MATHEMATICS MIDDLE SCHOOL

the perimeter of a rectangle is 32 centimeters. The length is 1 cm more than twice the width. Find the dimensions of the rectangle.

Answers

Answer 1

Answer:

Answer: length = 11cm , width = 5cm

Step-by-step explanation:

The formula for calculating the perimeter of a rectangle is given by :

P = 2 ( L + w )

The length is 1 cm more than twice the width implies:

L = 1 + 2w

substituting into the formula , we have

32 = 2 ( 1 + 2w + w )

32 = 2 ( 1 + 3w)

32 = 2 + 6w

32 - 2 = 6w

30 = 6w

Therefore :

w = 5

then

L = 1 + 2w

L = 1 + 2 ( 5 )

L = 1 + 10

L = 11

Therefore , the length is 11 cm and the width is 5cm

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324,087rounded to the nearest thousand
Use signed numbers to solve. A helicopter descended 1200 feet, rose 800 feet, and then descended 450 feet. What was the net gain or loss in altitude? A. lost 2450 ft B. lost 850 ft C. gained 850 ft D. gained 2450 ft
If 28% of a sum is 100.80 what is the sum
Which is bigger 4/5 or 9/10

A lawyer to charge her clients $310 per hour. Her new rate is $260 per hour. What was the percent of decrease in the billing rate?

Answers

Answer:

119.23%

Step-by-step explanation:

310/260=1.192307692307692 ---> 1.19.23%

Find the points where the line y = x - 1 intersects the circle x2 + y2 = 13

Answers

Answer:

$\large \boxed{(-2,-3) \text{ and } (3, 2)}$

Step-by-step explanation:

1. Solve the equations for x

$\begin{array}{lrcll}(1) & y & = & x - 1 & \n(2) & x^(2) + y^(2) &= &13& \n& x^(2) + (x - 1)^(2) &= & 13& \text{Substituted (1) into (2)}\n& x^(2) + x^(2) -2x +1 & = & 13 & \text{Squared (x - 1)} \n&2x^(2) -2x +1 & = & 13 & \text{Combined like terms} \n\end{array}\n$

$\begin{array}{lrcll}&2x^(2) -2x - 12 & = & 0 & \text{Subtracted 13 from each side}\n&x^(2) - x - 6 & = & 0 & \text{Divided each side by 2}\n& (x - 3)(x + 2) & = & 0 & \text{Factored the left-hand side} \n& x - 3 = 0 & \text{or} & x + 2 = 0 & \text{Applied zero product rule} \n& \mathbf{x = 3} & \text{or} & \mathbf{x = -2} & \text{Solved each equation separately} \n\end{array}$

2. Calculate the corresponding values of y

Insert the values into equation (1)

(a) x = 3

y = 3 - 1 = 2

One point of intersection is (3, 2).

(b) x = -2

y = -2 - 1 = -3

The second point of intersection is (-2, -3).

$\text{The line intersects the circle at $\large \boxed{\mathbf{(-2,-3)} \text{ and } \mathbf{(3, 2)}}$}$

The diagram shows the intersection of the two graphs.

Answer:

(-2,-3) and (3,2)

Step-by-step explanation:

sub in x-1 into y

x^2 + (x-1)^2 = 13

x^2 + (x-1)(x-1)=13

x^2 + x^2 -2x +1 = 13

2x^2 -2x-12=0

solve for x by factoring (quadratic formula, product sum etc..)

x= -2 and 3

plug in those values into y=x-1 and solve for y

What is (1/3b)^3 simplified?

Answers

The answer is 1 2/7b.
1/3b multiplied by itself 3 times is 1 2/7b.

Find the perimeter of the triangle 40 9

Answers

To solve for the perimeter of the triangle, first use Pythagorean theorem to solve for the hypotenuse and then add all of the sides together.

40 ^2 + 9^2
1600 + 81
1681 = C^2
41 = C

P = a + b + c
P = 40 + 9 + 41
P = 81 + 9
P = 90 units.

Suppose you draw a line from the center of a clock face to the number 12. When the minute hand gets to 3 on the clock face, the line and minute hand form a 90 degree angle. What angle does the line and the minute hand make when the minute hand is on 2?

Answers

The line and the minute hand make when the minute hand is on 2 make angle 60 degrees.

What is an angle?

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Given:

line is drawn from the center of the clock and face to number 12 on the clock.

When the minute hand gets to 3 on the clock face, the line and minute hand form 90 degree.

So, 1 on the clock face represent

=90/3

= 30 degrees.

If minute hand is on 2 then the angle between the line and the minute hand be

= 30*2

= 60 degrees.

Hence, the line and the minute hand make when the minute hand is on 2 make angle 60 degrees.

Learn more about this concept here:

brainly.com/question/23634272

#SPJ2

Just divide 90 by three so whe it hits 3 its 90 then 2 is 60 degrees and the one is 30 degrees

Mike works in a toy store. One week, he worked 38 hours and made $220. The next week, he received a raise, so when he worked 30 hours he made $180. How much was his raise (to the nearest cent)?

Answers

Answer:

$0.21

Step-by-step explanation:

Let x be the amount of money earned per hour before raise and y be amount of money earned per hour after raise.

We have been given that before raise he worked 38 hours and earned $220. We can represent this information as: $38x=220$

We are also told that the next week, he received a raise. After raise he worked 30 hours and made $180. We can represent this information as: $30y=180$ .