All categories

3 years ago

The area of the triangle is 22.4cm^2.

Mathematics

1 answer:

Ivanshal [37]3 years ago

6 0

Answer:

The longest side length b is approximately 13.172 cm

Step-by-step explanation:

The given parameters are;

The area of the triangle = 22.4 cm²

The given angles of the triangle = ∠97°

The given side of the triangle = 3.7 cm

The formula for the area of a triangle, A = 1/2 × a × b × sin(C)

Where;

a, and b are the side legs forming the angle C

Therefore, we have;

A = 22.4 = 1/2 × 3.7 × a × sin(97°)

a = 22.4/(1/2 × 3.7 × sin(97°)) ≈ 12.199

a ≈ 12.199 cm

Therefore, by cosine rule, we have;

b² = a² + c² - 2 × a × c × Cos(B)

Substituting the values, gives;

b² = 12.199² + 3.7² - 2 × 12.199 × 3.7 × Cos(97°)

b² ≈ 173.507

∴ b ≈ √173.507 ≈ 13.172

b ≈ 13.172 cm

You might be interested in

WILL MARK BRAINIEST!!! 20 POINTS!!! Determine the equivalent system for the given system of equations. 4x − 5y = 2 10x − 21y = 1

aniked [119]

Answer:

none of the options

Step-by-step explanation:

4x − 5y = 2 , 10x − 21y = 10

---------

the first equation is same in all answer choices, let's check which is equivalent to second, the easy way is to consider x/y ratio which is 10/ -21

4x − 5y = 2 , 3x − y = 4

no, ratio is 3/ -1

4x − 5y = 2 , 24x − 47y = 22

no, the ratio is 24/ -47

4x − 5y = 2 , 10x + 3y = 15

no, the ratio is 10/3

4x − 5y = 2 , 14x + 26y = 12

no, the ratio is 14/26

3 0

3 years ago

Please Answer Fast But make sure there right and answer like 1. 2. 3. 4. 5.

prohojiy [21]

Answer:

Step-by-step explanation:

1- A (0.166 repeating)

2- B (.28)

3- B (.7777 repeating)

4- A (.08333 repeating

5- 8.1 (3 gallons) 1.35 (1/2 gallon)

so 9.45 dollars

3 0

4 years ago

Read 2 more answers

Nine more than the quotient of a number and 4 is 12

Fudgin [204]

To solve this, let's first convert the equation to standard form:

9 + (x/4) = 12

Now, let's solve for x:

9 + (x/4) = 12
9 + (x/4) - 9 = 12 - 9
x/4 = 3
x/4 * 4 = 3 * 4
x = 12

8 0

3 years ago

A bag of birdseed that normally costs $22.25 is marked up to $25.30 what is the percent markup?

vovangra [49]

To get the answer to this problem, first we have to subtract the marked up cost to the cost of the product. So we first minus 25.3 and 22.25. When we do this, we will get a difference of 3.05. This is the profit that you will earn. So after that, we have to divide 3.05 and 25.30 to get the mark up percentage. When we do this, we will get an answer of 0.12. So in order to convert that into a percentage, we just have to multiply it by 100 and we will get 12%.

7 0

4 years ago

Calcium is an essential nutrient for strong bones and for controlling blood pressure and heart beat. Because most of the body’s

irakobra [83]

Answer:

No, because the 95% confidence interval contains the hypothesized value of zero.

Step-by-step explanation:

Hello!

You have the information regarding two calcium supplements.

X₁: Calcium content of supplement 1

n₁= 12

X[bar]₁= 1000mg

S₁= 23 mg

X₂: Calcium content of supplement 2

n₂= 15

X[bar]₂= 1016mg

S₂= 24mg

It is known that X₁~N(μ₁; σ²₁), X₂~N(μ₂;δ²₂) and σ²₁=δ²₂=?

The claim is that both supplements have the same average calcium content:

H₀: μ₁ - μ₂ = 0

H₁: μ₁ - μ₂ ≠ 0

α: 0.05

The confidence level and significance level are to be complementary, so if 1 - α: 0.95 then α:0.05

since these are two independent samples from normal populations and the population variances are equal, you have to use a pooled variance t-test to construct the interval:

[(X[bar]₁-X[bar]₂) ± $t_{n_1+n_2-2;1-\alpha /2}$ * $Sa*\sqrt{\frac{1}{n_1} +\frac{1}{n_2} }$ ]

$t_{n_1+n_2-2;1-/2}= t_{25;0.975}= 2.060$

$Sa= \sqrt{\frac{(n_1-1)S^2_1+(n_2-1)S^2_2}{n_1+n_2-2} }= \sqrt{\frac{11*529+14*576}{12+15-2} } = 23.57$

[(1000-1016)±2.060*23.57* $\sqrt{\frac{1}{12} +\frac{1}{15} }$ ]

[-34.80;2.80] mg

The 95% CI contains the value under the null hypothesis: "zero", so the decision is to not reject the null hypothesis. Then using a 5% significance level you can conclude that there is no difference between the average calcium content of supplements 1 and 2.

I hope it helps!

3 0

3 years ago