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Illusion [34]
3 years ago
14

Mary and roberto bought identical backpacks at different stores. marys backpacks originally cost $65 and was discounted 25%. rob

ertos backpack orignally cost $75 and was on sale for 30% off the original price.which backpack was a better buy?
Mathematics
1 answer:
garri49 [273]3 years ago
6 0
Mary's backpack: 25% of 65 = 0.25 * 65 = 16.25; 65 - 16.25 = $48.75
Roberto's backpack: 30% of 75 = 0.3 * 75 = 22.5; 75 - 22.5 = $52.5

Mary's backpack was a better buy because it was cheaper. 
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Find the constant difference for a hyperbola with foci (-3.5, 0) and (3.5, 0) and a point on the hyperbola (3. 5, 24).
Solnce55 [7]

Answer:

2a=1

Step-by-step explanation:

The constant difference for a hyperbola \dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1 is  2a.

1. Since hyperbola has foci (-3.5, 0) and (3.5, 0), then c=3.5. Note that c=\sqrt{a^2+b^2}, then

\sqrt{a^2+b^2}=3.5\Rightarrow a^2+b^2=3.5^2.

2. Since point (3.5,24) lies on the hyperbola, then

\dfrac{3.5^2}{a^2}-\dfrac{24^2}{b^2}=1.

3. Solve the system of two equations:

\left\{\begin{array}{l}a^2+b^2=3.5^2\\\dfrac{3.5^2}{a^2}-\dfrac{24^2}{b^2}=1\end{array}\right.

From the 1st equation,

b^2=3.5^2-a^2,

then

\dfrac{3.5^2}{a^2}-\dfrac{24^2}{3.5^2-a^2}=1,\\ \\\dfrac{3.5^2(3.5^2-a^2)-24^2a^2}{a^2(3.5^2-a^2)}=1,\\ \\3.5^4-3.5^2a^2-24^2a^2=3.5^2a^2-a^4,\\ \\a^4-a^2(2\cdot 3.5^2+24^2)+3.5^4=0,\\ \\a^4-600.5a^2+150.0625=0,\\ \\D=(-600.5)^2-4\cdot 150.0625=360000,\\ \\a^2_{1,2}=\dfrac{600.5\pm 600}{2}=\dfrac{1}{4},600\dfrac{1}{4}.

For a^2=\dfrac{1}{4},\ b^2=3.5^2-0.25=12.

For a^2=600\dfrac{1}{4},\ b^2=3.5^2-600.25 this is impossible, then a^2=600\dfrac{1}{4} is extra solution.

Hence, a=\dfrac{1}{2} and 2a=1.

5 0
3 years ago
The Elliot’s have budgeted $2000 to install new wood floors in their home. The materials cost them $1055. If the installer charg
Anna35 [415]

Answer:

27 hours

Step-by-step explanation:

2,000-1,055=945

945/35=27

27 hours is the most the installer can work before going over Elliot's budget hope this helps :D


4 0
3 years ago
Read 2 more answers
(3x^2-4+5)(x2-3x+2)? Multiply
SVETLANKA909090 [29]

Answer:

=(3x^2+1)(-x+2)

Step-by-step explanation:

(3x^2-4+5)(x*2-3x+2)=(3x^2+1)(-x+2)

3 0
3 years ago
The temperature outside dropped 13 degrees Fahrenheit in 7 hours. The final temperature was -2 degrees Fahrenheit. What was the
inysia [295]

Answer:

Step-by-step explanation:

11 degrees. 13 + -2 = 11. The starting temperature was 11 degrees farenheit

4 0
3 years ago
For the figures shown, FHJL ~ NPRS. The scale factor applied to FHJL to create NPRS is 4 to 3.
GrogVix [38]

Remark

For every 3 units for NP will be 4 units. You can set up a proportion.

\dfrac{3}{4} = \dfrac{45}{NP}\text{Cross Multiply}

3*NP = 4*45

3*NP = 180 Divide by 3

NP = 180/3

NP = 60

Answer C

7 0
3 years ago
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