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3 years ago

In a game, Ben’s score was 3 times Sam’s score. Together they scored 80 points. Find their scores.

Mathematics

2 answers:

Ket [755]3 years ago

7 0

Answer:

PROBABLY ABOUT 27 OR 26.6666666667

Bess [88]3 years ago

7 0

Answer:

Ben's Score = 60

Sam's Score = 20

Step-by-step explanation:

60 + 20 = 80

I really don't know how to explain this.

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For positive acute angles A and B, it is known that tan A = 35/12 and sin B = 20/29. Find the value of sin(A - B ) in the simple

almond37 [142]

Answer:

$\displaystyle \sin(A-B)=\frac{495}{1073}$

Step-by-step explanation:

We are given that:

$\displaystyle \tan(A)=\frac{35}{12}\text{ and } \sin(B)=\frac{20}{29}$

Where both A and B are positive acute angles.

And we want to find he value of sin(A-B).

Using the first ratio, we can conclude that the opposite side is 35 and the adjacent side is 12.

Then by the Pythagorean Theorem, the hypotenuse is:

$h = \sqrt{35^2 + 12^2} =37$

Using the second ratio, we can likewise conclude that the opposite side is 20 and the hypotenuse is 29.

Then by the Pythagorean Theorem, the adjacent is:

$a=\sqrt{29^2-20^2}=21$

Therefore, we can conclude that:

So, for A, the adjacent is 12, opposite is 35, and the hypotenuse is 37.

For B, the adjacent is 21, opposite is 20, and the hypotenuse is 29.

We can rewrite sin(A-B) as:

$\sin(A-B)=\sin(A)\cos(B)-\cos(A)\sin(B)$

Using the above conclusions, this yields: (Note that since A and B are positive acute angles, all resulting ratios will be positive.)

$\displaystyle \sin(A-B)=\Big(\frac{35}{37}\Big)\Big(\frac{21}{29}\Big)-\Big(\frac{12}{37}\Big)\Big(\frac{20}{29}\Big)$

Evaluate:

$\displaystyle \sin(A-B)=\frac{735-240}{1073}=\frac{495}{1073}$

6 0

3 years ago

How many solutions does the equation have?

Salsk061 [2.6K]

Answer: there is only one solution

Step-by-step explanation:

Combine like terms by performing the opposite operation of subtracting 4x on both sides of the equation

The 4x's will cross out on the right

4x - 4x = 0x = 0

On the left:

2x - 4x = -2x

Now the equation looks like:

-2x + 3 = 2

Continue to combine like terms by subtracting 3 on both sides of the equation

On the left:

3 - 3 = 0

On the right:

2 - 3 = -1

Equation:

-2x = -1

Isolate x by performing the opposite operation of dividing -2 on both sides of the equation

On the left:

-2x ÷ -2 = 1

On the right:

-1 ÷ -2 = 1/2

x= 1/2

4 0

3 years ago

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What is the value of x in the equation below?<br> 12 – 2(x-1)=6

JulijaS [17]

X=25 in this equation. But if u divide by 12 it’s -25

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3 years ago

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what is the simplified form of the following expression? Assume X 0 and y 0. 2(^4 sqrt 16 x) -2(^4 sqrt 2y )+3 (^4 sqrt 81x ) -4

eduard

For this case we have the following expression:

$2(\sqrt[4]{16x})-2(\sqrt[4]{2y})+3(\sqrt[4]{81x})-4(\sqrt[4]{32y})$

Rewriting the numbers within the roots we have:

$2(\sqrt[4]{2*2*2*2x})-2(\sqrt[4]{2y})+3(\sqrt[4]{3*3*3*3x})-4(\sqrt[4]{2*2*2*2*2y})$

Then, by properties of powers we have:

$2(\sqrt[4]{2^4x})-2(\sqrt[4]{2y})+3(\sqrt[4]{3^4x})-4(\sqrt[4]{2^42y})$

Then, by radical properties we have:

$2(2\sqrt[4]{x})-2(\sqrt[4]{2y})+3(3\sqrt[4]{x})-4(2\sqrt[4]{2y})$

Rewriting the expression we have:

$4\sqrt[4]{x}-2\sqrt[4]{2y}+9\sqrt[4]{x}-8\sqrt[4]{2y}$

Finally, adding similar terms we have:

$(4+9)\sqrt[4]{x}-(2+8)\sqrt[4]{2y}$

$13\sqrt[4]{x}-10\sqrt[4]{2y}$

Answer:

The simplified form of the expression is:

$13\sqrt[4]{x}-10\sqrt[4]{2y}$

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3 years ago

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2) The senior classes at High School A and High School B planned separate trips to the local

Karo-lina-s [1.5K]

Answer:

D) Van: 7, Bus: 20

Step-by-step explanation:

Add the amount of students together (455 students in total)

Then I added the amount of buses and vans together (5 Vans and 21 Buses)

Then I plugged in each answer

5 x 7 = 35

455 - 35 = 420

420 / 21 = 20

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3 years ago