Use a coordinate grid to write a coordinate proof of the following statement.
If the vertices of a triangle are A(0,0), B(2 a, b) , and C(4 a, 0) , then the triangle is isosceles.
c. Use the Distance Formula to write an expression for B C .

Answer:

f^-1 (x)= -6x+24

Step-by-step explanation:

the inverse function would be negative six (x) plus 24

Using the digits 1 to 9 at most one time each to make the largest quotient is 98 ÷ 12 .

According to the question we have to use digits 1 to 9 at most one time each to make the largest quotient.

Now we know that the number that is being divided is known as the dividend and the number by which we divide is known as the divisor.

Now dividend should be greater than the divisor.

So tot make the largest quotient the dividend and the divisor will be

98 and 12 respectively.

That is,     98 ÷ 12 = 8.2 which is the largest quotient.

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The area of the parallelogram is 42 units².

The area of a parallelogram can be calculated by finding the product of its base with the altitude. The base and altitude of a parallelogram are always perpendicular to each other.

i.e., The area of a parallelogram = base × height.

To find the perimeter of a parallelogram, add the lengths of the sides. Opposite sides of a parallelogram are equivalent.

Given:

base= 7 units

height = 6 units.

Now, area of a parallelogram,

= 7 × 6

= 42 units²

Hence, area of the parallelogram is 42 units².

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An octagon is known to be a type of polygon that is said to have up to 8 sides the octagon is an 8-sided polygon, also called 8-gon, in a two-dimensional plane then the measure of arc NPQ is 180°.

An inscribed angle of a circle is an angle whose vertex is a point A on the circle and whose sides are line segments (called chords) from A to two other points on the circle.

An octagon is known to be a type of polygon that is said to have up to 8 sides the octagon is an 8-sided polygon, also called 8-gon, in a two-dimensional plane. A regular octagon will have all its sides equal in length.

The surface area of a regular octagon encircled by a circle of radius one unit. Divide the octagon into eight congruent triangles. We can find the area of one triangle and multiply it by 8 to get the area of the entire octagon.

The complete question is:

A stop sign in the shape of a regular octagon is inscribed in a circle.

What is the measure of arc NPQ?

A. 45°

B. 90°

C. 135°

D. 180°

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The total cost of 10 brownies is $4 is the statement that best describes the meaning of f(4) = 10, if f(x) is the total cost, in dollars, of x brownies.

In mathematics, a function is an expression, rule, or law that specifies a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are widespread in mathematics and are required for the formulation of physical relationships in the sciences. The present concept of function was initially proposed in 1837 by the German mathematician Peter Dirichlet.

If a variable y is so closely tied to a variable x that whenever a numerical value is assigned to x, there is a rule that determines a unique value of y, then y is said to be a function of the independent variable x.

As we can see it is mentioned that f(x) = total cost = f(4)

So only option d. has 4 as total cost, that why d is the right option and statement as follows The total cost of 10 brownies is $4.

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The value of the other angles

∠1 = 180 - 82°

∠2 = ∠1 = 98°

∠3 = ∠ = 98°

∠4 = ∠5 = 82°

According to the given data,

m∠5=82° given

∠5 = ∠7 = ∠4 = ∠8 = ∠6 = ∠12

∠1 = ∠10 = ∠2 = ∠11 = ∠3 = ∠ 12 = 180° - ∠5

we get, measures of other angles

∠1 = 180 - 82°

∠2 = ∠1 = 98°

∠3 = ∠ = 98 °

∠4 = ∠5 = 82°

A transversal is a line that intersects two coplanar lines at two different points. In the figure,

line t is a transversal. The table summarizes the names of angle pairs formed by a transversal.

Corresponding angles lie on the same side of the transversal and on the same

sides of the intersected lines. ∠1 and ∠5

Same-side interior angles lie on the same side of the transversal and between

the intersected lines. ∠3 and ∠6

Alternate interior angles are nonadjacent angles that lie on opposite sides of

the transversal between the intersected lines. ∠3 and ∠5

Alternate exterior angles lie on opposite sides of the transversal and outside

the intersected lines. ∠1 and ∠7

Same-Side Interior Angles Postulate

If two parallel lines are cut by a transversal, then the pairs of same-side interior angles are supplementary

Alternate Interior Angles Theorem

If two parallel lines are cut by a transversal, then the pairs of alternate interior angles have the same measure.

Corresponding Angles Theorem

If two parallel lines are cut by a transversal, then the pairs of corresponding angles have the same measure.

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The equation of the circle (x - 3)^2 + (y + 1)^2 = 36 has a radius of 6 and a center located at (3 , -1).

The standard form of the equation of  circle is given by

(x - h)^2 + (y - k)^2 = r^2

where (h , k) is the location of the center and r is the radius of the circle.

On the other hand, the general form of the equation of  circle is given by

x^2 + y^2 + Dx + Ey + F = 0

where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.

If the equation of the circle, (x - 3)^2 + (y + 1)^2 = 36, is in standard form, then

h = 3

k = -1

r = 6

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Answer:

Step-by-step explanation:

F = 9/5 C + 32 is the correct formula.

9/5 C = F - 32

C = 5/9(F - 32)

So, 68 degrees Fahrenheit

= 5/9(68 - 32)

= 5/9 * 36

= 20 degrees C.

The slope of the line containing (6,-2) and (-3,-5) is  (3/8).

The slope of a straight line can be written as follows,

m =  [tex](y_{2} - y_{1} )/(x_{2} - x_{1} )[/tex]                 equation1

The line is containing the points (-3,3) and (4,3). So, we can write

[tex]y_{2}[/tex] = -5 , [tex]y_{1}[/tex] = -2 , [tex]x_{2}[/tex] = -3 , and [tex]x_{1}[/tex] = 6 .

On substituting the values of variables in equation1, we will get

m = ( (-5)-(-2) ) / ( (-3)-(6) ) = (-3/(-8)) = (3/8).

As the slope of a line is (3/8), so we can conclude that the given line is a straight line.

Here:

m = the slope of the line

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.

The slope of the line containing  (6,-2) and (-3,-5) is  (3/8).

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Answer:

a) [tex]\sqrt{3}[/tex]

b) 2

Step-by-step explanation:

a) tan 30 = opposite side / adjacent side 1/[tex]\sqrt{3}[/tex] so AC is [tex]\sqrt{3}[/tex]

b)3

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]1^{2}[/tex] +[tex]\sqrt{3} ^{2}[/tex] = [tex]c^{2}[/tex]

1 + 3 = [tex]c^{2}[/tex]

4 = [tex]c^{2}[/tex]

[tex]\sqrt{4}[/tex] =[tex]\sqrt{c^{2} }[/tex]

2 = c

The length of AC is √3 units and the length of AB is 2 units by Pythagoras' theorem

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The right-angled triangle ABC has an angle BAC of 30º.

The length of BC  be one unit

We have to find the length of AC

tan (30)= opposite side/ adjacent side

1/√3 = opposite side/ adjacent side

The adjacent side is √3  which is length of AC

Now let us find the length of AB by using pythagoras theorem

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides

AB² = AC² + BC²

AB²=√3² + 1²

AB²= 4

AB = 2 units

Hence, the length of AC is √3 units and the length of AB is 2 units by Pythagoras' theorem

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I should return after 7.7 minutes later to bathtub.

You want to turn the water off when the level in the bathtub is 8.5

66/8.5

7.7 minutes

A bathtub is a long, typically rectangular container that you sit in to bathe your body after filling it with water.

Let's start with the truth: Showers are cleaner than baths. Showers spray polluted water out of sight while distributing water evenly over your body.

Actually, there is nothing that sets one apart from the other. All of them include jets, bubbles, and frequently different colored lights and other decorations. They are all sizable hot water containers. Overall, the terms "whirlpool bath," "Jacuzzi," and "hot tub" all refer to the same thing.

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The equation of the parabola in vertex form is

P is -[tex]\frac{1}{2}[/tex]

(0,-[tex]\frac{1}{2}[/tex])

y=[tex]\frac{-1}{2}[/tex][tex]x^{2}[/tex] -[tex]\frac{1}{2}[/tex]

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a variety of seemingly unrelated mathematical descriptions, all of which may be shown to define the same curves.

One definition of a parabola includes a line and some extent  (the focus) (the directrix). The directrix isn't the main focus. The locus of points therein plane that is equally spaced apart from the directrix and the focus is known as the parabola. A right circular conical surface and a plane parallel to a different plane that is tangential to the conical surface intersect to form a parabola, which is additionally known as a conic section.

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Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

The simplified expression of -35 / (-5) is 7.

Let the given expression be -35 / (-5) then

-35 / (-5) = -35/-5

simplifying the above equation, we get

= 35/5

= 7

Therefore, the value of -35 / (-5) is 7.

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here is it friend...hope it is clear enough

Answer:

5/6x + 5/12 + 20/6

Simplfied

5/6x + 3 3/4

Step-by-step explanation:

5/6 ( x+ 1/2 + 4)

Distribute

Multiply the term outside the parentheses to each term inside the parentheses

5/6 ( x) + 5/6 *(1/2) +5/6 *( 4)

5/6x + 5/12 + 20/6

We need to get a common denominator for the constant terms

5/6x + 5/12 + 20/6

5/6x + 5/12 + 40/12

Add

5/6x + 45/12

45/12 is an improper fraction so we can make it a mixed number

12 goes into 45 3 times with 9 left over

3 9/12 which simplified to

3 3 /4

The simplified expression is

5/6x + 3 3/4

4x+5x+=6+11

9x=17

x=17/9

☞ user58580~ ♥

Answer:

x= 17/9

Step-by-step explanation:

4x+5x=6+11

Combine like terms

9x=17

x=17/9

the expression representing the total amount earned by Evelyn is $ 25 x + $ 90 y .

We are given that

Evelyn makes x haircuts for $ 25 and y perms for $ 90.

We need to write an expression representing the situation

We will use multiplication for the same.

So, Amount earned from the haircuts = x × $ 25 = $ 25 x

Amount earned from perms = y × $ 90 = $ 90 y

Total amount earned = $ 25 x + $ 90 y

Therefore, we get that, the expression representing the total amount earned by Evelyn is $ 25 x + $ 90 y .

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5 = (1/2)2 + 4 is an equation in intercept form for the line passing through the points (2,5) and (6,7)

A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.

The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.  

Therefore,

m =  y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.

Be aware that tan ∅ = y/x

We also refer to this tan as the line's slope.

We have been asked to write an equation in slope-intercept form for the line passing through (2,5) and (6,7)

First we will find the slope(m)

We know that slope = m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

For the pairs of points (2,5) and (6,7)

⇒ m = [tex]\frac{7- 5}{6 - 2}[/tex]

⇒ m = [tex]\frac{2}{4 }[/tex]

⇒ m = 1/2

We know that the equation for slope(m) and y - intercept(b) of a line is given by :

y = mx + b

Here lets take equation 5 = (1/2)2 + b .Here x and y is substituted with the first two points.

⇒  5 = (1/2)2 + b

⇒  5 = 1 + b

⇒  b = 5 - 1

⇒  b = 4

The equation in the slope intercept is as follows:-

5 = (1/2)2 + 4

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The street can be represented in slope intercept form as follows:

y = x + 4

Linear equation can be represented in slope intercept form as follows:

y = mx + b

where

Parallel lines have the same slope.

The street goes by the name y = x + 17.

The slope of the street is 1.

Therefore, the street parallel to that one should have the same slope.

The street can be represented in slope intercept form is as follows:

y = x + 4

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Answer:

Step-by-step explanation:

How many solutions does each of the following equations have?

10+5(x+2)=5x-20

10+5x+10=5x-20

10 + 10 = -20

20 = -20

this equation has no solution

Answer:

Step-by-step explanation:

10+5(x+2)=5x-20

10+5x+10=5x-20

5x-5x=-20-10-10

x = -40

Answer: 4.7 gallons

Step-by-step explanation:

The range is the difference in the highest number and the smallest number, so 2.8 - -1.9 = 4.7

For the given situation, we can clearly say that the change in one quantity will cause a change in the second quantity as well.

With an increase in the size of the car engine the power the engine will ultimately increase as well. This increased power can easily accommodate more people. So we can make relation from this deduction,

Engine size ∝ Number of People

This clearly states that by increasing one quantity we will increase the other quantity as well.

Similarly, now that they have a direct relation if we decrease the size of the engine, its power will decrease as well and hence the number of people will decrease.

A strong positive correlation we can call it.

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Answer:

c) 7.3 m/s

Step-by-step explanation:

We know that 87 is the total and 12 is the time do you take the total divided by the time so 87/12=7.25. 7.25 rounded is 7.3.

The latest time Alice can start making the cake batter is 8:33 A.M

Alice is making cake for her mother's birthday

It will take 24 minutes to make the cake batter

The cake also needs to be in the oven for 1 hour 2 minutes

The time needed to make the cake is

1 hour 2 minutes + 24 minutes

= 1 hour 26 minutes

The latest time to start making the cake batter is

9:59 - 1:26

= 8:33

Hence the latest time to start making the cake batter is 8:33 A.M

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Answer:

1. 68.1

2. 61.983

Step-by-step explanation:

nearest tenth is one digit after the decimal. nearest thousandth is three digits after the decimal. since 4 is less than 5, the 1 remains the same. in the second problem, the fourth digit is 6 which is greater than 5 so you change the 2 to a 3.

The number is represented by 6 tens 7 ones 67 .

Let the unit's place digit be " x " and ten's place digit be " y ".

Two digit number is given by = 10 y + x      .....(1)

It is given that 6 tens 7 ones.

Putting x = 6 and y = 7 in equation (1) , we get

10(6) + 7 = 60 + 7

              = 67

Hence , the number is 67 .

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Answer:

Slope of a perpendicular line:
[tex]\boldsymbol{\dfrac{1}{9}}[/tex]

Slope of a parallel line:
[tex]\boldsymbol{-9}[/tex]

Step-by-step explanation:

A line perpendicular to a line y = mx + b will have its slope as[tex]-\dfrac{1}{m}[/tex]
Here slope of given line = -9
[tex]\displaystyle \mathrm {reciprocal\; of\;} -9 = -\dfrac{1}{9}[/tex]

[tex]\mathrm {negative\; of \;reciprocal\;}= -\left(-\dfrac{1}{9}\right) = \dfrac{1}{9}\\[/tex]

parallel lines have the same slope so a parallel line will have slope = -9

Answer:

213.7°

Step-by-step explanation:

The bearing of B from D is angle ADB, which is ∠ADB = arctan(30/45)

≈ 33.7°

The bearing of D from B is that angle plus 180°, so is 180° +33.7° = 213.7°

Answer:

225°

Step-by-step explanation:

In mathematics, a bearing is defined as an angle measured clockwise from north.

See attached graph for a clearer guide to the explanations

Angle ABC is a right isosceles triangle with AB = 25 and AC = 25

m∠BAC =90°

So m∠ABC = m∠ACB = 45°

The angle at BC is 45° from the North (90°-45°)  measured clockwise is 45° so we say the bearing from C to B is 045°  (we use 3 digits for bearing)

The bearing from B to C on the other hand is determined by adding 180° to the bearing in the opposite direction (C to B) so the bearing from C to B is 180° +045° = 225°

(Here I am not sure whether you are supposed to answer the question in mathematical meaning of bearing or just state the direction in which BC lies relative to north. 45° clockwise from the North is in a NE direction so we can say C is NE from B but I am guessing that's not it)

The total amount subtracted from her account after 6 months of having the membership is −6|20| = −$120. option C

Given:

Cost of membership

Cost per month for a car wash membership = $20

Number of months = 6 months

Total amount subtracted from her account = Number of months × Cost per month for a car wash membership

= 6 (-20)

= -120

Therefore, the total amount subtracted from her account after 4 months of having the membership is −6|20| = −$120.

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