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vesna_86 [32]
3 years ago
15

Looking for geometry proof help on a problem with parallelograms and an isosceles triangle

Mathematics
1 answer:
Free_Kalibri [48]3 years ago
3 0

Answer:

Step-by-step explanation:

30. Given: rectangles QRST and RKST

     Prove: ΔQSK is isosceles

An isosceles triangle is a triangle which has two sides and two angles to be equal.

Thus,

From rectangle QRST, the diagonals of rectangles are similar.

i.e RT ≅ QS (diagonal property)

Also, RT ≅ SK (opposite sides of rectangle RKST)

Thus,

RT ≅ QS  ≅ SK

Therefore,

ΔQSK is an isosceles triangle.

31. Given: Rectangles QRST, RKST and JQST

     Prove: JT ≅ KS

From rectangle QRST, the diagonals of rectangles are similar.

i.e RT ≅ QS (diagonal property)

But,

JT // QS and RT // KS

Thus,

JT ≅ QS (opposite sides of rectangle JQST)

also,

RT ≅ KS (opposite sides of rectangle RKST)

So that,

JT ≅ QS ≅ RT ≅ KS

Therefore,

JT ≅ KS

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beks73 [17]

Since the number is a fraction make a number line using fractions. The inequality sign includes being equal to, so add a solid dot on -5/2 and since x is less than that, draw an arrow pointing to the left.

See attached drawing.

For interval notation since x can be any number less than or equal to -5/2 it would be written as (-∞, -5/2]

8 0
3 years ago
Fiona was thinking of a number. Fiona doubles it and adds 5.1 to get an answer of 11.5. Form an equation with x? Whats the answe
saveliy_v [14]

Answer:

3.2

Step-by-step explanation:

11.5 - 5.1 = 6.4

6.4 ÷ 2 = 3.2

4 0
2 years ago
Which step brings you closest to getting the variable alone on one side of the equation
Oliga [24]

Answer:

Adding 5 from both sides then dividing by 7

Step-by-step explanation:

The best way to isolate x is to add 5 to both sides first:

21 = 7x

Then to isolate x by itself divide both sides by 7

x = 3

That would be the value of x and your final answer.

5 0
3 years ago
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Use the regression calculator to compare the teams’ number of runs with their number of wins. a 2-column table with 9 rows. colu
-Dominant- [34]

The equation of the trend line is ŷ = 0.15x - 23.21

<h3>How to determine the average rate of change of the trend line?</h3>

The points are given as:

hr =>808, 768, 655, 684, 637, 619, 613, 609, 563

w =>  93, 94, 66, 81, 86, 75, 61, 69, 55.

Using a graphing calculator, we have the following calculation summary:

  • Sum of X = 5956
  • Sum of Y = 680
  • Mean X = 661.7778
  • Mean Y = 75.5556
  • Sum of squares (SSX) = 50569.5556
  • Sum of products (SP) = 7547.1111

The regression equation is represented as:

ŷ = bX + a

Where:

b = SP/SSX

b = 7547.11/50569.56

b = 0.14924

a = MY - bMX

a = 75.56 - (0.15*661.78)

a  = -23.20961

This gives

ŷ = 0.14924X - 23.20961

Approximate

ŷ = 0.15x - 23.21

Hence, the equation of the trend line is ŷ = 0.15x - 23.21

Read more about trend lines at:

brainly.com/question/2589459

4 0
2 years ago
Write a rule to describe the function shown. x y −6 −4 −3 −2 0 0 3 2 y equals start fraction two over three end fraction x y equ
sertanlavr [38]

Answer:

y=\frac{2}{3} x (y equals start fraction two over three end fraction x)

Step-by-step explanation:

Lest's organize the table values of our function first:

x    y

-6  -4

-3  -2

0   0

3   2

The simplest kind of of function is a linear function of the form y=mx+b where m is the slope and b is the y-intercept. Let's us check if our function is a linear one finding its equation and checking that all points are in the line.

The first step to find a linear equation is find the slope of the line; to do it, we are using the slope formula:

m=\frac{y_2-y_1}{x_2-x_1}

where

m is the slope of the line

(x_1,y_1) are the coordinates of the first point

(x_2,y_2) are the coordinates of the second point

We know from our table that the first and second points are (-6, -4) and (-3, -2) respectively, so x_1=-6, y_1=-4, x_2=-3, and y_2=-2.

Replacing values:

m=\frac{y_2-y_1}{x_2-x_1}

m=\frac{-2-(-4)}{-3-(-6)}

m=\frac{-2+4}{-3+6)}

m=\frac{2}{3)}

Now that we have the slope of our line we can use the point slope formula to complete our linear function:

y-y_1=m(x-x_1)

where

m is the slope

(x_1,y_1) are the coordinates of the first point

Replacing values:

y-y_1=m(x-x_1)

y-(-4)=\frac{2}{3)}(x-(-6))

y+4=\frac{2}{3)}(x+6)

y+4=\frac{2}{3} x+4

y=\frac{2}{3} x+4-4

y=\frac{2}{3} x

Now, to check if our function is valid, we can either check if each point satisfies the rule y=\frac{2}{3} x, or we can graph it and check if each lies is in the graph.

Let's check both:

We already know that points (-6, -4) and (-3, -2) satisfy the rule (after all, those were the point we used to came out with the rule in the first place), so we just need to check the points (0, 0) and (3, 2)

- For (0, 0):

y=\frac{2}{3} x

0=\frac{2}{3}(0)

0=0

The point satisfies the rule.

- For (3, 2):

y=\frac{2}{3} x

2=\frac{2}{3} (3)

2=2

The point satisfies the rule.

Since all the points of our table satisfies the rule y=\frac{2}{3} x, we can conclude that the rule describing the function shown is y=\frac{2}{3} x.

4 0
3 years ago
Read 2 more answers
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