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3 years ago

Please help me

Mathematics

1 answer:

jeyben [28]3 years ago

8 0

Use Pythagorean theorem
a^2 + b^2 = c^2
Other words, lengths of the shortest sides squared are equal to the longest squared

a^2 + 9^2 = 15^2
a^2 + 81 = 225
a^2 = 144
a = squareroot of 144
a = 12

Solution: a = 12

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IPS Math Grade 7 Final SY20-21 1 5 of 13

miv72 [106K]

Answer:

Actual distance between two city = 40 miles

Step-by-step explanation:

Given sample size;

1 inch = 10 miles

Distance between two city = 4 inch

Find:

Actual distance between two city

Computation:

Actual distance between two city = Sample size of 1 inch in miles x Distance between two city

Actual distance between two city = 4 x 10

Actual distance between two city = 40 miles

8 0

3 years ago

cain deposited $6033 into savings account 25 years ago the account has an interest rate of 4.2 and the balance is currently $720

Ksju [112]

Answer:

interest is compounded monthly

Step-by-step explanation:

there is a slight mistake in the question, the future value after 25 years is $17,208.63, not $7,208.63

the future value = present value x (1 + i/a)ⁿᵃ

future value = $17,208.63

present value = $6,033

i/a = 4.2%/a

n x a = 25a

(1 + 0.042/a)²⁵ᵃ = $17,208.63 / $6,033 = 2.852416708

²⁵√(1 + 0.042/a)²⁵ᵃ = ²⁵√2.852416708

(1 + 0.042/a)ᵃ = 1.042818

4.2818% would be the effective interest on the loan, so we can try different options for a. Since the effective interest is higher, I will try first with monthly compounding:

a = 12 (compounded monthly)

(1 + 0.042/12)¹² = (1 + 0.0035)¹² = 1.042818 ✓

7 0

3 years ago

Please help!! 20 POINTS

shepuryov [24]

<h2>Hello!</h2>

The answers are:

First image:

The answer is the second option, the angles is $53\°$

Second image:

The answer is the third option:

$\frac{5}{13}$

Third image:

The length of the adjacent leg is the first option:

$8\sqrt{2}units$

Fourth image:

The answer is the fourth option, $72\°$

Fifth image:

The answer is the fourth option, DF (hypothenuse) is equal to 25 units.

To solve these problems, we need to use the following trigonometric identities and the Pythagorean Theorem, since we are working with right triangles.

$Tan(\alpha)=\frac{y}{x}\\\\(Tan(\alpha))^{-1} =(\frac{y}{x})^{-1}\\\\\alpha =Arctan(\frac{y}{x})$

$Sin(\alpha)=\frac{opposite}{hypothenuse}$

Pythagorean Theorem:

$c^{2}=a^{2} +b^{2}$

So, solving we have:

First image:

We are given a right triangle that has the following lengths:

$base=x=6units\\height=y=8units\\hypothenuse=10units$

Then, calculating we have:

$\alpha =Arctan(\frac{y}{x})\\\\\alpha =Arctan(\frac{8}{6})\\\\\alpha =Arctan(1.33)\\\\\alpha =53\°$

Hence, the answer is the second option, the angles is $53\°$

Second image:

We are given a right triangle that has the following lengths:

$base=x=12units\\height=y=5units\\hypothenuse=13units$

Then calculating the sin ratio, we have:

$Sin(\alpha)=\frac{opposite}{hypothenuse}$

$Sin(\alpha)=\frac{5}{13}$

Thence, the answer is the third option:

$\frac{5}{13}$

Third Image:

We are given the following information:

$hypothenuse=16units\\\\\alpha =45\°$

Then, calculating one of the angle legs, since both will have the same length, using the sine trigonometric identity, we have:

$Sin(\alpha)=\frac{Opposite}{Hypothenuse}\\ \\Sin(45\°)=\frac{Opposite}{16}\\\\Opposite=Sin(45\°)*16\\\\Opposite=\frac{\sqrt{2} }{2}*16=8\sqrt{2}$

Hence, the answer is the first option the length of the adjacent leg is

$Opposite=\frac{\sqrt{2} }{2}*16=8\sqrt{2}units$

Fourth image:

We are given the following information:

$base=x=9units\\height=y=3units$

To calculate the angle at the B vertex, first, we need to calculate the angle at the C vertex, and then, calculate the B vertex by the following way:

Since the sum of all the interior angles of a triangle are equal to 180°, we have that:

$180\°=Angle_{B}+Angle{C}+90\°$

$Angle_{B}=180\° -90\°-Angle_{C}$

So, calculating the angle at the C vertex, we have:

$\alpha =Arctan(\frac{y}{x})$

$\alpha =Arctan(\frac{3}{9})$

$\alpha =Arctan(0.33)=18.26\°$

Then, calculating the angle at the B vertex, we have:

$Angle_{B}=180\° -90\°-18.26\°=71.74\°=71.8\°=72\°$

Hence, the answer is the fourth option, $72\°$

Fifth image:

We are given the following information:

$base=x=24units\\height=y=7units$

Now, to calculate the distance DF (hypothenuse) we need to use the Pythagorean Theorem:

$c^{2}=a^{2} +b^{2} \\\\hypothenuse^{2}=adjacent^{2}+opposite^{2}\\\\\sqrt{hypothenuse^{2}}=\sqrt{adjacent^{2}+opposite^{2}}\\\\hypothenuse=\sqrt{adjacent^{2}+opposite^{2}}$