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3 years ago

The amount of rainfall each month over the past four years is shown below

Mathematics

1 answer:

Angelina_Jolie [31]3 years ago

4 0

Unknown answer, not enough info.

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Which expressions are equivalent to 4(x+1) + 7(x+3)? Select two answers.

Natalija [7]

Answer:

9(x+3) + 2(x+3) or 10(x+2) +(x+5)

Step-by-step explanation:

First you want to distribute the equation.

4(x+1) + 7(x+3) multiplied out is

4x + 4 + 7x + 21

Now we add like terms so it comes out to

11x + 25

Two expressions that can come out to equal 11x + 25 is. 9(x+3) + 2(x+3) or 10(x+2) +(x+5)

7 0

3 years ago

Please dont ignore, Need help!!! Use the law of sines/cosines to find..

Ket [755]

Answer:

16. Angle C is approximately 13.0 degrees.

17. The length of segment BC is approximately 45.0.

18. Angle B is approximately 26.0 degrees.

15. The length of segment DF "e" is approximately 12.9.

Step-by-step explanation:

By the law of sine, the sine of interior angles of a triangle are proportional to the length of the side opposite to that angle.

For triangle ABC:

$\sin{A} = \sin{103\textdegree{}}$ ,
The opposite side of angle A $a = BC = 26$ ,
The angle C is to be found, and
The length of the side opposite to angle C $c = AB = 6$ .

$\displaystyle \frac{\sin{C}}{\sin{A}} = \frac{c}{a}$ .

$\displaystyle \sin{C} = \frac{c}{a}\cdot \sin{A} = \frac{6}{26}\times \sin{103\textdegree}$ .

$\displaystyle C = \sin^{-1}{(\sin{C}}) = \sin^{-1}{\left(\frac{c}{a}\cdot \sin{A}\right)} = \sin^{-1}{\left(\frac{6}{26}\times \sin{103\textdegree}}\right)} = 13.0\textdegree{}$ .

Note that the inverse sine function here $\sin^{-1}()$ is also known as arcsin.

By the law of cosine,

$c^{2} = a^{2} + b^{2} - 2\;a\cdot b\cdot \cos{C}$ ,

where

$a$ , $b$ , and $c$ are the lengths of sides of triangle ABC, and
$\cos{C}$ is the cosine of angle C.

For triangle ABC:

$b = 21$ ,
$c = 30$ ,
The length of $a$ (segment BC) is to be found, and
The cosine of angle A is $\cos{123\textdegree}$ .

Therefore, replace C in the equation with A, and the law of cosine will become:

$a^{2} = b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}$ .

$\displaystyle \begin{aligned}a &= \sqrt{b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}}\\&=\sqrt{21^{2} + 30^{2} - 2\times 21\times 30 \times \cos{123\textdegree}}\\&=45.0 \end{aligned}$ .

For triangle ABC:

$a = 14$ ,
$b = 9$ ,
$c = 6$ , and
Angle B is to be found.

Start by finding the cosine of angle B. Apply the law of cosine.

$b^{2} = a^{2} + c^{2} - 2\;a\cdot c\cdot \cos{B}$ .

$\displaystyle \cos{B} = \frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}$ .

$\displaystyle B = \cos^{-1}{\left(\frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}\right)} = \cos^{-1}{\left(\frac{14^{2} + 6^{2} - 9^{2}}{2\times 14\times 6}\right)} = 26.0\textdegree$ .

For triangle DEF:

The length of segment DF is to be found,
The length of segment EF is 9,
The sine of angle E is $\sin{64\textdegree}}$ , and
The sine of angle D is $\sin{39\textdegree}$ .

Apply the law of sine:

$\displaystyle \frac{DF}{EF} = \frac{\sin{E}}{\sin{D}}$

$\displaystyle DF = \frac{\sin{E}}{\sin{D}}\cdot EF = \frac{\sin{64\textdegree}}{39\textdegree} \times 9 = 12.9$ .

7 0

3 years ago

Jaina and Tomas compare their compound interest accounts to see how much they will have in the accounts after three years. They

MariettaO [177]

The question is incomplete. The complete question is :

Jaina and Tomas compare their compound interest accounts to see how much they will have in the accounts after three years. They substitute their values shown below into the compound interest formula. Compound Interest Accounts Name Principal Interest Rate Number of Years Compounded Jaina $300 7% 3 Once a year Tomas $400 4% 3 Once a year. Which pair of equations would correctly calculate their compound interests?

Solution :

It is given that Jaina and Tomas wants to open an account by depositing a principal amount for a period of 3 years and wanted to calculate the amount they will have using the compound interest formula.

<u>So for Jiana</u> :

Principal, P = $300

Rate of interest, r = 7%

Time, t = 3

Compounded yearly

Therefore, using compound interest formula, we get

$A=P\left(1+\frac{r}{100}\right)^{t}$

$=300\left(1+\frac{7}{100}\right)^{3}$

$=300(1+0.07)^3$

<u>Now for Tomas </u>:

Principal, P = $400

Rate of interest, r = 4%

Time, t = 3

Compounded yearly

Therefore, using compound interest formula, we get

$A=P\left(1+\frac{r}{100}\right)^{t}$

$=400\left(1+\frac{4}{100}\right)^{3}$

$=400(1+0.04)^3$

Therefore, the pair of equations that would correctly calculate the compound interests for Jaina is $A=300(1+0.07)^3$ .

And the pair of equations that would correctly calculate the compound interests for Tomas is $A=400(1+0.04)^3$ .

8 0

3 years ago

Read 2 more answers

Travis was attempting to make muffins to take to a neighbor that had just moved in down the street. The recipe that he was worki

aev [14]

A. The recipe required 3/4 cup of sugar and 1/8 cup of butter.
The ratio of the sugar to butter in the original recipe is

B. If Travis accidentally put a whole cup of butter in the mix, then he needs to put
cup of sugar.
C. Travis has to put 1/8 cup of butter, but he put 1 cup of butter. The ratio is

If Travis wants to keep the ratios the same as they are in the original recipe, he needs to put 8 times more of all the other ingredients.

4 0

2 years ago

Two cars are side by side. One is 3.9 meters long. The other is 6% shorter. How long is the second car?

GrogVix [38]

Answer:

3.66meters long

Step-by-step explanation:

since it's 6% shorter you calculate 3.9 times .94(which is basically 94 percent) which gives you 3.66 meters long

7 0

3 years ago