Sophia scored 33 points in a basketball game. She scored four more two-point baskets than three-point baskets. Write a system of equations in standard form that models this situation.
How many three-point baskets did Sophia make?
please right step by step :)

Answer:

Step-by-step explanation:

the student buys a total of 8 magazines for $14.00

x+y = 8

x = 8-y

2x+1.6y = 14

2(8-y)+1.6y = 14

16-2y+1.6y = 14

16-0.4y = 14

0.4y =16-14 = 2

y = 2/0.4 = 5

x = 8-y = 3

The correct equation best represents the situation is,

⇒ x + y = 8

And, 2x + 1.60y = 14.00

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A student buys (x) fashion magazines and (y) sports magazines.

And, Each fashion magazine costs $2.00 and each sports magazine costs $1.60.

Here, The student buys a total of 8 magazines for $14.00.

Hence, We can formulate;

⇒ x + y = 8

And, 2x + 1.60y = 14.00

Thus, The correct equation best represents the situation is,

⇒ x + y = 8

And, 2x + 1.60y = 14.00

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Answer:

y=x-3

Step-by-step explanation:

Answer:

76%

Step-by-step explanation:

Do turn decimals into percentages you just gotta multiply by 100.

0.76×100=76

Answer:

24

Step-by-step explanation:

Hey there!

I believe the answer to your question is 24.

If it's being reduced by 1/3, you are being left with 2/3, so we can take 2/3 of 9 and you get 6. Perimeter is adding up all the side lengths. Thus, we do 6 + 6 + 6 + 6, and that is 24.

Sorry for any confusion before, I didn't understand the problem before. Hope it helps! Have a great day, and sorry if it's late.

[tex]\frac{12}{5}[/tex]  or  [tex]2 \frac{2}{5\\}[/tex]

Keep [tex]\frac{2}{5}[/tex] the same

change the division sign to multiplication [tex]\frac{2}{5} \\[/tex] × [tex]\frac{1}{6\\}[/tex]

Flip  [tex]\frac{1}{6}[/tex]  so that the denominator is on top and the numerator is on the bottom like this [tex]\frac{6}{1\\}[/tex]

After doing those steps your new equation will look like this-  [tex]\frac{2}{5}[/tex] × [tex]\frac{6}{1}[/tex]

[tex]\frac{2}{5}[/tex] × [tex]\frac{6}{1}[/tex]        Now all you have to do is multiply

1st- multiply 2x6

2nd- multiply 5x1

[tex]\frac{2}{5}[/tex] × [tex]\frac{6}{1\\\\}[/tex] = [tex]\frac{12}{5}[/tex]

So your answer is [tex]\frac{12}{5\\}[/tex]  or [tex]2 \frac{2}{5}[/tex]

Hope my explanation helps you out!

Answer:

m∠C = 66°

Step-by-step explanation:

Given

m∠ A = 33°

m∠ B = 81°

To determine

m∠C = ?

We know that sum of angles of a triangle is 180°.

so using the equation

m∠ A + m∠ B +  m∠C = 180°

substituting m∠ A = 33°, and m∠ B = 81° in the equatio

33° + 81°+m∠C= 180°

114° + m∠C = 180°

m∠C = 180° - 114°

m∠C = 66°

Therefore,

Use the Pythagorean theorem

a^2 + b^2 = c^2

a^2 + 15^2 = 25^2

a^2 + 225 = 625

a^2 = 400

a = 20

Answer: 20 cm

Hope this helps!!

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Answer:

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Answer:

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35, 42, 105 respectively

Answer:

32, 42, 105

Step-by-step explanation:

(32)^2 = 32×32

= 1225

(42)^2 = 42×42

= 1764

(105)^2 = 105×105

=11025

Answer:

Y=−3x2+6x+9

Step-by-step explanation:

Answer:

[tex]r=9.0\:\mathrm{cm}[/tex]

Step-by-step explanation:

The volume of a sphere is given as [tex]\frac{4}{3}r^3\pi[/tex]. Therefore we have the following equation:

[tex]\frac{4}{3}r^3\pi=3026,\\r^3=\frac{3}{4}\cdot\frac{3026}{\pi},\\r^3=722.40428,\\r=\sqrt[3]{722.40428},\\r\approx \fbox{$9.0\:\mathrm{cm}$}[/tex].

Rounding this to the nearest tenth of a centimeter, the radius of the sphere is approximately 14.0 cm.

Volume refers to the amount of space occupied by an object or substance. In mathematics, it is usually measured in cubic units (e.g. cubic meters, cubic centimeters).

The volume of an object can be calculated using its dimensions and specific formulas that depend on the shape of the object.

For example, the volume of a cube is calculated by multiplying its length, width, and height, while the volume of a sphere is calculated using the formula [tex](4/3)\pi r^3[/tex], where r is the radius of the sphere.

The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius of the sphere and π (pi) is a mathematical constant approximately equal to 3.14159.

We can rearrange this formula to solve for r:

r = [tex](3V/4\pi)^{(1/3)[/tex]

Substituting the given volume V = 3026 [tex]cm^3[/tex], we get:

r = [tex](3(3026)/(4\pi))^{(1/3)[/tex] ≈ 14.0 cm

Thus, the radius of the sphere is approximately 14.0 cm, rounded to the nearest tenth of a centimetre.

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Answer:

C

Step-by-step explanation:

Answer:

c. 12

Step-by-step explanation:

if the pentagons are similar they have a common factor.

the factor between 16 cm and 8 cm is 2, so 6*2 is 12.

Answer:

6,9,2,4,10

Step-by-step explanation:

There are possible multiples that can be divisible by 54.

Answer:

z=-3

Step-by-step explanation:

Step 1: Subtract 9z from both sides.

Step 2: Subtract 3 from both sides.

Answer:

− 3.5 ( x + y )

Hope this helps

Step-by-step explanation:

Answer:

− 3.5 ( x + y )

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Step-by-step explanation:

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Answer: y = -1/2x - 1

Answer:

[tex]V(x) = -\frac{340}{3}x +2220[/tex]

[tex]V(8) = 1313.3[/tex]

Step-by-step explanation:

Given

Let x represent years and V represents the value.

So, we have:

[tex](x_1,v_1) = (0,2220)[/tex]

[tex](x_2,v_2) = (6,1540)[/tex]

Solving (a): The linear function

First, we calculate the slope (m)

[tex]m = \frac{v_2 - v_1}{x_2 - x_1}[/tex]

This gives:

[tex]m = \frac{1540-2220}{6-0}[/tex]

[tex]m = \frac{-680}{6}[/tex]

[tex]m = -\frac{340}{3}[/tex]

The linear function is calculated using:

[tex]v - v_2 = m(x - x_2)[/tex]

Where:

[tex](x_2,v_2) = (6,1540)[/tex]

[tex]m = -\frac{340}{3}[/tex]

So, we have:

[tex]v - 1540 = -\frac{340}{3}(x - 6)[/tex]

Open bracket

[tex]v - 1540 = -\frac{340}{3}x +\frac{340}{3}* 6[/tex]

[tex]v - 1540 = -\frac{340}{3}x +680[/tex]

Make v the subject

[tex]v = -\frac{340}{3}x +680+1540[/tex]

[tex]v = -\frac{340}{3}x +2220[/tex]

So, the function is:

[tex]V(x) = -\frac{340}{3}x +2220[/tex]

Solving (b): When x = 8

Substitute 8 for x in [tex]V(x) = -\frac{340}{3}x +2220[/tex]

[tex]V(8) = -\frac{340}{3}*8 +2220[/tex]

[tex]V(8) = -\frac{340*8}{3} +2220[/tex]

[tex]V(8) = -\frac{2720}{3} +2220[/tex]

Take LCM

[tex]V(8) = \frac{-2720+2220*3}{3}[/tex]

[tex]V(8) = \frac{-2720+6660}{3}[/tex]

[tex]V(8) = \frac{3940}{3}[/tex]

[tex]V(8) = 1313.3[/tex]

Hence, its value after 8 years is 1313.3

Answer:

x = 1/20 = 0.050

x = 0

Step-by-step explanation:

either of those

Answer:

Hey bro,

The answer should - 39x i.e minus 39x

Answer:

3x+9

Step-by-step explanation:

If it’s multiple choice the other one is

x +1+1+1+x +1+1+1+ x +1+1+1

I hope this helps!

Answer:

x= tm+5/4-t

Step-by-step explanation:

4x-5=t(x+5)

4x-5-=tx+tm   distributive

4x-5-tx=tm    substract tx from both sides

4x-tx=tm+5   add 5 to both sides

x * 4+ x(-t) =tm+5  factor x out 4x-tx

x(4-t)=tm+5   factor x out x*4 + x(-t)

x(4-t)/4-t= tm/4-t+ 5/4-t   divide each term in 4-t

x= tm/4-t + 5/4-t combine the numerators over the common denominator

x=tm+5/4-t

Answer:

(4,7)

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

38/2=19

Answer:

r = 19

Step-by-step explanation:

2r = 38 (Given)

r = 19 (Divide by 2 on both sides)

Answer:

[tex]y - 8 = \frac{5}{3}(x - 1)[/tex]

Step-by-step explanation:

1) Use the slope formula, [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex], and the given points to find the slope. [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of one point the line must intersect, and [tex]x_2[/tex] and [tex]y_2[/tex] represent the x and y values of another point the line must also intersect:

[tex]\frac{(3)-(8)}{(-2)-(1)}[/tex]

= [tex]\frac{-5}{-3}[/tex]

= [tex]\frac{5}{3}[/tex]

2) Using the point-slope formula, [tex]y-y_1 = m (x - x_1)[/tex], use the slope you just calculated and substitute it for m. Choose any of the two points given (I chose (1,8)) and substitute its x and y values for [tex]x_1[/tex] and [tex]y_1[/tex]. Don't worry, the equation of the line is the same no matter which point you choose (unless the question specifies which one you need to choose):

[tex]y - 8 = \frac{5}{3}(x - 1)[/tex]