Kristina used synthetic division to divide the polynomial f(x) by x−2, as shown on the table. What is the value of f(2)? −14 −11 −2 −1 A synthetic division setup with respective columns containing the following numbers column 1 containing two as a divisor, column 2 containing negative 1, blank and negative 1, column 3 containing negative 5, negative 2, negative 7, and column 4 containing three, negative 14, negative 11.There is a line above the numbers negative 1, negative 7 and negative 11.

Mr Lee drive 31 miles from his house to Brookville and there is an extra information that is parkside is 4 miles south of springfield which is not required.

Given that  

Mr. Lee drove 8 miles from his house to park side .  

Parkside is 4 miles south of springfield.

From Parkside he drove 3 miles to springdale  

Then he drove 20 miles from springdale to brookville.

Need to determine how far Mr Lee drive in all, from his house to Brookville.

Also need to identify Extra or missing information.

Complete drive of Mr Lee from his house to Brookville is equal to 8 miles from his house to park side then 3 miles from Parkside to springdale , then 20 miles from springdale to brookville.

=> Complete drive of Mr Lee from his house to Brookville in miles = 8 + 3 + 20 = 31 miles

Information that is parkside is 4 miles south of springfield is extra information which is not required to determine mr. Lee drive , from his house to Brookville .  

Hence Mr Lee drive 31 miles from his house to Brookville and there is an extra information that is parkside is 4 miles south of springfield which is not required.

The value of CosA is 0.8191

Step-by-step explanation:

Given SinA= 0.5736

We know that [tex]SinA^{2} + CosA^{2} = 1[/tex]

Replacing value of SinA,

[tex](0.5736)^{2} + CosA^{2} = 1[/tex]

[tex](0.3290) + CosA^{2} = 1[/tex]

[tex] CosA^{2} = 1-0.3290[/tex]

[tex] CosA^{2} = 0.6709 [/tex]

[tex] CosA = 0.8191 [/tex]

The value of CosA is 0.8191

Answer:

5. y-intercept is 8

6. slope is -1/2

7. y=-1/2x+8

Answer:

B, 9.625

Step-by-step explanation:

I know there's a more surefire method of doing this problem but since this is multiple choice, you can use process of elimination to solve it.

By proving that triangles DEA and EFB are congruent due to the Side-Angle-Side postulate and demonstrating that AE is parallel to FB as well as AD parallel to BC, we can conclude that EABC is a parallelogram.

To prove that quadrilateral EABC is a parallelogram, we can use the properties of triangles and the definition of a parallelogram. According to the given information, E is the midpoint of DA and F is the midpoint of DB. Additionally, we know that E, F, and C are collinear and that FC is congruent to EF.

Leveraging these pieces of information, we observe that triangle DEA is congruent to triangle EFB because they have a side (EF or DE), an angle (at point E, since DE is an extension of EF), and another side (EA or FB, which are halves of DA and DB, respectively) in common (Side-Angle-Side postulate).

Since the two triangles are congruent, angle DEA is congruent to angle EFB, and angle DAE is congruent to angle FEB. These congruent angles imply that line AE is parallel to line BF. Since E and F are midpoints, AE is half of DA and BF is half of DB. If we continue the line AE to meet CD at point A and the line BF to meet CD at point B, EA will be parallel to FB, and AD will be parallel to BC, meeting the definition of a parallelogram.

EABC is a parallelogram because opposite sides are parallel and equal due to the Midpoint Theorem.

Given:

E - midpoint of DA

F - midpoint of DB

E, F, C collinear, FC ≅ EF

To Prove: EABC is a parallelogram.

Proof:

1. By the Midpoint Theorem, EF || AB and EF = 1/2 * AB. (Midpoint Theorem)

2. Since E, F, C are collinear and FC ≅ EF, EC bisects EF at C. Therefore, AB || EC. (Definition of a parallelogram)

3. Since E is the midpoint of DA and C is the midpoint of EF, EC = 1/2 * DA. Since DA = AB, EC = 1/2 * AB. Similarly, EF = 1/2 * AB. Hence, EC = EF. Therefore, EA || BC. (Midpoint Theorem)

4. Since E is the midpoint of DA and C is the midpoint of EF, EC = 1/2 * DA. Since DA = BC, EC = 1/2 * BC. Similarly, EF = 1/2 * BC. Hence, EC = EF. Therefore, EB ≅ AC. (Midpoint Theorem)

Therefore, EABC is a parallelogram.

The price of less expensive equipment is $1575.

Step-by-step explanation:

Let,

Price of one equipment = x

Price of other equipment = y

According to given statement;

x+y=4000   Eqn 1

x = y+850    Eqn 2

Putting Eqn 2 in Eqn 1

[tex](y+850)+y=4000\\y+850+y=4000\\2y=4000-850\\2y=3150[/tex]

Dividing both sides by 2;

[tex]\frac{2y}{2}=\frac{3150}{2}\\y=1575[/tex]

Putting y=1575 in Eqn 2;

[tex]x=1575+850\\x=2425[/tex]

The price of less expensive equipment is $1575.

Keywords: linear equation, substitution method

Learn more about linear equations at:

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Final answer:

The price of the less expensive piece of equipment is $1575. This was calculated by setting up an equation based on the total cost and the difference in price between the two pieces of equipment and then solving for the unknown price.

Explanation:

To find the price of the less expensive piece of equipment, we will first assign variables to the two pieces of equipment. Let's call the cost of the less expensive piece of equipment x dollars. Since the other piece cost $850 more, the cost of the second piece would then be x + $850. We are given that the total cost of both pieces is $4000, so we can set up the following equation to represent this relationship:

x + (x + $850) = $4000

To solve for x, we combine like terms and get:

2x + $850 = $4000

Subtracting $850 from both sides gives us:

2x = $3150

Dividing both sides by 2, we find the value of x:

x = $1575

Therefore, the price of the less expensive piece of equipment is $1575.

Answer:

C) Side SW

Step-by-step explanation:

Hello! The included side between <S and <W is side SW. According to the included side rule, this would be the correct answer. I know this is not much of an explanation, but there is not much to it! Hope this helps.

According to the 2019 report Canada's Changing Climate Report (CCCR) which was commissioned by Environment and Climate Change Canada, Canada's annual average temperature over land has warmed by 1.7 C since 1948. The rate of warming is even higher in Canada's North, in the Prairies and northern British Columbia

L=4*W-5

10=W*2+(4*W-5)*2

10=W*2+8*W-10

20=10*W

2=W

L=4*2-5

L=3

Answer:

13.406

The drawing will help

Answer:

13.406

Step-by-step explanation:

Answer:

The two numbers are -419 and -2095.

Step-by-step explanation:

5x=y

x-y=1676

----------------

x-5x=1676

-4x=1676

x=1676/-4

x=-419

5(-419)=y

y=-2095

Dustin spends $13.6125 on going to work daily. It is 0.11 dollars per mile

Step-by-step explanation:

we have to caalculate the distance between Dustin's home and work

So

Given

Speed =s = 55 miles per hour

Time = t = 2 hours and 15 minutes

Converting time into fraction

Time = 2.25 hours

We know that

[tex]s = \frac{d}{t}\\d = s * t\\d = 55 * 2.25\\d = 123.75\ miles[/tex]

So the distance is 123.75 miles

The car travels 25 miles per gallon

We have to calculate the total number of gallon first

So,

[tex]No.\ of\ gallons = \frac{Miles}{Miles\ per\ gallon}\\=\frac{123.75}{25}\\=4.95\ gallons[/tex]

So the total amount is:

[tex]2.75*4.95\\= 13.6125\ dollars[/tex]

Total amount is $13.6125. Dividing it by total distance will give us the cost of each mile

So,[tex]Cost\ of\ mile = \frac{Total\ amount}{Distance}\\= \frac{13.6125}{123.75}\\=0.11\ dollars[/tex]

Hence,

Dustin spends $13.6125 on going to work daily. It is 0.11 dollars per mile

Keywords: Speed, Distance

Learn more about distance and speed at:

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Answer:

B.6 inches

Step-by-step explanation:

Given: Three boards with measurement  24, 36, and 42 inches.

For the longest length of board we have to find out the H.C.F.

And for H.C.F. we will find out the factors,

[tex]24=2\times2\times2\times3\\36=2\times2\times3\times3\\42=2\times3\times7[/tex]

Here 2 and 3 is the common factor of given length of boards.

So the H.C.F. is 6.

Hence the longest length of board that carpenter can cut is 6 inches.

Answer:

4/9

Step-by-step explanation:

(4/9)/(7/9) is equal to (4/9)*(9/7) because "keep change flip." So we keep the first number, change division into multiplication, and flip 4/9 (basically find the reciprocal) and that is 9/4. Thus,  (4/9)*(9/7) is equal to 4/9 because the 7's cancel.

I hope this helped!

Answer: 4/7

Step-by-step explanation: In this problem, we have 4/9 ÷ 7/9. Dividing by a fraction is the same as multiplying by its reciprocal. In other words, we can change the division to multiplication and flip the second fraction.

So here, 4/9 divided by 7/9 can be rewritten as 4/9 × 9/7.

Now we are simply multiplying fractions.

To multiply fractions, we multiply across the numerators and multiply across the denominators.

Image provided.

Notice however that 36/63 is not in lowest terms so we divide both the numerator and denominator by 9 and we get the equivalent fraction 4/7.

Therefore, 4/9 divided by 7/9 = 4/7.    

Answer: In general, a solution of a system in two variables is an ordered pair that makes BOTH equations true. In other words, it is where the two graphs intersect, what they have in common. So if an ordered pair is a solution to one equation, but not the other, then it is NOT a solution to the system

The right answer is Option B.

Step-by-step explanation:

Given expression is;

5x√2 - 3√2 + x√2

We can add or subtract square roots only when the values inside the square root are same and the variables are also same.

In the given expression, variable x is same with √2, therefore, adding both the roots

[tex]6x\sqrt{2} -3\sqrt{2}[/tex]

6x√2 - 3√2 is equivalent to 5x√2 - 3√2 + x√2.

The right answer is Option B.

Keywords: square roots, subtraction

Learn more about square roots at:

#LearnwithBrainly

Answer:

Here's the answer. I got it right on my quiz. Hope I could help:)

Answer:

10 square root over 30

Step-by-step explanation:

took the test

Answer:

True

Step-by-step explanation:

This is true because there is no common factor for 7 annd 9

Answer:

0.1187

Step-by-step explanation:

A = P (1 + k)^t

where A is the final amount,

P is the initial amount,

k is the monthly growth rate,

and t is the number of months.

70 = 50 (1 + k)^3

1.4 = (1 + k)^3

∛1.4 = 1 + k

k = -1 + ∛1.4

k = 0.1187

Answer:

[tex]\frac{1}{16}[/tex]

Step-by-step explanation:

[tex]\frac{1}{2} *\frac{1}{2} *\frac{1}{2} *\frac{1}{2} =[/tex][tex]\frac{1}{16}[/tex]

[tex]\frac{1}{2}*\frac{1}{2} =\frac{1}{4}[/tex]

[tex]\frac{1}{4} *\frac{1}{2} =\frac{1}{8}[/tex]

[tex]\frac{1}{8}*\frac{1}{2}=\frac{1}{16}[/tex]

Answer:

6

Step-by-step explanation:

4 divided by 2/3 is 6, because 4 x 2 = 8, and 8/3 is 6.

Answer:20592

Step-by-step explanation:

Because you multiply 5 times 2288

Leo has 2574 red marbles.

Let's say that the number of blue marbles Leo has is x. According to the given information, Leo has 9 times as many red marbles as blue marbles. So the number of red marbles Leo has is 9x.

It is also given that he has 2288 more red marbles than blue marbles, which means 9x = x + 2288.

Simplifying the equation, we can subtract x from both sides: 8x = 2288. Dividing both sides by 8, we find that x = 286.

Therefore, Leo has 9 times 286 red marbles, which equals 2574 red marbles.

Answer:

9 = [tex]3^{x}[/tex]

Step-by-step explanation:

Using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Given

[tex]log_{3}[/tex] 9 = x ⇔ 9 = [tex]3^{x}[/tex] ← in exponential form

Answer:

its A on edge

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\dfrac{1}{3}x<3x+8<-5x\qquad\text{multiply all sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\dfrac{1}{3\!\!\!\!\diagup_1}x<3\cdot3x+3\cdot8<3\cdot(-5x)\\\\x<9x+24<-15x\\\\\text{Let split it into two inequalities}\\\\(1)\qquad x<9x+24\ \text{and}\qquad (2)\qquad 9x+24<-15x[/tex]

[tex](1)\\x<9x+24\qquad\text{subtract}\ 9x\ \text{from both sides}\\\\-8x<24\qquad\text{change the signs}\\\\8x>-24\qquad\text{divide both sides by 8}\\\\\boxed{x>-3}\\\\(2)\\9x+24<-15x\qquad\text{add}\ 15x\ \text{to both sides}\\\\24x+24<0\qquad\text{subtract 24 from both sides}\\\\24x<-24\qquad\text{divide both sides by 24}\\\\\boxed{x<-1}\\\\\text{From (1) and (2) we have}\\\\-3<x<-1\to\text{There is only one integer in this solution: -2}[/tex]

Answer:

2x³ - 2

Step-by-step explanation:

Each term in the second factor is multiplied by each term in the first factor, that is

= x(2x² + 2x + 2) - 1(2x² + 2x + 2) ← distribute both parenthesis

= 2x³ + 2x² + 2x - 2x² - 2x - 2 ← collect like terms

= 2x³ - 2

Answer:

35 trials

Step-by-step explanation:

Probability = Favorable Outcome / Total Outcome

 P = 1/5

Favorable Outcome = 7

Substitute the values,  

1/5 = 7 / Total Outcomes

1/5 =7/x

Cross multiplication:

1x=5*7

x=35

Total Trials = 35

50 gallons of water leaked out of swimming pool.

Step-by-step explanation:

Total no. of gallons in swimming pool = 1000

Percentage of leaked water = 5%

Gallons of water leaked = 5% of total no. of gallons

[tex]Gallons\ of\ water\ leaked=\frac{5}{100}*1000\\\\Gallons\ of\ water\ leaked=\frac{5000}{100}\\\\Gallons\ of\ water\ leaked= 50\ gallons[/tex]

50 gallons of water leaked out of swimming pool.

Keywords: percentage, division

Learn more about division at:

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Answer:

The exponential function is [tex]C(t)=y(b)^t\ Or\ C(t)=1800(1.15)^1[/tex]

Step-by-step explanation:

Given

[tex]t[/tex] be the number of hours.

[tex]y[/tex] number of bacteria cells.

And we know that an exponential function is [tex]C(t)=y(b)^t[/tex],where [tex]b[/tex] is a positive real number, and in which the argument [tex]t[/tex] occurs as an exponent

The petri dish has [tex]1800[/tex] bacteria cells we can say that [tex]y=1800[/tex]

In the equation as [tex]C[/tex] is function of  time and [tex](t)[/tex] will vary as [tex]1,2,3[/tex] for respective hours.

To find the value of [tex]b[/tex] we have to understand that it is dependent on percent increase if there is increment of [tex]15\%[/tex] then [tex]b=1+15\%=1+\frac{15}{100}=1+0.15=1.15[/tex]

So the exponential function will be [tex]C(t)=y(b)^t[/tex] ,plugging the values it will be equivalent to [tex]C(t)=1800(1+0.15)^1[/tex]

Check:

[tex]15\% of 1800 =0.15\times 1800=270[/tex]

So in first hour the cells will increased by a quantity of [tex]270[/tex] cells.

The number of cells after an hour in the petri dish [tex]=(1800+270)=2070[/tex]

That can also be from the formula.

[tex]C(t)=1800(1.15)^1=2070[/tex]

So the exponential function is [tex]C(t)=y(b)^t\ Or\ C(t)=1800(1.15)^1[/tex]

[tex]y[/tex] will increase exponentially as the value of [tex]t[/tex] increase.

Final answer:

The exponential function to represent the growth of bacteria cells, y, after t hours with an initial amount of 1800 cells and a 15% hourly growth rate is y = 1800(1 + 0.15)^t.

Explanation:

To write an exponential function showing the relationship between the number of bacteria cells, y, and the time in hours, t, we begin by using the initial value of 1800 bacteria cells and apply a 15% increase each hour. The exponential growth formula is given by y = P(1 + r)^t, where P is the initial amount, r is the growth rate (expressed as a decimal), and t is the time.

Since the growth rate is 15%, we convert this to a decimal by dividing by 100, resulting in 0.15. The formula to model this bacterial growth would be y = 1800(1 + 0.15)^t. Therefore, for any given number of hours t, you can calculate the number of bacteria cells y.