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2 years ago

Decide if the function is an exponential function. If it is, state the initial value and the base. (5 points)

Mathematics

1 answer:

Irina18 [472]2 years ago

4 0

Answer:

Exponential Function; base = 7; initial value = - 9.3

Step-by-step explanation:

Base is a number/value which has a variable exponent;

Initial value is the value of a function (i.e. y) when the independent variable, i.e. x, is equal to 0.

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Does anyone know this

Phantasy [73]

The value of x is 20.

Solution:

Sides of one triangle are 2x – 4 and 39.

Sides of another triangle are x + 6 and 24.

Property of similar triangle:

If two triangles are similar then their corresponding angles are congruent and the corresponding sides are in the same ratio.

$$\frac{2x-4}{24} =\frac{39}{x+6}$

Do cross multiplication.

$(2x-4)(x+6)=39\times 24$

$2x^2+12x-4x-24=936$

$2x^2+8x-24-936=0$

$2x^2+8x-960=0$

Divide by 2 on each of the term.

$x^2+4x-480=0$

Solve using quadratic equation.

$(x-20)(x+24)=0$

$(x-20)=0, \ (x+24)=0$

$x = 20, \ x = -24$

Ignore the negative term, because if you substitute this you will get a negative terms only. But length of sides cannot be in negative measures.

Therefore x = 20.

4 0

2 years ago

What is the equation of the line that passes through the point (-3,5) and has a slope of -2

wariber [46]

Answer:

equation: y=-4x-7

Step-by-step explanation:

y=-4x+b

solve for b using given coordinates on the line (-3, 5)

5=-4(-3)+b

b=-7

6 0

3 years ago

Read 2 more answers

Solve the equation 4\pi =w-6\pi

maksim [4K]

Answer:

4/pi=w-6/pi

4 = w-6

Pi pi

Cross mutiply

Pi(w-6)=4(pi)

Wpi - 6pi =4pi

Collect like terms

Wpi=4pi + 6pi

Wpi =10pi

Divide both sides by pi

Wpi = 10pi

Pi pi

W = 10

5 0

3 years ago

Nadia plans to paint her jewelry box. The box is shaped like a rectangular prism with the dimensions

Pachacha [2.7K]

Answer:

$132\ in^{2}$ is closest to the total surface area of the box

Step-by-step explanation:

we know that

The surface area of the box is equal to

$SA=2B+PH$

where

B is the area of the base

P is the perimeter of the base

H is the height of the box

we have

$L=7\frac{3}{4}\ in=\frac{7*4+3}{4}=\frac{31}{4}\ in$

$W=3\frac{1}{4}\ in=\frac{3*4+1}{4}=\frac{13}{4}\ in$

$H=3\frac{7}{8}\ in=\frac{3*8+7}{8}=\frac{31}{8}\ in$

Find the area of the base B

$B=LW$

$B=(\frac{31}{4})(\frac{13}{4})=\frac{403}{16}\ in^{2}$

Find the perimeter of the base P

$P=2(L+W)$

$P=2(\frac{31}{4}+\frac{13}{4}))$

$P=2(\frac{44}{4})=22\ in$

Find the surface area

$SA=2(\frac{403}{16})+22(\frac{31}{8})$

$SA=(\frac{403}{8})+(\frac{682}{8})$

$SA=\frac{1,085}{8}=135.625\ in^{2}$

6 0

3 years ago

What's the slope of the line passing through the points -1, 8 - 7, 3

tatuchka [14]

Answer:

slope = 5/6

Step-by-step explanation:

Since you were given two points, you can use the point-slope formula to find the slope. The general equation looks like this:

y₁ - y₂ = m(x₁ - x₂)

In this formula, "m" represents the slope. To find the slope, plug the values from the two points into the equation. Make sure to put the values from the same point in the variable with the same number.

Point 1: (-1, 8)

Point 2: (-7, 3)

y₁ - y₂ = m(x₁ - x₂) <----- Original formula

8 - y₂ = m(-1 - x₂) <----- Plug in "x" and "y" values from Point 1

8 - 3 = m(-1 - (-7)) <----- Plug in "x" and "y" values from Point 2

5 = m(-1 - (-7)) <----- Simplify left side

5 = m(6) <----- Simplify inside parentheses

5/6 = m <----- Divide both sides by 6

5 0

1 year ago