In the diagram provided, line l is parallel to line m. Select which of the following statements could be used to prove that the interior angles of a triangle have a sum of 180°. You may choose more than one correct answer.

m 4 + m 5 + m 6 = 180.
1 and 4 are alternate interior angles.
m 5 = m 3 + m 2
. m 5 + m 1 = 180.

Answer:

Step-by-step explanation:

y = 600 * (1.04)¹⁵

= 600 * 1.80094351

= $ 1080.57

Answer:

x = 2

Step-by-step explanation:

0.3 (4 - x) = x - 1.4

1.2 - 0.3x = x - 1.4

-0.3x - x = -1.4 - 1.2

-1.3x = -2.6

x = 2

Answer:

Step-by-step explanation:

[tex]\displaystyle\ \Large \boldsymbol{} 0,3(4-x)=x-1,4 \\\\1,2-0,3x=x-1,4 \\\\x+0,3x=1,2+1,4\\\\1,3x=2,6 \\\\\underline{x=2 \ \ \ \ \ \ \ } \\\\0,3(4-2)=2-1,4 \\\\2\cdot 0,3=0,6 \\\\0,6=0,6[/tex]

Answer:

a/9 - 4

Step-by-step explanation:

The expression will be (x/9) - 4.

It is given that a number x is the quotient of a number and 9 decreased by 4.

We have to find the variable expression for this.

What will be the expression for , 2 times of a number minus 4 ?

The expression will be 2x -4.

Quotient of a number and 9

= x / 9

Decrease this by 4 ; we get

= (x / 9 ) - 4

Thus , the expression will be (x/9) - 4.

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Answer:

C

A

Step-by-step explanation:

adjacent means neighboring, right next to it. that would be 1 and 4.

supplementary means being a complementary, an additional angle, so that in sum both angles together have 180 degrees. and that is only 1.

so, C is the answer.

angle 7 = 115 degrees.

so, angle 8 is supplementary to angle 7.

they are being mirrored on the other side of the line.

so, angle 6 = angle 7, and angle 5 = angle 8.

and the same quadruple of angles have to appear, where the crossing line crosses another, parallel line. they have to be the same angles there again.

so, angle 3 = angle 7, angle 4 = angle 8, angle 1 = angle 5, angle 2 = angle 6.

and because angle 6 is also = angle 7, we have angle 2 = angle 7 = 115 degrees.

Answer:

C and A

Step-by-step explanation:

∠ 5 and ∠ 1 are adjacent ( next to each other) on the same line

The angles on a straight line sum to 180° ( supplementary )

Then ∠ 1 is adjacent and supplementary to ∠ 5 → C

----------------------------------------------------------------------------

∠ 2 and ∠ 7 are alternate exterior angles and are congruent , then

∠ 2 = ∠ 7 = 115° → A

Answer:

28x-16y+45.4

Step-by-step explanation:

Add up all the variables inside the bracket by first grouping like terms

Then, multiply through by 2 ✅✅

[tex]\\ \sf\longmapsto \dfrac{x}{y}+\dfrac{y}{x}=2[/tex]

[tex]\\ \sf\longmapsto \dfrac{x^2+y^2}{xy}=2[/tex]

[tex]\\ \sf\longmapsto x^2+y^2=2xy[/tex]

[tex]\\ \sf\longmapsto x^2+y^2-2xy=0[/tex]

[tex]\boxed{\sf (a-b)^2=a^2-2ab+b^2}[/tex]

[tex]\\ \sf\longmapsto (x-y)^2=0[/tex]

[tex]\\ \sf\longmapsto x-y=\sqrt{0}[/tex]

[tex]\\ \sf\longmapsto x-y=0[/tex]

Now

[tex]\\ \sf\longmapsto 4x-4y-4[/tex]

[tex]\\ \sf\longmapsto 4(x-y-4)[/tex]

[tex]\\ \sf\longmapsto 4(0-4)[/tex]

[tex]\\ \sf\longmapsto 4(-4)[/tex]

[tex]\\ \sf\longmapsto -16[/tex]

Answer:

14

Step-by-step explanation:

19 - 5 = 14

Answer:  assuming g(x) is the inverse of f(x)

domain of g(x) = range of f(x)

range of g(x) = domain of f(x)

Answer:

Step-by-step explanation:

Answer:

angle 1 = 80

angle 2 = 80

Step-by-step explanation:

in rhombus all sides are equal and also diagonals bisects each other

so

Answer:

24+p=t

Step-by-step explanation:

If he scored 24 points in the first half, and p in the next half, he scored a total of t points.

Answer:

It's 3/40

Step-by-step explanation:

Answer:

3/40

Step-by-step explanation:

Multiply the numerator by the other numerator (top number) to get 1*3=3.

Then multiply the denominator by the denominator (bottom number) to get 8*5=40.

Final answer is: 3/40

Answer:

8.1 = LM

Step-by-step explanation:

(whole secant) x (external part) = (tangent)^2

13 * 5 = LM^2

65 = LM^2

sqrt(65) = LM

8.06225 = LM

To one decimal place

8.1 = LM

Answer:

The salon would've made $1,240.

Step-by-step explanation:

Think of the customers as the numbers and the visits as variables. Then the equation would look something like this:

Revenue = 100(first visit) + 30(second visit) + 10(third visit)

And now, we just solve:

r = 100(10) + 30(6) + 10(6)

r = 1,000 + 180 + 60

r = $1,240

Answer: f(x) = -(x-1)^2+5

Explanation:

f(x) = h(x) + 6

f(x) = -(x-1)^2 - 1 + 6

f(x) = -(x-1)^2+5

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Answer:

Step-by-step explanation:

Answer:

A statistical method to identify cost behavior.

Step-by-step explanation:

Costing is the measurement of the cost of production of goods and services by assessing the fixed costs and variable costs associated with each step of production.

In Financial accounting, the three methods used to classify costs into their fixed and variable components includes high-low method, scatter diagrams and least-squares regression.

A least squares regression line is a standard technique in regression analysis used to make the vertical distance obtained from the data points running to the regression line to become very minimal or as small as possible.

Hence, the least-squares regression method is a statistical method that is typically used for identifying cost behavior.

Generally, the sum of the residuals of a least squares regression line is always equal to zero.

Answer:

2n+2

Step-by-step explanation:

the common difference is 4,6,8

again the common difference of 4,6,8 is 2,2

hence its common difference is 2

now, nth term,=a+(n-1) *d

4+(n-1)*2

4+2n-2

2n+2

Answer: x = 7

Step-by-step explanation:

6(2x-11)+15=3x+12

1) Distribute 6 (distributive-property)

12x - 66 + 15 = 3x + 12

12x - 51 = 3x + 12

Subtract 12 from both sides; what ever you do to one side, you need to do to ther other.

12x - 63 = 3x

Subtract 3x from both sides.

9x - 63 = 0

Add 63 to both sides.

9x = 63

Divide by 9 to getx by itself.

63/9 = 7

x = 7

Answer:

The answer is B and C.

Answer: B AND C

Step-by-step explanation:

Remote interior angles are angles that are opposite from the exterior angles (5 in this case).

Answer:

-11

0

Step-by-step explanation:

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Answer:

$28.5

Step-by-step explanation:

Step-by-step explanation:

the correct answer is option c

Answer:

I did this same answer on another app

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Answer:

42 units^2

Step-by-step explanation:

Break this into a rectangle and a triangle

The rectangle is 12 by 1

A = l*w = 12*1 =12

The triangle has a base of 6-1 =5  and a height of 12

A = 1/2 bh = 1/2 (5)*12 = 30

Add the areas together

12+30 =42

Answer:

[tex]42 \: {units}^{2} [/tex]

Step-by-step explanation:

First divide the shape into triangle and a rectangle

then find the Area of the triangle and the rectangle separately

Area of the rectangle

[tex]area = l \times b \\ = 12 \times 1 \\ = 12 \: \: {units}^{2} [/tex]

Area of the triangle

[tex]area = \frac{1}{2} \times bh \\ = \frac{1}{2} \times 5 \times 12 \\ = \frac{60}{2} \\ = 30 \: \: {units}^{2} [/tex]

Area of the shape

[tex]12 + 30 = 42 \: {units}^{2} [/tex]

Answer:

Step-by-step explanation:

Use the second equation:

Substitute this into first equation:

Now find y:

It is given that,

→ 2x - y = 2

Convert the equation as,

→ y = 2x - 2

First we should,

find the required value of x.

→ 3x + 4(2x - 2) = 36

→ 3x + 8x - 8 = 36

→ 11x = 44

→ [x = 4]

Let's find the required value of y,

→ y = 2x - 2

→ y = (2 × 4) - 2

→ y = 8 - 2

→ [y = 6]

Therefore, the value of y is 6.

Answer:

[tex]y=2x^2+1[/tex]

Step-by-step explanation:

The general equation for a parabola in vertex form is the following:

[tex]y=a(x-h)^2+k[/tex]

Where ([tex]h,k[/tex]) is the parabola's vertex and (a) is the stretch and compression factor. As one can see in the given graph, the parabola has a vertex at (0, 1), moreover, it passes through the point (1, 3). Substitute these points into the equation for the parabole, and simplify,

[tex]y=a(x-h)^2+k[/tex]

Vertex: (0, 1)

[tex]y=a(x-0)^2+1[/tex]

A point on the parabola: (1, 3)

[tex]3=a(1-0)^2+1[/tex]

[tex]3=a1+1\\3 = a + 1\\[/tex]

Inverse operations,

[tex]3=a+1[/tex]

[tex]2 = a[/tex]

Substitute back into the original expression:

[tex]y=a(x-h)^2+k[/tex]

[tex]y=2(x-0)^2+1[/tex]

Simplify to put in standard form:

[tex]y=2(x-0)^2+1[/tex]

[tex]y=2(x)^2+1[/tex]

[tex]y=2x^2+1[/tex]

Answer:

x = 5

Step-by-step explanation:

Given

4x - 14 + 6 = 12 , that is

4x - 8 = 12 ( add 8 to both sides )

4x = 20 ( divide both sides by 4 )

x = 5

Given:

The graph of a scatter plot.

To find:

The function that best fits the given points.

Solution:

From the given graph it is clear that the linear function is the best fit for the given points because the points lie on a straight line or near to it.

So, options B and C are incorrect because they represent exponential and quadratic function respectively.

Let as assume the two points on the graph are (0.80,-12.82) and (2,-12.79).

Using this two points, the equation of line is:

[tex]y-(-12.82)=\dfrac{-12.79-(-12.82)}{2-0.80}(x-0.80)[/tex]

[tex]y+12.82=\dfrac{-12.79+12.82}{2-0.80}(x-0.80)[/tex]

[tex]y+12.82=0.025(x-0.80)[/tex]

[tex]y+12.82=0.025x-0.02[/tex]

[tex]y=0.025x-0.02-12.82[/tex]

[tex]y=0.025x-12.84[/tex]

[tex]y=-12.84+0.025x[/tex]

It is the approximate function to the function that is in option A.

Therefore, the correct option is A.

Answer:

3 road bikes and 2 tandems

7 people

Step-by-step explanation:

25b + 40t = 155

b=3   and t = 2

Check

25*3  + 40*2 = 155

75+80 = 155

Assuming 1 person per road bike and 2 people per tandem

3*1 + 2*2 = 3+4 = 7