Express 45 = x as a logarithmic equation.

Answer:

Can you attach the quadratic equation?

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

PLATO user

49 ___ 3 + 32 ÷ 23

49 ___ 3 + 1.39

49 ___ 4.39

49 > 4.39 is the only possible answer. 49 is greater than 4.39.

To determine the correct symbol for the expression 49 ___ 3 + 32 ÷ 23, first calculate the right side following PEMDAS, resulting in 7. Then compare it with the left side (49), which shows that 49 is greater than 7, so the correct symbol is '>'.

The question asks which symbol makes the mathematical statement true for the expression 49 ___ 3 + 32 ÷ 23. We need to solve the right side of the equation first before we can determine the correct symbol to use.

To solve 3 + 32 ÷ 23, we need to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division as they appear from left to right, Addition and Subtraction as they appear from left to right). First, we solve the exponent 23, which equals 8. Then, we perform the division: 32 ÷ 8 = 4. Finally, we add 3 to the result: 3 + 4 = 7. So, our expression on the right side of the equation is equal to 7.

Now we compare the left side of the equation (49) with the result we calculated (7). It is evident that 49 is greater than 7, so the correct symbol to use would be '>'. Therefore, the complete and true mathematical statement would be: 49 > 3 + 32 ÷ 23 or 49 > 7.

https://brainly.com/question/15840745

#SPJ2

Answer:

B = 65

C = 115

Step-by-step explanation:

Givens

ABCD is a parallelogram

It is lettered in such a way that B is opposite D

B = 3n+20

D = 6n-25

Solution

<B = <D                      Property of Parallelogram

3n + 20 = 6n - 25      Add 25 to both sides

3n + 20 + 25 = 6n      Combine

3n +45 = 6n                Subtract 3n from both sides

3n +45 = 6n-3n           Combine

45 = 3n                        Divide by 3

45/3=3n/3                    

n = 15                            Value of n    

B = 3n + 20                  Find B. Let n = 15

B= 3*15+20                   Combine

B = 45 + 20                 Combine

B = 65                                

==================

B and C are supplementary. They add up to 180

B + C = 180

65 + C = 180

C = 180-65

C = 115

Answer:

(- [tex]\frac{9}{2}[/tex], [tex]\frac{1}{2}[/tex] )

Step-by-step explanation:

Using the midpoint formula

Given 2 points (x₁, y₁ ) and (x₂, y₂ ), then midpoint is

([tex]\frac{x_{1}+x_{2}  }{2}[/tex], [tex]\frac{y_{1}+y_{2}  }{2}[/tex])

with (x₁, y₁ ) = (- 1, 5) and (x₂, y₂ ) = (- 8, - 4), then midpoint

= ([tex]\frac{-1-8}{2}[/tex], [tex]\frac{5-4}{2}[/tex] )

= ( - [tex]\frac{9}{2}[/tex], [tex]\frac{1}{2}[/tex] )

Answer:-4.5,0.5

Step-by-step explanation:midpoint =x1+x2/2, y1+y2/2

-1+-8/2=x,-4+5/2=y

-9/2=x,1/2=y

-4.5=x, 0.5=y

Answer:

733 inches

Step-by-step explanation:

V= 3.14*5^2*28/3

Order of Operations (PEMDAS)

5^2=25

25*3.14= 78.5

78.5*28= 2198

2198/3=732.66

Round to nearest cubic inch

733 inches

Answer:

The range for the equation is all real numbers.

Step-by-step explanation:

The range of an equation is the set of y-values that you can get by plugging in all possible x-values.

Another way to put it is, when you graph the equation, whatever y-values the line produces, is its range.

Graphing y=2x-3, you can see it is a graph with a positive slope that extends from negative infinity y-value to positive infinity x-value.

Answer: its C. $669

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Say Jill picks the number x.

She multiplies it by 2 giving 2x.

It says add 5 to that product giving 2x+5.

She multiplies this sum by -3 giving -3(2x+5).

She then subtracts 7 from that product giving -3(2x+5)-7.

Her number after doing all of this is -40 so we hae -3(2x+5)-7=-40

To solve:

First: I would add 7 on both sides:  -3(2x+5)=-33

Second: I would divide boht sides by -3:  2x+5=11

Third: I would subtract 5 on both sides: 2x=6

Last: I would divide both sides by 2:  x=3

Answer:

The last one

Step-by-step explanation:

Your equation is p(x) = |x - 1|

The function equation can be represented by f(x) = a|x - h| + k

To find the vertex, you have to find (h,k)

In the equation p(x) = |x - 1|, 1 is h [since its (+h,k) not (-h,k)]

k is 0 since there is no +k after |x-1|.

So, your vertex will be at (1,0)

Thus, the answer is the last graph.

[I also graphed it on a graphing calculator so you can check. :) ]

The vertex will be at (1, 0).

Functions of graphs

The given equation is p(x) = |x - 1|

The function equation can be defined by f(x) = a|x - h| + k

To calculate the vertex, you have to identify (h, k)

In the given equation p(x) = |x - 1|, 1 exists h

[since its (+h, k) not (-h, k)]

k exists 0 since there does not exist +k after |x-1|.

So, the vertex will be at (1, 0).

Therefore, the graph represents the function p(x) = |x – 1| is option (d).

To learn more about the functions of graphs

https://brainly.com/question/4025726

#SPJ2

Answer:

The slope of A'B' = -1.2 ⇒ answer A

Step-by-step explanation:

* Lets talk about dilation

- A dilation is a transformation that changes the size of a figure.  

- It can become larger or smaller, but the shape of the

 figure does not change.  

- The scale factor, measures how much larger or smaller  

  the image will be

- If the scale factor greater than 1, then the image will be larger

- If the scale factor between 0 and 1, then the image will be smaller

- If the center of the dilation is the origin then multiply each coordinate

 by the scale factor

* In the problem

∵ Δ ABC is dilated by a scale factor of 3 with the origin as the center

  of dilation

- Let point A is (a , b) and point B is (c , d)

∵ The slope of the line which passes through points (x1 , y1) and (x2 , y2)

  is m = (y2 - y1)/(x2 - x1)

∴ The slope of AB = (d - b)/(c - a) = -1.2

∵ Point A' is (3a , 3b) and point B' is (3c , 3d)

∴ The slope of A'B' = (3d - 3b)/(3c - 3a)

- Take 3 as a common factor from up and down

∴ The slope of A'B' = 3(d - b)/3(c - a) ⇒ cancel 3 up with 3 down

∴ The slope of A'B' = (d - b)/(c - a) = the slope of AB

∵ The slope of AB = -1.2

∴ The slope of A'B' = -1.2

* The slope of A'B' = -1.2

Answer:

there isn't a direct answer for that because it depends on the shape.

but it has rotational symmetry if it can be rotated by an angle between 0° and 360°

Answer:

c. When a > 0 and b > 1, the function models exponential growth.

Step-by-step explanation:

You have exponential decay when a > 0 and 0 < b < 1.

The statement that is always true about the function y=a•b^xc is this: C. When a > 0 and b > 1, the function models exponential growth.

Exponential growth is a type of growth that occurs as there is an addition of numbers. This is reflected in the upward movement of the graph if such growth is represented in a graph.

So, the statement that best reflects this meaning of exponential growth is that when in a function, a > 0 and b > 1, then exponential growth is modeled. Thus, the correct option number is C. "When a > 0 and b > 1, the function models exponential growth."

Learn more about exponential growth here:

https://brainly.com/question/13223520

#SPJ6

Answer:

Part 1) h(g)=-4+g ----> the input is g

Part 2) f(h)=-h-7 -----> the input is h

Part 3) g(f)=-2f -----> the input is f

Step-by-step explanation:

Part 1) we have

h(g)=-4+g

we know that

The input  is the independent variable and the output is the dependent variable

so

the output is h(g) or 4+g

the input  is the variable g

Part 2) we have

f(h)=-h-7

we know that

The input  is the independent variable and the output is the dependent variable

so

the output is f(h) or h-7

the input  is the variable h

Part 3) we have

g(f)=-2f

we know that

The input  is the independent variable and the output is the dependent variable

so

the output is g(f) or 2f

the input  is the variable f

Answer: Questions are in different places than other people screen.

h(g) = -4+g     -       The input is G

g(f) = 2f          -       The input is F

f(h) = h - 7      -       The input is H

Step-by-step explanation:

Just put tha answer in nd get a good grade :)

Answer:

Step-by-step explanation:

note that the square root of any number can be expressed as  the number raised to a [tex]\frac{1}{2}[/tex] power

i.e √a = [tex]a^{\frac{1}{2} }[/tex]

Applying this to our expression

[tex](\sqrt{x} )^{5}[/tex]

= [tex]x^{\frac{1}{2} * 5 }[/tex]

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

The Answer Is...

x^5/2

[tex]x^ \frac{5}{2}[/tex]

Answer: Second option.

Step-by-step explanation:

Given the function f(x), which is:

[tex]f(x)=x[/tex]

And given the function g(x), which is:

[tex]g(x)=2[/tex]

You need to substiute the function [tex]g(x)=2[/tex]  into the function  [tex]f(x)=x[/tex] in order to find [tex](fog)(x)[/tex].

Therefore, through this procedure, you get this answer:

[tex](fog)(x)=(2)[/tex]

[tex](fog)(x)=2[/tex]

You can observe that this matches with the second option.

For this case we have the following functions:

[tex]f (x) = x\\g (x) = 2[/tex]

We must find [tex](f_ {0} g) (x).[/tex]

By definition of composite functions we have to:

[tex](f_ {0} g) (x) = f (g (x))[/tex]

We substitute g (x) into f (x), then we have:

[tex]f (g (x)) = 2[/tex]

Answer:

[tex]f (g (x)) = 2[/tex]

Option B

Answer:

1.48 m

Step-by-step explanation:

mean height of 14 boys is 1.56 m, so their total height is 14 * 1.56 = 21.84 m

mean height of 32 students is 1.515 m, so their total height is 48.48

48.48 - 21.84 = 26.64 (total height of the girls)

mean height of the girls is 26.64/18 = 1.48 m

Answer:

1.48 m.

Step-by-step explanation:

There are 32 - 14 = 18 girls in the class.

Total height of the whole class = 1.515 * 32

= 48.48 m..

Total height of all the boys = 14 * 1.56 =  21.84 m.

So the total height of the 18 girls = 48.48 - 21.84

= 26.64 m.

Therefore the mean height of the girls

= 26.64 / 18

= 1.48 m.

Answer:

I can't see Mathieu's work but I will show the right steps and maybe you can find where Mathieu went wrong.

f(x)=x^2+4x+3

f(x)=(x+3)(x+1)       Since 3*1=3 and 3+1=4

The x-intercepts can be found by setting y to 0 and solving for x

(in other words replace that f(x) thing with 0 and solve for x)

0=(x+3)(x+1)

Now set both factors equal to 0

x+3=0       or      x+1=0

x   =-3                    x=-1

The x-intercepts are at (-3,0) and (-1,0)

A function assigns the value of each element of one set to the other specific element of another set. The correct option is C.

A function assigns the value of each element of one set to the other specific element of another set.

The x-intercepts of the function f(x) = x² + 4x + 3 can be found as shown below.

f(x) = x² + 4x + 3

0 = x² + 4x + 3

0 = (x+3)(x+1)

x = -3, -1

Now, it can be seen that Mathieu has actually set the factored expressions equal to each other, which was wrong.

Hence, the correct option is C.

Learn more about Function:

https://brainly.com/question/5245372

#SPJ2

[tex]\bf \textit{lateral area of a cylinder}\\\\ LA=2\pi rh~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=4\\ h=5 \end{cases}\implies LA=2\pi (4)(5)\implies V=40\pi[/tex]

Answer: A

Step-by-step explanation: The converse of a conditional is when the two statements switch spots, for example:

Conditional: If someone like ice cream, they have brown hair

Converse: If someone has brown hair, they like ice cream

The converse of our given conditional would be:

If two lines do not intersect, they are parallel

This eliminates Option D

Next, the converse is false.

Skew lines (example attached) do not intersect and are also not parallel, meaning if two lines do not intersect, they could be either parallel or skew.

This eliminates Option C and B, leaving us with Option A

We want to find the converse statement to one given statement and see if it is true.

We will see that the correct option is a:

If two lines do not intersect, they are parallel. One statement is false. If two lines do not intersect, they could be skew.

A general statement is written as:

If P then Q.

Where P and Q are two given propositions.

The converse statement to the above shown is:

If Q then P.

For this question, we have the statement:

If two line are parallel, they do not intersect.

Then we can write the converse statement as:

If two lines do not intersect, they are parallel.

Which is false, in 3-dimensions we can have two non-parallel lines that don't intersect each other (parallel lines must not intersect and also live on the same plane).

Then the correct option is the first one:

a: If two lines do not intersect, they are parallel. One statement is false. If two lines do not intersect, they could be skew.

If you want to learn more you can read:

https://brainly.com/question/18152035

Answer:

positive 1.5

Step-by-step explanation:

by definition, the possible values for correlation coefficients are

-1 ≤ correlation coefficient ≤ 1

+1.5 lies outside this range and hence is not valid.

The correlation coefficient measures the strength and direction of a linear relationship between two variables, ranging from -1 to +1. Therefore, a value of positive 1.5, as listed in option D, is not a possible value for a correlation coefficient.

In mathematics, particularly in statistics, a correlation coefficient is a measure of the strength and direction of the linear relationship between two variables on a scatterplot. The value of a correlation coefficient ranges from -1 to +1. A correlation coefficient of +1 indicates a perfect positive linear relationship, a correlation coefficient of -1 indicates a perfect negative linear relationship, and a correlation coefficient of 0 indicates no linear relationship.

Therefore, the answer to the question is: D. positive 1.5. This is not a possible value for a correlation coefficient because it lies outside the acceptable range of -1 to +1.

https://brainly.com/question/33643115

#SPJ3

Answer:

3/8

Step-by-step explanation:

We must first find the LCD in order to add up the amounts taken from the basket.

The Least Common Denominator of 4 and 8 is 8.

We convert 1/4 so that it is a fraction over 8, which is 2/8

2/8+1/8=3/8

Answer:

3/8

Step-by-step explanation:

We want to find the total amount of cherries that Robin and Jim took

1/4 + 1/8

The common denominator is 8

1/4 *2/2 = 2/8

Replacing 1/4 with 2/8

2/8 + 1/8 = 3/8

The fraction that they took is 3/8

Answer:

409.86

Step-by-step explanation:

First find the mark up

230 *65%

230 * .65 = 149.50

The new cost of the tent is the original cost plus the mark up

230 + 149.50

379.50

Now we need to find the tax

379.50 * 8%

379.50 *.08

30.36

The total cost is the cost of the tent plus the tax

379.50 + 30.36

409.86

Answer:

409.86

is the correct answe rfor this question

Answer:

Step-by-step explanation:

The total number of shoes they share is

4 + 5 + 3 = 12

Kyra: 4/12 = 0.333333

Tennis Shoes: There are now 11 shoes. 5/11 = 0.46

The probability that Kyra selects a pair of sandals and her sister selects a pair of tennis shoes is 3/20.

To find the probability that Kyra selects a pair of sandals and her sister selects a pair of tennis shoes, we need to determine the total number of possible outcomes and the number of favorable outcomes.

There are 4 pairs of sandals, 5 pairs of tennis shoes, and 3 pairs of boots in the closet. Assuming Kyra selects a pair of sandals first, she has 4 options. After Kyra selects the sandals, there will be 3 pairs of sandals left.

Since the sandals are chosen without replacement, her sister will have 5 options for the pair of tennis shoes. The total number of possible outcomes is the product of the options for each step: 4 * 5 = 20.

Therefore, the probability that Kyra selects a pair of sandals and her sister selects a pair of tennis shoes is 3/20.

Answer:

I got 11.6

Step-by-step explanation:

Hope my answer has helped you in any way!

Answer:

Option  A.)−4

Step-by-step explanation:

we have

4x+5y=-12 -----> equation A

-2x+3y=-16 -----> equation B

Solve the system of equations by elimination

Multiply the equation B by 2

2*(-2x+3y)=-16*2

-4x+6y=-32 -----> equation C

Adds equation A and equation C

4x+5y=-12

-4x+6y=-32

-----------------

5y+6y=-12-32

11y=-44

y=-4

Answer with Step-by-step explanation:

We are given a system of linear equations:

4x + 5y = −12

-2x + 3y = −16

Multiply second equation by 2 and add it to first equation.

4x+5y-4x+6y= -12-32

⇒ 11y= -44

Dividing both sides by 11

⇒ y= -4

Hence, the y-value in the solution to the system of linear equations

4x + 5y = −12

-2x + 3y = −16    is:

A.)−4

You would need to divide the money by 2 ( both sisters) to get the equal amount they each need to pay. Then include the extra amount Carlotta owes.

The correct equation would be -28 ÷ 2- (-6)

Answer:

a

Step-by-step explanation:

[tex]\bf [cot(\theta )+csc(\theta )]^2=\cfrac{1+cos(\theta )}{1-cos(\theta )} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{doing the left-hand side}}{[cot(\theta )+csc(\theta )]^2}\implies cot^2(\theta )+2cot(\theta )csc(\theta )+csc^2(\theta ) \\\\\\ \cfrac{cos^2(\theta )}{sin^2(\theta )}+2\cdot \cfrac{cos(\theta )}{sin(\theta )}\cdot \cfrac{1}{sin(\theta )}+\cfrac{1}{sin^2(\theta )}\implies \cfrac{cos^2(\theta )}{sin^2(\theta )}+\cfrac{2cos(\theta )}{sin^2(\theta )}+\cfrac{1}{sin^2(\theta )}[/tex]

[tex]\bf \cfrac{\stackrel{\textit{perfect square trinomial}}{cos^2(\theta )+2cos(\theta )+1}}{sin^2(\theta )}\implies \boxed{\cfrac{[cos(\theta )+1]^2}{sin^2(\theta )}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{doing the right-hand-side}}{\cfrac{1+cos(\theta )}{1-cos(\theta )}}\implies \stackrel{\textit{multiplying by the denominator's conjugate}}{\cfrac{1+cos(\theta )}{1-cos(\theta )}\cdot \cfrac{1+cos(\theta )}{1+cos(\theta )}}[/tex]

[tex]\bf \cfrac{[1+cos(\theta )]^2}{\underset{\textit{difference of squares}}{[1-cos(\theta )][1+cos(\theta )]}}\implies \cfrac{[cos(\theta )+1]^2}{1^2-cos^2(\theta )} \\\\\\ \cfrac{[cos(\theta )+1]^2}{1-cos^2(\theta )}\implies \boxed{\cfrac{[cos(\theta )+1]^2}{sin^2(\theta )}}[/tex]

recall that sin²(θ) + cos²(θ) = 1, thus sin²(θ) = 1 - cos²(θ).

Answer:

x = 2, x = -3

Step-by-step explanation:

We are given the following quadratic equation and we are to solve it for x:

[tex] x ^ 2 + x - 6 = 0 [/tex]

We need to find such factors of -6 that when added give a result of 1 and when multiplied, give a product of -6.

[tex] x ^ 2 + x - 6 = 0 [/tex]

[tex] x ^ 2 - 2x + 3x - 6 = 0 [/tex]

[tex] x ( x - 2 ) + 3 ( x - 2 ) = 0 [/tex]

[tex](x-2) = 0, (x+3)=0[/tex]

x = 2, x = -3