What is the domain of the function y = 8x + 3/4

a) All real numbers
b) All real numbers except x = 4
c) All real numbers except x = -3/8
d) All real numbers except x = 3/8

the correct answer should be (b) 6 is extraneous.

If you look at the second row of the solution you see (x-6) as a factor in one of the denominators. That's a problem: if 6 were a solution this denominator would become 0. But denominators being 0 is bad (undefined), so while 6 comes out of the algebraic manipulation as a solution, it is invalid, or extraneous.

-3 is a fine solution.

The correct statement is B that is "6 is an extraneous solution because it creates a zero in the denominator" as the step 2 has x-6 as a term of denominator of the RHS.

The lower number in a fraction is known as the denominator. It demonstrates the equal division of something into parts. Four would be the denominator, for instance, if the fraction was 3/4. For instance, the fraction bar is the line that separates the numbers 4 and 5, and 4/5 is a fraction. Here, the numerator is the number above the fraction bar, and the denominator is the number below the fraction bar. The denominator, or number of parts out of the whole, is represented by a numerator. The bottom number alone serves as the denominator.

Here,

The right option is B, which means that "6 is an extraneous solution because it creates a zero in the denominator," since the RHS's step 2's denominator term is x-6.

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Look at the pictures (examples)

m∠1 = m∠6 → answer: none

m∠2 = m∠3 → answer: none

m∠2 = m∠C → answer: none

Answer:

B

Step-by-step explanation:

The two points going to the left that are roots are

(-3,0) and (-1,0)

So the factors are (x + 3)(x + 1)

The points going to the right are

(2,0)(3,0)

So the factors are (x - 2)(x - 3)

The answer is B

the answer to your question is B

Answer:

Step-by-step explanation:

s=5?

t=5?

3(5) - 3(5) +3

(15) -15 = 0

0 + 3 = 3

The value of 3s - 3t + 3 given that s - t = 5 is 18.

In this problem, we are given that s - t = 5. Now we have to find the value of 3s - 3t + 3. What we can do is factor out the '3' from 3s - 3t, then we can see it as 3(s - t) + 3. Our equation becomes 3 * 5 + 3 which simplifies to 15 + 3, and then 18.

So, the value of 3s - 3t + 3 given that s - t = 5 is 18.

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Answer : (0,3) U  (3, ∞)

We need to find  the interval(s) over which the function is decreasing

We look at the intervals of x  where the graph is decreasing

Decreasing interval of the graph is the part where the graph goes down

We look at the part where the graph changes direction

In the middle  inverted U shaped graph , the graph changes direction and start decreasing at x=0

the graph is decreasing till x=3

so first decreasing interval is x=0  to 3. we write it as (0,3)

After x=3 the graph starts decreasing and it goes to infinity

So the second decreasing interval is 3  to infinity . We write it as (3, ∞)

Now combine both intervals by a 'U' union

(0,3) U  (3, ∞)

Graph Behavior u3l10

1. (-∞,-1) U (-1,0)
2. (0,3) U (3,∞)
3. x-intercept: none | y-intercept: (0,-4)
4. x=-1, x=3, y=0
5. even
6. (-∞,-4)
7. x-intercepts: (0,0),(3,0) | y-intercepts: (0,0)
8. f(3)=6
9. There is a jump discontinuity at x=-3
10. neither
11. f(x)=x/x^8+8x^4-7 | f(x)=x^3+4x
12. f(x) --> -∞ as x --> ∞ and f(x) --> 0 as x --> -∞
13. 2nd and 3rd graph (2nd graph has left arm facing down and right arm facing up and 3rd graph looks like a W)
14. 1st and 4th graph (1st graph has 2 lines, the one on the left side is point upwards and the line on the right side is pointing downwards, 4th graph is 1 line with the left arm facing up and right arm facing down)
15. reciprocal; y=1/x
16. f(x)=x^3
17. power; y=x^n | root; y=n√x
18. power; y=x^n ; n is even and greater than 0 | absolute value; y=|x|
19. reflection over the x-axis | horizonal compression by a factor of 3
20. reflection over the y-axis | horizontal shift to the left 2 units
21. reflection
22. 1st graph (starts from the left side (-2,0) and points towards the right side a bit more downwards)
23. 1st graph (ill describe it as a right angle with the curve facing left on the negatives side or a point where the curve is on is (-2,0))

happy "studying"!

D. 27.6 is your answer

c or a !!!!!!!!!!!!!!!!!!!

Answer: [tex]4\frac{1}{7} ft[/tex]

Step-by-step explanation:

Area (A): [tex]36\frac{1}{4} = \frac{4(36)+1}{4} = \frac{144+1}{4} = \frac{145}{4}[/tex]

Length (L): [tex]8\frac{3}{4} = \frac{4(8)+3}{4} = \frac{32+3}{4} = \frac{35}{4}[/tex]

width (w): W

A = L x W

[tex]\frac{145}{4}[/tex] = [tex]\frac{35}{4}[/tex] x W

[tex](\frac{4}{35})[/tex][tex]\frac{145}{4}[/tex] = [tex](\frac{4}{35})[/tex][tex]\frac{35}{4}[/tex] x W

[tex]\frac{4(145)}{35(4)} = \frac{145}{35} = \frac{5(29)}{5(7)} = \frac{29}{7} = W[/tex]

[tex]\frac{29}{7} = \frac{7(4) + 1}{7} = 4\frac{1}{7}[/tex]

Let Upper Level = x

Middle level = 2x+40

Lower level = 3x-50

The sum of those 3 has to equal 15,002 seats.

X + (2x+40) + 3x-50) = 15, 002

Simplify the left side by combining the like terms:

6x - 10 = 15,002

Add 10 to each side:

6x = 15,012

Divide both sides by 6 to solve for x:

X = 15012 / 6

X = 2502

The upper level is X , so has 2,502 seats.

Middle level = 2x +40 = 2(2502) +b40 = 5004 + 40 = 5,044 seats

Lower level = 3x-50 = 3(2502) -50 = 7506 - 50 = 7,456 seats

The number of seats in the upper level is required.

The number of seats the upper level has is 2502.

Let the number of upper level seats be [tex]x[/tex]

The lower level seats are [tex]3x-50[/tex]

The middle level seats are [tex]2x+40[/tex]

The total number of seats are 15002

So,

[tex]x+3x-50+2x+40=15002\\\Rightarrow 6x-10=15002\\\Rightarrow x=\dfrac{15002+10}{6}\\\Rightarrow x=2502[/tex]

The number of seats the upper level has is 2502.

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The answers are 2 and 4

The graph of the equation is the set of all points that are solutions of the equation and point (10, 3) is on the graph of the equation thus, options (A) and (D) are correct.

A graph is a diametrical representation of any function between the dependent and independent variables.

The graph is easy to understand the behavior of the graph.

For example y = x² form a parabola now by looking at only the graph we can predict that it has only a positive value irrespective of the interval of x.

A graph is the locus of all points that are the solution of the function.

Substitute x = 10 into y = (1/2)x - 2

y = (1/2)10 - 2

y = 5 - 2 = 3 thus, (10,3) will be on the graph.

Hence "The graph of the equation is the set of all points that are solutions of the equation and point (10, 3) is on the graph of the equation".

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Answer:

Option C.

Step-by-step explanation:

A polynomial is defined as

[tex]P(x)=ax^n+bx^{n-1}+...+c[/tex]

where, [tex]ax^n[/tex] is leading term.

If n is even and a is positive, then the end behavior is up and up.

If n is even and a is negative, then the end behavior is down and down.

If n is odd and a is positive, then the end behavior is down and up.

If n is odd and a is negative, then the end behavior is up and down.

The given polynomial is  

[tex]P(x)=2x^7-8x^6-3x^5-3[/tex]

In this polynomial leading term is [tex]2x^7[/tex].

a=2 and n=7, which is odd.

Since n is odd and a is positive, therefore the end behavior is down and up.

We want to analyze the end behavior of a graph of a given polynomial by the degree and leading coefficient.

The correct option is C: "The leading term is 2x^7. Since n is odd and a is positive, the end behavior is down and up."

The general rule to know this is:

If the degree is even, then the two arms of the polynomial go in the same direction, then if the leading coefficient is positive, both ends go up.

If the leading coefficient is negative, both ends go down.

In the case where the degree is odd, each end go in a different direction.

If the leading coefficient is positive, the first end (the one for the negative values) go down, and the other end goes up.

When the leading coefficient is negative the inverse happens.

Here we have the polynomial:

p(x) = 2*x^7 - 8*x^6 - 3*x^5 - 3

We can see that the degree is 7, so it is odd, and the leading coefficient is positive (is equal to 2).

Then the first end goes down and the second goes up, thus the correct option is C.

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Answers: Angle A is 36 degrees, angle C is 54 degrees

=================================================================

Work Shown:

The angles A and C are complementary, meaning they add to 90 degrees.

(Angle A) + (Angle C) = 90

(2x-4) + (2x+14) = 90

(2x+2x)+(-4+14) = 90

4x+10 = 90

4x+10-10 = 90-10 .... subtract 10 from both sides

4x = 80

4x/4 = 80/4 ..... divide both sides by 4

x = 20

If x = 20, then,

angle A = 2x-4 = 2*20-4 = 40-4 = 36 degrees

angle C = 2x+14 = 2*20+14 = 40+14 = 54 degrees

Note how A+C = 36+54 = 90 which helps confirm our answers.

After investing $400 in an account with 3% interest compounded annually, the balance after one year will be $412.

The question is asking how much the balance will be after investing $400 in an account that pays 3% interest compounded annually after one year. The formula to calculate compound interest is [tex]A = P(1 +\frac{ r}{n})^{nt[/tex], where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years. As the interest is compounded annually, n is 1.

For this question, we substitute P with $400, r with 0.03 (3% as a decimal), n with 1 (since it's compounded annually), and t with 1 (since it's compounded for one year).

Now, our formula looks like this: [tex]A = 400(1 + \frac{0.03}{1})^{1*1[/tex] = 400(1 + 0.03) = 400 * 1.03 = $412.

Therefore, after one year, the balance in the account will be $412.

11.46% is the percent increase

Answer: The correct option is (B) [tex]\left(5,\dfrac{1}{2}\right).[/tex]

Step-by-step explanation: We are given to find the midpoint of the line segment shown in the figure.

From the figure, we see

a line segment with co-ordinates of the endpoints (5, 4) and (5, -3).

We know that

the co-ordinates of the midpoint of a line segment with endpoints (a, b) and (c, d) is given by

[tex]M=\left(\dfrac{a+c}{2},\dfrac{b+d}{2}\right).[/tex]

Therefore, the co-ordinates of the line segment shown is given by

[tex]M=\left(\dfrac{a+c}{2},\dfrac{b+d}{2}\right)=\left(\dfrac{5+5}{2},\dfrac{4-3}{2}\right)=\left(5,\dfrac{1}{2}\right).[/tex]

Thus, (B) is the correct option.

Hello,

The answer is A or y= 3/2x+9

How to solve;

The formula: Y=mx+b

Now solve the problem: 3x-2y=-18

Subtract -3x from both sides.

Now we have -2y=-3x-18

So divide both sides by y to get y by it self.

-2/-2=-3x-18/-2

Simplify and the answer is y=3/2x+9

Thus answer A

Hope that helps have a great day.

Answer:

D. two possible amounts by which the dimensions were increased

Step-by-step explanation:

The solutions to the equation (6 + x)(9 + x) = 88 represent two possible amounts by which the dimensions of the rectangular patio were increased.

The solutions to the equation (6 + x)(9 + x) = 88 represent two possible amounts by which the dimensions of the rectangular patio were increased. The equation represents the area of the larger patio, which is found by multiplying the increased length (6 + x) by the increased width (9 + x), and setting it equal to 88. By solving the equation, you can find the possible values of x, which represent the amounts by which the dimensions were increased.

QUESTION 1 ANSWER

The series is

[tex]\sum_{n=1}^{15}{ (2n-1)}[/tex]

So the nth term of this sequence is

[tex]U_n=2n-1[/tex]

We generate some few terms of the sequence as follows:

When [tex]n=1[/tex],

The first term of the sequence becomes,

[tex]U_1=2(1)-1[/tex]

[tex]U_1=1[/tex]

When [tex]n=2[/tex],

[tex]U_2=2(2)-1[/tex]

[tex]U_2=3[/tex]

When [tex]n=3[/tex],

[tex]U_2=2(3)-1[/tex]

[tex]U_2=5[/tex]

The constant difference is [tex]d=2[/tex].

The sum of the series is given by,

[tex]S_n=\frac{n}{2}(2a+(n-1)d)[/tex]

There are 15 terms in the series, therefore [tex]n=15[/tex]

 [tex]S_{15}=\frac{15}{2}(2(1)+(15-1)2)[/tex]

[tex]S_{15}=\frac{15}{2}(2+14(2))[/tex]

[tex]S_{15}=\frac{15}{2}(30)[/tex]

[tex]S_{15}=15\times 15[/tex]

[tex]S_{15}=225[/tex]

ANSWER TO QUESTION 2

The bottom row has [tex]23[/tex] boxes. This means [tex]a=U_1=23[/tex]

a) Since each row has 3 fewer boxes [tex]d=-3[/tex].

The nth row is given by,

[tex]U_n=23+(n-1)\times(-3)[/tex]

[tex]U_n=23+-3n+3[/tex]

[tex]U_n=23-3n[/tex]

The top row is the 6th row, meaning [tex]n=6[/tex].

[tex]U_6=23-3(6)[/tex]

[tex]U_6=23-18[/tex]

[tex]U_6=5[/tex]

b) The number of boxes in the entire display is given by

[tex]S_n=\frac{n}{2} (a+l)[/tex]

Where [tex]a=23[/tex], the first term(row) and [tex]l=5[/tex], the last term(row).

Since there are 6 rows,

[tex]S_6=\frac{6}{2} (23+5)[/tex]

[tex]S_6=3 (28)[/tex]

[tex]S_6=84[/tex]

ANSWER TO QUESTION 3

The number of visitors in the first week is [tex]a=5[/tex].

Since the number of visitors each week is doubled the number of visitors in the subsequent weeks, the sequence is a geometric progression with a common ratio of [tex]r=2[/tex].

The general term of a geometric sequence is

[tex]U_n=ar^{n-1}[/tex]

So in the 8th week, we have

[tex]U_8=5\times 2^{8-1}[/tex]

[tex]U_8=5\times 2^{7}[/tex]

[tex]U_8=5\times 128[/tex]

[tex]U_8=640[/tex]

Hence 640 people visited the website in the 8th week

14/25 , 29/50 , 53/100 , 13/20 and 3/5

Solution:

Put your numbers first in decimal form;

0.56 , 0.58 , 0.53 , 0.65 and 0.60

Then arrange them from the least to greatest;

0.53 , 0.56 , 0.58 , 0.60 and 0.65

Then revert your values to fraction form to give a final answer:

53/100 , 14/25 , 29/50 , 3/5 , 13/20

[tex]x^2+52=\\\\x^2-(-52)=\\\\(x-\sqrt{-52})(x+\sqrt{-52})=\\\\(x-2\sqrt{13}i)(x+2\sqrt{13}i)[/tex]

Answer: [tex]\text{Length of AG=}\frac{2\sqrt{63}}{3}[/tex]

Explanation:  

Please follow the diagram in attachment.  

As we know median from vertex C to hypotenuse is CM  

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

We are given length of CG=4  

Median divide by centroid 2:1  

CG:GM=2:1  

Where, CG=4

[tex]\therefore GM=2[/tex] ft

Length of CM=4+2= 6 ft  

[tex]\therefore CM=\frac{1}{2}AB\Rightarrow AB=12[/tex]

In [tex]\triangle ABC, \angle C=90^0[/tex]

Using trigonometry ratio identities  

[tex] AC=AB\sin 30^0\Rightarrow AC=6[/tex] ft

[tex] BC=AB\cos 30^0\Rightarrow BC=6\sqrt{3}[/tex] ft  

[tex] CN=\frac{1}{2}BC\Rightarrow CN=3\sqrt{3}[/tex] ft

In [tex] \triangle CAN, \angle C=90^0[/tex]  

Using pythagoreous theorem  

[tex]AN=\sqrt{6^2+(3\sqrt{3})^2\Rightarrow \sqrt{63}[/tex]

Length of AG=2/3 AN

[tex]\text{Length of AG=}\frac{2\sqrt{63}}{3}[/tex] ft

Trisha has 18 nickels and 14 dimes in her bag worth $2.80. The solution involves solving equations simultaneously to find the number of each coin.

Trisha has 18 nickels and 14 dimes. Let's break it down:

Let N represent the number of nickels and D represent the number of dimes.

We know that N + D = 32 (the total number of coins).

We also know that 0.05N + 0.10D = 2.80 (the total value in dollars).

Solving these two equations simultaneously gives N = 18 and D = 14.

Therefore, Trisha has 18 nickels and 14 dimes.

The answer is 256.25

EXPLANATION

Let [tex]x[/tex] represent the number.

Then, [tex]\frac{16}{100}x=41[/tex]

We cross multiply yo obtain,

[tex]16x=41\times 100[/tex]

We now divide both sides by 16.

[tex]x=\frac{4100}{16}[/tex]

This will give us,

[tex]x=256.25[/tex]

Therefore the number is 256.26

To find the number, divide 34,400 by 344%

To solve this problem, we need to translate the phrase into an equation and solve for the unknown number.

The phrase "344% of what number is 34,400" can be translated as 344% * x = 34,400.

To solve for x, we divide 34,400 by 344% or 3.44.

Therefore, the number is 10,000.

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To find the number, divide 34,400 by 344% (or 3.44), resulting in the number 10,000.

To solve this problem, we need to find what number 344% of is equal to 34,400. Here's how we can do it step by step:

Step 1:

Translate the problem into a mathematical equation.

Let's denote the unknown number as [tex]\( x \)[/tex]. The problem translates to:

[tex]\[ 344\% \text{ of } x = 34,400 \][/tex]

Step 2:

Rewrite the percentage as a decimal.

[tex]\[ 344\% = \frac{344}{100} = 3.44 \][/tex]

Step 3:

Write the equation using the decimal form of the percentage.

[tex]\[ 3.44 \times x = 34,400 \][/tex]

Step 4:

Solve for [tex]\( x \).[/tex]

[tex]\[ x = \frac{34,400}{3.44} \][/tex]

Step 5:

Perform the division.

[tex]\[ x = 10,000 \][/tex]

So, 344% of 10,000 is 34,400. Thus, the unknown number is 10,000.

a = 0.19

0.38/2 = 0.19

If s, r and t are given right lines in the same plane and with condition

s⊥t  and r⊥t we can conclude that s║r ( s and r are parallel).

Good luck!!!

The conclusion is;

line r and s are parallel lines.

Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other.

Given:

We have lines r, s and t in the same plane.

And s⊥t and r⊥t.

That means,

The conclusion is line r and s are parallel lines.

Therefore, r and s are parallel lines.

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To break even, the Waxmans need to make $5000 in profit. This can be achieved by selling 500 square yards of carpet, considering they make $10 profit per square yard.

In order for the Waxmans to break even, they will need to cover their startup costs through the profits they make selling carpet. The profit made per square yard of carpet sold is the selling price ($18) minus the cost per square yard ($8), which equals $10. Therefore, to break even, they would need to sell $5000 worth of profit. This means selling $5000/$10 = 500 square yards of carpet.

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