Select the correct answer.
Which expression is equivalent to the given expression? Assume the denominator does not equal zero.
cd4
c2d8
A cd4
ООО
OB.
Oc.
ca2
1
ca4
OD.cd2

Answer:

Step-by-step explanation:

You want the lengths of sides marked 'a' and 'b' in the given right triangle figure.

All of the triangles in the figure are similar to each other. This gives rise to some proportional relations that are useful for solving this problem.

short side/long side = 6/8 = a/6

  8a = 36 . . . . . . cross multiply

  a = 36/8 = 4.5

long side/hypotenuse = 8/10 = 6/b

  8b = 60 . . . . . . . cross multiply

  b = 60/8 = 7.5

The lengths 'a' and 'b' are 4.5 and 7.5, respectively.

__

Additional comment

These are sometimes given as "geometric mean" relationships:

  6 = √(8·a)

  b = √(a·(a+8))

  10 = √(8·(8+a))

where √(pq) is the geometric mean of p and q.

Another way to solve this is to recognize the given triangle is a 3-4-5 right triangle. The other similar triangles will have these same ratios:

  3 : 4 : 5 = a : 6 : b   ⇒   a = 3(6/4) = 4.5, b = 5(6/4) = 7.5

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Answer:

x = −8

Step-by-step explanation:

Answer:

42.95

Step-by-step explanation:

We just reverse the steps. So we take 92.9 and subtract by 7 to get 85.9. Then we divide that number by 2. So we get 42.95. To check our work, we can use this number and follow the steps Sara did. So 42.95*2=85.9+7=92.9

The original number that Sara was thinking of is 42.95.

A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.

Let's represent the original number "x".

According to the question, we know that:

x × 2 + 7 = 92.9

To determine the original number, we'll want to undo the operations that were done to it.

First, we'll subtract 7 from both sides to undo the addition:

x × 2 = 92.9 - 7

x × 2 = 85.9

Then, we'll divide both sides by 2 to undo the doubling:

x = 85.9 / 2

x = 42.95

Therefore, the original number that she was thinking of is 42.95.

Learn more about the number system here:

https://brainly.com/question/21751836

#SPJ2

Answer:

Option C

Step-by-step explanation:

Given the following question:

[tex]2x+4y=18[/tex]
[tex]-3x+2=y[/tex]

To find the answer we need to find the values of each of the variables by solving one equation at a time, and then substitute those answers into each equation in till we have our answers.

[tex]2x+4y=18[/tex]
[tex]-3x+2=y[/tex]
[tex]y-y=0[/tex]
[tex]-3x+2+ -y=0[/tex]
[tex]2-2=0[/tex]
[tex]-3x+-y=0+-2[/tex]
[tex]-3x+3x=0[/tex]
[tex]-y=3x-2[/tex]
[tex]-y\div-1=y[/tex]
[tex]3x+2\div-1=-3x+2[/tex]
[tex]y=-3x+2[/tex]

Substitute y for -3x + 2:
[tex]2x+4y=18[/tex]
[tex]y=-3x+2[/tex]
[tex]2x+4(-3x+2)=18[/tex]
[tex]2x+4(-3x+2)=18=-10x+8=18[/tex]
[tex]-10x+8=18[/tex]
[tex]8-8=0[/tex]
[tex]18-8=10[/tex]
[tex]-10x=10[/tex]
[tex]-10x\div10=x[/tex]
[tex]10\div-10=-1[/tex]
[tex]x=-1[/tex]

Substitute x for -1:
[tex]y=-3x+2[/tex]
[tex]x=-1[/tex]
[tex]y=-3(-1)+2[/tex]
[tex]-3\times-1=3[/tex]
[tex]y=3+2[/tex]
[tex]3+2=5[/tex]
[tex]y=5[/tex]

[tex]x=-1[/tex]
[tex]y=5[/tex]

Your answer is "(-1, 5)" or option C.

Hope this helps.

440d=60t            it would take jimmy 7.33 hours to get home if he drove at a constant rate of 60 Miles Per Hour

Answer:

∠ CDE = 134°

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 6 , then

sum = 180° × 4 = 720°

let ∠ BCD = x then ∠ CDE = 2x

sum the angles and equate to 720

121 + 144 + 129 + 125 + x + 2x = 720 , that is

519 + 3x = 720 ( subtract 519 from both sides )

3x = 201 ( divide both sides by 3 )

x = 67

Then

∠ CDE = 2x = 2 × 67 = 134°

cylinder volume = base area x height

                           = pi x r² x h

                           ≈ 3,14 x 7² x 10 ≈ 1500

Answer:

5 2/3

Hope this helps! Please mark Brainliest!

Answer:

17/3

Hope this helps!!! :)

[tex]\qquad\qquad\huge\underline{\boxed{\sf Answer}}[/tex]

Let's solve ~ ☂

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + 4x - 77[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + 11x - 7x - 77[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{} (x + 11) -7(x + 11)[/tex]

[tex]\qquad \sf  \dashrightarrow \: {}^{} (x + 11)(x - 7)[/tex]

Answer:

x = 7

x = -11

Step-by-step explanation:

x² + 4x = 77​

Complete the square to make it a square of a binomial

x² + 4x + 4 = 77 + 4

(x+2)² = 81

Square root both sides (two solutions)

x + 2 = 9

x = 7

x + 2 = -9

x = -11

Hope this helps :)

Have a nice day!

Answer:

12

Step-by-step explanation:

Answer:

$12

Step-by-step explanation:

$86-$14 = $72 that you have left for the 6 puzzles

72÷6 = 12

Answer:

x = 29, y = -63

Step-by-step explanation:

Solve the following system:

{4 y + 11 x - 67 = 0 | (equation 1)

{2 y + 5 x - 19 = 0 | (equation 2)

Express the system in standard form:

{11 x + 4 y = 67 | (equation 1)

v5 x + 2 y = 19 | (equation 2)

Subtract 5/11 × (equation 1) from equation 2:

{11 x + 4 y = 67 | (equation 1)

{0 x+(2 y)/11 = -126/11 | (equation 2)

Multiply equation 2 by 11/2:

{11 x + 4 y = 67 | (equation 1)

{0 x+y = -63 | (equation 2)

Subtract 4 × (equation 2) from equation 1:

{11 x+0 y = 319 | (equation 1)

{0 x+y = -63 | (equation 2)

Divide equation 1 by 11:

{x+0 y = 29 | (equation 1)

{0 x+y = -63 | (equation 2)

Collect results:

Answer: {x = 29, y = -63

Answer:

[tex]y=\frac{136}{9},\:x=\frac{7}{9}[/tex]

Step-by-step explanation:

[tex]\begin{bmatrix}4y+11x-67=2\\ y+5x-19=0\end{bmatrix}[/tex]

Isolate y for 4y+11x-67=2:

[tex]y=\frac{-11x+69}{4}[/tex]

[tex]\mathrm{Substitute\:}y=\frac{-11x+69}{4}[/tex]

[tex]\begin{bmatrix}\frac{-11x+69}{4}+5x-19=0\end{bmatrix}[/tex]

[tex]Simplify[/tex]

[tex]\begin{bmatrix}\frac{9x+69}{4}-19=0\end{bmatrix}[/tex]

Isolate x for [tex]\frac{9x+69}{4}-19=0:[/tex]

[tex]x=\frac{7}{9}[/tex]

[tex]\mathrm{For\:}y=\frac{-11x+69}{4}[/tex]

[tex]\mathrm{Substitute\:}x=\frac{7}{9}[/tex]

[tex]y=\frac{-11\cdot \frac{7}{9}+69}{4}[/tex]

[tex]\frac{-11\cdot \frac{7}{9}+69}{4}=\frac{139}{9}[/tex]

[tex]y=\frac{136}{9}[/tex]

[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]

[tex]y=\frac{136}{9},\:x=\frac{7}{9}[/tex]

Answer:

(-2, 10)

Step-by-step explanation:

All you have to do is add 4 to -6 and add 5 to 5. Since it was moved 4 units down and 5 units left, that means that those numbers were subtracted from the original coordinates. Although you are trying to find the original points, so instead you add 4 and 5 to the coordinates you have right now.

I hope that makes sense!

Answer:

15 minutes

Step-by-step explanation:

2 hours equals 120 minutes.

so if you divide 120 by 1/8 you get 15

which would be the amount of time she spent playing the trumpet.

Hope this helps!! :)

Answer:

Step-by-step explanation:

Given the point A (9, 9) and B(7, -1)

The slope of the line AB is expressed as:

slope = Δy/Δx

slope = y2-y1/x2-x1

slope = -1-9/7-9

slope = -10/-2

slope = 5

For two lines to be perpendicular, the product of their slope must be -1

mM = -1

M is the slope of the line perpendicular to AB

Substitute m = 5 into the equation

5M = -1

M = -1/5

Hence the  slope of a line that is perpendicular to the line joining point A and B is -1/5

Answer:

x=3

Step-by-step explanation:

plug it into the equation and see if it's correct

23y + 50 + 27y = 50y + 50     original equation

50y + 50 = 50y + 50                combine like terms

Because both sides of the equation are the same, meaning they are equal, the equation has INFINITELY MANY SOLUTIONS (y can be any number) .

Answer:

1-70mm

2-77m

Step-by-step explanation:

so to do this, take the first one as an exmple, to find the unknown line on the ground I added 15+8 to find the total on the bottom

still on the first question, to find the unknown number on the side, I subtracted 12-7

I hope this makes any sense, but I dont know

whats important is that you have the answers.

Answer:

Seat number 140 gets all three treats

Step-by-step explanation:

Given

[tex]Twizzlers = Multiples\ of\ 4[/tex]

[tex]Nachos = Multiples\ of\ 7[/tex]

[tex]Popcorn = Multiples\ of\ 10[/tex]

Required

Determine first person to get all kinds of treats

To do this, we simply need to determine the LCM of the given multiples:

[tex]4 = 1 * 2 * 2[/tex]

[tex]7 = 1 * 7[/tex]

[tex]10 = 1 * 2 * 5[/tex]

[tex]L.C.M = 1 * 2 * 2 * 7 * 5[/tex]

[tex]L.C.M = 140[/tex]

Seat number 140 gets all three treats

Answer:

[tex](x+10)^2+(y+6)^2=121[/tex]

Step-by-step explanation:

The standard form of a circle's equation is

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

Where (h,k) is the center and r is the radius of the circle.

The equation is given in general form, we need to convert it to the standard form. This can be done by completing squares.

The equation is:

[tex]x^2+y^2+20x+12y+15=0[/tex]

Rearrange x's and y's separate:

[tex]x^2+20x+y^2+12y=-15[/tex]

We have also subtracted 15. Now to complete squares, recall the formula:

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

The first two terms are equivalent to the first two terms of the above formula. It's clear that the second term is 2ab=20x. Solving for b:

b=10. Thus, to complete the square, we add 100 to the equation.

The third and fourth terms can also be used to complete the squares for y, knowing that 2ab=12y. In this case:

b=6. To complete this square, we add 36. The equation is now:

[tex](x^2+20x+100)+(y^2+12y+36)=-15+100+36=121[/tex]

Operating and simplifying, knowing that 121=11^2:

[tex]\boxed{\mathbf{(x+10)^2+(y+6)^2=121}}[/tex]

This corresponds to the first choice

Answer:

Answer is -5!

Step-by-step explanation:

Answer: x = -5

Explanation:

6-x-x=16

6-2x=16

6-6-2x=16-6

-2x=10

-2x/-2=10/-2

x = -5

Answer:

The answer is "21"

Step-by-step explanation:

mn + 3r

m = 5

n = 4

r = 1/3

Now just substitute the values given in the question into the equation

5(4) + 3(1/3)

Multiply 5 and 4 to get 20

20 + 3(1/3)

3(1/3) cancels out and becomes 1

20 + 1

Add 20 and 1

21

So "21" is your answer

Answer:

The answer is x = y - 30

Step-by-step explanation:

y=31 and x=1, therefore y-30=x

Answer:

1,000

Step-by-step explanation: