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Aloiza [94]
3 years ago
9

‼️WILL LIST BRAINLIEST ‼️Carlos went to an Astros game. He spent $25.50 each on two tickets, $10.00 for parking, and $27.75 on f

ood and drinks. How much money did Carlos spend? A) $63.25 B) $53.35 C) $88.75 D) $87.75​
Mathematics
1 answer:
algol133 years ago
3 0

Answer:

$88.75

Step-by-step explanation:

since he bought two tickets for $25.5 each you have to do 2(25.50) and since he also spent $10 and $27.75 you have to add that as well.

y=2(25.50)+10+27.75

y=51+10+27.75

y=61+27.75

y=88.75

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let sin(θ) =3/5 and tan(y) =12/5 both angels comes from 2 different right trianglesa)find the third side of the two tringles b)
statuscvo [17]

In a right triangle, we haev some trigonometric relationships between the sides and angles. Given an angle, the ratio between the opposite side to the angle by the hypotenuse is the sine of this angle, therefore, the following statement

\sin (\theta)=\frac{3}{5}

Describes the following triangle

To find the missing length x, we could use the Pythagorean Theorem. The sum of the squares of the legs is equal to the square of the hypotenuse. From this, we have the following equation

x^2+3^2=5^2

Solving for x, we have

\begin{gathered} x^2+3^2=5^2 \\ x^2+9=25 \\ x^2=25-9 \\ x^2=16 \\ x=\sqrt[]{16} \\ x=4 \end{gathered}

The missing length of the first triangle is equal to 4.

For the other triangle, instead of a sine we have a tangent relation. Given an angle in a right triangle, its tanget is equal to the ratio between the opposite side and adjacent side.The following expression

\tan (y)=\frac{12}{5}

Describes the following triangle

Using the Pythagorean Theorem again, we have

5^2+12^2=h^2

Solving for h, we have

\begin{gathered} 5^2+12^2=h^2 \\ 25+144=h^2 \\ 169=h^2 \\ h=\sqrt[]{169} \\ h=13 \end{gathered}

The missing side measure is equal to 13.

Now that we have all sides of both triangles, we can construct any trigonometric relation for those angles.

The sine is the ratio between the opposite side and the hypotenuse, and the cosine is the ratio between the adjacent side and the hypotenuse, therefore, we have the following relations for our angles

\begin{gathered} \sin (\theta)=\frac{3}{5} \\ \cos (\theta)=\frac{4}{5} \\ \sin (y)=\frac{12}{13} \\ \cos (y)=\frac{5}{13} \end{gathered}

To calculate the sine and cosine of the sum

\begin{gathered} \sin (\theta+y) \\ \cos (\theta+y) \end{gathered}

We can use the following identities

\begin{gathered} \sin (A+B)=\sin A\cos B+\cos A\sin B \\ \cos (A+B)=\cos A\cos B-\sin A\sin B \end{gathered}

Using those identities in our problem, we're going to have

\begin{gathered} \sin (\theta+y)=\sin \theta\cos y+\cos \theta\sin y=\frac{3}{5}\cdot\frac{5}{13}+\frac{4}{5}\cdot\frac{12}{13}=\frac{63}{65} \\ \cos (\theta+y)=\cos \theta\cos y-\sin \theta\sin y=\frac{4}{5}\cdot\frac{5}{13}-\frac{3}{5}\cdot\frac{12}{13}=-\frac{16}{65} \end{gathered}

4 0
1 year ago
Length times width is the formula for what quadrilateral?
Zarrin [17]

Answer:

area of rectangle and square

7 0
3 years ago
Jose invests $10900 in two different accounts. The first account paid 8 %, the second account paid 11 % in interest. At the end
navik [9.2K]

Answer: $4900 at 8%

$6000 at 11%

Step-by-step explanation:

Let x represent the amount which he invested in the account paying 8% interest.

Let y represent the amount which he invested in the account paying 11% interest.

Jose invests $10900 in two different accounts. The first account paid 8 %, the second account paid 11 % in interest. This means that

x + y = 10900

The formula for determining simple interest is expressed as

I = PRT/100

Considering the account paying 8% interest,

P = $x

T = 1 year

R = 8℅

I = (x × 12 × 1)/100 = 0.08x

Considering the account paying 11% interest,

P = $y

T = 1 year

R = 11℅

I = (y × 6 × 1)/100 = 0.11y

At the end of the first year he had earned $1052 in interest., it means that

0.08x + 0.11y = 1052 - - - - - - - - - -1

Substituting x = 10900 - y into equation 1, it becomes

0.08(10900 - y) + 0.11y = 1052

872 - 0.08y + 0.11y = 1052

- 0.08y + 0.11y = 1052 - 872

0.03y = 180

y = 180/0.03

y = 6000

x = 10900 - y = 10900 - 6000

x = 4900

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Find the measure of the indicated angle to the nearest degree
netineya [11]
The correct answer is 24
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Mkey [24]

Answer:

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Step-by-step explanation:

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3 years ago
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