Which properties justify the steps taken to solve the system {2a+7b=0 3a-5b=31

Drag the awnsers into the boxes to match each step ASAP

The farmer needs to purchase 66 feet of fencing to enclose the rectangular region.

Let's call the length of the side of the rectangle that is parallel to the barn "2x" (since it is twice the length of the adjacent side), and let's call the length of the adjacent side "x". The length of the side opposite the barn is also "x", since it is opposite to the adjacent side.

We know that the area of the rectangle is 242 ft^2. The formula for the area of a rectangle is:

area = length * width

So we can write an equation for the area of the rectangle in terms of "x":

242 = 2x * x

Simplifying this equation, we get:

242 = 2x²

Dividing both sides by 2, we get:

121 = x²

Taking the square root of both sides, we get:

11 = x

So the adjacent side of the rectangle is 11 feet, and the side parallel to the barn is twice as long, or 22 feet.

To find the amount of fencing needed, we need to add up the lengths of all three sides that are not parallel to the barn. The formula for the perimeter of a rectangle is:

perimeter = 2 * length + 2 * width

Since one of the sides is the barn, we only need to add up the lengths of the two sides opposite the barn:

Perimeter = 2 * length + 2 * width

Therefore, the farmer needs to purchase 66 feet of fencing to enclose the rectangular region.

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The area of the composite figure is equal to 60.75 m² square metres.

The composite figure is made up of a triangle and two rectangles, so we shall calculate for the areas of the three figures and then add the result to get the total area of the composite figure as follows:

area of the triangle = 1/2 × 7.5 m × 3 m

area of the triangle = 1/2 × 22.5 m²

area of the triangle = 11.25 m²

area of smaller rectangle = 4.5 m × 3 m

area of smaller rectangle = 13.5 m²

area of the bigger rectangle = 12 m × 3 m

area of the bigger rectangle = 36 m²

total area of the composite figure = 11.25 m² + 13.5 m² + 36 m²

total area of the composite figure = 60.75 m²

Therefore, the area of the composite figure is equal to 60.75 m² square metres.

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For a diamond having volume 161 mm³, the value for side length is 7 mm.

What is volume?

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

The formula for volume of diamond is given as -

V = 0.47 s³

Here, s represents the side length of each edge.

The value for volume of diamond is given as -

Volume = 161 mm³

Plug in the values in the equation -

Volume = 0.47 s³

161 = 0.47 s³

s³ = 161 / 0.47

s³ = 342.553

s = ∛342.553

s = ∛342.553

s = 6.996 mm

Therefore, the side length measures 6.996 ≈ 7 mm.

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The value of x and y is 13.5 and 7.

we have two set of equations as follows,

x + y = 20.5     ....[1]

x - y = 6.5       .....[2]

from equation [1] we have,

x +y = 20.5

x = 20.5 - y       .....[3]

put the value of x in equation [2]

x - y = 6.5

20.5 - y -y = 6.5

20.5 - 2y = 6.5

now like terms together ,

-2y = 6.5 -20.5

-2y = -14

now the minus sign cancel by each other,

2y = 14

y = 14/2

y = 7

now, put the value of y in equation [1]

x +y =20.5

x + 7 = 20.5

x = 20.5 - 7

x = 13.5

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Answer:|x-1|-2

Step-by-step explanation: see picture below!

After unit conversion of 24 in./s into ft/min the value will be 120

To measure and compare various things we use one term which is known as a unit. When all of the measuring units are the same, comparison is simple. Depending on their intended usage, different units can be categorized.

For example, for  length measurement we use units like:- meter, centimeter, inch, miles.

Given that,

A rate = 24 in./s

The value of rate in ft./min. = ?

It is known that,

1 feet = 12 inches

And 1 minute = 60 second

So,

1 inches = 1/12 feet

1 second  = 1/60 minute

⇒ 24 in./s

⇒  24 ((1/12)ft / (1/60)sec)

⇒ 24 × 60/12

⇒ 24 x 5

⇒ 120

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Answer: X=3  Y=8/5 and Z= 24/5

Step-by-step explanation:

The percent will the fraction decrease should be 80%.

Important information:

In the case when its numerator is decreased by 85% and its denominator is decreased by 25%

Calculation of percentage:

= (100-85) ÷ (100 - 25)

=  15%÷ 75%

= 20%

Now the decrease in percentage should be

= 100% - 20%

= 80%

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The correct answer is 80%

The size of angle BCA is 45 degrees

From the question, we have the following parameters that can be used in our computation:

AB = BC and AD = DC = AC

Also, we have

ABC = 90 degrees

Considering the triangle ABC, we have

A + B + C = 180

This is so because the sum of angles in a triangle is 180 degrees

Using the above as a guide, we have the following:

A + 90 + C = 180

So, we have

A + C = 90

Given that

AB = BC

We have

2C = 90

C = 45

Hence, the angle is 45 degrees

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Complete question

ABCD is a kite with AB = BC and AD = DC = AC, What is the size of angle  BCA

[tex]x^{\frac{8}{15} }[/tex] is the value of yz when x=y⁵=z³  and x is positive.

Two or more expressions with an Equal sign is called as Equation.

Since x=y⁵=z³

Solve for yz as follows:

we can take the fifth root of x to get y, and the cube root of x to get z:

We can solve for yz as follows:

[tex]y=x^{\frac{1}{5} }[/tex]

[tex]z=x^{\frac{1}{3} }[/tex]

Now yz=[tex]x^{\frac{1}{5} }.x^{\frac{1}{3} }[/tex]

=[tex]x^{\frac{8}{15} }[/tex]

Hence, option A is correct, if  x=y⁵=z³  then yz is [tex]x^{\frac{8}{15} }[/tex]

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The linear function modeled by the table is given as follows:

y = 2x - 5.

The slope and the intercept are given, respectively, by:

m = 2, b = -5.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

From the table, when x increases by 5, y increases by 10, hence the slope m is given as follows:

m = 10/5

m = 2.

Hence:

y = 2x + b.

When x = 3, y = 1, hence the intercept b is given as follows:

1 = 6 + b

b = -5.

Hence the function is:

y = 2x - 5.

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Answer:

= 74cm²

Step-by-step explanation:

Perimeter of a rectangle

[tex] = 2(l) + 2(w)[/tex]

therefore

= 2(18) + 2(19)

= 36 + 38

= 74cm².

Answer:

y

Step-by-step explanation: People there: S (Seti), A, B, C, D, E, F, G, H, I, J

friend group:

S is friends with A, B

A is friends with B, C

B is friends with C, D

C is friends with D, E

E is friends with F, G

F is friends with G, H

G is friends with H, I

H is friends with I, J

I is friends with J, S

J is friends with S, A

Answer:

Yes, it is possible

Step-by-step explanation:

Think the people as points in space and the friendship between two people as a line connecting two points.

Then the question is equivalent to asking whether it is possible for all 11 points being connected by lines such that every point is connected to exactly three other points.

Clearly this is possible, since we always have, for each point, ten other points to connect it to, so we can select any three of the ten.

Answer: linear function y=-2x+8, x-intercept at x=4, y-int at (0,8)

Step-by-step explanation:

if it is set equal to y, it is a linear function y=-2x+8, and if set equal to zero, it is an x-intercept to be solved. If an x-intercept is x=4 as you get x by itself by moving the eight over by subtracting and then dividing by negative 2.

(hope it helps as I am not sure what you are asking)

it is -2 multiplied by a number of x, plus 8

Answer:

This is an algebraic expression.

Step-by-step explanation:

This is an algebraic expression. It represents a linear function in which the variable "x" is multiplied by -2 and then 8 is added to the result. In mathematical terms, it represents a straight line with a slope of -2 and a y-intercept of 8. If we were to plot this expression on a graph, the line would have a negative slope and would cross the y-axis at the point (0, 8). The expression can be used to model a relationship between two variables, such as the relationship between time and distance, or between temperature and pressure, for example.

Answer:

In 287.9412, 9 is at the tenth place. So , the answer is 287.9.

Step-by-step explanation:

Answer:

Step-by-step explanation:

$7.75/6= $1.29

$8.33/7= $1.19

$10.45/9= $1.16

The better deal in the 9 candy bars for $10.45 because its only $1.16 PER candy bar.

The value of a is obtained as follows:

a = 5.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

When two lines are perpendicular, the multiplication of their slopes is of -1.

Then the equation to obtain the value of a is given as follows:

0.5(1 - a) x 0.5 = -1.

0.25(1 - a) = -1

1 - a = -4

a = 1 + 4

a = 5.

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Answer:

y = 7x

Step-by-step explanation:

it is simple : x times how much is y ?

2 × ? = 14

? = 7

control

4 × ? = 28

? = 7

identical, so it is correct, and y = 7x is the answer.

Answer:

Est: 4.62%

Step-by-step explanation:

The required (0,4) after dilation with a scale factor of 1/3  is (0, 4/3). Option C is correct.

The scale factor is defined as the ratio of the modified change in length to the original length.

here,
Since let the coordinate before dilation be (x, y),
Now when applying the scale factor to the coordinate, the transformation equation is given as,
(X, Y) = (sx , sy)  where s is the scale factor,

Since matching the above equation with the option,

(3.0) dilated by a scale factor of 1/3 a (0, 6) (False)
(3,4) dilated by a scale factor of 1/3 scale factor b (1,0)  (False)
(0,4) after dilation with a scale factor of 1/3 is  (0, 4/3)  (True)

Thus, the required (0,4) after dilation with a scale factor of 1/3  is (0, 4/3). Option C is correct.

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Kendra hits the target more often than Dalisay.

What is the hit rate?

Hit rate is a measure of performance that calculates the proportion of successful hits or positive outcomes in a given situation, usually expressed as a percentage.

To compare Kendra and Dalisay's performance in hitting the target, we need to determine the hit rate for each archer.

Kendra hits the target 3 times for every 5 misses. The hit rate for Kendra can be calculated as:

hit rate = 3 / (3 + 5) = 3/8

Dalisay hits the target 5 times for every 7 misses. The hit rate for Dalisay can be calculated as:

hit rate = 5 / (5 + 7) = 5/12

Comparing the hit rates, we see that Kendra has a higher hit rate than Dalisay.

Therefore, Kendra hits the target more often than Dalisay.

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Dividing with an area model and multiplying with an area model are similar in that they both involve partitioning a rectangular area into smaller parts.

However, dividing with an area model involves starting with the total area and then dividing it into equal parts to find the size of each part. For example, to divide 12 by 3, we could draw a rectangle with an area of 12 and then partition it into 3 equal parts to find that each part has an area of 4.

Multiplying with an area model involves starting with the size of the smaller parts and then combining them to find the total area. For example, to multiply 3 by 4, we could draw a rectangle with a width of 3 and a height of 4 and then calculate the area of the rectangle as 12.

So, while both methods involve using an area model, dividing starts with the total area and finds the size of the parts, while multiplying starts with the size of the parts and finds the total area.

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Check the picture below.

[tex]\cfrac{8^2}{6^2}~~ = ~~\cfrac{A_1}{A_2}\implies \cfrac{8^2}{6^2}~~ = ~~\cfrac{A_1}{(36)}\implies \cfrac{8^2(36)}{36}=A_1\implies 8^2=A_1\implies \stackrel{ mm^2 }{64}=A_1[/tex]

Answer:

20×5=100

380-100=280

280÷120=2 and 40 remain

40÷20=2

The expression to represent the total volume of the two storage spaces is s³+12.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Given that, the edge of the large cube s feet and the volume of the small cube is 12 ft³.

We know that, the formula to find the cube is side³.

Volume of large cube = s×s×s

= s³

Total volume of the two storage spaces =s³+12

If edge of large cube is 4 feet long, then the volume is

4³ = 64 ft³

Therefore, the expression to represent the total volume of the two storage spaces is s³+12.

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The probability that a student ordered a hamburger and a Slurpee is Option D) 23 over 137.

Generally, To find the probability that a student ordered a hamburger and a Slurpee, we need to divide the number of students who ordered a hamburger and a Slurpee by the total number of students.

From the table, we can see that 23 students ordered a salad and a water.

There were a total of 38 + 12 + 14 + 18 + 28 + 7 + 23 = 137 students in the cafeteria.

Therefore, the probability that a student ordered a salad and a water is 23/137, or about 0.17.

Therefore, the correct answer is d) 23 over 137.

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The value of x by using vertical angles is 4, and the measure of angle R is 34°

Vertical angles are angles that are formed and are opposite of each other when two lines intersect. Vertical angles are congruent angles, it implies that they exhibit the same angle measure. Vertical here refers to the fact that they have the same Vertex (corner point).

From the information given:

6x + 10 = 8x + 2

6x - 8x = 2 - 10

-2x = -8

x = -8/-2

x = 4

The measure of angle R = 6x + 10

= 6(4) + 10

= 24 + 10

= 34°

Therefore, we can conclude that the measure of angle R is 34°

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