Divide using synthetic division. (6x² + + X- -57) + (x-3) + X- - = (6x² + x - 57) +(x-3)= ( (Simplify your answer. Use integers or fractions for any numbers in the expression. Do not factor.)

Answer:

9) x,-1 or x> -1

10) x<-4 or x ≥ 2

11) -3≤x≤2

12) -2≤x≤2

Step-by-step explanation:

Answer:

14x+35y-35

Step-by-step explanation:

distribute the 7 to each term

the middle value in a data set when the values are put in order

For example, the set {3,1,2} sorts to {1,2,3} where the median is 2.

Another example: The set {1,2,3,4} has 2 and 3 tied for the middle most position. The midpoint is (2+3)/2 = 5/2 = 2.5 which is the median.

\( {5}^{12} \times {5}^{8} \\ = {5}^{12 + 8} \\ = {5}^{20} \)

Therefore,

\( a) \: {25}^{20} ≠ {5}^{20} \)

\(b) ({25}^{5} ) ^{4} \\ = {25}^{5 \times 4} \\ = {25}^{20} \\ ( {25}^{5} )^{4} ≠ {5}^{20} \)

\(c) \: ( {5}^{3} . {5}^{2} ) ^{4} \\ = ({5}^{3 + 2}) ^{4} \\ = ({5}^{5} )^{4} \\ = {5}^{20} \)

\(d) \: {(5 ^{5}) }^{4} \\ = {5}^{5 \times 4} \\ = {5}^{20} \)

Answers:

\(c)( {5}^{3} . {5}^{2} {)}^{4} \\ d) {(5}^{5} ) ^{4} \)

Hope you could understand.

If you have any query, feel free to ask.

Change in base of right angled triangle is - 1.5cm/minute

The rate of change in area is defined as the change in with respect to time.

dA/dt = 1/2(BdH/dt + HdB/dt)

where A is area, B is base, H is height

A = 1/2×B×H

94 = 1/2×11.5×B

⇒ B = 94×2/11.5 = 16.3cm

Rate of change in base,

dA/dt = 1/2(BdH/dt + HdB/dt)

3.5 = 1/2(16.3×1.5 + 11.5×dB/dt)

dB/dt = 7-24.45/11.5 = -1.5 cm/minute

Thus,base of triangle is decreasing by 1.5cm/minute.

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Answer:

Easy

Step-by-step explanation:

4m a second so 40 seconds cause4 x 10

Answer:

im not sure

1398100 meter

Step-by-step explanation:

4+4^(2)+4^(3)+4^(4)+4^(5)

+4^(6)+4^(7)+4^(8)+4^(9)

+4^(10)=1398100

Answer:

-6

Step-by-step explanation:

The value of \(b\) is the same as the value of \(y\) when \(x=0\).

Answer:

False

Step-by-step explanation:

-x^2+x is the same as x-x^2.

Only difference is the way it's written.

Answer:

10 1/8

Step-by-step explanation:

1. The probability of selecting exactly one tank with high-viscosity material is 0.

2. The probability of selecting at least one tank with high-viscosity material is 1.

3. The probability of selecting exactly one tank with high-viscosity material and exactly one tank with high impurities is 0.25.

1. The probability of selecting exactly one tank with high-viscosity material is calculated by the binomial distribution formula, P(X = n) = (nCx)p^x(1-p)^n-x, where n is the number of trials, x is the number of successes, and p is the probability of success. In this case, n = 4, x = 1, and p = 24/24 = 1. Therefore, P(X = 1) = (4C1)1^1(1-1)^4-1 = 0.

2. The probability of selecting at least one tank with high-viscosity material is calculated by the complement rule, P(X > 0) = 1 - P(X = 0). In this case, P(X > 0) = 1 - (4C0)1^0(1-1)^4-0 = 1.

3. The probability of selecting exactly one tank with high-viscosity material and exactly one tank with high impurities is calculated by the binomial distribution formula, P(X = n) = (nCx)p^x(1-p)^n-x, where n is the number of trials, x is the number of successes, and p is the probability of success. In this case, n = 8, x = 2, and p = 24/24 = 1. Therefore, P(X = 2) = (8C2)1^2(1-1)^8-2 = 0.25.

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Answer:

The numbers that you gave are ordered weird on my screen, but it should be the second answer - 18.4 glue and 9.2 glitter

Step-by-step explanation:

Just multiply all the numbers by 4

4.6 x 4 = 18.4

4 + 4 + 4 + 4 = 16

16 + 0.6 + 0.6 + 0.6 + 0.6 = 18.4

2.3 x 4 = 9.2

2 + 2 + 2 + 2 = 8

8 + 0.3 + 0.3 + 0.3 + 0.3 = 9.2

Answer:

Step-by-step explanation:

x=70°

Answer:

x=5

Step-by-step explanation:

Formulate and substitute:d=4v

Rearrange unknown terms to the left side of the equation: 4x=27-7

Calculate the sum or difference: 4x=20

Divide both sides of the equation by the coefficient of variable: x=20÷4

Calculate the product or quotient: x=5

So the Answer is: x=5

Answer:

Yes

Step-by-step explanation:

Just respond if you have a question

If Shureka Washburn has scores of ​69, 74​, 79​, and 62 on her algebra tests, then by using the inequality, the score she must make on the final exam to pass the course with an average of 71 or higher is 71

The scores she scored on test = 69, 74, 79, 62

Consider the final score she must make on the final exam as x

Sum of the scores = 69+74+79+62+2x

= 284+2x

Consider the average of score = Sum of scores / Number of subjects

= (284+2x)/6

She need average of 71 or higher

Then the inequality equation will be

(284+2x)/6 ≥ 71

284+2x ≥ 426

2x ≥ 426-284

2x ≥ 142

x ≥ 71

Hence, if Shureka Washburn has scores of ​69, 74​, 79​, and 62 on her algebra tests, then by using the inequality, the score she must make on the final exam to pass the course with an average of 71 or higher is 71

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Given the equation:

8x + 7y = -50

We will check the options to find which order pair is the solution of the equation

Point (-6 , -1)

8 * -6 + 7 * -1 = -48 - 7 = -55 ≠ -50

Point ( 0 , -6)

8 * 0 + 7 * - 6 = -42 ≠ -50

Point (-6, 0 )

8 * - 6 + 7 * 0 = -48 ≠ -50

Point (-1 , -6)

8 * -1 + 7 * -6 = -8 - 42 = -50

so, the order pair which is a solution for the equation is (-1 , -6 )

Answer:

(D)  \(\dfrac{27}{16}\)

Step-by-step explanation:

Volume of a Cylinder =\(\pi r^2h\)

Cylinder A

Height = 3 Units

Radius = 3 Units

\(Volume =\pi \times 3^2 \times 3 =27\pi$ cubic units\)

Cylinder B

Height = 4 Units

Radius = 2 Units

\(Volume =\pi \times 2^2 \times 4 =16\pi$ cubic units\)

\(\dfrac{\text{Volume of Cylinder A}}{\text{Volume of cylinder B}}=\dfrac{27\pi}{16\pi}\\\\=\dfrac{27}{16}\)

The correct option is D

Answer:

The equation of line is as follows:

Slope-intercept form: \(y = 7x-5\)

Standard Form: \(-7x+y = -5\)

Step-by-step explanation:

Given that

Slope of line: 7

Point : (1,2)

Slope-intercept form of equation of line is given by:

\(y = mx+b\)

Here m is the slope and b is y-intercept.

Putting the value of slope

\(y = 7x+b\)

To find the value of b, we have to put the point in the equation

\(2 = 7(1) +b\\2 = 7+b\\2-7 = b\\b = -5\)

So the equation will be:

\(y=7x-5\)

The standard form of equation of line is:

\(Ax+By = C\)

To convert the equation in standard form, subtracting 7x from both sides

\(y-7x = 7x-5-7x\\-7x+y = -5\)

Hence, the equation of line is as follows:

Slope-intercept form: \(y = 7x-5\)

Standard Form: \(-7x+y = -5\)

The equation of a line in slope-intercept and standard form through (1, 2), slope = 7 is  7x - y = 5.

To find the equation of a line in slope-intercept and standard form.

First, we can write the equation in point-slope form. The point-slope formula states:

(y − y₁) = m (x − x₁)

Where m is the slope and

(x1, y1) is a point the line passes through.

Substituting the values from the problem gives:

(y − 2) = 7(x − 1)

Now, we need to convert to standard form.

The standard form of a linear equation is:

Ax + By = C

where, if at all possible,

A, B, and C are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

We convert as follows:

y − 2 = (7 × x) − (7 × 1)

y − 2 = 7x − 7

−7x + y − 2  = − 7

Adding 2 in both side.

−7x + y − 2 + 2 = − 7 +2

-7x + y = -5

7x - y = 5

Therefore,  the equation of a line in slope-intercept and standard form is 7x - y = 5.

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The  probability that a product will operate properly within an expected time frame is the dimension of quality known as reliability

The probability is the ratio of the number of favorable outcomes to the total number of outcomes. The value of the probability is varies from zero to one

Here, the product will operate properly within an expected time frame is the dimension of quality

Reliability is expressed as the probability that a given item will perform its intended function with no failures for a given period of time under a given set of conditions that means the reliability is the complementary to the failure of probability

Therefore, the given statement is know as the reliability

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Answer:

B) 9

Step-by-step explanation:

2-(-7)=2+7=9

Answer:

1

Step-by-step explanation:

3(-2y) +2y = -4

-6y+2y=-4

-4y=-4

y=1

Product of two polynomials can be done by distribution of multiplication over addition. The product of \((x-3)^2\) is \(x^2 - 6x + 9\)

Suppose a, b and c are three numbers. Then we have:

\(a(b + c) = a\times b + a\times c\)

(a(b+c) means a multiplied to (b+c). The sign of multiplication is usually hidden when using symbols and both quantities which are in multiplication are written together without space)

For the given case, the product needed can be calculated as:

\((x-3)^2 = (x-3) \times(x-3) = x(x-3) - 3(x-3) = x^2 - 3x - 3x + 9\\\\(x-3)^2 = x^2 - (3+3)x + 9 = x^2 - 6x + 9\)

(coefficients of like terms were added)

Thus, the product result of given expression is

\(x^2 - 6x + 9\)

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Answer:

x^2 - 6x + 9

Step-by-step explanation:

Hope this helps! :D

The distribution in residence is different today at a 0.05 level of significance can be conclude because the p-value = 0.0172

from the data given we can make the table below:

Categories       Observed(fo)        Expected (fe)        (fo-fe)²/fe

NW Oregon        3109           4357*0.727=3167.539       1.082

SW Oregon        902             4357*0.207=901.899           0

Central Oregon    244          4357*0.048=209.136         5.812

Eastern Oregon    102           4357*0.028=121.996         3.277

Sum =                    4357        4357                                   10.171

first,  null and alternative hypotheses need to be tested:

H0​:p1​=0.727,p2​=0.207,p3​=0.048,p4​=0.028

Ha​: The population proportion partially deviates from the value given by the null hypothesis

This corresponds to a Chi-Square test for Goodness of Fit.

then, Based on the data provided, the significance level is α=0.05, the number of degrees of freedom is df=4−1=3, so then the rejection region for this test is R={\(X^{2}X^{2}\)>7.815}.

after that we should do test statistic

The Chi-Squared statistic is calculated as follows:

∑\(^{n} _{i=1}\)\(\frac{(Oi-Ei)}{y} \\\) =   1.082+0+5.812+10.171 +3.277= 10.171

the we can make a decision about the null hypothesis by

\(X^{2} = 10.71 > X^{2} _{c} = 7.815\)

it is then concluded that the null hypothesis is rejected.

Therefore, there is enough evidence to claim that some of the population proportions differ from those stated in the null hypothesis, at the α=0.05 significance level.

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Answer:

This was not done by me! Credit to another expert on Brainly named caylus.

As it is impossible to understand who have done what ,

the correct construction should be :

You are given point A, point B and point C.

Construct a line parallel to that line AB passing through point C.

1) Place the compass on point B, and swing an arc that crosses line AB and line BC.

 Label the points D and E.

2) Keep the compass at the same width, and place it on point C.

3) Swing an arc that crosses line BC, and label the point F outside the segment [BC] .

4) Open the compass to the width between points D and E.

 Keeping the compass at the same width, place it on point F.

5) Swing an arc that intersects the arc created from line BC at point C.

6) Mark the intersection of the two arcs as point G.

7) Draw a line through point C and point G.

You just have to discover who has done that.

Answer:

x = 18

Step-by-step explanation:

We Know

(10x - 4) + (x - 14) must equal 180°

Find the value of x.

Let's solve

10x - 4 + x - 14 = 180

11x - 18 = 180

11x = 198

x = 18

So, x = 18 is the answer.

Step-by-step explanation:

hope it helps.........

Answer:

The answer is 6.

Step-by-step explanation:

All you need to do is turn 33 and 44 into a fraction (\(\frac{33}{44}\)). Then you need to simplify it and it's simplest form is \(\frac{3}{4}\). then you up the fraction to \(\frac{6}{8}\) and that's your answer.

Answer:

55°,90°,35°

Step-by-step explanation:

the sum of interior in a triangle is 180° and 55 +90+35=180

To answer your questions, we need to analyze the given equations and variables:

Equation 1: C = 900 - 50T

Equation 2: Y = 400

Equation 3: (M/P) = 0.25 - 62.5r

Equation 4: (M/P) = 400

The equation of the IS curve represents the equilibrium relationship between real GDP (Y) and the real interest rate (r). From Equation 2, we can see that the equation of the IS curve is Y = 400.

The equation of the LM curve represents the equilibrium relationship between the real interest rate (r) and the level of real money supply (M/P). From Equations 3 and 4, we can equate the expressions for (M/P) and solve for r:

0.25 - 62.5r = 400

-62.5r = 400 - 0.25

-62.5r = 399.75

r ≈ -6.396

Therefore, the equation of the LM curve is r ≈ -6.396.

To find the equilibrium values of the real interest rate (r) and real GDP (Y), we need to find the point where the IS curve intersects the LM curve. From Equation 2, we already know that Y = 400. Substituting this into the equation of the LM curve, we can solve for r:

400 = -6.396

Therefore, the equilibrium values of the real interest rate and real GDP are r ≈ -6.396 and Y = 400.

The Keynesian multiplier represents the impact of changes in autonomous spending on the overall change in equilibrium output (GDP). In this case, we don't have information about autonomous spending (investment), so we can't calculate the Keynesian multiplier.

An increase in government spending (G) would shift the IS curve to the right. This would lead to an increase in GDP (Y) and potentially a decrease in the real interest rate (r) as the IS and LM curves intersect at a higher level of output. However, without more information about the magnitude of the increase in government spending, we cannot determine the exact impact on GDP and the rate of interest.

The impact on national savings and the government budget balance of the increase in government spending depends on the financing of the spending increase. If the government increases taxes (T) or borrows to finance the higher spending, it may impact national savings and the government budget balance. However, based on the given equations, we do not have sufficient information to determine the specific impact on these variables.

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Answer:

Step-by-step explanation:

Answer:

B 25.2

Step-by-step explanation:

AB = AC - BC

= 51.8 - 26.6 = 25.2