Mathematics High School

Classify the function as linear or quadratic and identify the quadratic, linear, and constant terms. f(x) = (3x + 2)(−6x − 3)

A) quadratic function; quadratic term: 6x^2; linear term: 24x; constant term: −6

B) linear function; linear term: −21x; constant term: −6

C) quadratic function; quadratic term: −18x^2; linear term: −21x; constant term: −6

D) linear function; linear term: −18x^2; constant term: −6

Answers

Answer 1

believe the answer is d, though I’m not completely sure. hope this helps

Answer 2

Answer:

The correct Option is C). quadratic function; quadratic term: −18x²; linear term: −21x ; constant term: −6

Step-by-step explanation:

Given : f(x) = (3x + 2)(-6x - 3)

Now, f(x) = -18x² -9x -12x - 6

⇒ f(x) = -18x² - 21x - 6

Now, since the highest degree of the given function f(x) is 2 so the function f(x) is quadratic.

Now, quadratic term is one which has highest power x = 2 So, quadratic term = -18x²

Linear term is one which has power x = 1 So, linear term = -21x

Constant term is one which has power of x = 0. So, constant term = -6

Hence, The correct Option is C). quadratic function; quadratic term: −18x²; linear term: −21x ; constant term: −6

Related Questions

in a simple random sample of 48 men, the mean wrist circumference of the men is 19.3 centimeters with a standard deviation of 1.2 centimeters. Round your answer to the nearest hundredth.

Which interval is the 95% confidence interval for the mean wrist circumference for all men?

18.99,19.61
18.96, 19.64
12.85, 19.75
19.14, 19.46

Answers

Answer: Choice B
The 95% confidence interval for the population mean mu is (18.96, 19.64)
--------------------------------------------------------------
--------------------------------------------------------------

Work Shown:

xbar = 19.3
s = 1.2
n = 48
z = 1.960 (use a calculator or table to compute this critical value)

Lower Limit L
L = xbar - z*(s/sqrt(n))
L = 19.3 - 1.960*(1.2/sqrt(48))
L = 18.9605180417166
L = 18.96

Upper Limit U
U = xbar + z*(s/sqrt(n))
U = 19.3 + 1.960*(1.2/sqrt(48))
U = 19.6394819582836
U = 19.64

The confidence interval is therefore (L,U) = (18.96, 19.64)

Final answer:

The 95% confidence interval for the mean wrist circumference for all men is 18.91 to 19.69 centimeters.

Explanation:

To calculate the confidence interval for the mean wrist circumference, we can use the formula: CI = x ± t(s/√n), where CI is the confidence interval, x is the sample mean, t is the t-value corresponding to the desired confidence level, s is the sample standard deviation, and n is the sample size.

In this case, the sample mean is 19.3 centimeters, the sample standard deviation is 1.2 centimeters, and the sample size is 48. We can find the t-value for a 95% confidence level using a t-table or calculator. Assuming a normal distribution, the t-value is approximately 1.96. Plugging in these values into the formula, we get:

CI = 19.3 ± 1.96(1.2/√48) = 19.3 ± 0.3956

Therefore, the 95% confidence interval for the mean wrist circumference is approximately 18.91 to 19.69 centimeters.

I conceived on september 27 when will the test show the results

Answers

There isn't an exact time it's whenever they figure it out

What proportion of a normal distribution corresponds to z scores greater than 1.04?

Answers

Final answer:

The proportion of a normal distribution for z scores greater than 1.04 is 0.1492, which is found by subtracting the area to the left (0.8508) from the total area under the curve (1).

Explanation:

To find the proportion of a normal distribution that corresponds to z scores greater than 1.04, we must look up the area to the left of the z-score using a z-table or a standard normal distribution table. Once we have the area to the left, we can calculate the area to the right by subtracting this value from 1 (since the total area under the curve is 1). For a z-score of 1.04, the z-table shows that the area to the left is approximately 0.8508. Therefore, the proportion that is greater than a z-score of 1.04 is 1 - 0.8508, which equals 0.1492.

The standard normal distribution (Z~N(0,1)) has a total area of 1 under the curve, and it is symmetric about the mean, which is 0. Z-scores give us a way to determine how many standard deviations an observation is from the mean. Additionally, common z-scores used to determine confidence intervals or the proportion of observations within a certain range are tied to the percentage areas under the curve. For example, a z-score of ±1 encompasses approximately 68% of the data, ±2 about 95%, and ±3 approximately 99.7%.

wich of the following is the correct graph of solution to the inequality -8 >-5x+2>-38

Answers

-5x + 2 > -38
-5x > -40
x < 8

-5x + 2 < -8
-5x < -10
x > 2

so the inequality becomes
2 < x < 8

so the graph will be a straight line with open circles on 2 and 8 and shading in between these values.

On Call 3.5 hours: $10 Talk Time 1/2 hours: $1.25 What is the unit rate in dollars per hour for each company?

Answers

On Call's unit rate is about $2.86 per hour, since $10/3.5 hours= $2.86/1 hour
Talk Time's unit rate is about $2.50 per hour, since $1.25/0.5 hours= $2.50/1 hour

What is the first step in solving an equation by completing the square?

Answers

Write the quadratic in the correct form, it must be in descending order and equal to zero.

Which of the following is the contrapositive of the conditional below?

If 3 + 4 = 6, then 2 · 5 = 10.

A. If 2 · 5 = 10, then 3 + 4 = 6.
B. If 3 + 4 ≠ 6, then 2 · 5 ≠ 10.
C. If 2 · 5 ≠ 10, then 3 + 4 ≠ 6.
D. If 3 + 4 ≠ 6, then 2 · 5 = 10.

Answers

Answer: If 2 · 5 ≠ 10, then 3 + 4 ≠ 6.

Step-by-step explanation:

Because a contrapositive is the contradiction the hypothesis and conclusion of something given and interchanging them. For example: "if not-B then not-A " is the contrapositive of "if A then B "

Answer:

If 2 · 5 ≠ 10, then 3 + 4 ≠ 6.

Step-by-step explanation: Hope This Helps You!!! :)))

20 points! If u can provide an explanation that would be great if not just tell me how certain that's the answer. Thanks a bunch

Answers

This is a linear programming problem. When I say "programming", I don't mean computers. This can be done without the use of a computer though I don't recommend doing it by hand.

Let
x = number of trays of corn muffins
y = number of trays of bran muffins

Given info: "baking a tray of corn muffins takes 4 cups of milk and 3 cups of wheat flour"
If we focus on the milk only then baking x trays of corn muffins means we use up 4*x (or simply 4x) cups of milk. Focus now on the wheat flour and it takes 3*x or 3x cups of wheat flour

Also given: "Baking a tray of bran muffins takes 2 cups of milk and 3 cups of wheat flour"
So we use up 2y cups of milk and 3y cups of wheat flour

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

So far we have used 4x cups of milk for the corn muffins plus 2y more cups of milk for bran muffins giving a total of 4x+2y cups of milk used. We only have 16 cups of milk which means we can say this

4x + 2y <= 16

where the "<=" symbol without quotes means "less than or equal to". That inequality above is one of the constraints placed.

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

Another constraint is this inequality

3x+3y <= 15

because
* we use 3x cups of wheat flour for the corn muffins
* we use 3y cups of wheat flour for the bran muffins
* we have a max of 15 cups of wheat flour

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

Additional contraints are:
x >= 0
y >= 0
indicating that we cannot have x or y be negative

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

The four constraints are:
4x + 2y <= 16
3x+3y <= 15
x >= 0
y >= 0

If you graph all of these inequalities and do the proper shading, you'll get what you see in the attached image. Specifically I'm talking about the blue shaded region. This region is known as the feasible region.

Now turn your attention to the red corner points aka the vertices. These points will be plugged into the objective function

P(x,y) = 3x+2y

This represents the profit (in dollars) of making x trays of corn muffins and y trays of bran muffins.
3x = 3*x = profit from just the corn muffins only
2y = 2*y = profit from just the bran muffins only
3x+2y = total profit (selling both corn and bran muffins)

The four corner points are:
A = (3,2)
B = (0,5)
C = (0,0)
D = (4,0)

Plug each of these points into P(x,y) = 3x+2y

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

Plug in A = (x,y) = (3,2)
P(x,y) = 3x+2y
P(3,2) = 3*3+2*2
P(3,2) = 13

We earn a profit of $13 if we sell 3 trays of corn muffins and 2 trays of bran muffins

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

Plug in (x,y) = (0,5) which is point B
P(x,y) = 3x+2y
P(0,5) = 3*0+2*5
P(0,5) = 10

The profit dropped to $10, so we can ignore point B. So far point A leads to the most profit.

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

Plug in point C, which is (x,y) = (0,0)
P(x,y) = 3x+2y
P(0,0) = 3*0+2*0
P(0,0) = 0

The profit drops even further. Ignore this point.

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

Plug in point D: (x,y) = (4,0)

P(x,y) = 3x+2y
P(4,0) = 3*4+2*0
P(4,0) = 12

The profit has gone back up but not at the same height as $13 back for point A. So we can cross this off the list too

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

The max profit happens at point A which again was
(x,y) = (3,2)
x = 3 ----> selling 3 trays of corn muffins
y = 2 ----> selling 2 trays of bran muffins

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

So the final answer is choice A "3 trays of corn muffins and 2 trays of bran muffins"

Rearrange the formula v = GM r for r.

Answers

The correct formula for [tex]$ r $[/tex] rearranged from [tex]$ v = \frac{GM}{r} $ is $ r = \frac{GM}{v} $[/tex].

To rearrange the formula [tex]$ v = \frac{GM}{r} $[/tex] to solve for [tex]$ r $[/tex], follow these steps:

1. Start with the given formula:

[tex]\[ v = \frac{GM}{r} \][/tex]

2. Multiply both sides of the equation by [tex]$ r $[/tex] to get rid of the denominator:

[tex]\[ vr = GM \][/tex]

3. Divide both sides of the equation by [tex]$ v $[/tex] to isolate [tex]$ r $[/tex]:

[tex]\[ r = \frac{GM}{v} \][/tex]

This gives us the rearranged formula for [tex]$ r $[/tex] in terms of [tex]$ G $, $ M $, and $ v $[/tex]

6-ounce bag of rice noodles makes 5 servings. at that rate, find how many ounces of noodles are needed for 88 servings, to the nearest ounce

Answers

6 / 5 = 1.2 oz per serving <== ur unit rate

for 88 servings :
88 * 1.2 = 105.6....105 oz of noodles are needed <==

What is the perimeter of the rectangle shown on the coordinate plane, to the nearest tenth of a unit?

15.3 units
20.4 units
30.6 units
52.0 units

Answers

To calculate the perimeter, consider each side separately. Since this is a rectangle, you have 2 pairs of sides of equal length, so you just have to calculate the length of one of each pair of sides and then double each and add them to find the perimeter.

Top side: If you look carefully, this side is really the hypotenuse of a triangle that is 2 units tall and 10 units long. Using the Pythagorean Theorem, you can calculate the length of the hypotenuse to be 2^2 + 10^2 = c^2 --> c = 10.2

Left side: Just like the top side, this side is the hypotenuse of a triangle that is 5 units tall and 1 unit long. Pythagoras again: 5^2 + 1^2 = c^2 --> c = 5.1

Since you have two of each side that are the same length, double each and add for the final perimeter: 10.2*2 + 5.1*2 = 30.6

firstly, we will name the points as the following:
(-6,4) will be named as A
(4,2) will be named as B
(3,-3) will be named as C
(-7,-1) will be named as D
then we will use the distance formula between any 2 points on the graph which equals=[tex] \sqrt({x}1-{x}2)^2 +({y}1-{y}2)^2[/tex]
So,
AB=[tex] \sqrt[/tex](-6-4)^2+(4-2)^2 =2[tex] \sqrt[/tex]26
BC=[tex] \sqrt[/tex](4-3)^2+(2+3)^2 = [tex] \sqrt[/tex]26
CD=[tex] \sqrt[/tex](3=7)^2+(-3+1)^2 = 2[tex] \sqrt[/tex]26
AD=[tex] \sqrt[/tex](-6+7)^2+(4+1)^2 =[tex] \sqrt[/tex]26
Now calculate the sum and it will equal=30.6

A $360,000 building is depreciated by its owner. the value y of the building after x months is: y = 360,000 – 1,500 x. how many months will it take until it is completely depreciated

Answers

Final answer:

To find when the building will be completely depreciated, you solve for x in the equation y = 360,000 - 1,500x by setting y to 0. The solution is x = 240, meaning the building will be totally depreciated after 240 months or 20 years.

Explanation:

In this case, you are looking to find the value of x (the number of months) when the value of the building (y) becomes 0. The equation given is y = 360,000 - 1,500x. Set y = 0 and solve for x

First, replace y with 0 in the given equation: 0 = 360,000 - 1,500x. Next, move the term with x to the other side by adding 1,500x to both sides, which gives: 1,500x = 360,000.Finally, solve for x by dividing both sides of the equation by 1,500. This gives you: x = 360,000 / 1,500 = 240.

So, the building will be completely depreciated after 240 months or 20 years.

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What is the value of x? (7x-8) (6x+11)

Answers

(7x-8) (6x+11)=0
7x-8 = 0 then x = 8/7
6x+11 = 0 then x = -11/6

answer
x = -11/6 and x = 8/7

Answer:

[tex]x=-\dfrac{11}{6},\dfrac{8}{7}[/tex]

Step-by-step explanation:

Given: [tex](7x-8)(6x+11)[/tex]

Set the expression to 0 to solve for x

[tex](7x-8)(6x+11)=0[/tex]

Set each factor to 0 and solve for x

7x-8 = 0 or 6x+11 = 0

7x = 8 or 6x = -11

[tex]x=\dfrac{8}{7}[/tex] or [tex]x=-\dfrac{11}{6}[/tex]

hence, The values of x are [tex]x=-\dfrac{11}{6},\dfrac{8}{7}[/tex]

Janine has two important tests to study for. If she plans to divide her study time equally between both tests, how long should she spend studying for each test if she wants to study for at most 90 minutes?

Answers

90/2 = 45
45 minutes each.

90 mins divide by 2 tests = 45 mins per test

What time is 3 hours and 30 minutes before 5:00 P.M.?

Answers

5 - 3 = 2

2 pm so far

2:00 - 0:30 = 1:30 pm

your answer is 1:30 pm

hope this helps

1:30p.m is the time it would be

A rancher needs to enclose two adjacent rectangular corrals, one for cattle and one for sheep. if the river forms one side of the corrals and 180 yd of fencing is available, find the largest total area that can be enclosed.

Answers

Refer to the diagram shown below.

x = the width of each rectangular fence
y = the length of each rectangular fence

The amount of fencing available is 180 yards, therefore
2x + 2y = 180
x + y = 90 (1)

The total fenced area is
A = 2xy (2)

From (1), obtain
y = 90 -x (3)
Substitute (3) into (2).
A = 2x(90 - x) = 180x - 2x²

To maximize A,
A'(x) = 180 - 4x = 0 => x = 180/4 = 45 yds
y = 90 -x = 45 yds

The largest total enclosed area is
A = 2*x*y = 2*45² = 4050 yd²

Answer: 4050 yd²

If (a+b)^2=25, and a^2+b^2=17, then what is a*b equal to? Thanks.

Answers

a^2 + b^2 = (a + b)^2 - 2a*b

substituting:-

17 = 25 - 2 a*b
a*b = (25-17) / 2 = 8/2 = 4 answer

How to determine the probability of an event with a small chance repeating?

Answers

OOH USE YOUR BRAiN AND THINK :D

Option 1: $30 per month and $100 membership fee. Option 2: $25 per month and $150 membership fee.

Michael is trying to determine which tennis club to join. If Michael chooses option 2, for which month will his total cost for option 2 be less than his total cost for option 1? A) month 8 B) month 9 C) month 10 D) month 11

Answers

Let us say that m is the number of months. So that the equations for option 1 (O1) and option 2 (O2) are:

O1 = 30 m + 100

O2 = 25 m + 150

TO determine this, we equate O1 and O2 so that:

30 m + 100 = 25 m + 150

5 m = 50

m = 10

So at the 10th month, the cost for both options are equal. So we select month 11.

Answer:

D) month 11

If molly walks 4 miles in 70 minutes, then molly will walk how far in 100 minutes if she walks at the same speed the whole time? if necessary, round your answer to the nearest tenth of a mile.

Answers

Find out how far Molly walks in 1 minute.

4/70 = 0.057 miles
In 100 minutes,
0.057x100 = 5.714 miles

Rounded to the nearest tenth, 5.7 miles.

Hope I helped :)

Evaluate the expression below when x = 5.

3x(2x - 7)

A.) 0
B.) 24
C.) 45
D.) 143

Answers

the answer is D 143. welcome

If 3 (x+1) =7 find the value of 3x

Answers

The value of 3x would be 4/3.
Distribute the 3 in the parenthesis and you get:
3x+3=7
Then subtract 1 on both sides of the equal side.
3x=4
Therefore, the value of 3x would be 4.

If 5kg more than 3 times mac’s mass is decreased by twice his mass the result is 60 kg. What is mac’s mass?

Answers

Let x be mac's mass

(3x+5)-(2x)=60
3x+5-2x=60
x=60-5
x=55

Therefore, Mac is 55 kg

Hope I helped :)

Mac's mass can be found by setting up the equation 3m + 5kg - 2m = 60kg, simplifying to m + 5kg = 60kg, and solving for m to get m = 55kg. Therefore, Mac's mass is 55kg.

The equation, according to the problem statement, is: 3m + 5kg - 2m = 60kg. This simplifies to m + 5kg = 60kg, from which we can subtract 5kg from both sides resulting in m = 55kg. So, Mac's mass is 55kg.

Steps to solve the problem:

Let m represent Mac's mass.

Write the equation according to the problem statement: 3m + 5kg - 2m = 60kg.

Simplify the equation: m + 5kg = 60kg.

Subtract 5kg from both sides: m = 55kg.

Conclude that Mac's mass is 55kg.

what is the equation of the line x-3y = 18 in slope-intercept form ?

Answers

Attached the solution and work.

a person mailing postcards earns a fixed amount for each postcard he mails yesterday his hourly wage was $14 an hour if he worked 5 hours yesterday and mailed 300 postcards how much does he earn for each postcard mailed? show you work

Answers

If he worked 5 hours and his rate is $14/hr, then he earned a total of $70.
He mailed 300 postcard, so each postcard mailed is $0.2333..

BTW, i actually think the question is incomplete, so this may actually be a wrong answer.

For each postcard person gets $14/60 or $0.2333.

What is ratio?

Ratio is basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, there ratio will be a:b .

Given that,

Wage for 1 hour = $14,

Since,

The person mailed 300 postcards in 5 hours,

therefore, in 1 hour 60 postcards will be mailed.

Person gets $14 for 60 postcards ,

So for 1 postcard person will get $14/60 or $0.2333 .

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Write a 10 digit number such that the first digit tells how many zeros

Answers

1234567890 or 2134567800 or 3000216789

Which symbol creates a true sentence when x equals 3?
8•3-4x_7(10-x)
A.<
B.=
C.>

Answers

Hi Tysona90!
Let's write it with the X as a 3
8*3-4*3_7(10-3) Now let's solve it 8*3 is 24 and 4*3 is 12 so then we do 24-12 which is 12. So now we have 12_7(10-3) so let's solve the other half which is 10-3 is 7 times 7 (since parenthesis can also mean multiplication) which is 49 so we now have 12_49 which means the answer is A.
Hope this helps!

A solution containing 30 percent juice is mixed with a solution containing 10 percent juice to make 100 gallons of a 12 percent juice mixture. how much of the 30 percent juice solution was used

Answers

let there be x gallons of 30 percent juice, then there are (100-x) gallons of 12 percent juice.

0.30x+0.10(100-x)=100*0.12
0.3x+10-0.1x=12
0.2x=2
x=10

10 gallons of 30 percent juice should be used.

10 gallons of 30% juice was mixed with 90 gallons of 10% juice to make 100 gallons of 12% juice.

What is an equation?

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

Let x represent the amount of 30% juice and y represent the amount of 10% juice, hence:

x + y = 100 (1)

Also:

0.3x + 0.1y = 0.12(100) (2)

From eqn 1 and 2:

x = 10, y = 90

10 gallons of 30% juice was mixed with 90 gallons of 10% juice to make 100 gallons of 12% juice.

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Use the conversion factor 4 quarts / 1 gallon to convert 5.25 gallons to quarts

Answers

There are 21 quarts in 5.25 gallons.

Answer: 21 quarts

Step-by-step explanation: In this problem, we are asked to convert 5.25 gallons into quarts. To convert gallons into quarts, we use the conversion factor for gallons and quarts.

Conversion factor ⇒ 4 quarts = 1 gallon

Next, notice that we are going from a larger unit "gallons" to a smaller unit "quarts" and when we go from a larger unit to a smaller unit we multiply.

We will multiply 5.25 by the conversion factor which is 4 to get 21 quarts.

Therefore, 5.25 gallons is equal to 21 quarts.

Ria is an Indian student who was admitted to a US university. Her annual tuition is $42,000. She has to pay her tuition fees in US dollars. She needs to calculate how many Indian rupees she will need to buy one dollar. The dollar to rupee exchange rate is 63.76 and rupee to dollar exchange rate is 0.015. How many Indian rupees will Ria need to buy one dollar?

50.00 rupees

56.00 rupees

63.76 rupees

76.63 rupees

Answers

1$ = 63.76 rupees (dollar to rupee exchange)
1 rupee = 0.015$ (rupee to dollar exchange)
To buy one dollar, Ria will need 63.76$
Answer: (c)

Now, Ria's annual fees is $42,000. To know how much this is in dollars, use cross multiplication as follows:
tuition fees = (42,000*63.76) / (1) = 2,677,920 rupees

Ria will need 2677920 Rupees to pay her tuition fees

Data;

Tuition fee = $42,000$1 = 63.76 rupees$1 rupees = $0.015

How Many Rupees will she need to buy a Dollar?

We need to convert the currency from dollars to rupees

From the data given in the question, $1 is equivalent to 63.7 Rupees.

This information can further be used to determine how many Rupees she needs to pay her Tuition fees.

[tex]\$1 = 63.76 Rupees\\\$42,000 = x\\x = 42000 * 63.76\\x = 2677920[/tex]

Ria will need 2677920 Rupees to pay her tuition fees

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