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The solution to the expression (3x³ + 5x² - 11x + 3)/(x + 3) is (x - 1/3)(x - 1)

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the expression:

(3x³ + 5x² - 11x + 3)/(x + 3)

= (x + 3)(x - 1/3)(x - 1) / (x + 3)

= (x - 1/3)(x - 1)

The solution to the expression (3x³ + 5x² - 11x + 3)/(x + 3) is (x - 1/3)(x - 1)

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The solution set of the equation x^2 + 2x - 48 = 0 is x = -1 ± 7

The equation is given as:

x^2 + 2x - 48 = 0

A quadratic equation is represented as:

ax^2 + bx + c = 0

By comparing both equations, we have

a = 1, b = 2 and c = -48

The solution of the quadratic equation is then calculated using

x = (-b ± √(b^2 - 4ac))/2a

Substitute values for a, b and c in the above equation

x = (-2 ± √(2^2 - 4 * 1 * -48))/2 * 1

This gives

x = (-2 ± √196)/2

Evaluate the square root of 196

x = (-2 ± 14)/2

Divide through by 2

x = -1 ± 7

Hence, the solution set of the equation x^2 + 2x - 48 = 0 is x = -1 ± 7

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The x-intercepts of the function y = 2x^2 -x - 120 are (-7.5, 0) and (8, 0)

The function is given as:

y = 2x^2 - x - 120

Set the function to 0

2x^2 - x - 120 = 0

Factor out 2

2(x^2 - 0.5x - 60) = 0

Divide by 2

x^2 - 0.5x - 60 = 0

Expand the function

x^2 + 7.5x - 8x - 60 = 0

Factorize the function

(x + 7.5)(x - 8) = 0

Split

x + 7.5 = 0 and x - 8 = 0

Solve for x

x = -7.5 and x = 8

Hence, the x-intercepts of the function y = 2x^2 -x - 120 are (-7.5, 0) and (8, 0)

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Answer:

If you have 6 chocolate and you have to divide that into 15 people than the answer will be 2 upon 5 or 0.4 for each.

Answer:

yxthgggggyhfffghgggggvggvvggvv

The results of dividing 1 into pieces that are each 1/9 of a whole is 9

1 ÷ 1/9

1 ÷ 1/9

= 1 × 9/1

= (1 × 9) / (1 × 1)

= 9/1

= 9

Complete question:

If 1 is divided into pieces that are each 1/9 of a whole, how many pieces are there

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The bottom edge of the window is 8 inches above the ground, computed using the Pythagoras Theorem.

According to the Pythagoras Theorem, in a right triangle, the square of the hypotenuse, that is, the side opposite to the right angle is equal to the sum of the square of the legs, that is, the two other sides.

If in a right triangle, c is the hypotenuse, and a and b are the two legs, then by the Pythagoras Theorem, we can write:

a² + b² = c².

In the question, we are informed that a building meets the ground at a right angle. The top of a 10-foot ladder is placed against the bottom edge of a window in the building, and the base of the ladder is placed 6 feet from where the building meets the ground.

We are asked to draw a diagram that represents the situation and find the height of the bottom edge of the window from the ground.

We assume the building to be DB, meeting the ground BC at a right angle. At point C, the ladder meets the ground and meets the bottom edge of the window at point A.

The diagram is attached.

Now, we get a right triangle ABC, right-angled at B.

By Pythagoras' Theorem, we know that:

AB² + BC² = AC²,

or, AB² + 6² = 10²,

or, AB² = 10² - 6² sq. inches,

or, AB² = 100 - 36 sq. inches,

or, AB = √64 inches,

or, AB = 8 inches.

Thus, the bottom edge of the window is 8 inches above the ground, computed using the Pythagoras Theorem.

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The provided question is incomplete. The complete question is:

"A building meets the ground at a right angle. The top of a 10-foot ladder is placed against the bottom edge of a window in the building, and the base of the ladder is placed 6 feet from where the building meets the ground. Draw a diagram that represents this situation. How far up from the ground is the bottom edge of the window?"

ANSWER :          -7x + 14

EXPLANATION, to reverse division multiply

3,471,738 this is the answer

A. True

Step by step explanation:

1. if we where given a graph and told to determine whether it's a function or not, we would have used a VERTICAL LINE TEST.

2. In this case we have points, and for every x value we have one corresponding y value which makes it a function that is a ONE-TO- ONE FUNCTION

The Canadian goose flew for 4 hours and the Great blue heron flew for 10 hours

An equation is an expression that shows the relationship between two or more variables and numbers.

Let a represent the time flown by the goose and b represent the time flown by the heron. Hence:

a + b = 14    (1)

Also:

20a + 10b = 180   (2)

From equation 1 and 2:

a = 4, b = 10

The Canadian goose flew for 4 hours and the Great blue heron flew for 10 hours

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The value of  [tex]k = 2P/x^2[/tex]

We are aware that an object's location might cause it to store energy. When a bow and arrow are used, the energy that is stored when the bow is pulled is what gives the arrow its kinetic energy when it is released.

when a spring is moved away from its equilibrium position, it gains some energy, which we can notice by the tension our hands experience as we stretch it. Potential energy is a type of energy that arises from a change in its position or condition, according to our definition

We know that P=1/2kx^2

Now solving for k

2P = kx^2

Therefore

k = 2P/x^2

Hence the value of k is 2P/kx^2

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Answer:

x = 4.

Step-by-step explanation:

Each angle in an equilateral triangle is 60 degrees, so we have:

10x + 20 = 60

10x = 40

x = 4.

Answer:

X = 4

Step-by-step explanation:

The angles of a triangle add up to 180 degrees and this is an equilateral triangle which means that all the angles are the same. which means you set up the equation:

10x + 20 + 10x + 20 + 10x + 20 = 180

Simplify: 30x + 60 = 180

                        - 60   - 60

You have : 30x = 120

(Divide by 30)

You end up with: X = 4

The population for this study is all registered voters from New York City.

What  is the population for a study?

it is given that the poll has been carried out among 1000 registered voters from New York City. These 1000 people have been selected randomly from the population of the study.

The available study subset of the target population for a study, for instance, schizophrenics in the researcher's hometown, is known as the study population or population of the study. The sample chosen for the study is known as the study sample.

Study Population In This Case

In this case, out of all the New Yorkers, only the registered voters of the city are eligible for making the target subset. Hence, the registered voters of the New York city make the study population. Furthermore, since 1000 random registered voters are chosen for the poll, those 1000 registered voters make the study sample.

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The graph of y=sin(x-3π/2) is the graph of the y =sinx shifted right by 3π/2 units.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

If we have a parent function y = Sin(x), the function

y = Sin(x-b) would be the parent shifted b units right

y = Sin (x+b) would be the parent shifted b units left

The function given is y=sin(x-3π/2)

So from the rules, we can clearly say that it is parent function shifted right by 3π/2 units.

Hence, the graph of y=sin(x-3π/2) is the graph of the y =sinx shifted right by 3π/2 units.

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Step-by-step explanation:

x=8-y

2x-y=7

2(8-y)-y=7

16-2y-y=7

-3y=-9

y=3

x=8-y

x=8-3=5

Answer:

Hello

Step-by-step explanation:

Méthode par combinaisons linéaires:

[tex]\left\{ \begin{array}{ccc|c|c}x+y&=&8&1&-2\\2x-y&=&7&1&1\\\end {array} \right.\\\\\\\left\{ \begin{array}{ccc}3x&=&15\\-3y&=&-9\\\end {array} \right.\\\\\\\boxed{\left\{ \begin{array}{ccc}x&=&5\\y&=&3\\\end {array} \right. }\\[/tex]

Proof:

5+3=8 and 2*5-3=7

Answer:

240 yards lost, if I understand the question correctly.

Step-by-step explanation:

If I read this correctly the team lost 85 yards lost in 8 plays.  Then they tripled their loss on the next 17.  3 x 85 = 255 yards lost in the last 17 plays.

Total yards lost was (85 + 255) = 240 yards in 22 plays.

Using the dimensions of a reduced rectangle and one given measurement of an original rectangle:

Reduction is a type of dilation that reduces the size of an original figure to form a new figure that is similar to the original. The corresponding lengths of both figures are therefore proportional.

Assuming the dimensions of the reduced rectangle are 10 cm by 4 cm, and the length of the original rectangle is given as 8 cm, to find the missing measure (x), do the following:

Set up a proportion using the corresponding parts

10/8 = 4/x

Solve the proportion using cross products to find x:

10x = (8)(4)

10x = 32

x = 32/10

x = 3.2 cm

The missing length is 3.2 cm.

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Answer:

Using the given measurements of both figures, set up a proportion that has the corresponding parts in the same position. Then solve the proportion using cross products to find the value for the unknown.

Step-by-step explanation:

A pole vaulter have to run at 18m/s speed.

According to the statement

The typical pole for pole vaulting is 17 feet long

we use the formula

1/2 m(v)^2 = mgh

Now rearrange the terms

(v)^2 = 2gh

here g = 10 and h = 15 then

substitute the values

(v)^2 = 2*10*15

v = 17.32

So, A pole vaulter have to run at 18m/s speed.

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Here null hypothesis is rejected in this problem.

According to the statement

We have a given that the evidence at alpha level is 0.02, ANd the sample size n is 67. And mean time equal to 330 minutes and the variance that is the sigma square is equal to 529 point.

And We have to make the decision to reject or feel fail to reject the null hypothesis to solve this problem.

Firstly we solve alternative and null hypothesis

So, the null hypothesis h naught will be that mu is less than equal to 327 point and alternative hypothesis ha will be.

That mu is greater than 327 point now. This alternative hypothesis is claimed.

Next we will find the value of s which is given by sigma divided by under root n.

So, s = 67/ (529)^1/2

s = 2.8099.

Now we find the value of Z

So, Z = 327 - 330 / 2.8099

Z = 1.0677

Now the critical value of z is 2.05

Critical, we can say fail to reject the null hypothesis, and this is the result from the null hypothesis test.

With this test, we can conclude that the the data do not support that. There is evidence at 0.02 level that the drug stays in the system for more than 327 minutes. So this is the conclusion for the test for the hypothesis test and the answer to the problem.

So, Here null hypothesis is rejected in this problem.

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By SAS property, ABC ≅  DCB.

In this question we have to proof ABCD has congruent diagonal. By SAS property and reflexive property it can be proved as follows:

Given:

ABCD is a rectangle.

Prove:

Diagonal AC ≅ Diagonal BD

From the question,

As we can see that, ABCD is a rectangle, it is also a parallelogram.

Thus, ABCD is a parallelogram, opposite sides of a parallelogram are congruent.

⇒ AB ≅  DC  

⇒ BC ≅ BC (Reflexive Property of Congruence)

Hence, ∠ABC and ∠DCB are right angles by the definition of rectangle.

∠ABC ≅ ∠DCB (all right angles are congruent)

Therefore, by SAS property,  ABC ≅  DCB.

⇒ segment AC ≅ segment BD

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Answer:

♣ = parallelogram side theorem

♦ = SAS

♠ = CPCTC

(Correct On Edgen)

Answer:(x-1)(x^2+x+1) / (x+1)(x-1)

Step-by-step explanation:

For x^3-「1」→ 1=1^3

For x^2-「1」→ 1=1^2. this way of thinking might help you understand better:)

You can just use a formula of factorizationヾ ^_^♪

There is a crossword that has three squares that need to be filled, how many possible three letter arrangements is 26!/23.

To find the number of possible three letter arrangements.

An arrangement of things in a certain sequence is what we refer to as a permutation. The constituents or components of sets are presented in this section in a sequential or chronological fashion. A coming together or merging of several parts or characteristics in which each of the constituent parts or traits retains its unique identity.

Given that:

26 possible letters

assuming you can repeat them

26*26*26

no listed

ok, lets assume that you can't repeat them

that is 26 times 25 times 24 (because you used 1 each time)

that is 26!/23 (because 26*25*24*23!=26!)

Hence, the number of possible three letter arrangements is 26!/23.

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Option is missing

A.26!

B.26!/3!

C.23!

D.26!/23

The quotient of the synthetic division is x^3 + 3x^2 + 4

The bottom row of synthetic division given as:

1 3 0 4 0

The last digit represents the remainder, while the other represents the quotient.

So, we have:

Quotient = 1 3 0 4

Introduce the variables

Quotient = 1x^3 + 3x^2 + 0x + 4

Evaluate

Quotient = x^3 + 3x^2 + 4

Hence, the quotient of the synthetic division is x^3 + 3x^2 + 4

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The probability of two successes in seven trials is 0.0774144.

The probability can be found using the binomial formula.

The probability of success is given as 0.6.

Therefore, the probability of failure is 0.4.

We have to find the probability of two successes in seven trials.

It is given by:

[tex]P = nC_x p^{n} q^{n-x}\\=7C_{2} (0.6)^{2} (0.4)^{7-2} \\=7C_{2} (0.6)^{2} (0.4)^{5} \\=\frac{(7)(6)}{(1)(2)} (0.36)(0.01024)\\=0.0774144[/tex]

The probability of two successes in seven trials is found to be 0.0774144.

Therefore, we have found that the probability of two successes in seven trials is 0.0774144.

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You did not provide directions. What do you want us to do with your 8th degree polynomial?

The percent increase in employment would be necessary for the number of workers to be greater than 375 is 25%

The given parameters are:

Initial = 350

Final = 375

The rate is calculated as:

Rate = Final/Initial - 1

So, we have:

Rate = 375/300 - 1

Evaluate

Rate = 1.25 - 1

This gives

Rate = 0.25

Express as percentage

Rate = 25%

Hence, the percent increase in employment would be necessary for the number of workers to be greater than 375 is 25%

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Nguyen saves 15% of his income

The given parameters are:

Savings = $120

Income = $800

The percentage saved is calculated as:

Percentage = Savings/Income * 100%

This gives

Percentage = 120/800 * 100%

Evaluate

Percentage = 15%

Hence, Nguyen saves 15% of his income

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 Total tax  from state and local taxes were withheld from her check:

 = $273.04

What is Percentage ?

A % is a number or ratio that, in mathematics, can be expressed as a fraction of 100. If we need to determine a percentage of a number, multiply it by 100 and divide it by the total. So, a part per hundred is what the percentage refers to. Percent signifies for every 100. The sign "percent" is used to denote it.

Solution:

Harriet earned for the month = $4334

state and local taxes are = 6.3%

                                                 = [tex]\frac{4334}{100} *6.3%[/tex]

                                                 =$273.04

Total tax  from state and local taxes were withheld from her check:

 = $273.04

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Answer:

Slope: 1

Y-intercept: -1

Step-by-step explanation:

The line touches the y-axis at -1, and using rise over run for the slope, it would be 1, since you go up 1 unit and move to the right 1 unit. 1/1 which is our rise/run would be 1 and that would make the slope 1.

I hope it helps! Have a great day!

bren~