Solve the system of linear equations by elimination.

3x−30=y
7y−6=3x

























Solve the system of linear equations by elimination.

3x−30=y
7y−6=3x

Answer:

−24= 12

Step-by-step explanation:

Answer:

-2=1

Step-by-step explanation:

-24=(-6)-(-18)

-24=(-6)+18

-24=12

-24/12 = 12/12

-2=1

(2 negatives make a positive)

Answer:

Smallest: 12.8 square meters

Largest: 13.5 square meters

Step-by-step explanation:

I'm not 100% sure I understand this correctly as it seems like a very strange problem, but here it goes.

The smallest number that rounds to 3.2 is 3.15, and the smallest number that rounds to 4.1 is 4.05.

[tex]3.15*4.05=12.7575[/tex]

The smallest possible area is 12.8 rounded to the nearest 10th.

The largest number that rounds to 3.2 is 3.24999... and the largest that rounds to 4.1 is 4.14999...

[tex]3.24999*4.14999=13.4875[/tex]

That rounds to 13.5.

Answer:

-20.5

-8

4.5

17

Step-by-step explanation:

y = 2.5x - 8

x = -5

y = 2.5(-5) - 8

y = -12.5 - 8

y = -20.5

x = 0

y = 2.5(0) - 8

y = 0 - 8

y = -8

x = 5

y = 2.5(5) - 8

y = 12.5 - 8

y = 4.5

x = 10

y = 2.5(10) - 8

y = 25 - 8

y = 17

The value of [tex]x[/tex] is 29.

The formulae for the surface area ([tex]A_{s}[/tex]) and volume ([tex]V[/tex]) are, respectively:

[tex]A_{s} = 2\cdot (h\cdot l + w\cdot l + h\cdot w)[/tex] (1)

[tex]V = w\cdot h \cdot l[/tex] (2)

Where:

According to the statement, we must equalize (1) and (2) and substitute the remaining variables:

[tex]2\cdot (h\cdot l + w\cdot l + h\cdot w) = w\cdot h\cdot l[/tex]

[tex]2\cdot h\cdot l + 2\cdot w \cdot l + 2\cdot h\cdot w = w \cdot h \cdot l[/tex]

[tex]2\cdot \log_{2}x\cdot \log_{4}x+2\cdot \log_{3}x\cdot \log_{4}x+2\cdot \log_{2}x\cdot \log_{3}x = \log_{2}x\cdot \log_{3}x\cdot \log_{4}x[/tex]

By applying logarithm properties, we simplify the expression:

[tex]2\cdot \log_{2}x\cdot \left(\frac{\log_{2}x}{\log_{2}4} \right) + 2\cdot \left(\frac{\log_{2}x}{\log_{2}3} \right)\cdot \left(\frac{\log_{2}x}{\log_{2}4} \right) + 2\cdot \log_{2}x\cdot \left(\frac{\log_{2}x}{\log_{2}3} \right) = \log_{2}x \cdot \left(\frac{\log_{2}x}{\log_{2}3} \right)\cdot \left(\frac{\log_{2}x}{\log_{2}4} \right)[/tex]

[tex]2\cdot \left[\frac{1}{\log_{2}4}+\frac{1}{\log_{2}3\cdot \log_{2}4}+\frac{1}{\log_{2}3}\right] = \left(\frac{1}{\log_{2}3\cdot \log_{2}4} \right)\cdot \log_{2}x[/tex]

[tex]2\cdot \left(\frac{\log_{2}3+\log_{2}4+1}{\log_{2}3\cdot \log_{2}4} \right) = \left(\frac{1}{\log_{2}3 \cdot \log_{2}4} \right)\cdot \log_{2}x[/tex]

[tex]\log_{2}x = 2\cdot (\log_{2}3 + \log_{2}4+1)[/tex]

[tex]\log_{2}x = \log_{2}9 + \log_{2}16 +2[/tex]

[tex]x = 9 + 16 + 4[/tex]

[tex]x = 29[/tex]

The value of [tex]x[/tex] is 29.

We kindly invite to check this question on logarithms: https://brainly.com/question/20838017

Nota - The statement of this question presents typing mistakes and is also incomplete, the corrected form is presented below:

A right rectangular prism whose surface area and volume are numerically equal has edge lengths [tex]\log_{2} x[/tex] (height), [tex]\log_{3}x[/tex] (width) and [tex]\log_{4}x[/tex] (length). What is [tex]x[/tex]?

 CD is 11 square root of 14.  

The measure of the side length CD in the given right angled triangle as per the measurements is equal to option C. 11√14 .

In right triangle ABE,

Measure of angle ABE = 90 degrees

Measure of angle AEB = 60 degrees

AB = 11√7

Using trigonometric ratio we have,

tan 60° = AB / BE

⇒ √3 = 11√7 / BE

⇒ BE = 11√7 / √3

⇒BE = 11√21 / 3

In right triangle BED,

Measure of angle BED = 90 degrees

Measure of angle EBD= 45°

⇒Measure of angle EDB= 45°

BE ≅ ED

BE = 11√21 / 3

⇒ED = 11√21 / 3

Using Pythagoras theorem,

BD² = BE² + ED²

⇒BD = √ 2 (11√21 / 3 )²

⇒BD = 11√21 / 3 × √2

⇒ BD = 11√42 / 3

In right triangle CDB,

Measure of ∠CDB = 90°

Measure of ∠DCB = 30°

tan 30° = BD / CD

⇒ ( 1/ √3) = 11√42 / 3 / CD

⇒ CD =  [11√42 / 3 ] × √3

⇒ CD = 11√14

Therefore, the length of the side CD in the triangle is equal to option C. 11√14 .

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Answer:

ancho: 12 cm

Largo: 14 cm

Step-by-step explanation:

[tex]P=2a+2l[/tex]

[tex]l=a+2[/tex]

[tex]P=2a+2(a+2)=2a+2a+4[/tex]

[tex]P=4a+4[/tex]

[tex]52=4a+4[/tex]

[tex]52-4=4a[/tex]

[tex]48=4a[/tex]

[tex]48/4=a[/tex]

[tex]12=a[/tex]

largo = ancho + 2 = 12 +12 = 14 cm

Hope this helps

Answer:

The polynomial x3 + 8 is equal to (x + 2)(x2 - 2x + 4).

One pipe takes 6 hours working alone.

The other pipe takes 12 hours working alone.

This is a rate of work problem. The formula utilized is

[tex]w=r\times t[/tex]

where

We are looking for how long it will take each pipe to completely fill the pool

For pipe 1 working alone to fill 1 pool, the work done is 1;

[tex]w=r\times t\\\\1 = r_1 \times t_1\\\\t_1=\frac{1}{r_1}[/tex]

For pipe 2 working alone to fill 1 pool, the work done is 1;

[tex]w=r\times t\\\\1 = r_2 \times t_2\\\\t_2=\frac{1}{r_2}[/tex]

From the question, it would take 9 hours if each pipe took turns to fill half the pool. That is;

[tex]\frac{t_1}{2}+\frac{t_2}{2}=9\\\\t_1+t_2=18[/tex]

However, if both pipes worked together, it would take 4 hours for each pipe. That is;

[tex]w_1+w_2=w\\\\r_1t_1+r_2t_2=w\\\\4r_1+4r_2=1\\\\r_1+r_2=\frac{1}{4}[/tex]

Remember that [tex]r_1=\frac{1}{t_1}[/tex] and [tex]r_2=\frac{1}{t_2}[/tex]. So,

[tex]\frac{1}{t_1}+\frac{1}{t_2}=\frac{1}{4}\\\\\frac{t_1+t_2}{t_1t_2}=\frac{1}{4}[/tex]

Also recall that [tex]t_1+t_2=18[/tex]. So,

[tex]\frac{18}{t_1t_2}=\frac{1}{4}\\\\t_1t_2=72[/tex]

The only factors of 72 that satisfy the conditions

[tex]t_1+t_2=18\\\\t_1t_2=72[/tex]

are 6 and 12.

Therefore, pipe 1 will take 6 hours, and pipe 2 will take 12 hours to fill the pool if working alone.

The link below has a similar problem on rate of work

https://brainly.com/question/21485928

Answer: It says it right there

Step-by-step explanation:

create a video explaning

The 14-ounce box is cheaper at a cost of $2.74 than the 10-ounce box.

In mathematics, divides left-hand operands into right-hand operands in the division operation. The primary purpose of the division is to generate equal groupings or to determine how many people are in each category after a fair distribution.

For example 4/2 = 2

First, we have to find the price for each ounce.

So for the 10-ounce box:

⇒ 2.12 / 10

Apply the division operation,

⇒ $0.212 per ounce.

Now for the 14-ounce box:

⇒ 2.74/ 14

Apply the division operation,

⇒ $0.19 per ounce.

Here the cost of the 14-ounce box is less than the 10-ounce box as 0.19 < 0.21

Therefore, the 14-ounce box is cheaper at a cost of $2.74.

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Answer:

2p -2

Step-by-step explanation:

To find the perimeter, add up all the lengths of each side of the rectangle.

Perimeter

= 2 +2 +p -3 +p -3

= 2 +2 -3 -3 +p +p

= -2 +2p

= 2p -2

Answer:e d

Step-by-step explanation:

Answer:

Well x + 6y = 6 can be written 6y = -1x + 6 or y = (-1/6)x + 1. Any line perpendicular to this line will have a slope that is the multiplicative inverse of -1/6 which is +6

So the line passing through( -1,-6) having slope 6 is (y - -6) / (x - -1) = 6 or…………..(y + 6) / (x + 1) = 6 and multiplying both sides by x + 1 gives y+6 = 6(x + 1) and finally subtracting 6 we have y = 6(x+1) - 6 or y = 6x + 0.

This turns out to be a line that passes through the origin having slope 6/1

Step-by-step explanation:

Answer:

.....

Step-by-step explanation:

Answer:

-1 , 1/2

Step-by-step explanation:

Each term is obtained by dividing by (-2)

-16/-2 = 8

So, the next two terms are:

2/-2 = -1

-1/-2 = 1/2

Answer:

15) 44.6 inches

16) 77.8 degrees

Step-by-step explanation:

15) we are given the angle and length of 16, drawing this out, 16 inches (the height) would be opposite of the angle and the length of the ramp would be hypotenuse.

we know that sine is opposite over hypotenuse, so we can use that to help find the length.

Rearrange:

sin21degrees = opposite/hypotenuse

hypotenuse*sin21degrees = opposite

hypotenuse = opposite/sin21degrees

Sub in values:

hypotenuse = 16/sin21degrees

hypotenuse = 44.6468 inches

16) we are given two side lengths and expected to find an angle, we now need to use the inverse of one of the trigonometric ratios.

Drawing this out, we are given the hypotenuse and adjacent lengths, so we can use the inverse cosine to find the angle

angle = cos^-1 adjacent/hypotenuse

angle = cos^-1 (7/26)

angle = 74.381 degrees

Answer:

number 5

Step-by-step explanation:

an equal sign means "is not equal to"

Answer:

51 yellow marbles

Step-by-step explanation:

60% of 85 can be found by multiplying 85 and 0.6 to get 51

Answer:

i got 51 marbles! simple.

The leading degree of the polynomial is 3. This shows that the polynomial described by the equation is a cubic polynomial

The standard form of a polynomial expression is written as:

[tex]a_nx^n+ a_{n-1}x^{n-1}+ a_{n-2}x^{n-2}+...[/tex]

A polynomial function has a leading degree that is greater than 2;

Given the polynomial function

[tex]P(x)=4x^3-31x^3-10058x+158040[/tex]

From the given polynomial, the leading degree of the polynomial is 3. This shows that the polynomial described by the equation is a cubic polynomial

Learn more here:https://brainly.com/question/19809286

Answer:

Step-by-step explanation:

A. What is the ratio of songs by the group from Michigan to the number of songs played?  3/15

B. In lowest terms, 3/15 is 1/5.

C. Suppose the station continues to play the ratio of songs. How many songs from the Michigan group will Blake hear in the next three hours?  To answer this, multiply the 1-hour unit rate by 3:  3*3 = 9 Michigan group songs over the next 3 hours.

Answer:

y=-2x+10

Step-by-step explanation:

Answer:

X=4

Step-by-step explanation:

Let's make an equation,

7/4 ÷ 14 = x ÷ 3

We can cross multiply

7/4 * 32 = x * 14

Now we have 56 = 14x

Divide both sides by 14

56 ÷ 14 = 4, 14x ÷ 14 = x

4 = x

x = 4

Answer:

48.95

Step-by-step explanation:

Answer:

y=4

Step-by-step explanation:

   y+2x=2

2(y+2x)=2(2)

 2y+4x=4

(2y+4x)-(y+4x)=4-0

                    y=4

Answer:

Below

Step-by-step explanation:

1 pound = 16 ounces

Therefore if you're looking for 8 ounces, divide $7.50 in half.

You get $3.75

Answer:

At this rate, the total cost of 8 ounce bag of trail mix would be $3.75.

Step-by-step explanation:

So first I found that for 1 LB (pound), there is 16 ounces so 8 oz is half of 16. If we know that, we have to divide 7.5 by 2 to get 3.75.

Answer:

4 dollars for 2 drinks (2 dollars for 1 drink)

Step-by-step explanation:

Okay, so you can get 3 snapple drinks from 6 dollars. and you want to know the cost of 2 snapple drinks.

3 ÷ 6 = 2

So 1 drink is 2 dollars, if you wanted to buy 2 drinks the cost would be 4 dollars! Have a great day friend! :D

Answer:

$4

Step-by-step explanation:

If 3 Snapple Iced teas cost $6, we can divide 6 by 3 to find the cost for one.

6/3 is 2 and 2 * 2 is 4, so 2 Snapple Iced teas would cost $4.

Answer: B: complementary

Step-by-step explanation: :)

I believe you are trying to find the most Cheapest cost?

Since the area had to be 1200m^2 the most biggest numbers we could divide with is 30 x 40, which equals to 1200.

30 x 20 (expensive one the lower) = 600 (wall 3) + 20 x 20 = 1000 (wall 3 + wall 1)

40 x 13 (cheapter one the higher) = 520 (wall 4) + 32 x 13 = 936 (wall 4 + wall 2)

Add all together, $1936 to build the whole fence.

(I don't know for sure if I am right. If I am right, can I have a brainliest?)

Answer:

skew

skew

parallel

parallel

Step-by-step explanation:

First see the below figure to understand parallel and skew lines

As you can see parallel lines lie on the same plane

skew lines lie on different plane and do not intersect

1)AB and GF

AB lies on ABCD plane

GF lies on EFGH plane

and they will never meet / intersect

so skew

2)DH and BF

DH lies on ADHE plane

BF lies on BCGF plane

they seem parallel but they are on different plane, so skew

3)EF and HG

EF and HG both lie on the same plane EFGH

and they both are parallel

4)for this see the second picture

both these planes are parallel

Hope this helps!