The lines below are parallel if the slope of the solid line is 2, what is the slope of the gas line?

Answer:

A) The height of the trapezoid is 6.5 centimeters.

B) We used an algebraic approach to to solve the formula for [tex]b_{1}[/tex].  [tex]b_{1} = \frac{2\cdot A}{h}-b_{2}[/tex]

C) The length of the other base of the trapezoid is 20 centimeters.

D) We can find their lengths as both have the same length and number of variable is reduced to one, from [tex]b_{1}[/tex] and [tex]b_{2}[/tex] to [tex]b[/tex]. [tex]b = \frac{A}{h}[/tex]

Step-by-step explanation:

A) The formula for the area of a trapezoid is:

[tex]A = \frac{1}{2}\cdot h \cdot (b_{1}+b_{2})[/tex] (Eq. 1)

Where:

[tex]h[/tex] - Height of the trapezoid, measured in centimeters.

[tex]b_{1}[/tex], [tex]b_{2}[/tex] - Lengths fo the bases, measured in centimeters.

[tex]A[/tex] - Area of the trapezoid, measured in square centimeters.

We proceed to clear the height of the trapezoid:

1) [tex]A = \frac{1}{2} \cdot h \cdot (b_{1}+b_{2})[/tex] Given.

2) [tex]A = 2^{-1}\cdot h \cdot (b_{1}+b_{2})[/tex] Definition of division.

3) [tex]2\cdot A\cdot (b_{1}+b_{2})^{-1} = (2\cdot 2^{-1})\cdot h\cdot [(b_{1}+b_{2})\cdot (b_{1}+b_{2})^{-1}][/tex] Compatibility with multiplication/Commutative and associative properties.

4) [tex]h = \frac{2\cdot A}{b_{1}+b_{2}}[/tex] Existence of multiplicative inverse/Modulative property/Definition of division/Result

If we know that [tex]A = 91\,cm^{2}[/tex], [tex]b_{1} = 16\,cm[/tex] and [tex]b_{2} = 12\,cm[/tex], then height of the trapezoid is:

[tex]h = \frac{2\cdot (91\,cm^{2})}{16\,cm+12\,cm}[/tex]

[tex]h = 6.5\,cm[/tex]

The height of the trapezoid is 6.5 centimeters.

B) We should follow this procedure to solve the formula for [tex]b_{1}[/tex]:

1) [tex]A = \frac{1}{2} \cdot h \cdot (b_{1}+b_{2})[/tex] Given.

2) [tex]A = 2^{-1}\cdot h \cdot (b_{1}+b_{2})[/tex] Definition of division.

3) [tex]2\cdot A \cdot h^{-1} = (2\cdot 2^{-1})\cdot (h\cdot h^{-1})\cdot (b_{1}+b_{2})[/tex] Compatibility with multiplication/Commutative and associative properties.

4) [tex]2\cdot A \cdot h^{-1} = b_{1}+b_{2}[/tex] Existence of multiplicative inverse/Modulative property

5) [tex]\frac{2\cdot A}{h} +(-b_{2}) = [b_{2}+(-b_{2})] +b_{1}[/tex] Definition of division/Compatibility with addition/Commutative and associative properties

6) [tex]b_{1} = \frac{2\cdot A}{h}-b_{2}[/tex] Existence of additive inverse/Definition of subtraction/Modulative property/Result.

We used an algebraic approach to to solve the formula for [tex]b_{1}[/tex].

C) We can use the result found in B) to determine the length of the remaining base of the trapezoid: ([tex]A= 215\,cm^{2}[/tex], [tex]h = 8.6\,cm[/tex] and [tex]b_{2} = 30\,cm[/tex])

[tex]b_{1} = \frac{2\cdot (215\,cm^{2})}{8.6\,cm} - 30\,cm[/tex]

[tex]b_{1} = 20\,cm[/tex]

The length of the other base of the trapezoid is 20 centimeters.

D) Yes, we can find their lengths as both have the same length and number of variable is reduced to one, from [tex]b_{1}[/tex] and [tex]b_{2}[/tex] to [tex]b[/tex]. Now we present the procedure to clear [tex]b[/tex] below:

1) [tex]A = \frac{1}{2} \cdot h \cdot (b_{1}+b_{2})[/tex] Given.

2) [tex]b_{1} = b_{2}[/tex] Given.

3) [tex]A = \frac{1}{2}\cdot h \cdot (2\cdot b)[/tex] 2) in 1)

4) [tex]A = 2^{-1}\cdot h\cdot (2\cdot b)[/tex] Definition of division.

5) [tex]A\cdot h^{-1} = (2\cdot 2^{-1})\cdot (h\cdot h^{-1})\cdot b[/tex] Commutative and associative properties/Compatibility with multiplication.

6) [tex]b = A \cdot h^{-1}[/tex] Existence of multiplicative inverse/Modulative property.

7) [tex]b = \frac{A}{h}[/tex] Definition of division/Result.

Answer:

He is a soccer player

Step-by-step explanation:

Lionel Andrés Messi is an Argentine professional footballer who plays as a forward and captains both Spanish club Barcelona and the Argentina national team.

Answer:

an Argentine professional footballer (soccer) who plays as a forward and captains both Spanish club Barcelona and the Argentina national team.

Step-by-step explanation:

Answer: yes because without the x the y does not have a corresonding oint

Answer:

B slope = 1 and y intercept is 3

Step-by-step explanation:

The y intercept is where the line crosses the y axis (x is zero).

The slope can be figured by how far the line rises and runs to the next intersection of lines. In this case it goes up 1 and to the right 1. The slope would be 1/1 or 1

Answer:

Slope =1 ; Y-intercept=3

Step-by-step explanation:

The y intercept would be the point on the vertical line that touches the graph which in this case is three.

then to get to the next point that's on the line would have to move over 1 once to the right and one time up. so the slope is 1 over 1 which would equal 1.

Answer:

20°

Step-by-step explanation:

Step 1:

x + 40° = 3x       Vertical ∠'s

Step 2:

40° = 2x      Subtract x on both sides

Step 3:

x = 40° ÷ 2     Divide

Answer:

x = 20°

Hope This Helps :)

Answer:

About 48 students play football

Step-by-step explanation:

400 times 12% is 48

Answer:

see below

Step-by-step explanation:

the current model costs $42,000.

next model = 6.8% less than $42,000

find;

1. how much will the price decrease in dollars?

2. what will be the price of the next model?

solution:

1. the price decrease = $42,000 x 0.068

2. price of next model = $42,000 - $2,856

Answer:

The garden is 14ft by 8ft.

The width of the walkway needs to be the same around each side of the garden, let's suppose that the width is X.

Then the area of the garden plus the walkway will be:

(14ft + X) by (8ft + X).

And we want that the total area of the garden and the walkway must be equal to 315 ft^2. Then we must solve the equation:

(14ft + X)*(8ft + X) = 315ft^2

Let's solve this for X.

112ft^2 + 14ft*X + 8ft*X + X^2 = 315ft^2

Let's move al the terms to the same side:

X^2 + (14ft + 8ft)*X + 112ft^2 - 315ft^2 = 0

X^2 + 22ft*X - 203ft^2 = 0.

Now to solve this we can use Bhaskara's equation:

[tex]X = \frac{-22ft +- \sqrt{(22ft)^2 - 4*1*(203ft^)} }{2} = \frac{-22ft +-36ft}{2}[/tex]

Then we have two solutions:

X = (-22ft - 36ft)/2 = -29ft

This solution is negative, and X represents a width, so must be positive, then we can discard this solution.

X = (-22ft + 36ft)/2 = 7ft

Then we can conclude that the width of the walkway must be 7ft.

Answer:

The retail price of the jeans was $81.25.

Second Choice: $81.25.

Step-by-step explanation:

Mrs. Jimenez paid $65 for some jeans.

She intended to sell them at her store by marking their price up by 25%.

We have to add 25% to $65:

25 * $65 / 100 = $16.25

$65 + $16.25 = $81.25

The retail price of the jeans was $81.25.

Second Choice: $81.25.

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

I hope this helps!

Answer:

20.44>2.044

Step-by-step explanation:

Answer:

Option D

Step-by-step explanation:

I got it right

Answer:

2/5=6/15 and that is less so....

Step-by-step explanation:

Answer:

0.91

explanation:

Answer: 99 sq meters

Step-by-step explanation:

break the figure up into smaller boxes. the far left is 48 m^2, the middle box is 15 m^2, and the right box is 36 m^2

Answer:

Area (A) [tex]\simeq[/tex] 0.0682

Step-by-step explanation:

The sketch for the region enclosed by the given curves can be found in the image attached below.

From the image below;

The two curves intersect in the area of tan 9x = 2 sin 9x

Recall that:

[tex]\dfrac{sin \ 9x }{cos \ 9x } = 2 \ sin \ 9x[/tex]

[tex]cos \ 9 x= \dfrac{1}{2}[/tex]

making x the subject; then:

[tex]x = \dfrac{1}{9} cos ^{-1}(\dfrac{1}{2})[/tex]

[tex]x = \dfrac{1}{9}(\dfrac{\pi}{3})[/tex]

[tex]x = \dfrac{\pi}{27}[/tex]

The subdivision of the domain is in two intervals [tex][-\dfrac{\pi}{27}, 0], [0, \dfrac{\pi}{27}][/tex]

where;

[tex]x \ \ \varepsilon \ \ [ -\dfrac{\pi}{27},0]; tan \ 9x > 2 sin \ 9x[/tex]

[tex]x \ \ \varepsilon \ \ [ 0,\dfrac{\pi}{27}]; tan \ 9x < 2 \ sin \ 9x[/tex]

Area (A) = [tex]\int ^0_{-\pi/27}}} ( tan \ 9x - 2 \ sin \ 9x ) \ dx + \int ^{\pi/27}_{0}(2 \ sin \ 9x - tan \ 9x \ ) \ dx[/tex]

[tex]= \begin {bmatrix} \dfrac{1}{9} In \ sec 9x + \dfrac{2}{9} \ cos \ 9x \end {bmatrix}^0_{-\pi/27} + \begin {bmatrix} -\dfrac{2}{7} cos 9x - \dfrac{1}{9} \ In \ sec \ 9x \end {bmatrix}^{-\pi/27} _0[/tex]

[tex]= \dfrac{1}{9}(1-In 2) + \dfrac{1}{9}(1-In 2)\\[/tex]

[tex]= \dfrac{2}{9}(1 - In 2)[/tex]

Area (A) = 0.06818

Area (A) [tex]\simeq[/tex] 0.0682

Answer:

+12 degrees

Step-by-step explanation:

You never showed a picture, but im pretty sure this is correct

I hope this helped, please mark Brainliest, thank you!

Answer:

es discurso que da un una persona sobre un hecho o circunstancia concreta, en éste, se especifican todos los detalles sobre estos, por lo que la mayor parte del tiempo está planificado. El uso de esta palabra está dirigido, principalmente, al campo jurídico.

Answer:

They are all obtuse scalene triangles I think

Answer:

1.5

Step-by-step explanation:

this is because 24 divided by 16 equals 1.5

Answer:

7 bars

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hope it helps!!

Triangle ABC with vertices A(2, 7), B(6,5) and C(4, 1): 90° counterclockwise transformation is A'(-7, 2), B'(-5, 6) and C'(-1, 4).

Given that, triangle ABC with vertices A(2, 7), B(6,5) and C(4, 1).

Here are the rotation rules: 90° clockwise rotation: (x, y) becomes (y, -x) 90° counterclockwise rotation: (x, y) becomes (-y, x) 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).

90° counterclockwise rotation: (x, y) becomes (-y, x)

A(2, 7) → A'(-7, 2)

B(6, 5) → B'(-5, 6)

C(4, 1) → C'(-1, 4)

Therefore, triangle ABC with vertices A(2, 7), B(6,5) and C(4, 1): 90° counterclockwise transformation is A'(-7, 2), B'(-5, 6) and C'(-1, 4).

Learn more about the rotation of 90° counterclockwise here:

brainly.com/question/1571997.

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Answer:

Yes. 3x²y and -5x²y are like terms because the variables x and y have the same exponents.

A fraction is a way to describe a part of a whole. The distance between -3/4 and 1 3/4 on a number line is 1 unit.

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

A mixed fraction is a fraction that contains a whole number and a fraction whose denominator is greater than the numerator. A mixed fraction can be converted as,

2 1/2

= (2×2 + 1)/2

= 5/2

= 2.5

The distance between -3/4 and 1 3/4 on a number line is,

Distance = 1 3/4  -  3/4

               = 7/4 - 3/4

               = (7-3)/4

               = 4/4 units

               = 1 units

Hence, the distance between -3/4 and 1 3/4 on a number line is 1 unit.

Learn more about Fraction here:

https://brainly.com/question/1301963

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Answer

I would say the 3rd one.

Step-by-step explanation:

I do not really remember this but I am in 8th grade math to (Algebra)

Answer:

You are right

Step-by-step explanation:

80

9 to 1 is equivalent to 72 to 8 and 72+8=80

Answer:

3x²-x+3

Step-by-step explanation:

Given

Height of the building =  3x^2 + x +1

distance from the floor of the cafeteria to the top of the building = 2x -2

To get the expression for the height from the ground to the floor of the cafeteria, we will use the formula:

Height of the building = (distance from the floor of the cafeteria to the top of the building ) + (he height from the ground to the floor of the cafeteria)

substitute the given parameter into the formula:

3x^2 + x +1 = 2x -2 + P

P = 3x^2 + x +1 - (2X-2)

P = 3x^2 + x +1 - 2x+2

collect like terms:

P = 3x^2 + x-2x+2+1

P = 3x²-x+3

Hence the expression for the height from the ground to the floor of the cafeteria is 3x²-x+3