = 16[/tex]

Subtract 8 from both sides

[tex]2x^2 = 8[/tex]

Divide by 2

[tex]x^2 = 4[/tex]

Take the square roots of both sides

x = ±2

Substitute x = ±2 in y = 1 - x

y = 1 - 2 = -1

y = 1 + 2 = 3

Hence, the solutions to the system of equations are (2, -1) and (-2,3)

Read more about system of equations at:

https://brainly.com/question/14323743

#SPJ2

Answer:

3/7 ÷ 2/3 = 9/14

Step-by-step explanation:

When we divide two fractions, such as 3/7 ÷ 2/3, we flip the second fraction and then we simply multiply the numerators with each other and the denominator with each other.

Answer:

h(6) = 32

Step-by-step explanation:

h (x) = x^2 – 4

h(6) =

Let x = 6

h (6) = 6^2 – 4

       = 36 -4

       = 32

Answer:

Step-by-step explanation:

ratio and proportion:

28 photos    =    21  photos

8 min                     x min.

21 (8) = 28 (x)

x = 168 / 28

x = 6 min.

Answer:

N = 6

Step-by-step explanation:

7 + N = 13

subtract 7 from both sides

N = 6

hope this helps

Hi!

Your answer will be: N=6

Reason being: 7+6=13

Therefore, the answer is 6.

Hope this helps!

Let me know if you need anymore help, I'd be delighted to!

Yours truly,

Answer:

a (9 - 8 a x)

Step-by-step explanation:

Simplify the following:

3 a - 2 a x×4 a + 6 a

-2 a x×4 a = -2 a^2 x×4:

3 a + -2 a^2 x×4 + 6 a

-2×4 = -8:

3 a + -8 a^2 x + 6 a

Grouping like terms, 3 a - 8 a^2 x + 6 a = -8 a^2 x + (3 a + 6 a):

-8 a^2 x + (3 a + 6 a)

3 a + 6 a = 9 a:

-8 a^2 x + 9 a

Factor a out of -8 a^2 x + 9 a:

Answer: a (9 - 8 a x)

The expression that is equivalent to [tex]3a - 2ax \times 4a +6a[/tex] is: [tex]\mathbf{a(9 - 8ax)}[/tex]

Given the expression:

[tex]3a - 2ax \times 4a +6a[/tex]

To find an expression that is equivalent to the above expression, we will need to simplify the expression.

[tex]3a - 2ax \times 4a + 6a\\\\3a - 8a^2x + 6a[/tex]

[tex]3a + 6a - 8a^2x\\\\9a - 8a^2x[/tex]

Simplify the expression further by factoring out

[tex]a(9 - 8ax)[/tex]

Therefore, the expression that is equivalent to [tex]3a - 2a \times 4a +6a[/tex] is [tex]\mathbf{a(9 - 8ax)}[/tex]

Learn more here:

https://brainly.com/question/11033026

Answer:

x= -7

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

2x+11=x+4

Step 2: Subtract x from both sides.

2x+11−x=x+4−x

x+11=4

Step 3: Subtract 11 from both sides.

x+11−11=4−11

x=−7

Answer:

Step-by-step explanation:

[tex]6( (5)-(7) )\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Calculate\:within\:parentheses}\:\left(\left(5\right)-\left(7\right)\right)\:\\:\quad -2\\\\=6\left(-2\right)\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:6\left(-2\right)\:\\:\quad -12\\\\=-12[/tex]

Step-by-step explanation:

The slope of the perpendicular line is the opposite inverse.  So the student should have used -1/4 as the slope of the perpendicular line, not 1/4.

Answer:

1st 3rd and 4th

Step-by-step explanation:

I just did that

Answer:

It's A.

Step-by-step explanation:

Answer:

y = 9 (x + one-half) squared minus thirteen-fourths

Step-by-step explanation:

i hope