Leila works mowing lawns and babysitting.She earns $8.80 an hour for mowing and $7.30 and hour and babysitting.How much will she earn for 1 hour of mowing and 5 hours of babysitting?

To prove that line segment a is parallel to line segment d, based on the given information, we can utilize the properties of perpendicular and parallel lines.

Given that a is perpendicular to b and b is perpendicular to c, we know that angles formed between a and b, as well as between b and c, are right angles. Let's denote these angles as ∠1 and ∠2, respectively.

Now, since c is parallel to d, we can conclude that the corresponding angles ∠2 and ∠3, formed between c and d, are congruent.Considering the fact that ∠2 is a right angle, it can be inferred that ∠3 is also a right angle.

By transitivity, if ∠1 is a right angle and ∠3 is a right angle, then ∠1 and ∠3 are congruent.Since corresponding angles are congruent, and ∠1 and ∠3 are congruent, we can deduce that line segment a is parallel to line segment d.

Thus, we have successfully proven that a is parallel to d based on the given information and the properties of perpendicular and parallel lines.

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The amount invested at 3% is $400, the amount invested at 4% is $700, and the amount invested at 5% is $1000.

Let's assume the amount invested at 4% is x dollars.

According to the given information, the amount invested at 5% is $1000 more than the amount invested at 4%.

So, the amount invested at 5% is (x + $1000).

The total amount invested is the sum of the amounts invested at each rate, which is $2100.

Therefore, we can write the equation:

x + (x + $1000) + (amount invested at 3%) = $2100

Now, we can calculate the amount invested at 3%.

We subtract the sum of the amounts invested at 4% and 5% from the total investment:

(amount invested at 3%) = $2100 - (x + x + $1000) = $2100 - (2x + $1000)

Given that Elena receives $95 per year in simple interest from the investments, we can use the formula for simple interest:

Simple Interest = Principal × Interest Rate

The interest earned from the investment at 3% is (amount invested at 3%) × 0.03, the interest earned from the investment at 4% is (amount invested at 4%) × 0.04, and the interest earned from the investment at 5% is (amount invested at 5%) × 0.05.

According to the problem, the total interest earned is $95.

So we can write the equation:

(amount invested at 3%) × 0.03 + (amount invested at 4%) × 0.04 + (amount invested at 5%) × 0.05 = $95

Now we can substitute the expression for (amount invested at 3%) and solve for x.

Once we have the value of x, we can calculate the amounts invested at 3%, 4%, and 5% using the given information.

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Answer:

Option D is the correct answer!

Answer:

You got it right. Triangle DAC

Step-by-step explanation:

Line segment DA is a perpendicular bisector(it cuts line segment CE perfectly in half making line segment AE an CA congruent. Since the triangle share line segment DA that makes them congruent by the SAS postulate

The triangle that is similar to triangle EAD using the Peices of right triangle would be; Triangle DAC

Line segment DA is a perpendicular bisector which cuts line segment CE perfectly in half making line segment AE and CA congruent.

Since the triangle share line segment DA that makes them congruent with the SAS postulate.

Therefore, Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

Therefore, the similar triangle is DAC

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The time and electricians it would take the remaining 3 electricians 8 hours to complete the job if one electrician does not report.

More people to do a task means less time it will take.

Less people to do a task means more time it will take.

Thus, they are inversely related.

If x men take y time for a work,

We can define a constant as "Manpower" needed for doing that specific work.

Let we define:

Manpower needed for a work = y + y + y + .. + y = Time per man × count of men

Manpower needed for a work = xy

We are given that;

Number of electricians= 4

Number of hours= 6

Now,

We can use the formula:

workers × time = work

where "workers" is the number of electricians, "time" is the number of hours they work, and "work" is the amount of work done.

In this case, we know that 4 electricians can complete the job in 6 hours. So:

4 × 6 = work

work = 24

This means that the total amount of work required to complete the job is 24 "units".

Now, if one electrician doesn't show up, we have only 3 electricians to do the work. Let's call the time it takes for the 3 electricians to complete the job "t".

So we have:

3 × t = 24

Dividing both sides by 3, we get:

t = 8

Therefore, by work and time answer will be 3 electricians and 8 hours.

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Answer:

Step-by-step explanation:

The value of the cash flows four years from today is $22,609.26.

The value of a set of cash flows can be calculated using the present value of an annuity formula. This formula takes into account the time value of money, which states that money has a different value at different points in time due to the opportunity cost of the money. In other words, the money you have today is more valuable than the money you will have in the future.

The present value of an annuity formula is PV = CF / (1 + r)^n, where PV is the present value, CF is the cash flow, r is the interest rate, and n is the number of periods. In this example, the cash flows are $3,000, $4,040, $5,885, and $7,975, the interest rate is 5.4%, and the number of periods is 4. Plugging these numbers into the formula, the present value is $22,609.26. This is the value of the cash flows four years from today.

The value of the cash flows four years from today is $22,609.26.

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Answer:

14

Step-by-step explanation:

The area of a parallelogram is

A = bh where b is the base and h is the height

140 = b*10

Divide each side by 10

140/10 = 10b/10

14 = b

Answer:

y=4x+3

Step-by-step explanation:

y=mx+b

m-slope

b-y-intercept

slope is 4/1  rise 4 ,run 1

m=4/1=4

y-intercept is 3

Answer:

Slope = 4

y-intercept = 3

Step-by-step explanation:

1. Find the slope

The slope of the line is the change in the line, it is also known as the \(\frac{rise}{run}\). It can be found by using the formula; \(\frac{y_2 - y_1}{x_2 - x_1}\). On the graph, one can see that points ( -1, -1 ) and ( -2, -5 ). Substitute these into the formula and solve for the slope;

\(=\frac{y_2 - y_1}{x_2 - x_1}\\\\=\frac{(-5) - (-1)}{(-2) - (-1)}\\\\=\frac{-5 + 1}{-2 + 1}\\\\=\frac{-4}{-1}\\\\= 4\)

The slope of the given line is 4

2. Find the y-intercept

The y-intercept is where the graph of the line intersects the y-axis. In this case, this point is visible, the point at which the graph intersects the y-axis is (0, 3). The y-intercept is the y-coordinate of this point, in other words (3).

The classroom would hold about 34,767 basketballs.

What is the volume of the rectangular prism?

To find the volume of a rectangular prism, you need to know its length, width, and height. Let's assume you have those measurements.

The formula for the volume of a rectangular prism is:

volume = length x width x height

We need to know the volume of the classroom in order to determine how many of a certain object it would hold.

The volume of a rectangular prism (like the classroom) is given by the formula:

volume = length x width x height

Plugging in the values we know:

volume = 24 feet x 28 feet x 10 feet

volume = 6720 cubic feet

Now we can divide the volume of the classroom by the volume of the object we want to find out how many will fit.

For example, if we want to know how many basketballs would fit in the classroom, we would need to know the volume of a basketball. According to the NBA, the standard size for a basketball is about 9.43 inches (0.7867 feet) in diameter. The volume of a sphere is given by the formula:

volume = (4/3) x π x radius^3

Plugging in the radius of the basketball:

volume = (4/3) x π x (0.7867/2)^3

volume ≈ 0.193 cubic feet

Dividing the volume of the classroom by the volume of a basketball:

6720 cubic feet / 0.193 cubic feet per basketball ≈ 34,767 basketballs

Hence, the classroom would hold about 34,767 basketballs.

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Answer:

$611.17 per acre

Step-by-step explanation:

11001 ÷ 18 = 611.16666...

So, the answer is an infinite decimal, so we round it to the nearest hundredth.

Answer:

false true true true

Step-by-step explanation:

The equation for x = 6 is true and would be equal to 6x = 12. and the rest are false.

An equation represents the equality of two or more mathematical expressions. When someone asks you to solve an equation, then they usually mean to find the values of the unknowns for which that equation would be true (the equality between expressions should hold for those values). Solutions to an equation are those values of the variables involved in that equation for which the equation is true.

The given equations are;

6x = 12

Substitute x = 6 to check whether the solution satisfies the equation;

6(6)  = 36

Thus, it is False.

5 + x = 11

Substitute x = 6 to check whether the solution satisfies the equation;

5 + x = 11

5+ 6 = 11

Thus, it is True.

x ÷ 2 = 3

Substitute x = 6 to check whether the solution satisfies the equation;

6/2 = 3

Thus, it is True.

17 – x = 11

Substitute x = 6 to check whether the solution satisfies the equation;

17 - 6 = 11

Thus, it is True.

Hence, the equation for x = 6 is true and would be equal to 6x = 12. and the rest are false.

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Answer:

the 3 numbers are 20,22,and 24 and the smallest of which is 20

Step-by-step explanation:

Hope this helped

Answer:

r=-2, y=-3

Step-by-step explanation:

Answer:

A. y-intercept is 8, Slope is -4/3

Step-by-step explanation:

Answer:

[4,∞)

Step-by-step explanation:

x≥4

[4,∞)

Multiplication equations can be modeled using decimal models.

The multiplication equation is: \(\mathbf{0.50 \times 0.90 = 0.45}\)

From Phil model, we have the following highlights

So, the multiplication expression is:

\(\mathbf{\frac{50}{100} \times \frac{90}{100}}\)

Express as decimals

\(\mathbf{0.50 \times 0.90}\)

Multiply

\(\mathbf{0.50 \times 0.90 = 0.45}\)

Hence, the multiplication equation is: \(\mathbf{0.50 \times 0.90 = 0.45}\)

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Answer:

x = 42

y = 21

Step-by-step explanation:

Since its a right triangle, we have:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

\(sin (60) = \frac{21\sqrt{3} }{x} \\\\x= \frac{21\sqrt{3} }{sin (60)} \\\\x= \frac{21\sqrt{3} }{\frac{\sqrt{3} }{2} } \\\\x = \frac{21\sqrt{3} *2 }{\sqrt{3} } \\\\x = 21*2\\\\x = 42\)

\(cos (60) = \frac{y}{x}\\\\cos (60) = \frac{y}{42}\\\\y = cos (60)*42 \\\\y = \frac{1}{2} * 42\\\\y = 21\)

Answer:

All you need to do is subtract the coefficient.

Step-by-step explanation:

For example a minus b is c. So this is simply going to be c times d to the e you can do that if these two are the same.

Answer:

  $28.40

Step-by-step explanation:

You want the cost of gas for a 389.2 mile trip in a vehicle averaging 29.6 miles per gallon using gas costing $2.16 per gallon.

The cost can be figured by converting miles to dollars using the given conversion factors.

 \((389.2\text{ mi})\times\dfrac{1\text{ gal}}{29.6\text{ mi}}\times\dfrac{\$2.16}{1\text{ gal}}=\dfrac{\$2.16\cdot389.2}{29.6}=\boxed{\$28.40}\)

The gasoline for the trip will cost about $28.40.

Answer:

20 + 75 = 95

Step-by-step explanation:

10 - 5 = 5 x 4 = 20

5 x 15 = 75

Add them together,

75 + 20 = 95

The property illustrated in equation 4(-8+5) = -32 + 20 is the Distributive Property.

The Distributive Property states that when a number is multiplied by a sum or difference in parentheses, it can be distributed or multiplied by each term inside the parentheses separately, and then the results can be added or subtracted.

In this case, the number 4 is multiplied by the sum (-8 + 5). By applying the Distributive Property, we distribute the 4 to each term inside the parentheses:

4(-8 + 5) = (4 * -8) + (4 * 5)

This simplifies to:

4(-8 + 5) = -32 + 20

Finally, we can perform the addition:

-32 + 20 = -12

Therefore, the equation demonstrates the application of the Distributive Property.

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Hello :D

To do this we need to do:

$2.40/12 = $0.20

Answer = $0.20

Answer: 0.20

Step-by-step explanation:

Above is correct! and same question as you

Step-by-step explanation:

y=kx

25= k(-5)

k= -5

y= -5x

y = -5 ×3 = -15

Answer: m = 1/2

Step-by-step explanation: To find the slope of the line, we would first put the equation in y = mx + b form to get y by itself on the left side.

So divide both sides by 2 to get y = 1/2x - 4.

Now the slope is the coefficient of the x term which is 1/2.

This is a positive slope.

An equation to represent the situation and solve the equation of the number of cans of beans Jason can buy is x = 8.69/0.61 and x = 14.

An equation is a statement in mathematical terms that show that two or more algebraic expressions are equal or equivalent.

Algebraic expressions are formed with variables, constants, values, and numbers, in addition to mathematical operands without the equal sign (=).

The total budget on beans = $8.69

The unit price for a can of beans = $0.61

Let the number of cans of beans = x

x = 8.69/0.61

x = 14.2

x = 14

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The price of a can of beans is $0.61

Answer:

Step-by-step explanation:

400 ÷ 16 = 25.

16 ÷ 16 = 1.

1 gallon = 25 miles.

275 ÷ 25 = 11

In conclusion, the car used 11 gallons for 275 miles.

Hope this helps!