Consider the following equation.
-16p + 37 =49 - 21 the equation that has the same solution

By using factoring by grouping or synthetic division, we find that \(x = -2\) is a real solution.

Checking for Rational Roots

Using the rational root theorem, the possible rational roots of the polynomial are given by the factors of the constant term (24) divided by the factors of the leading coefficient (-4).

The possible rational roots are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24.

By substituting these values into \(f(x)\), we find that \(f(-2) = 0\). Hence, \(x + 2\) is a factor of \(f(x)\).

Dividing \(f(x)\) by \(x + 2\) using long division or synthetic division, we get:

Now, we have reduced the problem to factoring \(-4x³ + 18x² - 16x + 12\).

Attempt 2: Factoring by Grouping

Rearranging the terms, we have:

Factoring out common factors, we obtain:

Now, we have \(2x^2(-2x + 9) + 4(4x - 3)\). We can further factor this as:

Therefore, the fully factored form of \(f(x) = -4x⁴  + 26x³  - 50x² + 16x + 24\) is \(f(x) = (x + 2)(2x² + 4)(-2x + 9)\).

Solutions to the polynomial equations:

Using polynomial division or synthetic division, we can find the quadratic equation \((x + 2)(x² + 2x - 3)\). Factoring the quadratic equation, we get \(x² + 2x - 3 = (x +

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The application rate is 3 (per DM$).

The given below table shows the monthly production volume, direct materials, direct labor, and manufacturing overheads for the past three months at Gizzard Wizard (GW):

Month Prod. Volume DM ($)DL ($)MOH ($)May 1000$400.00$600.00$1200.00

June 400160.00240.00480.00

July 1600640.00960.001920.00

By using DM$ to apply overhead, we have to find the application rate. We know that the total amount of manufacturing overheads is calculated by adding the cost of indirect materials, indirect labor, and other manufacturing costs to the direct costs. The formula for calculating the application rate is as follows:

Application rate (per DM$) = Total MOH cost / Total DM$ cost

Let's calculate the total cost of DM$ and MOH:$ Total DM$ cost = $400.00 + $160.00 + $640.00 = $1200.00$

Total MOH cost = $1200.00 + $480.00 + $1920.00 = $3600.00

Now, let's calculate the application rate:Application rate (per DM$) = Total MOH cost / Total DM$ cost= $3600.00 / $1200.00= 3

Therefore, the application rate is 3 (per DM$).

Hence, the required answer is "The application rate for GW is 3 (per DM$)."

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The length of PR from the similar triangles is PR = 6 units

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be ΔABC

Let the second triangle be ΔPQR

And , the measure of ∠ABC = measure of ∠PQR

The measure of ∠BCA = measure of ∠QRP

So , the angles are similar

where the corresponding sides of similar triangles are in the same ratio

On simplifying , we get

x / 5 = 24 / 20

Multiply by 5 on both sides , we get

x = ( 6/5 ) x 5

x = 6 units

Hence , the measure of x from triangle is x = 6 units

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As we know that perimeter of a shape is the sum of all it's boundaries. Also , let assume that the missing side be y . So ,here ;

\({:\implies \quad \sf (4x-4)+(3x+1)+y=13x-8}\)

\({:\implies \quad \sf 4x-4+3x+1+y=13x-8}\)

\({:\implies \quad \sf y+7x-3=13x-8}\)

\({:\implies \quad \sf y=13x-8-7x+3}\)

Collecting like terms :

\({:\implies \quad \sf y=(13x-7x)+(-8+3)}\)

\({:\implies \quad \bf \therefore \quad \underline{\underline{y=6x-5}}}\)

Hence , the length of Missing side is 6x-5

Answer: A triangular prism has a base of a rectangle as shown in this picture.

Step-by-step explanation: If your having trouble recognizing prisms here's a tip. All prisms have a rectangular base. :)

Answer:

a:t

b:t

c:t

d:t

Step-by-step explanation:

(a) The expression for the total revenue from the sale of x laptops is R(x) = x(1200 - 6x).
(b) To find the value of x that leads to maximum revenue, we can take the derivative of R(x) and set it equal to zero, resulting in x = 100.
(c) Substituting x = 100 into R(x), we find that the maximum revenue is $60,000.

(a) The total revenue from the sale of x laptops can be calculated by multiplying the price per laptop, p(x), by the number of laptops sold, x. Given that p(x) = 1200 - 6x, the expression for total revenue, R(x), is:
R(x) = x(1200 - 6x)
(b) To find the value of x that leads to maximum revenue, we can find the critical point by taking the derivative of R(x) with respect to x and setting it equal to zero. Let's differentiate R(x):
R'(x) = 1200 - 12x
Setting R'(x) equal to zero, we have:
1200 - 12x = 0
12x = 1200
x = 100
Therefore, x = 100 leads to maximum revenue.
(c) To find the maximum revenue, we substitute x = 100 into R(x):
R(100) = 100(1200 - 6(100))
= 100(1200 - 600)
= 100(600)
= $60,000
Hence, the maximum revenue is $60,000.

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Answer: slope for line b is 2

Step-by-step explanation:

If a line is parallel to another, that means they have the same slope, different y-intercept.

Since it's given that a is parallel to b, that means the slope is the same, thus the slope of b is 2.

Answer:

8 miles

Step-by-step explanation:

:p

Answer:

10/1

Step-by-step explanation:

You do

6÷ 3/5

Flip the 3/5 then multiply

6 ° 5/3

Reduce the numbers with the greatest common factor 3

So 2•5

And that's 10

Ans is 10.

The numbers in 6 divided by 3/5 are labeled below:

6 = whole number

3 = numerator

5 = denominator

To make it a fraction form answer, you multiply the whole number by the denominator and make the result the new numerator. The old numerator becomes the new denominator:

6 x 5/3 = 30/3

Thus, the answer to 6 divided by 3/5 in fraction form is:

30/3

To make the answer to 6 divided by 3/5 in decimal form, you simply divide the numerator by the denominator from the fraction answer above:

30 / 3 = 10

The answer is rounded to the nearest two decimal points if necessary.

30/3 can be simplified to 10/1.

10/1 is an improper fraction and should be written as 10.

Before the price change, the optimal consumption choice (A) is determined by equalizing the marginal utilities of x and y.

Using the utility function U(x, y) = xy, and considering prices of Px = 1 and Py = 2, along with an income of 40, we find that the utility equalization condition leads to y = x/2.

With the budget constraint of x + 2y = 40, we solve for x = 20 and y = 10, giving the optimal consumption choice (20, 10) labeled as point A on the graph.

After the price change, with the price of y falling to 1, the consumer aims to maintain the same utility level. Setting MUX/Px = MUY/Py, we find x = y, and using the budget constraint x + y = 40, we get x = y = 20, resulting in the optimal consumption choice (20, 20) labeled as point B.

The substitution effect is illustrated by a movement from A to B along the budget constraint. The new optimal consumption choice (C) after the price change is determined by the new budget constraint x + y = 40, where x = 30 and y = 10, labeled as point C on the graph.

The income effect is depicted by the parallel shift of the budget constraint line outward from the origin.

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Answer:

x = 18

These two angles are formed by a transversal that cuts through 2 parallel lines. This means that (5x + 2) on line m corresponds to the angle on the right of (5x-2) on line n.

Now that we can see (5x + 2) and (5x - 2) are on a straight line, we can say that (5x + 2) + (5x - 2) = 180

10x + 0 = 180

10x = 180

x = 180/10

x = 18

the measurement of the side, GH is 30.6 units

The properties of the triangle are: The sum of all the angles of a triangle (of all types) is equal to 180°. The sum of the length of the two sides of a triangle is greater than the length of the third side. In the same way, the difference between the two sides of a triangle is less than the length of the third side.

Given, Triangle DEF is congruent to the triangle GHI from the AA theorem.

So,

EF/HI = DE /GH

GH = (DE*HI)/EF

GH = 13*33/14

GH = 30.6

Therefore, the measurement of the side, GH is 30.6 units

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Answer: Figure D

Figure D is a 180 degree rotation of figure A.

The value of an unknown number x will be equal to ( 15 / 4).

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given that 5 times, the difference between a number and 3 is x. The value of the unknown number will be calculated as:-

5 ( x - 3 ) = x

5x - 15 = x

4x = 15

x = 15 / 4

Therefore, the value of an unknown number x will be equal to ( 15 / 4).

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Answer:

150

Step-by-step explanation:

The measure of angle a is 15 degrees and this can be determined by using the properties of the isosceles triangle.

In geometry, interior angles are formed in two ways. One is inside a polygon, and the other is when parallel lines cut by a transversal. Angles are categorized into different types based on their measurements.

Given:

The following steps can be used in order to determine the measure of angle a:

Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.

Step 2 - Apply the sum of interior angle property on triangle PQR.

\(\angle\text{Q}+\angle\text{P}+\angle\text{R}=180\)

\(\angle\text{Q}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-60\)

\(\angle\text{R}=60^\circ\)

Step 3 - Now, apply the sum of interior angle property on triangle PSR.

\(\angle\text{P}+\angle\text{S}+\angle\text{R}=180\)

\(\angle\text{S}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-90\)

\(\angle\text{R}=45^\circ\)

Step 4 - Now, the measure of angle a is calculated as:

\(\angle\text{a}=60-45\)

\(\angle\text{a}=15\)

The measure of angle a is 15 degrees.

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Answer:

1.55

Step-by-step explanation:

you just change the fractions to decimals

Answer:

Step-by-step explanation:

x^-n = 1/x^n

The negative exponent means means raise the reciprocal to the nth power

Step-by-step explanation:

Soln,

The given data are (-3,-1) and (9,4)

d^2=(9+3)^2+(4+1)^2

d^2=12^2+5^2

d^2=144+25

d^2=169

d=[square root]169

d=13

The distance is 13.

Answer:

(-3,-1)=(x1,y1)

(9,4)=(x2,y2)

d=\( \sqrt{(x2 - x1) ^{2} + (y2 - y1)^{2} } \)

\( \sqrt{ ( 9 + 3) ^{2} + (4 + 1) ^{2} } \)

\( \sqrt{12 ^{2} + {5}^{2} } \)

\( \sqrt{144 + 25} \)

\( \sqrt{169}\)

=13

hope it helps you

make me brainliest plz

Answer:

(tan(theta)-1)^3

= (tan(theta)-1)(tan(theta)-1)(tan(theta)-1)

= (tan^2(theta)-2tan(theta)+1)(tan(theta)-1)

= tan^3(theta)-2tan^2(theta)+tan(theta)-tan^2(theta)+2tan(theta)-1

= tan^3(theta)-3tan^2(theta)+3tan(theta)-1

Hope this helps :)

Answer:

50 papers

Step-by-step explanation:

50% of the 200 papers would be 100 papers graded because half of 200 is 100.

25% would be 1/4 of the 200 papers.

So you have to divide.

200 divided by 4 is 50.

Therefore 50 papers have been graded so far.

The property of congruence illustrated in the statement is the transitive property.

The transitive property states that if A is congruent to B and B is congruent to C, then A is congruent to C. In other words, if two things are congruent to a third thing, they are also congruent to each other.

here,

In the statement "If AB ≅ DE, EF ≅ DE then AB ≅ EF," AB is congruent to DE, and EF is congruent to DE, so AB must also be congruent to EF according to the transitive property.

The other properties you listed are not applicable in this case. The symmetric property states that if A is congruent to B, then B is congruent to A. The reflexive property states that every object is congruent to itself. And multiplication is not a property of congruence.

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a. The average acceleration in the time interval t = 0 to t = 2.0 s is -10 m/s². b. The acceleration at t = 2.0 s is -20 m/s².

a. To find the average acceleration in the time interval t = 0 to t = 2.0 seconds, we need to first find the initial and final velocities:

Initial velocity (t = 0 s):
v0x = (40 - 5(0)²) m/s = 40 m/s

Final velocity (t = 2.0 s):
v2x = (40 - 5(2)²) m/s = (40 - 5(4)) m/s = 20 m/s

Average acceleration is defined as the change in velocity divided by the change in time:
a_avg = (v2x - v0x) / (t2 - t0) = (20 m/s - 40 m/s) / (2.0 s - 0 s) = -20 m/s² / 2.0 s = -10 m/s²

b. To determine the acceleration at t = 2.0 s, we need to find the derivative of the velocity expression with respect to time (t):

v_x(t) = 40 - 5t²

Taking the derivative with respect to time:
a_x(t) = dv_x(t)/dt = -10t

Now, we can find the acceleration at t = 2.0 s:
a_x(2.0) = -10(2.0) = -20 m/s²

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To estimate the area under the graph of f(x) = 3√x from x = 0 to x = 4 using four approximating rectangles, we can divide the interval [0, 4] into four subintervals of equal width and calculate the area of each rectangle using either the right endpoints or the left endpoints.

(a) Using right endpoints:

The width of each rectangle is Δx = (4 - 0) / 4 = 1.

The right endpoints for the four subintervals are x = 1, 2, 3, and 4.

We can calculate the height of each rectangle by evaluating f(x) = 3√x at the right endpoints:

f(1) = 3√1 = 3

f(2) = 3√2

f(3) = 3√3

f(4) = 3√4 = 6

The area of each rectangle is then the product of the width and the height.

R1 = 1 * 3 = 3

R2 = 1 * f(2)

R3 = 1 * f(3)

R4 = 1 * 6

To estimate the total area, we sum up the areas of the four rectangles:

R4 = R1 + R2 + R3 + R4

(b) Using left endpoints:

Similar to part (a), the width of each rectangle is Δx = (4 - 0) / 4 = 1.

The left endpoints for the four subintervals are x = 0, 1, 2, and 3.

We can calculate the height of each rectangle by evaluating f(x) = 3√x at the left endpoints:

f(0) = 3√0 = 0

f(1) = 3√1 = 3

f(2) = 3√2

f(3) = 3√3

The area of each rectangle is the product of the width and the height.

L1 = 1 * 0 = 0

L2 = 1 * f(1)

L3 = 1 * f(2)

L4 = 1 * f(3)

To estimate the total area, we sum up the areas of the four rectangles:

L4 = L1 + L2 + L3 + L4

Now, to determine whether the estimates are underestimates or overestimates, we compare them to the actual area under the curve.

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The statement is incorrect due to the invalid assumption of f(x) = g(x) = 0, and the incorrect application of the comparison test.

The comparison test states that if 0 ≤ f(x) ≤ g(x) and the integral of g(x) dx diverges, then the integral of f(x) dx also diverges. However, the statement assumes that f(x) and g(x) are equal to zero, which means that 0 ≤ f(x) ≤ g(x) is not satisfied.

Additionally, the assumption that g(x) dx diverges does not necessarily imply that f(x) dx also diverges. For example, let g(x) = 1/x^2 and f(x) = 0 for all x. Then g(x) dx diverges, but f(x) dx converges to zero.

In conclusion, the statement is incorrect due to the invalid assumption of f(x) = g(x) = 0, and the incorrect application of the comparison test.

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The idea that group work theories are appropriate for all clients all the time is a myth (Third option).

About Group Process:

The term "group process" describes how people collaborate within an organization to complete tasks. Typically, organizations invest a lot of time and effort into defining and achieving goals, but little thought is usually given to how those goals are affecting the most valuable resource of a group - its people.

Since different clients have different demands and priorities, group work might not be suitable for many, but not for all. Different types of clients require different types of collaboration, type of group or individuals, and working strategies that work for their goals the best.

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Answer:

1144

Step-by-step explanation:

100 + 98 + 96 +.... + 78+76 =

(12-0)/2 (176)  

(6.5) (176) = 1144

The sum of the series will be 1068.

We have the following expression -

\(\sum_{i=0}^{12} 100 - 2i\)

We have to rewrite the series as the sum.

A series in mathematics is the sum of a list of numbers that are generated according to some pattern.

We have the following expression -

\(\sum_{i=0}^{12} 100 - 2i\)

The terms of this series can be calculated by calculating the value of the function at different values of i.

The series is as follows -

100 + 98 + 96 +.... + 78+76

This is an arithmetic progression with a = 100 and d = - 2 and n = 12. The sum of this series is -

\(S = \frac{n}{2} \times {2a + (n-1)d}\)

S = \(\frac{12}{2} [{2 \times 100 + (12 -1)(-2)] = 6[200+ 11 \times -2] = 6[200 -22]\)

S = 6 x 178 = 1068

The sum of the series will be 1068.

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