Dan made 90 free throws in 30 minutes Alex made 60 free throws in 20 minutes compare the unit rates

A) Dan made more free throws per minute

B) Alex made more free throws per minute

C) they made the same free-throw‘s per minute

Step-by-step explanation:

by trigonometry,

cos 30 = x/12√3 =√3/2

→ x=18

sin 30 =y/12√3=1/2

→ y=6√3

The values of x and y are 18 and 10.392 respectively.

The definition for a right triangle states that if one of the angles of a triangle is a right angle - 90º, the triangle is called a right-angled triangle or simply, a right triangle. In the given image, triangle ABC is a right triangle, where we have the base, the altitude, and the hypotenuse. Here AB is the base, AC is the altitude, and BC is the hypotenuse.

Given right triangle

hypotenuse = 12√3

base = x and height  = y

angle of base  = 30°

cosФ = b/h

cos30 = x/12√3

x = 12√3 x √3/2

x = 18

and sin30 = p/h

sin 30 = p/12√3

p = 1/2 x 12√3

p = 6√3

p = 10.392

Hence the values of x= 18 and y = 10.392.

Learn more about right triangles;

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Answer:48miles

solution on the picture

if it's helpful ❤❤❤

THANK YOU

Answer:

a. 25%

b. 6.5%

c. 20%

Step-by-step explanation:

Answer:

-14r + 6

Step-by-step explanation:

-12r + 6 - 2r

Answer:

Given that you're providing only a single term, asking for a difference doesn't make a lot of sense.  I assume you're asking to have the expression simplified?

If so, then it can be reduced to (x - 17) / 3x

Step-by-step explanation:

You can simplify by multiplying both terms each by a different ratio that equals one, but also gives the terms common denominator.  Multiplying the first one by x²/x² and the second by 3x/3x will do that for you.

After that you can group the terms into one fraction and simplify:

[tex]\frac{x - 8}{3x} - \frac{3x}{x^2} \\\\= \frac{x - 8}{3x}\times\frac{x^2}{x^2} - \frac{3x}{x^2} \times\frac{3x}{3x} \\\\= \frac{x^3 - 8x^2}{3x^3} - \frac{9x^2}{3x^3} \\\\= \frac{x^3 - 8x^2 - 9x^2}{3x^3} \\\\= \frac{x - 8 - 9}{3x}\\\\= \frac{x - 17}{3x}\\[/tex]

Answer:

The difference of [tex]\frac{x-8}{3x}-\frac{3x}{x^2}[/tex]  is [tex]\mathbf{\frac{x-17}{3x}}[/tex]

Step-by-step explanation:

We need to find the difference: [tex]\frac{x-8}{3x}-\frac{3x}{x^2}[/tex]

Simplifying to find the difference:

[tex]\frac{x-8}{3x}-\frac{3x}{x^2}[/tex]

x is common in both 3x and x^2 so, we can cancel it out and we get:

[tex]=\frac{x-8}{3x}-\frac{3x}{x(x)}\\=\frac{x-8}{3x}-\frac{3}{x}[/tex]

Now, taking LCM of 3x and x we get 3x, We will multiply 3x with both terms and then solve we get:

[tex]=\frac{x-8-3(3)}{3x}\\=\frac{x-8-9}{3x}\\=\frac{x-17}{3x}[/tex]

It cannot be further simplified, so we get [tex]\frac{x-17}{3x}[/tex] as answer.

So, The difference of [tex]\frac{x-8}{3x}-\frac{3x}{x^2}[/tex]  is [tex]\mathbf{\frac{x-17}{3x}}[/tex]

Answer:

[tex] {x}^{2} +2 x + 1 = 4 \\ {(x + 1)}^{2} = 4 \\( x + 1) = + 2 \: and \: (x + 1) = - 2 \\ \boxed{x = 1 \: and \: x = - 3}[/tex]

Answer:

The values of x and y that make the quadrilateral is a parallelogram are x = 12 and y = 21

Step-by-step explanation:

In the given figure

If DEFG is a parallelogram, then DE = GF and DG = EF

∵ DE = GF

∵ DE = 6x - 12 and GF = 2x + 36

→ Equate them

∴ 6x - 12 = 2x + 36

→ Subtract 2x from both sides

∵ 6x - 2x - 12 = 2x - 2x + 36

∴ 4x - 12 = 36

→ Add 12 to both sides

∵ 4x - 12 + 12 = 36 + 12

∴ 4x = 48

→ Divide both sides by 4

∴ x = 12

∵ DG = EF

∵ DG = 6y - 42 and EF = 4y

→ Equate them

∴ 6y - 42 = 4y

→ Add 42 to both sides

∵ 6y - 42 + 42 = 4y + 42

∴ 6y = 4y + 42

→ Subtract 4y from both sides

∵ 6y - 4y = 4y - 4y + 42

∴ 2y = 42

→ Divide both sides by 2

∴ y = 21

∴ The values of x and y that make the quadrilateral is a parallelogram are

   x = 12 and y = 21

Answer:

I'm pretty sure it's the 1 or tha last one

Answer:

[tex]y=\frac{1}{4}x-1[/tex]

Step-by-step explanation:

Parallel lines always have equal slopes. Therefore, this eliminates two options and we just need to find the y-intercept. Since the line passes through [tex](-4,-2)[/tex], we have:

[tex]-2=\frac{1}{4}(-4)+b,\\b=-1[/tex].

Therefore, the equation of the line is:

[tex]y=\frac{1}{4}x-1[/tex]

Answer:

pretty sure its the first one

Step-by-step explanation:

Answer:

stage 1 -280

stage 2 -220

stage 3 -160

stage 4 - 100

it takes 6 stages to return to the surface.

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

good job, it's correct.

Answer: 0.44

Step-by-step explanation:

Answer: the answer is the first one ,the third one , and the fourth

Step-by-step explanation:5x5 25

15x15 225

Step-by-step explanation:

[tex] \underline{ \underline{ \text{Given}}} : [/tex]

[tex] \underline{ \underline{ \text{To \: find}}} : [/tex]

[tex] \underline{ \sf{∠ACD= ∠ABC\: + \: ∠BAC}}[/tex] { Exterior angle of a triangle is equal to sum of the two non - adjacent interior angles }

[tex] \sf{x \degree = 60 \degree + 60 \degree}[/tex]

[tex] \sf{x \degree = 120 \degree}[/tex]

[tex] \blue{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \underline{ \tt x = 120 \degree}}}}}}[/tex]

Hope I helped ! ♡

Have a wonderful day / night ! ツ

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Answer:

The answer is A. 5m - 3

Step-by-step explanation:

Ella bought 5 packs of muffins but since we don't know how many muffins are in each pack, we put a variable in place so it's 5m. Since she saved $3 off the total, that means you would subtract 3 from the total, so the problem would be 5m - 3

Answer:

You already have the answer so ima just get the points

Have a good night

Answer:

:)

Step-by-step explanation:

The answer is ≈1761.76886

Answer:

7/6

Step-by-step explanation:

trust me i promise this is right

Answer:

2/-2

Step-by-step explanation:

X-axis is first and Y-axis

Answer:

Slope: [tex]m=-\frac{1}{2}[/tex]

y-intercept: [tex](0,-1)[/tex]

Equation: [tex]y=-\frac{1}{2}x-1[/tex]

Step-by-step explanation:

Slope-intercept form of an equation is written as [tex]y=mx+b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.

The slope of a line that passes through the points [tex](x_1,\: y_1)[/tex] and [tex](x_2, \: y_2)[/tex] is [tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]. Using the coordinates [tex](-2, 0)[/tex] and [tex](2,-2)[/tex] as given in the problem, we have slope of this line to be:

[tex]m=\frac{-2-0}{2-(-2)}=\frac{-2}{4}=-\frac{1}{2}[/tex].

Now using this slope we've found and any point the line passes through, we can find the y-intercept of this equation:

[tex]0=-\frac{1}{2}(-2)+b, \\ b=-1[/tex]

Therefore, the equation of this line in slope-intercept form is [tex]\fbox{$y=-\frac{1}{2}x-1$}[/tex].

The y-intercept occurs when [tex]x=0[/tex]:

[tex]y=-\frac{1}{2}(0)-1, \\\\y=1[/tex]

Thus, the y-intercept is

[tex](0, -1)[/tex]

Answer:

A.

Step-by-step explanation:

Combine 7 and -3 to get 4

4+7xy is the answer

Answer:

Yes, you can combine the 7 and the -3. Simplified expression is 4 + 7xy

Step-by-step explanation:

Answer:

15 people voted yes and 3 people voted no.

Step-by-step explanation:

Given that:

Ratio of yes to no = 5 : 1

Total number of board members who voted = 18

Let,

x be the number of times.

5x+x = 18

6x = 18

Dividing both sides by 6

[tex]\frac{6x}{6}=\frac{18}{6}\\x=3[/tex]

People who voted yes = 5(3) = 15

People who voted no = 3

Hence,

15 people voted yes and 3 people voted no.

Answer:

Step-by-step explanation:

Answer is p/320

Answer:

2x + 3y = -6

Step-by-step explanation:

The equation of the new line will be identical to that of the given line except that the constant term will differ.

Start with the given 2x + 3y = 3 and replace x with 3 and y with -4.  We get:

2(3) + 3(-4) = C, and C = 6 - 12 = -6

The equation of the new line is therefore 2x + 3y = -6

Answer:

C≈31.42

Step-by-step explanation:

Radius=5 (10 divided by 2)

C=2πr

Brainly plss