How is perpendicular bisector used in justifying the sss triangle congruence theorum?

san4es73 [151]

4)
Area=(base x height) / 2
area=24 in²
therefore:
(b*3b)/2=24 in²
3b²/2=24 in²
b²=(24*2)/3 in²
b²=16 in²
b=√(16 in²)= 4 in

answer: 4 in

5)
if x=9
x²+z=103
(9)²+z=103
81+z=103
z=103-81=22

if x=-9
(-9)²+z=103
81+z=103
z=103-81=22

Answer: 23

1)
n²-49=0
n²=49
n=⁺₋√49=⁺₋7

Answer: ⁺₋7

2)
x²+64=0
x²=-64
x²=⁺₋√-64 These numbers are not real.

Answer:no solution

3)
area=slide²
slide=+√area

slide=+√(144x²)=12x

answer: 12 x

6 0

4 years ago

A kite is flying 79 ft off the ground, and its string is pulled taut. The angle of elevation of the kite is 50°. Find the length

Art [367]

Answer:

If the kite has an 11 ft line attached to it and it casts an 8 feet shadow, we will have a rectangle triangle (see picture below).

To find the height x of the kite, we can apply the Pythagorean theorem.

x² = 11² - 8²

x² = 121 - 64

x² = 57

x =√57

Step-by-step explanation:

4 0

2 years ago

What is the answer? And how do I Solve, you get brainiest if you show steps clearly.

scoundrel [369]

Step-by-step explanation:

solution,

given

DF = 42

DE = 7x+1

EF = 4x-3

DE = ?

here,

or, DF = DE +EF

or, 42 = 7x+1+4x-3

or, 42 = 11x-2

or, 42+2 = 11x

or, 44/11 = x

or, 4 = x

then,

replacing value of x in DE

DE = 7x+1

= 7*4+1

= 28+1

= 29

4 0

4 years ago

Determine if the following relations represent y as a function of x.

lana [24]

<h3>Answers:</h3>

A) No, it is not a function
B) Yes it's a function
C) Not a function
D) Yes it's a function
E) Yes it's a function

================================================

Explanation:

If y has an exponent of 2, 4, 6, etc (basically any even number) then it leads to having inputs with multiple outputs.

Consider something like y^2 = x. If x = 100, then y = 10 or y = -10 are possible. A function can only have exactly one y output for any valid x input. Similar issues happen for things like y^4 = x and so on. So this is why A and C are not functions.

The other equations do not have y values with such exponents, so we can solve for y and have each x input lead to exactly one y output. Therefore, they are functions.

5 0

3 years ago

The increasing annual cost (including tuition, room, board, books, and fees) to attend college has been widely discussed (Time).

NeX [460]

Answer:

(a) PRIVATE COLLEGES

Sample mean is $42.5 thousand

Sample standard deviation is $6.65 thousand

PUBLIC COLLEGES

Sample mean is $22.3 thousand

Sample standard deviation is $4.34 thousand

(b) Point estimate is $20.2 thousand. The mean annual cost to attend private colleges ($42.5 thousand) is more than the mean annual cost to attend public colleges ($22.3 thousand)

(c) 95% confidence interval of the difference between the mean annual cost of attending private and public colleges is $19.2 thousand to $21.2 thousand

Step-by-step explanation:

(a) PRIVATE COLLEGES

Sample mean = Total cost ÷ number of colleges = (51.8+42.2+45+34.3+44+29.6+46.8+36.8+51.5+43) ÷ 10 = 425 ÷ 10 = $42.5 thousand

Sample standard deviation = sqrt[summation (cost - sample mean)^2 ÷ number of colleges] = sqrt([(51.8-42.5)^2 + (42.2-42.5)^2 + (45-42.5)^2 + (34.3-42.5)^2 + (44-42.5)^2 + (29.6-42.5)^2 + (36.8-42.5)^2 + (51.5-42.5)^2 + (43-42.5)^2] ÷ 10) = sqrt (44.24) = $6.65 thousand

PUBLIC COLLEGES

Sample mean = (20.3+22+28.2+15.6+24.1+28.5+22.8+25.8+18.5+25.6+14.4+21.8) ÷ 12 = 267.6 ÷ 12 = $22.3 thousand

Sample standard deviation = sqrt([(20.3-22.3)^2 + (22-22.3)^2 + (28.2-22.3)^2 + (15.6-22.3)^2 + (24.1-22.3)^2 + (28.5-22.3)^2 + (22.8-22.3)^2 + (25.8-22.3)^2 + (18.5-22.3)^2 + (25.6-22.3)^2 + (14.4-22.3)^2 + (21.8-22.3)^2] ÷ 12) = sqrt (18.83) = $4.34 thousand

(b) Point estimate = mean annual cost of attending private colleges - mean annual cost of attending public colleges = $42.5 thousand - $22.3 thousand = $20.2 thousand.

This implies the the mean annual cost of attending private colleges is greater than the mean annual cost of attending public colleges

(c) Confidence Interval = Mean + or - Margin of error (E)

E = t×sd/√n

Mean = $42.5 - $22.3 = $20.2 thousand

sd = $6.65 - $4.34 = $2.31 thousand

n = 10+12 = 22

degree of freedom = 22-2 = 20

t-value corresponding to 20 degrees of freedom and 95% confidence level is 2.086

E = 2.086×$2.31/√22 = $1.0 thousand

Lower bound = Mean - E = $20.2 thousand - $1.0 thousand = $19.2 thousand

Upper bound = Mean + E = $20.2 thousand + $1.0 thousand = $21.2 thousand

95% confidence interval is $19.2 thousand to $21.2 thousand

6 0

3 years ago