Solve for x. (x+16) (4x-5)° 11 7 9 13

Given: KPST is a trapezoid, KP=ST, MN is a midsegment, MN=20, h=15, PS:KT=3:7 Find: KS and KP

lions [1.4K]

Answer:

Length of KS = 25 units and

Length of KP = 17 units.

Step-by-step explanation:

Given: KPST is a trapezoid, KP =ST, MN is a mid segment, h is the height =15

Also it is given that, MN = 20 , h = 15 and PS:KT = 3:7.

If two sides of the trapezoid are equal then, it is an isosceles trapezoid.

Mid-segment of a trapezoid is a line segment which connects the midpoints of the non-parallel sides.

A trapezoid mid segment connects the midpoints of two congruent sides of the trapezoid and is parallel to the pair of parallel sides.

Length of the mid segment is the sum of two bases divide by 2

Since, the length of Mid-segment MN = 20.

Also, it is given: PS:KT = 3:7

Let PS = 3x and KT = 7x respectively.

then;

$\frac{PS+KT}{2} = 20$

$\frac{3x+7x}{2} = 20$

$\frac{10x}{2} =20$

On Simplify, we get;

5x =20

Divide both sides by 5 we get;

x =4

Then:

Length of base PS = 3x = 3(4) = 12 and Length of base KT = 7x = 7(4) = 28.

Now, In triangle PLK

Using Pythagoras theorem to find KP;

It is given here, PL =h =15 and KL= 8 {you can see in the figure as shown below};

$KP^2= PL^2 + KL^2$

$KP^2 = 15^2+8^2 =225 +64 = 289$

$KP = \sqrt{289}$

Simplify:

KP = 17

therefore, the length KP = 17 units

To, construct a line: Join K and S

Now, in triangle KRS

KR = KL +LR = 8 +12 =20 and SR = h= 15

Using Pythagoras theorem in KRS to find KS;

$KS^2 = SR^2+KR^2$

$KS^2 = 15^2 + 20^2 = 225 + 400 = 625$

$KS = \sqrt{625}$

On simplify:

KS = 25

Therefore, the length of KS is, 25 units.

4 0

3 years ago

Square root of 36 rounded to the nearest hundredth

Digiron [165]

The square root of 36 is 6.00. I know this because six squared (6*6) is 36.

4 0

3 years ago

Substitute 9 into each equation to determine if 9 is the solution. Drag each equation into the correct column.

IRISSAK [1]

Answer:

m times 3 = 27

b plus 4 = 13

p minus 5 = 4

Those can all be solved with 9

the other can not

Step-by-step explanation:

i hope this helped

4 0

3 years ago

Which of the following equations is the translation 2 units left of the graph of y = |x|?

nignag [31]

Answer:

The correct option is 1.

Step-by-step explanation:

The given function is

$y=|x|$

It is an absolute function. The transformation of function is defined as

$y=|x+a|+b$

Where, a is horizontal shift and b is vertical shift.

If a>0, then graph shifts a units left, if a<0, then graph shifts a units right.

If b>0, then graph shifts b units up, if b<0, then graph shifts b units down.

If is given that the graph translate 2 units left. Therefore the value of a is 2 and the value of b is 0.

The required function is

$y=|x+2|+0$

$y=|x+2|$

Therefore the correct option is 1.

6 0

3 years ago

Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are sum

s344n2d4d5 [400]

The contingency tables serve to record the frequencies with which an object appears according to the measured variables, in this case two variables, each with two scales, the scratch resistance and the shock resistance, both measured as high and low.

The information is organized in such a way that the value of each box represents the total number of objects that meet the characteristics measured for each variable, for example in this case we have 70 discs with high shock resistance and high scratch resistance, 9 with high scratch resistance and low shock resistance, 16 with high shock resistance and low scratch resistance and finally 5 discs with low scratch and shock resistance.

We complete the table like this to obtain other total values:

$\qquad\qquad\qquad\qquad\qquad\text{Shock resistance}\\\text{Scratch resistence}\left[\begin{array}{cccc}&\text{high}&\text{low}&\text{total}\\\text{high}&70&9&79\\\text{low}&16&5&21\\\text{total}&86&14&100\end{array}\right]$

With this information, and taking into account that the values presented are frequencies, to obtain the probability, each one must be divided into the total number of objects and multiply by 100, for this case as 100 objects, the frequency is the same percentage or probability .

Answer

a) The probability that, when selecting a random disk, its scratch resistance is high and its shock resistance is high is 70%, since this is the value that corresponds to the intersection of both variables in the table.

b) the probability that, when selecting a random disk, its resistance to scratches is high or that its resistance to impacts is high is 95% because the probability that its resistance to scratches is high is 79 % and the probability that its impact resistance is high is 86%, as one or the other requests, this is the sum of both minus the intersection, that is 79% + 86% -70% = 95%

c) the two events described are not mutually exclusive, that is, they cannot pass through, since the table informs us that of the analyzed discs 70, these two characteristics possessed, high shock resistance and high scratch resistance

8 0

3 years ago