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System of equation consists of two or more equations with unknow variables. A possible step used in eliminating the y-term is (y + z  6) *5

System of equation consists of two or more equatons with unknow variables.

Given the system of equations

y + z = 6

5y + 9z =1

In order to eliminate the variable "y", we will multiply equation 1 by 5 and subtract from equation 2;

5y + 5z = 30

5y + 9z = 1

Subtract

5z - 9z = 30 - 1

-4z =29

This leaves only the variable "z" eliminating variable. "y"

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Step-by-step explanation:

Example for my opinion

3) 2r = 5 cm

2 pi r = 5 × 3.14 = 15.7

Answer:

c

Step-by-step explanation:

6x+42+3x

6x+3x +42

9x+ 42

Step-by-step explanation:

Given expression,

[tex]\\ {\longrightarrow \qquad{ \sf{6(x + 7) + 3x}}}\\ \\ [/tex]

Using distributive property we get,

[tex] \\ {\longrightarrow \qquad{ \sf{6x + 42 + 3x}}}\\ \\ [/tex]

Adding like terms (6x and 3x) we get,

[tex]\\ {\longrightarrow \qquad{ \sf{9x + 42 }}}\\ \\ [/tex]

So, From the given options, Option C is equivalent to 6(x + 7) + 3x .

Answer:

The time it takes the ball to hit the ground is 3.05secs

step - by - step explanation:

In order to find height from where ball is dropped, you have to find height or h(t) when time or t is zero.So plug in t=0 into your quadratic equation:h(0) = -16.1(0^2) + 150h(0) = 0 +150h(0) = 150 ft is the height from where ball is dropped. When ball hits the ground, the height is zero. So plug in h(t) = 0 and solve for t.0 = -16.1t^2 + 15016.1 t^2 = 150t^2 = 150/16.1t = sqrt(150/16.1)t = ± 3.05Since time cannot be negative, your answer is positive solution i.e. t = 3.05

Answer:x=9

Step-by-step explanation:

6x+25=79

    -25 -25

     6x=54

   /6     /6

         x=9

x=9

6x +25 =79

- 25

6x. = 54

÷6

x = 9

Hope this helps!

Step-by-step explanation:

for the table on the left (Q5)

y(-1) = -5

y(1) = -1

y(3) = 3

for the table on the left (Q7)

y(0) = 5

y(1) = 2

y(2) = -1

y(3) = -4

Answer:

1/343    = .00291545

Step-by-step explanation:

= 1/(7*7*7) =

The value of the exponential equation is A = ( 1/343 ) = ( 1/7 )³

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the exponential equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = ( 1/7 ) x ( 1/7 ) x ( 1/7 )   be equation (1)

On simplifying the equation , we get

A = ( 1/7 )³

Now , on further simplification , we get

A = ( 1/343 )

And , the value of A = 0.002915

Hence , the exponential equation is A = ( 1/7)³

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Answer:

The surface area of the triangular prism is 223.789 cm^2.

Step-by-step explanation:

Answer:

144

Step-by-step explanation:

cross section area multiply by length.

i.e

(1/2*4*6) *12

Answer:

2.5% believe.

Step-by-step explanation:

I may be wrong but heres how I solved it.

Take the 8 hours and convert it to minutes.

8 hours - 480 minutes total

12 minutes out of 480 minutes is 2.5%

The equivalent expression of the expression [tex]\sqrt[3]{\frac{12x^2}{16y}}[/tex] is [tex](\frac{3x^2}{4y})^\frac 13[/tex]

The expression is given as:

[tex]\sqrt[3]{\frac{12x^2}{16y}}[/tex]

Divide 12 in the expression by 4

[tex]\sqrt[3]{\frac{3x^2}{16y}}[/tex]

Divide 16 in the expression by 4

[tex]\sqrt[3]{\frac{3x^2}{4y}}[/tex]

Apply the power rule of indices

[tex](\frac{3x^2}{4y})^\frac 13[/tex]

Hence, the equivalent expression of [tex]\sqrt[3]{\frac{12x^2}{16y}}[/tex] is [tex](\frac{3x^2}{4y})^\frac 13[/tex]

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The probability that the spinner will land on a number greater than 4 or on a shaded section is five-sixt

Probability is the likelihood or chance that an event will occur. Mathematically;

Probability = Expected/Total

If the spinner is spinned, the total outcome is 1/6

Pr(greater than 4) = 2/6 = 1/3

Pr(shaded section) = 3/6 = 1/2

Pr(number greater than 4 or on a shaded section) = 1/3 + 1/2
Pr(number greater than 4 or on a shaded section)  = 5/6

Hence the probability that the spinner will land on a number greater than 4 or on a shaded section is five-sixths

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Answer:

D. 5/6

Step-by-step explanation:

i can feel the course of the correct answer pierce through my veins, trust me... its correct.

Answer:

He rode 15 on his bike today.

Step-by-step explanation:

78 / 6 = 13 and 13 + 2 = 15

Answer:

Step-by-step explanation:

Answer:

3. (2x-5)(6x+1) 6. (7x-2)(3x+1)

Step-by-step explanation:

3. 12x²-28x-5

12x²+2x-30x-5

Find common factor:

2x(6x+1)-5(6x+1)

Rewrite in factored form:

(2x-5)(6x+1)

6. 21x²+x-2

21x²+7x-6x-2

Find common factor:

7x(3x+1)-2(3x+1)

Rewrite in factored form:

(7x-2)(3x+1)

Answer:

Again let's plug in the values.

we get

[tex]8 \frac{1}{8} [/tex]

Answer:

16 feet.

Step-by-step explanation:

Midsegment = (10+22)/2

= 32/2

= 16.

Answer:

36

Step-by-step explanation:

Answer:

3^12=3*3*3*3*3*3*3*3*3*3*3*3=9*9*9*9*9*9=81*81*81=6561*81=531,441

Step-by-step explanation:

Answer:

8/15 is the fraction I think

The answer is that 50% of the sweaters cost $50 or less.

To determine the fraction of sweaters that cost $50 or less, we need to look at the box plot and identify the range of prices that fall within that category.

Looking at the box plot, we can see that the box extends from $40 to $60, which means that 50% of the sweaters sold were priced between $40 and $60. Additionally, we can see that the left whisker of the box plot extends down to $30, which means that some sweaters were sold for less than $40.

Therefore, to find the fraction of sweaters that cost $50 or less, we need to calculate the portion of the box plot that falls below $50.

From the box plot, we can see that the distance between $40 and $50 is half of the total distance of the box or 25%. And the distance between $30 and $40 is also 25%. Therefore, the total fraction of sweaters that cost $50 or less is 25% + 25% = 50%.

So, the answer is that 50% of the sweaters cost $50 or less.

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Answer:

4 5/6

Step-by-step explanation:

[tex]3 \frac{1}{3} + 1 \frac{1}{2} [/tex]

the simplest form.

[tex] \frac{10}{3} + \frac{3}{2} [/tex]

[tex] = \frac{(10 \times 2) + (3 \times 3)}{3 \times 2} [/tex]

[tex] = \frac{20 + 9}{6} [/tex]

[tex] = \frac{29}{6} [/tex]

[tex] = 4 \frac{5}{6} [/tex]

By applying fundamental trigonometry and the values for common angles, we have that (1 - cos² 60°) · (1 + cos² 300°) is equivalent to 2 · sin² 120° + sin⁴ 60°.

In this question we have to prove the trigonometric expression by means of fundamental trigonometric relationships and known values for certain angles. We proceed to prove that one side of the expression is equivalent to the other side:

By applying fundamental trigonometry and the values for common angles, we have that (1 - cos² 60°) · (1 + cos² 300°) is equivalent to 2 · sin² 120° + sin⁴ 60°.

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The sets of measurements that can form a triangle are:

90°, 3 inches, 7 inches

5 inches, 6 inches, 7 inches.

To determine which sets of measurements can form a triangle, we need to apply the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's analyze each set of measurements:

35°, 15, 130°:

This set cannot form a triangle because the angles are not appropriate. The sum of the angles in a triangle must be 180°, but the given angles add up to 180° - (35° + 130°) = 15°, which is not possible.

90°, 3 inches, 7 inches:

This set can form a triangle. The sum of the two shorter sides (3 inches + 7 inches) is greater than the longest side (10 inches), satisfying the triangle inequality theorem.

70°, 70°, 70°:

This set cannot form a triangle because the angles are not appropriate. The sum of the angles in a triangle must be 180°, but the given angles add up to 210°, which is greater than 180°.

17 inches, 8 inches, 2 inches:

This set cannot form a triangle. The sum of the two shorter sides (2 inches + 8 inches) is less than the longest side (17 inches), violating the triangle inequality theorem.

5 inches, 6 inches, 7 inches:

This set can form a triangle. The sum of the two shorter sides (5 inches + 6 inches) is greater than the longest side (7 inches), satisfying the triangle inequality theorem.

Therefore, the sets of measurements that can form a triangle are:

90°, 3 inches, 7 inches

5 inches, 6 inches, 7 inches.

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Answer:

218.5

Step-by-step explanation:

Hi brielleha

X = 3/2 = 1.5

4 x 1.5 = 6

B = 17

6 + 17 = 23

A = 8

8 x 1.5 = 12

12 + 9 = 21

6 x 1.5 = 9

9 + 10 =19

19, 21 23

A = 23 x 19

437/2 = 218.5

The minimum number of calories the group is expected to consume during the entire trip from current location to southpole and back to camp is 375 kilo calories.

Pythagoras theorem says that in a right angle triangle the square of hypotenuse side is equal to the sum of square of other two legs of right angle triangle.

There are total 5 miles in one block and current location to the South Pole there are 5 blocks on map. Thus, the total distance from current location to the South Pole is,

[tex]x=5\times5\\x=25\rm\; miles[/tex]

There are total 12 blocks from current location to the camp on map. Thus, the total distance from current location to the camp is,

[tex]y=12\times5\\y=60\rm\; miles[/tex]

The shortest distance from South Pole to camp is,

[tex]z=\sqrt{25^2+60^2}\\z=\sqrt{4225}\\z=65\rm\; miles[/tex]

Total distance group travel from if it wants to travel from its current location on the map to the South Pole, and then directly back to base camp, passing through their current location is,

[tex]n=65+60\\n=125\rm\; miles[/tex]

The group travel an average of 10 miles per day. Thus, number of days to cover distance,

[tex]\dfrac{125}{10}=12.5\rm\; days[/tex]

There are total 5 people in group and they consume each person needs 6000 calories per day. Thus, total calories,

[tex]C=12.5\times6000\times5\\C=375000 \rm\;C\\C=375 \rm\; kC[/tex]

Thus, the minimum number of calories the group is expected to consume during the entire trip from current location to southpole and back to camp is 375 kilo calories.

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Answer:

Jacob should work minimum of 14 hours washings cars to meet his requirement.

Step-by-step explanation:

Let the number of hours of washing cars be 'x'.

Let the number of hours of landscaping be 'y'.

Given:

Cost for Per hour for washing cars = $10

Cost for per hour Landscaping = $8

Total number of hours of working

Amount to be earned this weekend

So we can say that;

Also,

Amount to be earned this weekend should be greater than or equal to sum of Cost for Per hour for washing cars multiplied by number of hours of washing cars and Cost for per hour Landscaping multiplied by number of hours of landscaping.

framing in equation form we get;

Now Number of hours he worked for landscaping

So we get;

Subtracting both side by 32 we get;

Dividing both side by 10.

Hence Jacob should work minimum of 14 hours washings cars to meet his requirement.

Step-by-step explanation:

Answer:

4 0 5     7 3 2 6

Step-by-step explanation:

Just did the assignment

Answer: B

Step-by-step explanation:

Answer:

b

Step-by-step explanation: