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makkiz [27]
2 years ago
5

A ball is thrown into the air from the edge of a 48-foot-high cliff so that it eventually lands on

Mathematics
1 answer:
DedPeter [7]2 years ago
6 0

Answer: 2.5 < x < 5.5

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Given ∆ABC with vertices A(−4, −3), B(0, 0), C(2, −3) and ∆DEF with vertices D(3, 1), E(6, -3), F(3, −5), use the definition of
dimaraw [331]

By SSS congruency criteria ΔABC ≅ ΔDEF

<h3>What is congruency?</h3>

Two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

The given vertices of the triangles are;

ΔABC: A(−4, −3), B(0, 0), C(2, −3)

ΔDEF:  D(3, 1), E(6, -3), F(3, −5)

The lengths of the sides of ΔABC are

AB = √((0+4)² + (0+3)²) = √25 = 5

BC = √((2-0)² + (-3 - 0)²) = √13  

AC = √((2+4)² + (-3 +3)²) = √36 = 6

The lengths of the sides of ΔDEF are;

DE = √25=5

EF = √13

DF = √36 = 6

As,

AB= DE, BC = EF , AC= DF

So, By SSS congruency criteria ΔABC ≅ ΔDEF

Learn more about this concept here:

brainly.com/question/6563819

#SPJ1

6 0
2 years ago
Help me solve for x. the angles they give to you are 138, 78, and 94. please help ​
Taya2010 [7]

Answer:

x = 8

Step-by-step explanation:

180 = 78 + 94 + x

180 =172 + x

-172 -172

18 = x

7 0
3 years ago
Help ill give brainliest!!!!!!!<br><br> ^^
Strike441 [17]

Answer:

15 days

Step-by-step explanation:

Well, as you would be able to tell, you just have to find the LCM of 3 and 5. These do not have one before 3 x 5, so it is 15.

3 0
2 years ago
A consumer group has determined that the distribution of life spans for gas ranges (stoves) has a mean of 15.0 years and a stand
Art [367]

Answer:

b. Mean = 1.6 years, standard deviation - 0.92 years, shape: approximately Normal.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction of normal Variables:

When we subtract normal variables, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.

A consumer group has determined that the distribution of life spans for gas ranges (stoves) has a mean of 15.0 years and a standard deviation of 4.2 years. Sample of 35:

This means that:

\mu_G = 15

s_G = \frac{4.2}{\sqrt{35}} = 0.71

The distribution of life spans for electric ranges has a mean of 13.4 years and a standard deviation of 3.7 years. Sample of 40:

This means that:

\mu_E = 13.4

s_E = \frac{3.7}{\sqrt{40}} = 0.585

Which of the following best describes the sampling distribution of the difference in mean life span of gas ranges and electric ranges?

Shape is approximately normal.

Mean:

\mu = \mu_G - \mu_E = 15 - 13.4 = 1.6

Standard deviation:

s = \sqrt{s_G^2+s_E^2} = \sqrt{0.71^2+0.585^2} = 0.92

So the correct answer is given by option b.

8 0
3 years ago
I need help i need the statement and reason
Marina86 [1]
For number one
S: supplement.
R: angle1+angle8 =18
#2
S: supplement
R: angle 3+ angle 6=180
6 0
2 years ago
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