Solve the system, enter the smallest x coordinate first

The angle congruent to ∠6 are ∠8, ∠3, ∠9 and ∠14

When parallel lines are cut by a transversal, angle relationships are formed. They include corresponding , alternate and many more.

L║m

n ║ q

Therefore, the angles congruent to ∠6 by alternate or corresponding relationship are as follows:

∠6≅∠8≅∠3≅∠9≅∠14

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Answer:

Step-by-step explanation:

Area of trapezoid = ½ (a + b) h

½ (22 + 10) 8 =

½ 32 × 8 =

16 × 8 =

128 cm²

The sum of the vectors given is -i

Vectors consists of y and x axis. They are plotted on an xy plane known as the argand diagram.

Given the following vectors

u = 3i - 8j

v = -4i + 8j

Take the sum of the vectors

u + v = (3i - 8j) + (-4i + 8j)

Take the sum to have

u + v = (3i-4i)+(-8j+8j)

u + v = -I

Hence the sum of the vectors given is -i

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SOLUTION :-

AREA of sector = ( ∆/360° ) × πr²

∆ = given angle , r = radius

hence ,

AREA of sector for given angle

= ( 120°/360° ) × π 12² mi²

= ⅓ × π × 144 = 150.79 mi² = 151 mi² ( rounded off )

________________________________

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Answer:

Sector area = 151 mi²

Step-by-step explanation:

We can use the formula for sector area:

Area = [tex]\frac{\theta}{360} \pi\ r^2[/tex]

where:
θ = central angle (120°),

r = radius of circle (12 mi) .

Substituting these values into the formula:

Area = [tex]\frac{120}{360} \pi\ \times (12)^2[/tex]

        ⇒ 48 π

        ⇒ 150.796

        ≈  151 mi²   (rounded to the nearest whole number)

By taking the quotient between the money that they make and the time spent to make that money, see can see that Amy earned more profit.

Here we can define profit as the ratio between the money that they make, and the number of hours that they worked to make that money.

Matt earned $125, and spent $50 on shoes for his work, so he earned $75.

And worked 120 hours for these $75, so his profit per hour is:

M = $75/120 = $0.625

Amy worked for 110 hours, won $230 and spent $30 on clippers, then she won a total fo $200.

Her profit per hour is:

A = $200/110h = $1.82

We can see that Amy earned more profit.

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The radius of the sector of the circle with the given area is: B. 3.

Area of sector of a circle = ∅/360 × πr².

Given the following:

Area of sector = 9/8 π cm².

∅ = 45 degrees

Plug in the values into the formula

9/8π = 45/360 × πr²

1.125 = 0.125 × r²

1.125/0.125 = r²

9 =  r²

r = 3 cm

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Answer: 8.2

Step-by-step explanation:

As angles in a triangle add to 180 degrees,

[tex]\angle A=180^{\circ}-121^{\circ}-31^{\circ}=28^{\circ}[/tex]

So, by the Law of Sines,

[tex]\frac{a}{\sin A}=\frac{b}{\sin B}\\\\a=\frac{b \sin A}{\sin B}\\\\a=\frac{9 \sin 28^{\circ}}{\sin 31^{\circ}}\\\\a \approx \boxed{8.2}[/tex]

The solution to the variables using equations 1, 2 and 3 is x = 2, y = -1 and z = 3 and the solutions in part b hold for equation 4

There are three variables in the system

To solve the three variables, there must be at least three equations in the system of equations

Hence, the variables cannot be solved because the number of equations is not enough

We have:

3x + z + y = 8

5y - x = -7

3z + 2x - 2y = 15

Make x the subject in (2)

x = 5y + 7

Substitute x = 5y + 7 in (1) and (3)

3(5y + 7) + z + y = 8

15y + 21 + z + y = 8

16y + z = -13

3z + 2(5y + 7) - 2y = 15

3z + 10y + 14 - 2y = 15

3z + 8y = 1

Multiply 16y + z = -13 by 3

48y + 3z = -39

Subtract 3z + 8y = 1 from 48y + 3z = -39

48y - 8y + 3z - 3z = -39 - 1

40y = -40

Divide by 40

y = -1

Substitute y = -1 in x = 5y + 7

x = 5(-1) + 7

x = 2

Make z the subject in 16y + z = -13

z = -13 - 16y

Substitute y = -1

z = -13 - 16(-1)

z = 3

Hence, the solution to the variables using equations 1, 2 and 3 is x = 2, y = -1 and z = 3

We have:

4x + 5y - 2z = -3

Substitute x = 2, y = -1 and z = 3

4(2) + 5(-1) - 2(3) = -3

Evaluate

-3 = -3 --- this is true

Hence, the solutions in part b hold for equation 4

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Missing part of the question

The following equations are given:

Equation #1: 3x + z + y = 8

Equation #2: 5y - x = -7

Equation #3: 3z + 2x - 2y = 15

Equation #4: 4x + 5y - 2z = -3

Answer: 3 units²

Step-by-step explanation: The area of a triangle is 1/2 (Bh); 1*1= 1 (1/2)= 1/2 units². For the other shape, I cut it into a square and another triangle. The square area is length times width; 1*1= 1 units². The final triangle is 3*1= 3*1/2= 1.5 units². Lastly you add all the areas together: 1.5+0.5+1= 3 units²

Answer:

about 18.3 square meters

Step-by-step explanation:

Since the circle has radius 4 meters, the area of the circle is (4^2)π, or 16π square meters, The area of the square is (4√2)^2, or 32 square meters. Subtracting, we have 16π-32, or about 18.3 square meters, for the area of the shaded region.

Let the numerator be x & denominator be y then,

ATQ,

x+1/y-1=12/11

11x+11=12y-12

11x-12y+11+12=0

11x-12y+23=0....(1)

&

x+3/y-3=14/9

9x+27=14y-42

9x-14y+27+42=0

9x-14y+69=0....(2)

Multiplying eq . 1 by 9 & eq. 2 by 11

We get,

99x-108y+207=0....(3)

99x-154y+759=0....(4)

Subtracting eq. 4 by eq. 3

99x-108y+207=0

99x-154y+759=0

______________

0 + 46y - 552 =0

______________

46y= 552

________

y=552/46

________

y=12

____

putting the value of y in eq. 1,

11x-12y+23=0

11x-12*12+23=0

11x-144+23=0

11x-121=0

11x=121

x=121/11

x=11

So, y = 12 & x = 11 & the fraction is 11/12

ㅤㅤㅤㅤㅤㅤ

ㅤㅤㅤㅤㅤㅤ

-lyricalblues

Answer:

assume X dollar is $100

If so then,

$100-10% =$90

Thus,

$90x125%=$112.5

The blanks can be filled with definitions of property bisector,  Substitution property of equality, and Distributive property, respectively.

When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."

The given blanks can be filled as,

Hence, the blanks can be filled with definitions of property bisector,  Substitution property of equality, and Distributive property, respectively.

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Answer:

y=1/2x+1

Step-by-step explanation:

First use slope formula.

[tex]\frac{y2-y1}{x2-x1}[/tex]

Plug in the information needed.

[tex]\frac{1-3}{0-4}=\frac{-2}{-4}=\frac{1}{2}[/tex]

The slope is [tex]\frac{1}{2}[/tex].

Now, use point-slope formula.

y-y1=m(x-x1)

Plug in the information needed.

y-3=1/2(x-4)

y-3=1/2x-2

y=1/2x+1

The equation of the line in slope-intercept form is y=1/2x+1.

Hope this helps!

If not, I am sorry.

Answer:

A

Step-by-step explanation:

The first picture shows the parent function,

A function assigns a x for only one y.

The inverse is opposite

The inverse assign a y for only one x.

So the answer is the table that swap x and y values.

The coordinates for the parent function are

(0,0)

(2,1)

(4,2)

So the inverse should have

(0,0)

(1,2)

(2,4)

A shows that, so a is the answer

The relationship given in the graph is not function. Option C. is True.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is independent variable while Y is dependent variable.

The relationship given in the system is not a function. because the values of y is repeating at certain values of x. And the curve has number of discontinuity.

Thus, from the options given only option c describe the relationship given in the graph is not a function because there more than one value of x corresponding yo y - 2.  

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The value of the composition of functions f(g(3)) is given by (A) -1.

Here given that the functions are,

f(x) = 3x-7

g(x) = (x+1)/(x-1)

To find the value of g(3) we have to first substitute the value x = 3 in the given function g(x), doing that we get,

g(3) = (3+1)/(3-1) = 4/2 =2

Thus the value of g(3) = 2

Now in order to find the value of composition of functions f(g(3)) we have to substitute the value of x = g(3) = 2 in the given function f(x), doing that we get,

f(g(3)) = f(x = g(3)) = f(x = 2) = f(2) = 3*2-7 = 6-7 = -1

Thus the value of the required composition of functions f(g(3)) is given by -1.

Hence the correct option is given by (A).

The question is incomplete. Find the full content below.

Consider these functions:

f(x) = 3x-7

g(x) = (x+1)/(x-1)

What the value of f(g(3))?

(A) -1

(B) 0

(C) 3

(D) 5

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Answer: 11

Step-by-step explanation:

By the secant-secant theorem,

[tex]5(5+7)=(JK)(15)\\\\60=(JK)(15)\\\\JK=4\\\\\implies IJ=15-4=11[/tex]

1) ray

2) line

3) line segment

4) adjacent angles

5) vertical angles

Answer:

1) RAY

2) LINE

3) LINE SEGMENT

4) VERTICAL ANGLES

5) VERTICAL ANGLES

Answer:

[tex]3 \log 2[/tex]

Step-by-step explanation:

Given expression:

[tex]\log 2 + \log \left(\dfrac{3}{2}\right)+\log \left(\dfrac{4}{3}\right)+\log \left(\dfrac{5}{4}\right)+\log \left(\dfrac{6}{5}\right)+\log \left(\dfrac{7}{6}\right)+\log \left(\dfrac{8}{7}\right)[/tex]

[tex]\textsf{Apply the \underline{Log Product Law}}: \quad \log_ax + \log_ay=\log_axy[/tex]

[tex]\implies \log \left(2 \cdot \dfrac{3}{2} \cdot \dfrac{4}{3} \cdot \dfrac{5}{4} \cdot \dfrac{6}{5} \cdot \dfrac{7}{6} \cdot \dfrac{8}{7}\right)[/tex]

Cross out common factors:

[tex]\implies \log \left(\diagup\!\!\!\!2 \cdot \dfrac{\diagup\!\!\!\!3}{\diagup\!\!\!\!2} \cdot \dfrac{\diagup\!\!\!\!4}{\diagup\!\!\!\!3} \cdot \dfrac{\diagup\!\!\!\!5}{\diagup\!\!\!\!4} \cdot \dfrac{\diagup\!\!\!\!6}{\diagup\!\!\!\!5} \cdot \dfrac{\diagup\!\!\!\!7}{\diagup\!\!\!\!6} \cdot \dfrac{8}{\diagup\!\!\!\!7}\right)[/tex]

Therefore:

[tex]\implies \log 8[/tex]

Factor the number:  8 = 2³

[tex]\implies \log 2^3[/tex]

[tex]\textsf{Apply the \underline{Log Power Law}}: \quad \log_ax^n=n\log_ax[/tex]

[tex]\implies 3 \log 2[/tex]

Using it's concept, the domain of the function in interval notation is given by:

(-4,2).

The domain of a function is the set that contains all possible input values for the function. In a graph, it is the set that contains the values of x.

For this function, x varies between -4 and 2, with an open circle, meaning that -4 and 2 are not part of it, hence the domain is:

(-4,2).

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1. 80 sheep when increase in the ratio 5:4 becomes 100 sheep.

2. The perimeter of the shape is : 26cm

Perimeter is the outside boundary of a shape.

It is usually calculated by summing up all the length of the sides of that shape.

Analysis:

1. if the sheep is increased in the ratio 5:4

 then new number of sheep becomes 5/4 x 80 = 400/4 = 100 sheep

2. The perimeter of the shape is the sum of all the sides of the shape = 7 + 4 + 10 +5 = 26cm

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The fraction of the course that are male is 1/4

The given parameter is:

Female = 3 * Male

As a fraction, we have:

Female + Male = 1

Substitute Female = 3 * Male in the above equation

3 * Male + Male = 1

This gives

4 * Male = 1

Divide by 4

Male = 1/4

Hence, the fraction of the course that are male is 1/4

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Answer:

534 = R + 211

Step-by-step explanation:

So the amount of texts Riley received can be expressed as a variable, and in this case I'll use "R". So we know Bella received 534 texts. and that's 211 MORE than riley. So R+211 should be the as 534. This gives you the equation: 534 = R + 211. and if you want to solve for R, you can subtract 211 from both sides to solve for R

The distance between the home plate and the second base is 127.3 feet

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the distance between the home plate and the second base. Using Pythagoras theorem:

x² = 90² + 90²

x = 127.3 feet

The distance between the home plate and the second base is 127.3 feet

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The distance between home plate and second base is  2√4050 feet.

In a square, all sides are equal in length.

If the distance between each pair of bases is 90 feet, it means that each side of the square (representing the distance along the edge) is also 90 feet.

Since home plate and second base are opposite corners of the square, they are connected by the diagonal of the square.

In a square, the diagonal forms a right triangle with the sides of the square.

Using the Pythagorean theorem, we can find the length of the diagonal (the distance between home plate and second base):

diagonal² = side² + side²

diagonal² = 90² + 90²

diagonal²= 8100 + 8100

diagonal² = 16200

diagonal =√16200

diagonal = 2√4050 feet.

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Answer:

Range and median

Step-by-step explanation:

Range = 9 - 3 = 6

Median = 6

Mode = 9

The error Giovanna made in her calculation is multiplying 7 by 2 and adding with 5/8(step 3)

Her calculation:

Her error was multiplying 7 by 2 and adding with 5/8(step 3)

Correct calculation:

7(2 + 5/8)

= 14 + 35/8

= (112+35) /8

= 147/8

= 18 3/8

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Answer:

A) [tex]\frac{15}{8}[/tex]

Step-by-step explanation:

remember Soh Cah Toa!!

[tex]sin=\frac{opposite}{hypotenuse}\\ cos=\frac{adjacent}{hypotenuse} \\tan=\frac{opposite}{adjacent} \\\\cos=\frac{8}{17}\\\\a^2+b^2=c^2\\8^2+b^2=17^2\\64+b^2=289\\b^2=225\\\sqrt{b^2} =\sqrt{225}\\b=15=opposite\\\\tan=\frac{15}{8}[/tex]