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Anna11 [10]
3 years ago
15

The population of two different cities are modeled by the equations shown below. The population (in thousands) is represented by

Y in the number of years since 1970 is represented by X. What year(s) did the cities have the same population? What was the population of both cities during the year(s) of equal population?
Mathematics
1 answer:
lesya [120]3 years ago
7 0

Answer: years of equal population are 1995 and 2022.

in 1995, population was 425,000 people and in 2022, population was 1,910,000 people.

Step-by-step explanation: Baskinville: y = x2 - 22x + 350

Cryersport: y = 55x - 950

Note that x2 is xsquare not x2

Resolving the quadratic equations carefully will give the values of y and x which represent the population and years.

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Solve 5^3x+1 = 4^x-5 for x
tensa zangetsu [6.8K]

For the equation 5^{3x+1}=4^{x-5} take the \log from both sides:

\log 5^{3x+1}=\log 4^{x-5},\\ \\(3x+1)\log 5=(x-5)\log 4.

Find x:

3x\log 5+\log 5=x\log 4-5\log 4,\\ \\3x\log 5-x\log 4=-5\log 4-\log 5,\\ \\x(3\log 5-\log 4)=-5\log 4-\log 5,\\ \\x=\dfrac{-5\log 4-\log 5}{3\log 5-\log 4}=\dfrac{5\log 4+\log 5}{\log 4-3\log 5}.

Answer: correct choice is D

7 0
3 years ago
Read 2 more answers
rectangular cake pans X and Y are similar. The ratio of the width of the pan X to the width of pan Y is 3 : 4. The length of pan
Vikki [24]
We have two rectangles such as:
Rectangle 1 = X
Rectangle 2 = Y
Where the ratio of the two is:
Ratio = X / Y = 3/4
If x length is 10, we can solve for y length such as:
10 /Y length =3/4
Y length = 40/3 = 13.33

If x width is 5, then we can solve for y width such as:
5/y width = 3/4
y width = 20/3 = 6.67

The Perimeter of Pan Y is shown below:
Y perimeter = 2(6.67) + 2(13.33)
Y perimeter = 40

The answer is 40 inches.
3 0
3 years ago
If a coin is flipped three times in a row, what is the probability of getting tails on all three flips?
telo118 [61]
Probability of getting tails on first flip = 1/2

Probability of getting tails on second flip = 1/2

Probability of getting tails on third flip = 1/2

Probability of getting all 3 tails =  1/2 * 1/2 * 1/2 = 1/8
4 0
4 years ago
Businesses deposit large sums of money into bank accounts. Imagine an account with 10 million
Nikitich [7]

Answer:

The account will earn in one year the amount of $10,512,000

Step-by-step explanation:

Given as :

The principal in the account = $10,000,000

The rate of interest = 5.12% at simple interest

The time period = 1 years

Let The amount that account earn after 1 year = $A

<u>From Simple interest method</u>

Simple interest = S.I = \dfrac{\textrm principal\times \textrm rate\times \textrm time}{100}

or, S.I = \dfrac{\textrm 10,000,000\times \textrm 5.12\times \textrm 1}{100}

or, S.I = \dfrac{51200000}{100}

or, S.I = $512,000

So, Simple interest = S.I = $512,000

Now, Amount = Principal + Interest

I.e A =  $10,000,000 + $512,000

Or, A = $10,512,000

So, Amount = A = $10,512,000

Hence The account will earn in one year the amount of $10,512,000 Answer

8 0
3 years ago
Points S,U, and T are the midpoints of the sides of PQR. Which statements are correct ? 1/2QP=UT 1/2TS=RQ SU=PR SU||RP UT=RP
cricket20 [7]

Answer:

\frac{1}{2} QP = UT

Step-by-step explanation:

GIVEN : In ΔPQR

              S is the mid point of QP

              U is the mid point of PR

              T is the mid point of  QR

Solution :

i) is true i.e \frac{1}{2} QP = UT

Refer the attached file

By mid segment theorem i.e. In a triangle, the line joining the midpoints of any two sides will be parallel to the third side and that same line joining the midpoints is also half of length of third side .

UT is the line joining the two mid points . So, by theorem given above UT is parallel to PQ and  1/2QP=UT.

So, (i) statement is true i.e. \frac{1}{2} QP = UT

6 0
3 years ago
Read 2 more answers
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