1. Which logarithm bases can you use to solve for x in the exponential equation 4^3+x= 25 ? (Select all that apply.)
log base 10
log base x
log base 4
log base 25

Answer:

y = 2x - 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, - 2) and (x₂, y₂ ) = (1, 0) ← 2 points on the line

m = [tex]\frac{0-(-2)}{1-0}[/tex] = [tex]\frac{0+2}{1}[/tex] = [tex]\frac{2}{1}[/tex] = 2

the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2

y = 2x - 2 ← equation of line

Answer:

y = 2x - 2

Step-by-step explanation:

The equation y = mx + b is a standard form of a linear equation in one variable. It represents a straight line on a graph

In this equation, y is the dependent variable, which is the variable that is being measured or predicted. The independent variable is x, which is the input or cause in the relationship.

The coefficient m is the slope of the line, which tells you the rate of change between the two variables. It represents how much the value of y changes for each unit change in the value of x. A positive slope means that the line goes up as you move from left to right, while a negative slope means that the line goes down.

- Our slope is positive

- slope (m) = rise / run = 2/1 = 2

The constant b is the y-intercept, which is the point where the line crosses the y-axis. It represents the value of y when x is equal to 0.

- Our y-intercept is -2

m is 2 and b is -2, the equation y = 2x - 2 represents a line with a slope of 2 and a y-intercept of -2. This means that for every 1 unit increase in the value of x, the value of y increases by 2 units, and the line crosses the y-axis at the point (0, -2).

Answer:

5 hours lifeguarding and two hours babysitting.

Step-by-step explanation:

5(20) = 100

10(2) = 20

100 + 20 = 120

The product of the given irrational number  ∛5 × √2 is equal to

option b. [tex]\sqrt[6]{200}[/tex]

As given in the question,

Given irrational numbers are:

∛5 × √2

Take the least common multiple of 3 and 2

Least common multiple of 3 and 2 is 6.

∛5 = [tex]5^{2 \times\frac{1}{2}\times \frac{1}{3} }[/tex]

    = [tex]\sqrt[6]{5^2}[/tex]

    = [tex]\sqrt[6]{25}[/tex]

√2 = [tex]2^{3 \times\frac{1}{3}\times \frac{1}{2} }[/tex]

    =[tex]\sqrt[6]{2^3}[/tex]

    = [tex]\sqrt[6]{8}[/tex]

Product of ∛5 × √2 is given by:

∛5 × √2 = [tex]\sqrt[6]{25} \times \sqrt[6]{8}[/tex]

             = [tex]\sqrt[6]{25 \times 8}[/tex]

             = [tex]\sqrt[6]{200}[/tex]

Therefore, the product of the given irrational number is equal to [tex]\sqrt[6]{200}[/tex] .

The complete question is:

What is the following product?

∛5 × √2

a. [tex]\sqrt[6]{10}[/tex]

b. [tex]\sqrt[6]{200}[/tex]

c. [tex]\sqrt[6]{500}[/tex]

d. [tex]\sqrt[6]{10000}[/tex]

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The height of the tree after 12 years is 21.401 feet.

In this problem we find the case of a tree that grows exponentially, the height of the tree is defined by the following formula:

h = a · (1 + r / 100)ⁿ

Where:

If we know that a = 4 ft, r = 15 and n = 12, then the final height of the tree is:

h = 4 · (1 + 15 / 100)¹²

h = 21.401

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Answer:

88 ft^2

Step-by-step explanation:

we can make this a full 10 by 10 rectangle and find the area

10x10

100

And now we subtract the 6 by 2 triangle area that we added

6x2

12

100-12

88 ft^2

Hopes this helps please mark brainliest

Answer:

Answer = 88 ft²

Step-by-step explanation:

Step 1: Divide the composite shape into two separate parrellagrams

    1. Dimensions of shape 1: Length is 10 ft, and width is 4 ft

    2. Dimensions of shape 2: Length is 8 ft, and width is 6 ft

Step 2: Multiply the length by the height of each shape

    Area = lw

    3. Area of shape 1: 10 ft ∙ 4 ft = 40 ft²

    4. Area of shape 2: 8 ft ∙ 6 ft = 48 ft²

Step 3: Add both areas together to get the total area of the composite shape

    5. 40 ft² + 48 ft² = 88 ft²

    Hence, the total area of this composite figure is 88 ft²

Answer:  

A) 15

B) Summer Swim

Step-by-step explanation:

How to solve problem "A":

45+3.50x =6.50x

Take 3.50 from each side.

6.50-3.50=3

45=3x

Now you divide 45 divided by 3.

45/3=15

So after 15 visits, you'll be charged the same amount.

6.50 (15)=97.5

3.50 (15)+45= 97.5

So it's definitely correct.

_________________________________________________________

How to solve problem "B":

All we have to do is plug 32 into "x"

Equation 1: 45+3.50(32)= 157

Equation 2: 6.50 (32)=208

So equation 1 definitely is cheaper. So it's the Summer Swim that's cheaper

I hope this helps!!!

Answer:

2.4 × 101

Step-by-step explanation:

that is 24 in scientific notation

Answer:

24 * 10^1

Step-by-step explanation:

Hope this helps. :)

The normal approximation to the binomial distribution is C ( n , r ) * p^r * q^n - r .

a )

the binomial distribution .

Null hypothesis H0: μ = 19.4

Alternative hypotheses H1: μ ≠ 19.4

19.4 with minus sign, we get

n = 20, x = 4 and n/2 = 10

Here x < n/2

Therefore, from table the computed P-Value is.

b )

the normal approximation to the binomial distribution ,

P = 2P(X ≤ 4 when θ = 1/2 )

= 2 (0.0059)

= 0.0118

Hence the P value, 0.0118, is less than 0.05, the null hypothesis must be rejected, and we conclude that the mean of the population is not 19.4 minutes.

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Answer:

How many ways can they fill the 4 positions?

The Answer is B. 210

Answer: b. 210

Step-by-step explanation:

Answer:

$560.30 & $60.30

Step-by-step explanation:

A = $560.30

A = P + I where

P (principal) = $500.00

I (interest) = $60.30

Answer: x + 2/3(x)

Step-by-step explanation:

x = distance F walks to school

2/3(x) = distance T walks to school

Felipe walks first to school, then walks to Tim's house, so total distance Felipe walks:  x + 2/3(x)

The attached graph is defined by f(x) = x² + 5|x| + 6.

What is the graph function?

The graph of a function f is the set of all points in the plane of the form (x, f(x)). We could also define the graph of f to be the graph of the equation y = f(x). So, the graph of a function is a special case of the graph of an equation.

We have,

y = x² + 5|x| + 6

we know,

|x|² = x² use this ,

y = |x|² + 5|x| + 6

Steps for drawing y = |x|² + 5|x| + 6

step1 :- first draw y = x² + 5x + 6, this graph is quadratic equation .

step2:- Leave the part of y=x² + 5x + 6 right side to the y-axis and also take its image with respect to the y-axis as a plane mirror.

step3 :- now remove the part of y = x² + 5x + 6 to left side from y - axis .

now your graph is ready

you can see in the figure attached.

Hence, the attached graph is defined by f(x) = x² + 5|x| + 6.

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You see from the graph that when x = 0, y = 2 so the y-intercept is ( 0 , 2).

you are given points (-6 , 3) and (6 , 1). Find slope:

slope = change in y / change in x

slope = (3 - 1) / (-6 - 6)

slope = 2/-12

slope = -1/6

slope-intercept form: y = mx + b where m = slope and b = y intercept.

y = -1/6x + 2

The value of f(-3) + g(-3) Or (f + g)(-3) is 11.

When the output of one function is given to the input of another function they are called composite functions. In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).

Given, f(-3) is 9 and g(-3) is 2.

We know f(x) + g(x) = (f + g)(x).

∴ (f + g)(-3) = 9 + 2.

(f + g)(-3) = 11.

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Answer:

1)1

2)3

Step-by-step explanation:

Have a look at some tables online

The required quotient is x² + x + 1 + (2/ x -1) which is determined by the synthetic division.

A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient.

Use the divisor and find x :

x - 1 = 0  add 1

x= 1

Now we'll divide with the number one:

Take the coefficients from the terms in front of them.

Make careful to include 0's for x² and x since all terms must be included.

set it up with a 1 in a box:

1|  1   0   0  1   bring the first number down

____________

    1                    multiply the boxed number by the first number and add it                                 to the second number

1|  1   0   0  1  

____+1_____       repeat with the rest of the terms

    1   1  

1|  1   0    0    1

 ___+1_+1_+1  

    1   1    1    2                              

When you're finished, use the new numbers to build an equation that begins with a term that has one fewer degree than the previous equation.

Because there is a remnant, divide it by the original divisor.

final answer:

x² + x + 1 + (2/ x -1)

Thus, the required quotient is x² + x + 1 + (2/ x -1) which is determined by the synthetic division.

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Answer:153000394836295938

Step-by-step explanation:

;)

The diagram that models the ratio in the story is the first diagram.

Puppies = Seven green boxes.

Adults = Four violet boxes.

There are 66 dogs enrolled together.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number of puppies = 7

Number of adult dogs = 4

This can be written as,

7 puppies = 4 adult dogs

Multiply 6 on both sides.

42 puppies = 24 adult dogs

Now,

The total number of enrolled dogs.

42 + 24 = 66 dogs

Thus,

The ratio that models the story is the first diagram.

The total number of enrolled dogs is 66.

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it must be A because it's is going down word

Answer:

Slope is negative

Step-by-step explanation:

from one point to the next, it goes down 1 (-1) and over 4 (4)

or, from one point it goes left 4 (-4) and up 1 (1) just depending on how tou look at it.

Step-by-step explanation:

These two angles are same side corresponding interior angles so they are equal to each other

[tex]5x + 20 = 120[/tex]

[tex]5x = 100[/tex]

[tex]x = 20[/tex]

Answer:

(A) ∠Y ≅ ∠C.

Step-by-step explanation:

To prove that two triangles are congruent by ASA (Angle-Side-Angle), you need to show that two angles in one triangle are congruent to two corresponding angles in the other triangle, and that the side between the two angles is congruent to the corresponding side in the other triangle.

Given that ∠X ≅ ∠D and ∠DE ≅ ∠XW, the third congruence needed to prove that ΔXWY ≅ ΔDEC by ASA is:

(A) ∠Y ≅ ∠C

This is because ∠Y and ∠C are the corresponding angles in the two triangles that have not been shown to be congruent.

So the answer is (A) ∠Y ≅ ∠C.

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Answer: The discount is 25% * $20 = $5.

The sale price of the item is $20 - $5 = $15.

Answer:

The coordinates of the vertices of triangle ΔABC, A(0, -1), B(6, 5), and C(-4, 3), indicates that the triangle ΔABCD is a right triangle with all sides of different length.

Step-by-step explanation:

The algebraic expression is (3X + 4)²

Word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation.

From the question

To express the worded problem algebraically using X as your unknown

To express the worded problem algebraically using X as your unknown

The number is X

Now if we multiply the number X by 3 we get 3X

When we add 4 with 3X we get 3X + 4

Finally the squaring the result 3X + 4 we get (3X + 4)²

Hence the required algebraic expression for the worded problem is (3X + 4)²

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Answer:500

Step-by-step explanation:

Answer:

the third onei

Step-by-step explanation:

it describes a quadratic equation/

Average velocity of the car as calculated from the given data is 6m/s.

The average velocity is calculated by dividing the total distance travelled by the whole time that has passed. Given the velocity as a function of time, you may integrate the velocity function from t = 4 to t = 8 to determine the total distance travelled.

The opposite of taking a derivative is to integrate; in other words, the function I get when I take a derivative is 2t1/2 + 1. Assuming you are aware of how to do that If not, you can input the aforementioned integral into your TI-84 to obtain the result.

The integral turns out to be

(4/3)t^3/2 + 4t so x(t)

= (4/3)t3/2 + 4t and x(8) - x(4)

= (4/3)(8)3/2 + 4(8) - [(4/3)(4)3/2 + 4(4)]

= 24 meters

The distance travelled in total was 24 meter and it took 4 seconds (8-4) to do it, so the average velocity is 24 /4 = 6 m/s.

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