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Lilit [14]
3 years ago
10

What proportional segment lengths verify that BC¯¯¯¯¯∥DE¯¯¯¯¯ ? Fill in the boxes to correctly complete the proportion. $$ = $$

A triangle with vertices labeled as A, B, C. Side B C is base. Sides A B and A C contain midpoints D and E, respectively. A line segment is drawn from D to E. Side A D is labeled as 4. Side D B is labeled as 6. Side A E is labeled as 3.2. Side E C is labeled as 4.8.

Mathematics
2 answers:
Alborosie3 years ago
5 0

answer is

4/6 then 3.2

took the test

ivanzaharov [21]3 years ago
5 0

Answer:

\frac{4}{10}=\frac{3.2}{8.0}

Step-by-step explanation:

Given,

ABC is a triangle,

In which, AD = 4 unit, DB = 6 unit, AE = 3.2 unit and EC = 4.8 unit,

⇒  \frac{AD}{AB}=\frac{4}{4+6}=\frac{4}{10}=0.4

\frac{AE}{EC}=\frac{3.2}{3.2+4.8}=\frac{3.2}{8}=0.4

\implies \frac{AD}{AB}=\frac{AE}{EC}

⇒ Δ ADE  ≅  Δ ABC  

⇒ ∠ADE ≅ ∠ABC  and ∠AED ≅ ∠ACB

By the converse of alternate interior angle theorem.

BC ║ DE

Hence, the required proportion of segment is,

\frac{4}{10}=\frac{3.2}{8.0}

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tatyana61 [14]

Considering the sequences given, the first number that appears in both sequences is given by: 45.

<h3>What numbers appear in the first sequence?</h3>

The rule is multiply by 3 starting from 5, hence the numbers are:

(5, 15, 45, 135, ...).

<h3>What numbers appear in the second sequence?</h3>

The rule is add 9 starting from 18, hence the numbers are:

(18, 27, 36, 45, ...).

45 is the first number that appeared in both sequences.

More can be learned about sequences at brainly.com/question/6561461

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5 0
2 years ago
Jim will be x years old in two years. At that time, his sister will be twice as old as he will be. How old is Jim's sister now?
lozanna [386]
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3 0
4 years ago
A recent study compared the time spent together by single- and dual-earner couples. According to the records kept by the wives d
sergij07 [2.7K]

Answer:

There is evidence to show that  the single-earner couples on average spend more time watching television together

Step-by-step explanation:

Given that a recent study compared the time spent together by single- and dual-earner couples. According to the records kept by the wives during the study, the mean amount of time spent together watching television among the single-earner couples was 61 minutes per day, with a standard deviation of 15.5 minutes. For the dual-earner couples, the mean number of minutes spent watching television was 48.4 minutes, with a standard deviation of 18.1 minutes.

H_0: \bar x=\bar y\\H_a: \bar x > \bar y

(Right tailed test where x stands for single earner and y for double)

Let us assume sample sizes are 500 each.

Difference -12.600

Standard error 1.066

95% CI -14.6913 to -10.5087

t-statistic  -11.823

DF  998

Significance level P < 0.0001

Since p is less than alpha we reject null hypothesis.

There is evidence to show that  the single-earner couples on average spend more time watching television together

4 0
3 years ago
Elyria Warehousing desired to locate a central warehouse to serve five Ohio markets. Placed on a grid system, its five markets h
Iteru [2.4K]

Answer:

The correct option is 2.

Step-by-step explanation:

According to the the center-of-gravity technique, the coordinates of the center-of-gravity location are

(\frac{\sum x_iL_i}{\sum L_i},\frac{\sum y_iL_i}{\sum L_i})

Where ((x_i,y_i) represent the coordinates and L_i is demand.

We have to find the Y-coordinate of the center-of-gravity location.

The sum of product of demand and corresponding y coordinates is

\sum y_iL_i=65\times 2200+55\times 900+95\times 1300+200\times 1750+175\times 3100=1208500

The sum of demanded units is

\sum L_i=2200+900+1300+1750+3100=9250

The Y-coordinate of the center-of-gravity location is

y_0=\frac{\sum y_iL_i}{\sum L_i}

y_0=\frac{1208500}{9250}

y_0=130.6486

y_0\approx 131

The Y-coordinate of the center-of-gravity location is 131. Therefore the correct option is 2.

7 0
3 years ago
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