Y varies directly with x,and y=7 when x=2. What is the value of y when x=5?

For each of the following angles, name the angle that is congruent.

Hitman42 [59]

isosceles

Step-by-step explanation:

it just is trust me

6 0

3 years ago

Half of the product of two consecutive numbers is 105. To solve for n, the smaller of the two numbers, which equation can be use

alexdok [17]

There are several information's already given in the question. Based on those information's the answer can be detrmined.
Smaller of the two integers = n
Larger of the two integers = n + 1
Then
(1/2) * [(n) * ( n + 1)] = 105
(1/2) * (n^2 + n) = 105
m^2 + n = 210
n^2 + n - 210 = 0
From the above deduction, it can be concluded that the correct option among all the options that are given in the question is the first option or option "A".

6 0

3 years ago

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twice a number minus 4 is less than three times the number. (define a variable, write an inequality, and solve for the problem)

Simora [160]

X will represent unknown
2x-4<3x
treat the < sign as a = sign
2x-4=3x
subtract 2x form both sides
-4=x
put the < sign back
-4<x
-4 is less than than x or
x is greater than -4

4 0

3 years ago

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Misha measured a distance of 60 feet from her kitchen to the bedroom. What is the equivalent number of meters.

Nikitich [7]

1 feet = 0.3048 meters
So we do a unit conversion to cancel out the feet unit.
Look at my picture to see the work

Please let me know if this helped!

3 0

3 years ago

A business has two loans totaling $50,000. One loan has a rate of 8% and the other has a rate of 12%. This year, the business ex

Debora [2.8K]

Answer:

the 8% loan has a principal of $37500

the 12% loan has a principal of $12500

Step-by-step explanation:

Let's start by writing the general equation for the interest hwre I is the interest, P is the principal (in our case would be loan amounts), "r" is the interest rate in decimal form (in our case one would be 0.12, and the other one 0.08), and t is the time in years (in our case 1 year).

$I=P*r*t$

Then we write the interest equation coming from each loan at the end of this year (we call I1 the interest coming from the 12% loan and I2 the interest coming from the 8% one). Since we don't know the loan amounts (in fact those are what we need to find) we will name one "x" and the other "y":

$I=P*r*t\\I1=x * 0.12*1\\I2=y*0.08*1$

Next, we add these last two equations term by term, and replace the addition of both interests by $4500 as given in the information:

$I1=x * 0.12*1\\I2=y*0.08*1\\I1+I2 = 0.12x+0.08y\\4500=0.12x+0.08y$

This is our first equation in the variables x and y which are our unknowns.

Now we generate the second equation on x and y by writing in agebraic terms the other piece of information we have: "the total of the two loans is $50000. That is the addition of the principals x and y should equal $50000:

$x+y=50000$

We solve for y in this last equation and replace its form in terms of x in the equation of the interest, and solve for the unknown x:

$y=50000-x\\4500 = 0.12x +0.08 y\\4500=0.12x+0.08(50000-x)\\4500=0.12x+4000-0.08x\\4500=0.12x-0.08x+4000\\4500=0.04x+4000\\4500-4000=0.04x\\500=0.04x\\x=\frac{500}{0.04} =12500$

Therefore the amount of the loan at 12% is $12500

Now to find the amount of the second loan "y" we use the equation for the totals of the loans:

$x+y=50000\\12500+y=50000\\y=50000-12500=37500$

Therefore, the loan at 8% is $37500

5 0

3 years ago