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3 years ago

The sum of two integers is greater than 12. One integer is 10 less than the other. What are the values of the integers?

1 answer:

5 0

Let's set up an equation:

x plus y is greater than 12

x + y > 12

One of the integers is ten less than twice the other one

x = 2y -10

Time to start solving:

(2y-10) + y > 12
2y + y > 12 + 10
3y > 22
3y=24
y=8

Now its time to find the value of x:

x=2(8) - 10
x=16-10
x= 6

6 + 8 > 12, 6+8 is greater than twelve.

In conclusion we can wrap up that 6 and 8 are the least value integers.

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4 years ago

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Which congruence theorems can be used to prove △EFG ≅ △JHG? Check all that apply.

sasho [114]

Answer:

ASA and AAS

Step-by-step explanation:

We do not know if these are right triangles; therefore we cannot use HL to prove congruence.

We do not have 2 or 3 sides marked congruent; therefore we cannot use SSS or SAS to prove congruence.

We are given that EF is parallel to HJ. This makes EJ a transversal. This also means that ∠HJG and ∠GEF are alternate interior angles and are therefore congruent. We also know that ∠EGF and ∠HGJ are vertical angles and are congruent. This gives us two angles and a non-included side, which is the AAS congruence theorem.

Since EF and HJ are parallel and EJ is a transversal, ∠JHG and ∠EFG are alternate interior angles and are congruent. Again we have that ∠EGF and ∠HGJ are vertical angles and are congruent; this gives us two angles and an included side, which is the ASA congruence theorem.

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3 years ago

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Some students were asked what kinds of animals they have at home.

Nataly_w [17]

(a) Animals by popularity; Dogs, Cats, Others, Horses.

(b) If 250 students were interviewed, 20 students have other pets.

(c) No, it was incorrect.

Step-by-step explanation:

Step 1; We arrange the different pets in chronological order, from the highest percent to the lowest percent;

1. Dogs - 67%,

2. Cats - 20%

3. Others - 8%,

4. Horses - 1%.

None is not included in this list.

Step 2; If 250 students were interviewed, 8% of those have other pets. So we need to calculate how much 8% of 250 is.

8% of 250 = $\frac{8}{100}$ × 250 = 0.08 × 250 = 20.

So 20 students had other pets.

Step 3; 20% of the interviewed students had cats. If 75 students had cats, we need to equate 20% to the 75 and find out how many students were actually interviewed.

20% × x = 75, 0.2 × x = 75,

x = $\frac{75}{0.2}$ = 375.

So if 375 students were interviewed, 75 students would have cats. So the estimate of 250 students being interviewed is incorrect.

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3 years ago