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3 years ago

A bed is on sale for 25% off of its original price. It originally cost $879.00. How much is the sale price of the bed?

Mathematics

2 answers:

marin [14]3 years ago

6 0

Answer:

224.25

Step-by-step explanation:

think of quarters, one is 25 cents, and it takes four to make a dollar. Then if you have a dollar and you want a quarter of it, you divide the dollar by 4, divide $879.00 by four to get 224.25!

Arturiano [62]3 years ago

5 0

Answer:

$659.25

Step-by-step explanation:

Since its 25 percent off we need to see what it would look as a decimal

1-.25=.75

879times.75= 659.25

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NO LINKS!!! What is the equation of these two graphs?

S_A_V [24]

Answer:

$\textsf{1.} \quad y=-\dfrac{1}{30}x^2+\dfrac{1}{2}x+\dfrac{68}{15}\:\:\textsf{ where}\:\:x \geq \dfrac{15-\sqrt{769}}{2}\\\\\quad \textsf{or} \quad y=2\sqrt{x+5}$

$\textsf{2.} \quad y=-|x+1|+5$

Step-by-step explanation:

<h3>Question 1</h3>

Method 1 - modelling as a quadratic with restricted domain

Assuming that the points given on the graph are points that the curve passes through, the curve can be modeled as a quadratic with a limited domain. Please note that as the x-intercept has not been defined on the graph, I am not including this in this first method.

Standard form of a quadratic equation:

$y=ax^2+bx+c$

Given points:

(-4, 2)
(-1, 4)
(4, 6)

Substitute the given points into the equation to create 3 equations:

Equation 1 (-4, 2)

$\implies a(-4)^2+b(-4)+c=2$

$\implies 16a-4b+c=2$

Equation 2 (-1, 4)

$\implies a(-1)^2+b(-1)+c=4$

$\implies a-b+c=4$

Equation 3 (4, 6)

$\implies a(4)^2+b(4)+c=6$

$\implies 16a+4b+c=6$

Subtract Equation 1 from Equation 3 to eliminate variables a and c:

$\implies (16a+4b+c)-(16a-4b+c)=6-2$

$\implies 8b=4$

$\implies b=\dfrac{4}{8}$

$\implies b=\dfrac{1}{2}$

Subtract Equation 2 from Equation 3 to eliminate variable c:

$\implies (16a+4b+c)-(a-b+c)=6-4$

$\implies 15a+5b=2$

$\implies 15a=2-5b$

$\implies a=\dfrac{2-5b}{15}$

Substitute found value of b into the expression for a and solve for a:

$\implies a=\dfrac{2-5(\frac{1}{2})}{15}$

$\implies a=-\dfrac{1}{30}$

Substitute found values of a and b into Equation 2 and solve for c:

$\implies a-b+c=4$

$\implies -\dfrac{1}{30}-\dfrac{1}{2}+c=4$

$\implies c=\dfrac{68}{15}$

Therefore, the equation of the graph is:

$y=-\dfrac{1}{30}x^2+\dfrac{1}{2}x+\dfrac{68}{15}$

$\textsf{with the restricted domain}: \quad x \geq \dfrac{15-\sqrt{769}}{2}$

Method 2 - modelling as a square root function

Assuming that the points given on the graph are points that the curve passes through, and the x-intercept should be included, we can model this curve as a square root function.

Given points:

(-4, 2)
(-1, 4)
(4, 6)
(0, -5)

The parent function is:

$y=\sqrt{x}$

Translated 5 units left so that the x-intercept is (0, -5):

$\implies y=\sqrt{x+5}$

The curve is stretched vertically, so:

$\implies y=a\sqrt{x+5} \quad \textsf{(where a is some constant)}$

To find a, substitute the coordinates of the given points:

$\implies a\sqrt{-4+5}=2$

$\implies a=2$

$\implies a\sqrt{-1+5}=4$

$\implies 2a=4$

$\implies a=2$

$\implies a\sqrt{4+5}=6$

$\implies 3a=6$

$\implies a=2$

As the value of a is the same for all points, the equation of the line is:

$y=2\sqrt{x+5}$

<h3>Question 2</h3>

Vertex form of an absolute value function

$f(x)=a|x-h|+k$

where:

(h, k) is the vertex
a is some constant

From inspection of the given graph:

vertex = (-1, 5)
point on graph = (0, 4)

Substitute the given values into the function and solve for a:

$\implies a|0-(-1)|+5=4$

$\implies a+5=4$

$\implies a=-1$

Substituting the given vertex and the found value of a into the function, the equation of the graph is:

$y=-|x+1|+5$

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1 year ago

Compare and contrast converting customary units of length and converting metric units of length . PLEASE HELP THIS IS DUE TOMORR

Stolb23 [73]

Metres are the standard unit of length.
1000mm=1m
100cm=1m
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3 0

3 years ago

Write the equation of the line that passes through the points (8, 14) and (-2,-16) in slope-intercept form.

Schach [20]

Answer:

y = 3x - 10

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (8, 14) and (x₂, y₂ ) = (- 2, - 16)

m = $\frac{-16-14}{-2-8}$ = $\frac{-30}{-10}$ = 3 , then

y = 3x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (8, 14 ) , then

14 = 24 + c ⇒ c = 14 - 24 = - 10

y = 3x - 10 ← equation of line

7 0

3 years ago

Today's cafeteria specials at a high school in Westford are a deluxe turkey sandwich and a chef salad. During early lunch, the c

OLEGan [10]

Answer:

dont know sorry

Step-by-step explanation:

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3 years ago

In a certain lake, trout average 12 in. in length with standard deviation 2.75 in. and the bass average 4 lb. in weight with sta

NISA [10]

Answer:

The bass fish was the better catch

Step-by-step explanation:

From the question we are told that

The population mean for trout is $\mu_1 = 12 \ in$

The standard deviation is $\sigma_1 = 2.75 \ in$

The population mean for base is $\mu _2 = 4 \ lb$

The standard deviation is $\sigma_2 = 0.8 \ lb$

The number of trout caught $x_1 = 18$

The number of bass caught $x_2 = 6$

Generally z-value(standardized value ) for the of number trout caught is mathematically represented as

$z_1 = \frac{x_1 - \mu_1}{\sigma_1 }$

substituting value

$z_1 = \frac{18 - 12}{2.75 }$

$z_1 = 2.18$

Generally z-value(standardized value ) for the of number bass caught is mathematically represented as

$z_2 = \frac{x_2 - \mu_2}{\sigma_2 }$

substituting value

$z_2 = \frac{6 - 4}{0.8 }$

$z_2 = 2.5$

From our calculation we see that $z_2 > z_1$

The fish that was the better catch is the bass fish

3 0

3 years ago