If f(x) = 3x + 10 and g(x) = 2x– 4, find (f+ g)(x).

Answer:

There are no extraneous solutions

Reasoning:

An extraneous solution is a solution that isn't valid, it might be imaginary like the square root of a negative number.

first we want to isolate z:

1+sqrt(z)=sqrt(z+5)

^2 all      ^2 all

(1+sqrt(z))(1+sqrt(z))=z+5

expand

1+2sqrt(z)+z=z+5

-1              -z  -z -1

2sqrt(z)=4

/2           /2

sqrt(z)=2

^2 all    ^2 all

z=4

Since there is one solution and it is a real number, there are no extraneous solutions.

[tex]D:z\geq 0\wedge z+5\geq 0\\D:z\geq 0\wedge z\geq -5\\D:z\geq0\\\\1+\sqrt z=\sqrt{z+5}\\1+2\sqrt z+z=z+5\\2\sqrt z=4\\\sqrt z=2\\z=4[/tex]

[tex]4\in D[/tex] so there are no extraneous solutions.

x-3y= 1

The equation needs to be rewritten in proper Slope intercept form ( y = mx+b) where m is the slope and b is the y-intercept.

x-3y = 1

Subtract x from each side:

-3y = 1-x

Divide both sides by -3:

y = 1/-3 - x/-3

Simplify:

y = 1/3x - 1/3

The slope is 1/3

Answer:

9√3in^2 hope this helps. found an answer...

Answer:

9 sqrt 3

Step-by-step explanation:

It was correct on my quiz

1/4 x 6 squared x sqrt 3

Answer: b

Step-by-step explanation:

The boxplot of the distribution 66, 62, 58, 52, 48, 46, 44, 34, 33, 31, 31, 30, 27, 25, 24, 21, and 19 is given below.

The correct option is B.

The given distribution is as follows: 66, 62, 58, 52, 48, 46, 44, 34, 33, 31, 31, 30, 27, 25, 24, 21, 19.

To create a boxplot, we need to identify the minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum values.

Arranging the data in ascending order, we have: 19, 21, 24, 25, 27, 30, 31, 31, 33, 34, 44, 46, 48, 52, 58, 62, 66.

The minimum value is 19, the maximum value is 66, and the median (Q2) is the middle value of the sorted data, which is 33.

To find the quartiles, we need to locate the positions that divide the data into quarters. The lower quartile (Q1) is the median of the lower half of the data, and the upper quartile (Q3) is the median of the upper half.

Counting from the minimum, we find that Q1 is 27, and counting from the maximum, we find that Q3 is 48.

With this information, the box plot is given in the attached image below.

Therefore, the correct option is B.

To learn more about the box-and-whisker plot ;

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Answer:

The game’s expected value of points earned for a turn is 71.

Step-by-step explanation:

Here we know that:

Points     Frequency

50           55

75            32

150          13

Here points earned is a random variable.

We need to find its expected value,

Finding Expected value:

Expected value of a random variable is its mean value. So we will first find the mean value of points earned per turn from the table we are given.

Total number of turns = sum of frequencies

= 55 + 32 + 14 = 100

Total points earned = 50(55) + 75(32) + 150(13)

= 7100

Expected value of points earned for a turn = Mean value of points

= Total points/no. of turns

= 7100/100

= 71

Answer:

A and E

Step-by-step explanation:

A line has a slope of -4/5, then a perpendicular line has a slope 5/4, because

[tex]-\dfrac{4}{5}\cdot \dfrac{5}{4}=-1[/tex]

Find the slopes of the lines in all options:

A. True

[tex]\dfrac{5-0}{2-(-2)}=\dfrac{5}{4}[/tex]

B. False

[tex]\dfrac{-5-5}{4-(-4)}=-\dfrac{5}{4}[/tex]

C. False

[tex]\dfrac{0-4}{2-(-3)}=-\dfrac{4}{5}[/tex]

D. False

[tex]\dfrac{-5-(-1)}{6-1}=-\dfrac{4}{5}[/tex]

E. True

[tex]\dfrac{9-(-1)}{10-2}=\dfrac{5}{4}[/tex]

Answer:

C

Step-by-step explanation:

=(0-4)/(2+3)

=-4/5

Answer:

61300000000000000

Step-by-step explanation:

Multiplying 20,000,000,000,000 by 3,065 results in 61,300,000,000,000,000.

Write down the numbers in standard form:

2 x[tex]10^{13}[/tex] for 20,000,000,000,000 and

3.065 x 10³ for 3,065.

Multiply the two standard forms:

(2 x [tex]10^{13}[/tex]) * (3.065 x 10³).

Combine the powers of 10:

2 * 3.065 = 6.13 and

[tex]10^{13}[/tex] * 10³ = [tex]10^{16}[/tex]

The result is 6.13 x [tex]10^{16}[/tex]

In standard numerical form, this is 61,300,000,000,000,000.

So, 20,000,000,000,000 x 3,065 equals 61,300,000,000,000,000.

Complete Question:

Multiply 20000000000000 x 3065.

Answer:

[tex]x=-243[/tex]

Step-by-step explanation:

The equation is

[tex]-3^{-5}=\frac{1}{x}[/tex]

Solve for x

we know that

[tex]-3^{-5}=-\frac{1}{3^{5}}=-\frac{1}{243}[/tex]

substitute

[tex]-\frac{1}{243}=\frac{1}{x}[/tex]

so

[tex]x=-243[/tex]

Answer:

-5

Step-by-step explanation:

Answer:

$29.99

Step-by-step explanation:

This is a division problem.

$209.93/7 = $29.99

Answer: $29.99

Answer:

$29.99

Step-by-step explanation:

$209.93 divided by 7 is $29.99

Answer:

7

Step-by-step explanation:

This operation is identical to subtracting 6 from 13.  The correct result is 7.

Answer:

Option 4 is correct.

Step-by-step explanation:

Given the following options

we have to choose the difference of cubes.

Option 1:

[tex]9w^{33}-y^{12}[/tex]

[tex]9(w^{11})^{3}-(y^4)^3[/tex]

which is not the difference of cubes

Option 2:

[tex]18p^{15}-q^{21}[/tex]

[tex]18(p^5)^3-(q^7)^3[/tex]

which is not the difference of cubes

Option 3:

[tex]36a^{22}-b^{16}[/tex]

[tex](6a^{11})^2-(b^8)^2[/tex]

which is the difference of square

Option 4:

[tex]64c^{15}-a^{27}[/tex]

[tex](4c^5)^3-(a^9)^3[/tex]

which is the difference of cubes.

Answer:

(7x + 3y)(7x + 3y)  or we could write it as (7x + 3y)^2.

Step-by-step explanation:

49x 2 + 42xy + 9y 2

The square root of 49xy^2 = 7x and the square root of 9y^2 = 3y.

Now  7x *3y = 21xy  and 2 * 21xy  = 42xy so the factors are:

(7x + 3y)(7x + 3y).

49x 2 + 42xy + 9y 2 is a perfect square trinomial.

Answer:

[tex](7x+3y)(7x+3y)[/tex]

Step-by-step explanation:

We are given that an expression

[tex]49x^2+42xy+9y^2[/tex]

We have to find the factor of given expression

[tex](7x)^2+2\times (7x)\times 3+(3y)^2[/tex]

Identity:[tex](a+b)^2=a^2+2ab+b^2[/tex]

Using the identity,then we get

[tex](7x+3y)^2[/tex]

[tex](7x+3y)(7x+3y)[/tex]

Hence, the factor of given expression is given by

[tex](7x+3y)(7x+3y)[/tex]

Answer:

10

Step-by-step explanation:

x=2

f(2)=5x3-2=15-2=13/2=6.5=f

g(2)=2+1=3/2=1.5=g

(6.5-1.5)(2)=(13-3)=10

Answer:

5x³ - x - 3

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

f(x) - g(x)

= 5x³ - 2 -(x + 1) = 5x³ - 2 - x - 1 = 5x³ - x - 3

Answer:

Step-by-step explanation:

it will have no sol. when a1/a2=b1/b2!=c1/c2

!= means not equal to

kx+3y=k+2

kx+3y-(k+2)=0 equation 1

12x+ky=0

taking a1/a2=c1/c2

k/12=3/k

k^2=36

k=6

when k= 6 it will have no sol

Answer:

x=-15

Step-by-step explanation:

Change 2 to a denominator of 4 2x4=8

1/12x+8/4=3/4 (take away 8/4)

1/12x=-5/4 ( 5multiply by 12)

x=-60/4 (divided by 3)

x=-15

Step-by-step explanation:

2x + 2y = 184 ---- eqn 1

y = 184 - 2x / 2

y = 92 - x ---- eqn 2

In thinking about what number each term may be multiplied by to eliminate the fractions, we can take one of two courses:

1) Find the lowest common multiple, ie. the lowest value that each of the fraction denominators have in common as a multiple.

Now a multiple is basically that number multiplied by an integer - for example, multiples of 2 are 2, 4, 6, 8, 10, etc.

So, let us write out the first few multiples for each of the denominator values:

4 (from 3/4): 4, 8, 12, 16, 20

3 (from 1/3): 3, 6, 9, 12, 15, 18

2 (from 1/2): 2, 4, 6, 8, 10, 12, 14, 16

Looking at the values above, we can see that the lowest value that occurs in all three sets of numbers is 12, thus 12 is the lowest common multiple.

Therefor, in order to eliminate the fractions before solving, each term must be multiplied by 12.

2) You could alternatively try multiplying the equation (or simply each fraction) by each of the possible answers and seeing if that will eliminate all of the fractions - this may seem quicker at first but it is always worthwhile understanding how to calculate this question without having possible answers, and as you complete more questions, the process of finding the lowest common multiple will become more natural and even quicker in the end. Nonetheless, let us try this method:

a) Multiplying each fraction by 2

(3/4)*2 = 3/2

This does not eliminate the fraction, therefor 2 is not the answer.

b) Multiplying each fraction by 3

(3/4)*3 = 9/4

This does not eliminate the fraction, thus 3 is not the answer.

c) Multiplying each fraction by 6

(3/4)*6 = 9/2

This does not eliminate the fraction, therefor 6 is not the answer.

d) Multiplying each fraction by 12

(3/4)*12 = 9 (this works so far)

(1/3)*12 = 4 (this also works so far)

(1/2)*12 = 6 (this also works)

Since multiplying each fraction by 12 will eliminate the fractions, 12 is the answer.

Answer:

D is the answer

Step-by-step explanation:

Answer:

5.

Step-by-step explanation:

What you require is the area of the rectangle  whose base is between 210 and 215.

The number having levels between 210 and 214

= 20 * the relative frequency

= 20 * 0.25

= 5 (answer).

Answer:

103

Step-by-step explanation:

Evaluate 4k2 + 3

To evaluate 4k² + 3, when k = 5, which means when you sees k, put 5 in replacement

4k² + 3 = 4(5)² + 3

4(5×5) + 3

4(25) + 3

open the bracket

4 × 25 = 100

∴ 100 + 3 = 103

Please mark me brainliest  

[tex]\text{Hey there!}[/tex]

[tex]\text{If k = 5 the replace the 'k' value with 5}[/tex]

[tex]\text{4(5)}^2+3[/tex]

[tex]\text{(5)}^2=5\times5=25[/tex]

[tex]\text{4 (25)+ 3 = ?}[/tex]

[tex]\text{4 (25) = 25 + 25 + 25 + 25 = 100}[/tex]

[tex]\text{100 + 3 = 103}[/tex]

[tex]\boxed{\boxed{\bf{Your\ answer: 103}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

9

Step-by-step explanation:

1 feet is 12 inches, so 12 feet is 12 * 12 = 144 inches.

If studs are placed 18 inches apart, in 144 inches, there will be:

[tex]\frac{144}{18}=8[/tex]

But remember, there is a stud at the very beginning (at 0 feet).

So in total there are going to be 9 studs

To find the number of studs placed on the wall, subtract 2 from the total number of spaces between the studs, making total as 10 studs.

To find the number of studs placed on the wall, we need to calculate the number of spaces between the studs.

Since there are studs on each end of the wall, we subtract 2 from the total number of spaces.

The wall is 12 feet long, which is equal to 12 * 12 = 144 inches.

Each stud is placed every 18 inches, so the number of spaces between the studs is 144 / 18 = 8.

Therefore, the total number of studs placed is 8 + 2 = 10 studs.

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Answer:

y=−x−1/3x−8

Step-by-step explanation:

y=8x−1/3x+1

To find the inverse function, swap x and y, and solve the resulting equation for x.

If the initial function is not one-to-one, then there will be more than one inverse.

So, swap the variables: y=8x−1/3x+1 becomes x=8y−1/3y+1.

Now, solve the equation x=8y−1/3y+1 for y.

y=−x−1/3x−8

Sorry I was in a rush and couldn't do the fractions as formulae. Hope it helped anyways.

The domain is the input value for x, which can be any real number.

The range would be the output value, which in this equation would be any number greater than 0.

The answer is B.

Answer:

ITS B

Step-by-step explanation:

Hope this helps

Answer: Another angle would be 65 and two other angles would be 115.

Step-by-step explanation: Attachment shown.

Answer:

Your answer is 56.

Step-by-step explanation:

To solve this problem, we simply need to plug in the given numbers into the expression.

If we do this, we get the following:

u + xy

2 + (9*6)

Using PEMDAS, we know that we have to perform the multiplication in this problem before the addition.  Thus the first step in simplification is multiplying 9 and 6 together.  If we do this, we get:

2 + 54

Next, we simply add together the two remaining terms.

54 + 2 = 56

Therefore, your answer is 56, the first option.

Hope this helps!

Answer:

Step-by-step explanation:

Use Angle Bisector theorem (look at the picture).

We have the equation:

[tex]\dfrac{3}{x}=\dfrac{x-4}{4}[/tex]        cross multiply

[tex]x(x-4)=(3)(4)[/tex]          use the distributive property

[tex]x^2-4x=12[/tex]           subtract 12 from both sides

[tex]x^2-4x-12=0\\\\x^2+2x-6x-12=0\\\\x(x+2)-6(x+2)=0\\\\(x+2)(x-6)=0\iff x+2=0\ \vee\ x-6=0[/tex]

[tex]x+2=0[/tex]        subtract 2 from both sides

[tex]x=-2<0[/tex]

[tex]x-6=0[/tex]       add 6 to both sides

[tex]x=6[/tex]

Answer:

Option A is the correct answer.

Step-by-step explanation:

Let the work plow a field be x.

Annmarie can plow a field in 240 minutes.

   Rate at which Annmarie can plow[tex]=\frac{x}{240}[/tex]

Gladys can plow a field 80 minutes faster

Time taken by Gladys = 240 - 80 = 160 minutes.

   Rate at which Gladys can plow[tex]=\frac{x}{160}[/tex]

If they combine time taken to plow [tex]=\frac{x}{\frac{x}{240}+\frac{x}{160}}=\frac{240\times 160}{240+160}=96\texttt{ minutes}[/tex]

Option A is the correct answer.

the time taken for Annmarie and Gladys to plow the field together is 96 minutes. The correct answer is A) 96 min.

Annmarie can plow a field in 240 minutes, and Gladys can do it in 160 minutes (since she is 80 minutes faster). To find out how long it would take for them to plow the field together, we can use the formula for combined work rates:

Let A be Annmarie's work rate and G be Gladys's work rate. Annmarie's work rate is 1 field per 240 minutes, or 1/240 fields per minute. Gladys's work rate is 1 field per (240 - 80) minutes, or 1/160 fields per minute.

Combined work rate of Annmarie and Gladys: A + G = 1/240 + 1/160.

Now, to find the time it would take them working together, we take the reciprocal of the combined work rate.

The combined work rate is:

1/240 + 1/160 = 1/240 + 1/160 = (1x160 + 1x240) / (240x160) = (160 + 240) / (240x160) = 400 / (240x160)

The time it takes for them to work together is the reciprocal of 400 / (240x160), which is (240x160) / 400.

Calculate: (240x160) / 400 = 38400 / 400 = 96

Therefore, the time taken for Annmarie and Gladys to plow the field together is 96 minutes. The correct answer is A) 96 min.

Answer:

x ≥ 176 and x ≤ 321

Step-by-step explanation:

Let

x -----> the number of steaks the restaurant owner can order

we know that

[tex]x\geq 176[/tex] ----> inequality A

[tex]x\leq 321[/tex] ----> inequality B

so

the compounded inequality is equal to

[tex]176 \leq x \leq 321[/tex]

Explanation of modeling the number of steaks a restaurant owner can order using a compound inequality.

To model the number of steaks the restaurant owner can order using a compound inequality, we represent the situation with x ≥ 176 and x ≤ 321. This means the owner can order any amount of steaks from 176 to 321. So, the correct compound inequality is x ≥ 176 and x ≤ 321.

Answer:

The area of the circle is [tex]A=6.25\pi\ units^{2}[/tex]

Step-by-step explanation:

step 1

Find the diameter of circle

we know that

The diameter of the circle is equal to the distance AB

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

substitute the values

[tex]AB=\sqrt{(5-1)^{2}+(5-2)^{2}}[/tex]

[tex]AB=\sqrt{(4)^{2}+(3)^{2}}[/tex]

[tex]AB=\sqrt{25}[/tex]

[tex]AB=5\ units[/tex]

therefore

the diameter of the circle is

[tex]D=5\ units[/tex]  

step 2

Find the area of the circle

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

[tex]r=5/2=2.5\ units[/tex]  ----> the radius is half the diameter

substitute

[tex]A=\pi (2.5)^{2}[/tex]

[tex]A=6.25\pi\ units^{2}[/tex]