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3 years ago

What else would need to be congruent to show that ABC is congruent to DEF by ASA?

Mathematics

1 answer:

cestrela7 [59]3 years ago

5 0

Answer:

∠ A ≅ ∠ D

Step-by-step explanation:

We have to prove Δ ABC and Δ DEF are congruent or Δ ABC ≅ Δ DEF applying the Angle-Side-Angle or ASA rule.

In order to maintain the sequence, in ASA rule we have to make congruent two angles and one side in between them.

Therefore, if ∠ B and ∠ E are proved to be congruent and segment AB and segment DE are proved to be congruent, then we have to consider another two angles which must be ∠ A and ∠ D to be congruent.

Therefore, option D is correct. (Answer)

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Evaluate 2a + 6b for a = 4 and b = 5. 12a+60 = 2a + 6b=

galina1969 [7]

Answer:

38 and 108

Step-by-step explanation:

2a + 6b

2 (4) + 6 (5) Plug in values

8+30 = 38

12a + 60

12 (4) + 60 = 108

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2 years ago

Read 2 more answers

Name the set or sets of numbers to which the square root of 28 belongs to.

ki77a [65]

SOLUTION: name the set or sets of numbers on a numbers to which each real number bleongs question 1) negative square root of 64 question 2) 8/3 question 3) square root 28 questio. , so it is a Real Number, Rational Number, and Integer. is a fraction, so it is a Real Number and a Rational Number.

Hope this helped! Brainliest?

8 0

3 years ago

What is the answer to x/16=45/40

AveGali [126]

The answer is x = 18

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3 years ago

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A lab technician needs 60mL of 25% acid solution for a certain experiment , but he has only 10% solution and 40% solution. How m

V125BC [204]

Answer:

10%: 30 mL
40%: 30 mL

Step-by-step explanation:

The needed concentration is exactly halfway between the available concentrations, hence they must be mixed equally.

He should mix 30 mL each of the 10% and 40% solutions.

_____

The first step in solving any problem is to look at the given information, and at what is being asked for. Here, the mix that is being asked for is exactly halfway between the given concentrations, so you know without any further contemplation that the mix will be 50%/50% of each.

If the mix were something else, there are several ways the problem can be solved. I like to use a diagram that puts the available concentrations on the left in a column with the highest on top, the needed concentration in the next column in the middle, and the differences of these numbers on the diagonals in the right column.

Example: if the needed mix is 15%, the diagram would look like ...

40 5

10 25

The numbers on the right tell you the proportions required (5:25 = 1:5). For this example, you need 1 part 40% solution and 5 parts 10% solution to make a mix that is 15%. That's a total of 6 parts, so each "part" is 10 mL for 60 mL of solution.

We chose this example so every number in the diagram is different, so you could see how the instructions for use apply.

Another way to solve this is to let a variable represent the amount needed of the highest concentration. If we let that variable be x, for the given problem, we can write the equation for the amount of acid in the mix as ...

40%(x) + 10%(60 -x) = 25%(60)

0.30x = 9 . . . . . . . . subtract 6, simplify

x = 9/0.30 = 30 . . . . . mL of 40% solution

6 0

3 years ago

In selecting a sulfur concrete for roadway construction in regions that experience heavy frost, it is important that the chosen

Lesechka [4]

Step-by-step explanation:

Given - In selecting a sulfur concrete for roadway construction in regions that experience heavy frost, it is important that the chosen concrete has a low value of thermal conductivity in order to minimize subsequent damage due to changing temperatures. Suppose two types of concrete, a graded aggregate and a no-fines aggregate, are being considered for a certain road. The table below summarizes data on thermal conductivity from an experiment carried out to compare the two types of concrete.

Type ni xi si

Graded 42 0.486 0.187

No-fines 42 0.359 0.158

To find - a. Formulate the above in terms of a hypothesis testing problem.

b. Give the test statistic and its reference distribution (under the null hypothesis).

c. Report the p-value of the test statistic and use it to assess the evidence that this sample provides on the scientific question of difference in mean conductivity of the two materials at the 5% level of significance.

Proof -

a.)

Hypothesis testing problem :

H0 : There is significant difference between mean conductivity for the graded concrete and mean conductivity for the no fines concrete.

H1 : There is no significant difference between mean conductivity for the graded concrete and mean conductivity for the no fines concrete.

Test statistic :

$Z = \frac{x_{1} - x_{2} }{\sqrt{\frac{s_{1} ^{2} }{n_{1}} + \frac{s_{2}^{2} }{n_{2}} } }$

$Z = \frac{0.486 - 0.359 }{\sqrt{\frac{0.03496 }{42} + \frac{0.02496 }{42} } }$

$Z = \frac{0.127 }{\sqrt{0.001468}}$

$Z = \frac{0.127 }{0.0377}$

⇒Z(cal) = 3.3687

Z(tab) = 1.96

As Z (cal) > Z(tab)

So, we reject H0 at 5% Level of significance

p-value = 0.99962

Hence

There is significant difference in mean conductivity at the two materials.

5 0

2 years ago