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3 years ago

Which Algebraic expressions have like terms?

Mathematics

2 answers:

chubhunter [2.5K]3 years ago

6 0

The third option has like terms as they can be added based on the term. For example numbers with x, x^2, x^3 etc can be added together. For example x+x can be added but x+x^2 can’t. They have different terms that make them different.

Papessa [141]3 years ago

5 0

Answer:7n^3+4n-3n^3-5n^2

Step-by-step explanation: Like terms are terms that contain the same variables raised to the same power. Only the numerical coefficients are different. in this algebraic expression there are 2 like terms which consist of the power of three.

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1,030 at 4% compounded semiannually for 2 years

kotegsom [21]

Answer: $1114.91

Step-by-step explanation:

The formula for compound interest is

$A= P(1+\frac{r}{n})^{nt} \\$

Where

A = final amount

P = initial principal balance (1030 for this)

r = interest rate (0.04 for this)

n = number of times interest applied per time period (2 for this)

t = number of time periods elapsed (2 for this)

$A= 1030(1+\frac{.04}{2})^{(2)(2)} \\\\A= 1030(1+0.02)^{4} \\A=1030(1.02)^4\\A=1114.905125$

This rounds up to $1114.91

6 0

3 years ago

I have no clue how to get the answer for this

Kisachek [45]

Hoped if helped x=74

8 0

3 years ago

An automobile manufacturer claims that its car has a 33.7 miles/gallon (MPG) rating. An independent testing firm has been contra

Gnoma [55]

Answer:

$z=\frac{34-33.7}{\frac{1.6}{\sqrt{120}}}=2.05$

And the p value would be given by:

$p_v= 2*P(z>2.05) = 0.0404$

And since the p value is higher than the significance level we have enough evidence to fail to reject the null hypothesis.

Step-by-step explanation:

Data given and notation

$\bar X=34$ represent the sample mean

$\sigma=\sqrt{2.56}= 1.6$ represent the population standard deviation

$n=120$ sample size

$\mu_o =33.7$ represent the value that we want to test

$\alpha=0.02$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

System of hypotheses.

We need to conduct a hypothesis in order to check if the true mean is 33.7 mpg or no, the system of hypothesis would be:

Null hypothesis: $\mu =33.7$

Alternative hypothesis: $\mu \neq 33.7$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{34-33.7}{\frac{1.6}{\sqrt{120}}}=2.05$

And the p value would be given by:

$p_v= 2*P(z>2.05) = 0.0404$

And since the p value is higher than the significance level we have enough evidence to fail to reject the null hypothesis.

6 0

3 years ago

Explain how to evaluate f(g(0)).

alekssr [168]

Answer as a fraction: 17/6

Answer in decimal form: 2.8333 (approximate)

==================================================

Work Shown:

Let's use the two black points to determine the equation of the red f(x) line.

Use the slope formula to get...

m = slope

m = (y2-y1)/(x2-x1)

m = (4-0.5)/(2-(-1))

m = (4-0.5)/(2+1)

m = 3.5/3

m = 35/30

m = (5*7)/(5*6)

m = 7/6

Now use the point slope form

y - y1 = m(x - x1)

y - 0.5 = (7/6)(x - (-1))

y - 0.5 = (7/6)(x + 1)

y - 0.5 = (7/6)x + 7/6

y = (7/6)x + 7/6 + 0.5

y = (7/6)x + 7/6 + 1/2

y = (7/6)x + 7/6 + 3/6

y = (7/6)x + 10/6

y = (7/6)x + 5/3

So,

f(x) = (7/6)x + 5/3

We'll use this later.

---------------------

We ultimately want to compute f(g(0))

Let's find g(0) first.

g(0) = 1 since the point (0,1) is on the g(x) graph

We then go from f(g(0)) to f(1). We replace g(0) with 1 since they are the same value.

We now use the f(x) function we computed earlier

f(x) = (7/6)x + 5/3

f(1) = (7/6)(1) + 5/3

f(1) = 7/6 + 5/3

f(1) = 7/6 + 10/6

f(1) = 17/6

f(1) = 2.8333 (approximate)

This ultimately means,

f(g(0)) = 17/6 as a fraction

f(g(0)) = 2.8333 as a decimal approximation

8 0

3 years ago

What ratio forms a proportion with 14/42?<br> A. 1/4<br> B. 7/21<br> C. 12/40<br> D. 28/80

koban [17]

Hey there!

"What ratio forms a proportion with $\frac{14}{42}$ ?"

- $\frac{14}{45} =0.56$ (for the decimal)

$A) \frac{1}{4}$ $=0.25$ $(incorrect)$
$B) \frac{7}{21}$ $=0.33$ $(Incorrect)$
$C) \frac{12}{40}$ $0.3$ $(incorrect)$
$D) \frac{28}{80}$ $0.7$ $(incorrect)$

But in order for you to solve this particular equation you'd have to go in with two (like multiplying by two)

$1\times2= 2$ ; $4\times2 = 8$ $(incorrect)$
$7\times 2= 14$ ; $21\times2 = 42$ $(correct)$
$12 \times2 = 24$ ; $40\times 2 = 80$ $(incorrect)$
$2 \times 28 = 56$ ; $2\times 80 = 160$ $(incorrect)$

Your result: $\boxed{Answer: B. \frac{7}{21} }$

Good luck on your assignment and enjoy your day!

~ $\bold{LoveYourselfFirst:) }$

3 0

3 years ago