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Answer:

y = 3x - 8

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x + 9 ← is in slope- intercept form

with slope m = 3

• Parallel lines have equal slopes, thus

y = 3x + c ← is the partial equation of the parallel line

To find c substitute (2, - 2) into the partial equation

- 2 = 6 + c ⇒ c = - 2 - 6 = - 8

y = 3x - 8 ← equation of parallel line

Answer:

[tex](x + 3) {}^{2} - 16[/tex]

Step-by-step explanation:

[tex] {x}^{2} + 6x - 7 = (x + 3) {}^{2} - (3) {}^{2} - 7 \\ = (x + 3) {}^{2} - 16[/tex]

The equation x^2 + 6x - 7 can be written in the form (x+a)^2 + b as (x + 3)^2 - 16 by completing the square.

To solve this, we will complete the square for the polynomial x^2 + 6x - 7. The equation (x+a)^2 + b involves squaring a binomial (x+a) and adding a constant. Completing the square can convert x^2 + 6x - 7 to this form.

Step 1: Half of the coefficient of x is (6/2)=3 so a=3. Then we square a to get a^2 = 9.

Step 2: We adjust the original equation by subtracting and adding a^2 within it: (x^2 + 6x + 9) - 9 - 7.

Step 3: Simplify the equation to get (x + 3)^2 - 16, which is the form we desired.

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The answer is:

The correct option is the first option,

[tex]y=\frac{5}{4} (x-1)[/tex]

To solve this problem, we need to remember that the point-slope form of a line is given by the following equation:

[tex]y-y_{1}=m(x-x_{1})\\\\y-0=\frac{5}{4}(x-1)[/tex]

We are given two points of the line,

[tex](5,5)\\(1,0)[/tex]

Where,

[tex]x=5\\x_{1}=1\\y=5\\y_{1}=0\\[/tex]

Then, substituting the given points into the equation ,to calculate m (slope), we have:

[tex]m=\frac{y-y_{1}}{x-x_{1}}[/tex]

[tex]m=\frac{5-0}{5-1}=\frac{5}{4}[/tex]

The slope of the function is [tex]\frac{5}{4}[/tex]

Now, substituting "x1" and "y1" and the slope in the point-slope equation, we have:

[tex](y-0)=\frac{5}{4} (x-1)[/tex]

[tex]y=\frac{5}{4} (x-1)[/tex]

Hence, the correct option is the first option,

[tex]y=\frac{5}{4} (x-1)[/tex]

Have a nice day!

Answer:

The correct answer is first option

y = 5/4(x - 1)

Step-by-step explanation:

It is given two coordinates (5, 5) and (1, 0)

To find the slope

Slope = (y₂ - y₁)/(x₂- x₁)

slope = (5 - 0)/(5 - 1) = 5/4

To find the equation

(y - y₁)/(x - x₁) = 5/4

(y - 0)/(x - 1) = 5/4

y = 5/4(x - 1)

The correct answer is first option

her dance class start at quater past 4

Patti's dance class starts at a quarter past 4, which is 4:15 p.m. This term refers to 15 minutes after the hour.

This question demands basic understanding of clocks and related concepts.

Patti's dance class starts at quarter past 4, which means it starts at 4:15 p.m.. In time telling, a quarter past the hour refers to 15 minutes after the hour mark. So when you're looking at a clock, this would be the time when the minute hand is on the 3 (as there are 60 minutes in an hour and 15 minutes is a quarter of that).

Therefore, as per the above explaination, the correct answer is  4:15 p.m.

x^2 = x3

x^2 - 3x = 0

x(x - 3) = 0

x = 0 and x -3 = 0 or x = 3

x cannot equal zero, therefore the answer is three

The numbers that when squared equal to three times themselves are 0 and 3. This is found by solving the quadratic equation x² = 3x, which factors to x(x - 3) = 0.

To express this mathematically, we let 'x' represent the number, so the equation becomes x² = 3x. This is a quadratic equation that can be solved by rearranging the terms and factoring, resulting in x(x - 3) = 0. Applying the Zero Product Property, we have two potential solutions for x: 0 or 3. Therefore, the numbers that fit the condition are 0 and 3.

Answer:

if p(x) is the given polynomial then -p(x) represents its additive inverse.

Step-by-step explanation:

We need to explain about what is the addictive inverse of the polynomial.

We know that additive inverse of a polynomial is basically another polynomial that adds to the given polynomial to give result 0.

which can be done by take opposite sign of each term in the given polynomial.

For example if p(x) is the given polynomial then -p(x) represents its additive inverse.

8.99 rounded to 1 decimal place is 9.0, since the number after the decimal is 9, which is 5 or over, hence, the rounding up.

In mathematics, rounding means to replace a number with an approximate value that has a shorter, simpler, or more explicit representation. To round the number 8.99 to 1 decimal place, you need to look at the second number after the decimal point. Since that number is 9, which is 5 or over, we round up the first number after the decimal point, which is 8. Thus, 8.99 rounded to 1 decimal place is 9.0.

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Answer:

diabeties

Step-by-step explanation:

jfghnfuigbdihgbuneughei

The square root of 104 is approximately 10.198039, which can be confirmed using a calculator. It’s not a perfect square, so rounding it to 10.2 is often sufficient for practical purposes.

To find the square root of 104, we will use a calculator since it's not a perfect square. The square root of 104 is approximately 10.198039.

Here’s a step-by-step approach:

The exact value includes more decimal places, so for most purposes, you can round it to an appropriate value, such as 10.2 for simplicity.

Answer:

22x + 99

Step-by-step explanation:

Given

9(2x + 9) + 2(2x +9) ← factor out (2x + 9) from each term

= (2x + 9)(9 + 2)

= 11(2x + 9) ← distribute parenthesis

= 22x + 99

Here's two ways you can solve this exercise: you can expand the multiplications and sum like terms:

[tex]9(2x+9)+2(2x+9) = 18x+81+4x+18 = 22x+99[/tex]

Or you can factor the parenthesis:

[tex]9(2x+9)+2(2x+9) = (2x+9)(9+2) = 11(2x+9) = 22x+99[/tex]

For this case we must find the inverse of the following function:

[tex]f (x) = - \frac {1} {2} \sqrt {x + 3}[/tex]

We follow the steps below:

Replace f(x) with y:

[tex]y = -\frac {1} {2} \sqrt {x + 3}[/tex]

We exchange the variables:

[tex]x = - \frac {1} {2} \sqrt {y + 3}[/tex]

We solve for "y":

[tex]- \frac {1} {2} \sqrt {y + 3} = x[/tex]

Multiply by -2 on both sides of the equation:

[tex]\sqrt {y + 3} = - 2x[/tex]

We raise both sides of the equation to the square to eliminate the radical:

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

We subtract 3 from both sides of the equation:

[tex]y = 4x ^ 2-3[/tex]

We change y by f ^ {- 1} (x):

[tex]f ^ {- 1} (x) = 4x ^ 2-3[/tex]

Answer:[tex]f ^ {- 1} (x) = 4x ^ 2-3[/tex]

Answer:

[tex]f(x)^{-1}= 4x^{2} -3 [/tex] .

Step-by-step explanation:

Given : [tex]f(x) =-\frac{1}{2}\sqrt{x+3}[/tex].

To find : Find the inverse of the given function.

Solution : We have given

[tex]f(x) =-\frac{1}{2}\sqrt{x+3}[/tex].

Step 1: take f(x) = y

[tex]y =-\frac{1}{2}\sqrt{x+3}[/tex].

Step 2 : Inter change y and x.

[tex]x =-\frac{1}{2}\sqrt{y+3}[/tex].

Step 3 : Solve for y

Taking square both sides

[tex]x^{2} = \frac{1}{4}(y+3)[/tex].

On multiply both sides by 4.

[tex]4x^{2} = (y+3)[/tex].

On subtraction both sides by 3.

[tex]4x^{2} -3 = y[/tex].

Here, [tex]f(x)^{-1}= y[/tex] is inverse of f(x)

[tex]f(x)^{-1}= 4x^{2} -3 [/tex] .

Therefore, [tex]f(x)^{-1}= 4x^{2} -3 [/tex] .

Answer:

24 cubic feet

Step-by-step explanation:

The formula is V = Length x width x height

the first has a length of 2, a width of 2 and a height of 2 = 8 cubic feet

The second has a length of 4, a width of 2 and a height of 2 = 16 cubic feet

8 + 16 = 24 cubic feet

Three sides adds up to 3ft squared.

Answer:18

Step-by-step explanation:I did the question and got it right

Answer:

B

Step-by-step explanation:

The range is the set of y-values for which the function is defined.

** Attached is the graph of the function

By looking at the graph, we can clearly see that there aren't any y-values that is not permitted in the graph. The function is defined for all y-values. Hence the range is set of all real numbers, or, the range is (-∞, +∞)

Answer choice B is right.

Final answer:

The range of the reciprocal function 1/x is all real numbers except zero, expressed in interval notation as (-∞, 0) ∪ (0, +∞).

Explanation:

The range of the reciprocal function, which is denoted as 1/x, can be understood by considering the behavior of the function as x approaches different values. As x approaches zero from the positive side (x → 0+), the reciprocal 1/x becomes increasingly larger, theoretically 'going to infinity' (∞). Similarly, as x approaches zero from the negative side (x → 0-), 1/x becomes increasingly negative, 'going to negative infinity' (-∞). Thus, the range of the reciprocal function excludes zero, but includes all other real numbers. In interval notation, the range is expressed as (-∞, 0) ∪ (0, +∞).

Answer:

Step-by-step explanation:

If the polynomial is degree 2, then it has 2, 1 or 0 zeros.

If the polynomial is degree 2 and the zeros are 2 irrational numbers, then they are in the form a + b√c and a - b√c.

Therefore if one of the zero is 2 + √3, then the other zero is 2 - √3.

Answer:

the answer is C

Step-by-step explanation:

x2−162x2−9x+42x2+14x+244x+4

=4x3+4x2−64x−644x4+10x3−70x2−160x+96

=2x3+2x2−32x−322x4+5x3−35x2−80x+48

=2(x+1)(x+4)(x−4)(2x−1)(x+3)(x+4)(x−4)

=2x+22x2+5x−3

B. False

Bi = 2

Binomial = 2 possible outcomes

ANSWER

A. 22 in

EXPLANATION

The volume of a cone is calculated using the formula:

[tex]Volume = \frac{1}{3} \times \pi {r}^{2} h[/tex]

It was given that: the volume is 2,279.64 in³

The height of the cylinder is also given as: h=18 in.

We substitute, the given values into the formula to get:

[tex]2279.64= \frac{1}{3} \times (3.14) \times {r}^{2} \times 18[/tex]

[tex]2279.64= 18.84 {r}^{2} [/tex]

[tex] {r}^{2} = \frac{2279.64}{18.84} [/tex]

[tex] {r}^{2} = 121[/tex]

We take positive square root to get;

[tex]r = \sqrt{121} [/tex]

[tex]r = 11in[/tex]

Therefore the diameter is 2(11) which is equal to 22 inches.

There’s an app called Socratic it will help u with the steps

Question 1:

For this case we have to simplify the following expression:

[tex]\sqrt {54n ^ 7}[/tex]

We can rewrite the 54 as:

[tex]54 = 9 * 6 = 3 ^ 2 * 6[/tex]

In addition, we have to:

[tex]n ^ 7 = n ^ 6 * n[/tex] (According to the multiplication of powers of the same base)

Also, by definition of properties of powers and roots we have to:

\sqrt [n] {a ^ m} = a ^ (\frac {m} {n})

Then, we can rewrite the expression as:

[tex]\sqrt {3 ^ 2 * n ^ 6 * 6 * n} =\\3n ^ 3 \sqrt {6n}[/tex]

Answer:

Option C

Question 2:

For this case we have by definition, that a perfect square is the result of multiplying a number by itself. Also, the perfect squares are the numbers that have exact square roots.

So:

2 and 10 are not perfect squares.

Answer:

Option A and D

Question 3:

For this case we must simplify the following expression:

[tex]\sqrt {75x ^ 2 * y ^ 4}[/tex]

We can rewrite the 75 as:[tex]75 = 25 * 3 = 5 ^ 2 * 3[/tex]

Also we have that by definition of properties of powers and roots that:

[tex]\sqrt [n] {a ^ m} = a ^ (\frac {m} {n})[/tex]

So, we rewrite the expression:

[tex]\sqrt {5 ^ 2 * x ^ 2 * y ^ 4 * 3} =\\5xy ^ 2 \sqrt {3}[/tex]

Answer:

Option B

Answer:

The common ratio for the given geometric sequence is -1/2.

Step-by-step explanation:

The common ratio in a geometric sequence is simply the number that multiplies one term to arrive at the next term. From the sequence given, we can let the common ratio be x and determine its value using any of the following set of equations;

1/2 * x = -1/4

-1/4 * x = 1/8

1/8 * x = -1/16

using the first equation;

1/2 * x = -1/4

we divide both sides by 1/2 to solve for x.

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

x = -1/4 * 2

x = -1/2

Thus, the common ratio for the given geometric sequence is -1/2.  

Answer:

Common ratio is -1/2

Step-by-step explanation:

Common ratio is the amount between each number in a geometric sequence.

It is called the common ratio because it is the same to each number.

Common ratio is the ratio between two successive numbers in a geometric sequence.

Common is a gotten by either division or multiplication.

Therefore in the case above

1/2 x -1/2 = -1/4 ......

-1/4 x -1/2 = 1/8 ......

1/8 x -1/2 = -1/16 ....etc

Therefore our common ratio is -1/2

On dividing both the numerator and the denominator of [tex]\frac{20a^2b}{5ab^2}[/tex] by 5b, the result is [tex]\frac{4a}{b}[/tex].

In order to evaluate and solve this expression, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the expression to the right.

Lastly, the mathematical operations of addition or subtraction would be performed from left to right.

Note: Let the variable x represent the unknown expression or missing term.

Based on the information provided, we can logically set up the following mathematical equation:

[tex]\frac{20a^2b}{5ab^2} \div \frac{x}{x} =\frac{4a}{b}[/tex]

Next, we would solve the equation in parts by using the numerators and denominators as follows;

[tex]20a^2b \div x = 4a\\\\\frac{20a^2b}{x} =4a\\\\x4a=20a^2b\\\\x=\frac{20a^2b}{4a} \\\\x=5a\\\\\\\\\frac{5ab^2}{x} =b\\\\xb=5ab^2\\\\x=\frac{5ab^2}{b} \\\\x=5a[/tex]

Complete Question:

Select the correct answer from the drop-down menu.

Find the missing term.

On dividing both the numerator and the denominator of [tex]\frac{20a^2b}{5ab^2}[/tex] by ___, the result is [tex]\frac{4a}{b}[/tex].

Answer:

Step-by-step explanation:

$2.770,00. Hello friend, for reach that answer you have to add all values:

200+150+250+260+285+380+200+225+200+250+220+150= 2770.

It will be easier if you do ir by parts, like:

(200+150) + (250+260) + ...

Thank you for asking!

Have a nice day.

The average pay for Tim Worker's second job income monthly is $232.50.

To calculate the average, first, sum up all the monthly incomes:

200 + 150 + 250 + 260 + 285 + 380 + 200 + 225 + 200 + 250 + 220 + 150 = $2970

Next, divide the total income by the number of months (12 in this case) to find the average:

2970 / 12 = $232.50

So, the average monthly income from Tim Worker's second job is $232.50.

To find the average income, you add up all the monthly incomes and then divide by the total number of months. In this case, adding up Tim Worker's monthly incomes gives us $2970. Then, dividing by 12 (the number of months) gives us the average monthly income of $232.50. This method ensures that each month's income contributes equally to the overall average, regardless of fluctuations in individual months. So, despite variations in Tim Worker's monthly income, the average remains consistent at $232.50 per month.

Complete question:

Tim Worker receives the following income monthly from a second job.

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

$200 $150 $250 $260 $285 $380 $200 $225 $200 $250 $220 $150

In dollars and cents the average pay will be?

Answer:

B. -9+4 1/3

Step-by-step explanation:

If you distribute -1 to -4 1/3 and just bring down the -9, you'd end up with

-9+4 1/3.

The to this question is b I hope this is helpful

Answer:

20x - 8

Step-by-step explanation:

using the distributive property to simplify (5x-2)4, you would multiply the outside term (4) by each inside term (5x-2).

for example:

4 × 5x = 20x

4 × -2 = -8

once you distribute the 4 into 5x-2, you are left with 20x - 8 which needs no further simplifying

Answer:

Step-by-step explanation:

The distributive property: a(b + c) = ab + ac

(5x - 2) · 4 = 4(5x - 2) = (4)(5x) + (4)(-2) = 20x - 8

Answer:

9 weeks.

Step-by-step explanation:

We need to find about how many weeks (w) it will take before Factory B has printed as many books (b) as Factory A.

In other words we need to find the value of week (w) when number of books from both factories are equal.

so set both equation equal

[tex]50w+650=100w+200[/tex]

[tex]50w-100w=200-650[/tex]

[tex]-50w=-450[/tex]

[tex]w=\frac{-450}{-50}[/tex]

[tex]w=9[/tex]

Hence final answer is 9 weeks.

It’s says factory a has printed 650 books and prints200 books just divide

Answer:

150°

Step-by-step explanation:

To calculate the angle

angle = [tex]\frac{xsomewhatagree}{total}[/tex] × 360°

         = [tex]\frac{300}{720}[/tex] × 360° (cancel 360 and 720 by 2 )

         = [tex]\frac{300}{2}[/tex] = 150°

Answer:

86%

Step-by-step explanation:

30^2+43^2= x^2

900 +1849= 2749

sqr root of 2749 = x

the answer is about 52 in.

The size of the TV will be equal to 52 inches.

Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides.

Given that the space where you want to put the TV measures 30 inches high and 43 inches wide.

The size of the TV will be calculated as,

30²+43²= x²

900 +1849= 2749

√2749 = x

x = 52 inches

Therefore, the size of the TV will be equal to 52 inches.

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Answer:

[tex]\large\boxed{L.A.=153\pi\ mm^2}\\\boxed{S.A.234\pi\ mm^2}[/tex]

Step-by-step explanation:

The formula of a lateral area of a cone:

[tex]L.A.=\pi rl[/tex]

r - radius

l - slant height

The formula of a surface area of a cone:

[tex]S.A.=\pi r^2+\pi rl[/tex]

We have r= 9mm and l = 17mm. Substitute:

[tex]L.A.=\pi(9)(17)=153\pi\ mm^2[/tex]

[tex]S.A.=\pi(9^2)+153\pi=81\pi+153\pi=234\pi\ mm^2[/tex]

Answer:

y=15

Step-by-step explanation:

The formula for direct variation is

y = kx

5 =k*2

Solve for k

Divide by 2

5/2 = k

y = 5/2 x

Now we substitute x=6

y = 5/2(6)

y = 15

Answer:

y = 15

Step-by-step explanation:

If the variables are directly proportional, increasing one by a factor of 3 will mean the other one also increases by a factor of 3.

6 is 3 times 2, so the value of y will be 3 times 5, or 15.

___

You can write the relation as a proportion:

y/x = 5/2 = ?/6

Multiplying by 6 gives ...

(5/2)·6 = ? = 15

___

Or, you can bother with an equation relating x and y:

y = kx

5 = k·2 . . . plug in the given values and solve for k

5/2 = k . . . divide by 2

Then ...

y = (5/2)·6 = 15 . . . . same as the proportion, above.

If you rearrange this to y = 5·(6/2) then you see the relation described at the beginning of this solution. The new value of y is the old value multiplied by the factor by which x changes.

Answer:

Option D. [tex]\$6,139.25[/tex]

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=4\ years\\ P=\$5,350\\ r=0.035\\n=1[/tex]  

substitute in the formula above  

[tex]A=\$5,350(1+\frac{0.035}{1})^{1*4}[/tex]

[tex]A=\$5,350(1.035)^{4}=\$6,139.25[/tex]

Final answer:

The future amount of money in the account after 4 years with annual compound interest is approximately $6,139.25, which is option D.

Explanation:

The student's question pertains to the calculation of compound interest over a period of 4 years on a principal amount at a given interest rate. To calculate compound interest, we use the formula A = P(1 + r)^n, where A is the total amount after n periods, P is the principal amount, r is the annual interest rate (as a decimal), and n is the number of years the money is compounded. Applying this formula:

P = $5,350 (the principal amount)

r = 0.035 (since 3.5% as a decimal is 0.035)

n = 4 (compounding for 4 years)

Using the formula:

A = $5,350(1 + 0.035)^4

A = $5,350(1.035)^4

A = $5,350 * 1.14888281

A ≈ $6,139.25

Thus, the amount of money in the account at the end of 4 years, with compound interest, will be approximately $6,139.25, which corresponds to option D.