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igor_vitrenko [27]
3 years ago
12

There are 172 South American animals in the Springdale zoo. That is 45 more than half the number of african animals in the zoo.

Write an equation you could use to find n, the number of African animals in the zoo.
Mathematics
1 answer:
patriot [66]3 years ago
6 0
N=number of African animals in the zoo;
we suggest this equation:
172=45+n/2
Least common multiple=2
172*2=45*2+n
344=90+n
n=344-90
n=254

Answer: there are 254 African animals in the zoo.
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Find four numbers that form a geometric progression such that the third term is greater than the first by 12 and the fourth is g
olchik [2.2K]

If x is the first number in the progression, and r is the common ratio between consecutive terms, then the first four terms in the progression are

\{x,xr,xr^2,xr^3\}

We want to have

\begin{cases}xr^2-x=12\\xr^3-xr=36\end{cases}

In the second equation, we have

xr^3-xr=xr(r^2-1)=36

and in the first, we have

xr^2-x=x(r^2-1)=12

Substituting this into the second equation, we find

xr(r^2-1)=12r=36\implies r=3

So now we have

\begin{cases}9x-x=12\\27x-3x=36\end{cases}\implies x=\dfrac32

Then the four numbers are

\left\{\dfrac32,\dfrac92,\dfrac{27}2,\dfrac{81}2\right\}

4 0
3 years ago
PLEASE HELP!!!
RoseWind [281]

Answer:

Increased by a factor of 4

Step-by-step explanation:

The original circumference is:

C1 = 2 * pi * r1

The new circumference is:

C2 = (2 * pi * r2)

"circumference that is 4 times larger than the original"

(2 * pi * r2) = 4 (2 * pi * r1)

Rewriting:

r2 = 4r1

Answer:

The radius of the original circle is:

increased by a factor of 4

Hope this helps :)

5 0
2 years ago
Read 2 more answers
Simplify the following by removing parentheses and combining terms<br> -(2q+6)+3(2q+4)-2q
Gelneren [198K]

Answer:

2q+6

Step-by-step explanation:

So basically, you would do this.

-2q-6+6q+12-2q

Next

-4q+6q = 2q

12-6=6

2q+6

7 0
2 years ago
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Determine the projection of w onto u.
irina [24]

Answer:

A.6.2i-4.2 j

Step-by-step explanation:

We are given that

u=9i-6j

v=-3i-2j

w=19i+15j

We have to find the projection of w on to u.

The project of vector a on b

=\frac{a\cdot b}{\mid b\mid^2}b

w.u=(19i+15j)\cdot (9i-6j)=171-90=81

\mid u\mid=\sqrt{x^2+y^2}=\sqrt{9^2+(-6)^2}=\sqrt{117}

Using the formula

The projection of w on to u

=\frac{u\cdot w}{\mid u\mid^2}(u)=\frac{81}{117}(9i-6j)

The projection of w on to u=6.2i-4.2j

Hence, option A is true.

4 0
3 years ago
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Calculate the distance between the points C=(-7, 7) and M=(-2, 3) in the coordinate plane.
pishuonlain [190]

Answer:

d = Sqrt 41 = 6.4

Step-by-step explanation:

d = sqrt [(x-x)^2 + (y-y)^2]

d = sqrt [(-7 - - 2)^2 + (7-3)^2]

d = sqrt[(-7+2)^2 + (4)^2]

d = sqrt [(-5)^2 + (4)^2]

d= sqrt (25 + 16)

d = sqrt 41 = 6.4

6 0
3 years ago
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