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Vanyuwa [196]
3 years ago
13

5. At Michael's store, a paint set is on sale for $39.99. The original price was

Mathematics
2 answers:
rusak2 [61]3 years ago
6 0

around 50%

Step-by-step explanation:

because 30 of half of 60

Artyom0805 [142]3 years ago
3 0

Answer:

$ 26.66

Step-by-step explanation:

Minus the orignal price and the sale price and then you will get the answer

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Cheryl is moving to a new house. Her old house is 3 kilometers and 457meters from her new house. How many meters is her old hous
MrRissso [65]

Answer:

Her old house is 3000m+457m = 3457m from her new house.

Step-by-step explanation:

Conversion of units problems can always be modeled as a rule of three problem.

Rule of three problem:

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too. In this case, the rule of three is a cross multiplication

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease. In this case, the rule of three is a line multiplication.

In the case of a conversion of units problem, the measures are:

- the value in one unit

- the value in another unit

As the value of the first unit increases, so will the value of the second unit. It means that in a conversion of units problem, we will always have a direct rule of three.

The problem states that Cheryl's new house  is 3 kilometers and 457meters from her old house. The problem wants to know this distance purely in meters, so we have to convert 3km to meters. 1km = 1000m, so:

1km - 1000m

3km - xm

x = 1000*3

x = 3000m

Her old house is 3000m+457m = 3457m from her new house.

5 0
3 years ago
How do the constant of proportionality and slope relate to the unit rate
Pepsi [2]

Answer:

When a relationship is proportional, all y over x ratios simplify to the slope of the line which is the constant of proportionality or the unit rate, with one as a denominator. Example: Consider the equation y = 60x. The slope is 60. The rate of change is 60 units for every one unit.

Step-by-step explanation:

7 0
3 years ago
Trig proofs with Pythagorean Identities.
lorasvet [3.4K]

To prove:

$\frac{1}{1-\cos x}-\frac{\cos x}{1+\cos x}=2 \cot ^{2} x+1

Solution:

$LHS = \frac{1}{1-\cos x}-\frac{\cos x}{1+\cos x}

Multiply first term by \frac{1+cos x}{1+cos x} and second term by \frac{1-cos x}{1-cos x}.

        $= \frac{1(1+\cos x)}{(1-\cos x)(1+\cos x)}-\frac{\cos x(1-\cos x)}{(1+\cos x)(1-\cos x)}

Using the identity: (a-b)(a+b)=(a^2-b^2)

        $= \frac{1+\cos x}{(1^2-\cos^2 x)}-\frac{\cos x-\cos^2 x}{(1^2-\cos^2 x)}

Denominators are same, you can subtract the fractions.

       $= \frac{1+\cos x-\cos x+\cos^2 x}{(1^2-\cos^2 x)}

Using the identity: 1-\cos ^{2}(x)=\sin ^{2}(x)

       $= \frac{1+\cos^2 x}{\sin^2x}

Using the identity: 1=\cos ^{2}(x)+\sin ^{2}(x)

       $=\frac{\cos ^{2}x+\cos ^{2}x+\sin ^{2}x}{\sin ^{2}x}

       $=\frac{\sin ^{2}x+2 \cos ^{2}x}{\sin ^{2}x} ------------ (1)

RHS=2 \cot ^{2} x+1

Using the identity: \cot (x)=\frac{\cos (x)}{\sin (x)}

        $=1+2\left(\frac{\cos x}{\sin x}\right)^{2}

       $=1+2\frac{\cos^{2} x}{\sin^{2} x}

       $=\frac{\sin^2 x + 2\cos^{2} x}{\sin^2 x} ------------ (2)

Equation (1) = Equation (2)

LHS = RHS

$\frac{1}{1-\cos x}-\frac{\cos x}{1+\cos x}=2 \cot ^{2} x+1

Hence proved.

5 0
3 years ago
A city pool has 3 wading pools. Each pool is in the shape of a parallelogram with a
Vikki [24]

Answer:

i think it's 13.44

Step-by-step explanation:

im not really sure, but let me know if im wright pls!!

hope this helped!!

6 0
2 years ago
Solve 5x^2 = -30x - 65
dalvyx [7]

Answer:

+65=-30x-5x^2

+65=-35x

=-1.9

3 0
3 years ago
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