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3 years ago

Owen used these steps to solve the equation 4x+7=1+2(2x+3). Which choice describes the meaning of his result, 7=7?

Mathematics

1 answer:

ivanzaharov [21]3 years ago

6 0

Answer:

Option D. All values of x make the equation true

Step-by-step explanation:

<u><em>The options of the question are</em></u>

a.The result is not correct because Step 2 has an error.

b.The solution is x=7.

c.No values of x make the equation true.

d.All values of x make the equation true

we have the equation

$4x+7=1+2(2x+3)$

solve for x

Apply distributive property right side

$4x+7=1+4x+6$

Combine like terms

$4x+7=4x+7$

subtract 4x both sides

$7=7$

The equation has infinity solutions

.All values of x make the equation true

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Julie brought 3 bags of sugar. She got a total of 9 1/2 bags of sugar. How many cups of sugar were in each bag. plz help and exp

lara31 [8.8K]

My answer is like in guessing...2 because i did it in my head for two cups :)

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3 years ago

A student is saving money to buy a video game. The student currently has $20 and plans to save $10 every month. Write a function

spayn [35]

Y = total amount
x = number of months

Equation : y = 20 + 10x

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Ans: y = 20 + 10x
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5 0

3 years ago

Read 2 more answers

A student graphed f(x)=x and g(x)= f(x)-8 on the same coordinate grid. Which statement best describes how the graph of f and g a

luda_lava [24]

Answer:

The correct option is D

The graph of f is shifted 8 units down to create the graph of g.

Explanation:

Given f(x) = x

If the graph of this function is shifted 8 units down, we have

x - 8

This is the function f(x) - 8

Since g(x) = f(x) - 8, we conclude that the graph of f is shifted 8 units down to create the graph of g.

7 0

2 years ago

As part of your retirement plan, you want to set up an annuity in which a regular payment of $35,000 is made at the end of each

Finger [1]

Answer:

Option d)$401,447.24

Step-by-step explanation:

We are given that as part of your retirement plan, you want to set up an annuity in which a regular payment of $35,000 is made at the end of each year at rate of 6% compounded annually for 20 years

So first of all we need to find the future value of annuity using the formula as shown below :

$FV= p\frac{[(1+\frac{r}{n})^{(n)(t)}-1)]}{\frac{r}{n}}$

Here, FV = future value of annuity

p = $35000 (annual deposit)

r is rate = 6% = 0.06

n = number of compounding = 1 ( as we are compounding annually )

t = number of years = 20

So plugging in all the values in the formula , we get

$FV= 35000\frac{[(1+\frac{0.06}{1})^{(1)(20)}-1)]}{\frac{0.06}{1}}$

Simplifying further , we get

$FV= 35000\frac{[(1+0.06)^{20}-1)]}{0.06}$

Plugging in the given values in the calculator , we get

FV = $ 1287495.69

So far we have got the Total amount for annuity , from here we need to use the concept of compound interest and find the principal amount to be deposited to get the required total amount of $ 1287495.69

The formula for compound interest when compounded annually is given by:

$A=P(1+r)^t$

Here A = 1287495.69 (Total amount required)

P = ( principal amount to be deposited to meet the required total amount )

r = 6% = 0.06

t = 20

So plugging in all the known values in the formula , we get

$1287495.69= P(1+0.06)^{20}$

simplifying further, we get

$\frac{1287495.69}{(1.06)^{20}}= P$

so required amount to be deposited is given by :

P = $401,447.24

Hope it was helpful !:)

6 0

3 years ago

Mateo is culturing bacteria that have a growth rate of 5.3% per hour. If the current population is 38,762 bacteria, how many bac

Taya2010 [7]

..Given:

$\begin{gathered} a=38762 \\ r=5.3\%=\frac{5.3}{100}=0.053 \\ t=20 \end{gathered}$

To Determine: The number of bacteria after 20 hours

Using the future value formula for growth rate

$\begin{gathered} P_a=P_c(1+r)^t \\ P_a=(Bacteria,final,population) \\ P_c(Bacteria,current,population)=38762 \\ r(rate)=0.053,t(time,in,hour)=20 \end{gathered}$

Therefore

$\begin{gathered} P_a=38762(1+0.053)^{20} \\ P_a=38762(1.053)^{20} \\ P_a=38762(2.809101) \\ P_a=108886.39 \\ P_a\approx108886 \end{gathered}$

Hence, population of bacteria in 20 hours is 108,886

8 0

2 years ago