Erica earned a total of 67,150 last year from her two jobs. The amount she earned from her job at the store was 1,550 more than three times the amount she earned from her job at the college. How much did she earn (in dollars) from her job at the college

The correct option regarding the quotient of the two fractions is given as follows:

B. [tex]\frac{(4x^2 + 6)(x + 2)}{10x^2 + 15}[/tex], no values must be excluded.

The division of two fractions is given by the multiplication of the first fraction by the inverse of the second fraction.

The first fraction for this problem is given as follows:

(4x² + 6)/(x - 2).

The second fraction for this problem is given as follows:

(10x² + 15)/(x² - 4).

Applying the subtraction of perfect squares, we have that:

x² - 4 = (x + 2)(x - 2).

Then the division of the two fractions is given as follows:

(4x² + 6)/(x - 2) x [(x + 2)(x - 2)/(10x² + 15)]

Simplifying the x - 2 terms, we have that:

[tex]\frac{(4x^2 + 6)(x + 2)}{10x^2 + 15}[/tex]

No values must be excluded, as the denominator would be never zero, as:

10x² + 15 = 0

10x² = -15.

x² is always positive, hence 10x² will never be equals to -15.

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[tex]-10w=-9[/tex]

Divide both sides by -10(to isolate the variable):

[tex]\dfrac{-10w}{-10} =\dfrac{-9}{-10}[/tex]

[tex]=0.9[/tex]

Answer:

Step-by-step explanation:

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Answer:

0.35

Step-by-step explanation:

Answer: Nicole Kicked the ball Father by  22 feet than Tyrell.

The force of gravity caused the soccer ball to return to the girl.

By means of gravity, a planet or other body pulls items toward its center.

It is, in ideal circumstances, abiding by Newton's third law of gravitation and force.

Each action has a corresponding and opposing reaction.

So, when a boy kicks a ball and it comes back, that signifies he is abiding by the law.

Nicole kicked the ball 57 feet

Tyrel kicked the ball 35 feet

Nicole  Kicked the ball Father by = 22feet

This is gotten by subtracting the distance Nicole kicked from that of Tyrel

=57 feet - 35feet = 22feet

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Answer:

c.

Step-by-step explanation:

this graph is exponential equation

Answer:

Step-by-step explanation:

The area of the triangle KLM is found using Heron's formula as:

A = 60 in².

     S = (a+b+c)/2

     where a, b, and c are the triangle's three sides.

The sides of the triangle KLM are:

Then,

Semi perimeter s = a + b + c / 2

s = (13 + 13 + 10)/ 2

s = 18 in

Thus,

s - a : 18 - 13 = 5

s -b : 18 - 13 = 5

s - c : 18 - 10 = 8

By Heron's formula;

area of triangle KLM = √(s - a)(s -b)(s - c)

A = √18*5*5*8

A = 60

Thus, the area of triangle KLM is found using Heron's formula as:

A = 60 in².

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The length of RZ is obtained as follows:

RZ = 11.5.

From the kite given by the image at the end of the answer, the segment lengths are given as follows:

Segments WX and WZ are congruent, hence segment WZ has the length given as follows:

WZ = 14.

Then the length of RZ is obtained considering a right triangle, for which:

The Pythagorean Theorem states that the length of the hypotenuse squared is equals to the sum of the lengths squared of the sides.

Considering the Pythagorean Theorem, the length RZ is obtained as follows:

x² + 8² = 14².

[tex]x = \sqrt{14^2 - 8^2}[/tex]

x = 11.5.

RZ = 11.5.

The problem is given by the image presented at the end of the answer.

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Answer:

The distance between two points in the coordinate plane can be found using the distance formula, which is:

distance = √((x2 - x1)^2 + (y2 - y1)^2)

In this case, the two points are (3,2) and (6,0), so we can plug in the values to get:

distance = √((6 - 3)^2 + (0 - 2)^2)

distance = √((3)^2 + (-2)^2)

distance = √(9 + 4)

distance = √13

So the distance between the two points (3,2) and (6,0) is approximately 3.61 units.

Answer: 6

Step-by-step explanation:

Let's start by rewriting the expression. Essentially, this is asking us for 3 * (times) √4 (square root of four).

Now, we can solve √4. Since we know that 2*2 = 4. That means that 2² = 4, so essentially, if we take the square root of 4, we will get back to two.

Now, we can solve the rest: 3 * 2 = 6

In the end, 3√4 = 6. Hope this helps!

Answer:

a) Yes

The experienced person costs more per hour, but also increases sales per customer. To determine if it is more cost-effective to hire the experienced person, you would need to calculate the net gain or loss from hiring them.

You can do this by multiplying the increase in sales per customer by the number of customers per hour, and comparing that to the difference in hourly wages.

(12 customers/hour * $3/customer) - ($19/hour - $13/hour) = $36/hour - $6/hour = $30/hour

Since the net gain is positive, it is more cost-effective to hire the experienced person.

The change between outputs found by dividing one output by its previous output is called output elasticity.

What is output elasticity?

Output elasticity is defined as the division of change in output by change in input which is the previous output.

General, elasticity is a concept that is used to measure the change in the aggregate quantity demanded of a good or service in relation to price movements of that good or service.

A product is considered to be elastic if the quantity demand of the product changes more than proportionally when its price increases or decreases.

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The linear inequality represented by the graph is defined as follows:

y ≥ -2x + 1.

The ordered pairs that are solutions to the inequality x < -3 are given as follows:

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the coefficients are given as follows:

The function in this problem crosses the y-axis at y = 1, hence the intercept b is given as follows:

b = 1.

When x increases by one, y decays by two, hence the slope m is given as follows:

m = -2.

The shaded region, considering the solid line, is given by the values to the right of the line, hence the inequality is defined as follows:

y ≥ -2x + 1.

The inequality for this problem is defined as follows:

x < -3.

The ordered pairs have the following format:

(x,y).

Hence all the ordered pairs that have x < -3, no matter the coordinate of y, are solutions to the inequality.

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Answer:

[tex]\huge\boxed{\sf b = 6.9}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{15}{b} =\frac{24}{11} \\\\Cross \ Multiply\\\\15 \times 11 = b \times 24\\\\165 = 24b\\\\Divide \ both\ sides\ by\ 24\\\\165/24=b\\\\6.9=b\\\\b = 6.9\\\\\rule[225]{225}{2}[/tex]

Answer: By SSS, ΔSUR ≅ ΔTVR.

Step-by-step explanation:

This might be a longer method, but still here you go.

Given, ΔSTU ≅ ΔTSV

By CPCT, we have the following.

∠TUS / ∠RUS = ∠SVT / ∠RVT  ----   1

SU = TV   ----    2

SV = TU ---- 3

∠STU / ∠STR = ∠TSV / ∠TSR

Now, in the triangle TRS,

TR = SR ( ∠TSR = ∠STR) ---- 4

SV= TU

SV - SR = TU - TR (SR= TR)

UR = VR ---- 5

Now, we can use SSS in the triangles ΔSUR and ΔTVR

SU = TV (2)

SR = TR (4)
UR = VR (5)
Therefore, by SSS, ΔSUR ≅ ΔTVR.
Cheers

Answer:

The inequality that describes the situation is 5x + 6y < 120

Step-by-step explanation:

This inequality states that the total cost of purchasing x hammers and y wrenches must be less than $120. Each hammer costs $5 and each wrench costs $6, so the total cost is represented by the expression 5x + 6y.

The inequality states that 5x + 6y < 120 which means for any number of hammers and wrenches she buys it should be less than 120.

The other options:

6x + 5y < 120: the coefficient of x is 6 instead of 5 and that of y is 5 instead of 6.

5x + 6y > 120: the inequality is greater than instead of less than, which means that the total cost should be greater than $120 which is not the case.

6x + 5y ≥ 120 : the inequality is greater than or equal to instead of less than, which means that the total cost should be greater than or equal to $120 which is not the case.

Answer: 464

Step-by-step explanation: 232+232 = 464

Answer:

464 is answer very easy.........

Answer:-7,-7

Step-by-step explanation:

Answer:

Option 2

Step-by-step explanation:

The associative property of multiplication states that you get the product of the numbers no matter what way you arrange the equation and multiply the numbers, you can begin with any two numbers and go on multiplying with the rest, you get the same product!

The two expressions in the second row and one expression in the first row will be 11t - 2u & 10t + 2u and 21t, respectively.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The three expressions in the third row are given below.

4t - 6u, 7t + 4u, and 3t - 2u

The two expressions in the second row are given as,

4t - 6u + 7t + 4u = 11t - 2u

7t + 4u + 3t - 2u = 10t + 2u

The one expression in the first row is calculated as,

11t - 2u + 10t + 2u = 21t

The two expressions in the second row and one expression in the first row will be 11t - 2u & 10t + 2u and 21t, respectively.

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Answer:

7 and 4/9

Step-by-step explanation:

The value of  2(3 + 2) to the third power minus 6 is 2.187.

An expression is combination of variables, numbers and operators.

The given sentence is 2(3 + 2) to the third power minus 6

Mathematically is can be written as [tex]2(3+2)^{\frac{1}{3}-6}[/tex]

Let us solve the exponent part

1/3-6

1-18/3=-17/3

Now [tex]2(3+2)^{\frac{-17}{3}}[/tex]

[tex]10^{-5.6}[/tex]

2.187

Hence, the value of  2(3 + 2) to the third power minus 6 is 2.187.

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Answer:

a = √63

Step-by-step explanation:

We are given a right triangle (notice the right angle).

We know that the hypotenuse (the side opposite of the right angle) is 12.

We also know that one leg (a side that makes up the right angle) is 9, and that the other one is a.

We want to find what a is.

We can use the Pythagorean Theorem to help us find a.

The Pythagorean Theorem says a² + b² = c², where a and b are the legs and c is the hypotenuse.

Since we already know the values of the legs and hypotenuse, we can substitute these values in the theorem, but let's first label the values of everything to avoid confusion / mistakes.

a = a

b = 9

c = 12

Now, plug into the formula.

a² + 9² = 12²

Simplify:

a² + 81 = 144

Subtract 81 from both sides

a² = 63

Square root both sides to get the value of a.

a = √63

Answer:

[tex]a=1, b=-3[/tex]

Step-by-step explanation:

[tex](3,1) \implies 3a-b=6 \\ \\ (0,2) \implies -2b=6 \implies b=-3 \\ \\ \therefore 3a-(-3)=6 \implies a=1[/tex]

Answer:

a) To determine an equation for the revenue, y, when x packages of batteries are sold, we need to know the price of each package of batteries.

Since the price of a package of batteries is $5.00, the revenue, y, when x packages of batteries are sold is given by y = 5x, where x is the number of packages of batteries sold and y is the revenue in dollars.

b) To find the maximum daily revenue that Rahj can expect from battery sales, we need to find the value of x that maximizes y = 5x.

Given that for every increase of 10¢ in the price A of a package of batteries, sales decrease by 10 packages per day. And the store normally sells 700 packages of batteries per day, at $5.00 per package.

It means that the store will sell a maximum number of batteries when the price is at $5.00

And the maximum daily revenue will be $5 * 700 = $3500.

So the maximum daily revenue that Rahj can expect from battery sales is $3500. And the number of packages of batteries sold when the revenue is at a maximum is 700.

The equation is y = 5x, where x is the number of packages of batteries sold and y is the revenue in dollars.

The zeroes of the equation are the points at which the function crosses the x and y-axis.

The x-intercept is the point at which the function crosses the x-axis. It happens when y = 0. So the x-intercept of this equation is (0,0)

The y-intercept is the point at which the function crosses the y-axis. It happens when x = 0. So the y-intercept of this equation is (0,0)

Step-by-step explanation:

Answer:

(a) 1/6. One out of six sides will give you the desired result.

(b) 3/6. 3 out of 6 sides will give you the desired result.

(c) 2/3. 4 out of 6 sides will give you the desired result.

Answer: The probability of not taking a yellow ball can be found by using the formula:

Probability of event A = (Number of favorable outcomes) / (Total number of outcomes)

In this case, the event of not taking a yellow ball is the favorable outcome, and the total number of outcomes is the total number of balls in the bag, which is 10 yellow, 5 orange, and 5 green balls. So, the total number of outcomes is 20.

The number of balls that are not yellow is 5 orange + 5 green = 10.

So, the probability of not taking a yellow ball is

Probability of not taking a yellow ball = (Number of non-yellow balls) / (Total number of balls) = 10/20 = 1/2

So the answer is 1/2.

Step-by-step explanation: