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Alborosie
3 years ago
6

Aidan buys 3 bicycles for $252. Each bicycle was the same price.

Mathematics
2 answers:
Elza [17]3 years ago
8 0

Answer:84 dollars per bike :)

Step-by-step explanation:

Masja [62]3 years ago
5 0

Answer:

$84 each

Step-by-step explanation:

All you are doing for this problem is dividing the total by the amount of bicycles (total = 252) (bicycles = 3) and after dividing you would get $84 per bicycle. To check this work, you can do the inverse operation of division (multiplication) and multiply 3 by 84, to still end up with $252. Hope this helps!

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Let f(x)=a(2)^x. This exponential function is intersected twice by the line g(x)=x+b. One intersection is at point P(-2,2). Find
mr_godi [17]

Answer:

See below

Step-by-step explanation:

To find the values of a and b, we use the intersection point P.

Since the graph of f is intersected by P=(-2,2), f(-2)=2, that is, a(2)^(-2)=2. Then a=2(2)²=8.

Since the graph of g is intersected by P=(-2,2), g(-2)=2, that is, -2+b=2. Then b=2+2=4.

Hence a=8, b=4.

To find the other point of intersection Q, we need to find a number x such that f(x)=g(x), that is, 8(2)^(x)=x+4. Rewrite this equation as follows:

f(x)=8(2^x)=2^3(2^x)=2^{3+x}=g(x)=x+4

It is not easy to solve this equation analitically. Instead, you can apply a quantitative method. First, the left hand side is an exponential function, so it is always positive. Then the solution will be a number in which the right side (x+4) is positive, that is, x > -4. The solution is an integer, then the possible values are x=-3,-2,-1,0,1,2,...

Now, the RHS must be a power of two, so the possible integers are x=-3,-2,0,4,12,28,... However, the LHS grows very quickly, while the LHS grows slowly. Then, it is only necessary to test small integer values (we already know that x=-2 is a solution).

If we test with x=-1, we get 2²=4=3, then x=-1 is not a solution. Any x>-1 will not be a solution, because f increases much faster than g, and then they won't intersect. So our possibilities reduce to x=-3,-2. Taking x=-3, we get f(-3)=2⁰=1=-3+4=g(-3). Thus, (-3,0) is the other point of intersection Q. (r=-3, s=0).  

7 0
3 years ago
The smaller triangle is a dilation of the larger triangle with a center of dilation at (2,−1) .
andrew-mc [135]

Answer:

Option B. 1/2

Step-by-step explanation:

The smaller triangle is a dilation of the larger triangle with the center of dilation at (2, -1).

we have to calculate the scale factor of the dilation.

One point of the large triangle is (-4, -1). After dilation it has become (-1, -1) of the smaller one.

If we consider the x coordinates of the point x = -4 has reduced down to -1 therefore scale factor = side of small triangle/side of the large triangle = (2 + 1)/(2 + 4) = 3/6 = 1/2

Therefore Option B. 1/2 is the answer.

3 0
3 years ago
Read 2 more answers
Tim has $20 to buy snacks for 12 people in an office. Each person will get one snack. Tim is buying bags of pretzels that cost $
Greeley [361]

Answer:

  8 bags of pretzels

Step-by-step explanation:

Let x represent the number of bags of pretzels Tim buys. We assume he spends exactly $20 on exactly 12 bags of snack food. Then his purchase is ...

  1.50x + 2.00(12-x) = 20.00

  -0.50x +24.00 = 20.00 . . . eliminate parentheses, collect terms

  -0.50x = -4.00 . . . . . . . . . . .subtract 24

  x = 8 . . . . . . . . . . divide by -0.50

Tim will buy 8 bags of pretzels.

4 0
3 years ago
Bill is bisecting an angle with technology Which of the following describes his next step?
maw [93]

Answer:

  Mark point E where the circle intersects segment BC

Step-by-step explanation:

Apparently, Bill is using "technology" to perform the same steps that he would use with compass and straightedge. Those steps involve finding a point equidistant from the rays BD and BC. That is generally done by finding the intersection point(s) of circles centered at D and "E", where "E" is the intersection point of the circle B with segment BC.

Bill's next step is to mark point E, so he can use it as the center of one of the circles just described.

___

<em>Comment on Bill's "technology"</em>

In the technology I would use for this purpose, the next step would be "select the angle bisector tool."

6 0
3 years ago
Read 2 more answers
Nobody is helping me on this pls answer and ty
Aleks [24]

Answer:

38.7

Step-by-step explanation:

\frac{sinA}{A}=\frac{sinB}{B}=\frac{sinC}{C}

A, B and C are the sides of the triangle and sinA, sinB and sinC are the opposing angles

\frac{sin95}{43}=\frac{A}{27}

A = sin^{-1} (\frac{27*sin95}{43} )=38.72018809

3 0
3 years ago
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