Mathematics College

For the given functions f and g, complete parts (a)-(h). For parts (a)-(d), also find the domain.

Answers

Answer 1

Given the function (f + g) (x) as

[tex]4x^2+x-7[/tex]

The domain of the function above is the set of x values except the for x- values that will make the function undefined

For the function above, the domain is defined at all set of real numbers and the interval notation is given as

[tex]-\inftyHence, the correct option is B

Related Questions

Sean and Darryl are racing on a track. Sean runs 6 miles per hour and gets a 0.25 mile head start. Darryl runs 0.7 mile per hour faster than Sean. If Darryl and Sean run the same distance, how many hours, x, do they run? 6x + 0.25 = 0.7x 0 6x - 0.25 = 3.7x 0 6x +0.25 = 6.7x D 6x + 0.25 = 4.7x

Answers

The relation between speed, distance and time is express as :

[tex]\text{ Sp}eed\text{ =}\frac{Dis\tan ce}{Time}[/tex]

Sean and Darryl are racing on a track.

Sean runs 6 miles per hour and gets a 0.25 mile head start.

Speed of Sean = 6

x is the time taken by Sean

So, Distance = speed x Time

Distance travel by sean = 6x

Since, Sean gets a 0.25 mile head start.

So, total distance travel = 6x + 0.25

Darryl runs 0.7 mile per hour faster than Sean,

Speed of darryl = 0.7 + Speed of sean

Speed of daryl = 0.7 + 6

Speed of darryl = 6.7 miles per hour

x is the time taken by Darryl

So, Distance = Speed x Time

Distance = 6.7x

Distance travel by Darryl = 6.7x

Since distance travel by darryl and sean is equal so,

6x + 0.25 = 6.7x

Answer : C) 6x + 0.25 = 6.7x

Find the probability of selecting a 10 or diamond when a card is drawn from a standard deck of cards.

Answers

The probability of selecting a 10 or Diamond when a card is drawn from a standard deck of cards is: 17/52

The question asks us to find the probability of picking a 10 or diamond from a deck of cards.

A standard deck of cards contains 52 cards in total.

The deck contains 4 "10s"

And the deck also contains 13 diamond cards.

Thus, we can find the probability of drawing a "10" as:

[tex]P(10)=\frac{n\text{umber of 10s}}{total\text{ number of cards in deck}}=\frac{4}{52}[/tex]

Similarly, we can find the probability of drawing a diamond as:

[tex]P(\text{diamond)}=\frac{n\text{umber of diamonds}}{total\text{ number of cards in deck}}=\frac{13}{52}[/tex]

Now that we have the individual probabilities, we can find the probability of drawing a 10 or a diamond using the OR probability:

[tex]\begin{gathered} P(A\text{ OR B)= P(A) + P(B)} \\ \text{where, A and B are independent events} \end{gathered}[/tex]

Therefore, we can solve the question. This is done below:

[tex]\begin{gathered} \text{Probability of selecting a 10 or a diamond P(10 OR Diamond)=} \\ P(10)+P(\text{Diamond)} \\ \\ \text{But P(10)=}\frac{4}{52} \\ P(\text{Diamond)}=\frac{13}{52} \\ \\ \therefore P(10\text{ OR Diamond)=}\frac{4}{52}+\frac{13}{52}=\frac{17}{52} \end{gathered}[/tex]

Thus, the probability of selecting a 10 or Diamond when a card is drawn from a standard deck of cards is: 17/52

10. Given: BD || CE25= 26Prove: AC = AE(a) BD ICE(b) AC AE(c) 25* LC; 26 = LE(d) 25 = 26(e) LC= LE6DE

Answers

The image contains a figure in which angles and sides are named, some data is given, and the proof is to be provided.

Every proof starts with the given data.

Thus, from the options, we select those containing the information provided:

a) BD is parallel to CE

d) Angle 5 is congruent to angle 6

Now we can see the segments AB and AD have one tick mark. This means they are congruent or have the same measure.

AB is congruent to AD

The triangle ABD, having two equal sides, is isosceles. Every isosceles triangle has two congruent angles, in this case, angles 5 and 6.

Thus, the next step in the proof is:

c) Angle 5 is congruent to C and angle 6 is congruent to E

Because of the transitive property of congruence, it follows:

e) Angles C and D are congruent

Being two angles in a triangle congruent, it follows the triangle is isosceles, thus:

b) AC and AE are congruent

This is the final step of the proof

A-) who won the race? a1)By how many yards of difference? B-) How many yards behind the starting line does Yolanda have to leave for the race to end in a draw?

Answers

EXPLANATION

Let's see the facts:

Race = 100-yard

Toko--> 10 yards < Yolanda

Second part:

Yolanda --> 10 yards behind the starting line

If each geil ran at the same speed as the first race, the appropiate relationship is as follows:

Yolanda's speed = 100 yards/race

Yoko's speed = 90 yards/race

Distance= ratex time

For the second race, Yolanda ran 110 yards at the same speed --> So it will take 110/100 = 1.1 times to finish the race.

Yoko runs 100 yards at the same speed so it will take her 100/90= 1.11111... times to finish the run.

As 1.11 is less time than 1.1111, Yolanda will win the race.

b) In order to finish in a tie, the times must be the same.

Let x be the head start given to Yoko so that they tie.

time = distance / rate

[tex]\frac{100+x}{100}=\frac{100}{90}[/tex]

Multiplying both sides by 100:

[tex]100+x=100\cdot\frac{100}{90}[/tex]

Subtracting -100 to both sides:

[tex]x=100\cdot\frac{100}{90}-100[/tex]

Simplifying:

[tex]x=111.11111\ldots-100=11.111\ldots[/tex]

So, if Yoko has 11.111... head start, they should tie on the next race.

Instructions for a chemical procedure state to mix salt, baking soda, and water in a 22 : 14 : 5 ratio by mass. How many grams of baking soda would be required to make a mixture that contains 55 grams of salt?

Answers

35 grams of baking soda will be required for the mixture

The ratio of mix salt to baking soda to water = 22:14:5

Let x be the total quantity of the mixture

A mixture is a substance composed of two or more unrelated chemical components. A physical blending of two or more substances that maintains their own identities takes the form of solutions, suspensions, or colloids.

Now the sum of the ratio is 22+14+5 = 41

So, 55 grams of salt = 22/41x

Solving for x we get:

x = 55*41/22

x = 102.5 grams

The total quantity of the mixture is 102.5 grams

Quantity of baking soda required = 14/41 of 102.5

= 14/41*102.5

= 35 grams

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19. Which repon(s) represent students that enjoy wimming and tennis?TennisSwimmingAFHikingA BBDC. (BAND D)D. IA AND C)

Answers

To determine the regions that represent the students that enjoy swimming and tennis, we need to determine the intersection between the Swimming group and the Tennis group. This intersection is represented by the groups B and D. The correct answer is C.

LOTS OF POINTS!!!!! The table of values represents a linear function g(x), where x is the number of weeks that have passed and g(x) is the balance in the bank account. Find the slope of the function.

A.
-500

B.
-1/100

C.
-100

D.
-1/500

Answers

Answer: easy it's A -500

The slope of the function (x) is -500!! :D

The number of people in thousands who own a cell phone is a function of the time in years starting in 1990 where p(t) = 20(1.075)^tGrowth or Decay?What is the initial amount of people who own cell phones?Determine the growth/decay rate.

Answers

Solution

[tex]\begin{gathered} 1)\text{ Answer, This is GROWTH } \\ 2)\text{ The initial amount of people wo own a cell phone is },\text{ means when t = 0} \\ P(t)=20(1.075)^t \\ p(t)\text{ = }20(1.075)^0 \\ p(t)\text{ = 20 }\times\text{ 1} \\ p(t)\text{ = 20} \end{gathered}[/tex][tex]\begin{gathered} 3)\text{ To }\det er\min e\text{ the growth/decay rate, we have} \\ p(t)=20(1.075)^t \\ p(t)=20(1+0.75)^t \\ \text{Answer, growth rate is: 0.75 =0.75\%} \\ \end{gathered}[/tex]

The table shows the linear relationship between the balance of a student's savings account and the number of weeks he has been saving Savings Account Week 0 1 13 Balance (dollars) 123 Based on the table, what was the rate of change of the balance of the student savings account in dollars and cents per week?

Answers

7 dollars per week

Explanation:

Rate of change = change in balance (dollars)/change in weeks

for (0, 32) and (1, 39)

Rate of change = (39 - 32)/(1 - 0)

Rate of change = 7/1 = 7

For (1, 39) and (3, 53)

Rate of change = (53 - 39)/(3 - 1)

Rate of change = 14/2

Rate of change = 7

Since the rate of change is constant from calculation, then the rate of change of the balance of the student savings account in dollars and cents per week is 7 dollars per week

Luisa bought 4.4 kilograms of apples. How
many ounces of apples did she buy? Use the
conversion rates 1 kilogram = 2.20 pounds
and 1 pound = 16 ounces. Round to the
nearest ounce.

Answers

Answer:

155

Step-by-step explanation:

4.4(2.2)=9.68

9.68(16)=154.88

Hi Please help me with math

Answers

Answer:12

Step-by-step explanation:

Please help! Will give brainliest!

Answers

f’(1)=-20
f’(-1 x 2) =-5

Equation: y =
Write an equation of the line that passes through the given point and is parallel to the given I
(-4, 2); y = 1/4x + 1

Answers

The equation of the line that passes through the point (-4,2) and the parallel to the line y = 1/4x + 1 is y = (1/4)x+3

The equation of the line parallel to the line is

y = 1/4 x +1

The slope intercept form is

y = mx + b

Where m is the slope of the line and b is the y intercept

By comparing the given equation and slope intercept form of the line

The slope of the line is m = 1/4

Then the point slope form is

[tex](y-y_1)= m(x-x_1)[/tex]

The line is passing through the point (-4,2)

Substitute the values in the equation

(y-2) = 1/4(x-(-4))

y-2 = 1/4(x+4)

y-2 = (1/4)x+1

y = (1/4)x+3

Hence, the equation of the line that passes through the point (-4,2) and the parallel to the line y = 1/4x + 1 is y = (1/4)x+3

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Question: Between what two conSecutive integers does v145 fall?{ } { }

Answers

We can find the answer to this question by using the known exact square roots of the following numbers:

[tex]\begin{gathered} \sqrt[]{144}=12 \\ \sqrt[]{169}=13 \end{gathered}[/tex]

And as you can see, the number 145 is between 144 and 169.

Thus, its square root, must be between the integer values of 12 and 13.

7. Write the slope-intercept form of the equation of the line through the given point with the given slope. Write answer as y=mx+b. through: (-1, 1), slope = -6 Vour answer

Answers

Answer:

y = -6x - 5

Explanation:

The equation of a line with slope m that passes through the point (x1, y1) can be calculated using the following equation:

[tex]y-y_1=m(x-x_1)[/tex]

So, replacing (x1, y1) by (-1, 1) and m by -6, we get:

[tex]\begin{gathered} y-1=-6(x-(-1)) \\ y-1=-6(x+1) \end{gathered}[/tex]

Now, to write the answer as y = mx + b, we need to solve the equation for y, so we get:

[tex]\begin{gathered} y-1=-6(x)-6(1) \\ y-1=-6x-6 \\ y-1+1=-6x-6+1 \\ y=-6x-5 \end{gathered}[/tex]

Therefore, the answer is y = -6x - 5

find the x and y intercepts of 2x-5y=12 (write all answers as points)

Answers

[tex]\begin{gathered} x-\text{intercept is (6,0)} \\ y-\text{intercept is (}0,\text{ -}\frac{12}{5}) \end{gathered}[/tex]

Here, we want to find the x and y intercepts of the given line

We start by writing the equation of the line in the standard form

The standard form is;

[tex]y\text{ = mx + b}[/tex]

where m is the slope and b is the y-intercept

We have the equation re-written as;

[tex]\begin{gathered} 5y\text{ = 2x - 12} \\ y\text{ = }\frac{2}{5}x\text{ - }\frac{12}{5} \end{gathered}[/tex]

As we can see, we have the y-intercept at the point y = -12/5

The coordinate form at this point is (0,-12/5)

To find the x-intercept, we simply set y to zero

This is;

[tex]\begin{gathered} 0\text{ = }\frac{2}{5}x\text{ - }\frac{12}{5} \\ \\ \frac{2}{5}x\text{ = }\frac{12}{5} \\ \\ 2x\text{ = 12} \\ x\text{ = }\frac{12}{2} \\ x\text{ = 6} \end{gathered}[/tex]

The x-intercept is thus (6,0)

Polygon KLMN is drawn with vertices at K(1, 5), L(1, 0), M(−1, −1), N(−4, 2). Determine the image vertices of N′ if the preimage is rotated 90° counterclockwise. N′(−4, 2) N′(4, −2) N′(−2, −4) N′(2, 4)

Answers

ANSWER

N'(-2 , -4) Option C

EXPLANATION

Given:

A polygon KLMN with vertices at K(1, 5), L(1, 0), M(−1, −1), N(−4, 2).

Desired Outcome:

Image vertices of N′ if the preimage is rotated 90° counterclockwise

Answer: The correct answer is C

Step-by-step explanation:

I was correct on the quiz. WOWWWW

help meeeeeee pleaseee !!!!

Answers

The equation of the line that passes through point (8,-1) and perpendicular to 8y = x - 16 is f(x) = -8x + 63.

What is the equation of line that passes through the given points and is perpendicular to the given line?

Given the data in the question;

Equation of line: 8y = x - 16Point: (8,-1)

First we determine the slope of the initial line using the slope intercept-form. y = mx + b

8y = x - 16

y = (1/8)x - 2

Compared with the slope intercept form,

Slope m = 1/8

Now, for the equation of line perpendicular to the initial line, its slope must be a negative reciprocal of the initial slope.

Hence, slope of the perpendicular line is;

Slope m = -1/1/8 = -8

To find the equation of the perpendicular line, we use the point slope formula.

y - y₁ = m( x - x₁ )

Plug in the slope m ( -8) and point (8,-1).

y - (-1) = (-8)( x - 8 )

y+1 = -8x + 64

y = -8x + 64 - 1

y = -8x + 63

Therefore, the equation of the perpendicular line is y = 8x + 63

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Maleri Designs sells cartons of cloth face masks ($18) and cartons of hand-sanitizer ($9) on eBay. One of their
customers, Mod World, purchased 21 cartons for $297. How many of cartons of each did Mod World purchase?
Check your answer. Hint: Let F= Face masks.

Answers

Answer:

F=12 C=9

Step-by-step explanation:

$18 12 times is $216 $9 9 times is $81 $216+81=$297

Find the value of X in the length of VR

Answers

Since V is between R and T, then:

[tex]RT=VR+VT\text{.}[/tex]

Substituting VR=3x, VT=5x+9, RT=33, and solving for x we get:

[tex]\begin{gathered} 33=3x+5x+9, \\ 33=8x+9, \\ 33-9=8x, \\ 8x=24, \\ x=3. \end{gathered}[/tex]

Substituting x=3 in VR we get:

[tex]\text{VR}=3\cdot3=9.[/tex]

Answer:

The value of x is 3.

The length of VR is 9.

If 35% of your candies was 42 candies, how many candies do you have?

Answers

Answer:

120 candles

Step-by-step explanation:

42/35 = x/100 and solve for x

x = 120

Answer:

120

Step-by-step explanation:

35%/100=42/x

in a classroom challenge,students had to create a triangular pyramid using various items. Each group then use your measurements to remind the volume . which group found the volume of triangle pyramid with a base area of 16 square in?

Answers

[tex]\frac{1}{3}(\frac{8×4}{2})\times q\text{ (option D)}[/tex]Explanation:

Volume of a triangular pyramid = 1/3 × base area × height

We have been given base area as 16 square in

Volume of a triangular pyramid = 1/3 × 16 × height

We need to check the options for the expression whose result will give a base area of 16 square in.

From the options:

(8×3)/2 = 12

(11×4)/2 = 22

(16 ×18)/2 = 144

(8 × 4)/2 = 16

1/3 and the height is common to all options. The expression in bracket represent the base area.

Hence, the group that found the volume of triangle pyramid with a base area of 16 square in is

[tex]\frac{1}{3}(\frac{8 ×4}{2})\times q\text{ (option D)}[/tex]

Tank B, which initially contained 80 liters of water, is being drained at a rate of 2.5 liters per minute. For how many minutes has the water been draining when Tank B contains 75 liters of water?

Answers

We get that the function that models this situation is

[tex]L=80-2.5m[/tex]

where L is the liters the tank contains and m is the minutes that has passed. So we get:

[tex]75=80-2.5m\rightarrow m=\frac{-80+75}{-2.5}=2[/tex]

so the tank has been drained for 2 minutes

Find the length of the minor axis of the ellipse described by the equation:x squared over 12 plus y squared over 13 equals 1

Answers

This equation of the ellipse can be modeled by

[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]

The major axis is the y-axis and minor axis is the x-axis.

So, the length of the minor axis of this ellipse is "2a".

First, let's find "a",

[tex]\begin{gathered} a^2=12 \\ a=\sqrt[]{12} \end{gathered}[/tex]

The length of the minor axis is >>>

[tex]\begin{gathered} 2a \\ =2(\sqrt[]{12}) \\ =2\sqrt[]{12} \end{gathered}[/tex]Answer[tex]2\sqrt[]{12}[/tex]

18. ALGEBRA Angles Q and R are supplementary. If m angle Q = 4x + 9 and m angle R = 8x + 3, what is the measure of each angle?

Answers

[tex]\begin{gathered} \text{When angles are supplementary, it means the sum of the Two angles is 180}^{\circ} \\ \text{ Q + R = 180}^{\circ} \\ (\text{ }4X\text{ + 9 ) + (8X + 3) = 180} \\ \text{ 4X + 9 + 8X + 3 = 180} \\ \text{ 12X + 12 = 180} \\ \text{ 12x = 180 -12} \\ \text{ 12X = 168} \\ \text{ X = }\frac{168}{12} \\ \text{ X = 14} \\ Angle\text{ Q = 4x + 9} \\ \text{ = 4 }\times\text{ 14 + 9 = }65^{\circ} \\ ^{^{\text{ }}}\text{ }Angle\text{ R = 8x + }3 \\ \text{ = 8 }\times\text{ 14 + 3} \\ \text{ =}112+3=115^{\circ} \end{gathered}[/tex]

Orlandis earned 2.5% interest on a bank balance of $80. What is the amount of interest earned?

Answers

Given

Bank balance = $80

Interest rate = 2.5%

Amount of interest earned = 2.5% of $80

Amount of interest earned = 2.5/100 of $80

Amount of interest earned = (2.5*80)/100

Amount of interest earned = 200/100

Amount of interest earned = $2.0

hence the amount of interest rate is $2.0

Suppose 72% of students chose to study French their freshman year, and that meant that there were 378 such students. How many students chose not to take French their freshman year?

Answers

The number of students who chose not to take French their freshman year is 147.

According to the question,

We have the following information:

72% of students chose to study French their freshman year.

Now, 72% of students is equal to 378.

Let's take the number of students to be x.

So, we have:

72x/100 = 378

72x = 378*100

x = (378*100)/72

x = 525

Now, we have to find the number of students who chose not to take French their freshman year:

(100%-72%)

28%

Now, we have to find the 28% of total number of students:

(28*525)/100

14700/100

147

Hence, the number of students who chose not to take French their freshman year is 147.

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A+(b+c)=(a+b)+c what property is this? The options are as follows
Identity property of multiplication
Associative property of multiplication
Identity prop. Of addition
Multiplicative inverse prop.
Additive inverse prop.
Commutative prop of addition
Commutative prop of multiplication
Transitive property
Properties

Answers

Given:

The properties and their notations are given.

To match:

Explanation:

31. It is given that,

[tex]a+0=a[/tex]

Since zero is the additive identity.

So, the property is an identity property of addition.

32. It is given that,

[tex]a+b=b+a[/tex]

Here, the property is the commutative property of addition.

33. It is given that,

[tex]a\cdot(b\cdot c)=(a\cdot b)\cdot c[/tex]

Here, the property is an Associative property of multiplication.

34. It is given that,

[tex]a+(-a)=0[/tex]

Since -a is the additive inverse of a.

So, the property is the Inverse property of addition.

35. It is given that,

[tex]a\cdot1=a[/tex]

Since 1 is the multiplicative identity.

So, the property is an identity property of multiplication.

36. It is given that,

[tex]a\cdot(b+c)=ab+ac[/tex]

Here, the property is a distributive property of addition.

37. It is given that,

[tex]a\cdot b=b\cdot a[/tex]

Here, the property is a commutative property of multiplication.

38. It is given that,

[tex]a\cdot\frac{1}{a}=1[/tex]

Here, the property is an inverse property of multiplication.

39. It is given that,

[tex]a+(b+c)=(a+b)+c[/tex]

Here, the property is an Associative property of addition.

Final answer:

31. E

32. A

33. D

34. AC

35. AB

36.

Can someone please help me solve this pleaseeee, I’m struggling and depressed

Answers

Step-by-step explanation:

your teacher gave you the formula, the values, even did the tricky part by telling you that 63 months are 5.25 years.

all you need to do is put everything into the formula and calculate.

so, calm down, breathe and just use common sense :

after 2 years (means t = 2) :

2000 × (1.025)^(2×2) = 2000 × (1.025)⁴ =

= 2000 × 1.103812890625 =

= $2,207.62578125 ≈ $2,207.63

as rounding to the nearest cent means rounding to 2 positions after the decimal point.

after 63 months = 5.25 years (t = 5.25)

2000 × (1.025)^(2×5.25) = 2000 × (1.025)^10.5 =

= 2000 × 1.295986825... =

= $2,591.973651... ≈ $2,591.97

$2,000

because, even t = 0 we have

2000 × (1.025)^(2×0) = 2000 × (1.025)⁰ = 2000 × 1 =

= $2,000

Due to increased mailing costs, the new rate will cost publishers $50 million; this is 12.5% more than they
paid the previous year. How much did it cost publishers last year? Round to the nearest hundreds.

Answers

The amount it will cost the publishers last year is 44.4 million

How to calculate the amount it will cost the publishers?

The first step is to write out the parameters

The cost of mailing increased for the last one year

Due to this increase, it will cost the publishers $50 million for this current year

The increase is at the rate of 12.5%

The amount it will cost the publishers last year can be calculated as follows

= 12.5/100

= 0.125 + 1

= 1.125

The next step is to calculate last year cost

last year cost= 50/1.125

= 44.4 million

Hence the publishers spent 44.4 million last year