Which choices contain equivalent statements? Check all that apply.

Which Choices Contain Equivalent Statements? Check All That Apply.

Answers

Answer 1

Answer:

A C and E

Step-by-step explanation:

Edge

Answer 2

The choices that contain equivalent statements are:

a) ln 3x = 6 → 3x = e⁶

c) log 4x = 8 → 4x = 10⁸

e) 5.6554 = 10ˣ → log 5.6554 = x

To determine which choices contain equivalent statements, let's analyze each option one by one:

a) ln 3x = 6 → 3x = e⁶

This statement is true. It represents the inverse relationship between the natural logarithm (ln) and the exponential function with base e. Taking the exponential of both sides of the equation allows us to isolate the variable.

b) log 3x = 9 → 9x = 10³

This statement is not true. It seems to confuse the base of the logarithm. If the logarithm is not specified with a base, it is usually assumed to be base 10 (log base 10). In this case, the correct equivalent statement would be 3x = 10⁹.

c) log 4x = 8 → 4x = 10⁸

This statement is true. Similar to the previous option, assuming a base 10 logarithm (log base 10), the equivalent statement would be 4x = 10⁸.

d) 0.577 = e⁵ˣ → ln 5 = x / 0.577

This statement is not true. The equation given at the beginning, 0.577 = e⁵ˣ, cannot be transformed into the second equation using the properties of logarithms or exponentials. The two statements are unrelated.

e) 5.6554 = 10ˣ → log 5.6554 = x

This statement is true. It correctly represents the relationship between the logarithm and exponential functions. By taking the logarithm (base 10) of both sides of the equation, we can solve for x.

In summary, the choices that contain equivalent statements are:

a) ln 3x = 6 → 3x = e⁶

c) log 4x = 8 → 4x = 10⁸

e) 5.6554 = 10ˣ → log 5.6554 = x

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Related Questions

Mike had some candy to give to his four
children. He first took two pieces for
himself and then evenly divided the rest
among his children. Each child received
two pieces. With how many pieces did he
start?

Answers

10 pieces there was five people each got two pieces
^yeah what he said!!!

Nadya has 19 1/4 yards of ribbbon she cuts ribbon into peices that measure 1 3/4 how many pieces of ribbon doe Nadya have?

Answers

Answer:

11

Step-by-step explanation:

Well basically i took 19 1/4 and divided it by 1 3/4 and there for i got 11. YOUR WELCOME.

There are 11 pieces of ribbon doe Nadya have.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Nadya has 19 1/4 yards of ribbon she cuts ribbon into pieces that measure 1 3/4.

Now, We can find the number of pieces as;

⇒ 19 1/4 ÷ 1 3/4

⇒ 77/4 ÷ 7/4

⇒ 77/4 × 4/7

⇒ 77/7

⇒ 11

Therefore, There are 11 pieces of ribbon doe Nadya have.

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Translate (-2, -3) up 2 units.
Then reflect the result over the x-axis.
What are the coordinates of the final point?

Answers

Answer:

0,1

Step-by-step explanation:

i believe that’s the answer sorry if it’s incorrect

What value of x is in the solution set of 3(x-4) 5x + 2?
1) -10
2) 5
3) 5
4) 10

Answers

Answer:

the answers is -10. I hope this helps you out

The solution to the inequality 3(x-4) ≥ 5x + 2 is when x = -10

Therefore, the correct answer is Option A. -10

Given data:

The inequality relation is represented as 3(x-4) ≥ 5x + 2

On simplifying the equation:

From the distributive property:

3x - 12 ≥ 5x + 2

Adding 12 on both sides:

3x ≥ 14 + 5x

Subtracting 5x on both sides:

-2x ≥ 14

Divide by -2 on both sides:

x ≤ -7

The inequality relation changes when the operand is -1.

So, the values of x should be less than -7

Hence, the solution is when x = -10, the inequality satisfies.

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The complete question is attached below:

What value of x is in the solution set of 3(x – 4) ≥ 5x + 2?

–10

–5

5

10

use the slope to determine if lines AB and CD are parallel, perpendicular, or neither. (please help asap!!)

Answers

Answer:

It’s perpendicular

Step-by-step explanation:

If the slopes are the same and the y-intercepts are different, the lines are parallel. If the slopes are different, the lines are not parallel. Unlike parallel lines, perpendicular lines do intersect.

lines AB and CD are perpendicular to each other

This is all about getting the slope of a line between two coordinates.

The formula for the slope in this case is;

m = (y2 - y1)/(x2 - x1)

We are given coordinates of A and B as;

A(9, 2) and B(-1, 8)

Thus;

m = (8 - 2)/(-1 - 9)

m = 6/-10

m_ab = -6/10 = -3/5

For coordinates of C and D, we have;

C(-5, 16) and D(-8, 11)

Thus;

m_cd = (11 - 16)/(-8 - (-5))

m_cd = -5/-3 = 5/3

For the slopes to be parallel, they have to be equal but for the slopes to be perpendicular, one of them would have to be negative inverse of the other.

We see that; m_cd = 5/3 is same as -1/(m_ab) = -1/(-3/5) = 5/3

Thus, lines AB and CD are perpendicular to each other.

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solve the system of equations by the addition method

5x + 2y = 6

4x - 3y = 14​

Answers

Answer: x=2, y=-2

Step-by-step explanation:

1) I will find x first, so make the amount of Ys same

   3(5x+2y=6)

   2(4x-3y=14)

2) 15x+6y=18

    8x-6y=28

3) combine them together so Ys are all cancelled and 23x=46

4) x=2

5) for solving y, you can just plug in the x to any of that 2 equations, then 4(2)-3y=14

6) 8-3y=14

7) -3y=6

8) y=-2

please i need help!!! Beth enlarged the triangle below by a scale of 5.


A triangle with a base of 4 centimeters and height of 3.5 centimeters.



She found the area of the enlarged triangle. Her work is shown below.


One-half (4) (3.5) (5) = 35 centimeters squared

Answers

Answer:

Your answer is: There is a mistake in Beth's answer the mistake was that she multiplied the area of the original triangle by the scale factor.

Step-by-step explanation:

Hope this helped : )

Work out the size of angle x

Answers

Answer:

angle X will be 180-47=133

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

Your answer would be 133.

Aubrey is looking to purchase sons for her phone. Plan A will cost $2.00 per song. Plan B will require a $15 joining fee and $1.49 per song. When will Plan A be a less expensive option for Aubrey? When will Plan B be a less expensive option for Aubrey? (SHOW ALL WORK BY TYPING HERE). * 3 points

Answers

Given :

Plan A will cost $2.00 per song. Plan B will require a $15 joining fee and $1.49 per song.

To Find :

When will Plan A be a less expensive option for Aubrey? When will Plan B be a less expensive option for Aubrey?

Solution :

Let, after x songs Plan A will be less expensive.

So,

2x < 15 + 1.49x

0.01x < 15

x < 29.41 i.e x < 30

Before, 30 songs Plan A will be less expensive.

After, 30 songs Plan B will be less expensive.

Hence, this is the required solution.

1
Amber ran 1
miles over a period of
1
of an hour. How fast in miles per hour is Amber running?

Answers

Answer: 1mph

Step-by-step explanation:

She s running 1 mile per hour because that's what it says in the problem.

My brother is 6ft tall. How tall is he in centimeters? (1 inch = 2.54cm)

Answers

Answer:

182.88cm

Step-by-step explanation:

multiply the length value by 30.48

Help me solve this problem please

Answers

Answer:

h(3) = 2

Step-by-step explanation:

The absolute value function always gives a positive value, that is

| - a | = | a | = a

To find h(3) substitute x = 3 into h(x), that is

h(3) = | 5(3) - 17 | = | 15 - 17 | = | - 2 | = 2

Paul's car is 16 feet long. He is making a model of his car that is 1/8 the actual size. What is the length of the model?

Answers

The length of the model car is 2 feet

Paul's car is 16 feet long. To create a model of his car that is 1/8 the actual size, we need to determine the length of the scaled-down model.

To find the length of the model, we multiply the length of the actual car by the scaling factor of 1/8.

Length of the model = Length of the actual car * Scaling factor

Length of the model = 16 feet * (1/8)

Length of the model = 16 feet * 1/8

Length of the model = 16/8 feet

Length of the model = 2 feet

Therefore, the length of the model car is 2 feet. The model car is 1/8 the size of the actual car, so it measures 2 feet in length.

This scaled-down model allows Paul to create a representation of his car that is much smaller and more manageable while maintaining the same proportions as the original car.

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(w-2) (w+5)
I need help I don't understand ...

Answers

Answer: w^2 + 3w - 10

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

Work Shown:

Let x = w-2

This will allow us to replace the (w-2) with x to get...

(w-2)(w+5)

x(w+5)

x*w + x*5 ... distribute

w(x) + 5(x)

Now replace x with w-2 and distribute again

w(x) + 5(x)

w(w-2) + 5(w-2)

w*w + w*(-2) + 5*w + 5*(-2)

w^2 - 2w + 5w - 10

w^2 + 3w - 10

(w-2) (w+5)
w^2 + 5w - 2w - 10
w^2 + 3w - 10

How many times greater is 5.6 x 10^6 than 1.4 x 10^2

Answers

Answer:

b

Step-by-step explanation:

Which one of these show the multiplication property of equality? I know what is it I just don’t see it on here, 5 and 9 both look like the substitution property but I don’t know.

Answers

Answer:

5 is c 9 is f

What is the image of (8,-5) after a reflection over the line y = -x?

Answers

Answer:

(8,−5)

Step-by-step explanation:

Given the speeds of each runner below, determine who runs the fastest. Emily runs 15 feet per second. Noah runs 358 feet in 36 seconds. Liz runs 1 mile in 405 seconds. Zach runs 768 feet in 1 minute.

Answers

Brooke
Step-by-step explanation:
Since the first is already given in terms of rate (10 feet per second), we need to find the other rates. Remember, to convert to feet/sec rates.
Noah:
10 ft/sec
Brooke:
489 feet in 36 seconds means:
489/36 = 13.58 ft/sec
Stephanie:
1 mile is 5280 feet, so we can say:
5280 feet is 557 seconds, so rate is:
5280/557 = 9.48 ft/sec
Liz:
732 feet in 1 minutes. We know 1 minute is 60 seconds, so we can say:
732 feet in 60 seconds, so rate is:
732/60 = 12.2 ft/sec
Comparing all the rates (in ft/sec), we can say that "Brooke" is the fastest.

I’m doing a review but I forgot how to do this can someone help?

Answers

Answer:

-3x+10=5x-8

so basically its like grouping.

so answer is

8x=18?

Step-by-step explanation:

sorry if incorrect

Answer:

x=2.25

Step-by-step explanation:

three -x make -3x and 10 +1s make +10 and 5 xs make 5x and 8 -1s make -8

which makes

-3x+10=5x-8

just solve

18=8x

2.25=x

Which is the simplified form of r Superscript negative 7 Baseline + s Superscript negative 12?

Answers

Answer:1/r7+1 over 8 and 12

Step-by-step explanation:

The simplified form of expression r Superscript negative 7 Baseline + s Superscript negative 12 is,

⇒ [tex]\frac{s^1^2 + r^7}{s^1^2 r^7}[/tex]

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

r Superscript negative 7 Baseline + s Superscript negative 12

⇒ r ⁻⁷ + s ⁻¹²

Now, We can simplify the expression as;

⇒ r ⁻⁷ + s ⁻¹²

⇒ 1 / r⁷ + 1 / s ¹²

⇒ [tex]\frac{s^1^2 + r^7}{s^1^2 r^7}[/tex]

Thus, The simplified form of expression r Superscript negative 7 Baseline + s Superscript negative 12 is,

⇒ [tex]\frac{s^1^2 + r^7}{s^1^2 r^7}[/tex]

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Record the length of this line shown in centimeters.

Answers

Answer:

12

Step-by-step explanation:

the ruler measured 12

PLEASE HELP ME ASAP!

Divide.

(2x^3 - 5x^2 + 7) divided by (x - 2)

Answers

Answer:

2x^2 -x - 2 + (3/x-2)

Step-by-step explanation:

The masses of two objects are compared during Mrs. Mobley’s Science experiment. It is determined that object A has a mass of 3 × 10^−2 grams and object B has a mass of 2 × 10^−3 grams. Mrs. Mobley offers extra credit to the first team that can determine how many times larger is the mass of object A than the mass of object B?

Answers

Answer:

15 times larger than b

Step-by-step explanation:

=3×10^-2/2×10^-3

=15×10^-1×10^+1

=15

Are the triangles similar?

Answers

No the side’s are different

I need help (please explain the answer and how you got it)

Answers

Answer:

c

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Ok! So you want to find slope! First, you will need two points which you already have. Next, you will want to plot those two points on a graph. Once, you have that you can draw a straight line between the two points and until the end of the graph. After that, you want to find the rise/run or rise over run. Rise meaning up or down and run meaning left or right. Sometimes your problem will want you to keep the rise/run format and sometimes your problem will ask for a who number in which case you will divide your rise/run (rise ÷ run). How to find the rise over run you ask, simple! Draw a line-up or down from your first (or second) point whichever works, until you reach the y-value of your second (or first) point one your two points are connected, count the rise (up or down) and then the run (left or right). If your run goes left its a negative, right a positive. If your rise goes up its a positive, down a negative.

Boom! You know how to find slope!

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

does anyone know it i think ik it but im not sure so i need help

Answers

Answer:

The "if" part is the hypothesis.

The "then" part is the conclusion.

Hypothesis: an animal is a poodle

Conclusion: it is a dog

II. Let f(x) = 9 – x , g(x) = x2 + x, and h(x) = x – 2. Compute the following:

9. H(g(x)) and h(g(f(x)))

Answers

Answer:

[tex]h(g(x))=x^2+x-2[/tex]

[tex]h(g(f(x))= x^2-19x+88[/tex]

Step-by-step explanation:

Composite Function

Suppose f(x) and g(x) are real functions, the composite function named [tex](f\circ g)(x)[/tex] is defined as:

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

The composite function can be found by substituting g into f.

We are given these functions:

[tex]f(x)=9-x[/tex]

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

[tex]h(x)=x-2[/tex]

Find:

a) h(g(x))

Substituting g into h:

[tex]h(g(x))=x^2+x-2[/tex]

b) h(g(f(x))

First we find g(f(x)):

[tex]g(f(x))=(9-x)^2+(9-x)[/tex]

Operating:

[tex]g(f(x))=81-18x+x^2+9-x[/tex]

Simplifying:

[tex]g(f(x))=90-19x+x^2[/tex]

Now find h(g(f(x)) replacing the above equation into h:

[tex]h(g(f(x))= 90-19x+x^2-2[/tex]

Simplifying and rearranging:

[tex]h(g(f(x))= 88-19x+x^2[/tex]

[tex]h(g(f(x))= x^2-19x+88[/tex]

The graph of the linear equation 3x + 5y
= 15 cuts the x-axis at the point ________.​

Answers

Answer:

(0,5)

Step-by-step explanation:

3x-5y=15

Plug in 0 for y, because we are trying to find the value of x, when y is 0

so, 3x-5(0)=15

3x=15     Divide both sides by 3

x=5

so the answer in coordinate form is (0,5)

The original amount borrowed is called the

A.principal
B.Time
C.interest
D.rate

Answers

D. Is the correct answer which is rate

Kk someone explain this i feel so dumb thanks

Answers

Answer:

Yes

Step-by-step explanation:

The reason is all u do is 12 +1=13 aka 1pm then 30 +50=80 making the time 2:20

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