Solve system of equations.
1/2x-y=-1
x-2 y=5

∠1 and ∠2 will have the values 33° and 147° respectively when they form a Linear Pair.

In the question, It is given that ∠1 and ∠2 form a Linear Pair.

So, ∠1 and ∠2 = 180°, Also it is stated that ∠1 is 18° lesser than 5 times ∠2.

Taking ∠2 = x we get ∠1 = 5x-18

Now for Linear Pair, we have ∠1 + ∠2 = 180°

putting values of ∠1 and ∠2  we get :  (5x-18) + x = 180

Solving the equation  => (5x-18) + x = 180   =>   6x = 198

=>  x = 33

Putting the value of x in both ∠1 and ∠2  we get :

∠2 = 33°  and ∠1  = 5(33) - 18 =>  ∠1  = 147°

Hence, we get ∠1 and ∠2  measures 147° and 33° respectively.

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Using compound interest, it is found that the annual rate of increase was of 3.10%.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

For this problem, the parameters are given as follows:

t = 9, A(t) = 6, A(0) = 4.5, n = 12.

Hence we solve for r to find the interest rate as follows:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]6 = 4.5\left(1 + \frac{r}{12}\right)^{12 \times 9}[/tex]

[tex]1 + \frac{r}{12}\right)^{108} = 1.33[/tex]

[tex]\sqrt[108]{1 + \frac{r}{12}\right)^{108}} = \sqrt[108]{1.33}[/tex]

[tex]1 + \frac{r}{12} = (1.33)^{\frac{1}{108}}[/tex]

1 + r/12 = 1.0026.

r/12 = 0.0026

r = 12 x 0.0026

r = 0.031.

The annual rate of increase was of 3.10%.

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Using trigonometric relations, we can see that the length of the wire is  1,454.5 ft.

We can think of this as a right triangle, such that the height of the tower is one of the legs, and the wire is the hypotenuse.

In this case, we know that the angle between the tower and the wire measures 55.4°, and the height is the adjacent cathetus to this angle.

Then we can use the relation:

cos(a) = (adjacent cathetus)/(hypotenuse)

Where:

a = 55.4°

adjacent cathetus = 600ft

hypotenuse = L = length of the wire.

Replacing that we get:

cos(55.4°) = 600ft/L

L = 600ft/cos(55.4°) = 1,454.5 ft

We conclude that the length of the wire is 1,454.5 ft.

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Answer:

1) 4

2) 16

Step-by-step explanation:

It will take the object 1/5 hour to travel 2 1/5 mi

The given parameters are

Speed = 9 4/5 mi/h

Distance = 2 1/5 mi

The time is calculated as

Time = Distance/Speed

So, we have

Time = (2 1/5)/(9 4/5)

Approximate the factors

Time = (2)/(10)

Evaluate

Time = 1/5

Hence, it will take the object 1/5 hour to travel 2 1/5 mi

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Answer:

18,6,2

Step-by-step explanation:

To get from the first term to the second term we divide by 3 .

To get from the second term to the third term we divide by 3 .

So we continue this pattern to find the next 3 terms :

So 54 ÷ 3 = 18

18 ÷ 3 = 6

6 ÷ 3 = 2

Hope this helped and have a good day

Answer:

Step-by-step explanation:

2 pounds / 5 people

x pounds / 13 people

2/5 pounds per person so 2/5 * 13 = 26/5

5 1/5 i think

sorry if its wrong

Answer: The answer of the question is 2 and 3/5.

Step-by-step explanation: Every pound of meat serves one person, because 10 divided by 2 people is 5. Then, there are 3 pieces of meat left over, and since every person eats 5/5, or 1 whole, then there are 3/5 pieces left over. You then add 2 and 3/5 together, getting your answer 2 3/5.

Answer: Hope it helps!!

I believe it is B. as well

Desmos Graphing calculator is great for problems as well!

If he makes the cubes as large as possible, the maximum number of cubes is equal to 900 cubes.

In order to determine the number of cubes that would be produced by Richard when the rectangular prism is cut into congruent cubes without any part of the rectangular prism leftover, we would make the edges of the cube 100 times larger and then evaluate:

Note: The greatest common factor (GCF) of the dimensions above is 75.

Next, we would divide each of the dimension by 75:

Length of cube = = 450/75 = 6 feet.

Breadth of cube = 750/75 = 10 feet.

Height of cube = 1125/75 = 15 feet.

Therefore, the maximum number of cubes is given by:

Maximum number of cubes = 6 × 10 × 15

Maximum number of cubes = 900 cubes.

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Complete Question:

Richard cuts a 4 1/2 ft × 7 1/2 ft × 11 1/4 ft rectangular prism into congruent cubes without any part of the prism leftover. If he makes the cubes as large as possible, how many will he produce?

Answer:

56

Step-by-step explanation:

(1+2*3)^2+7

(1+6)^2+7

7^2+7

49+7

56

Answer:

Step-by-step explanation:

Using PEMDAS, first find the product of the parentheses. 2*3=6. 1+6=7. 7² is 49. 49+7=56.

We have proved that the line joining the midpoints of two sides of a triangle is parallel to the third side and half its length by using a vector.

A quantity or phenomenon with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature. A quantity or phenomenon that just exhibits magnitude and no specific direction is referred to as a scalar. (Weight is the force produced by the acceleration of gravity acting on a mass.) Scalars include things like velocity, mass, electrical resistance, and hard disk storage space.

In the triangle ABC, D is the midpoint of AB, and E is the midpoint of AC.

Now, using the triangle rule for triangle ADE,

AE+AD = ED

And for triangle ABC,

CA+AB = CB

2AE+2AD = CB [as AD = 1/2AB and AE=1/2AC]

=> 2(AE+AD) = CB

=> 2ED = CB

=> ED = CB/2

We can write two vectors equal to each other with only difference in magnitude only when they are parallel, i.e., the angle between ED  and CB is 0.

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One and one fifth pounds of chicken will be needed for a single serving.

Adapting recipes to fit the requirements of various contexts is common. Changing the amount of individual servings a recipe yields is the most frequent cause for recipe modifications. A typical recipe, for instance, might be written to make 25 pieces. The recipe must be properly altered if a circumstance develops when 60 servings of the item are required.

Changes in portion sizes (which may entail adjusting the recipe's batch size) and improved use of the preparation tools available are two additional reasons to modify recipes (for example, you need to divide a recipe to make two half batches due to a lack of oven space).

4 servings requires 4 and 4/5th pounds = 4+4/5= 24/5 pounds

1 serving will require = 24/5 pounds / 4 = 6/5 = (1+1/5) pounds

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Answer: 1 1/5

Step-by-step explanation: I took the test

After the rotation of the point, we get the point as (5, 2)

We are given a point:

C (2, -5)

We first need to rotate it 180°.

When rotating a point 180 degrees counterclockwise about the origin our point A(x, y) becomes A'(-x, -y). So all we do is make both x and y negative.

So, we get the point as:

( - 2 , 5 )

Now, we need to rotate it 270°

The algebraic rule for a figure that is rotated 270° clockwise about the origin is (y, -x).

So, we get the point as:

(5, 2)

Therefore, after the rotation of the point, we get the point as (5, 2)

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-120... I would be easier if you used a scientific calculator

Answer:   24

Step-by-step explanation:

[Solve brackets first]

[tex](-7--9)\\-7+9 = 2[/tex]

[Perform the multiplication]

[tex]8[/tex] x [tex]2 = 16[/tex]

[Finally do the Addition]

[tex]16 + 8 = 24[/tex]

General Rule:

Brackets Indices Division Multiplication Addition Subtraction

[tex]Negative + Negative = Positive \\Negative + Positive = Negative[/tex]

Answer:

(l) y=2x-2

(ll) y=4x+1

(lll) y=5x+13

(lV) y=-3x-6

(V) y=-5x-17

(Vl) y=(2/3)x-3

Answer:

23

Step-by-step explanation:

38/13 = 3

69/3 = 23

Answer:

Step-by-step explanation:

Write an expression for the perimeter of a rectangle with a length of

(3x² + x + 2) and a width of (-x² – 5x + 1).

P = 2 × (L + W)

2 × [(3x² + x + 2) + (-x² – 5x + 1)] =

if you want the result:

4x²−8x+6

Answer:

(3+9)/(5-2)x5 = 20

Step-by-step explanation:

It's a rather tedious type of task, because there's no simple way to solve them, except kind of by brute force or by trial and error. Here we can start by noticing x5 at the end, so if we can force everything before to be 4 it's gonna be dandy:

can we add brackets to 3+9/5-2 to be equal to 4 (because 20 / 5)?

fortunately, 3+9 is 4 times more than 5-2, so (3+9)/(5-2) = 4

so (3+9)/(5-2)x5=20 is a correct solution

Answer:

The height is 5.

Step-by-step explanation:

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This is the correct answer

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The equation of the line is [tex]5y+4x-35=0[/tex]

Given,

Point is (5,3)

Slope m=-4/5

so formula of  equation of line is

[tex](y-y_{1})=m(x-x_{1})[/tex]

[tex](y-3)=-4/5(x-5)[/tex]

[tex]5y-15=-4x+20\\5y+4x-15-20=0\\5y+4x-35=0[/tex]

A line's equation can be formed using the slope of the line and a point on the line. To better understand the formation of a line equation, let us learn more about the slope of the line and the required point on the line. The slope of a line is its inclination with respect to the positive x-axis, and it is expressed as a numeric integer, fraction, or the tangent of the angle it makes with respect to the positive x-axis. The term "point" refers to a coordinate system point with the x and y coordinates.

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[tex]f(x) = (3 {x}^{4} + 1) {}^{2} \\ f(x) = 0 \\ (3 {x}^{4} + 1) {}^{2} = 0 \\ 3x {}^{4} + 1 = 0 \\ 3x {}^{4} = -1 \\ x {}^{4} = \frac{ - 1}{3} [/tex]

[tex]f(x) \: admits \: no \: real \: roots[/tex]

Answer:

6 yards

Step-by-step explanation:

Answer:

[tex]5\frac{3}{4}[/tex]

Step-by-step explanation:

bottom is below, so we use a negative number

[tex]bottom = -3\frac{1}{2}\\top = 2\frac{1}{4}\\distance = top - bottom = 2\frac{1}{4} - (-3\frac{1}{2}) = 2\frac{1}{4} + 3\frac{1}{2} = 5\frac{3}{4}[/tex]

The width of the rectangular mat is 7/10 units.

We know that the area of rectangle is A = length × width

For given question,

Let w be the width of the rectangular mat and l be the length of the rectangular mat.

The length of the mat is 5/6.

⇒ l = 5/6

A rectangular mat has an area of 7/12.

⇒ A = l × w

⇒ 7/12 = 5/6 × w

⇒ w = 7/12 × 6/5

⇒ w = 7/10

Therefore, the width of the rectangular mat is 7/10 units.

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The height to the top of the nth story of the building is  ( 24 + 18(n-1) ).

Height of first story of a building = 24 feet

Height of each additional story = 18 feet

Total number of stories in a building = n

The Height of first story of a building is fixed to be 24 feet and Height of each additional story is 18 feet. We first need to calculate total number of additional stories to write an equation.

The total number of additional stories =  ( total number of stories in a building - 1) = (n-1)

The height of total additional stories = 18 (n-1)

Total height of the building = (Height of first story of a building + height of total additional stories) = ( 24 + 18(n-1) ).

The height to the top of the nth story of the building is  ( 24 + 18(n-1) ).

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Answer:

(0,-5)

(2,1)

5,3

Step-by-step explanation:

Answer: 1.29 x 104 lbs.

Step-by-step explanation:

4.23 x 103 lbs. and 8.7 x 103 lbs.

4.23 x 103 + 8.7 x 103 =

4.23 x 10^3 + 8.7 x 10^3 =

(4.23+8.7) x 10^3 =

(4.23+8.70) x 10^3 =

(12.93) x 10^3 =

1.293 x 10 x 10^3 =

1.293 x 10^1 x 10^3 =

1.293 x 10^(1+3) =

1.293 x 10^4 =

1.293 x 10^4 = 1.29 x 104 lbs.

The total weights of the two animals in scientific notation is

13.32 x 10² lbs

What is scientific notation ?

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.

According to the given question,

First animal weight 4.23 x 103 lbs

Second animal weigh 8.7 x 103 lbs

adding both the animal weights

= 4.23 x 103 + 8.7 x 103

= (4.23 + 8.7 ) x 103

= 12.93 x 103

= 1331.79 lbs

converting into scientific notation

= 13.3179 x 10² lbs  (rounding off)

≈ 13.32 x 10² lbs

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Answer: 97°

Step-by-step explanation:

∠XWY = 153°

∠2 = 56°

∠1 = ?

∠XWY-∠2=∠1

153°-56°=?

? = 97°

The system of equations involving x + y = -6 and 2x - y = 3 has the solution x = -1 and y = -5.

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given two linear equations in x and y,

x + y = -6     (equation 1)

2x - y = 3     (equation 2)

Express y in terms of x in one of the equations,

x + y = -6     (equation 1)

y = -x - 6

and then substitute it in the 2nd equation.

2x - y = 3     (equation 2)

2x - (-x - 6) = 3

2x + x + 6 = 3

3x = 3 - 6

3x = -3

x = -1

Substituting the value of x in the equation of y,

y = -x - 6

y = -(-1) - 6

y = 1 - 6

y = -5

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We get that the absolute inequality will be | x + 16 | < 8.

We are given two inequalities:

x < - 8 and  x > 24

We need to write one inequality by combining both the inequalities.

We know that:

x < - 8 means that x can have any value less than - 8

x ∈ ( - ∞ ,  - 8 )

Also, x > 24 means that:

x ∈ ( 24 , ∞ )

So, combining these, we get that:

x = ( - ∞ ,  - 8 ) U ( 24 , ∞ )

Inequality will be:

| x + 16 | < 8

Therefore, we get that the absolute inequality will be | x + 16 | < 8.

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