Use​ Descartes' Rule of Signs to determine the possible numbers of positive and negative real zeros of f (x )equals x cubed plus 5 x squared plus 7 x plus 6f(x)=x3+5x2+7x+6. What are the possible numbers of positive real​ zeros?

The equation d=50+20w represents the relationship between dollar amount in her bank account and the number of weeks of savings.

Step-by-step explanation:

Amount in bank account = $50

Amount deposited by Priya = $20

Time period = 12

Let,

d be the dollar and w be the weeks

Therefore, we will multiply the number of week,w, with 20 to find total savings  and add the amount that she has initially in her account.

Therefore,

[tex]d=50+20w[/tex]

The equation d=50+20w represents the relationship between dollar amount in her bank account and the number of weeks of savings.

Keywords: linear equation, addition

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The equation that represents Priya's savings over time is y = 50 + 20x. In this equation, y is the total amount in the bank account and x is the number of weeks.

The relationship described in the problem can be represented by a linear equation. Here, the initial $50 in Priya's bank account is the starting value (or y-intercept). The $20 she deposits each week represents the constant rate of change (or slope), and the number of weeks is the variable.

Therefore, the relationship can be represented by the equation y = 50 + 20x, where y represents the total dollar amount in the bank account and x is the number of weeks Priya has been saving.

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Answer:

Step-by-step explanation:

The ratio of nickels to dimes is 2 : 3 = 4 : 6.

The ratio of dimes to quarters is 2 : 5 = 6 : 15.

Then the ratios of nickels : dimes : quarters are ...

  4 : 6 : 15

There are a total of 4+6+15 = 25 ratio units representing 500 coins, so each one represents 500/25 = 20 coins. Then the numbers of coins are ...

  nickels : dimes : quarters = 4·20 : 6·20 : 15·20 = 80 : 120 : 300

There are 80 nickels, 120 dimes, and 300 quarters in the piggy bank.

To determine the number of nickels, dimes, and quarters in the piggy bank, set up equations based on the given relationships and the total number of coins. Solve the system of equations to find the values of 'n', 'd', and 'q'.

Let's start by assigning variables to the number of nickels, dimes, and quarters. Let's say there are 'n' nickels, 'd' dimes, and 'q' quarters. From the given information, we know that for every 2 nickels, there are 3 dimes, and for every 2 dimes, there are 5 quarters.

Therefore, we can set up the following equations:
2n = 3d
2d = 5q

Additionally, we know that there are a total of 500 coins, so we can write 'n + d + q = 500'.

Using these equations, we can solve for the values of 'n', 'd', and 'q'.

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Answer: Length = 11 feet

Width = 6 feet

Step-by-step explanation:

A rectangle is a four sided shape that has 2 equal lengths,L and 2 equal widths,W

The perimeter of the rectangular piece of land is the total distance around it. It is expressed as

Perimeter = 2L + 2W = 2(L+W)

The perimeter is given as 34ft. It means that

34 = 2(L+W) - - - - - - - -1

The length of the rectangular piece of land is 5ft more than two times its width. It means that

L = W + 5

Substituting L = W + 5 into equation 1, it becomes

34 = 2(W + 5 +W) = 2(2W + 5)

2W + 5 = 34/2 = 17

2W = 17 - 5 = 12

W = 12/2 = 6 feet

L = W + 5 = 6+5

L = 11 feet

Answer:

D. 5x^2-6/2

Step-by-step explanation:

5x^2-18/6 , 18/6 is 6/2

5x^2-6/2 ,

After simplification, the equation obtained is 5x² - 6/2. Hence, option D is correct.

A phrase must be simplified and made shorter using a variety of methods. The steps required to decrease something are carried out according to a specified order known as BOD MAS.

Make a fraction simpler by reducing it to the base form. If both the numerator and denominator of a fraction only include the integer, the fraction is considered to be in its basic form.

As per the given information in the question,

The given equation in the question is,

15x² - 18/6

Divide the equation by 3,

= 5x² - 6/2.  

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Answer:

  (E)  xy/(y-x)

Step-by-step explanation:

The sum of the individual rates is the total rate. Each machine's rate is nails per hour is the inverse of its rate in hours per nail.

  total rate = (800 nails)/(x hours) = 800/x nails/hour

  A rate = (800 nails)/(y hours) = 800/y nails/hour

We want to find the time "b" such that ...

  B rate = (800 nails)/(b hours) = 800/b nails/hour

__

As we said, the total rate is the sum of the individual rates:

  800/x = 800/y + 800/b

Multiplying by xyb/800, we get

  yb = xb + xy

Solving for b, we have ...

  yb -xb = xy

  b(y -x) = xy

  b = xy/(y-x) . . . . . matches choice E

It takes Machine B xy/(y-x) hours to produce 800 nails.

Answer:

A. 18x8 is 144 then divided by 2 is 72

Answer:

Step-by-step explanation:

Answer:

she keeps her earnings the same

Answer: it will take her 56.67 seconds or 0.945 minutes to race 2 laps

Step-by-step explanation:

It takes Ella 1 minute and 25 seconds to complete the cheep beach course.

We can express this time in seconds or minutes. Expressing it in seconds,

1 minute = 60 seconds

Therefore,

1 minute and 25 seconds = 60 +25 = 85 seconds

If the course is 3 laps long, that means she completed 3 laps in 85 seconds. The time it will take her to race 2 laps would be

(2 × 85)/3

= 56.67 seconds

Converting to minutes, it will be

56.7/60 = 0.945 minutes

Answer:

a) Yes b) No

Step-by-step explanation:

Given that the p value for a two-sided test of the null hypothesis H0: μ = 10

is 0.06

a) [tex]p value = 0.06.\\Confidence level = 95%\\Significance level = 100-95 = 5%\\Alpha = 0.05\\\\p  \geq \alpha is true[/tex]

Hence we accept null hypothesis

This implies that 10 will be within the confidence interval of 95%

b) If confidence level = 90%

[tex]\alpha = 0.10\\p value = 0.06\\p \leq 0.10[/tex]

So we have to reject null hypothesis.

So we do not have 10 in the confidence interval

The reason is the lower the confidence level, the narrower the confidence interval.  In this case, 10 has gone outside the narrower interval hence we get this.

Answer:

The  square feet of space per employee is more in building B .

Step-by-step explanation:

Given as :

The office space of building A = 7,500 ft²

The number of employee in building A = 320

Let The space in building A per square feet per employee = x ft²

So,  x = [tex]\dfrac{\textrm office space in building A}{\textrm number of employee in building A}[/tex]

I.e x = [tex]\frac{7500}{320}[/tex]

∴   x = 23.43 per square feet per employee

So, For building A  23.43 per square feet per employee

Again ,

The office space of building B = 9,500 ft²

The number of employee in building B = 317

Let The space in building B per square feet per employee = y ft²

So,  y = [tex]\dfrac{\textrm office space in building B}{\textrm number of employee in building B}[/tex]

I.e y = [tex]\frac{9500}{317}[/tex]

∴   y = 29.96 per square feet per employee

So, For building B 29.96 per square feet per employee

So , from calculation it is clear that the square feet of space per employee is more in building B .

Hence The  square feet of space per employee is more in building B .  Answer

Answer:

a) [tex]\bar x= 56.8[/tex]

b) The 95% confidence interval is given by (55.282;58.318)  

c) [tex]P(X<52) = P(Z<\frac{52-56.8}{\sqrt{6}})=P(Z<-1.96) = 0.025[/tex]

Step-by-step explanation:

1) Notation and definitions  

n=10 represent the sample size  

[tex]\bar X[/tex] represent the sample mean  

[tex]s[/tex] represent the sample standard deviation  

[tex]\sigma^2= 6[/tex]

m represent the margin of error  

Confidence =95% or 0.95

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

2) Calculate the mean (Point of estimate for [tex]\mu[/tex]) and standard deviation for the sample

On this case we need to find the sample standard deviation with the following formula:

[tex]s=\sqrt{\frac{\sum_{i=1}^15 (x_i -\bar x)^2}{n-1}}[/tex]

And in order to find the sample mean we just need to use this formula:

[tex]\bar x =\frac{\sum_{i=1}^{15} x_i}{n}[/tex]

The sample mean obtained on this case is [tex]\bar x= 56.8[/tex] and the deviation s=2.052. Since we know the population standard deviation [tex]\sigma^2=6[/tex] and [tex]\sigma=2.449[/tex]

3) Calculate the critical value tc  

In order to find the critical value is important to mention that we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 95% of confidence, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex].

We can find the critical values in excel using the following formulas:  

"=NORM.INV(0.025,0,1)" for [tex]t_{\alpha/2}=-1.96[/tex]  

"=NORM.INV(1-0.025,0,1)" for [tex]t_{1-\alpha/2}=1.96[/tex]  

The critical value [tex]zc=\pm 1.96[/tex]  

3) Calculate the margin of error (m)  

The margin of error for the sample mean is given by this formula:  

[tex]m=z_c \frac{\sigma}{\sqrt{n}}[/tex]  

[tex]m=1.96 \frac{2.449}{\sqrt{10}}=1.518[/tex]  

4) Calculate the confidence interval  

The interval for the mean is given by this formula:  

[tex]\bar X \pm z_{c} \frac{\sigma}{\sqrt{n}}[/tex]  

And calculating the limits we got:  

[tex]56.8 - 1.96 \frac{2.449}{\sqrt{10}}=55.282[/tex]  

[tex]56.8 + 1.96 \frac{2.449}{\sqrt{10}}=58.318[/tex]  

The 95% confidence interval is given by (55.282;58.318)  

On the basis of these very limited data, what is the probability that an individual snack pack selected at random is filled with less than 52 grams of candy?

On this case we can use as point of estimate for the mean the result from part a, [tex]\bar x= 56.8[/tex] and the variance is [tex]\sigma^2 =6[/tex], so [tex]\sigma =\sqrt{6}[/tex]. And we are interested on this probability:

[tex]P(X<52) = P(Z<\frac{52-56.8}{\sqrt{6}})=P(Z<-1.96) = 0.025[/tex]

Answer:

your answer is 1/4

Step-by-step explanation:

part 1

7/8 + -2/3 = 5/24

part 2

5/24÷5/6 = 1/4

Answer:

$8,000.00 /yr

Step-by-step explanation:

The original fuel cost was 30% of 400,000 or $120,000.

If the previous cost was 1.50/L, then 120,000/1.5 = 80,000L/yr

The extra $0.10/L thus adds .1(80,000) = $8,000.00 /yr

Answer:

Option D - [tex]\frac{2}{7}[/tex].

Step-by-step explanation:

Given : From a group of 8 volunteers, including Andrew and Karen, 4 people are to be selected at random to organize a charity event.

To find : What is the probability that Andrew will be among the 4 volunteers selected and Karen will not?

Solution :

Choosing 4 people out of 8 volunteers is [tex]^8C_4[/tex]

[tex]^8C_4=\frac{8!}{4!(8-4)!}[/tex]

[tex]^8C_4=\frac{8\times 7\times 6\times 5\times 4!}{4!\times 4\times 3\times 2}[/tex]

[tex]^8C_4=70[/tex]

Choosing a group of 4 with Andrew and no karein is given by,

One position is fixed by Andrew and Karein the number of volunteer left is 6.

Rest 3 volunteers is chosen from 6.

Choosing 3 people out of 6 volunteers is [tex]^6C_3[/tex]

[tex]^6C_3=\frac{6!}{3!(6-3)!}[/tex]

[tex]^6C_3=\frac{6\times 5\times 4\times 3!}{3!\times 3\times 2}[/tex]

[tex]^6C_3=20[/tex]

The probability that Andrew will be among the 4 volunteers selected and Karen will not is given by,

[tex]P=\frac{^6C_3}{^8C_4}[/tex]

[tex]P=\frac{20}{70}[/tex]

[tex]P=\frac{2}{7}[/tex]

The probability that Andrew will be among the 4 volunteers selected and Karen will not is [tex]\frac{2}{7}[/tex].

Therefore, option D is correct.

Answer:

0.156

Step-by-step explanation:

Using binomial probability formula, we have :

P( a out of n ) =ⁿCₐ x pᵃ x qⁿ⁻ᵃ  ------------------------------------------------- (1)

Where n = total number of sample

           a = number of success

            p = probability of success

            q = probability of failure

            n-a = number of failures

From the question:

n =10 , a = 7, p=0.54, q = 1-p = 0.46

Substituting into equation (1) we have:

P (7 out of 10) =  ¹⁰C₇ x (0.54)⁷x (0.46)¹⁰⁻⁷

                      = 0.1563

                     ≈ 0.156

Answer:

Step-by-step explanation:

A function is increasing when it is rising to the right. Here, that is everywhere right of x=-1.

A function is decreasing when it is falling to the right. Here, that is everywhere left of x=-1.

A function is constant when its graph is horizontal. There are no places on this graph like that.

Answer:

The first number (or x value) of an ordered pair.

Step-by-step explanation:

Abscissa is the first number (or x value) of an ordered pair.

A coordinate plane is a way of locating points in a plane that consists of a horizontal and a vertical number line intersecting at the zeros.

Coordinates are an ordered pair, (x, y), that describes the location of a point in the coordinate plane.

Ordinate is the second number (or y value) of an ordered pair.

Origin is the point of intersection, (0, 0), of the axes in the coordinate plane.

A quadrant is a region in the coordinate plane.

X axis is the horizontal axis in the coordinate plane.

Y axis is the vertical axis in the coordinate plane.

Line A is the  

✔ y-axis .

Region B is  

✔ a quadrant .

Point C is the  

✔ origin .

Line D is the  

✔ x-axis .

hope this helps :)

Answer: the number of students that were surveyed is 40

Step-by-step explanation:

Let x = total number of students that were surveyed about their favorite colors

1/4 of the students preferred red.

This means that the number of students that preferred red is 1/4 × x = x/4

1/8 of the students preferred blue.

This means that the number of students that preferred blue is 1/8 × x = x/8

The remaining number of students will be the total number of students - the sum of the number of students that preferred red and the number of students that preferred blue. It becomes

x - (x/4 + x/8) = x - 3x/8 = 5x/8

3/5 of the remaining students were for green. This means that the number of students that preferred green is 3/5 × 5x/8 = 3x/8

if 15 students prefer green, then

3x/8 = 15

3x = 120

x = 120/3 = 40 students

Answer:

First you would translate triangle ABC to the right . next you would then translate triangle ABC up . Last you would rotate triangle ABC clockwise and matched angle A with angle D.

Step-by-step explanation:

Answer:

a) mean= 158.4 , standard deviation = 3.394

b)  Best option : B. Yes, since the original population is normal, the sampling distribution of the sum will also be approximately normal.

c)  P(X>160) = P(Z>0.471) = 1-P(Z<0.471) = 0.3188

Step-by-step explanation:

1) Notation

n = sample size = 8

[tex] \mu [/tex] = population mean = 19.8

[tex] \sigma [/tex] = population standard deviation = 1.2

2) Definition of the variable of interest

Part a

The variable that we are interested is [tex] \sum x_i  [/tex] and the mean and the deviation for this variable are given by :

E([tex] \sum x_i [/tex]) =  [tex] \sum E(x_i) [/tex] = n [tex] \mu [/tex] = 8x19.8 = 158.4

Var([tex] \sum x_i [/tex]) =  [tex] \sum Var(x_i) [/tex] = n [tex] \sigma^2 [/tex]

Sd([tex] \sum x_i [/tex]) =   [tex] \sqrt{n \sigma^2} [/tex] = [tex] \sqrt(8) [/tex]  x 1.2 = 3.394

Part b

For this case the populations are normal, then the distribution for the sample ([tex] \sum x_i [/tex])  is normal too.

Based on this the distribution for the variable X would be normal, so the best option should be:

B. Yes, since the original population is normal, the sampling distribution of the sum will also be approximately normal.

Part c

From part a we know that the mean = 158.4 and the deviation = 3.394

The z score is defined as

Z = (X -mean)/ deviation = (160-158.4)/ 3.394 = 0.471

Then we can find the probability P(X>160) = P(Z>0.471) = 1-P(Z<0.471) = 0.3188

Answer:

a. [tex]x-y > 0[/tex]

b. [tex]x+y \leq 50[/tex]

c. x=26; y=24 or (24,26)

Step-by-step explanation:

Let x = number of teachers hired.

Let y = number of tutors hired.

Now solving for part a we get

a. Write an inequality that represents the statement that the number of teachers hired must exceed the number of tutors hired.

[tex]x-y > 0[/tex]

solving for part b we get;

b. Write an inequality that represents the statement that the maximum number of teachers and tutors is 50.

[tex]x+y \leq 50[/tex]

solving for part c we get;

c. Choose a point that satisfies the situation, and explain why you chose that number of tutors and teachers.

Now we know that [tex]x-y > 0[/tex] also [tex]x+y \leq 50[/tex]

x=26; y=24

(24,26)

Explanation: To make number of teacher more than number of tutors this is the maximum value we can achieve for the requirement.

a. The inequality x > y represents the statement that the number of teachers hired must exceed the number of tutors hired. b. The inequality x + y ≤ 50 represents the statement that the maximum number of teachers and tutors is 50. c. The point (25, 10) satisfies both inequalities and represents hiring 25 teachers and 10 tutors.

a. To represent the statement that the number of teachers hired must exceed the number of tutors hired, you can write the inequality x > y. This means that the number of teachers, represented by x, must be greater than the number of tutors, represented by y.

b. To represent the statement that the maximum number of teachers and tutors is 50, you can write the inequality x + y ≤ 50. This means that the total number of teachers and tutors hired, represented by x + y, cannot exceed 50.

c. Let's choose the point (25, 10) which represents hiring 25 teachers and 10 tutors. This point satisfies both inequalities: 25 > 10 and 25 + 10 ≤ 50.

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Number of calories in 6 ounces of pumpkin is 61.5 calories.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, 8 ounces of canned pumpkin has 82 calories

Now, number of calories in 1 ounce = Total number of calories ÷ Number of ounces

= 82/8

= 10.25 calories

Number of calories in 6 ounces of pumpkin

= 6×10.25

= 61.5 calories

Therefore, number of calories in 6 ounces of pumpkin is 61.5 calories.

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Answer:

The angles formed on line b when cut by the transversal are congruent with ∠2 are [tex]\angle{6}\text{ and }\angle{7}[/tex]

Step-by-step explanation:

Consider the provided information.

If transversal line crossed by two parallel lines, then, the corresponding angles and alternate angles are equal .

The angles on the same corners are called corresponding angle.

Alternate Angles:  Angles that are in opposite positions relative to a transversal intersecting two lines.

∠2 and ∠6 are corresponding angles

Therefore, ∠2 = ∠6

∠2 and ∠7 are alternate exterior angles

Therefore, ∠2 = ∠7

Hence, the angles formed on line b when cut by the transversal are congruent with ∠2 are [tex]\angle{6}\text{ and }\angle{7}[/tex]

To estimate the proportion of cyanobacteria in algae samples with a 99% confidence level and a margin of error ≤ 0.01, Ian would need a sample size of at least 12111.

To determine the required sample size (n) for estimating the proportion of cyanobacteria in the algae samples with a margin of error of at most (0.01) and a (99%) confidence level, you can use the formula for the margin of error in estimating a population proportion:

[tex]\[ E = Z \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \][/tex]

Given:

- Margin of error (E) = 0.01

- Confidence level = (99%), which corresponds to a Z-score of approximately 2.576

- Estimated proportion [tex](\(\hat{p}\)) = \(\frac{38}{50} = 0.76\)[/tex] (from the given sample)

Now, the formula can be rearranged to solve for (n):

[tex]\[ n = \frac{\hat{p}(1-\hat{p})}{\left(\frac{E}{Z}\right)^2} \][/tex]

Substitute the given values:

[tex]\[ n = \frac{0.76 \times (1 - 0.76)}{\left(\frac{0.01}{2.576}\right)^2} \][/tex]

Now calculate:

[tex]\[ n \approx \frac{0.76 \times 0.24}{\left(\frac{0.01}{2.576}\right)^2} \][/tex]

n ≈  12111

Therefore, Ian would need a sample size of at least 12111 algae samples to estimate the proportion of cyanobacteria with a margin of error of at most (0.01) in a (99%) confidence interval.

Ian would require a sample size of approximately 12,102 algae to estimate the proportion of cyanobacteria with a margin of error of at most 0.01 in a 99% confidence interval.

To determine the required sample size for estimating the proportion of algae samples that are cyanobacteria with a margin of error of at most 0.01 and a 99% confidence level, we can use the formula for the confidence interval for a proportion:

[tex]\[ n = \left(\frac{z_{\alpha/2} \cdot \sqrt{p(1-p)}}{E}\right)^2 \][/tex]

where:

-  n is the sample size,

- [tex]\( z_{\alpha/2} \)[/tex] is the z-score corresponding to the desired confidence level (for 99%, [tex]\( z_{\alpha/2} = 2.576 \),[/tex]

- p is the estimated proportion of the population that has the characteristic of interest (in this case, being cyanobacteria),

-  E  is the margin of error.

The estimated proportion  p  can be taken from the initial sample of 50 algae, where 38 were cyanobacteria. Thus,  pis estimated as:

[tex]\[ p = \frac{\text{Number of cyanobacteria}}{\text{Total sample size}} = \frac{38}{50} = 0.76 \][/tex]

Now, we plug in the values into the formula:

[tex]\[ n = \left(\frac{2.576 \cdot \sqrt{0.76(1-0.76)}}{0.01}\right)^2 \][/tex]

[tex]\[ n = \left(\frac{2.576 \cdot \sqrt{0.76 \cdot 0.24}}{0.01}\right)^2 \][/tex]

[tex]\[ n = \left(\frac{2.576 \cdot \sqrt{0.1824}}{0.01}\right)^2 \][/tex]

[tex]\[ n = \left(\frac{2.576 \cdot 0.427}{0.01}\right)^2 \][/tex]

[tex]\[ n = \left(\frac{1.101}{0.01}\right)^2 \][/tex]

[tex]\[ n = (110.1)^2 \][/tex]

[tex]\[ n \ = 12101.01 \][/tex]

Since we cannot have a fraction of an algae sample, we round up to the nearest whole number:

[tex]\[ n \ = 12102 \][/tex]

Answer:

  x < -7

Step-by-step explanation:

Eliminate parentheses:

  3x -12 > 5x +2

  -14 > 2x . . . . . . . . . add -2-3x

  -7 > x . . . . . . . . . . . divide by 2

Any value of x less than -7 is in the solution set.

Answer:

The answer is 6 hours

Step-by-step explanation:

The inequality

39 + 5.90 *t < 74.40 - 39

5.90 *t <35.4

t<  35.4/5.9

= 6 hours

Answer:

option (b) 12.5 V

Step-by-step explanation:

Given:

Number of turns, N = 500

Area of the coil, A = 0.050 m²

Angular speed, ω = 20 rad/s

Magnetic field, B = 0.050 T

Angle to the field, θ = 30°

Now,

EMF induced, ε = NBAωsinθ

on substituting the values, we get

ε = 500 × 0.050 × 0.050 × 20 × sin30°

or

ε  = 25 × 0.5

or

ε  = 12.5 V

Hence,

option (b) 12.5 V

The zeros of a polynomial are the solutions to the polynomial equation. The function [tex]x^4+3x^3+5x^2-3x-6[/tex] has exactly 4 zeros due to the Fundamental Theorem of Algebra. The polynomial  [tex]f(x)=x^4+2x^3-6x^2+4x-16[/tex]can be factored by grouping.

1.) The zeros of the polynomial  [tex]f(x)=x^4-x^3-16x^2+4x+48[/tex] are the solutions to the equation  [tex]x^4-x^3-16x^2+4x+48=0[/tex]. Unfortunately, this equation does not have simple solutions and would require numerical techniques to solve.

2.) The function  [tex]f(x)=x^4+3x^3+5x^2-3x-6[/tex] is a fourth degree polynomial, implying that it has exactly 4 zeros in the complex number system. This is a consequence of the Fundamental Theorem of Algebra, which states that every non-zero, single-variable, degree n polynomial with complex coefficients has exactly n roots in Complex Numbers.

3.) The polynomial [tex]f(x)=x^4+2x^3-6x^2+4x-16[/tex] can be factored by grouping as follows [tex]: f(x)=x^4+2x^3-6x^2+4x-16=(x^4+2x^3)-(6x^2-4x+16) = x^3(x+2)-2(x^3-2x+8)=x^3(x+2)-2(x-2)^2.[/tex]

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Answer:

Part 1) The perimeter of triangle ABC is 24 units

Part 2) [tex]y=97\°[/tex]

Step-by-step explanation:

Part 1) we know that

The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side

see the attached figure to better understand the problem

so

Applying the midpoint theorem

step 1

Find the value of BC

[tex]BC=\frac{1}{2}XY[/tex]

[tex]XY=2AY[/tex] ---> because A is the midpoint

substitute the given value of AY

[tex]XY=2(7)=14\ units[/tex]

[tex]BC=\frac{1}{2}(14)=7\ units[/tex]

step 2

Find the value of AC

[tex]AC=\frac{1}{2}YZ[/tex]

[tex]YZ=2BZ[/tex] ---> because B is the midpoint

substitute the given value of BZ

[tex]YZ=2(8)=16\ units[/tex]

[tex]AC=\frac{1}{2}(16)=8\ units[/tex]

step 3

Find the value of AB

[tex]AB=\frac{1}{2}XZ[/tex]

substitute the given value of XZ

[tex]AB=\frac{1}{2}(18)=9\ units[/tex]

step 4

Find the perimeter of triangle ABC

[tex]P=AB+BC+AC[/tex]

substitute

[tex]P=9+7+8=24\ units[/tex]

Part 2) Find the measure of angle y

step 1

Find the measure of angle z

we know that

The sum of the interior angles in a triangle must be equal to 180 degrees

so

[tex]55\°+42\°+z=180\°[/tex]

solve for z

[tex]97\°+z=180\°[/tex]

[tex]z=180\°-97\°[/tex]

[tex]z=83\°[/tex]

step 2

Find the measure of angle y

we know that

[tex]z+y=180\°[/tex] ----> by supplementary angles (form a linear pair)

we have

[tex]z=83\°[/tex]

substitute

[tex]83\°+y=180\°[/tex]

solve for y

[tex]y=180\°-83\°[/tex]

[tex]y=97\°[/tex]

Answer:4 students will be in each group.

Step-by-step explanation:

28 and 36. The 2 numbers are divisible by 4 without remainder

Answer:

4 students will be in each group.

Step-by-step explanation:

28 and 36. The 2 numbers are divisible by 4 without remainder

brainilest pl.z? i've never got brainilest.