Two angles form a linear pair. The measure of one angle is 1/3 the measure of the other angle. Find the measure of each angle.

By elimination, the solution of the system of equations, 5x - 2y = -19 and 2x + 3y = 0, is (-3 , 2).

A system of 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 all the equations.

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

1. Elimination

2. Substitution

3. Graphing

Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.

First, multiply the first equation by 3 and the second equation by 2.

5x - 2y = -19 ⇒ 15x - 6y = -57     (equation 1)

2x + 3y = 0 ⇒ 4x + 6y = 0     (equation 2)

Adding the two equations will eliminate the variable y.

15x - 6y = -57     (equation 1)

4x + 6y = 0     (equation 2)

19x        = -57

x = -3

Substitute the value of x to any of the two equation and solve for y.

2x + 3y = 0     (equation 2)

2(-3) + 3y = 0

3y = 6

y = 2

Hence, the solution of the system of equations is (-3 , 2).

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The required amount of weed killer is 48.6 quarts.

To find the amount of weed killer required, first we will find the total acres of land of two fields.

So, total area of land is -

Area of land = [tex]22\frac{1}{2} + 38\frac{1}{4}[/tex]

Converting mixed fraction to fraction

Area of land = ((2×22)+1)÷2 + ((4×38)+1)÷4

Solving the bracket -

Area of land = 45÷2 + 153÷4

Area of land = 22.5 + 38.25

Area of land = 60.75 acres

Now, for 1 acre of land the required amount of weed killer = 0.8 quarts

So, for 60.75 acres of land the required amount of weed killer = 0.8×60.75

Performing multiplication to find the amount of weed killer

Amount of weed killer required = 48.6 quarts

Hence, the amount of weed killer required is 48.6 quarts.

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The complete question is -

Alan is putting weed killer on a field to get it ready for planting. The directions on the container say to use 4/5 of a quart for each acre of land. How much weed killer will Alan need for two fields, one that is 22 1/2 acres and one that is 38 1/4 acres?

Given numbers[tex]\sqrt{14} , \sqrt{5/2} , \sqrt{9/16} , 1, 11[/tex]  in decreasing order are as follows:

[tex]11, \sqrt{14} , \sqrt{5/2}, 1, \sqrt{9/16}[/tex] .

As given in the question,

Given numbers are as follow : [tex]\sqrt{14} , \sqrt{5/2} , \sqrt{9/16} , 1, 11[/tex]

Approximate value of all given numbers

[tex]\sqrt{14} =3.74\\\\\sqrt{5/2}= 1.58\\ \\\sqrt{9 /16} = 0.75\\ \\1 =1.00\\\\11=11.00[/tex]

Arrange the given numbers in decreasing order :

11 > 3.74 > 1.58 > 1 > 0.75

[tex]\implies 11 > \sqrt{14} > \sqrt{5/2} > 1 > \sqrt{9/16}[/tex]

Therefore, given numbers[tex]\sqrt{14} , \sqrt{5/2} , \sqrt{9/16} , 1, 11[/tex]  in decreasing order are as follows:  [tex]11, \sqrt{14} , \sqrt{5/2}, 1, \sqrt{9/16}[/tex] .

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"If the congruent sides in one isosceles triangle have the same measure as the congruent sides in another isosceles triangle, then the triangles are congruent."

The given statement true.

When two angles become congruent, their degree measures are the same. The reverse of something like the Isosceles Triangle Theorem asserts that the sides of a triangle opposing congruent angles are also congruent.

If two two triangles are congruent, then perhaps the sides opposite the congruent angles are equal, in accordance with the isosceles triangle theorem converse.

Mathematics is defined by theorems. A theorem is a proposition that has been proven true by a rigorous proof, which is a type of logical argument.

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The height of the flagstaff by suing trigonometric ratios is found to be 27 m.

Given,

Height of the ladder, AD = 18 m

The distance to the point below the top of a vertical flagstaff where the ladder reaches, CD = 18m

Angle of elevation of flagstaff from the foot of the ladder, ∠ CAB = 60 °

Δ ACD is isosceles triangle.(Image is attached)

∠ ACB = ∠ CAD = 30 °

In △ ABD, by using the trigonometric ratios, we get that:

Sin 30 ° =  BD / AD

1 / 2 = BD / 18

BD = 9 m

So, the height of the flagstaff will be:

BC = BD + DC =9 + 18 = 27 m

Therefore, we get that, the height of the flagstaff by using trigonometric ratios is found to be 27 m.

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The translation vector will be as follows:

(x, y) → (x - 3, y + 5)

Regina travelled 3 blocks west and 5 blocks north.

The interpretation vector is the distance through which a particle should be moved (made an interpretation of) to be in the following unit cell. The image for an interpretation vector is television. The television ought to be indicated toward the finish of the math.

The distance that an atom must travel in order to transfer to the following unit cell is known as the translation vector. A translation vector is denoted by the letter Tv. At the conclusion of the geometry, the Tv should be provided. Real or fake atoms shouldn't follow a Tv, but symmetry information and other things are acceptable.

Let us consider the direction similar to map where north is positive y-axis , east is positive x-axis , west is negative x-axis and south is negative y-axis.

Therefore the translation vector will be as follows:

(x, y) → (x - 3, y + 5)

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A proportion is an equation stating that two ratios are equivalent.

Ratio is defined as the comparison of two quantities. The ratio between quantities a and b can be expressed as a : b or a/b.

example:

There are 3 girls for every 5 boys in a class. Then, the ratio of girls to boys is 3 : 5 or 3/5.

On the other hand, proportion is defined as the equality between two or more ratios.

a : b = c : d

Two ratios are equivalent if their cross-products are equal. Cross products are the products of the extremes and means.

If a : b = c : d, then ad = bc.

example:

2 : 3 = 6 : 9 is proportion since 2(9) = 3(6) ⇒ 18 = 18

3 : 5 and 4 : 6 is not a proportion since 3(6) ≠ 5(4) ⇒ 18 ≠ 20

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Answer:

Hello,

Step-by-step explanation:

P(x)=x^3-5x^2-7x+51

Since the coefficients are all reals,

4+i (conjugate of 4-i) is also a root.

The polynomial est divisible by (x-4-i)(x-4+i)=(x-4)²+1=x²-8x+17

If we divide P(x) by x²-8x+17 we find the quotient (x+3) and the remainder 0

P(x)=(x+4)(x-4-i(x-4+i)

Roots are -4,4+i and 4-i

Answer:

All the roots are -3, 4-i and 4+i.

Step-by-step explanation:

If oine root is 4 - i then another one is 4 + i as complex roots occur as conjugate pairs.

(4 - i)(4 + i)

= 16 - i^2

= 17.

As the last term = 51 = 3 * 17

looks like the other root is 3 or -3.

By the Factor theorem

If x = 3 then f(3) = 0

f(3) = 27 - 5(3)^2 - 7(3) + 51

     = 27 - 45 - 21 + 51 = 12 so 3 is not a root.

If x = -3:

f(-3) = -27 - 45 _ 21 + 51

      = 0

So,  x = -3 is a root.

Answer:

-9/7

Step-by-step explanation:

Distribute

2x + 8 = -5x - 1

Get variables on left; constants on right

2x + 5x = -1 -8

Gather like terms and do the math

7x = -9

x = -9/7

Answer:

No 1.  3/31

No 2. 3/8

No3. 3/16

Step-by-step explanation:

you mainly just turn it into an improper fraction and then turn it upside down

Brainiest, please :) tysm

Answer:

a) 3/31

b) 3/8

c) 3/16

Step-by-step explanation:

You take the mixed number, turn it into an improper fraction (to do that, you multiply the whole number with the denominator on the fraction, and then you take that number and add it to the numerator of the fraction), and then you flip that improper fraction.

The height of the candle after burning for 2 hours is 16.25 inches.

Given that, a candle is 16 inches tall after burning for 3 hours. after 5 hours, it is 15.5 inches tall.

We need to write a linear equation to model the relationship between the height h of the candle and time t.

An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has an exponent of more than 1. The graph of a linear equation always forms a straight line.

Let t be the time in hours and h be the height in inches.

Now, the ordered pair of the given situation is A(3, 16) and B(5, 15.5).

Find the slope m of the linear equation between points A and B

We know that the formula to calculate the slope between two points is equal to m=(y2-y1)/(x2-x1)

=(15.5-16)/(5-3)=-0.5/2

=-1/4

We know that the equation of the line in the point-slope form is (y-y1)=m(x-x1)

⇒y-16=(-1/4)(x-3

⇒4y-64=-x+3

⇒4y=-x+3+64

⇒4y=-x+67

We need to find how tall the candle will be after burning for 2 hours.

That is, put x=2

4y=-2+67

⇒4y=65

⇒y=16.25 inches

Therefore, the height of the candle after burning for 2 hours is 16.25 inches.

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The expression which represents the function evaluation (f -g)(x) according to the task content is; (f -g)(x) = 2x³ +5x² -8x -4.

It follows from the task content that the required function evaluation required is; (f -g)(x).

Given;

f(x) = 2x³ +5x² - 6x - 7

g(x)=2x-3

To find;

(f-g)(x).

Since; (f -g)(x) = f(x) - g(x), the resulting expression for (f -g)(x) is;

(f -g)(x) = 2x³ +5x² -6x -7 -2x +3

Collect like terms;

(f -g)(x) = 2x³ +5x² -6x -2x -7 +3

Hence, (f -g)(x) = 2x³ +5x² -8x -4

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Mr. Wong paid 63.75 for the car rental.

The cost of rental car will be added one time to the total rent. The cost of trip will be calculated based on the distance covered.

So, forming the equation -

Total cost = 30 + 45 × 0.75

Performing multiplication on Right Hand Side of the equation to find the cost of business trip based on miles distance traveled

Total cost = 30 + 33.75

Performing addition on Right Hand Side of the equation to find the total cost based on one time rent of car and distance traveled

Total cost = 63.75

Hence, the total cost of car rental on business trip is 63.75.

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The probability of the event P(A is on [tex]\bar{CD}[/tex]) is 6/13.

Probability:

The term probability defines the possibility of the favorable event across the total event.

Given,

Point A is chosen at random on [tex]\bar{BE}[/tex].

Here we need to find the the probability of the following event.

P(A is on [tex]\bar{CD}[/tex]).

Let us consider the following image, in order to solve this.

Based on the image we have identified that the probability of the event  P(A is on [tex]\bar{CD}[/tex]) is calculated by dividing the length of CD by the length of BE.

So, the probability of the event P(A is on [tex]\bar{CD}[/tex]) is,

P(A is on [tex]\bar{CD}[/tex]) =  (length of CD) / (length of BE)

Apply the values then we get,

P(A is on [tex]\bar{CD}[/tex]) = 12 / ( 5 + 12 + 9)

P(A is on [tex]\bar{CD}[/tex]) = 12 / 26

And it can be simplified as,

P(A is on [tex]\bar{CD}[/tex]) = 6/13

Therefore, the probability of the event P(A is on [tex]\bar{CD}[/tex]) is 6/13.

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[tex]\angle g=112^{\circ}[/tex] (vertical angles)

[tex]\angle h=68^{\circ}[/tex] (linear pair)

[tex]\angle k=92^{\circ}[/tex] (vertical angles)

[tex]\angle m=88^{\circ}[/tex] (linear pair)

Answer:

:D

Step-by-step explanation:

1.) One ticket out of eighty can be represented by a fractions, 1/80. To find the percentage, you can change 80 to 100 proportionally and then the difference (multiply/divide) to the 1 to find the percentage. You can also cross multiply to find the answer ("a")

[tex]\frac{1}{80} =\frac{x}{100}[/tex]

0.0125 is the chance of getting the ticket, and multiply by 100 to get percentage.

a = 1.25%

2.)
Same thing as #1, different equation :)

[tex]\frac{5}{80} =\frac{x}{100}[/tex]

x = 6.25%

3.)
Same thing as #2, but now, on the bottom is not 80, but instead 70.

[tex]\frac{5}{70} =\frac{m}{100}[/tex]

m = 7.14285714286%

m = 7.14%

Answer:

12a) 1/80=0.0125 = 1.25%

12b) 5/80=0.0625 = 6.25%

12c) 5/70=0.07142 = 7.14%

Step-by-step explanation:

Answer:

x = 7

Hope this helps :)

Explanation and Check part below.

Step-by-step explanation:

1. Isolate variable by doing the inverse operation which is in this case subtracting 9 on both sides of the equation.

3x + 9 = 30

- 9 - 9

3x = 21

2. Divide both sides of the equation by 3 since this is the inverse operation.

3x = 21

--- ---- <-------- fraction bar, divide

3 3

x = 7

Check:

3(7) + 9 = 30

21 + 9 = 30

30 = 30 ✓

Answer:

x=2

angle 1= 27°

angle 2= 27°

Step-by-step explanation:

(x+6) =( 3x -36)

2x=42

x=21

In the account of Rodney's will have the higher ending balance after 1 year.

Given that:

Rodney invests a sum of money, P, into an account that earns interest at a rate of r, compounded yearly.

Gerald invests half that amount into an account that pays twice Rodney’s interest rate.

To find:

Which of the accounts will have the higher ending balance after 1 year?

So, according the question

We have,

For Rodney,

p = Principle = P

r = Interest rate = r

t = time expressed in year = 1 year

n = Number of periods in a year = 1

We, know that the formula to calculate the compound interest for new balance of Rodney ,

    B = [tex]p (1 + \frac{r}{n} )^{nt}[/tex]

Now, putting the values,

    B = [tex]p (1 + \frac{r}{n} )^{nt}[/tex]    

    B = [tex]P(1+\frac{r}{1} )^{1\times 1)[/tex]

    B = [tex]P (1 + r )[/tex]  

    B = P + Pr

Now, For Gerald,

p = Principle = P/2 ( Invest half of the money from Rodney )

r = Interest rate = 2r ( Twice the rate of Rodney's)

t = time expressed in year = 1 year

n = Number of periods in a year = 1

We know that the formula to calculate the compound interest for new balance of Gerald ,

    B = [tex]p (1 + \frac{r}{n} )^{nt}[/tex]

Now, putting the values,

    B = [tex]p (1 + \frac{r}{n} )^{nt}[/tex]    

    B = [tex]\frac{P}{2} (1+\frac{2r}{1} )^{1\times 1)[/tex]

    B = [tex]\frac{P}{2} (1+ 2r)[/tex]  

    B = [tex]\frac{P}{2}[/tex] + Pr

Now compare the amounts of their accounts, so we can say that the amount of Rodney's account will have the higher ending balance after 1 year.

So, In the account of Rodney's will have the higher ending balance after 1 year.

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Answer: 18 Days

Step-by-step explanation: 30x18=540

The two-column proof are:

The angle WXV is congruent to angle YXZ

Triangle WXV congruent triangle YXZ

In this question, we are given;

X as the midpoint of line segment WY and line segment VZ

Therefore, it is correct for us to conclude that;

segment XZ is congruent to segment XV, segment XW is congruent to segment XY

Thus, angle WXV is congruent to angle YXZ

Triangle WXV congruent triangle YXZ

We then conclude that;

VW = ZY

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Trent writes 10×6=60, then in multiplication equation 10 represents the quantity of muffin boxes, 6 represents the numbers of muffins in each box and 60 represents the full numbers of muffins.

According to the statement

We have to find that the multiplication equation.

So, For this purpose, we know that the

The linear equation is defined as an equation that is written in the form of Ax+By=C.

From the given information:

Given,

Trent writes 10×6=60,

Here,

10 represents the quantity of muffin boxes

And

6 represents the numbers of muffins in each box

Then

60 represents the overall numbers of muffins

Hence, Trent writes 10×6=60, then within the multiplication equation 10 represents the amount of muffin boxes, 6 represents the numbers of muffins in each box and 60 represents the full numbers of muffins.

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Answer:

Proportion says that two ratios (or fractions) are equal.

La proporción dice que dos razones (o fracciones) son iguales.

( translated )

The equation of the line passing throigh the given points is given by y = x/7 + 3.

The slope of a line indicates its steepness and direction.

The slope of a line can be calculated using any two distinct points on it. The slope of a line formula calculates the ratio of "vertical change" to "horizontal change" between two distinct points on a line.

Given: Point (28,7)

An equation of perpendicular line y = -7x.

We know if fwo lines are perpendicular then their slopes are negative inverse of each other.

i.e., [tex]m_{1} = \frac{1}{m_{2} }[/tex]

Therefore, y = -7x

Slope, [tex]m_{1}[/tex] = - 7x

Slope of other line will by be  [tex]$\frac{1}{m_1}$[/tex].

[tex]$$m_2=\frac{+1}{7}$$[/tex]

Slope of required equation = 1/7

Substitute [tex]\left(x_1, y_1\right)[/tex] = (28,7), m=1/7 in

(y-[tex]y_1[/tex]) = m (x-[tex]x_1[/tex])

(y -7) = 1/7 (x - 28)

(y - 7) = x/7 - 4

y = x/7 + 3

This is the required equation of line.

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O( 0,0 ) A(9 , 0 ) D( 0,3 ) ( 9, 2) , ( 6 , 3 ) that are vertices of the feasible region.

What do math vertices mean?

The line 2x + 6y = 30

when x = 9 , 18 + 6y = 30

                     y = 2

So B = ( 9, 2)

So, C= ( b , 3 )

then , we can show O( 0,0 ) A(9 , 0 ) D( 0,3 )

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Answer:

(a): 26.1

(b): 27.9

Please see below for the steps.

Step-by-step explanation:

(a):

Use points (0,0) and (3, 78.3)

Use slope formula. The slope formula is also used to find average rate of change (just so you know).

y2-y1/x2-x1

78.3-0/3-0=78.3/3=26.1

Answer for (a) is 26.1

(b):

Use points (4, 147.6) and (9, 287.1)

Use slope formula.

y2-y1/x2-x1

287.1-147.6/9-4=139.5/5=27.9

The answer for (b) is 27.9

Hope this helps!

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Have a great day!

Answer:

2x²+10x+8

Step-by-step explanation:

you have to multiply the brackets first the multiply the 2 in

2(x+1)(x+4)

2(x²+4x+x+4)

2(x²+5x+4)

2x²+10x+8

Answer:

Reflect back on a time when you did something you later were at least somewhat uncomfortable with. Maybe it was something you said or did, but upon reflection you knew it wasn't the right thing to do. If you can't think of a real situation, you can create a hypothetical one.

[tex]\pink{ \rule{2pt}{99999pt}}[/tex]

The roots of the equation will be imaginary. Then the number of real solutions will be zero.

The discriminant represents the types of the root. And the discriminant (D) of the equation ax² + bx + c = 0 is given as

D = b² - 4ac

The type of roots will be given below.

The equation is given below.

x² + 4x + 5 = 0

The discriminant of the given equation will be

D = 4² - 4 x 1 x 5

D = 16 - 20

D = - 4

D < 0

The roots of the equation will be imaginary. Then the number of real solutions will be zero.

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