Slope-intercept form of the equation of the line that is perpendicular to -2x + 3y = 10 and contains P(10,-10)

Answer:

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

Step-by-step explanation:

Given

[tex](2,16)[/tex]

[tex](5,1,024)[/tex]

Required

Determine the exponential function [tex]y = a.b^x[/tex]

In [tex](2,16)[/tex]

[tex]x=2[/tex] and [tex]y = 16[/tex]

Substitute these values in [tex]y = a.b^x[/tex]

[tex]16 = a.b^2[/tex] --- (1)

In [tex](5,1,024)[/tex]

[tex]x = 5[/tex] and [tex]y = 1024[/tex]

Substitute these values in [tex]y = a.b^x[/tex]

[tex]1024 = a.b^5[/tex] --- (2)

Divide (2) by (1)

[tex]\frac{1024}{16} = \frac{a.b^5}{a.b^2}[/tex]

[tex]\frac{1024}{16} = \frac{b^5}{b^2}[/tex]

[tex]64 = \frac{b^5}{b^2}[/tex]

Apply second law of indices

[tex]64 = b^{5-2[/tex]

[tex]64 = b^3[/tex]

Express 64 as an exponent of 3

[tex]4^3 = b^3[/tex]

[tex]4 = b[/tex]

[tex]b = 4[/tex]

Substitute 4 for b in (1)

[tex]16 = a.b^2[/tex]

[tex]16 = a * 4^2[/tex]

[tex]16 = a * 16[/tex]

[tex]16 = 16a[/tex]

Solve for a

[tex]a=\frac{16}{16}[/tex]

[tex]a = 1[/tex]

Substitute 1 for a and 4 for b in [tex]y = a.b^x[/tex]

[tex]y = 1 * 4^x[/tex]

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

The exponential function is given by y = 100(0.4)ˣ

An exponential function is in the form:

y = abˣ

where y, x are variables, a is the initial value of y and b is the factor.

At point (2, 16):

16 = ab²      (1)

At point (5, 1.024):

1.024 = ab⁵      (2)

Dividing equation 2 by equation 1:

b³ = 0.064

b = 0.4

16 = a(0.4)²

a = 100

The exponential function is given by: y = 100(0.4)ˣ

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Answer:

60%

Step-by-step explanation:

its right

If a company’s stock was selling at 35$ a share. a month later it was selling at 14$ a share then the percent of loss is 60%.

percentage, a relative value indicating hundredth parts of any quantity.

Given that a company’s stock was selling at 35$ a share.

After a month later it was selling at 14$ a share.

We need to find the percent of loss.

Original share price=35

new share price=14

We calculate the percentage by finding the difference and dividing the difference with the original share price.

35-14/35

0.6

Now multiply this 0.6 with 100 as it is a hundredth part.

0.6×100

60%

Hence, if a company’s stock was selling at 35$ a share. a month later it was selling at 14$ a share then the percent of loss is 60%.

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Answer:

1

Step-by-step explanation:

It is being subtracted by four everytime

Answer:

3x^2-4x+9 remainder -20/x+2

Step-by-step explanation:

Answer:

triangle BFD

75 degrees

Answer:

$150

Step-by-step explanation:

5 x 6 = 30

25 x 6 = 150

Answer:

If it is a solution of equations, then plug your solution into the equations you are working on to make sure that all equations are satisfied by your solution.

Step-by-step explanation:

I hope that this was helpful.

Answer:

0,5

Step-by-step explanation:

slope: 0

y-intercept:(0,5)

Answer: mutiply x by itself to get y

Step-by-step explanation:

Answer:

3rd quadrant

Step-by-step explanation:

D. The function shown on the graph has a smaller rate of change and a lower starting point. Sorry if incorrect i hope i helped.

Answer:

FOIL

Step-by-step explanation:

" is just a mnemonic. It helps some people to remember all the steps needed to multiply two binomials. It "makes sense" because it's methodical and gives the right answer.

Answer:

Ok im too too sure but I think that it is the one with the filled in dot -->

Step-by-step explanation:

We want the equation in the form y = mx + b.

We are given that m = -7.

The y-intercept (our b) is 8.

Here it is:

y = -7x + 8

Answer:

∠ EFG = 83°, ∠ GCE = 97°

Step-by-step explanation:

Since FE and FG are tangents to the circle then

∠ FGC and ∠ FEC are right angles

The sum of the angles in quadrilateral CEFG = 360°

Sum the 4 angles and equate to 360

3x + 11 + 90 + 5x - 23 + 90 = 360, that is

8x + 168 = 360 ( subtract 168 from both sides )

8x = 192 ( divide both sides by 8 )

x = 24

Thus

∠ EFG = 3x + 11 = 3(24) + 11 = 72 + 11 = 83°

∠ GCE = 5x - 23 = 5(24) - 23 = 120 - 23 = 97°

Answer:

um 3

Step-by-step explanation:

whats 24 divided by 3 mate? 3

i mean all u need is a calculator im dumb as hell and i know that...

hope...this helps you :) have a great day

do u like beans?Step-by-step explanation: hope it helps

Answer:

-0.2z

Step-by-step explanation:

-0.5z + 0.9z - ( -0.3z+0.9z) open paranthesis and change the sign of all terms

-0.5z + 0.9z + 0.3z - 0.9z combine terms

-0.5z+0.3z= -0.2z

Answer:

3

Step-by-step explanation:

slop of given point is 3

Answer:

\tan \left(\frac{\sin \left(x\right)-\cos \left(x\right)}{\cos \left(x\right)+\sin \left(x\right)}\right)

Step-by-step explanation:

Step-by-step explanation:

Here are some hints: "At the same time,"means you need to set up a proportion (two ratios equal each other).

The shadow is always on the ground.

A person and a flagpole always stands up straight, like a wall (vertical height)

Underline key words and numbers. Draw a picture for sure.

|

|X 5.5 ft. |

|____________ |____

flagpole=50 feet person's shadow=4 feet

shadow

Since it is easier to work with one type of measurement, change the person's height to feet only. The person is 5feet, 6inches Note: 12 inches= 1 foot, so 6 inches= 1/2 a feet and 6 inches= .5 feet

Answer:

y = 51-0.4x

Step-by-step explanation:

From the question, we can see that the amount of water left in the pool was 45 inches deep within 12:15-12:00 = 15 minutes

However, within 10 minutes there was a loss of 45-41 = 4 inches

So what this means is that per minute, the amount of loss expected is 4 inches/10 minutes = 0.4 inches per minute

what we are saying is that a loss of 4 inches depth of water is needed per minute

So we want to write an equation, representing the depth after x minutes

So what we have here is that the total inches at present will be;

45 + 0.4(15) = 45 + 6 = 51 inches

The pool was 51 inches deep initially before the pumping out began

That will be;

y = 51-0.4x

where is the depth and x is the number of minutes

Answer:

24 inches

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the sides of triangle be a, b and c

Perimeter

New sides

New perimeter

Correct choice is D

Answer:

The equation of a line that is parallel to x−2y=−4 and passes through the point (0, 0) will be:  [tex]x-2y=0[/tex]

Step-by-step explanation:

Given the line

[tex]x-2y=-4[/tex]

[tex]x+4 = 2y[/tex]

[tex]y=\left(\frac{1}{2}\right)x+2[/tex]

[tex]m_1=\frac{1}{2}[/tex]

so, the slope of the line parallel to the given line would have

the same slope as  [tex]\frac{1}{2}=m[/tex], and passed through the point (0, 0).

Therefore, the equation of the required line is given by

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

[tex]y=\left(\frac{1}{2}\right)x+0[/tex]

[tex]y=\left(\frac{1}{2}\right)x[/tex]

[tex]2y=x[/tex]

[tex]x-2y=0[/tex]

Therefore,  the equation of a line that is parallel to x−2y=−4 and passes through the point (0, 0) will be:  [tex]x-2y=0[/tex]

answere:

You can't simplify

explanation:

there is no need to simplify because 3/16 and 6/11 is the simplest form.

Answer:

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

Step-by-step explanation:

Given the function

[tex]f\left(x\right)=\sqrt{x+3}[/tex]

We can find the inverse function by exchanging x and y, and then solve for y.

[tex]y=\sqrt{x+3}[/tex]

Replace x with y.

[tex]x=\sqrt{y+3}[/tex]

square both sides

[tex]x^2=y+3[/tex]

[tex]y=x^2-3[/tex]

Hence,

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

Answer:

Answer:

120

Step-by-step explanation:

14-6=8x15=120

Answer:

Step-by-step explanation:

4= 0 degree

2z= 1 degree

4r^2st^3= 6 degree

3xyz^2= 4 degree