Find the inverse.

f(x)= 2x-5/3x+4

Answer:

y = 3500(3/7 ) ^ 1/3

y = 239.23

Step-by-step explanation:

For exponential decay

y =a b^x

a = 3500

b<1

We can use the point (3, 1500)

1500 = 3500 * b^3

Divide each by 3500

1500/3500 = 3500/3500 b^3

15/35 = b^3

3/7 = b^3

Take the cube root of each side

(3/7) ^ 1/3 = b^3 ^ 1/3

b = (3/7 ) ^ 1/3

The function is

y = 3500 (3/7) ^ 1/3 x

We want to find y when x=9.5

y = 3500 (3/7) ^ (9.5 /3)

y = 3500 ( 3/7) ^ 3. 166666666

y = 3500 (.06835)

y = 239.23

Lets check a point and see if we a close

(7,500)

y = 3500 (3/7)^ (1/3*7)

y = 3500 (3/7) ^ (7/3)

y = 484.68

That is pretty close.  We do not know the exact value since we are reading from a graph.

Final answer:

By defining variables for the prices and setting up a system of equations, we determine that each shirt costs $12 and each pair of jeans costs $40 after solving the system using the elimination method.

Explanation:

The subject of this question is a problem involving systems of equations, which falls under the category of Mathematics. We are given a scenario where Lucy and Ethel are buying clothing at the same prices, but in different quantities and we need to determine the cost of each item. First, let's define variables: let s be the price of a shirt and j be the price of a pair of jeans. We then have two equations based on the purchases:

To solve these equations using the elimination method, we will multiply the first equation by 5 and the second by 4 to eliminate the jeans variable:

Subtract the second equation from the first:

Now divide by 2 to find the price of one shirt:

We can substitute s = $12 into the first original equation to find the price of a pair of jeans:

Answer:

LE > VO

Step-by-step explanation:

This is a short answer, but I assure you that it is 100% correct.

Hope it helps.

Answer:

11

Step-by-step explanation:

I guess

Answer:

A. 34 millimeters.

B. 118 millimeters.  

Step-by-step explanation:

We have been given that after m months the height of a plant is [tex]10+3m[/tex] millimeters.

To find the height of plant after 8 months we will substitute m=8 in our given expression.

[tex]\text{The height of plant after 8 months}=10+3\times 8[/tex]

[tex]\text{The height of plant after 8 months}=10+24[/tex]

[tex]\text{The height of plant after 8 months}=34[/tex]

Therefore, the height of plant after 8 months will be 34 millimeters.

B. Now let us find height of plant after 3 years.

First of all we will convert 3 years into months by multiplying 3 by 12 as 1 year equals to 12 months.

[tex]\text{3 years}=3*12\text{ months}=36\text{ months}[/tex]

Now let us substitute m=36 in our given expression.

[tex]\text{The height of plant after 36 months}=10+3\times 36[/tex]

[tex]\text{The height of plant after 36 months}=10+108[/tex]

[tex]\text{The height of plant after 36 months}=118[/tex]

Therefore, the height of plant after 3 years (36 months) will be 118 millimeters.

Solution:

[tex]\frac{3}{5}=\frac{6}{10}=\frac{9}{15}[/tex]

Two or more fractions are said to be equivalent , if reduced in lowest terms that is numerator and denominator are co-prime, they are equal.

[tex]\frac{3}{5}[/tex] Three out of five is shaded.

Equivalent fraction of

[tex]\frac{3\times 6}{5\times 6}=\frac{18}{30} \\\\  \frac{3\times 8}{5\times 8}=\frac{24}{40}[/tex]

Answer:

Step-by-step explanation:

m<1 is 90 degrees

m<2 is 121 degrees

m<3 is 42 degrees

m<4 is 42 degrees

m<5 is 35 degrees

m<6 is 90 degrees

m<7 is 48 degrees

m<8 is 35 degrees

m<9 is 35 degrees

Answer:

[tex]y=(x+3)^{2} -1[/tex]

Step-by-step explanation:

General equation of a parabola that opens up is [tex]y=a(x-h)^{2} +k[/tex] , a>0

So equation becomes [tex]y=(x-h)^{2} +k[/tex] which implies option A and option B can never be true for this parabola.

Also this parabola's vertex lies in 3rd quadrant where coordinates of both x and y will be negative.

So, the equation of parabola will be of the form [tex]y=(x+h)^{2} - k[/tex]

Hence, option 4 that is [tex]y=(x+3)^{2} -1[/tex] is correct.

The correct equation of the graph is: x² + 6x - 35y + 8 = 0.

The equation of the graph shown, which is a parabola that opens upwards and crosses the x-axis at -2 and -4, can be determined by examining its key features.

The fact that the parabola opens upward indicates that the coefficient of the squared term (x²) in the equation must be positive.

The parabola crosses the x-axis at -2 and -4. This means that the two x-intercepts are -2 and -4.

Putting this information together, we can form the equation:

y = a * (x - r1) * (x - r2)

where 'a' is a positive constant (coefficient of x²), and r1 and r2 are the x-intercepts.

Since the x-intercepts are -2 and -4, the equation becomes:

y = a * (x - (-2)) * (x - (-4))

y = a * (x + 2) * (x + 4)

Now, let's find the value of 'a.' We are given that the parabola passes through the point (3, 1). We can substitute these coordinates into the equation to find 'a':

1 = a * (3 + 2) * (3 + 4)

1 = a * 5 * 7

a = 1 / (5 * 7)

a = 1 / 35

Now that we have the value of 'a,' we can finalize the equation:

y = (1/35) * (x + 2) * (x + 4)

Expanding the equation:

y = (1/35) * (x² + 6x + 8)

To put the equation in standard form, we can multiply both sides by 35 to eliminate the fraction:

35y = x^2 + 6x + 8

Finally, rearrange to get the equation in standard form:

x² + 6x - 35y + 8 = 0

So, the correct equation of the graph is: x² + 6x - 35y + 8 = 0.

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Answer:

The range is  { -1,3,7,11,15}

Step-by-step explanation:

The range is just the output values

f(-2) = 4(-2) +7 = -8+7 =-1

f(-1) = 4(-1) +7 = -4+7 = 3

f(0)= 4(0) +7 = 7

f(1) = 4(1) + 7 = 11

f(2) = 4(2) +7 = 8+7 = 15

Answer:

The answer is B

Step-by-step explanation:

First you should make a table to explain it better to yourself. Make 2 columns named Domain(Input) and Range(Output). Now put your ordered pair in the range area. Now calculated the function by replacing X with the range. Calculate.

To find a rectangular field with the same perimeter but a larger area than the original field (115m x 70m), we should search for dimensions that sum up to half of the perimeter (185m) and form a shape closer to a square. An example would be a field measuring 92.5m by 92.5m, which has the same 370m perimeter but a larger area.

You have asked about the length and width of another rectangular field that has the same perimeter but a larger area than a field measuring 115 meters in length and 70 meters in width. To find the dimensions of such a field, we must first calculate the perimeter of the original field.

The formula for the perimeter (P) of a rectangle is P = 2(length + width). Plugging in the given dimensions, we get P = 2(115m + 70m) = 2(185m) = 370 meters. Now we need to find dimensions that add up to half this perimeter, since length + width = P/2, which is 185 meters, but form a rectangle with a larger area.

Area (A) is calculated by the formula A = length x width. To maximize the area for a given perimeter, the rectangle should be closer to a square because a square has the largest area for a given perimeter. Hence, the dimensions we are looking for should be closer to each other compared to the original dimensions of 115m x 70m.

An example of dimensions that meet these criteria would be 92.5 meters by 92.5 meters. Although this results in a square, it fulfills the condition of having the same perimeter (since 2(92.5m + 92.5m) = 370m) but a larger area (92.5m x 92.5m = 8556.25 square meters) than the original rectangular field (115m x 70m = 8050 square meters).

Answer:

C) 68 in

Step-by-step explanation:

We use sine ratio

= 68 inches

Thank you.

Answer:

The equation of this line would be y + 8 = 4(x - 3)

Step-by-step explanation:

In order to get this we can start with the base form of point-slope.

y - y1 = m(x - x1)

Now that we've got this, we can plug in the slope for m. We can also plug in the point for (x1, y1).

y + 8 = 4(x - 3)

Answer:

(-4,-1)

Step-by-step explanation:

The solution to the system of equations is where the two lines cross.

The x coordinate is -4

The y coordinate is -1

Answer:

<C =120

Step-by-step explanation:

Since the figure in inscribed in the circle, <A = <C  and <B = <D

<B= <D

2x-1=3x-59

Subtract 2x from each side

2x-2x-1=3x-2x-59

-1= x-59

Add 59 to each side

-1+59 = x-59+59

58 =x

<A = 2x+4

<A= 2(58) +4

    = 116+4

<A =120

<C = <A

<C =120

Answer:

The percentage of left-handed 6th graders is 20%.

Step-by-step explanation:

To find this, start by finding the total number of lefties.

19 girls + 11 boys = 30 students.

Next find the total number of students

90 girls + 60 boys = 150 students

Now divide the lefties by the total number.

30/150 = 20%

Olivia drinks 0.375 gallons of water.

Problem-solving is defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.

Problem-solving starts with identifying the issue. For example, a trainer may need to figure out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.

Calculation:-

Quantity of water Olivia took = half a gallon i.e 0.5 gallons.

Quantity of water Olivia drank =0.75 of 0.5

      ∴  75% of 0.5 gallons

          = 75/100 × 0.5

           = 0.375 gallons.

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Answer:

-5+√3i  is the given root so -5-√3i  must be the other root

Step-by-step explanation:

We know that complex roots must come in pairs. The pairs are complex conjugates.  (a+bi)  and (a-bi)

You are missing a sign between -5 and the square root

So if - 5+ sqrt(3) i  is a root, then -5 - sqrt(3) i   must be a root  

if -5 - sqrt(3)i   is a root, then -5 + sqrt(3)i   must be a root.

I will assume you missed a + sign

-5+√3i  is the given root so -5-√3i  must be the other root

Answer: is A

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

4.50=15%

30=100%

check;

30*0.85=25.5

30-25.5=4.50

Answer:

a(n) = 0.55 + (n -5)0.07

Step-by-step explanation:

The cost goes up $0.07 for each additional minute, so that is the slope of the linear function. In point-slope form the equation can be written ...

... a(n) - 0.55 = 0.07(n -5)

adding 0.55, and rearranging slightly, this becomes ...

... a(n) = 0.55 +(n -5)0.07

Answer:

B

Step-by-step explanation:

Rotation 180° is accomplished by negating both the x- and y-coordinates. That is, you multiply each of them by -1. You want the opposite of the identity matrix, so matrix B.

We have that the Rotation of matrix [tex]Matrix =\begin{pmatrix}1 \\3\end{pmatrix}[/tex] will be rotated 180 degree if [tex]Matrix =\begin{pmatrix}1 \\3\end{pmatrix}[/tex] is multiplied by [tex]\begin{pmatrix}-1 & 0\\0 & -1\end{pmatrix}[/tex]  

Option D is correct

From the Question we are given

[tex]Matrix =\begin{pmatrix}1 \\3\end{pmatrix}[/tex]

it is important to note that the rotation of the identity matrix  [tex]\begin{pmatrix}1 & 0\\0 & 1\end{pmatrix}[/tex] rotating across the Cartesian co-ordinate is a [tex]180 \textdegree[/tex] is going to give a matrix   [tex]\begin{pmatrix}-1 & 0\\0 & -1\end{pmatrix}[/tex]  

Therefore

The Rotation of matrix [tex]Matrix =\begin{pmatrix}1 \\3\end{pmatrix}[/tex] will be rotated 180 degree if [tex]Matrix =\begin{pmatrix}1 \\3\end{pmatrix}[/tex] is multiplied by [tex]\begin{pmatrix}-1 & 0\\0 & -1\end{pmatrix}[/tex]  

Option D is correct

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Answer:

The equation would be y = 1/23x - 251/23

Step-by-step explanation:

To start, you need to locate the slope of the first equation. Since the slope is the coefficient of x, we know it to be -23. Now, the perpendicular slope is the opposite and reciprocal of that, which makes the new slope 1/23.

Now that we have this, we can use the point and the slope in point-slope form to get the equation.

y - y1 = m(x - x1)

y - 11 = 1/23(x - 2)

y - 11 = 1/23x - 2/23

y = 1/23x - 251/23

Answer:

Step-by-step explanation:

Answer:

An expression y = 10+ 2x

Step-by-step explanation:

As per the statement: To play bingo,there is a $10 cover charge plus $2 per bingo card.

Let x represents the number of bingo card and y represents cost .

"$2 per bingo card" means 2x

"$10 cover charge plus $2 per bingo card" means 10 + 2x

then,

an expression to represents this statement;

y = 10 + 2x

Answer:

[tex]\frac{13}{20}[/tex]

Step-by-step explanation:

First, we need to add the two fractions together. To do this we need to make the denominator a factor of both 8 and 5. Easy way to do this is to multiply each fraction by the denominator of the other fraction:

[tex]\frac{3}{5} * 8 = \frac{24}{40}[/tex]

[tex]\frac{6}{8} * 5 = \frac{30}{40}[/tex]

[tex]\frac{24}{40} + \frac{30}{40} = \frac{54}{40}[/tex]

We can also show 2 brownies as [tex]\frac{2}{1}[/tex] or [tex]\frac{80}{40}[/tex]

Now we can subtract the two:

[tex]\frac{80}{40} -  \frac{54}{40} = \frac{26}{40}[/tex]

Simplify the fraction down by dividing by two:

[tex]\frac{13}{20}[/tex]

Which is the fraction of brownie left!

ANSWER

g(x) > h(x) for x = -1 is TRUE

For positive values of x, g(x) > h(x) is TRUE

For negative values of x, g(x) > h(x) is also TRUE

EXPLANATION

The given functions are

[tex]g(x)={x}^{2}[/tex]

and

[tex]h(x)=-{x}^{2} [/tex]

If

[tex]x=0[/tex]

[tex]g(0)={0}^{2}=0[/tex]

[tex]h(0)=-({0})^{2}=0[/tex]

Based on this options A and B are FALSE.

When

[tex]x=-1[/tex]

[tex]g(-1)={( - 1)}^{2}=1[/tex]

[tex]h(-1)=-{(-1)}^{2}=-1[/tex]

[tex]g( - 1)>\:h(-1)[/tex]

for x=-1 is True.

When x=3,

[tex]g(3)={3}^{2}=9[/tex]

and

[tex]h(3)=-{3}^{2}=-9[/tex]

[tex]g(3)>\: h( 3)[/tex]

g(x) < h(x) for x = 3 is a FALSE statement.

For positive values of x, g(x) > h(x) is TRUE

See graph.

For negative values of x, g(x) > h(x) is also TRUE

See graph

The statements that are true for the functions g(x) = x^2 and h(x) = -x^2 are: h(x) will always be greater than g(x), g(x) < h(x) for x = 3, and for positive values of x, g(x) > h(x).

The statements that are true for the functions g(x) = x^2 and h(x) = -x^2 are:

These statements can be verified by plugging in values for x and comparing the outputs of the functions.

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B) 6 hours

Let h represent the total trip time. Then h/2 is the time spent traveling at each speed. The distance covered is ...

... distance = speed · time

The sum of the distances in each mode is the total distance.

... 1020 = 55·h/2 +285·h/2

... 2040 = h·(55+285) . . . . multiply by 2

... 2040/340 = h = 6 . . . . . . . divide by the coefficient of h

The trip took a total of 6 hours.

Answer:

78*50/100= 78/2 ( half of 78) = 39

Step-by-step explanation:

Answer:

250%

Step-by-step explanation:

First, set the equation.

35/14 x 100% = answer

Simplify.

2.5 x 100 = answer

250 = answer

250% is your answer

~

Answer:

The answer is 2.5

Step-by-step explanation:

14*2.5%=35

Answer:

Rational

Step-by-step explanation:

A rational number would be a number or a fraction that has a repeating decimal, or as ones say it ... "terminating decimal".