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3 years ago

The difference of two integers is thirty. the larger integer is two more than five times the smaller integer. Find the integers

1 answer:

5 0

X=2+5y
x-y=30

basically, all you're doing here is solving a system of equations. use the second equation to find out what x or y means. i'm going to solve it for x.

this is the new equation : x=30+y

now i plug this equation into the first one.

30+y=2+5y

30=2+5y-y
30=2+4y
28=4y
y=7

now that you know what y is, take that second equation we did in the beginning and plug in y.

x-7=30

solve for x

x=37

the two integers are 37 and 7.

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[need math help] Study buddies part #2

rosijanka [135]

Answer:

Part A) The distance between Whitney's house and Anh's house is 6.5 miles.

Part B) The total distance traveled by Whitney during the trip was 9.5 miles.

Step-by-step explanation:

Part A)

Notice that during Whitney's journey to Anh's house, her velocity was negative for some time. So, Whitney was travelling backwards. Hence, the total distance Whitney traveled will be greater than the actual distance from Whitney's house to Anh's.

So, instead, we can calculate Whitney's total displacement. Total displacement is given by:

$\displaystyle \text{Displacement}=\int_a^bv(t)\, dt$

Where v(t) is the velocity function.

So, the displacement of Whitney when she traveled from her house to Anh's house will be:

$\displaystyle \text{Displacement}=\int_0^{24}v(t)\, dt$

To calculate the integral, we can split it off at t = 11, t = 16, and t = 24.

The three regions represent three geometric figures, which we can use to calculate the area and then find the integral. Rewriting:

$\displaystyle \text{Displacement}=\int_0^{11}v(t)\, dt+\int_{11}^{16}v(t)\, dt+\int_{16}^{24}v(t)\, dt$

Now, we can calculate the area of each figure.

The first figure is a trapezoid with a height of 0.8 and two bases of 11 and 3. So, its area is:

$\displaystyle A_1=\frac{1}{2}(0.8)(11+3)=5.6\text{ miles}$

The second figure is a triangle with a height of 0.6 and a base of 5. So, its area is:

$\displaystyle A_2=\frac{1}{2}(0.6)(5)=1.5\text{ miles}$

Lastly, the third figure is another triangle will a height of 0.6 and a base of 8. So, its area is:

$\displaystyle A_3=\frac{1}{2}(0.6)(8)=2.4\text{ miles}$

However, notice that the second figure is below the x-axis. During that interval, Whitney was traveling backwards. Hence, we will subtract the second area from the rest of the areas.

Then the displacement will be:

$\displaystyle \text{Displacement}=5.6-1.5+2.4=6.5\text{ miles}$

So, the distance between Whitney's house and Anh's house is 6.5 miles.

Part B)

The total distance differs from displacement in that it includes all the distances in both directions. It is given by:

$\displaystyle \text{Distance}=\int_a^b|v(t)|\, dt$

In other words, all of our values are now positive. We will utilize the same strategy:

$\displaystyle \text{Distance}=\int_0^{11}|v(t)|\, dt+\int_{11}^{16}|v(t)|\, dt+\int_{16}^{24}|v(t)|\, dt$

Substitute. The only difference is that we will add 1.5 instead of subtracting it. So:

$\displaystyle \text{Distance} =5.6+1.5+2.4=9.5$

Therefore, in this instance, Whitney traveled a total of 9.5 miles to get to Anh's house.

6 0

3 years ago

Can I get some help on this

nordsb [41]

Answer: Choice C

The vertical asymptote at x = -4 tells us that -4 is not part of the domain. This only applies to 1/(x+4). If we plug in x = -4, we get...

f(x) = 1/(x+4)
f(-4) = 1/(-4+4)
f(-4) = 1/0
f(-4) = undefined; because of the division by zero error

The value x = -4 is allowed in the other answer choices.

5 0

3 years ago

PLS HELP TEST ILL GIVE BRAINLIEST

topjm [15]

Answer:

Answer attached

Step-by-step explanation:

With reference to my figure

Shape 1 = square

Shape 2 = rectangle

5 0

3 years ago

I need helppppppppppppppppppppppppp

omeli [17]

The answer is sometimes

3 0

3 years ago

Joe went shopping and purchased a pair of pants for $56 and a pair of shoes for $45. The tax in Joe's city is 4%. How much will

Nimfa-mama [501]

Answer:

$105.04

Step-by-step explanation:

First add $56 plus 45$ and you will get $101, then times $101 and 1.04 together.

Your answer should be $105.04.

6 0

1 year ago