Simplify Using the Distributive Property –(3a2 + 5a - 4)​

Answer:

Step-by-step explanation:

these functions are both straight lines with a slope of 1

f(x) = x      passes through the origin (0,0)

h(x) = x-4      is parallel to f(x) = x    and passes through the y axis at (0, -4) and is below the line f(x) = x

Answer:

There are 70 total boys and 20 more boys than girls

Step-by-step explanation:

If the ratio is 7:5, and there are 50 girls, this means that there are 70 boys. And of course, 70-50=20.

Answer:

There are 20 more boys than girls.

Step-by-step explanation:

The ratio of girls two boys in the soccer team is 7 to 5.

We know that there are 50 girls.  

The ratio represents the girls as 5.

50 divided by 5 is 10.

This would mean that amount of boys will be 7 x 10.

7 * 10 equals 70.

50 - 70 equals 20.

There are 20 more boys than girls.

Hope this helps.

Answer:

y=3

Step-by-step explanation:

9514 1404 393

Answer:

  3x +2y = -38

Step-by-step explanation:

When a point and the slope are given for a line, the point-slope form of the equation is useful.

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

  y -(-4) = -3/2(x -(-10))

  y + 4 = -3/2x -15

Multiplying by 2 gives ...

  2y +8 = -3x -30

Adding 3x-8, we get ...

  3x +2y = -38

Answer:

3x + 2y = -38

Just plug in the x and y values to get the answer!

We already know that when x is -10 y = -4 so all we have to do is substitute them.

y = mx + b

-4 = -3/2(-10) + b

-4 = 30/2 + b

-4 = 15 + b

-19 = b

Answer:

19

Step-by-step explanation:

P.E.M.D.A.S

2X8=16

15/5= 3

Answer:

27

Step-by-step explanation:

1) Write it out using operations

2) Organise it into PEMDAS

P: There are no brackets

E: There are no exponents (powers)

M: We need to put  2 × 8 in brackets (to make sure we know what to do first

D: We need to put 15 ÷ 5 in brackets

A&S: As the numbers we need to add and subtract will be part of the brackets we can move on!

3) Solve!

First we need to do the brackets

Then the rest

Hope this helps, have a great day!!

Answer:

i dont understand

Step-by-step explanation:

If your target number of calories to lose weight is 1,703 per day, but you are consuming 2,399 calories per day, then your target is to consume approximately 70% of the calories you are currently consuming.

To find the percentage of the target calories in relation to the current calories, we can divide the target calories by the current calories and multiply by 100. So, the calculation would be:

Percentage = (Target Calories / Current Calories) * 100

Substituting the values, we get:

Percentage = (1,703 / 2,399) * 100 ≈ 70%

Therefore, your target is to consume approximately 70% of the calories you are currently consuming in order to meet your weight loss goal.

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Answer:

f(4) is 9

f(-5) is -9

f(0) is 1

f(1/2) is 2

Answer: 0.6 Liters of powdered milk can produce 60 cups of milk.

Explanation: 120 grams of powdered milk makes 12 cups of milk. 120 divided by 12 is 10. 60 times 10 is 600. So 600 grams of powdered milk to make 60 cups of milk. That is equal to 0.6 kilograms and that is equal to 0.6 liters.

Answer:

4.5

Step-by-step explanation:

Put numbers in order, 1,3,3,4,5,8,9,12

Divide by 2 because there are 2 numbers

Because 4.5 is in the middle of 4 and 5 that is your median

the prime factors of 24 are 2 and 3, which combine to give the unique prime factorization of 24 as 2^3 × 3.

There are no factors of 24 that are prime numbers. A factor of a number is a whole number that divides that number without leaving a remainder. Prime numbers, on the other hand, are numbers that are divisible only by 1 and themselves, and cannot be expressed as the product of any other numbers.

The prime factors of 24 are 2, 2, and 3. We can factorize 24 as 2 × 2 × 2 × 3 or 2^3 × 3. Here, 2 and 3 are both prime numbers, but they are not factors of 24 in isolation. They are only prime factors of 24 when combined in the manner shown.

This fact highlights an important concept in number theory: the uniqueness of prime factorization. Every composite number can be expressed as a unique product of prime numbers. This fundamental theorem of arithmetic is crucial in many areas of mathematics, including cryptography, where it is used to secure communications and protect sensitive information.

In summary, there are no factors of 24 that are prime numbers. However, the prime factors of 24 are 2 and 3, which combine to give the unique prime factorization of 24 as 2^3 × 3.

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Answer:

x = 2

KJ = 12

KI = 23

Step-by-step explanation:

KJ + JI = 12x - 1

5x + 2 + 11 = 12x - 1

5x + 13 = 12x - 1

5x - 12 x = - 1 - 13

-7x = - 14

x = - 14/-7

x = 2

KJ = 5x + 2 = 5*2 + 2 = 10 + 2

KJ = 12

KI = 12 + 11

KI = 23

Answer:

\(\huge\boxed{\sf 8 + 4\sqrt{2} \ cm }\)

Step-by-step explanation:

\(\theta = 45 \textdegree\)

opposite = 4 cm

Using tan first to find the adjacent side:

\(\displaystyle tan \theta = \frac{opposite}{adjacent} \\\\tan \ 45 = \frac{4}{adjacent}\\\\1 = \frac{4}{adjacent} \\\\Multiply \ 'adjacent' \ to \ both \ sides\\\\adjacent = 4 \ cm\)

Finding Hypotenuse now by using Pythagorean theorem:

\((Hyp)^2 = (base)^2 + (perp)^2\)

where base = 4, hyp = 4

(Hyp)² = (4)² + (4)²

(Hyp)² = 16 + 16

(Hyp)² = 32

Take sqrt on both sides

\(Hyp = 4\sqrt{2}\) cm

Exact perimeter of triangle:

= base + perpendicular + hypotenuse

= 4 + 4 + 4√2

= \(8 + 4\sqrt{2}\) cm

\(\rule[225]{225}{2}\)

Answer:

2x x 3y x 3x is 18x4y  hope it helps

Step-by-step explanation:

Answer:

B=28

Step-by-step explanation:

6,520 units must be sold.

How to find sold units?

Let x be the number of units sold.

The total revenue (TR) generated by selling x units is:

TR = 210x

The total variable costs (TVC) incurred in producing x units is:

TVC = 138x

The total cost (TC) of producing x units is the sum of the fixed costs (FC) and the total variable costs (TVC):

TC = FC + TVC

= 422,000 + 138x

The pretax income (PI) is the difference between the total revenue (TR) and the total cost (TC):

PI = TR - TC

= 210x - (422,000 + 138x)

= 72x - 422,000

To find the number of units x that must be sold to earn a pretax income of $47,440, we set PI equal to $47,440 and solve for x:

72x - 422,000 = 47,440

72x = 469,440

x = 6,520

Therefore, the firm must sell 6,520 units to earn a pretax income of $47,440.

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Using the volume x³ + 10x² + 19x  - 30, the missing side of the rectangular prism is (x + 6)

Two sides of a rectangular prism are x + 5 and x - 1. The volume of the rectangular prism is given as x³ + 10x² + 19x  - 30.

Let's find the missing side of the rectangular prism.

Therefore,

volume of a rectangular prism = lwh

where

Therefore,

volume of the prism = x³ + 10x² + 19x  - 30

Let's factorise it to find the missing side length

x³ + 10x² + 19x  - 30  = 0

(x - 1)(x² + 11x + 30)

let's factorise x² + 11x + 30

x² + 11x + 30

x² + 5x + 6x + 30

x(x + 5) + 6(x + 5)

(x + 6)(x + 5) = 0

Therefore, the side length of the rectangular prism are (x - 1), (x + 5) and (x + 6)

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Answer:

Answer:

40 degreses

Step-by-step explanation:

there is a right angle and that means it is 90 degreese then it gives you 50 degreese so you add them up and get 140 then you subtract that 140 from 180 and get 40 degreese.

Answer:

c

Step-by-step explanation:

cause it is

Answer:

85.71 %

Step-by-step explanation:

26-14=12

12/14= 0.8571

0.8571x100= 85.71

Answer:

A change from 14 to 26 represents a positive change (increase) of 85.7142857143%

Step-by-step explanation:

Use the formula:

New - Old / Old x 100%

In other words, new(26) minus old(14) divided by old(14) time 100%

14 is the old value and 26 is the new value. In this case we have a positive change (increase) of 85.7142857143 percent because the new value is greater than the old value.

Answer: 14q + 8 is the answer

Step-by-step explanation:

Answer:

8 + 14q

Step-by-step explanation:

2 x 4 = 8

2 x 7q = 14q

(8 + 14q)

Hoped it helps! :D

Answer:

60 degrees

Step-by-step explanation:

Answer:I think the answer is B

Step-by-step explanation:

Answer:

This is actually really confusing cause there is to options its either B or C

Step-by-step explanation:

Answer:

64.7%

Step-by-step explanation:

To solve this problem we use compounded interest formula.

\(a = p(1 + (r \div n))^{nt} \)

a = amount

p = principle

r = interest rate

n = number of times compounded in a period

t = time period

\(a = 1000(1 + (.05 \div 12)^{12 \times 10} \)

a = 1647.01

1647.01-1000 = 647.01

647.01/1000 = 0.64701

0.64701*100% = 64.7%

Answer:

CI = 28 ± 3.09

Step-by-step explanation:

The sample size, n = 25

The sample mean, m = 28

Standard deviation, s = 7.5

Confidence interval is given as:

CI = Sample mean ± margin of error

We want to find 95% confidence level:

First, let us find the margin of error:

Margin of error = Critical value * standard error

To find the critical value, we need some parameters:

Standard error = \(s / \sqrt{n}\)

=> \(SE = 7.5 / \sqrt{25}= 7.5 = 5 = 1.5\)

The alpha value, ∝ = 1 - (confidence level / 100) = 1 - 95/100 = 1 - 0.95 = 0.05

Critical probability, p, is given as:

p = 1 - ∝/2 = 1 - 0.05/2 = 1 - 0.025 = 0.975

Now we need the degree of freedom:

df = n - 1 = 25 - 1 = 24

Therefore, the critical value is 2.06 (you can use an online t value calculator).

=> Margin of error = 2.06 * 1.5 = 3.09

Therefore, the confidence interval for the population mean is:

CI = 28 ± 3.09

The Policeman’s rate of change is $10 per hour and the firefighter's rate of change is $10 per hour

The Policeman’s rate of change

From the question, we have the following parameters that can be used in our computation:

The graph

On the line of the policeman, we have the following point

(x, y) = (4, 40)

So, the rate of change is

Rate = y/x

This gives

Rate = 40/4

Evaluate

Rate = 10

The firefighter's rate of change

On the line of the firefighters, we have the following point

(x, y) = (4, 60)

So, the rate of change is

Rate = y/x

This gives

Rate = 60/4

Evaluate

Rate = 15

Hence, the rate is $15 per hour

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Answer:

\( q = 2(3r + 8) \)

Step-by-step explanation:

There are two variables, q and r in the expression given. To make r the independent variable, it simply means, make q the subject of the formula, so that variable q would be dependent on variable r. As r changes, q changes also.

Thus,

\( q - 10 = 6(r + 1) \)

Open the parenthesis

\( q - 10 = 6r + 6 \)

Add 10 to both sides

\( q - 10 + 10 = 6r + 6 + 10 \)

\( q = 6r + 16 \)

\( q = 2(3r + 8) \)