5(2y-3)-4y=8-2y-15
Justify each step with a property of algebra. Drag the property to the correct row.

The value of 8,590 − 4,586 is half the value of 2 x (8,590 − 4,586).

An equation is an expression that shows the relationship between two or more numbers and variables. The basic operations performed on an equation are addition, subtraction, multiplication and division.

The value of 8,590 − 4,586 = 4004

Half the value of 2 x (8,590 − 4,586) = (1/2) of 2 x (8,590 − 4,586) = 4004

The value of 8,590 − 4,586 is half the value of 2 x (8,590 − 4,586).

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f - green (A)

f' - red (B)

f'' - blue (C)

The graph of f attains local extrema at the same points that f' = 0. There's evidence of this at x = 0 and between x = 3 and x = 3.5. (At both points, curve A attains a maximum, while curve B crosses the x-axis.)

Similarly, the graph of f' attains local extrema at the same points that f'' = 0. This is seen between x = 1.5 and x = 2. (B has a max, C crosses axis)

Also, the graph of A is continuous at x = 1.5 but exhibits a sharp turn, so at this point f is not differentiable and the graph of f' (and subsequently f'') is not continuous.

Answer:

I also believe it is -4.9 but I may be mistaken

Step-by-step explanation:

2 cos 35 sin 67 can be expressed as the sum of sin(102) and -sin(32).

To express 2 cos 35 sin 67 as a sum, we can use the trigonometric identity for the product of two sine or cosine functions.

Specifically, the identity states that 2 cos A sin B can be written as

sin(A + B) + sin(A - B).

Applying this identity, we have:

2 cos 35 sin 67 = sin(35 + 67) + sin(35 - 67)

Simplifying the expressions inside the sine functions:

sin(102) + sin(-32)

Since the sine function is an odd function,

sin(-x) = -sin(x),

so we can rewrite the equation as:

sin(102) - sin(32)

Therefore, 2 cos 35 sin 67 can be expressed as the sum of sin(102) and -sin(32).

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Answer:

l=8/3h equation demonstrates this

The range of all possible values of $x$

I. (x + 15) + (2x + 15) > 4x + 15 —-> 3x + 30 > 4x + 15 —-> 15 > x ---> x < 15

II. (x + 15) + (4x + 15) > 2x + 15 —-> 5x + 30 > 2x + 15 —-> 3x > -15 ---> x > -5

III. x + 15 + (2x + 15) + (4x + 15) — 6x + 30 > x + 15 —-> 5x > -15 ---> x > -3

Since the sum of any two sides of a triangle must be bigger than the sum of its third side, if you are only examining all real numbers as potential replacements for x in the triangle whose sides are x + 15, 2x + 15, and 4x + 15, then there are these three possibilities:

I. (x + 15) + (2x + 15) > 4x + 15 —-> 3x + 30 > 4x + 15 —-> 15 > x ---> x < 15

II. (x + 15) + (4x + 15) > 2x + 15 —-> 5x + 30 > 2x + 15 —-> 3x > -15 ---> x > -5

III. x + 15 + (2x + 15) + (4x + 15) — 6x + 30 > x + 15 —-> 5x > -15 ---> x > -3

The solution is (-3, 15). If you substitute a number of -4 or -5 for x, one of the triangle's sides will be negative.

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           [ 9(a + h) - 3 - 9a + 3]/h =

          9h /h = 9

Answer:

\(\textsf{(d)} \quad \boxed{9a+9h-3}\)

\(\textsf{(e)} \quad \boxed{9a+9h-6}\)

\(\textsf{(f)} \quad \boxed{9}\)

Step-by-step explanation:

Given function:

\(f(x) = 9x - 3\)

Part (d)

To find f(a + h), substitute x = a + h into the function:

\(\begin{aligned}\implies f(a+h)&=9(a+h)-3\\&=9a+9h-3\end{aligned}\)

Part (e)

Find f(a) by substituting x = a into the function:

\(\implies f(a)=9a-3\)

Find f(h) by substituting x = h into the function:

\(\implies f(h)=9h-3\)

Therefore:

\(\begin{aligned}\implies f(a)+f(h)&=(9a-3)+(9h-3)\\&=9a-3+9h-3\\&=9a+9h-6\end{aligned}\)

Part (f)

\(\begin{aligned}\implies \dfrac{f(a+h)-f(a)}{h}&=\dfrac{(9(a+h)-3)-(9a-3)}{h}\\\\&=\dfrac{9a+9h-3-9a+3}{h}\\\\&=\dfrac{9h}{h}\\\\&=9\end{aligned}\)

Answer:

Answer below :)

Step-by-step explanation:

128 = $76.20132= $77.80134= $78.60144= $82.60

Answer: 128 = $76.20132= $77.80134= $78.60144= $82.60

Answer:

A

Step-by-step explanation:

ita a bc i know its I did this before

The total income lisa earned from her part-time job would be $1,490

In business and accounting, net income is an entity's income minus cost of goods sold, expenses, depreciation and amortization, interest, and taxes for an accounting period.

We have been given that Lisa is a third-year college student living alone in an apartment and works 20 hours a week at a local bank by which  makes $10 per hour.

She has a savings account that she built up during high school and by working full-time summer jobs.

Lisa Gross monthly income from her part-time job= 20 x $10 = $200;

$200 x 4 = $800

Net monthly income from her part-time job = $800 x 0.80 = $640

Net monthly income from her part-time job = $640

Income from her savings = $30

Given Support from her parents is $00

The Total Income = $1,490

Therefore, The total income lisa earned from her part-time job would be $1,490

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To divide a mixed number by a fraction, we need to convert the mixed number into an improper fraction and then multiply it by the reciprocal of the fraction.

Step 1: Convert the mixed number to an improper fraction:

7 5/6 = (6 * 7 + 5) / 6 = 47/6

Step 2: Multiply the improper fraction by the reciprocal of the fraction:

47/6 ÷ 2/3 = 47/6 * 3/2

Step 3: Simplify the fraction if possible:

47/6 * 3/2 = (47 * 3) / (6 * 2) = 141/12

Step 4: Simplify the fraction further, if necessary:

141/12 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3:

141/12 = (141 ÷ 3) / (12 ÷ 3) = 47/4

Therefore, 7 5/6 ÷ 2/3 is equal to 47/4 or 11 3/4.

Answer:$31,500

Step-by-step explanation:

To calculate the total amount Mario will pay, including the loan amount and interest, for the loan from First Bank of Trust, we need to calculate the interest and add it to the loan amount.

The formula to calculate simple interest is:

Interest = (Loan Amount) x (Interest Rate) x (Loan Length)

Let's plug in the values given:

Loan Amount = $25,000

Interest Rate = 6.5% (or 0.065 as a decimal)

Loan Length = 4 years

Interest = $25,000 x 0.065 x 4 = $6,500

Now, let's calculate the total amount Mario will pay:

Total Amount = Loan Amount + Interest = $25,000 + $6,500 = $31,500

Therefore, the total amount Mario will pay, including the loan amount and interest, for the First Bank of Trust loan is $31,500.

The simplified form of 13¹/3 + 2¹/3 - 10/2 is a fraction 64/6 that can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2 the final answer is 32/3.

Given

13¹/3+2¹/3-10/2​

Required simplified it =?

First, we have simplified both constants separately

13¹/3 = (3 * 13 + 1) / 3 = 40/3

2¹/3 = (3 * 2 + 1) / 3 = 7/3

now the expression become = 40/3 + 7/3 - 10/2

now taking LCM of 3 and 2 which is 6.

                                                = 80/6 + 14/6 - 30/6

 now we have to simplify this fraction by dividing by 2 = 64/6

Therefore, the simplified form of 13¹/3 + 2¹/3 - 10/2 is 32/3.

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The ratio of w to y from the given numbers is 8:9 .

The given ratios are w:z = 4:3 and y:z = 3:2 and from z to x is 1: 6.

Now we have to find the ratio w : y .

w:z = 4:3

this can be written as w/z = 4/3 ,

therefore  w = 4z / 3

Again  y : z = 3 : 2

therefore y = 3z / 2

Now we have to find the ratio w : y

Therefore :

w : y =  4z / 3 ÷ 3z / 2 = 8 / 9

An ordered pair containing integers, a fraction with the first number as the numerator and the second largely in the denominator, and even the value represented by this fraction can all be thought of as ratios.

Rational numbers, and occasionally natural numbers as well, are ratios of counts stated in terms of (non-zero) natural numbers. When two numbers are measured with the same unit, which happens frequently, their ratio is a single parameter.

Therefore the ratio of w to y is 8:9 .

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Answer:

x=18 or x=6

Step-by-step explanation:

2x=36

x=18

if it was x^2 then

x^2=36

x=6

SOLUTION:

From the Z-score probability table;

P < 81 = 0.7123

CONCLUSION:

If one adult female is randomly selected, the probability that her pulse rate is less than 81 beats per minute is 0.7123

Answer:

It would take 20 years for it to double

Step-by-step explanation:

5% of 4200 is 210 so then divide 4200 by 210 to find the number of years it will take for it to double and you get 20

The exact expression for g(x) is 2.25cos((2π/4.5)×(x-3.5)) - 4.

A function can be represented using a formula or an equation, and it can be graphed on a coordinate plane. The input values are typically represented on the x-axis and the output values on the y-axis.

From the given information, we know that the function g(x) has a maximum point at (3.5, -4) and a minimum point at (-1, -5).

The general form of a cosine function is f(x) = A×cos(Bx + C) + D, where A is the amplitude, B is the period, C is the phase shift, and D is the vertical shift.

Since the function has a maximum point at (3.5, -4), we know that the graph has been shifted to the left by 3.5 units. Therefore, we can write the function as g(x) = A×cos(B(x - 3.5)) + D.

Similarly, since the function has a minimum point at (-1, -5), we know that the graph has been shifted upwards by 1 unit. Therefore, we can write the function as g(x) = A×cos(B(x - 3.5)) - 4.

To determine A and B, we can use the fact that the period of the function is 4.5 units (the distance between the maximum and minimum points). Therefore, we have B = 2*pi/4.5.

To determine A, we can use the fact that the amplitude is half the distance between the maximum and minimum points, which is 0.5*(5-(-4)) = 4.5. Therefore, we have A = 4.5/2 = 2.25.

Substituting these values into the equation for g(x), we have:

g(x) = 2.25cos((2π/4.5)×(x-3.5)) - 4

Therefore, the exact expression for g(x) is:

g(x) = 2.25cos((2π/4.5)×(x-3.5)) - 4.

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Answer:

  2 mph

Step-by-step explanation:

The relationship between time, speed, and distance is ...

  time = distance/speed

If s is the speed going up the mountain, then s+1 is the speed coming down. The total trip time for 6 miles up and 6 miles down is ...

  6/s +6/(s+1) = 5

  6(s+1) +6s = 5(s)(s+1)

  5s^2 -7x -6 = 0 . . . . subtract the left side, simplify to standard form

  (s -2)(5s +3) = 0 . . . . factor

  s = 2 or -3/5 . . . . values that make the factors 0

Their speed was 2 miles per hour going up the mountain.

__

Check

It took 6/2 = 3 hours to go up the mountain, and 6/(2+1) = 2 hours to come down, for a total of 5 hours.

The growth rate function indicates that the number of years The Iron Man's net worth will reach the net worth of T'Challa is about 87 years

The growth rate is the rate of growth of a function with regards to the input variable.

T'Challa's net worth in the Marvel comics = 80 trillion (8 × 10¹³) Dollars

The Iron Man's net worth = 20 billion (2 × 10¹⁰) Dollars

The growth rate per annum of The Iron Man's net worth = 10% per annum

The number of years it will take to reach T'Challa can therefore, be found as follows;;

(2 × 10¹⁰) × (1 + 0.1)ˣ = (8 × 10¹³)

(1 + 0.1)ˣ = (8 × 10¹³)/(2 × 10¹⁰)

x·ln(1 + 0.1) = ln((8 × 10¹³)/(2 × 10¹⁰))

x = (ln((8 × 10¹³)/(2 × 10¹⁰)))/(ln(1 + 0.1)) ≈ 87 years

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Answer:

the are so many numbers but here's one of them

Step-by-step explanation:

Since the number is less than 700, it cannot begin with a 7 or an 8.

So the hundreds digit can only be a 2 or a 5.

Now the tens digit can be any digit not occupying the hudreds digit. So there would be 3 possibilities, and there remain two possibilities for the units digit.

Hence, the number of such numbers is 2x3x2 which is 12.

The number of two-digit or three-digit numbers that can be made using the digits 1, 7, 8, 5, and 2 will be 150.

A sample is a group of clearly specified components. The number of items in a finite set is denoted by a curly bracket.

The number of two-digit numbers that can be made using the digits 1, 7, 8, 5, and 2 is calculated as,

⇒ 5 x 5

⇒ 25

The number of three-digit numbers that can be made using the digits 1, 7, 8, 5, and 2 is calculated as,

⇒ 5 x 5 x 3

⇒ 125

The number of two-digit or three-digit numbers that can be made using the digits 1, 7, 8, 5, and 2 is calculated as,

⇒ 125 + 25

⇒ 150

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Answer:

112.5 ft not sure though

Answer:

112.5 ft

Step-by-step explanation:

15 is to 40 what x is to 300

15/40 = x/300 (cross multiplication)

(15 * 300) / 40 = 112.5 ft

Another way to find 4x2x5 is to multiply two of the digits and multiply the last digit with the product of two.

Multiplication is when you take one number and add it together a number of times. Example: 5 multiplied by 4 = 5 + 5 + 5 + 5 = 20. We took the number 5 and added it together 4 times. This is why multiplication is sometimes called "times".

Given are three numbers multiplied, 4x2x5, we need to find the another way to solve it,

So,

4x2x5 = 40

So, in another method,

Multiply 4 and 2, we get, 8 as product, now multiply the product 8 to the last number 5,

8x5 = 40

Hence, the another way to find 4x2x5 is to multiply two of the digits and multiply the last digit with the product of two.

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The question is incomplete solved for:

Find the another method to solve 4x2x5

Answer: $18

Step-by-step explanation:

60% of original cost means 40% is taken off

40% = 0.4

30 x 0.4 = 12 so that is how much will be taken off

30-12= 18

$18

Answer:

  73/39

Step-by-step explanation:

The slope of the given line is the coefficient of x in the given equation, which we recognize as being in slope-intercept form.

The slope of the perpendicular line will be the opposite reciprocal of this:

  -1/(-39/73) = 73/39 . . . . slope of the perpendicular line

Answer:

9

Step-by-step explanation:

The \(n\)term is \(2n+1\).

\(S_n=\frac{3+2n+1}{2}(n)=99 \\ \\ \frac{n(2n+4)}{2}=99 \\ \\ n(n+2)=99 \\ \\ n^2+2n-99=0 \\ \\ (n+11)(n-9)=0 \\ \\ n=9 \text{ } (n>0)\)

The number of terms that needed to make the sum to 99 is 9

The first term of the arithmetic progression = 3

The common difference = 2

The sum of n term is = (n/2) [2a+(n-1)d]

Where a is the initial term

d is the common difference

Substitute the values in the equation

(n/2) [2(3)+(n-1)2] = 99

(n/2) [6 + 2n - 2] = 99

(n/2)[4+2n] = 99

n(2 + n) = 99

2n + \(n^2\) = 99

\(n^2\) + 2n - 99 = 0

Split the terms

\(n^2\) - 9n +11n - 99 =0

n(n -9) + 11(n - 9) = 0

(n + 11)(n - 9) = 0

n = -11 or 9

Since n cannot be a negative number, therefore n = 9

Hence, the number of terms that needed to make the sum to 99 is 9

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Answer:

x=1

Step-by-step explanation:

y=3x so just add 1+3=4 then add veriable y=4x

Answer:

\( \frac{20}{10} = \frac{2}{1} = 2 \)

Answer:

7 hours

Step-by-step explanation:

here,

270/18=105/x

x=(105*18)/270

x=7

Chau made $270 for 18 hours of work. At the same rate,  Therefore Chau would have to work 7 hours at the same rate to make $105.

To find out how many hours Chau would have to work to make $105 at the same rate, we can set up a proportion using the given information:

Let x be the number of hours Chau needs to work to make $105.

We know that Chau made $270 for 18 hours of work, so the rate of earnings per hour is:

Rate = Total earnings / Number of hours

Rate = $270 / 18 hours

Rate = $15 per hour

Now, we can set up the proportion:

$15 per hour = $105 / x hours

To find x, we can cross-multiply:

$15 × x = $105

Now, solve for x:

x = $105 / $15

x = 7 hours

So, Chau would have to work 7 hours at the same rate to make $105.

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