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2 years ago

Based on the information marked in the diagram, ABC and DEF must be congruent.

Mathematics

2 answers:

ziro4ka [17]2 years ago

7 0

Hello!

As you can see, both AB and DE both have one dash mark. This means they are congruent. Angles C and F are congruent as well. A and D both have right angles. These triangles are congruent.

I hope this helps!

drek231 [11]2 years ago

3 0

Answer:

Option A is correct

True, ΔABC and ΔDEF must be congruent.

Explanation:

LA theorem or Postulates states that given two right triangles, where one acute angle and a leg of one of the triangles are congruent to an angle and a leg of the other triangle, then the two triangles are congruent.

In ΔABC and ΔDEF

AB = DE [Leg] [Given in the figure]

$\angle BAC = \angle EDF = 90^{\circ}$ [Given]

$\angle BCA = \angle EFD$ [Acute angle] [Given in the figure]

Then, by the LA theorem or Postulates;

therefore, ΔABC $\cong$ ΔDEF .

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A chef bought some green and red peppers. She bought 18 green peppers, which was 3/4 the total number.

Nezavi [6.7K]

A: Their would be 24 red peppers because I did 18 divided by 3/4 and got 24 and 24 times 3/4 is 18
B:She bought 42 peppers all together because 18 plus 24 is 42

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2 years ago

The first three terms of an arithmetic series are 6p+2, 4p²-10 and 4p+3 respectively. Find the possible values of p. Calculate t

Doss [256]

Answer:

First Case:

$\displaystyle p=\frac{5}{2}\text{ and } d=-2$

Second Case:

$\displaystyle p=-\frac{5}{4}\text{ and } d=\frac{7}{4}$

Step-by-step explanation:

We know that the first three terms of an arithmetic series are:

$6p+2, 4p^2-10, \text{ and } 4p+3$

Since this is an arithmetic sequence, each subsequent term is d more than the previous term, where d is our common difference.

Therefore, we can write the second term as;

$4p^2-10=(6p+2)+d$

And, likewise, for the third term:

$4p+3=(6p+2)+2d$

Let's solve for d for each of the equations.

Subtracting in the first equation yields:

$d=4p^2-6p-12$

And for the second equation:

$2d=-2p+1$

To avoid fractions, let's multiply the first equation by 2. Hence:

$2d=8p^2-12p-24$

Therefore:

$8p^2-12p-24=-2p+1$

Simplifying yields:

$8p^2-10p-25=0$

Solve for p. We can factor:

$8p^2+10p-20p-25=0$

Factor:

$2p(4p+5)-5(4p+5)=0$

Grouping:

$(2p-5)(4p+5)=0$

Zero Product Property:

$\displaystyle p_1=\frac{5}{2} \text{ or } p_2=-\frac{5}{4}$

Then, we can use the second equation to solve for d. So:

$2d_1=-2p_1+1$

Substituting:

$\begin{aligned} 2d_1&=-2(\frac{5}{2})+1 \\ 2d_1&=-5+1 \\ 2d_1&=-4 \\ d_1&=-2\end{aligned}$

So, for the first case, p is 5/2 and d is -2.

Likewise, for the second case:

$\begin{aligned} 2d_2&=-2(-\frac{5}{4})+1 \\ 2d_2&=\frac{5}{2}+1 \\ 2d_2&=\frac{7}{2} \\ d_2&=\frac{7}{4}\end{aligned}$

So, for the second case, p is -5/4, and d is 7/4.

By using the values, we can determine our series.

For Case 1, we will have:

17, 15, 13.

For Case 2, we will have:

-11/2, -15/4, -2.

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1 year ago

A machine can collate 126 400 page books in 14 days. if it continues to collate at this same rate, how many 400 page books could

beks73 [17]

For this case we can make the following rule of three to solve the problem:
126 --------> 14
x -----------> 30
We clear the value of x:
x = (30/14) * (126)
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Answer:
it could collate in 30 days about:
x = 270 400 page books

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2 years ago

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Diano4ka-milaya [45]

Answer:

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Step-by-step explanation:

Given in the question that,

total cost of DVD bought by Adela = $210

Step 1

Adela makes a down payment of $30

$210 - $30 = $180

Remaining cost = $180

Step 2

Adela pays $15 each week

$15 = 1 week

$180 = ?

$1 = 1 week/15

$180 = 180/15 week

= 12 weeks

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