MATHEMATICS COLLEGE

A hole is punched in a piece of metal to make a part for a machine. What is the area of the metal part, or the shaded region shown?

Answers

Answer 1

Answer:

The area of the metal part, or the shaded region shown is 10x + 45.

calculation:

$= (x+ 7)^2 - (x-2)^2\n\n= (x^2 + 14x + 49) - (x^2 - 4x + 4)\n\n= (14 - 4)x + (49 - 4)$

= 10x + 45

Learn more about the area here; brainly.com/question/17064026

Answer 2

Answer:

Answer:

The area of the metal part or shaded area is S=10x+45.

Step-by-step explanation:

The shaded area can be calculated substracting the little square area (the hole) from the big square area (the original metal part).

This is:

$S=S_(original)-S_(hole)=(x+7)^2-(x-2)^2\n\nS=(x^2+14x+49)-(x^2-4x+4)\n\nS=(14-4)x+(49-4)\n\nS=10x+45$

The area of the metal part or shaded area is S=10x+45.

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Daryl invested $2,200 for 3 years. He received interest of $264. What was the interest rate?

Answers

Answer:

Step-by-step explanation:

264 interest/3 years=88 interest/year

principal x interest rate =interest/year

2200 x interest rate =88

interest rate =88/2200

interest rate =.04 or 4%

HELP!How do you derive the equation of a circle?
How do you identify the center and radius of a circle?
How do you define the radian measure of an angle?
How are arc length and area of a sector related to proportionality?

Answers

Answer:

How do you derive the equation of a circle?

you can reverse the circle formula

How do you identify the center and radius of a circle?

You can identify the center because it is the middle of the circle and the radius can be draw from the center to the round part.

How do you define the radian measure of an angle?

it is the ratio of the length of the arc the angle forms÷the radius of the circle

How are arc length and area of a sector related to proportionality?

sector x radian

area = (r^2 x)/2

arc length = r x

they are not propotional

because Area / arc length = r/2 , (it's not a constant)

High Hopes

Barrii

A 1-kg model airplane has 12.5 joules of kinetic energy and 98 joules of gravitational potential energy. What is its speed? What is its height?

Answers

The formula for the kinetic energy is:

Ke = 0.5mv^2

Where ke is the kinetic enrgy

M is the mass

V is the velocity

Ke = 0.5mv^2

12.5 = 0.5(1) v^2

Solve for v

V = 5 m/s

Potential energy, pe = mgh

Where m is mass

G is accelearation due to gravity 9.8 m/s2

H is the height

98 = (1)(9.8) h

H = 10 m

A cocktail nut mix should have the following minimum requirements in a can of 1 pound being sold at $3.99 a can at retail stores. The following information is given: Nut Type Minimum Amt Maximum Amt Cost per pound Almond 10% 100% $2.75 Peanut 0% 50% $0.55 Walnut 20% 100% $1.70 Cashew 0% 40% $1.20 The can costs $0.10. Find the proportion of these nuts by weight to maximize the profit of the nut manufacturer. Use those proportions to select the answer closest to the profit that can be made per can if it is sold to the retail store at $3.00 a can. Group of answer choices $1.65 $1.35 $2.76 $1.77

Answers

By maximizing the amount of cheaper nuts and minimizing the amount of expensive nuts, the manufacturer should use a mix of 50% peanuts, 40% cashews, and 10% almonds. The profit per can will be $1.87, closest to $1.77 out of the given choices.

This problem involves linear programming, and it is a problem of maximizing profit under given constraints. The proportions of nuts can be found using optimization techniques that are usually covered in calculus or advanced algebra classes, but a quick answer can be given here by considering the cost of each type of nut.

The manufacturer should maximize the amount of the cheapest nuts in the mix to increase the profit. So, they should fill the can with 50% peanuts ($0.55 per lb), 40% cashews ($1.20 per lb), and 10% almonds ($2.75 per lb) to meet the minimum requirement for almonds and maximum constraints for peanuts and cashews. The average cost of this mix per pound will be (0.5x0.55)+(0.4x1.2)+(0.1x2.75) which equals $1.025 per lb. If the can costs $0.10, the total manufacturing cost per can becomes $1.125.

If the nut mix is sold at $3.00, the profit per can will be $3.00 - $1.125 which equals $1.87. This is closer to $1.77. Therefore, the answer should be $1.77 if we consider rounding to the closest number. Note that we can't fill a full can because the total proportion is already 100%, but we have ignored the volume taken up by the can itself in this calculation.

Learn more about Linear Programming here:

brainly.com/question/24361247

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Answer:

Nut

Step-by-step explanation:

Please help ASAP in math I have a picture

Answers

Answer:

x = 25

Step-by-step explanation:

Those 2 angles together form a straight line which is equal to 180°. So you can set up an equation:

3x + 18 = 93

-18 -18

3x = 75

Divide both sides by 3

x = 25

Using the quadratic formula to solve 5x = 6x2 – 3, what are the values of x? StartFraction 5 plus-or-minus 3 StartRoot 11 EndRoot Over 12 EndFraction StartFraction 5 plus-or-minus StartRoot 97 EndRoot Over 12 EndFraction StartFraction 5 plus-or-minus StartRoot 47 EndRoot Over 12 EndFraction StartFraction negative 5 plus-or-minus StartRoot 97 EndRoot Over 12 EndFraction

Answers

The required value of the quadratic function which is determined by the using quadratic formula would be $x = (5\pm√(97))/(12)$ which is the correct answer would be an option (B).