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2 years ago

Please help, last two questions.

Mathematics

1 answer:

Novay_Z [31]2 years ago

5 0

First problem.
The function is f(x) = 3^x.
The base, b, is 3 since 3 is raised to power x.
The question is what value of x used in 3^x makes the expression 3^x equal to 3?
Look at the graph, and find the point that has y-value 3.
Which x-value does that point have?
The point is (1, 3), and the x-value is 1.

Second question.
The question is similar to the question above using a different exponential function.
(1/4)^1 = 1/4, so the answer is x = 1

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You are designing a wall Mural that will be composed of squares of different sizes. One of the requirements of your design is th

Oxana [17]

Answer:

1. Area of a square = (x^2)^2 = x^4

(each side is x^2, area of a square = side^2

so (x^2)(x^2) = x^4 )

2. when x = 5

area = 5^4 = 625

3. when x = 10

area = 10^4 = 10000

Step-by-step explanation:

Hope its right!

6 0

2 years ago

g Given the system of equations: 15 c1 – 5 c2 – c3 = 2400 - 5 c1 + 18 c2 – 6 c3 = 3500 - 4 c1 - c2 + 12 c3 = 4000 (a) Calculate

denpristay [2]

Answer

(a)

$A^{-1} = \frac{1}{3493} \begin{pmatrix} 210 && -59 && -12 \\ 84 && 176 && 95 \\ 77 && -5 && 295 \end{pmatrix}$

(b)

$A^{-1} b = \begin{pmatrix} \frac{500}{7} \\\\ \frac{2400}{7} \\\\ \frac{2700}{7} \end{pmatrix}$

Step-by-step explanation:

Remember that when you want to solve a problem like this, you express the equation as following

$Ax = b$

So, if you know the inverse of $A$ then

$x = A^{-1} b$

For this case

$A = \begin{pmatrix} 15 && 5 && -1 \\ -5 && 18 && -6 \\ -4 && -1 && 12 \end{pmatrix}$

Now for this case the inverse of A would be

$A^{-1} = \frac{1}{3493} \begin{pmatrix} 210 && -59 && -12 \\ 84 && 176 && 95 \\ 77 && -5 && 295 \end{pmatrix}$

Then when you multiply with the vector solution

$A^{-1} b = \frac{1}{3493} \begin{pmatrix} 210 && -59 && -12 \\ 84 && 176 && 95 \\ 77 && -5 && 295 \end{pmatrix} * \begin{pmatrix} 2400 \\ 3500 \\ 4000 \end{pmatrix} = \frac{1}{3493} \begin{pmatrix} 249500 \\ 1197600 \\ 1347300 \end{pmatrix}\\\\\\= \begin{pmatrix} \frac{500}{7} \\\\ \frac{2400}{7} \\\\ \frac{2700}{7} \end{pmatrix}$

So from that information you can conclude that the solution to the system of equations is x = 500/7 y = 2400/7 and z = 2700/7

7 0

2 years ago

Find the general expression for the slope of a line tangent to the curve of y=2x^2+4x at the point P(x,y) . Then find the slopes

ArbitrLikvidat [17]

Complete Question

Find the general expression for the slope of a line tangent to the curve of y=2x^2+4x at the point P(x,y) . Then find the slopes for $x = 3$ and x=0.5. Sketch the curve and the tangent lines. What is the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) ?

Answer:

The generally expression for the slope of $y = 2x^2 + 4x$ is $y' = 4x +4$

The graph is shown on the first uploaded image

The generally expression for the slope of $y=2x^2+4$ is $y' = 4x$

Step-by-step explanation:

From the question we are told that

The equation of the curve is $y = 2x^2 + 4x$

First we differentiate the equation

$y' = 4x +4$

Therefore the generally expression for the slope tangent to the curve $y=2x^2+4x$ is $y' = 4x +4$

The next step is to substitute for x = 3 and x = 0.5

So for $x_1 = 3$

$y' = 4(3) +4$

$y' =m_1= 16$

And for $x_2 = 0.5$

$y' = 4(0.5) +4$

$y' =m_2= 6$

Here m_1 and m_2 are slops of the curve

Next we obtain the coordinates of the tangent lines

So at $x_1 = 3$

$y_1 = 2(3)^2 + 4(3)$

$y_1 = 21$

So the coordinate for the first tangent line is

$(x_1 , y_1 ) = (3 , 21)$

At $x_2 = 0.5$

$y_2 = 2(0.5)^2 + 4(0.5)$

=> $y_2 = 2.5$

So the coordinate for the second tangent line is

$(x_2 , y_2 ) = (0.5 , 2.5)$

Next we obtain the equation for the tangent lines

So generally the slope is mathematically represented as

$m = \frac{y - y_1 }{x-x_1}$

For $(x_1 , y_1 ) = (-3 , 21)$ and $y' =m_1= 16$

$16 = \frac{y -21 }{x-3)}$

=> $y = 16x - 27$

For $(x_2 , y_2 ) = (0.5 , 2.5)$ and $y' =m_2= 6$

$6 = \frac{y -2.5 }{x-0.5}$

$y = 6x -0.5$

Generally the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) is mathematically evaluated by differentiating y=2x^2+4 as follows

$y' = 4x$

7 0

2 years ago

Eduardo earns a base salary of $30,000 per year and earns $1,875 per car he sells. Which equation can be used to find the number

agasfer [191]

Answer:

The equation is, A =30,000 + 1875n.

He sold 9 cars the year he made that amount of money.

Step-by-step explanation:

Before calculating, let's assign letters to certain variables:-

✓ let "A" be used to represent the total amount earned after adding his base salary to the amount he earned as commission per car he sells.

✓ "P" will be used to represent his base salary (a constant = 30,000)

✓ "n" will represent the number of cars sold within a given year.

✓ "B" will be used to represent his commission per car he sells.

Fixing them into a formula, we have:

A = P + n(B)

Since "P" and "B" are constants of 30000 and 1875 respectively, we substitute the letters for their actual amount in the formula:-

A = 30,000 + n(1875)

A = 30,000 + 1875n +This is now the equation that can be used to calculate the number of cars he sold in the year he earned 46,875).

So, since "A" is now $46,875, we substitute accordingly to find the number of cars he sold in the year he earned such amount.

46,875 = 30,000 + 1875b

1875n = 46,875 - 30,000

1875n = 16875

n = 16875/1875

n = 9 cars

Therefore the equation to be used to determine how many cars he sold when he earned $46,875 is:

A = 30,000 + 1875n

He sold 9 cars the year he earned $46,875.

7 0

2 years ago

Someone help ASAP! Weill give brainliest. (Not a quiz or test or anything)

denpristay [2]

Answer:

17.8

Step-by-step explanation:

First:

put the equation together

(2x+3) * (x+2)=91

Secondly:

condense

parenthisis can be dropped and normal problem solving can be used.

5x+2=91

subtract 2 from either side of the =

this will give you 5x=89

next divide 5 from each side because it is multiplying the x

x=17.8

8 0

2 years ago