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2 years ago

What is the value of x in the equation 25x2 = 16. A. 5/4. B. 4. C. 4/5. D. 16/25

Mathematics

1 answer:

Sergeeva-Olga [200]2 years ago

6 0

Answer:

x = ⅘

Step-by-step explanation:

For clarity, exponents should be marked with a ^. 25x² can be written as 25x^2.

25x² = 16

divide both sides by the 25

x² = 16/25

take the square root of both sides

x = √(16/25) = √16/√25 = 4/5

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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

2 years ago

X-2y=-26 x-y=-2 solution of systems equation

svp [43]

If we subtract the 2 equations we eliminate x:-

x - x - 2y - (-y) = -26--2
-y = -24
y = 24
Plug this into the first equation:-
x - 2(24) = -26
x = -26 + 48 = 22

Answer is x = 22 and y = 24

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3 years ago

How many significant numbers in 34.6209

JulijaS [17]

Answer:

Step-by-step explanation:

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2 years ago

If there are 4 trucks for every 5 animals, then how many trucks would there be if there were 20 animals?

mel-nik [20]

There would be 16 trucks if there was 20 animals

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2 years ago

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At Burnt Mesa Pueblo, archaeological studies have used the method of tree-ring dating in an effort to determine when prehistoric

Zanzabum

Answer:

a) (1215, 1297)

b) (1174, 1338)

c) (1133, 1379)

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 1256

Standard Deviation, σ = 41

Empirical Rule:

Also known as 68-95-99.7 rule.
It states that almost all the data lies within three standard deviation for a normal data.
About 68% of data lies within 1 standard deviation of mean.
About 95% of data lies within two standard deviation of mean.
About 99.7% of data lies within 3 standard deviation of mean.

a) range of years centered about the mean in which about 68% of the data lies

$\mu \pm 1(\sigma)\\=1256 \pm 41\\=(1215, 1297)$

68% of data will be found between 1215 years and 1297 years.

b) range of years centered about the mean in which about 95% of the data lies

$\mu \pm 2(\sigma)\\=1256 \pm 2(41)\\=1256 \pm 82\\=(1174, 1338)$

95% of data will be found between 1174 years and 1338 years.

c) range of years centered about the mean in which about all of the data lies

$\mu \pm 3(\sigma)\\=1256 \pm 3(41)\\=1256 \pm 123\\=(1133, 1379)$

All of data will be found between 1133 years and 1379 years.

3 0

3 years ago