Justify each step in solving the equation 4x=7(x-3) by writing a reason for each statement.
Answer:
Statement Reason
1. 4x=7(x-3) 1. given
2. 4x=7x-21 2.
3. -3x=-21 3.
4. x=7 4.

Answer:

x = 10 / (y + 4)

Step-by-step explanation:

Keep in mind both of these angles are equal to each other meaning the equation will have a = So...

4x+7=5(x-4)

Now multiply 5 to x and 4

4x+7=5x-20

Now subtract 4x from 5x

7=1x-20

Now add  20 to both sides

27=x

So x=27

*(Answer)*= (2,1)

*(Information)*= There is an attachment of the graph

its false or open because 17-8 = 9 and you cannot divide 8 by 9 so you will not find x

Since you already know the solution, you need to substitute every occurrence of x and y with those values: the first equation checks out, because it becomes

[tex] 3\cdot 4 - 2 \cdot 2 = 12-4 = 8 [/tex]

The second becomes

[tex] 2 \cdot 4 + 3 \cdot 2 = Q \iff 8+6 = Q \iff Q = 14 [/tex]

Divide total miles between airports by the airplane's speed to find the time it took to travel by plane:

1450 miles / 350 mph = 4.142 hours = 4 hours 9 minutes

Then add the time the bus traveled:

4 hours 9 minutes  + 20 minutes = 4 hours 29 minutes

Answer:

4 hours and 29 mins

Step-by-step explanation:

18.85 = 3.14d

Divide both sides by 3.14

x=6

The answer is C. 6m

For this case we have to:

The circumference or perimeter of a circle is given by:

[tex]c = \pi d\\[/tex]

where d is the diameter of the circle.

Substituting the given value of c, [tex]c = 18.85m[/tex], we have:

[tex]18.85 = \pi d\\[/tex]

[tex]d = \frac{18.85}{\pi } \\\\d = 6\\[/tex]

Therefore, the diameter of the circle is 6m.

Answer:

Option C

Julio initially started with the number 20, because cubing the number and then taking the cube root returns the original number.

If Julio cubes a number and then takes the cube root of the result, and ends up with 20, then the number he started with is also 20. This is because the cube of a number n is n
to the power of 3 (n³), and the cube root of a number is the inverse operation, which will return the original number. In symbolic form, if n is cubed to get n³, then taking the cube root of n³ will return n. Since Julio ends up with 20, the number he started with must have been 20.

the subset of -3 and 8 is: { }, {-3}, {8}, {-3,8}, {8,-3}

–31.7 + 4.5x, when x = 2.1.

-31.7 + 4.5(2.1)

-31.7 + 9.45

Myra should have multiplied 4.5 and 2.1 first.

Answer:

B.Myra should have multiplied 4.5 and 2.1 first.

Step-by-step explanation:

We are given that Myra is evaluating the expression

-31.7+4.5 x when x=21.

We have to find the error in Myra's calculation

When x=2.1

-31.7+4.5(2.1)

-31.7+9.45

=-22.25

By using DMAS rule

D=Divide

M=Multiply

A=Addition

S=Subtraction

But Myra first add  -3.7 to 4.5 then multiply

Hence, Myra should have multiplied 4.5 and 2.1 first instead of add.

Answer:B.Myra should have multiplied 4.5 and 2.1 first.

y = 8/5( x - 9 ) + 16

8/5 = 1.6

y = 1.6x - 14.4 + 16

y = 1.6x + 1.6

The slope is therefore 1.6 and

The y-intercept is 1.6

Answer: First portion is greater than second portion.

Step-by-step explanation:

Time taken to hiked down a trail = 10 minutes

Change in elevation = (-) 170 feet

Speed is given by

[tex]Speed=\frac{Distance}{Time}\\\\Speed=\frac{170}{10}\\\\Speed=17\text{ feet per minute}[/tex]

Similarly,

Time taken to hiked down a trail = 20 minutes

Change in elevation = (-)220 feet

Speed is given by

[tex]Speed=\frac{Distance}{Time}[/tex]

[tex]Speed=\frac{220}{20}\\\\Speed=11\text{ feet per minutes}[/tex]

So, we can see that first portion of the hike where he hiked down a trail at a steady rate for 10 minutes and her change in elevation was (-) 170 feet, was her rate of change in elevation greater.

As 17 feet per minutes is greater than 11 feet per minutes.

the answer is 5k^2+6k+1

For this question, you simply take the x value from the given chart and plug it into the equation, then if the outcome makes sense based on the chart then you use another value of x and plug the second value in and if that also makes sense then you continue plugging in all the x values from the chart until all of them match. There is only one chart which contain the correct table of values.

To start of, let’s plug in the x values from graph 1, the first two values seems to be correct. However, in the third value, it does not match, therefore the first option is in correct.

Moving on to the second option, we could already determine that this table of values is incorrect because the very first x value does not match.

Moving onto the third table of values, we determine that all of the x values are in accordance with the y-values, therefore this option is correct.

Answer: Third option

The answer is B) The initial number of bacteria is 57, and the growth rate is 31% per hour.

The expression shown is an exponential expression.  An exponential expression usually takes the form [tex]ab^{x}[/tex], as this one does.  A represents the initial value, in this case-the initial number of bacteria.  B represents the growth rate.  When it is an increasing growth rate, it will begin with 1, because it will have everything it had before, plus the percent increase, the decimal portion.  In this case, a=57, and b=0.31.

Hope this makes sense!

The answer to your problem is Substitution (A) due to y being 4.

Answer:  D. If an angle does not measure ninety degrees then it is not a right angle.

Step-by-step explanation:

Hi, to obtain the inverse of a conditional statement we have to negate the hypothesis and the conclusion of the conditional statement.

In this case, the hypothesis is "If an angle measures ninety degrees"

The negative form is  "If an angle does not measure ninety degrees" .

The conclusion of the statement is, "then it is a right angle."

The negative form is  "then it is not a right angle."

In conclusion, the correct option is option  D. If an angle does not measure ninety degrees then it is not a right angle.

Feel free to ask for more if it´s necessary or if you did not understand something.

Answer: Point-Slope

Step-by-step explanation:

Point-Slope: y - y₁ = m(x - x₁)  ; where m is the slope and (x₁ , y₁) is the point

Slope-Intercept: y = mx + b  ; where m is the slope and b is the y-intercept

************************************************************************************************

y - 2 = -3(x - 1) is in Point-Slope form where -3 is the slope and (1, 2) is the point

Answer:

The amount of her commission is $1,324.952

Step-by-step explanation:

1. You have the following information given in the problem above:

- Erin has $45,688 in sales.

- Erin's commission rate is 2.9% (0.029).

2. Therefore, to solve this exercise you must multiply the commission rate by her sales, as following:

[tex](45,688)(0.029)=1,324.952[/tex] dollars

ANSWER

The correct answer is A

[tex]f^{-1}(x)=\frac{x+b}{a}[/tex]

EXPLANATION

Given [tex]f(x)=ax-b[/tex].

We can find the inverse by taking the steps.

1. Let  [tex]y=ax-b[/tex]

2. Interchange x and y

[tex]x=ay-b[/tex]

3. Make y the subject

[tex]x+b=ay[/tex]

[tex]\frac{x+b}{a}=y[/tex]

The new function we got now is the inverse of f(x)

[tex]f^{-1}(x)=\frac{x+b}{a}[/tex]

x + b/a Replace f(x) with y, interchange x and y and solve for y.

Sugar is actually sweet and lemons are sour, both those statements are false so the answer is: F F → F

A triangle has 3 sides, a rectangle has 4, both those statements are also false, so the answer would be: F F → F

Answer:

Step-by-step explanation:

1)

We are given first statement as:

           Sugar is sour, and lemons are sweet.

This is a false statement since both the statements are opposite.

Sugar is sweet while lemons are sour.

Hence, the truth value of the given statements is:

              F  F → F

2)

The statement is given as:

A triangle has four sides, and a rectangle has three sides.

It is again a false statement since a triangle is a polygon with three sides and a rectangle is a polygon with four sides.

Hence, both the statements given in it are false.

Hence, the answer is:

                 F  F → F

[tex]y = e^{-sin(x)}[/tex]

[tex]y' = -e^{-sin(x)}(cos(x))[/tex]

[tex]0 = -e^{-sin(x)}(cos(x))[/tex]

When is cos (x) = 0?  at 90° (aka π/2)

Answer: [tex]\frac{\pi}{2}[/tex]

Answer: Hello there!

We have the function f(x) = exp(-sin(x)) and we want to see in wich point the slope is 0.

This is equivalent to see when f'(x) = 0

where f'(x) is the derivative of f(x)

Then the first step is derivate the function f(x)

if we have a function of the form g(h(x)), his derivate is:

g'(h(x))*h'(x)

In our case, g(x) = exp(x) and h(x) = - sin(x)

then f'(x) = exp(-sin(x))*(-cos(x))

Now we know that exp(-sin(x)) is never equal to 0, then we need to se when the cosine is equal to zero.

cos(90°) = 0, and 90° is equivalent to pi/2

Then f'(pi/2) = exp(-sin(pi/2))*(-cos(pi/2)) = 0

this means that the function f(x) has a slope of 0 in the point x = pi/2

we are given

6 × 8 = 48

we know that

commutative property of multiplication:

[tex]a \times b =b \times a[/tex]

now, we will verify each options

option-A:

we have

6 × 8 = 48

now, we can find it's commutative

so, we get

8 × 6 = 48

so, this is TRUE

option-B:

we have

6 × 8 = 48

now, we can find it's commutative

so, we get

8 × 6 = 48

so, this is FALSE

option-C:

we have

6 × 8 = 48

now, we can find it's commutative

so, we get

8 × 6 = 48

so, this is FALSE

To solve the given problem, we set up an equation based on the information that one number is 4 more than the other and the difference between their squares is 56. After simplifying the equation, we find that the numbers in question are 5 and 9.

Let's denote the two numbers as n and n+4.

According to the problem, one number is 4 more than the other, and the difference between their squares is 56.

We can create an equation based on this information:

(n+4)^2 - n^2 = 56

Expanding the equation:

n^2 + 8n + 16 - n^2 = 56

The n^2 terms cancel out:

8n + 16 = 56

Subtracting 16 from both sides gives us:

8n = 40

Dividing by 8:

n = 5

The other number would be:

n+4 = 5+4

n+4 = 9

So, the two numbers are 5 and 9.

Final answer:

To find the numbers, set up an equation using variables. Solve for the variables to find the values of the numbers.

Explanation:

To solve this problem, let's assign variables to the numbers. Let the first number be x. Since the other number is 4 more than the first number, we can represent it as x + 4. The difference between their squares is 56, so we can set up the equation (x + 4)² - x² = 56.

Expanding the equation, we get x² + 8x + 16 - x² = 56. Simplifying further, we have 8x + 16 = 56. Subtracting 16 from both sides, we get 8x = 40. Dividing both sides by 8, we find x = 5.

So, the numbers are 5 and (5 + 4) = 9.

Here is the equation:

[tex]f(x)=4x+1[/tex]

You need to find f(3). To do that, substitute all the x's with 3:

[tex]f(x)=4x+1 \rightarrow f(3)=4\times3 + 1[/tex]

The first thing you need to do is multiply 4 by 3. Multiply:

[tex]4 \times 3 = 12[/tex]

Here is your new equation:

[tex]f(3)=12+1[/tex]

To get your answer, you need to add 12 and 1. Add:

[tex]12+1 = 13[/tex]

That means:

[tex]\bf f(3)=13[/tex]

If you have any questions, feel free to ask in the comments! :)

F(x)= 4x+1

To find f(3) you substitute it into x.

F(3)= 4(3)+1

F(3)=12+1

F(3)=13