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3 years ago

I need help with this please

Mathematics

1 answer:

yan [13]3 years ago

8 0

Step-by-step explanation:

I don't see the options I can select, but it should be something like "sum".

it is also the "sum" of the areas of the rectangles separated by the dashed line (6×5 and 6×4). so, 6(9) = 6(5) + 6(4).

it is strangely written.

but 6(9) simply means 6×9 or 6×(9). one could also write (6)(9). and the same for 6(5) and 6(4).

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Indicate the equation of the given line in standard form. Show all your work for full credit. the line containing the median of

alukav5142 [94]

Answer:

* The equation of the median of the trapezoid is 10x + 6y = 39

Step-by-step explanation:

* Lets explain how to solve the problem

- The slope of the line whose end points are (x1 , y1) , (x2 , y2) is

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

- The mid point of the line whose end point are (x1 , y1) , (x2 , y2) is

$(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

- The standard form of the linear equation is Ax + BC = C, where

A , B , C are integers and A , B ≠ 0

- The median of a trapezoid is a segment that joins the midpoints of

the nonparallel sides

- It has two properties:

# It is parallel to both bases

# Its length equals half the sum of the base lengths

* Lets solve the problem

- The trapezoid has vertices R (-1 , 5) , S (! , 8) , T (7 , -2) , U (2 , 0)

- Lets find the slope of the 4 sides two find which of them are the

parallel bases and which of them are the non-parallel bases

# The side RS

∵ $m_{RS}=\frac{8-5}{1 - (-1)}=\frac{3}{2}$

# The side ST

∵ $m_{ST}=\frac{-2-8}{7-1}=\frac{-10}{6}=\frac{-5}{3}$

# The side TU

∵ $m_{TU}=\frac{0-(-2)}{2-7}=\frac{2}{-5}=\frac{-2}{5}$

# The side UR

∵ $m_{UR}=\frac{5-0}{-1-2}=\frac{5}{-3}=\frac{-5}{3}$

∵ The slope of ST = the slop UR

∴ ST// UR

∴ The parallel bases are ST and UR

∴ The nonparallel sides are RS and TU

- Lets find the midpoint of RS and TU to find the equation of the

median of the trapezoid

∵ The median of a trapezoid is a segment that joins the midpoints of

the nonparallel sides

∵ The midpoint of RS = $(\frac{-1+1}{2},\frac{5+8}{2})=(0,\frac{13}{2})$

∵ The median is parallel to both bases

∴ The slope of the median equal the slopes of the parallel bases = -5/3

∵ The form of the equation of a line is y = mx + c

∴ The equation of the median is y = -5/3 x + c

- To find c substitute x , y in the equation by the coordinates of the

midpoint of RS

∵ The mid point of Rs is (0 , 13/2)

∴ 13/2 = -5/3 (0) + c

∴ 13/2 = c

∴ The equation of the median is y = -5/3 x + 13/2

- Multiply the two sides by 6 to cancel the denominator

∴ The equation of the median is 6y = -10x + 39

- Add 10x to both sides

∴ The equation of the median is 10x + 6y = 39

* The equation of the median of the trapezoid is 10x + 6y = 39

7 0

3 years ago

Rearrange the following equation to solve for the variable indicated. -4x+2Y=8 solve for y

Alecsey [184]

Answer:

y = 8 + 4x / 2

Step-by-step explanation:

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3 years ago

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The polynomial p(x) has factors of x-5 and x-8. Which must be correct ?

aleksandrvk [35]

Answer:

Find an answer to your question The polynomial p(x) has factors of x – 5 and x + 8. Which MUST be correct?

Step-by-step explanation:

If x – a is indeed a factor of p(x), then the remainder after division by x – a will be ... the polynomial (courtesy of the Remainder Theorem), but x – a is also a factor ... completed division: 2 2 5 0 7 ... x + 4 is a factor of 5x4 + 16x3 – 15x2 + 8x + 16.

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3 years ago

What is the value of g?

Lina20 [59]

Answer: G is 31 degrees

Step-by-step explanation: that angle is a right angle which means it measures 90 degrees. if we subtract the given measurement from 90 we get 31

4 0

2 years ago

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Quadrilateral ABCD is inscribed in this circle. What is the measure of angle B? Enter your answer in the box. m∠B= ° A quadr

Over [174]

Answer:

m∠B = 157°

Step-by-step explanation:

Cyclic quadrilateral is the quadrilateral whose vertices lie on the edge of the circle

In the cyclic quadrilateral each two opposite angles are supplementary (the sum of their measures is 180°)

∵ Quadrilateral ABCD is inscribed in a circle

- That means its four vertices lie on the edge of the circle

∴ ABCD is a cyclic quadrilateral

<em>Each two opposite angles in the cyclic quadrilateral are supplementary (The sum of their measures is 180°)</em>

∵ ∠B and ∠D are opposite angles in the quadrilateral ABCD

∴ m∠B + m∠D = 180° ⇒ opposite ∠s in a cyclic quadrilateral

∵ m∠B = (6x + 19)°

∵ m∠D = x°

- Substitute them in the rule above

∴ (6x + 19) + x = 180

- Add the like terms in the left hand side

∴ (6x + x) + 19 = 180

∴ 7x + 19 = 180

- Subtract 19 from both sides

∴ 7x = 161

- Divide both sides by 7

∴ x = 23

<em>Substitute the value of x in the expression of the measure of ∠B to find its measure</em>

∵ m∠B = 6(23) + 19

∴ m∠B = 138 + 19

∴ m∠B = 157°

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3 years ago