A basketball trophy is 1.5 feet tall and casts a 2 foot shadow.
if a basketball hoop casts a 16 foot shadow, how tall is the hoop

Answer:

1. α²+β² = 25/36

2. 1/α+1/β​ = 1/2

Step-by-step explanation:

Formula :

Consider the quadratic equation ax² + bx + c = 0

Where x₁ and x₂ are the zeros of the equation.

Then

[tex]x_{1}+x_{2}=-\frac{b}{a} \\x_{1}\times x_{2}=\frac{c}{a}[/tex]

……………………………………

α and β are the zeros of the quadratic polynomial f(x) = 6x²+x-2

Then

[tex]\alpha +\beta =-\frac{1}{6}[/tex]

[tex]\alpha \times \beta =-\frac{1}{3}[/tex]

……………………

[tex]\alpha^{2} +\beta^{2} =\left( \alpha +\beta \right)^{2} -2\alpha \beta[/tex]

            [tex]=\alpha^{2} +\beta^{2} =\left( -\frac{1}{6} \right)^{2} -2\times(-\frac{1}{3} )[/tex]

            [tex]=\frac{25}{36}[/tex]

………………………………

[tex]\frac{1}{\alpha } +\frac{1}{\beta } =\frac{\alpha +\beta }{\alpha \beta }[/tex]

          [tex]=\frac{-\frac{1}{6} }{-\frac{1}{3} } =\frac{1}{2}[/tex]

Answer:

See below

Step-by-step explanation:

y = -3 x^7   is NOT a parabola....   y = -3x^2  IS a parabola that opens downward due to the negative coefficient (-3)

Answer:

Common factor

5x^{2}+35x

5(x^{2}+7x)

2

Rewrite in factored form

5(x^{2}+7x)

5x(x+7)

Solution

5x(x+7)

Step-by-step explanation:

mark me brainlist

multiply left to right:

-4 x 542 = -2,168

-2,168 x 5 = -10,840

answer: -10,840

The simplified expression is -4x^(547).

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To simplify -4x^(542)x^5.

You can use the property of exponents that states that when you multiply two terms with the same base, you add their exponents.

So,

-4x^(542)x^5

= -4x^(542+5)

= -4x^(547)

Thus,

The simplified expression is -4x^(547).

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Answer:

[tex]\textsf{Mean}\:\overline{X}=\sf \dfrac{\textsf{sum of all the data values}}{\textsf{total number of data values}}[/tex]

[tex]\implies \sf Mean\:(Nilo)=\dfrac{5+6+14+15}{4}=\dfrac{40}{4}=10[/tex]

[tex]\implies \sf Mean\:(Lisa)=\dfrac{8+9+11+12}{4}=\dfrac{40}{4}=10[/tex]

[tex]\displaystyle \textsf{Standard Deviation }s=\sqrt{\dfrac{\sum X^2-\dfrac{(\sum X)^2}{n}}{n-1}}[/tex]

[tex]\begin{aligned}\displaystyle \textsf{Standard Deviation (Nilo)} & =\sqrt{\dfrac{(5^2+6^2+14^2+15^2)-\dfrac{(5+6+14+15)^2}{4}}{4-1}}\\\\& = \sqrt{\dfrac{482-\dfrac{40^2}{4}}{3}}\\\\& = \sqrt{\dfrac{82}{3}}\\\\& = 5.23\end{aligned}[/tex]

[tex]\begin{aligned}\displaystyle \textsf{Standard Deviation (Lisa)} & =\sqrt{\dfrac{(8^2+9^2+11^2+12^2)-\dfrac{(8+9+11+12)^2}{4}}{4-1}}\\\\& = \sqrt{\dfrac{410-\dfrac{40^2}{4}}{3}}\\\\& = \sqrt{\dfrac{10}{3}}\\\\& = 1.83\end{aligned}[/tex]

Nilo has a mean score of 10 and a standard deviation of 5.23.

Lisa has a mean score of 10 and a standard deviation of 1.83.

The mean scores are the same.

Nilo's standard deviation is higher than Lisa's.  Therefore, Nilo's test scores are more spread out that Lisa's, which means Lisa's test scores are more consistent.

Answer:

3/2 + 3/2 + 3/2 = 3/1

so 3 over 1 times 1 over 2

Answer:

[tex]\sf 2 x-5y +25=0[/tex]

Explanation:

Equation:

[tex]\dashrightarrow \sf y - y_1 =m(x - x_1)[/tex]

[tex]\dashrightarrow \sf y - 1 = \dfrac{2}{5} (x - (-10))[/tex]

[tex]\dashrightarrow \sf y = \dfrac{2}{5} x +4 + 1[/tex]

[tex]\dashrightarrow \sf y = \dfrac{2}{5} x +5[/tex]

[tex]\dashrightarrow \sf 5y = 2 x +25[/tex]

Total courses =5

Each course has 3 options

5 courses has

Hence

Answer: m = 15

Explanation:

Each (1 course) has 3 options

By multiplication,

5 courses shall have: (5 × 3) = 15 choices

By addition,

Sum of choices for 5 courses: (5 + 5 + 5) = 15 choices

Answer:

V = 324 cm³

Step-by-step explanation:

the volume (V) of the pyramid is calculated as

V = [tex]\frac{1}{3}[/tex] Ah ( A is the area of the base and h the height )

here A = 9² = 81 cm² and h = 12 , then

V = [tex]\frac{1}{3}[/tex] × 81 × 12 = 27 × 12 = 324 cm³

Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. The principal at the end of 3 years is $248.

Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,

SI = (P × R × T)/100

where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.

The principal at the end of 3 years is,

Principal after 3 years = P + (P × R × T)

= $200 + ($200 × 0.08 × 3)

= $200 + $48

= $248

Hence, the principal at the end of 3 years is $248.

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Answer:

21.99

Step-by-step explanation:

Answer:

[tex]x = 2~\text{and} ~x = -3[/tex]

Step-by-step explanation:

[tex]~~~~~~f(x) = g(x)\\\\\implies -x +4 =x^2 -2\\\\\implies x^2 -2+x -4=0\\\\\implies x^2 +x -6 = 0\\\\\implies x^2 +3x -2x -6 =0\\\\\implies x(x+3) - 2(x+3) = 0\\\\\implies (x-2)(x+3) = 0\\\\\implies x = 2,~ x = -3[/tex]

Answer:

x = -3 and x = 2

Step-by-step explanation:

Plotting the graphs :

f(x)

⇒ Find two points (preferably the x and y intercepts)

⇒ 0 = -x + 4

⇒ x = 4

⇒ Point 1 : (4, 0)

⇒ f(x) = 0 + 4

⇒ f(x) = 4

⇒ Point 2 : (0, 4)

g(x)

⇒ g(x) = 0 - 2

⇒ g(x) = -2

⇒ Point 1 : (0, -2)

⇒ g(x) = 2² - 2

⇒ g(x) = 2

⇒ Point 2 : (2, 2)

* Graph with both functions is attached below *

=============================================================

Finding the solutions :

⇒ Equate f(x) and g(x)

⇒ -x + 4 = x² - 2

⇒ x² + x - 6 = 0

⇒ x² + 3x - 2x - 6 = 0

⇒ (x + 3)(x - 2) = 0

⇒ x = -3 and x = 2

The length of DE in the triangles is 5.9

The given parameters are:

DB = 6.3

AC = 9.4

AD : DB = 3 : 5

Substitute DB = 6.3 in AD : DB = 3 : 5

AD : 6.3 = 3 : 5

Express as fraction

AD / 6.3 = 3 / 5

Multiply both sides by 6.3

AD = 3.78

The length DE is then calculated using the following ratio:

BD : DE = BA : AC

Where:

BA = BD + AD

This gives

BD : DE = BD + AD : AC

Substitute known values

6.3 : DE = 6.3 + 3.78 : 9.4

Simplify

6.3 : DE = 10.08 : 9.4

Express as fraction

DE/6.3 = 9.4/10.08

Multiply both sides by 6.3

DE = 5.9

Hence, the length of DE is 5.9

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Answer:

1233cm^2

Step-by-step explanation:

a of triangle = 1/2 bh

1/2 x 12 x 9 = 54

108 x 2 = 108

a of regtangle = l x w

25 x 15 = 375

375 x 3 = 1125

total surface area = 1125 + 108 = 1233cm^2

Answer:

-1.5

Step-by-step explanation:

h(-1/2)=2 [tex](\frac{-1}{2})^{2}[/tex] -2

h(-1/2)= [tex]\frac{1}{2} -2\\[/tex]

h(-1/2)=-1.5

Answer:

$42 would be the correct answer.

Polynomial is an expression that consists of indeterminate(variable) and coefficients. The roots of the given polynomial are -2, -1, 0, and 2.

Polynomial is an expression that consists of indeterminate(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponential.

The roots of the given polynomial when plotted on graph are the point at which the graph intersect the x-axis. Therefore, the roots of the given polynomial is,

x = -2, -1, 0, 2

Hence, the roots of the given polynomial are -2, -1, 0, and 2.

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Answer:

It's A. -2, -1, 0, 2

Step-by-step explanation:

[tex]\\ \rm\Rrightarrow 77x+93=360[/tex]

[tex]\\ \rm\Rrightarrow 77x=360-93[/tex]

[tex]\\ \rm\Rrightarrow 77x=367[/tex]

[tex]\\ \rm\Rrightarrow x=4.77[/tex]

[tex]\\ \rm\Rrightarrow x=4.8[/tex]

Aswer with Nina ^-^

Don't report my answer ✅

Answer:

20ft²

Step-by-step explanation:

Answer:

A money market fund is a type of mutual fund that invests in high-quality, short-term debt instruments and cash equivalents.

Answer:

What you need to remember for answering this question is that the probability of any event is the number of sample points in the event divided by the number of sample points in the sample space.

If you have multiple trials and if the sampling is with replacement then, no matter how many samples are drawn, the probabilities remain the same for each trial.

Answer:

D) y = 1x + 2

Step-by-step explanation:

The general structure of an equation in slope-intercept form is:

y = mx + b

In this equation, "m" stands for the slope and "b" stands for the y-intercept. You can substitute the given value of the slope into the equation. Since you are not given "b", you can plug the value of the points into the half-completed equation (with the slope) and isolate "b".

slope = m = 1

y = (1)x + b

(3,5) ------> y = 5 and x = 3

5 = 1(3) + b

5 = 3 + b

2 = b

Final Equation:

y = 1x + 2

Answer:

See below

Step-by-step explanation:

Basically, the associative property states that when an expression has three terms, they can be grouped in any way to solve that expression.

For example, [tex](8*4)*5=8*(4*5)[/tex] if you're doing multiplication, or [tex](8+4)+5=8+(4+5)[/tex], if you're doing addition.

Looking at the problem, what we must do to complete this question is to completely factor the expression that was provided.  The expression that was provided is [tex]15c^2 - 5c[/tex].

The first step that we must do is to take a look at the expression and see what the two pieces of the expression have in common.  We can see that both [tex]15c^2[/tex] and [tex]-5c[/tex] have the number 5 and the variable c associated with them so we can factor out those two.

Factor out 5c

Now we have completely factored out the expression that was provided in the problem statement and we came to final answer of [tex]5c(3c - 1)[/tex].

Answer:

5c(3c - 1)

Step-by-step explanation:

Take out the 5c to factor out completely

Answer:

112.8

Step-by-step explanation:

Hope this help!!

Answer:

4/6

Step-by-step explanation:

if the pas is a dozen brownies

1/2 of a pan is 6 2/3 of 6 would be 4/6

Answer:

20cm²

Step-by-step explanation:

We can solve this by dividing the volume of the cuboid by the height of the cuboid. The formula for the volume of a cuboid is Length * Width * Height, so dividing the volume will leave us with the Length * Width, which is also the area of the shaded face.

100cm³/5cm = 20cm²

The area of the shaded face is 20cm².

We can solve this by dividing the volume of the cuboid by the height of the cuboid. The formula for the volume of a cuboid is Length * Width * Height, so dividing the volume will leave us with the Length * Width, which is also the area of the shaded face.

The area of the shaded face is 20cm².