Find the greatest common factor of -30x 4 yz 3 and 75x 4 z 2.

You and Michael have a total of $19.75. If Michael has $8.25, how much

ser-zykov [4K]

Answer:

You have a total of $11.50

Step-by-step explanation:

We first subtract $19.75 by $8.25 and the result will be $11.50

7 0

3 years ago

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The first three terms of arithmetic progression are -5,-1 and 3.Find the six term.

vodomira [7]

Answer:

15

Step-by-step explanation:

The pertinent general formula for this arithmetic progression is

a(n) = a(1) + d(n - 1), where d is the common difference. That difference is d = 4.

Here, a(n) = -5 + 4(n -1)

Therefore, a(6) = -5 + 4(5) = 15

8 0

3 years ago

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Your school sells yearbooks every spring. The total profit p made depends on the amount x the school charges for each yearbook.

xz_007 [3.2K]

Answer:

84inches sjbsjsbs km s

8 0

4 years ago

Do you hypotenuse of a triangle is 1 foot more than twice the length of the shorter leg the longer leg is 7 feet longer than the

Lera25 [3.4K]

Answer:

Shorter leg: 8 units

Longer leg: 15 units

Hypotenuse: 17 units

Step-by-step explanation:

We are given $h=1+2s$ where $h$ is the hypotenuse and $s$ is the length of the shorter leg.

We got this equation from reading that the "hypotenuse of a triangle is 1 foot more than twice the length of the shorter leg". I replaced the "hypotenuse of a triangle" with $h$ , "is" with $=$ , "1 foot more than" with $1+$ and finally "twice the length of the shorter leg" with $2s$ .

We also have "longer leg is 7 feet longer than the shorter leg".

I'm going to replace "longer leg" with $L$ .

I'm going to replace "is" with $=$ .

I'm going to replace "7 feet longer than the shorter leg" with $7+s$ .

So we have the equation $L=7+s$ .

So we have a right triangle since something there is a side being referred to as the hypotenuse. We can use Pythagorean Theorem to find a relation between all these sides.

So by Pythagorean Theorem, we have: $s^2+L^2=h^2$ .

Let's make some substitutions from above:

$s^2+(7+s)^2=(1+2s)^2$

Let's expand the powers using:

$(a+b)^2=a^2+2ab+b^2$

Applying this now:

$s^2+(49+2(7)s+s^2)=(1+2(1)(2s)+(2s)^2)$

$s^2+49+14s+s^2=1+4s+4s^2$

Combine like terms on right hand side:

$2s^2+49+14s=1+4s+4s^2$

Subtract everything on left hand side to get 0 on that side:

$0=(1-49)+(4s-14s)+(4s^2-2s^2)$

Simplify:

$0=(-48)+(-10s)+(2s^2)$

Reorder into standard form for a quadratic:

$0=2s^2-10s-48$

Every term is even and therefore divisible by 2. I will divide both sides by 2:

$0=s^2-5s-24$

I'm going to see if this is factoroable.

We need to see if we can come up with two numbers that multiply -24 and add up to be -5.

Those numbers are -8 and 3.

So the factored form is:

$0=(s-8)(s+3)$

This implies that either $s-8=0$ os $s+3=0$ .

The first equation can be solved by adding 8 on both sides: $s=8$ .

The second equation can be solved by subtracting 3 on both sides: $s=-3$ .

The only solution that makes sense for $s$ is 8 since it can't the shorter length cannot be a negative number.

$s=8$

$L=7+s=7+8=15$

$h=1+2s=1+2(8)=1+16=17$

So the dimensions of the right triangle are:

Shorter leg: 8 units

Longer leg: 15 units

Hypotenuse: 17 units

6 0

4 years ago

You are baking brownies for your class. There are 28 total students in your class and you have baked 23 brownies. Write and solv

barxatty [35]

Answer:

2(28)=23+x

Step-by-step explanation:

There are 28 students and each student needs two brownies. You have to multiply 28 by 2 so you will have to total number on one side.

On the other you need to have the number of brownies you have at the moment and x for the number you need to bake. You want to add them because you will need to put those numbers together to get the number on the opposite side.

28x2=56 so 56=23+x. Subtract the 23 from both sides to get 33=x. x=33

To check plug 33 into x to get 2(28)=23+33. 56=23+33. 56=56

you need 33 more brownies.

So the equation would be 2(28)=23+x.

Hope that helps.

3 0

3 years ago