One more and I should be good, i'm pretty familar with this but i'd like to make sure,

Two brothers, Bill and Eric, are 4 years apart, and Bill is the older of the two. If the sum of the boys' ages is 28, how old is bill and how old is eric?

Both boys age is unknown, yet we can mark both with say,
x = Eric's age
y = Bills' age

There are many ways to solve this, but we DO know they're 4 years apart, so it'd have to be
x + y4 = ?,

actually that's off but you understand what i'm saying... Thanks!

Answer:

True

Step-by-step explanation:

If the crew members used 3 gal of paint per hour and bought 30 gal of paint for a job, then they will work 30:3=10 hours.

Conclusion: the only possible sketch is A.

Answer: correct choice is A.

We can use the formula:

F = P · ( 1 + i )^n

where: P = $125,000, i = 0.019 ( 1.9 %), n = 10

F = $125,000 · ( 1 + 0.019 )^10

F = $125,000 · 1.019^10

F = $125,000 · 1.207096

F = $150,887

And we have to add $48,3000 ( for renovations and improvements )

$150,887 + $48,300 = $199,187 ≈ $199,200

Answer: You will be sell the house for $199,200.

Answer:

$199,200

Step-by-step explanation:

Answer:

Option C. $1.67

Step-by-step explanation:

The price of a bag of candy at wholesale = $1.15

The markup on candy at the discount store = 45%

The retail price for the candy = 1.15 +(45% × 1.15)

                                                = 1.15 + ([tex]\frac{45}{100}[/tex]×1.15)

                                               = 1.15 + (0.45 × 1.15)

                                               = 1.15 + 0.5175

                                               = 1.6675 ≈ $1.67

The retail price for the candy would be $1.67.

Answer: A fifth degree polynomial could have 5 linear factors. But the factors   do not have to be be distinct.

Step-by-step explanation:

Thus by corollary to fundamental theorem of algebra, a fifth degree polynomial must have 5 zeroes . But A fifth degree polynomial could have 5 linear factors if all zeroes are real numbers.

The factors could be distinct or similar.

Thus , The factors do not have to be distinct .

Answer:

(x-5y)^2 or (x-5y)(x-5y).

Step-by-step explanation:

hope this helps have a nice day! :D

Final answer:

To find the factors of x² + 25y², use the properties of complex numbers like i² = -1. The factors are (x + 5yi)(x - 5yi), representing complex conjugates.

Explanation:

The factors of x² + 25y² are (x + 5yi)(x - 5yi).

To factorize the expression, we use the fact that i² = -1, so we can rewrite 25y² as (5y)²

By factoring this expression, we can see that it represents a sum of two squares in the form of complex conjugates.

Answer:

C.3

Step-by-step explanation:

We are given that

f(w) varies inversely with w.

f(w)=0.75 when w=8

We have to find the value of f(w) when w=2

According to question

[tex]f(w)\propto\frac{1}{w}[/tex]

[tex]f(w)=\frac{k}{w}[/tex]

Where k=proportionality constant

Substitute the given values then, we get

[tex]0.75=\frac{k}{8}[/tex]

[tex]k=0.75\times 8[/tex]

[tex]k=6[/tex]

Substitute the value of k then, we get

[tex]f(w)=\frac{6}{w}[/tex]

Substitute the value of w=2

Then, we get

[tex]f(w)=\frac{6}{2}=3[/tex]

[tex]f(w)=3[/tex]

Hence, option C is true.

Answer:

10 pounds

Step-by-step explanation:

We are given that Alice hall makes an apple cake (serves 6) for her family

Apples=[tex]2\frac{1}{2}=\frac{5}{2}[/tex]pounds

Flour=[tex]2\frac{1}{4}=\frac{9}{4}[/tex] cups

Margarine=[tex]\frac{1}{4}[/tex] cups

Sugar=[tex]1\frac{1}{4}=\frac{5}{4}[/tex] cups

Eggs=4

For 6 persons , apples required =[tex]\frac{5}{2}[/tex] pounds

For 24 persons=[tex]\frac{\frac{5}{2}}{6}\times 24[/tex]

For 24 persons=[tex]\frac{5}{12}\times 24=10[/tex] pounds

Hence, she should use 10 pounds of apples.

The price of household items increases is a  result of inflation, option C is correct.

Inflation typically leads to a general rise in prices across the economy.

As the value of money decreases, it takes more money to purchase the same goods and services.

Therefore, the prices of household items, along with other consumer goods, tend to increase during periods of inflation.

However, it's important to note that inflation does not affect all goods and services uniformly.

Some prices may rise more rapidly than others, leading to changes in relative prices.

To learn more on Inflation click here:

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Answer:

9/5×c+32 I.e.

if it is equal to 0 then

c=-32 ×5/9

c = -160/9

Step-by-step explanation:

Answer:

Step-by-step explanation:The employees must sell 78 pizzas in order to get the bonus.

The percentage decrease is 0.05%

Step-by-step explanation:

Number of pizzas sold yesterday is 65 pizzas.

The owner offers the employees a bonus if the number of pizzas sold increases by 20%

So 20% of 65 pizzas is,  pizzas.

Therefore, the employees must sell 65+13=78 pizzas in order to get the bonus.

But the actual number of pizzas sold today was 60. So the number of pizza sold has decreased. Then the percent decrease is,

Therefore, the percentage decrease

To determine sin(5π/12) using the half-angle formula, we establish a known cos value for the double of the angle, i.e., cos(5π/6)=-√3/2. Substituting it into the half-angle sin formula: Sin(5π/12)=±√{(1+√3/2)/2}. Simplifying gives Sin(5π/12)=√{3+√3/4}.

The half angle formula for sine is given by:

Sin(x/2) = ±√{(1 - cos x) / 2}

To solve for sin(5π/12) using the half angle formula, we would look for an angle whose double is easily recognized in terms of standard angles (multiples of 30° or 45°). Luckily, the double of 5π/12 is 5π/6, a recognizable angle, and we know that cos(5π/6) = -√3/2.

Step 1: Substitute cos x value (-√3/2) into the formula:

Sin(5π/12) = √{(1 - (-√3/2 )) / 2}

Step 2: Simplify the expression inside the square root:

Sin(5π/12) = √{(1 + √3 / 2) / 2}

Step 3: Calculate the square root:

Sin(5π/12) = ± √{3 + √3 / 4}

Usually, we choose the positive root for a result in the first or second quadrant and the negative root for a result in the third or fourth quadrant. Since the angle 5π/12 is in the first quadrant, we choose the positive root:

Sin(5π/12) = √{3 + √3 / 4}

So, sin(5π/12) using the half angle formula is √{3 + √3 / 4}.

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Final answer:

To find dy/dx using implicit differentiation, differentiate both sides of the equation with respect to x. Then apply the chain rule and simplify.

Explanation:

To find dy/dx using implicit differentiation, we first differentiate both sides of the equation with respect to x. Let's go through the steps:

The answer is (5,-2)

To find the coordinates of vertex R' in the reflected triangle, we can use the midpoint formula. Using the given point P' at (7, -6) and the original point P at (x, y), the x-coordinate of vertex R' is 5. Similarly, using the given point P' at (7, -6) and the original point R at (x, y), the y-coordinate of vertex R' is -2.

To find the coordinates of vertex R', we need to map the reflection of triangle PQR onto triangle P'Q'R'. Since vertex P' is at (7, -6), we can use the midpoint formula to find the coordinates of the reflected point R'.

The midpoint formula states that the x-coordinate of the midpoint is the average of the x-coordinates of the two endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the two endpoints.

Using the given point P' at (7, -6) and the original point P at (x, y), we can write the equation:

(x + 7) / 2 = 7

Solving for x, we get x = 5.

Similarly, using the given point P' at (7, -6) and the original point R at (x, y), we can write the equation:

(y - 6) / 2 = -2

Solving for y, we get y = -2.

Therefore, the coordinates of vertex R' are (5, -2).