Marylou buys a package of 50 jewels to decorate 4 different pair of jeans.She uses the same number of jewels on each pair of jeans.How many jewels will she use for each pair of jeans?

Answers

Answer 1

Answer:

She can use 12 jewels for each pair of jeans. In fact, using 12 jewels per jeans implies that she will use $12 \cdot 4 = 48$ jewels. The two remaining jewels can't be used on any pair of jeans, otherwise she wouldn't use the same number of jewels for each jeans.

This derives from the fact that, if you divide 50 by 4, you get a result of 12 with a remainder of 2.

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What is the answer when you get the same number on bboth sides of a equation?

What is the distance between the points (3,7) and (15,16)?

Answers

distance between the point formula is
d= $√((y2-y1)^2+(x2-x1)^2)$
where (x1,y1) and (x2,y2) are coordinates points

here points are given (3,7) (15,16)

put those points into distance formula
d= now u can do this

Calculate cos theta to two decimal places

Answers

Answer:

B. 0.72

Step-by-step explanation:

In order to find the answer we need to use the following formula:

$a^2=b^2+c^2-2bc*cos(\theta)$ where:

a, b, c are the length of the sides and $\theta$ the angle, so:

$7^2=10^2+8^2-(2*10*8)*cos(\theta)$

$49=164-(160)*cos(\theta)$

$cos(\theta)=0.71875$

In conclusion, $cos(\theta)=0.72$ , so the answer is B.

Help me im just too lazy to figure it out :)

Answers

Answer:

m=-16

Step-by-step explanation:

To solve the equation, we want to find out what m is. In order to do this, we have to get m by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.

-35=m-19

19 is being subtract from m (-19). The opposite of subtraction is addition. Add 19 to both sides (+19) The -19 and +19 equal 0, and therefore cancel each other out.

-35+19=m-19+19

-35+19=m

-16=m

Let's check our solution. Plug -16 back in for m in the original equation.

-35=m-19

-35=-16-19

-35=-35

Both sides of the equation are the same, so we know that m is equal to -16.

The top and bottom margins of a poster are each 15 cm and the side margins are each 10 cm. If the area of printed material on the poster is fixed at 2400 cm2, find the dimensions of the poster with the smallest area.--------- cm (width)--------- cm (height)

Answers

Answer:

Step-by-step explanation:

let the sides be x and y

x y=2400

$y=(2400)/(x)\nnew~ dimensions ~are ~x+30~and~y+20\narea~A=(x+30)(y+20)\n=xy+20x+30y+600\n=2400+600+20x+30*(2400)/(x)\n=3000+20x+(72000)/(x)\n(dA)/(dx)=20-(72000)/(x^2)\n(dA)/(dx)=0~gives\n20 x^2=72000\nx^2=3600\nx=√(3600) =60\n(d^2A)/(dx^2)=(144000)/(x^3)>0~at ~x=60\ny=(2400)/(60)=40\n$

so A is minimum when x=60

y=40 cm

so dimensions are 60+30=90 cm

and 40+20=60 cm

Final answer:

The dimensions of the poster that provide the smallest total area, while maintaining a fixed printed area of 2400 cm², are 80 cm in width and 70 cm in height. This is obtained by applying calculus to optimize the area function of the poster.

Explanation:

The subject of this question is related to optimizing the area of a rectangular poster by adjusting its dimensions. Given that the area of printed material is fixed at 2400 cm², let's denote the width of the printed area as x (in cm) and so its height will be 2400/x (in cm).

Therefore, the total area of the poster, including margins, would be $(x+20)(2400/x + 30).$ We want to minimize this area. This is a calculus problem - take the derivative of the area with respect to x, set it equal to zero and solve for x. You'll obtain two possible dimensions for the width of the printed area: 40 cm and 60 cm. By testing these in the second derivative, you'll find that a width of 60 cm gives the minimum area. Therefore, the dimensions of the poster that gives the smallest total area are 60+20=80 cm (width) and $2400/60+30=70$ cm (height).