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2 years ago

A direct variation function contains the points (2,14) and (4,38) which equation represents the function

1 answer:

3 0

You are given two points on a line, and told that the function is "direct variation." You can save a lot of time by recognizing that the y-intercept here is zero (0). Thus, the line passes through the origin.

A line through (2,14) and (4,38) is NOT direct variation, because the line connecting those two points does NOT pass through the origin, and thus has a vertical intercept.

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Addie walked 2 1 2 miles in 45 minutes. Suzie covered 2 2 5 miles in 2 3 of an hour. Which girl walked faster? By how much?

kobusy [5.1K]

Answer:

Suzie walks faster by 0.27 miles per hour.

Step-by-step explanation:

Addie walked $2\frac{1}{2}$ miles in 45 minutes and Suzie covered $2\frac{2}{5}$ miles in $\frac{2}{3}$ of an hour.

So, Addie walked 2.5 miles in 45 minutes i.e. $\frac{45}{60} = 0.75$ hours.

Therefore, the walking speed of Addie is $\frac{2.5}{0.75} = 3.33$ miles per hour.

Again, Suzie covered $2\frac{2}{5}$ i.e. 2.4 miles in $\frac{2}{3}$ i.e. 0.67 hours.

So, the walking speed of Suzie is $\frac{2.4}{0.67} = 3.6$ miles per hour.

Hence, Suzie walks faster by (3.6 - 3.33) = 0.27 miles per hour. (Answer)

7 0

2 years ago

Are triangles ADC and EBC congruent? triangle ADC is overlapping triangle EBC so that they both share angle ACE, point B is on s

Olin [163]

Answer:

Yes, by AAS ⇒ 2nd answer

Step-by-step explanation:

* Lets revise the cases of congruence

- SSS ⇒ 3 sides in the 1st Δ ≅ 3 corresponding sides in the 2nd Δ

- SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 corresponding

sides and including angle in the 2nd Δ

- ASA ⇒ 2 angles and the side whose joining them in the 1st Δ ≅

2 corresponding angles and the side whose joining them in the 2nd Δ

- AAS ⇒ 2 angles and one side in the first triangle ≅ 2 corresponding

angles and one side in the 2ndΔ

* Lets solve the problem

- In 2 Δs ADC and EBC

∵ ∠ACE is a common angle in the two triangles ⇒ given

∵ ∠CAD ≅ ∠CEB ⇒ because they marked with the same symbol

∵ DC ≅ BC ⇒ because they marked with the same symbol

- Two angles and one side in Δ ADC ≅ two corresponding angles

and one side in Δ EBC

∴ Triangles ADC and EBC congruent by AAS

* Yes Triangles ADC and EBC congruent by AAS

8 0

2 years ago

Read 2 more answers

An ostrich can run 6 mph faster than a giraffe. An ostrich can run 7 miles in the same time that a giraffe can run 6 miles. Find

LUCKY_DIMON [66]

NOTE THIS IS AN EXAMPLE:

Let t = time, s = ostrich, and g = giraffe.

Here's what we know:

s = g + 5 (an ostrich is 5 mph faster than a giraffe)

st = 7 (in a certain amount of time, an ostrich runs 7 miles)

gt = 6 (in the same time, a giraffe runs 6 miles)

We have a value for s, so plug it into the first equation:

(g + 5)t = 7

gt = 6

Isolate g so that we can plug that variable value into the equation:

g = 6/t

so that gives us:

(6/t + 5)t = 7

Distribute:

6 + 5t = 7

Subtract 6:

5t = 1

Divide by 5:

t = 1/5 of an hour (or 12 minutes)

Now that we have a value for time, we can plug them into our equations:

1/5 g = 6

multiply by 5:

g = 30 mph

s = 30 + 5

s = 35 mph

Check by imputing into the second equation:

st = 7

35 * 1/5 = 7

7 = 7

5 0

2 years ago

A family travels 513 miles in 7.2 hours. How many miles did they travel in one hour?

nignag [31]

Answer:

71.25 mph

Step-by-step explanation:

5 0

2 years ago

The cost in dollars to produce x cups of lemonade is represented by the function C(x) = 10 + 0.20x. The revenue in dollars earne

vlada-n [284]

Revenue > Cost
R(x) > C(x)
0.50x > 10+0.20x
0.50x-0.20x > 10
0.30x > 10
x > 10/0.30
x > 33.333 which is approximate

Round up to the nearest whole number to get x = 34. You need to sell at least 34 cups of lemonade to have the revenue R(x) be larger than the cost C(x)

Answer: 34

8 0

2 years ago