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RoseWind [281]
2 years ago
9

2. All of the girls in Danielle’s cabin at camp are the same age. Their counselor is 3 times their age. Danielle’s age and her c

ounselor’s ages add up to 28. Write and solve an equation that can be used to find the ages of Danielle and her counsel
Mathematics
1 answer:
Aloiza [94]2 years ago
4 0

Answer:

Danielle is 7 and her counselor is 21

Step-by-step explanation:

Let x be the age of Danielle and y be the age of her counselor then:

y=3x

x+y=28

We can solve this using substitution. In this case, substitute 3x for y since y=3x...

x+3x=28

   4x=28

Divide both sides by 4 (division property of equality)

x=7

y=3x=3(7)=21

Danielle is 7 and her counselor is 21

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200 feet in 5 minutes
aleksandrvk [35]

Answer:

Step-by-step explanation:

Feet per minute is a unit of Speed or Velocity in both US Customary Units as well as the Imperial System. It measures the number of feet traveled in a minute. The symbol for feet per minute is ft/m.

4 0
3 years ago
Complete the square to the problem X^2+6x-16=0
marishachu [46]

Answer:

<h2>x = -8 or x = 2</h2>

Step-by-step explanation:

(a+b)^2=a^2+2ab+b^2\qquad(*)\\\\-------------------------------\\\\x^2+6x-16=0\qquad\text{add 16 to both sides}\\\\x^2+6x=16\\\\x^2+2(x)(3)=16\qquad\text{add}\ 3^2\ \text{to both sides}\\\\\underbrace{x^2+2(x)(3)+3^2}_{(*)}=16+3^2\\\\(x+3)^2=16+9\\\\(x+3)^2=25\Rightarrow x+3=\pm\sqrt{25}\\\\x+3=-5\ \vee\ x+3=5\qquad\text{subtract 3 from both sides}\\\\\boxed{x=-8\ \vee\ x=2}

3 0
3 years ago
Determine which lines are parallel and which are not parallel. Explain your reasoning.
NeX [460]

Answer:

If M and N are parallel, then the correspondent angles generated by the intersection with line R (or line S) should be equal.

So, if M and N are parallel, we should get that angles 2 and angle 4 are equal, as both of these are on the fourth quadrant of the intersection with the same line.

Similarly, if R and S are parallel, then correspondent angles generated by the intersection with line M (or line N) should be equal, this means that:

angle 3 and angle 7 should be equal.

Also remember that if we have two lines intersecting, generating 4 angles, any pair of two adjacent angles will always add to 180°.

Here we have two cases:

1)  m∠3=69°, m∠7=71°

Here we can see that:

m∠3 ≠ m∠7

Thus, lines  R and S are not parallel.

And here we do not have any information on the angles 1, 2, 5, and 6, so we can't compare the angles generated by line N with the ones generated by line M, so we can not know if lines N and M are parallel or not.

2) Now we have that:

m∠3=76°  , m∠8=114°

Notice that angle 8 and angle 7 are adjacent, then we have that:

∠7 + ∠8 = 180°

And we know that:

∠8 = 114°

Then:

∠7 + 114° = 180°

∠7 = 180° - 114° = 76°

Then we have:

∠7 = ∠3

From this we can conclude that lines R and S are parallel.

(again, we can not do anything with lines N and M)

6 0
2 years ago
A recipe for cookies called for 2/3 of a cup of sugar per batch.Elena used 5 1/3 cups of sugar to make multiple batches of cooki
Nookie1986 [14]

Answer: 8 batches

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5 0
2 years ago
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What is the mean of the set of numbers?
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The mean of your question would be -2.5
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3 years ago
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