5(2x – 3) = 5 Part A: How many solutions does this equation have? (4 points) Part B: What are the solutions to this equation? Show your work. (6 points)

45:15 =

15:5 =

3:1

Normally, the ratio would be 45:15, but you should simplify like shown above.

The book to magazine ratio of the numbers of books and magazines Manny read over the summer is 3:1.

The student's question pertains to finding the ratio of books Manny read over the summer to the magazines he read. Given that Manny read 45 books and 15 magazines, these numbers can be turned into a ratio by placing them over each other (books/magazines). Therefore, the book to magazine ratio would be 45:15. However, this ratio can be simplified by dividing both numbers by their greatest common divisor, which in this case is 15. When both numbers are divided by 15, the simplified book to magazine ratio is 3:1. Hence, for every 3 books Manny reads he also reads 1 magazine.

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Answer:

$136.00

Step-by-step explanation:

100 + 12 +12 + 12

simple interest is only against the loan itself

compound interest is the loan plus interest . . .then that sum . . .again then that some

Answer:

Inequality: 50-1.99x=30

She has 10 days.

Step-by-step explanation:

So, she starts off with with $50. From there, she is buying songs that are $1.99 (everyday). You could do this multiple ways:

Guess and Check, or use Algebra.

But for Algebra:

If we graph this out, the y intercept would be (0, 50), because she is starting out with $50. From there, she is spending 1.99 each day, so the slope would be 1.99/1. So basically, we would write this as 50-1.99x (that is the expression).

We would also set this equal to 30, because we are trying to see how many days it would take to still keep her balance above $30, but make it as close to 30 as possible. (x represents the # of days.

So the inequality would be 50-1.99x=30

And, when we isolate the variable and solve, we would see that she can buy a total of 10 songs over 10 days. (So basically, she has 10 days to stay over $30).

Sarah can use her $50 gift card to download a $1.99 song for 10 full days before her balance falls below $30. This is found by solving the inequality 50 - 1.99d > 30, which indicates the maximum days she can download with the card's balance staying above the threshold.

Sarah's problem can be represented by an inequality that describes the number of $1.99 song downloads she can make before her $50 music gift card drops below $30. To find out how many days she can continue to download a song without going below a $30 balance, we'll represent the number of days as d, and the cost per day as $1.99.

The inequality will be: 50 - 1.99d > 30.

Step 1: Subtract 50 from both sides to isolate the term with d.

-1.99d > -20

Step 2: Since we're dealing with a negative coefficient for d, divide both sides by -1.99, and flip the inequality sign (a rule when dividing by a negative).

d < 20/1.99

d < 10.05

Since Sarah can't download a fraction of a song, she can download a song for full days without the balance going below $30 for 10 days.

Therefore, Sarah can download a song for 10 full days with the balance of her gift card staying above $30. After that, her balance would drop below $30 if she continues.

Answer:

y = - 4x - 13

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 )

here m = - 4, thus

y = - 4x + c ← is the partial equation of the line

To find c substitute (- 2, - 5) into the partial equation

- 5 = 8 + c ⇒ c = - 5 - 8 = - 13

y = - 4x - 13 ← equation of line

The equation of the line with slope -4 passing through the point (-2, -5) is y = -4x - 13.

To find the equation of a line with a given slope that passes through a specific point, you can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through. In this case, the slope is -4 and the line passes through the point (-2, -5). Plugging these values into the point-slope form, the equation becomes y - (-5) = -4(x - (-2)), which simplifies to y + 5 = -4(x + 2). Expanding the right side gives y + 5 = -4x - 8. To solve for y, subtract 5 from both sides to get y = -4x - 13.

Answer:

Less than 100. Z=83

Step-by-step explanation:

The mean is the average found by adding the sum of the data points and dividing by the number of them. Here there are 3 cars whose speeds are 101, 116, and Z or unknown. The mean of them is 100. Solve for Z.

100 =(101+116+Z)/3

300=217+Z

83=Z

Answer:

B. 5040

Step-by-step explanation:

We want to find the value of [tex]7![/tex].

We read [tex]7![/tex] as ''seven factorial''

By definition, [tex]n!=n(n-1)(n-2)...3\cdot2\cdot1[/tex]

We need to find the product of all the positive integers less than or equal to the given number.

This implies that:

[tex]7!=7\times 6\times 5\times 4\times 3\times 2\times 1[/tex]

[tex]7!=5040[/tex]

Answer:

1.25315*102

Step-by-step explanation:

The number 125.315 is already in standard form. This form, also known as scientific notation, simplifies the representation of large or small numbers. However, 125.315 doesn't need this kind of simplification.

The number 125.315 is already in standard form. In Mathematics, standard form, also known as scientific notation, refers to expressing a number as a number between 1 and 10 multiplied by a power of 10. The purpose is to simplify the representation of very large or very small numbers. For instance, 2000 would be written as 2 x 10^3 in scientific notation. However, 125.315 is not a large enough number that needs to be simplified in such a manner.

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The answer would be 5227. If you subtract what is in parenthesis first and then multiply it that should be your answer.

Answer:  [tex]5,227[/tex]

Step-by-step explanation:

Given the expression [tex]63*83-(6-4)[/tex] you can simplify it by applying these steps:

First, make the subtraction of the numbers that are inside of the parentheses:

 [tex]=63*83-(2)[/tex]

Apply multiplication of signs to eliminate the parentheses. Remember that:

[tex](-)(-)=+\\(+)(+)=+\\(-)(+)=-[/tex]

Then:

[tex]=63*83-2[/tex]

Now, make the multplication indicated:

[tex]=5,229-2[/tex]

Finally, subtract both numbers:

[tex]=5,227[/tex]

Answer:

It is the secon option ∆TRS ≈ ∆TPQ ; SAS

Step-by-step explanation: angle t is equal to angle t because it is the same angle

line TR divided by line TP is equal to line TS divided by TQ

Answer:  The correct option is

[tex](B)~\triangle TRS\sim \triangle TPQ,~SAS\sim.[/tex]

Step-by-step explanation:  We are given to check whether the triangles in the figure are similar or not. If so, we are to state the similarity statement.

From the figure, we note that

in the triangles TPQ and TRS, we have

[tex]TP=42,~TQ=28,TR=42+6=48,~~TS=28+4=32.[/tex]

Therefore, the ratios of the corresponding sides of two triangles are

[tex]\dfrac{TP}{TR}=\dfrac{42}{48}=\dfrac{7}{8},\\\\\\\dfrac{TQ}{TS}=\dfrac{28}{32}=\dfrac{7}{8}.[/tex]

Now, in ΔTPQ and ΔTRS, we have

[tex]\dfrac{TP}{TR}=\dfrac{TQ}{TS},\\\\\\m\angle TPQ=m\angle TRS~~~\textup{[common angle]}[/tex]

So, triangles TPQ and TRS are similar by SAS proportionality postulate.

Thus, the correct option is

[tex](B)~\triangle TRS\sim \triangle TPQ,~SAS\sim.[/tex]

Answer:

8x+3

Step-by-step explanation:

Take 1/5 of 15x and 15

Then add 5x

8x+3 is the answer

the third option

because 1/3 is not equal to three

where as if we replace the x with one in all the other we would find that the equation is correct.

Answer:

x = 12 is the excluded value

Step-by-step explanation:

An excluded value is the value/s of x that make the denominator of the rational function equal to zero as this would make the function undefined.

Equate the denominator to zero and solve for x

6x - 72 = 0 ⇒ 6x = 72 ⇒ x = 12 ← excluded value

Answer: x=12

Step-by-step explanation:

D and B because you at the picture

The correct answers are A, B, and C for the given function y = (2/3)x.

The slope of a line is defined as the gradient of the line.

The equation y = (2/3)x represents a line in the coordinate plane, where the x value of a point on the line is multiplied by the constant 2/3 to get the y value of that point.

A. The equation y = (2/3)x represents a proportional relationship because for every change in x by some unit, there is a corresponding change in y by 2/3 times that unit.

B. The unit rate of change of y with respect to x is 2/3. This means that for every unit increase in x, the value of y will increase by 2/3 times that unit.

C. The slope of the line is 2/3. The slope of a line gives you the rate of change of y with respect to x, and in this case, the slope is 2/3.

D. A change of three units in x results in a change of two units in y. Since the unit rate of change of y with respect to x is 2/3, a change of three units in x will result in a change of 2/3 × 3 = 2 units in y.

E. A change of three units in x results in a change of one unit in y is not true, because the unit rate of change of y with respect to x is 2/3, which is different from 1.

Therefore, the correct answers are A, B, and C.

Learn more about the Slope of the Line here:

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job a would be the biggest money maker job. $15 an hour working at most 15 hours = $225. $8 an hour working 34 hours = $272. You would make $47 more at job a

Answer:

You should choose Job A.

Step-by-step explanation:

I did the math.

1 quarter = 25 cents

1 nickel = 5 cents

2 quarters = 25*2 = 50 cents

50 cents + 5 cents = 55 cents, or $0.55

2 quarters and one nickel is 55cents

Divide the number of wooden cabinets by the number of days.

24 / 8 = 3

Carlos installed an average of 3 cabinets each day.

To find the average number of cabinets installed each day, we divide the total number of cabinets installed by the number of days. In this case, Carlos installed 24 cabinets in 8 days, so we divide 24 by 8 to get an average of 3 cabinets installed each day.

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Answer: Reflection

Step-by-step explanation:

Looking at this as a reference they reflect across the y-axis

Answer:

10.4 cents

Step-by-step explanation:

40 pecans/$3.84 gives you pecans per dollar

Final answer:

To find the probability of Damon choosing two white socks, calculate the probabilities step by step. The probability of Damon picking two white socks is approximately 33%.

Explanation:

To find the probability of Damon choosing two white socks from his drawer, we can calculate it step by step:

Picking the first white sock: 14 white socks out of 24 total socks, so probability = 14/24

Picking the second white sock: 13 white socks left out of 23 total socks, so probability = 13/23

Multiplying the two probabilities together: (14/24) x (13/23) = 91/276, which simplifies to approximately 0.330 or 33%.

Answer:

Her monthly principal payment is D: $579.81 and monthly interest payment is 0.4375.

Step-by-step explanation:

Ok, in order to calculate the monthly principal and interest payment, we can use this relatively simple equation. The equation is:

[tex]M=P\frac{r(1+r)^{n} }{((1+r)^{n}-1) }[/tex]

Where variables represent the following:

M is your monthly payment.

P is your principal.

r is your monthly interest rate, calculated by dividing your annual interest rate by 12.

n is your number of payments (the number of months you will be paying the loan throughout the 30 years)

Then, in this case:

M=?

P=$105,000

5.25%=5.25/100=0.0525, then [tex]r=\frac{0.0525}{12} =0.004375[/tex]

[tex]n=12*30=360[/tex]

So, [tex]M=105,000\frac{0.004375(1+(0.004375))^{360} }{((1+(0.004375))^{360}-1)}[/tex] $

Solving this,

[tex]M=105,000\frac{0.004375(1.004375))^{360} }{((1.004375))^{360}-1)}[/tex] $

[tex]M=105,000\frac{0.004375(4.8141) }{((4.8141))-1)}[/tex] $

[tex]M=105,000\frac{0.02106 }{3.8142}[/tex] $

[tex]M=105,000(0.005522)/tex] $

[tex]M=579.81[/tex] $

Her monthly principal payment is $579.81.

Answer: $579.81 APEX

Answer:

Slope = 1/5

Step-by-step explanation:

passing through points A(5,4) and B(0,3)

Slope = (4 - 3)/(5 - 0) = 1/5

Answer:

E(m) = 12m

Step-by-step explanation:

Your earnings will be the amount of times you mow the lawn * $12 per job

so if m is the amount of times and 12 is the amount your Earnings(E) = 12m

Answer:

I think it’s C

Step-by-step explanation:

The answer would be B, Supplementary Angle, Since half the circle would be 180 degrees also if this isn’t enough information,

2

You know that OA = 4 because the radius of the circle on the left is 4. So, subtract that from OP to find that AP = 5.

Finally, subtract BP, which is 3 because of the circle’s radius. You then find that AB = 2

Answer:

The answer is 2 i think.

Step-by-step explanation:

Answer:

slope = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (8, 1) and (x₂, y₂ ) = (24, 9)

m = [tex]\frac{9-1}{24-8}[/tex] = [tex]\frac{8}{16}[/tex] = [tex]\frac{1}{2}[/tex]

Answer:

Step-by-step explanation:

The general form of a linear function is ax + b.

f(x) = ax + b

f(1) = a + b = -7

f(2) = 2a + b = -10

So using a system of equations we solve for 'a' and 'b'.

a + b = -7 | 2a + b = -10

We multiply the first one by -1.

-a - b = 7 | 2a + b = -10

And then we solve the system by elimination(by adding the equations):

a = -3

Solving for b: a + b = -7 <=> -3 +b = -7 => b = -4

So the general rule of the function is:

f(x) = -3x - 4

Answer:

y = 11.2 in

Step-by-step explanation:

Given a tangent and a secant from an external point to a circle, then

The square of the measure of the tangent is equal to the product of the external part and the entire secant, that is

5(5 + y) = 9²

25 + 5y = 81 ( subtract 25 from both sides )

5y = 56 ( divide both sides by 5 )

y = 11.2

Answer: y = 11.2

Step-by-step explanation:

Answer:

8.46

Step-by-step explanation:

59+6=65 65 divided by 508= 7.815 (7.82) 6 divided by 508=84.666 (8.67) then subtract 8.67 from 508 = 499.33 divided by 59 = 8.46 thats your answer.

Answer:

$8

Step-by-step explanation:

x=chaperone tickets

59(x+2)+6x=508

59x+118+6x=508

65x+118=508

65x=508

x=6

therefore 6+2=8

Answer:

x=-1 should be your answer

Answer:

see explanation

Step-by-step explanation:

Given

y = x² + 2x + 1

To find the zeros let y = 0, that is

x² + 2x + 1 = 0 ← x² + 2x + 1 is a perfect square

(x + 1)² = 0

x + 1 = 0 ( subtract 1 from both sides )

x = - 1 with multiplicity 2 ← zero

This indicates that the graph has a minimum turning point at (- 1, 0)

Note from your table

the value for x = - 1 should be y = 0 ( not - 2 )

Answer:

X * (X +1) = 420

X^2 + X = 420

X^2 + X -420 = 0

X = 20

Step-by-step explanation:

For this case we have [tex]20 * 21 = 420.[/tex] We must find an equation that allows us to find the smallest value. So:

Let "x" be the variable that represents the smallest number. Thus, "x + 1" represents the consecutive integer. The equation would be given by:

[tex]x * (x + 1) = 420\\x ^ 2 + x = 420\\x ^ 2 + x-420 = 0[/tex]

To factor, we must find two numbers that multiply as a result -420 and sum as a result 1.

These numbers are:

[tex]21, -20\\21-20 = 1\\21 * (-20) = -420[/tex]

Thus, the factorization is:

[tex](x-20) (x + 21) = 0[/tex]

The roots are:

[tex]x = 20\\x = -21[/tex]

Effectively, the smallest integer was found,[tex]x = 20[/tex].

Answeer:

[tex]x ^ 2 + x-420 = 0\\(x-20) (x + 21) = 0[/tex]