First, you need to find the height, in which it says “a height that’s half the length of the longer base side. Can you guess what that is between 7 and 5? It is 7. And you would find half of that which is 3.5. Now you know the height is 3.5. The formula to find a rectangular pyramid's volume is lwh/3 which you would do 7 * 5 * 3.5, which is equal to 122.5, and then you would divide that by 3, which is 40.833 which would round to 40.8, so there is your answer.
It is 40.8 units^3

7 0

3 years ago

You have invested $5000 in stocks and bonds. The interest you earned on the stocks was 7%. The interest you earned on the bonds

Sphinxa [80]

Money invested S + B = $5000 - - - - (a)
Money earned can be represented in S & B as follows:
0.07*S + 0.14*B =$500 - - - - (b)

Equations a & b are two equations with two unknowns.

From equation a:
S = 5000 - B
Replace S in equation b
0.07*(5000 - B) + 0.14*B =$500
0.07B = 500 - 350 = $150
B = 150/0.07 = $2142.86
S = 5000 - 2142.86 = $2857.14

Good luck

8 0

3 years ago

Find an equation of the circle that satisfies the given conditions. (Give your answer in terms of x and y.)

masya89 [10]

Answer:

$(x-4)^2+(y+5)^2=90$

Step-by-step explanation:

The equation of a circle of radius r, centered at the point (a,b) is

$(x-a)^2+(y-b)^2=r^2$

We already know the center is at $(4,-5)$ , we are just missing the radius. To find the radius, we can use the fact that the circle passes through the point (7,4), and so the radius is just the distance from the center to this point (see attached image). So we find the distance by using distance formula between the points (7,4) and (4,-5):

radius $=\sqrt{(7-4)^2+(4-(-5))^2}=\sqrt{3^2+9^2}=\sqrt{90}$

And now that we know the radius, we can write the equation of the circle:

$(x-4)^2+(y-(-5))^2=\sqrt{90}^2$

$(x-4)^2+(y+5)^2=90$

5 0

3 years ago