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blagie [28]
2 years ago
9

In ΔCDE, the measure of ∠E=90°, the measure of ∠C=83°, and DE = 8.6 feet. Find the length of EC to the nearest tenth of a foot.

Mathematics
1 answer:
agasfer [191]2 years ago
8 0

​

 Answer : 1.0559≈1.1 feet

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What is one of the solutions to the following equations? y2+x2=53<br> Y-x=5
Olenka [21]
(1)  y² + x² = 53
(2)  y - x = 5 ⇒ y = x + 5

subtitute (2) to (1)

(x + 5)² + x² = 53      |use (a + b)² = a² + 2ab + b²

x² + 2x·5 + 5² + x² = 53

2x² + 10x + 25 = 53     |subtract 53 from both sides

2x² + 10x - 28 =0     |divide both sides by 2

x² + 5x - 14 = 0

x² - 2x+ 7x - 14 = 0

x(x - 2) + 7(x - 2) = 0

(x - 2)(x + 7) = 0 ⇔ x - 2 = 0 or x + 7 = 0 ⇔ x = 2 or x = -7

subtitute the values of y to (2)

for x = 2, y = 5 + 2 = 7
for x = -7, y = 5 + (-7) = 5 - 2 = 3

Answer: x = 2 and y = 7 or x = -7 and y = 3
4 0
3 years ago
Given f(x) = 2x + 3 and g(x) = x - 9, what is f(x) + g(x)?
Orlov [11]
Solution:

f(x) = 2x + 3
g(x) = x - 9

f(x) + g(x)
= (2x + 3) + (x - 9)
= 2x + x + 3 - 9
= 3x - 6
6 0
3 years ago
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match the rectangles formed by the sets of points
tigry1 [53]

IJKL=80 square units

QRST =100 square units

UVWX =300 square units

ABCD =50 square units

you are welcome!!!

6 0
3 years ago
Read 2 more answers
Simplify the given expression.<br> (3x+8)(2x+6)
sladkih [1.3K]
(3x+8)(2x + 6)

6x^2+18x+16x+42
6x^2+34x+42

using the foil method, you can expand the given expression. It is already in simplified form with the given (3x+8)(2x+6)
7 0
3 years ago
Historically, the proportion of students entering a university who finished in 4 years or less was 63%. To test whether this pro
Neporo4naja [7]

Answer:

z(c)  = - 1,64

We reject the null hypothesis

Step-by-step explanation:

We need to solve a proportion test ( one tail-test ) left test

Normal distribution

p₀ = 63 %

proportion size  p = 51 %

sample size  n = 114

At 5% level of significance   α = 0,05, and with this value we find in z- table z score of z(c) = 1,64  ( critical value )

Test of proportion:

H₀     Null Hypothesis                        p = p₀

Hₐ    Alternate Hypothesis                p < p₀

We now compute z(s) as:

z(s) =  ( p - p₀ ) / √ p₀q₀/n

z(s) =( 0,51 - 0,63) / √0,63*0,37/114

z(s) =  - 0,12 / 0,045

z(s) = - 2,66

We compare z(s) and z(c)

z(s) < z(c)      - 2,66 < -1,64

Therefore as z(s) < z(c)  z(s) is in the rejection zone we reject the null hypothesis

5 0
3 years ago
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