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3 years ago

A rectangular patio is 11 feet by 13 feet. What is the length of the diagonal of the patio?

Mathematics

1 answer:

Andrei [34K]3 years ago

6 0

Answer:

Step-by-step explanation:

use pythagoras

diagonal = $\sqrt{11^{2} + 13^{2} } \\$

= $\sqrt{290}$ feet or 17.03 feet

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Ben bought 8 fairy sodas and 5 fairy hotdogs and spent $30.75 fairy dollars. Holly bought 7 fairy sodas and 6 fairy hotdogs and

wlad13 [49]

Set up the system of equations:

$8x + 5y = 30.75$
$7x + 6y = 33$

We'll use elimination to solve this system of equations.

Take the coefficients for y in both problems. Multiply one of them by -1:

$5 \times -1 = -5$

Since this coefficient is taken from the first problem, we'll multiply the entire second problem by this negative coefficient:

$(7x + 6y = 33) \times -5 = -35x - 30y = -165$

Take the coefficient for y in the second problem and multiply the entire first problem by that coefficient:

$(8x + 5y = 30.75) \times 6 = 48x + 30y = 184.50$

Your system should now look like this:

$48x + 30y = 184.50$
$-35x - 30y = -165$

Combine these two equations to cancel out y:

$13x = 19.50$

Divide both sides by 5 to get x by itself:

$x = 1.5$

A fairy soda costs $1.50.

Because we know the value of one of the variables, we can plug it into one of the equations:

$8(1.5) + 5y = 30.75$
$12 + 5y = 30.75$

Subtract 12 from both sides:

$5y = 18.75$

Divide both sides by 5 to get y by itself:

$y = 3.75$

A fairy hotdog costs $3.75.

6 0

3 years ago

Read 2 more answers

Help help please please please

Katarina [22]

Answer:

[?] = 3

Step-by-step explanation:

8 0

3 years ago

What is a solution to the system of equations that includes quadratic function f(x) and linear function g(x)? f(x) = 2x2 + x + 4

olga_2 [115]

The solution to the system of equations that includes quadratic function f(x) and linear function g(x) is

$(\sqrt{2},\sqrt{-2} )$ and $((7+\sqrt{2)} ,(7+\sqrt{-2}))$

We have given that,

f(x) = 2x^2 + x + 4

x g(x)

-2 1

-1 3

0 5

1 7

2 9

<h3>What is a polynomial function?</h3>

A polynomial function is a relation where a dependent variable is equal to a polynomial expression.

A polynomial expression is an expression including numbers and variables, where variables are raised to non-negative powers.

The general form of a polynomial expression is:

a₀ + a₁x + a₂x² + a₃x³ + ... + anxⁿ.

The highest power to a variable is the degree of the polynomial expression. When degree = 2, the function is a quadratic function.

When degree = 1, the function is a linear function.

<h3>How do we solve the given question?</h3>

The quadratic function is given to us:f(x) = 2x^2 + x + 4.

We need to determine the linear equation g(x).

Since it's a linear equation we use the two-point method to determine the equation.

<h3>What is the two-point?</h3>

y-y₁ = ((y₂-y₁)/(x₂-x₁))*(x-x₁)

We take the points g(-2) =1, g(-1) = 3

g(x) - g(1) = ((g(-2)-g(-1))/(-2+1))*(x-1)or,

g(x) - 1 = ((-2-(-1))/(-2+1))*(x-1)or, g(x) - 1 = -1(-x+1)or,

g(x) = x - 1 + 1 = x

∴ g(x) = x , is the linear function g(x)

We are asked to find the solution to the system of equations f(x) and g(x).To find the solution we need to check what is the common solution to both f(x) and g(x).

For that, we equate f(x) and g(x).2x^2 + x + 4 = x or, 2x² - x +x- 4 = 0or, 2x^2 - 4 = 02(x^2-2)=0x^2-2=0 $x^2-\sqrt{2}=0$ $(x-\sqrt{2}) (x+\sqrt{2})=0$ $(x-\sqrt{2})=0 \\x=\sqrt{2} or x=-\sqrt{2}$ g(-1) = 3(from the table) $g(\sqrt{2})=\sqrt{2} \ and \ g(\sqrt{-2}) =-\sqrt{2}$ $f(\sqrt{2}) = 2(\sqrt{2} )^2 + (\sqrt{2} ) + 3\\=2(2)+\sqrt{2} +3\\=7+\sqrt{2}$ $g(-\sqrt{2} )= 2(\sqrt{-2} )^2 + (\sqrt{-2} ) + 3\\=2(2)+\sqrt{-2} +3\\=7+\sqrt{-2}$

The solution to the system of equations that includes quadratic function f(x) and linear function g(x) is $(\sqrt{2},\sqrt{-2} )$ and $((7+\sqrt{2)} ,(7+\sqrt{-2}))$

Learn more about linear and quadratic equations at

brainly.com/question/14075672

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5 0

2 years ago

Please help me how to solve steps by steps and answer.

ivolga24 [154]

84,000/15 = 5600

2 x 5600 = 11,200

The first person will get $11,200

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3 years ago

Poem about relation in math

ExtremeBDS [4]

Answer:

in math what type of poem???

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3 years ago