When measuring the length a and the width b of a rectangle, it was found that 5.4< a< 5.5 and 3.6< b< 3.7 (in centimeters). Find the possible values of: the perimeter of the rectangle

Answers

Answer 1

Answer:

The possible values of the perimeter of the rectangle is between 18 and

18.4 cm ⇒ [18 < perimeter of rectangle < 18.4] cm

Step-by-step explanation:

* Lets explain how to solve the problem

- The perimeter of any quadrilateral is the sum of the length of its

  four sides

- The rectangle is a quadrilateral with each two opposite sides are

  equal in lengths, then its perimeter = 2l + 2w, where l, w are its

  length and width

∵ The the length of the rectangle is a

∵ 5.4 < a < 5.5 cm

∵ The perimeter of the rectangle = 2a + 2b

- Lets multiply the inequality by 2

∴ 5.4 × 2 < a × 2 < 5.5 × 2

10.8 < 2a < 11 ⇒ (1)

∵ The width of the rectangle is b

∵ 3.6 < b < 3.7 cm

- Lets multiply the inequality by 2

∴ 3.6 × 2 < b × 2 < 3.7 × 2

7.2 < 2b < 7.4 ⇒ (2)

- Add inequalities (1) and (2)

∵     10.8 < 2a < 11

  +   7.2 < 2b < 7.4

∴  18 < 2a + 2b < 18.4

∵ 2a + 2b represents the perimeter of the rectangle

∴ The possible values of the perimeter of the rectangle is between

  18 and 18.4 cm ⇒ [18 < perimeter of rectangle < 18.4] cm


Related Questions

An airplane descended 4,000 feet before landing. The integer that represents how many feet the airplane was above the ground before it’s descent is ?

Answers

Answer:

Since, an airplane descended 4,000 feet before landing.

Now, we have to determine the integer which represents the number of feet, the airplane was above the ground before its descent.

Before the descent, airplane was at the height of 4,000 feet.

And the distance above the ground is represented by the positive integers and distance below the ground is represented by the negative integers.

Since, 4,000 feet is the distance of airplane above the ground.

So, the airplane was +4,000 feet above the ground before its descent.

Determine which statement is true about the zeros of the function graphed below.



A.
Function f has one real solution and one complex solution.
B.
Function f has exactly two complex solutions.
C.
Function f has exactly one real solution and no complex solutions.
D.
Function f has exactly two real solutions.

Answers

Answer:

The correct answer is B.

Step-by-step explanation:

In this graph we can see a "Parabola", this is the curve for a second degree polynomial function, and based on "Fundamental theorem of algebra" we can know that this polynomial has 2 roots (they can be real or imaginary).

In this graph, the curve doesn't touch the X axis, so we know that this function has not real root. So both roots are complex

Plsss help im stuck!!

Answers

Answer:

33.25

Step-by-step explanation:

Answer: 36.5

Step-by-step explanation:

A line passes through (-1, 7) and (2, 10).

Which answer is the equation of the line?

a. -x+y=12
b. -3x+y=4
c. -3x + y = 16
d. -x+y=8

Answers

Answer:

d. -x + y = 8

Step-by-step explanation:

First find the rate of change [slope]:

-y₁ + y₂\-x₁ + x₂ = m

[tex]\frac{-7 + 10}{1 + 2} = \frac{3}{3} = 1[/tex]

Then, we can go ahead and use the Slope-Intercept Formula instead of the Point-Slope Formula because you get it done swifter. It does not matter which ordered pair you choose:

10 = 1[2] + b

2

8 = b

y = x + 8 >> Line in Slope-Intercept Form

Since the exercise wants the equation in Standard Form:

y = x + 8

-x -x

________

-x + y = 8 >> Line in Standard Form

__________________________________________________________

7 = 1[-1] + b

-1

8 = b

y = x + 8 >> Line in Slope-Intercept Form

y = x + 8

-x -x

________

-x + y = 8 >> Line in Standard Form

** You see? I told you it did not matter which ordered pair you chose because you will always get the exact same result, plus the fact that I told you it was alot swifter than the Point-Slope Formula.

* Tip: Use the Point-Slope Formula when it tells you to, otherwise keep using the Slope-Intercept Formula. That way, you get your work done in a jip!

I am joyous to assist you anytime.

3. A telephone company offers its customers a discount of $15 for even
month that they also sign up for Internet service. How much is the
annual discount? (Hint: There are 12 months in the year, and they give
a $15 discount per month)

Answers

$180 is the annual discount
Final answer:

The telephone company offers a $15 monthly discount for customers who also sign up for their internet service. The annual discount is calculated by multiplying the monthly discount by the number of months in a year, resulting in an annual discount of $180.

Explanation:

The telephone company offers a discount of $15 every month for customers that also enroll in their internet service. To find out the annual discount, we need to multiply this monthly discount by the number of months in a year.

So, the calculation is as follows: $15 (monthly discount) x 12 (months in a year) = $180. Therefore, the annual discount offered by the company is $180.

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3(3x+4)=10+2(4x-5) solve

Answers

Answer:

x = -12

Step-by-step explanation:

9x + 12 = 10 + 8x - 10

9x + 12 = 8x + 10 -10

9x + 12 = 8x

12 = 8x -9x

12 = -x

12/-1

x = -12

9x+12= 10 +8x-10
9x+12=8x
12= -x
-12=x

what is 18/60 simplified?

Answers

Answer: 3/10

Step-by-step explanation:

18/60 divide each number by 3

6/20 divide by 2

3/10

Answer: 3/10

Step-by-step explanation: To write the fraction 18/60 in lowest terms, we divide the numerator and the denominator by the greatest common factor of 18 and 60 which is 6.


Which of the following is an equation of the circle in
the xy-plane that has center (0,0) and radius 4?
A) x2 + y2 = 4
B) x2 + y2 = 8
C) x2 + y2 = 16
D) x2 + y2 = 64​

Answers

Answer:

C

Step-by-step explanation:

The equation of a circle centred at the origin is

x² + y² = r² ← where r is the radius

here r = 4, thus

x² + y² = 4², that is

x² + y² = 16 → C

Answer:

C). x^2 + y^2 = 16.

Step-by-step explanation:

The equation of a circle with  center (0, 0) and radius r is

x^2 + y^2 = r^2

So our equation  (with r = 4) is:

x^2 + y^2 = 4^2

x^2 + y^2 = 16.

which integer is equivalent to 25^ 3/2

Answers

25^(3/2) = sqrt{25^3}

Now 25^3 = 15,625.

sqrt{15, 625} = 125

Done.

What is 3/4x2 in simplest form

Answers

Answer:

3/2

Step-by-step explanation:

1) Reduce the numbers with greatest common divisor (2 goes into 4 2 times, so your new problem would be 3/2 x1)

2) Multiply (3/2 times 1 equals 3/2)

Answer:

5

Step-by-step explanation:

Multiply (3x2)=6

the 4 on top add that with 6 (6+4)= 10

keep the denominator so 10/2

10/2 = 5/1 = 5

heyyyyy help pls
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Answers

Answer:

-30

Step-by-step explanation:

1) Remove unnecessary parenthesis:

-20-10

2) Calculate the difference:

-30

Hey!

-----------------------

Solution:

= (-20) - (10)

= -20 - 10

= -30

-----------------------

Answer:

A. -30

-----------------------

Hope This Helped! Good Luck!

Two objects are ________ when they have the same size and shape. What’s the blank?

Answers

Answer:

I think the answer is 'congruent'. :)

Step-by-step explanation:

Use the point-slope formula to write an equation of the line that passes through (-5,3) and
(4,6). Write the answer in slope-intercept form (if possible).

Answers

Answer:

The equation in point slope form is [tex]y-6=\frac{1}{3}(x-4)[/tex]

The equation in slope intercept form is [tex]y=\frac{1}{3}x-\frac{14}{3}[/tex]

Step-by-step explanation:

step 1

Find the slope m

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

[tex](-5,3),(4,6)[/tex]

Substitute the values

[tex]m=\frac{6-3}{4+5}[/tex]

[tex]m=\frac{3}{9}[/tex]

simplify

[tex]m=\frac{1}{3}[/tex]

step 2

Find the equation of the line in point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=\frac{1}{3}[/tex]

[tex](4,6)[/tex]

substitute

[tex]y-6=\frac{1}{3}(x-4)[/tex] ---> equation in point slope form

step 3

Find the equation of the line in slope intercept form

[tex]y=mx+b[/tex]

[tex]y-6=\frac{1}{3}(x-4)[/tex] ----> convert to slope intercept form

[tex]y-6=\frac{1}{3}x-\frac{4}{3}[/tex]

[tex]y=\frac{1}{3}x-\frac{4}{3}+6[/tex]

[tex]y=\frac{1}{3}x-\frac{14}{3}[/tex]

Jada bought 3 1/2 yards of fabric for $21. How much did each yard cost

Answers

Answer:

6

Step-by-step explanation:

3 1/2 = 3.5

21/3.5 = 6

The cost of one yard of fabric is required.

The cost of one yard of fabric is [tex]\$6[/tex]

Cost of [tex]3\dfrac{1}{2}\ \text{yards}[/tex] of fabric is [tex]\$21[/tex]

[tex]3\dfrac{1}{2}=\dfrac{7}{2}\ \text{yards}=\$21[/tex]

We need to divide both sides by [tex]\dfrac{7}{2}[/tex]

[tex]1\ \text{yard}=\dfrac{21}{\dfrac{7}{2}}[/tex]

[tex]=21\times \dfrac{2}{7}=\$6[/tex]

The cost of one yard of fabric is [tex]\$6[/tex]

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The base of a triangle exceeds the height by 3 feet. If the area is 350 square feet, find the length of the base and the height of the triangle.

Answers

Answer:

base is 28 feet squared

height is 25 feet squared

Final answer:

From the conditions given, we set up an equation (1/2) * (h + 3) * h = 350. By solving for h, we find the height of the triangle is 20 feet and the base, which is 3 feet more, is 23 feet.

Explanation:

In this problem, we are given that the base of a triangle exceeds the height by 3 feet and the area of the triangle is 350 square feet. We need to use the formula for the area of a triangle, which is (1/2)bh, where b is the base and h is the height. We can set up an equation from the given conditions: (1/2) * (h + 3) * h = 350. Solving for h, we get h = 20 feet. Therefore, the base b = h + 3 = 20 + 3 = 23 feet. So, the height of the triangle is 20 feet and the base is 23 feet.

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What is the circumference of a circle with a diameter of 3.4 cm?

Use 3.14 for pi.

Enter your answer as a decimal in the box.

Answers

The answer to the problem is 10.676

Answer: 10.676 cm

Step-by-step explanation:

We know that ,

The circumference of a circle is given by :_

[tex]\text{Circumference}=\pi d[/tex] , where d= diameter.

Given : Diameter of circle = 3.4 cm

Then Circumference of circle = [tex](3.14)(3.4=10..676\text{ cm}[/tex]

Hence, the circumference of a circle with a diameter of 3.4 cm is 10.676 cm.

Please need help on this

Answers

Answer:

○ B x² + 3x - 6

Step-by-step explanation:

Here is the Quadratic Equation:

y = Ax² + Bx + C

Find the expression that is in this form, which would be answer choice B.

I am joyous to assist you anytime.

How are dilations similar to scale drawings?

Answers

Scale drawings and dilated figures are alike in that all corresponding angles are congruent and all corresponding distances are in the equivalent ratio, , called the scale factor. A dilation of a figure produces a scale drawing of that figure.

8 to the power of 2 + 3 ( 36 divided by 6 ) - 2

Answers

[tex]\huge\boxed{80}[/tex]

Let's start off by writing this with symbols. [tex]8^2+3(\frac{36}{6})-2[/tex]

Follow the order of operations and start with the exponent. [tex]64+3(\frac{36}{6}-2[/tex]

Now, solve the parentheses. [tex]64+3*6-2[/tex]

Multiply. [tex]64+18-2[/tex]

Add. [tex]82-2[/tex]

[tex]\boxed{80}[/tex]

Final answer:

Explanation of solving an arithmetic expression with exponents, division, addition, and subtraction following the order of operations.

Explanation:

To solve the expression 82 + 3 ×(36 / 6) - 2, follow the order of operations (PEMDAS):

Calculate the exponential term: 82 = 64

Divide 36 by 6: 36 / 6 = 6

Multiply 3 by the result of the division: 3 ×6 = 18

Substitute the values back into the original expression: 64 + 18 - 2

Perform the addition and subtraction: 64 + 18 = 82, then 82 - 2 = 80

Therefore, the result of the expression 82 + 3 ×(36 / 6) - 2 is 80.

Write the equation of the line perpendicular to y= -1/2x - 5 through the point (1,-4)

Answers

Answer:

y = 2x - 6

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - [tex]\frac{1}{2}[/tex] x - 5 ← is in slope- intercept form

with slope m = - [tex]\frac{1}{2}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{2} }[/tex] = 2, thus

y = 2x + c ← is the partial equation of the line

To find c substitute (1, - 4) into the partial equation

- 4 = 2 + c ⇒ c = - 4 - 2 = - 6

y = 2x - 6 ← equation of line

What is 60,000 rounded to the nearest thousand?

Answers

60,000 rounded to the nearest thousand is 6000

3/4 m = 66
What is the answer?

Answers

Answer:

m=88

Step-by-step explanation:

First we have to isolate the variable. In this case, it would be by multiplying the reciprocal of the fraction the both sides. M will be alone and the other side should come out to be 88. Assuming you know how to multiply with fractions, of course.

a fraction that is a repeating decimal between 0.5 and 1

Answers

The fraction [tex]\( \frac{2}{3} \)[/tex] results in a repeating decimal [tex]\( 0.\overline{6} \)[/tex], which falls between 0.5 and 1.

Sure, here's a step-by-step explanation:

1. Start with the fraction: We begin with the fraction [tex]\( \frac{2}{3} \)[/tex].

2. Convert to decimal: To convert this fraction to a decimal, divide the numerator (2) by the denominator (3).

[tex]\[ \frac{2}{3} = 0.66666... \][/tex]

The decimal representation of [tex]\( \frac{2}{3} \) is \( 0.\overline{6} \)[/tex], which means the digit 6 repeats infinitely.

3. Determine where it falls between 0.5 and 1: Since the decimal [tex]\( 0.\overline{6} \)[/tex] is greater than 0.5 and less than 1, the fraction [tex]\( \frac{2}{3} \)[/tex] indeed fits the criteria of being a fraction with a repeating decimal between 0.5 and 1.



1. One day, 758 people visited the
Monkey House at the zoo. What is
758 rounded to the nearest hundred?​

Answers

Good morning ☕️

______

Answer:

800

_____________________

Step-by-step explanation:

758 rounded to the nearest hundred 800 because 5 is greater than 4.

:)

H - 26 = -29 linear equation solving show steps

Answers

Answer:

H = -3

Step-by-step explanation:

H - 26 = -29

    +26   +26

H = -3

H-26=-29

move -26 to the other side

sign changes from -26 to +26

H-26+26=-29+26

H=-29+26

Answer: H=-3

8.9 x 10^-5 in standard notation​

Answers

Answer:

the answer = 0.000089x

Step-by-step explanation:

(5 to the power of 4) to the power of 3

Answer as a exponent.

Answers

Answer:

5^12

Step-by-step explanation:

When you have a question where a number is raised to the power of twice you just multiply both exponents. In this case 4x3=12

So 5 to the power of 4 to the power of 3 is 5 to the power of 12

-7y+11y+9=-3 what does y equal

Answers

Answer:

y=-3

Step-by-step explanation:

-7y+11y+9=-3

1) Combine alike terms:

4y+9=-3

2) subtract a 9 on both sides:

4y=-12

3) divide both sides by 4:

y=-3

two numbers have a sum of 24. if one number is P, express the other number in terms of P

Answers

Say the other number is a. The sum is a+P, which also equals 24.

Write it as, a+P=24.

Now subtract P from both sides.

you get, a = 24-P

So, the other number in terms of P is 24 - P

To express the other number in terms of P when the sum of the two numbers is 24, subtract P from 24: Q = 24 - P.

In Mathematics, when you have a sum of two numbers, and you know the value of one number, you can find the other number by subtracting the known number from the total sum.

This is known as solving for a variable.

In this specific question where two numbers have a sum of 24, and if one number is P, the other number can be expressed in terms of P as 24 - P.

It is a simple equation derived from the basic formula: Sum = Number1 + Number2

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A rectangular school banner has a length of 54 inches and a width of 36 inches. A sign is made that is similar to the school banner and has a length of 17 inches. What is the ratio of the area of the school banner to the area of the sign?

Answers

Answer:

It is about 3.18 inches

Step-by-step explanation:

54 divide by 17 equals to 3.17647058824

estimate 3.17647058824 to hundredth place equals to 1.18

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