find the slope of the line

Answer:

a=14

b=6

Step-by-step explanation:

a+b = 20

2•a+4•b=52

a+b = 20

2a+4b = 52

Kindly note that the data supplied is not up to 20. Hence, the answer will be based on the number of data given.

Answer:

Step-by-step explanation:

Given the following data:

BMI of 20 females :

17.7. 33.5. 26.6 24.7

28.8. 23.8. 18.3. 22.1

19.2. 22.6. 22.7. 38.9

27.3. 44.9. 32.2. 23.9

Lower class limit (LCL) = 15.0

Class width = 6.0

Class_interval_____frequency

15.0 - 20.9 _________3

21.0 - 26.9 _________7

27.0 - 32.9 _________3

33.0 - 38.9 _________2

39.0 - 44.9 _________1

Answer:

The answer is -3 - 2/3

Step-by-step explanation:

Just subtract

Answer:

B) 4,700

Step-by-step explanation:

6000 - 4000 = 2000

2000 in 15 year, find how much for each year

2000/ 15 = 133.3333333

133.3333333 estimated = 133

133 approximately for each year

1975 to 1980 is five years

133 x 5 = 665

4000 + 665 = 4665

4665 rounded the the nearest hundred

4700

The graph of h(x) = (x-1)^2 - 9 is a U-shaped parabola that opens upwards, with the vertex at (1, -9), and it extends indefinitely in both directions.

The function h(x) = (x-1)^2 - 9 represents a quadratic equation. Let's analyze the different components of the equation to understand the behavior of the graph.

The term (x-1)^2 represents a quadratic term. It indicates that the graph will have a parabolic shape. The coefficient in front of the quadratic term (1) implies that the parabola opens upwards.

The constant term -9 shifts the graph downward by 9 units. This means the vertex of the parabola will be at the point (1, -9).

Based on this information, we can draw the following conclusions:

The graph will be a U-shaped curve with the vertex at (1, -9).

The vertex represents the minimum point of the parabola since it opens upward.

The parabola will be symmetric with respect to the vertical line x = 1 since the coefficient of the quadratic term is positive.

The graph will extend indefinitely in both directions.

To accurately plot the graph, you can choose several x-values, substitute them into the equation to find the corresponding y-values, and then plot the points on the graph. Alternatively, you can use graphing software or calculators that can plot the graph of the equation for you.

Remember to label the axes and indicate the vertex at (1, -9) to provide a complete representation of the graph of h(x) = (x-1)^2 - 9.

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Answer:

14

Step-by-step explanation:

630÷45=14

Answer:

Step-by-step explanation:

3 4/7 -2 1/5 rounded to the nearest half is simplified as: 1½

To round 3 and 4/7 - 2 and 1/5 to the nearest half, we first need to convert the mixed numbers to improper fractions:

3 and 4/7 = (3 x 7 + 4)/7 = 25/7

2 and 1/5 = (2 x 5 + 1)/5 = 11/5

So the expression becomes:

25/7 - 11/5

To simplify this, we need to find a common denominator. The least common multiple of 7 and 5 is 35:

(25/7) x (5/5) = 125/35

(11/5) x (7/7) = 77/35

So the expression becomes:

125/35 - 77/35 = 48/35

To round to the nearest half, we need to look at the fraction in terms of eighths. To do this, we multiply both the numerator and denominator by 8:

(48/35) x (8/8) = 384/280

Next, we divide the numerator by the denominator and get:

384 ÷ 280 = 1 and 104/280

To round to the nearest half, we look at the fraction 104/280 in terms of halves, which is:

(104/280) x (2/2) = 208/560

We can simplify this to:

208/560 = 13/35

Since 13/35 is more than half of a whole (which is 1/2), we round up to the nearest half. Therefore:

3 and 4/7 - 2 and 1/5 rounded to the nearest half is 1 and 1/2.

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Answer:

it looks like you have it right

Step-by-step explanation:

Answer:

w<13

Step-by-step explanation:

Works identically to a normal single-variable equation.
Subtract 7 on both sides in order to isolate w--->w+7-7<20-7
The answer (which cannot be simplified any further) is w<13.

Answer:

w < 1`3

Step-by-step explanation:

Isolate the variable w on one side of the inequality sign.

w+7<20

w<20 - 7

w<13.

Answer:

5 in, 15 in, 17 in

Step-by-step explanation:

Let x = the first side

the second side = 3x

the third side = 3x + 2

The perimeter = x + 3x + (3x + 2) = 7x + 2 = 37

7x = 37 - 2 = 35

x = 35/7 = 5 inches

3x = 3*5 = 15 inches

3x + 2 = 17 inches

Answer:

A

Step-by-step explanation:

16 x 100 = 1600

1600 / 40 = 40.0

Answer:

A. 40.0

Step-by-step explanation:

Answer:

D) 34.98

Step-by-step explanation:

Answer:

2.51 x 10^5

Step-by-step explanation:

Scientific notation gives you a number between 1 and 10 multiplied by a power of ten. In this case, you'll want to use the significant digits, 251, and divide or multiply by a power of ten to get a number between 1 and 10.

251,000 can become 2.51 (which is between 1 and 10) multiplied by 10 to a certain exponent. All you need to do is calculate the exponent.

2.51 x 10^(?) = 251,000

For each power of 10, the decimal moves a space. Since you want the decimal to move 5 spaces, you'll want to multiply 2.51 by 10^5.

2.51 x 10 = 25.1

2.51 x 10^2 = 251

2.51 x 10^3 = 2510

2.51 x 10^4 = 25,100

2.51 x 10^5 = 251,000

Answer:

2.83333333333

Step-by-step explanation:

(3 2/5) / (1 1/5) = 2.83333333333

Answer:

85/30 or 2.833333333

Step-by-step explanation:

When dividing fractions, you must find the reciprocal of the second number and multiply it as usual.

It is also much easier to solve after you convert these numbers to improper fractions.

In this case,

3 2/5 = 17/5

1 1/5 = 6/5

17/5 ÷ 6/5

17/5 x 5/6

85/30 (17/6 reduced)

or

2.83333333333333333333

Answer:

x = - \(\frac{3}{4}\) , x = 1

Step-by-step explanation:

4x² = x + 3 ← subtract x + 3 from both sides

4x² - x - 3 = 0 ← in standard form

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 4 × - 3 = - 12 and sum = - 1

the factors are - 4 and + 3

use these factors to split the x- term

4x² - 4x + 3x - 3 = 0 ( factor the first/second and third/fourth terms )

4x(x - 1) + 3(x - 1) = 0 ← factor out (x - 1) from each term

(x - 1)(4x + 3) = 0 ← in factored form

equate each factor to zero and solve for x

4x + 3 = 0 ( subtract 3 from each side )

4x = - 3 ( divide both sides by 4 )

x = - \(\frac{3}{4}\)

x - 1 = 0 ( add 1 to both sides )

x = 1

solutions are x = - \(\frac{3}{4}\) , x = 1

Answer:

The ones that can be used are (B and A)

The ones that cannot be used are (C and D)

Step-by-step explanation:

Because the panthers got 6 less and the tigers got 22…

b+6 would make 22 (panthers plus 6 makes tigers)

22-b would also be 6 because 6+b makes 22, so subtracting b from 22 makes 6

Answer: x = 10

Step-by-step explanation:

4x+89=129

(2 parallel straight lines have congruent angles)

then solve for x.

Step 1: Subtract 89 from both sides of the equation.

4x = 40

(We want to isolate the variable x on one side of the equation. To do this, we need to get rid of the number 89 that is currently on the right side of the equation. To do this, we subtract 89 from both sides of the equation.)

Step 2: Divide both sides of the equation by 4.

x = 10

(To isolate the variable x further, we need to get rid of the coefficient 4 that is currently in front of x. To do this, we divide both sides of the equation by 4.)

Answer:

See picture. I made a 100.

Step-by-step explanation:

Weekly: $17253.46

Daily: $17254.01

Monthly: $17251.29

Quarterly: $17245.69

Semi-Annually: $17237.36

Continuously: $17254.11

With a 12% housekeeping gratuity, the hotel bill for 4 nights comes to $891.52.

"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."

We always count the unit or amount value first and then calculate the more or less amount value.

For this reason, this procedure is called a unified procedure.

Many set values ​​are found by multiplying the set value by the number of sets.

A set value is obtained by dividing many set values ​​by the number of sets.

According to our question-

Total cost = Bill before tip + Tip

Total cost = $796 + $95.52

Total cost = $891.52

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The area of the Region bounded by y = √x, y = 2-x², and y = -√2x is $\frac{32}{15}$.

To find the area of the region bounded by y = √x, y = 2-x², and y = -√2x, we need to graph the equations and determine the points of intersection. Then we can integrate to find the area.

Firstly, we'll graph the equations and find the points of intersection:

y = √xy = 2-x²y = -√2xGraph of y = √x, y = 2-x², and y = -√2xWe need to solve for the points of intersection, so we'll set the equations equal to each other and solve for x:√x = 2-x²√x + x² - 2 = 0Let's substitute u = x² + 1:√x + u - 3 = 0√x = 3 - u

(Note: Since we squared both sides, we have to check if the solution is valid.)u = -2x²u + x² + 1 = 0 (substituting back in for u

)Factoring gives us:u = (1, -2)We can then solve for x and y:x = ±1, y = 1y = 2 - 1 = 1, x = 0y = -√2x = -√2, x = 2y = 0, x = 0Graph of y = √x, y = 2-x², and y = -√2x with points of intersection to find the area, we need to integrate.

The area is bounded by the x-values -1 to 2, so we'll integrate with respect to x:$$\int_{-1}^0 (2 - x^2) - \sqrt{x} \ dx + \int_0^1 \sqrt{x} - \sqrt{2x} \ dx$$

We can then simplify and integrate:$$\left[\frac{2x^3}{3} - \frac{2x^{5/2}}{5/2} + \frac{4}{3}x^{3/2}\right]_{-1}^0 + \left[\frac{2x^{3/2}}{3} - \frac{4x^{3/2}}{3}\right]_0^1$$$$= \frac{4}{3} + \frac{4}{3} - \frac{4}{15} + \frac{4}{3} - \frac{4}{3}$$$$= \frac{32}{15}$$

Therefore, the area of the region bounded by y = √x, y = 2-x², and y = -√2x is $\frac{32}{15}$.

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a. It will take 7 months to pay off the credit card.

b. it will take 4 months to pay off the credit card.

Since, APR stands for Annual Percentage Rate. It is the interest rate charged on a loan or credit card, expressed as a yearly percentage rate. The APR takes into account not only the interest rate, but also any fees or charges associated with the loan or credit card.

a. If you put half of the available money each month toward the credit card, then you are paying $150.00 per month towards the credit card balance.

We can use the formula for the present value of an annuity to find how many months it will take to pay off the credit card:

PV = PMT × ((1 - (1 + r)⁻ⁿ) / r)

where:

PV is the present value of the debt

PMT is the payment amount per period

r is the monthly interest rate

n is the number of periods

Substituting the values, we get:

754.43 = 150 × ((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)

Simplifying and solving for n, we get:

n = log(1 + (PV ×r / PMT)) / log(1 + r)

n = log(1 + (754.43×0.011333 / 150)) / log(1 + 0.011333)

n = 6.18

Therefore, it will take 7 months to pay off the credit card if you put half of the available money each month toward the credit card.

b. If you put all of the available money each month toward the credit card, then you are paying $300.00 per month towards the credit card balance.

754.43 = 300 ×((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)

Simplifying and solving for n, we get:

n = log(1 + (PV × r / PMT)) / log(1 + r)

n = log(1 + (754.43× 0.011333 / 300)) / log(1 + 0.011333)

n = 3.43

Therefore, it will take 4 months to pay off the credit card if you put all of the available money each month toward the credit card.

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Answer:

$2.25

Step-by-step explanation:

To find the cost per pound you have to divide $54 by 24.

The answer of the given question based on the expression is , the value of the summation when m = 3 is 137.

In mathematics, an expression is a combination of numbers, variables, and operators that represents a value or a set of values. It can be a simple combination of numbers and variables or a more complex combination involving mathematical operations like addition, subtraction, multiplication, division, exponents, and roots. Expressions can be used to represent a wide range of mathematical concepts, from simple arithmetic to complex functions and equations.

To evaluate the summation 1(1!) + 2(2!) + 3(3!) + 4(4!) + m(m!), where m = 3, we substitute m = 3 and simplify:

1(1!)+2(2!) +3(3!) +4(4!) +3(3!)

= 1(1) + 2(2) + 3(6) + 4(24) + 3(6) (since n! = n(n-1)! for all positive integers n)

= 1 + 4 + 18 + 96 + 18

= 137

Therefore, the value of the summation when m = 3 is 137.

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Answer:

8700kg

Step-by-step explanation:

b = mass of bricks

l = mass of lorry

b+l = total mass = 11600kg

b = 3l  ==>  l = b/3

substitute: b + b/3 = 11600

multiply every term by 3 to get rid of denominator: 3b + b = 34800

simplify and solve:  4b = 34800  ==>  b = 8700

check:  l = 8700/3 = 2900

2900 + 8700 = 11600?  YES

Answer: -7

Step-by-step explanation:

I’m doing the test

After four years, Arianna will have a total of $60 in her savings account.

What is Compound Interest ?

Compound interest is interest that is calculated not only on the initial principal amount, but also on the accumulated interest of previous periods. In other words, the interest earned is added to the principal amount and then the interest for the next period is calculated based on the new total amount, which includes both the principal and the previously earned interest.

For example, if you deposit $1,000 in a savings account with a 5% annual interest rate, and the interest is compounded annually, at the end of the first year, you would earn $50 in interest, and your balance would be $1,050. If you leave the money in the account and don't make any further deposits or withdrawals, in the second year, you would earn interest not only on the original $1,000, but also on the $50 in interest earned in the first year, which would be a total of $52.50 in interest. Your new balance at the end of the second year would be $1,102.50.

The power of compound interest lies in the fact that the interest earned in each period is added to the principal, so the amount of interest earned in each subsequent period increases, resulting in a larger and larger balance over time.

Since the interest is not compounded, the interest earned each year will be the same, and it can be calculated as:

Interest earned each year = Principal * Annual interest rate

So for Arianna, the interest earned each year will be:

Interest earned each year = $50 * 0.05 = $2.50

After one year, Arianna will have $50 + $2.50 = $52.50

After two years, she will have $52.50 + $2.50 = $55

After three years, she will have $55 + $2.50 = $57.50

After four years, she will have $57.50 + $2.50 = $60

Therefore, after four years, Arianna will have a total of $60 in her savings account.

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