MATHEMATICS HIGH SCHOOL

The Length of a standard jewel case is 7cm more than its width. The area of the rectangular top of the case is 408cm. Find the length and width of the jewel Case

Answers

Answer 1

Answer:

The length of the case is 24 cm and its width is 17cm.

Step-by-step explanation:

The Length of a standard jewel case is 7cm more than its width.

Let the length be represented by L and the width be represented by W, this means that:

L = 7 + W

The area of the rectangular top of the case is 408cm². The area od a rectangle is given as:

A = L * W

Since L = 7 + W:

A = (7 + W) * W = 7W + W²

The area is 408 cm², hence:

408 = 7W + W²

Solving this as a quadratic equation:

=> W² + 7W - 408 = 0

W² + 24W - 17W - 408 = 0

W(W + 24) - 17(W + 24) = 0

(W - 17) (W + 24) = 0

=> W = 17cm or -24 cm

Since width cannot be negative, the width of the case is 17 cm.

Hence, the length, L, is:

L = 7 + 17 = 24cm.

The length of the case is 24 cm and its width is 17cm.

Related Questions

Triangle inequality theorem-are the lengths 7, 4, and 2 of a triangle possible?
Which expression gives the x-coordinate of the solution of the system?
20 hundreds equal how many thousands
A group of students is taking a CPR course. The total cost for the course is $275. The room in which the course will be held can hold a maximum of 25 people, including the instructor. What is the minimum number of students needed to take the course so that the cost per student will be less than $15? A. 11 B. 17 C. 18 D. 19
The sum of the first 65 odd, positive integers is?I know the answer is 4225, but I don't know how to solve.

Write an equation in point-slope form for the line through the given point with the given slope(8,-3);m= -1/4

Answers

Answer: y+3= -1/4(x-8)

Step-by-step explanation: so if y-y1=m(x-x1) and y1= -3 and x1=8 and m=(-1/4) u just plug in those number to the equation

To get to work, matt walks 0.75 miles from his house to the bus stop and rides the bus 3.8 miles to his office. if he walks at a pace of 3.6 miles per hour and the bus drives at an average speed of 15 miles per hour, how long is his commute?

Answers

4.16666667 is what i got

300 reduced by twice my age is 192

Answers

If 300 reduced by twice your age is equal to 192, your age (represented by x) would be 54 years old.

To solve the given equation "300 reduced by twice my age is 192," we can represent the equation using algebraic notation.

Let's assume "x" represents your age. The equation can be written as:

300 - 2x = 192

Now, let's solve for x:

300 - 192 = 2x

108 = 2x

54 = x

Therefore, if 300 reduced by twice your age is equal to 192, your age (represented by x) would be 54 years old.

To know more about algebraic notation:

brainly.com/question/29047493

#SPJ2

well u divide 300 by 2 which is 150 so u will be 150

For a standard normal distribution, which of the following expressions must always be equal to 1?A) P(z≤-a)-P(-a≤z≤a)+P(z≥a)
B) P(z≤-a)-P(-a≤z≤a)+P(z≥a)
C) P(z≤-a)+P(-a≤z≤a)-P(z≥a)
D) P(z≤-a)+P(-a≤z≤a)+P(Z≥a)

Answers

P(z ≤ -a) + P(-a ≤ z ≤ a) + P(z ≥ a) = 1 - P(z ≤ a) + [P(z ≤ a) - P(z ≤ -a)] + 1 - P(z ≤ a) = 2 - 2P(z ≤ a) + P(z ≤ a) - [1 - P(z ≤ a)] = 2 - P(z ≤ a) - 1 + P(z ≤ a) = 1

Therefore, option D is the correct answer.

Answer:

D. $P(z\le -a)+P(-a\le z\le a)+P(z\ge a)$

Step-by-step explanation:

Properties of normal distribution-

The normal curve is symmetrical about the mean (μ).
The mean is at the middle of the graph and it divides the area into two equal halves.
The total area under the curve is equal to 1.

The total area under the curve can be divided into parts like,

area below $-a$ , i.e $z\le -a$ ,
area between $-a$ to $a$ , i.e $-a\le z\le a$
area above $a$ , i.e $z\ge a$

Therefore, $P(z\le -a)+P(-a\le z\le a)+P(z\ge a)=1$

Brandon bought snacks for his team's practice. He bought a bag of popcorn for $2.11 and a 6-pack of juice bottles. The total cost before tax was $11.41. Write and solve an equation which can be used to determine x, how much each bottle of juice costs?