Find the sum and express it in simplest form.
(-2y3 + 2y2 - 9) + (-4y3 + 5y2 + 7)

Answer:

Round to the nearest whole dollar, the median weekly earnings of young adults with associate degrees in 2013 were $ 775.

Step-by-step explanation:

Given that in 2013 the median weekly earnings of young adults with bachelor degrees were $ 1108, and this represents a 43% increase over the weakly median earnings of young adults with associate degrees, to determine the median weekly earnings of the latter, the following must be done calculation:

X x 1.43 = 1108

X = 1108 / 1.43

X = 774.82

Therefore, round to the nearest whole dollar, the median weekly earnings of young adults with associate degrees in 2013 were $ 775.

we are given the following expression:

we are asked to plug in the following constants, b = -9 and k = 4, to do that, we will replace the values given for b and k in the expression, like this:

Now we will solve the multiplications inside the parenthesis, like this:

Now we will solve the operation inside the parenthesis, we get:

Now we solve the multiplication:

therefore, the final answer after pluging in b and k is -792.

The function represents the total number of seats will be 80x² + 560x. The correct option is B.

The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.

Given that the number of rows in an auditorium can be represented by the function f(x) = 80x. The number of seats in each row can be represented by the function g(x) = x + 7.

The total number of seats will be:-

h(x)  = f(x)  x g(x)

h(x) = 80x ( x + 7 )

h(x) = 80x² + 560x

Therefore, the function represents the total number of seats will be 80x² + 560x. The correct option is B.

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Answer:

The number has two digits. The sum of the digits is eight. If the digits are reversed, the results is 18 less than the original number. The answer of your question is 35. !!! ;)

The total contribution to Sharon's account over the 25-year period is $64,800.

To find the total contribution to Sharon's account, we need to consider both her contribution and her employer's contribution.

Social Security taxes are generally split evenly between the employee and the employer, with each paying half of the tax.

Sharon paid $32,400 in Social Security taxes over the 25-year period, which represents her share (half) of the total Social Security taxes paid.

To find the total contribution to her account, we simply need to double her share to include the employer's contribution:

Total contribution = Sharon's contribution + Employer's contribution

Total contribution = $32,400 + $32,400

Total contribution = $64,800

The total contribution to Sharon's account over the 25-year period is $64,800.

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the step 3 is

the answer is the last one

Answer:

f(x) = 1(x - 4.5)² - 6.25

Step-by-step explanation:

Hello!

Let's find the Vertex Form of the quadratic by Completing the Square.

The formula for a Perfect Square Trinomial is (a+b)² = a² + 2ab + b².

To find b², we need to divide -9 by 2 and square it.

Add this number to both sides and factor. Remember, the b term here is simply half of the b term in the equation (-4.5).

Convert this back to function form:

The equation is f(x) = 1(x - 4.5)² - 6.25.

To reflect a point over the y-axis, we negate the x-coordinate of the point. To reflect the resulting point over the x-axis, we negate the y-coordinate of the point. So, to find the new point A'', we can perform these operations on the original point A:

1. Reflect A over the y-axis to get A': (-2, 2)

2. Reflect A' over the x-axis to get A'': (-2, -2)

Therefore, the new point A'' is (-2, -2).

b

Step-by-step explanation:

The x - coordinate of the Point A is -

\($\frac{\sqrt{5} +1}{4}\)

We have a Point A(x, y) on the graph.

We have to find out the x-coordinate of Point A(x, y).

For any position vector (say OA), having magnitude of 'M' Units, making an angle \($\theta\) with the x - axis, can be resolved along the x and y axes as -

OA = (M cos \($\theta\)) \(a_{x}\) + (M sin \($\theta\))\(a_{y}\)

According to the question, we have -

\($\theta =\frac{\pi }{5}\)

We have to find the x - component of the position vector OA.

The circle has a radius of 1 units. Therefore, |OA| = 1

Assume that the x - coordinate of Point A is x.

Now -

x = |OA| cos (\($\frac{\pi }{5}\))

x = 1 x \(\frac{\sqrt{5} +1}{4}\)

x = \(\frac{\sqrt{5} +1}{4}\)

Hence, the x - coordinate of the Point A is -

\($\frac{\sqrt{5} +1}{4}\)

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Answer:

23

Step-by-step explanation:

3x + 18 + 93 = 180

3x + 111 = 180

3x = 69

x = 23

This is due to the fact that angles 2, 3, and 5 are interior angles of the triangle, and the total of the inner angles of a triangle is always 180 degrees. Therefore, m∠2 + m∠3 + m∠5 = 180°.

A triangle is a closed, two-dimensional geometric object composed of three line segments, known as sides, that intersect at three locations, known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all sides equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles less than 90 degrees), right (one angle equal to 90 degrees), or obtuse (all angles greater than 90 degrees). The area of a triangle can be computed using the formula A = (1/2)bh, where A is the area, b is the triangle's base, and h is the triangle's height.

Regarding the given diagram, the following claims are always true:

m∠3 + m∠4 + m∠5 = 180°

m∠5 + m∠6 = 180°\s= m∠2 (the measure of the external angle at angle 2). (the measure of the exterior angle at angle 2). And because angles 2 and 3 are likewise interior triangle angles, we get m2 + m3 = m6, which can be rearranged to yield m5 + m6 = m3 + m4 + m5 = 180°.

m∠2 + m∠3 + m∠5 = 180°

This is due to the fact that angles 2, 3, and 5 are interior angles of the triangle, and the total of the inner angles of a triangle is always 180 degrees. Therefore, m∠2 + m∠3 + m∠5 = 180°.

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Answer:90

Step-by-step explanation:

breath air

Answer:

C

Step-by-step explanation:  

An equation can be written to determine the number of students that went on this trip is: C. \(\frac{1259}{s} + 12=\frac{1259}{s+9}\)

In order to write an equation to determine the number of students that went on this trip, we would have to assign a variable and an expression to the number of students who went on the trip and the original number of students who had planned to go on the trip as follows;

Since a total of $1259 was collected from all of the students with 9 students dropping out and their portion of the money collected given back to them while the students that are all still going must contribute an additional $12, an equation to determine the number of students that went on this trip is given by;

\(\frac{1259}{s} + 12=\frac{1259}{s+9}\)

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Complete Question:

A high school class is planning a field trip to an art museum in their city. The class collected a total of $1259 from all of the students, which will go towards renting a bus, museum admission, and lunch.

However, a week before the trip 9 students had to drop out and their portion of the collected money had to be given back to them. Due to this, the students that are all still going must contribute an additional $12 each to cover all of the cost.

Now let s be the number of students who went on the trip and s + 9 be the original number of students who had planned to go on the trip

What equation can be written to determine the number of students that went on this trip?

Answer:

Options 2, 3 and 5 (Just sub r as a specific value and make sure each LHS is same in the options as the qn and RHS same in options as qn)

Step-by-step explanation:

Topic: Inequalities

If you like to venture further, do check out my insta (learntionary) where I regularly post useful math tips! Thank you!

Answer:

actually its 1,3,4

Step-by-step explanation:

i got it right on edgeniuty

Given that

We have to find the 50th percentile of the first seven prime numbers.

Explanation -

The first 7 prime numbers are 2, 3, 5, 7, 11, 13, 17

We have to find the 50th percentile of this data and the meaning of the 50th percentile is Median.

So we have to find the Median of this data.

The formula of the median is

Here the value of n is 7. On substituting we have

Final answer -

Answer:

-4

Step-by-step explanation:

Answer is - 4

X= 4* (-1)

Let's solve your equation step-by-step.

Step 1: Simplify both sides of the equation.

Step 2: Multiply both sides by 4.

Step-by-step explanation:

Answer:

First, we need to convert the volume of the pit from cubic yards to gallons, so that we can compare it with the daily flow rate of wastewater:

20 cubic yards = 20 * 27 cubic feet = 540 cubic feet

1 cubic foot = 7.48 gallons

540 cubic feet = 540 * 7.48 gallons = 4045.2 gallons

So, the pit can hold 4045.2 gallons of screenings.

The amount of screenings generated per day is 35 gallons. Therefore, the number of days the pit will last is:

4045.2 gallons / 35 gallons per day ≈ 115.58 days

Rounding to the nearest whole number, we get 116 days.

So the answer is option 3. 115 d.

The required image T of triangle ABC under the transformation (x,y) → (x-4, y+1) is formed by connecting the vertices A'(a-4, b+1), B'(c-4, d+1), and C'(e-4, f+1)

To find the image T of triangle ABC under the transformation (x,y) → (x-4, y+1), apply this transformation to each of the vertices of triangle ABC and then connect the new vertices to form the image T.

Let's assume that the coordinates of the vertices of triangle ABC are A(a,b), B(c,d), and C(e,f).

To find the image of vertex A under the transformation, we substitute x = a and y = b into the transformation equation:

(x,y) → (x-4, y+1)

(a,b) → (a-4, b+1)

Therefore, the image of vertex A is A'(a-4, b+1).

Similarly, we can find the images of vertices B and C:

B'(c-4, d+1)

C'(e-4, f+1)

Therefore, the image T of triangle ABC under the transformation (x,y) → (x-4, y+1) is formed by connecting the vertices A'(a-4, b+1), B'(c-4, d+1), and C'(e-4, f+1)

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If two figures can be mapped onto one another or if all pairings of angles and side lengths are congruent, the figures are said to be congruent.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

If two triangles are the same size and shape, they are said to be congruent. To establish that two triangles are congruent, not all six matching elements of either triangle must be located. There are five requirements for two triangles to be congruent, according to studies and trials. The congruence properties are SSS, SAS, ASA, AAS, and RHS.

here, we have,

Both triangles are said to be congruent if the three angles and three sides of one triangle match the corresponding angles and sides of the other triangle.

In Δ PQR and ΔXYZ, as shown in figure,

we can identify that PQ = XY, PR = XZ,

and QR = YZ

and ∠P = ∠X,

∠Q = ∠Y and ∠R = ∠Z.

Then we can say that Δ PQR ≅ ΔXYZ.

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Answer:

Step-by-step explanation:

Both parts of the ratio can be divided by 9

81/9 = 9

72/9 = 8

The ratio is 9:8

54/48 is also 9:8

54 / 6 = 9

48/6 = 8

The ratio is 9:8

63:56 is also an answer

63 / 7 = 9

56/7 = 8

The ratio  is 9:8

The others don't work. You can just look at them to see why.

Answer:

I DONT KNOW BUT YOU HAVE TO CHECK OUT MY QUESTION NO OE CAN SOLVE IT I BET

Step-by-step explanation:

Roland's percent error is approximately 3.889%.

This means that his measured value differs from the actual value by 3.889% or 0.03889 in decimal form.

The positive sign indicates that Roland's measured value is slightly lower than the actual value.

To calculate Roland's percent error, we can use the formula:

Percent Error = (|Measured Value - Actual Value| / Actual Value) \(\times\) 100

Given that Roland measured a current of 0.173 amps while expecting a current of 0.180 amps, we can substitute these values into the formula:

Percent Error = (|0.173 - 0.180| / 0.180) \(\times\) 100

Simplifying the expression within the absolute value:

Percent Error = (|-0.007| / 0.180) \(\times\) 100

Since the absolute value of -0.007 is 0.007, we have:

Percent Error = (0.007 / 0.180) \(\times\) 100

Calculating the division:

Percent Error = 0.03889 \(\times\) 100

Percent Error = 3.889%.

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Direct distance from the base of the Space Needle to Kasie's house = 1429 feet.

The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.

Given,

Height of the observation deck AB = 520 feet

Angle of depression = 70°

Distance of the Space needle base to house BC = ?

By the figure,

tan70° = AB/BC

BC = tan70°(AB)

BC = 2.7475(520)

BC = 1428.7 feet

Distance of the Space needle base to house to nearest foot = 1429 feet

Hence, 1429 feet is the distance between base of the Space Needle to Kasie's house.

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The equivalent expressions are B: 2(12m-6p+36) and (c): 12(2m-p+6)

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

24m-12p+72

Factor out 2 from the expression

So, we have

2(12m-6p+36)

This represents the option (b)

Factor out 12 from the expression

So, we have

12(2m-p+6)

This represents the option (c)

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An ellipse is defined as the set of all points such that the sum of the distances between the point and the two foci is constant. The equation of an ellipse can be represented in the standard form as:

(x-h)^2/a^2 + (y-k)^2/b^2 = 1

where (h, k) is the center of the ellipse, a is the distance from the center to a vertex, and b is the distance from the center to the focus.

Given that the center of the ellipse is at (2, 1), one vertex is at (2, -4), and one focus is at (2, -2), we can use this information to find the values of a and b, and represent the equation of the ellipse:

a = distance from center to vertex = |1 - (-4)|/2 = 2.5

b = distance from center to focus = |1 - (-2)|/2 = 1.5

The equation of the ellipse is:

(x-2)^2/2.5^2 + (y-1)^2/1.5^2 = 1

which can also be written as:

(x-2)^2/6.25 + (y-1)^2/2.25 = 1

This equation represents the ellipse with center at (2, 1), one vertex at (2, -4), and one focus at (2, -2)

Answer:

Answer is A

Step-by-step explanation:

Subtract 47 from both sides to get 0

3x² - 18x - 42 = 0

Use Quadratic formula to get

\(3+\sqrt{23} \\3-\sqrt{23}\)

Answer:

Step-by-step explanation:

Polynomial M is 2(x - \((\frac{1}{12}a)^{2}\) - (1/72)\(a^{2}\) + by

To find the polynomial M, we need to rearrange the equation given to us. We can start by adding M to both sides of the equation to isolate the constant term. This gives us:

2\(x^{2}\) - (1/3)ax + by = M

Now, we have the polynomial M in terms of x, a, b, and y. However, this is not in its simplest form yet. We can simplify this further by factoring out the coefficient of x. This gives us:

2(\(x^{2}\) - (1/6)ax) + by = M

Now, we can complete the square inside the brackets to get a perfect square trinomial. This means taking half of the coefficient of x, squaring it, and adding it and subtracting it inside the brackets. This gives us:

2((x - \((\frac{1}{12}a)^{2}\)  - (1/144)\(a^{2}\)) + by = M

Simplifying this further, we get:

2(x - \((\frac{1}{12}a)^{2}\)  - (1/72\(a^{2}\) + by = M

Therefore, the polynomial M is given by:

M = 2(x - \((\frac{1}{12}a)^{2}\)  - (1/72)\(a^{2}\) + by

This is the final answer for the polynomial M.

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Answer:

Impossible

Step-by-step explanation:

Answer:

1/7778

Step-by-step explanation:

We multiply each event

1/6 x 1/6 x 1/6 x 1/6 x 1/6 =

1/36 x 1/36 x 1/6

= 1/7776