What is the coefficient of y in the expression? 4x + 8y + 12z

Answer: [tex]\bold{(12x - 7 - i\sqrt{47})(12x - 7 + i\sqrt{47})=0}[/tex]

Step-by-step explanation:

[tex]\dfrac{21x^2-7x - 16}{3x^2-4}=5[/tex]

cross multiply:  21x² - 7x - 16 = 15x² - 20

set equal to 0:  6x² - 7x + 4 = 0

Use quadratic formula to find the roots:

a=6, b=-7, c=4

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]

   [tex]=\dfrac{-(-7) \pm \sqrt{(-7)^2-4(6)(4)}}{2(6)}[/tex]

   [tex]=\dfrac{7 \pm \sqrt{49-96}}{12}[/tex]

   [tex]=\dfrac{7 \pm \sqrt{-47}}{12}[/tex]

   [tex]=\dfrac{7 \pm i\sqrt{47}}{12}[/tex]

[tex]x_1 =\dfrac{7 + i\sqrt{47}}{12} \qquad >>\qquad (12x - 7 - i\sqrt{47})= 0[/tex]

[tex]x_2 =\dfrac{7 - i\sqrt{47}}{12} \qquad >>\qquad (12x - 7 + i\sqrt{47})= 0[/tex]

For each part A through D below, the idea is to find the common factor between the terms, which you'll then use the distributive property to pull out.

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Part A

3x + 18 = 3(x+6)

Note how we pulled out a 3. If we distribute it back in, we end up with 3x+18 again. The other problems are done in a similar fashion

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Part B

2x - 14 = 2(x - 7)

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Part C

6x + 4 = 2(3x + 2)

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Part D

9x - 15 = 3(3x - 5)

To find the area that is shaded red, you find the area of the rectangle and subtract it by the area of the triangle.

Area of a rectangle:

A = l × w             [ l = 11 in ; w = 6in ]    Plug these numbers into the equation

A = 11 · 6

A = 66 in²

Area of a triangle:

[tex]A=\frac{1}{2}bh[/tex]     [ b = 4 in ; h = 6 in ] Plug these #s into the equation

[tex]A = \frac{1}{2}(4)(6)[/tex]

[tex]A=\frac{24}{2}[/tex]

A = 12 in²

Area of rectangle - Area of triangle = Area of the shaded region

66 in² - 12 in ² = 54 in²

Your answer is B

The required red shaded region has the area of 54 in²

A figure bounded by 4 sides in which the opposite sides are equal and all the internal angles are 90 ° is called a rectangle.

A figure bounded by 3 sides and all the internal angles add up to 180 ° is called a triangle.

Area  = (1/2)(base)(height)

Area of the rectangle = (11 x 6) in² = 66 in²

Area of the right angled triangle = (1/2)(6 x 4)  in² = 12 in²

∴ Area of the red shaded region = (66 - 12)  in² = 54 in²

Option B is correct.

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So to factor this expression, I'm going to be factoring by grouping. Firstly, what two terms have a sum of 4x and a product of -32x²? That's going to be 8x and -4x. Replace 4x with 8x - 4x:

[tex]x^2+8x-4x-32[/tex]

Now, factor x² + 8x and -4x - 32 separately. Make sure that they have the same quantity on the inside of the parentheses:

[tex]x(x+8)-4(x+8)[/tex]

Now you can rewrite the expression as:

[tex](x-4)(x+8)[/tex]

In short, the two binomial factors are (x - 4) and (x + 8).

Answer:

x-4 and x+8

Step-by-step explanation:

Factoring a quadratic equation of the form x^2+bx+c:

Divide b into two numbers p and q, so that p+q = b and p*q = c

8 + (-4) = 4 = b

8 * (-4) = -32 = c

x^2+8x-4x-32

Factor by grouping

(x^2+8x)+ (-4x-32) =

x*(x+8) + -4* (x+8) = (x-4)(x+8)

Answer:

72 / 50 = 36/25

x^16 / x^36  

= x^-20

Answer:

[tex]\frac{36}{25x^{20} }[/tex]

Step-by-step explanation:

In order to simplify this function, we have to divide by the maximum common divisor:

[tex]\frac{72x^{16} }{50x^{36} }\\ 72/2=36\\50/2=25\\\frac{36}{25} \\(x^{16} )(x^{-36})=x^{-20}=\frac{1}{x^{20} } \\\frac{36}{25x^{20} }[/tex]

By doing this you can simplify the function into the simplified form.

Answer:

78

Step-by-step explanation:

[tex](f-g)(x)=f(x)-g(x)\\\\\text{We have}\ f(x)=2x^2-5\ \text{and}\ g(x)=3x+3.\ \text{Substitute:}\\\\(f-g)(x)=(2x^2-5)-(3x+3)=2x^2-5-3x-3=2x^2-3x-8\\\\Answer:\ \boxed{(f-g)(x)=2x^2-3x-8}[/tex]

Answer:

D

Step-by-step explanation:

From the box- plot the left hand side of the box represents the lower quartile

that is [tex]Q_{1}[/tex] = 2 → D

Answer:

Let 5 consecutive no's be x,x+1,x+2,x+3,x+4

90 = x+ x+1+x+2+ x+3+x+4

90 = 5x+10

18 = x+2

x= 16

so smallest is 16

greatest = 16+4 = 20

sum = 16 +20 = 36

Answer:

y = 250x + 2175

Step-by-step explanation:

Mr. Jensen month pay = 2175

Commission per policy = 250

Let "x" be the number of policy he sells and "y" is the total paycheck including the commission.

y = 250x + 2175

Thank you.

Answer:

y = 250x + 2175

Step-by-step explanation:

Answer:

21/32 square inches.

Step-by-step explanation:

The area of a rectangle = length x width

The area of her picture = length x widht

= 7/8 x 3/4

= 21/32

The area of her picture is 21/32 square inches.

Yes, I agree the area of the picture is 21/32 square inches.

The area must be in square inches. So she need to specify it.

Thank you.

Answer: the answer is 23

Step-by-step explanation: since you are trying to find the number of boxes, b, the first thing you do is isolate it by dividing 4b by 4 this eliminates the 4, and because you did it on one side you have to do it on the other so you work would look like this 4b/4=92/4 you equation would look like this when done b=23

To find the number of boxes Mr. Reed bought, we solve the equation 4b = 92. This involves dividing 92 by 4 which results in 23 boxes of markers.

The subject of this question is Mathematics, particularly algebra. We need to solve the equation 4b = 92, where 'b' represents the number of boxes Mr.Reed bought.

Step 1: Write down the equation: 4b = 92.

Step 2: We solve for 'b' by dividing each side of the equation by 4. This gives us: b = 92/4.

Step 3: Doing the division, we find that 'b' is 23. Therefore, Mr. Reed purchased 23 boxes of markers with $92.

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This question is asking us to find the sum.

8,792 + 9,491 + 9,629 =  27, 912

They lay 27, 912 bricks in all.

Hope helps!-Aparri

Answer: Three bricklayers from the Emerald Construction Company are working on the new addition to an office building. The first bricklayer laid 8,792 bricks; the second laid 9,491 bricks; and the third laid 9,629 bricks this week. They lay a total of 8,792 + 9,491 + 9,629 = 27, 912 bricks.

Step-by-step explanation:

First Brick Layer Laid: 8,792

Second Brick Layer Laid: 9,491

and lastly the

Third Brick Layer Laid 9,629

Now if you take all the bricks that each Brick layer has laid and add them all up (break down)

8,792+9,491+9,629= 27,912 bricks laid in all

that's the break down I hope this helps you all

Answer:

y=5x+17

Step-by-step explanation:

perpendicular slope is 5

y-7=5(x+2) convert this equation into slope intercept and that's your answer

Answer:

Option A is correct.

[tex]x = -6 \pm \sqrt{30}[/tex]

Explanation:

Given the expression: [tex]x^2+12x+6 = 0[/tex]

[tex]x^2+12x+6=0[/tex]  

Subtract 6 from both sides, we get

[tex]x^2+12x=-6[/tex]  

halve linear coefficient,then  square it, and add it to both sides

[tex]x^2+12x+36=30[/tex]

Now, the left side is a perfect square

[tex](x+6)^2=30[/tex]  

Now, take square root to both sides.

[tex]x+6=\sqrt{30}[/tex] 

Subtract 6 from both sides, we get;

[tex]x = -6 \pm \sqrt{30}[/tex]

So, the solutions are : [tex]x = -6 \pm \sqrt{30}[/tex]

Answer:

The correct answer is A

[tex]x=-6\pm \sqrt{30}[/tex]

Step-by-step explanation:

The given expression is

[tex]x^2+12x+6=0[/tex]

Add [tex]-6[/tex] to both sides

[tex]x^2+12x=-6[/tex]

Add [tex](\frac{12}{2} )^2=(6)^2[/tex] to both sides.

[tex]x^2+12x+(6)^2=-6+(6)^2[/tex]

We got a perfect square on the left hand side

[tex](x+6)^2=-6+36[/tex]

Simplify the left hand side to get,

[tex](x+6)^2=30[/tex]

Take square root of both sides

[tex](x+6)=\pm \sqrt{30}[/tex]

Solve for [tex]x[/tex].

[tex]x=-6\pm \sqrt{30}[/tex]

Answer:

2,428

Step-by-step explanation:

(18 × 106) + (5 × 104)

      1908 + 520

= 2,428

I'm really sorry if this isn't what you meant... but if it is then... Hope this helps you! :)

Answer:

sooo sorry im in the third grade and notised that this is not my onw level but i really thought i could help u sorry ;(

Step-by-step explanation:

Answer:

The number of loaves sold

Step-by-step explanation:

Answer:

The answer is B and E

Step-by-step explanation:

Julia runs 5 time and lifts 5 times in B. She also runs 10 times and lifts 10 times in E.

1 feet is 12 inches.

We have 5 feet and 6 inches. First, let's convert the feet to inches. 5 times 12 is 60, so 5 feet is 60 inches.

Now add 60 inches to the 6 inches that we didn't mention. 60 plus 6 is 66. Thus, 5 feet and 6 inches is 66 inches.

Answer:

The answer is 66

Step-by-step explanation: 1 foot is 12 inches so you do 12 times 5 and get 60 and then add the next 6 inches... :)

Answer:

They drove 300 miles on the first day

Step-by-step explanation:

They drove 1200 miles

They drove 1/4 on the first day

1200 * 1/4 = 300 miles

They drove 300 miles on the first day

y = 2x + 2

for x = 0 → y = 2(0) + 2 = 0 + 2 = 2 → (0, 2)

for x = -1 → y = 2(-1) + 2 = -2 + 2 = 0 → (-1, 0)

y = x - 1

for x = 0 → y = 0 - 1 = -1 → (0, -1)

for x = 1 → y = 1 - 1 = 0 → (1, 0)

Look at the picture.

Answer:

True

Step-by-step explanation:

Each week the amount of radio active material is 100*(1/4)^x which is correct.

So at the end of 4 weeks she will have

amount = 100*(1/4)^x

amount = 100*(1/4)^4

amount = 100 * (1/256)

amount = 0.390625 grams after 4 weeks.

Answer:

Step-by-step explanation:

There is the answer.

Answer:

[tex]\frac{(L x M)}{6}[/tex]

Step-by-step explanation:

The greatest common factor is the greatest number that will divide two values. We have two values L and M. Each has numbers which multiply together to give the number. The highest value or most in common they share is 6. This is the GCF.

The least common multiple is the smallest positive number which is a multiple of the two. This means both L and M divide into it evenly.

We know L x M is a multiple because L and M will be factors of it. But we don't know its the least.

As an example if L= 42 and M = 60, they have GCF 6. We can multiply them to find a multiple 42 x 60 = 2520 but we don't know this is the smallest or least multiple we can find. If we divide by the GCF, 2520/6=420. Interestingly, 42 x 10 =420 and 60 x 7 =420. This means 420 is the least common multiple.

We can multiply (L x M) and then divide by the GCF of L & M to find the least common multiple.

[tex]\frac{(L x M)}{6}[/tex]

Answer:

Y= -3

Step-by-step explanation:

5y-10=-25     Add 10 on both sides

5y=-15      Divide by 5 on both sides

y=-3

Problem 1

a) y = 8 and c) x = 2 are perpendicular lines to one another. The first is horizontal and the second is vertical.

The other two lines are not perpendicular because their slopes (1/8 and 8) do not multiply to -1. This rule only applies to lines that are neither horizontal nor vertical.

Answers: A and C.

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Problem 2

Equations b) y = (-1/2)x - 4 and c) y-4 = 2(x+3) are perpendicular. Equation B has a slope of -1/2, while equation C has a slope of 2. Those two values multiply to -1. One slope is the negative reciprocal of the other. It might help to think of 2 as 2/1.

The other two equations are not perpendicular to each other, nor are they perpendicular to B or C. Equation A has a slope of 0. Equation D has a slope of -2.

Answers: B and C

Answer:

It will take 12 minutes

Step-by-step explanation:

We can use ratio's to solve the problem

2/3 mile          1 miles

------------   = ------------------

8 minutes      x minutes

Using cross products

2/3 * x = 8*1

Multiply each side by 3/2 to isolate x

3/2 * 2/3 x = 3/2 * 8

x = 12

Jeff's net pay is $1,065.70 per week.

To calculate Jeff Jones's net pay, we need to consider several deductions from his gross pay.

1. Gross Pay: Jeff earns $1,200 per week.

2. Social Security Deduction: Social Security tax is 6.2% of the first $118,500 of earnings. Jeff's earnings are below this threshold, so his Social Security deduction is 6.2% of his gross pay.

Social Security deduction = 6.2% of $1,200 = 0.062 * $1,200 = $74.40

3. Medicare Deduction: Medicare tax is 1.45% of all earnings.

  Medicare deduction = 1.45% of $1,200 = 0.0145 * $1,200 = $17.40

4. Health Insurance Deduction: $42.50 is deducted for health insurance.

5. Total Deductions: Add up all deductions.

Total deductions = Social Security deduction + Medicare deduction + Health insurance deduction

= $74.40 + $17.40 + $42.50

= $134.30

6. Net Pay: Subtract total deductions from gross pay.

Net pay = Gross pay - Total deductions

= $1,200 - $134.30

= $1,065.70

Therefore, Jeff's net pay is $1,065.70 per week.