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LESSON 6 SESSION 1
Rectangular paintings hang on the wall of an art gallery.
One painting has an area of 24 ft. Another painting has an
area of 32 ft. The paintings have whole-number side lengths
and have one pair of side lengths in common.
a. What could the common side length be? Show your work.
C
SOLUTION
b. Check your answer to problem 3a. Show your work

Answers

Answer 1

Step-by-step explanation:

I don't really understand. Comment the question without "lesson/session/cancel/done" bc it's ALL confusing

Answer 2

The common side length of the rectangular paintings on the wall that having area of 24ft and 32ft  is 8 feet.

How to find side length ?

There are numerous methods for calculating the length of a rectangle. If you have an area A and a width w, the length w is calculated as h = A/w. If you know the perimeter P and the width w, you can calculate the length h = P/2w.

The area of any quadrilateral can be calculated by multiplying its base length by its height. We know that all sides are equal length because the shape is square. Working backwards, we can find the length of one side by taking the square root of the area.

The given parameters are

Area of painting 1 = 24 square feet

Area of painting 2 = 32 square feet

Express the areas as the product of their factors

So, we have

24 = 2 * 2 * 2 * 3

32 = 2 * 2 * 2 * 4

Multiply the common factors

Common factors =2 * 2 * 2

Evaluate the product

Common factors = 8

This represents the common side length

Hence, the common side length of the paintings is 8 feet

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Related Questions

Which trigonometric function is an odd function and why?

Answers

Answer:

Last one D.

Step-by-step explanation:

Just remember x, f(–x) = –f(x).

A party rental company has chairs and tables for rent. The total cost to rent 5 chairs and
3 tables is 31$. The total cost to rent 2 chairs and 6 tables is 52$. What is the cost to rent each chair and each table?

Answers

Answer:

1 Chair= $1.25     1 table= $8.25

Step-by-step explanation:

5c+3t=31

2c+6t= 52

-2(5c+3t=31)

-10c-6t=-62

+

2c+6t=52

= -8c=-10

/-8      /-8

c= 1.25 or 1 1/4

2c+6t=52

2(1.25)+6t=52

2.5+6t=52

-2.5        -2.5

6t= 49.5

/6      /6

t= 8 1/4

A group of students at a high school took a standardized test. The number of students who passed or failed the exam is broken down by gender in the following table. Determine whether gender and passing the test are independent by filling out the blanks in the sentence below, rounding all probabilities to the nearest thousandth.

Answers

Answer:

Since P(male)xP(fail) = 0.0549 and and P(male and fail) = 0.0773, the two results are different, so the events are not independent.

what is the answer to this?

Answers

Answer:

i can only say that you should use this forumla, the sins law

sin(a)/A = sin(b)/B = sin(c)/C

Step-by-step explanation:

Mrs. Stancil is planning to use
wrapping paper to cover a gift box that is the
shape of a rectangular prism with dimensions of
3ft by 4ft by 5ft. If the wrapping paper costs
S0.05 per square foot, how much will it cost?

Answers

Answer:

4.70

Step-by-step explanation:

there are 6 sides on a box

2 sides are 12 square feet (3*4), 2 sides are 15 square ft (3*5), and 2 sides are 20 square ft (4*5)

12*2+15*2+20*2=24+30+40=94 square feet

if each square foot costs $0.05 (I think that's what it says) then you would do 94*0.05= $4.70

so, your answer is $4.70

Not sure if this is right, but I tried

What is the area of the triangle?

Answers

Answer:

120

Step-by-step explanation:

since its a right-angled triangle you will use the formula:1/2 of the base × height

Answer:

[tex]120^{2}[/tex]

Step-by-step explanation:

Heron's formula

(for every triangle, you can use this same formula. just change the value of the letters)

a = 26

b = 10

c = 24

s = area

S = [tex]\sqrt{s(s - a)(s - b)(s - c)}[/tex]

S =  [tex]\frac{(a+b+c)}{2}[/tex]

If you do this for me you get Brainlyist

Answers

Answer:

v - √19

Step-by-step explanation:

the answer is v - √19

Exact value using sum and difference, Sin75°

Answers

Answer:

sin(75°) = [tex]\frac{\sqrt{2}+\sqrt{6} }{4}[/tex]

Step-by-step explanation:

Given: sin(75°)

Rewrite: sin(30° + 45°)

Use sum and difference identity:

sin(α + β) = sinαcosβ + cosαsinβ

sin(30°+45°) = sin(30°)cos(45°) + cos(30°)sin(45°)

sin(30°+45°) = (1/2)(√2 / 2) + (√3 / 2)(√2 / 2)

sin(30°+45°) = (√2 / 4) + (√6 / 4)

sin(30°+45°) = [(√2 + √6) / 4]

sin(75°) = [(√2 + √6) / 4]

PLEASE PLEASE HELP ILL MARK U AS BRAINLIST I NEED HELP ASAP !

Answers

Answer:

4.24 is the answer

Select the graph that represents the given set. (Click on the graph until the correct one is showing.)

E = {(6, 2), (7, 3), (6, -1), (5, 4)}

Answers

Answer:

Hi! The answer is in the pic below!!

Step-by-step explanation:

☆*: .。..。.:*☆☆*: .。..。.:*☆☆*: .。..。.:*☆☆*: .。..。.:*☆

☆Brainliest is greatly appreciated!☆

Hope this helps!!

- Brooklynn Deka

how do you solve 6 1/2 x 16?​

Answers

Answer:

Step-by-step explanation:

Make 6 1/2 an irrational fraction: 13/2 (I dunno know if its called that )

divide 16 by 2: 8

multiply that by 13: 104

Tell me if this helps or not bc I'm not really sure, but I really hope I helped!

Find: AABCD in square unit.

Answers

Answer:

in triangle ACD

<D =<B=90° inscribed angle from the diameter is 90°

base AC=2×OA=2×15=30unit

perpendicular =CD=12unit

area of triangle ACD

=1/2 base×perpendicular=1/2×30×12=180unit²

In triangle ABC

base=AC=30 unit

perpendicular=BC=18unit

area of traingle ABC =

1/2 base×perpendicular=1/2×30×18=270unit²

Area of quadrilateral =area of traingle [ABC+ACD]

=180+270=450 square unit ans..

Marcus has a bag of 10
red chips, 15 blue chips,
and 5 black chips. How
many times would he
expect to pick a red chip if
he did the experiment 60
times?
A) 10
B) 20
C) 30
D) 45

PLEASE HELP THIS IS DUE TODAY

Answers

Answer:

B

Step-by-step explanation:

Marcus can expect to have red chip 20 times.

What is probability?

Probability denotes the possibility of the outcome of any random event. The meaning of this term is to check the extent to which any event is likely to happen.

Given that, Marcus has a bag of 10 red chips, 15 blue chips, and 5 black chips.

He did an experiment 60 times and we need to find that how many times would he expect to pick a red chip,

So,

Here the favorable outcomes = red chips (10)

Total outcomes = all the chips = 15+5+10 = 20

So, the probability of finding a red chips for the 60 times = 10/20 x 60

= 30

Hence, Marcus can expect to have red chip 20 times.

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ASAP Point A, located at (-3, -3) is translated 6 units up, resulting in the location of point A'. What other transformation would result in the same location for point A'? A reflection in the x-axis A translation of 6 units to the left A reflection in the y-axis A rotation of 180°

~I KNOW ITS NOT A REFLECTION IN THE Y-AXIS

Answers

Answer:

(3,3)

Step-by-step explanation:

A reflection of this across the y-axis is (-3,3). A reflection of Point A, (-3,-3), over the x-axis is also (-3,3).

(2+√2) is

an integer

a rational number

an irrational number

none of these​

Answers

Answer:

Irrational number

Step-by-step explanation:

√2 is an irrational number.

So, when a integer or rational number is added to irrational number, we will get irrational numbers

2 + √2 is an irrational number.

Ina class of 44 pupil 3/4 are girls . How many girls would be there altogether.

Answers

Answer:

33 girls

Step-by-step explanation:

This is the answer because:

1) 3/4 of 44 is 33 because 1/2 of 44 is 11

               a) 11 x 3 = 33

Hope this helps! :)

Answer:

33 girls

Step-by-step explanation:

44/4= 11

11x3=33

plz mark me as brainliest.

. An oil refnery is located on the north bank of a straight river that is 2 km wide. A pipeline is to be constructed from the refnery to storage tanks located on the south bank of the river 6 km east of the refnery. The cost of laying pipe is $400,000ykm over land to a point P on the north bank and $800,000ykm under the river to the tanks. To minimize the cost of the pipeline, where should P be located

Answers

Answer:

The point P should be located at 0,51 Km from point B, to minimize costs

Step-by-step explanation:

The oil refinery ( point A ) the opposite point ( B) in the south bank, and the storage tank (point C) these three points shape a right triangle. Let´s call x the distance between point A and point P ( the arriving point of the pipeline in the south bank ) then:

Cost = cost of pipeline in-ground* ( 6 - x ) + cost of pipeline in water* L

where L is the hypothenuse of the right triangle  ( A , B , P )

Cost ($) = 400000 * ( 6 - x ) + 800000 * √ 2² + x²

C (x) = 400000* ( 6 - x ) + 800000* √4 + x²

C(x) = 2400000 - 400000*x  + 800000* √4 + x²

Tacking derivatives on both sides of the equation

C´(x) = - 400000 + 800000* ( 2x)/√4 + x²

C´(x) = 0         - 400000 + 1600000*x / √4 + x²  = 0

- 400000* (√4 + x² )  + 1600000*x  = 0

- (√4 + x² ) + 4* x = 0

- (√4 + x² )  = - 4*x

Squaring both sides

4 + x²  = 16*x²

15*x² = 4

x² = 4/ 15

x = ± √0,27

x = ± 0,51

We should dismiss the negative solution

x = 0,51 Km

The point P should be located at 0,51 Km from point B

Simplify the following expression. x(x - 3) - 4(x2 + 7)

Answers

-3x^2 (2 squared) - 3x -28

Answer:

[tex]x^{2} -11x-28[/tex]

Step-by-step explanation:

We start of with this.

[tex]x(x-3)-4(2x+7)[/tex]

First, use the distributive property, and distribute the x to the (x-3) to get: [tex]x^{2} -3x-4(2x+7)[/tex]

Next, distribute the -4 to the (2x+7) to then get:

[tex]x^{2} -3x-8x-28[/tex]

Then, combine like terms. In this case, combine -3x and -8x since they are alike and get:

[tex]x^{2} -11x-28[/tex]

The answer is already in standard form, so we're done. To write a polynomial in standard form, write the monomial with the variable, with the largest exponent first. In this case, [tex]x^{2}[/tex] goes before [tex]-11x[/tex] because of the exponent of 2. Monomials without a variable go last, so that's why -28 is last.

1. a. The equation of a straight line is 2y = 3x +4,
Find the gradient of this line,​

Answers

Answer:

3/2

Step-by-step explanation:

2y = 3x + 4

y = (3/2)x + 2

^ ^ ^ ^

y = m x + c

m = 3/2

A small hair salon in Denver, Colorado, averages about 30 customers on weekdays with a standard deviation of 6. It is safe to assume that the underlying distribution is normal. In an attempt to increase the number of weekday customers, the manager offers a $2 discount on 5 consecutive weekdays. She reports that her strategy has worked since the sample mean of customers during this 5 weekday period jumps to 35.

Required:
What is the probability to get a sample average of 35 or more customers if the manager had not offered the discount?

Answers

Answer:

0.0314 = 3.14% probability to get a sample average of 35 or more customers if the manager had not offered the discount

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

A small hair salon in Denver, Colorado, averages about 30 customers on weekdays with a standard deviation of 6.

This means that [tex]\mu = 30, \sigma = 6[/tex]

5 consecutive weekdays.

This means that [tex]n = 5, s = \frac{6}{\sqrt{5}} = 2.6832[/tex]

What is the probability to get a sample average of 35 or more customers if the manager had not offered the discount?

This is 1 subtracted by the pvalue of Z when X = 35.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{35 - 30}{2.6832}[/tex]

[tex]Z = 1.86[/tex]

[tex]Z = 1.86[/tex] has a pvalue of 0.9686

1 - 0.9686 = 0.0314

0.0314 = 3.14% probability to get a sample average of 35 or more customers if the manager had not offered the discount

what is the arc length of s in the figure below​

Answers

Answer:

2.18ft

Step-by-step explanation:

what is the arc length of s in the figure below​

Length of the arc = theta/360 * 2πr

r is the radius = 1ft

theta = 125 degrees

Substitute into the formula

Length of the arc = 125/360 * 2(3.14)* 1

Length of the arc = 785/360

Length of the arc  = 2.18ft

Hence the length of the arc is 2.18ft

Describe the shape that results from a cross section that is parallel to the base of a right cylinder.

Answers

Answer:

Circles

Step-by-step explanation:

Think of a soup can sitting on its base on a kitchen counter.  The counter is an example of a plane (through) parallel to the base.  The points where the can and counter intersect form a circle.  Put a book on top of the can.  Again, the plane of the book is parallel to the base and the book and can intersect in a circle.

The same thing would happen if you cut the can open with a plane anywhere in between the two mentioned above, but it would make a mess!

The answer is circles. If you cut this shape in half you will get two circles.

4. Find the greatest number which divides 171 and 251 leaving the remainders
3 and 6 respectively.​

Answers

Answer:

The answer is 7.


A ball is thrown from an initial height of 2 feet with an initial upward velocity of 21 fts. The ball's height h (in feet) after seconds is given by the following.

Answers

Answer:

h(t)=

h(t)=vt-21t+2

Step-by-step explanation:

initial height =2

initial velocity=21ft/s

dh/dt=v

dh=vdt

intergrating both sides

h(t)-h(i)=vt-v(i)t

h(t)-2=vt-21t

h(t)=vt-21t+2

Simplify 45÷3[90÷45{6+3(19-16)}]​

Answers

Step-by-step explanation:

45÷3[90÷45{6+3(19-16)}]

45÷3[90÷45{6+3(3)}]

45÷3[90÷45{6+9}]

45÷3[90÷45{15}]

45÷3 [90÷675]

[tex]\frac{\cancel{45}^\ {15}}{\cancel3} * \frac{6}{45}[/tex]

[tex] \cancel{15} × \frac{6}{\cancel{45}^\ {3}}[/tex]

6/3

2

[tex]\\\\\\[/tex]

The equation of [tex]$\frac{45}{3}\left[\frac{90}{45}+3\left(19-16\right)\right][/tex] is 165.

What is PEMDAS rule?

PEMDAS exists as an acronym for the terms parenthesis, exponents, multiplication, division, addition, and subtraction.

How to simplify the equation of [tex]$\frac{45}{3}\left[\frac{90}{45}+3\left(19-16\right)\right][/tex]?

Given:

[tex]$\frac{45}{3}\left[\frac{90}{45}+3\left(19-16\right)\right][/tex]

45/3 = 15

Simplifying the given equation, we get

[tex]$\frac{45}{3}\left[\frac{90}{45}+3\left(19-16\right)\right]=15\left[\frac{90}{45}+3(19-16)\right][/tex]

90 / 45 = 2

By simplifying the above equation, then we get

= 15[2 + 3(19 -16)]

By using the PEMDAS rule

15[2 + 3(19 -16)] = 11

[tex]$\frac{45}{3}\left[\frac{90}{45}+3\left(19-16\right)\right]= 15*11[/tex]

= 165

Therefore, the equation of [tex]$\frac{45}{3}\left[\frac{90}{45}+3\left(19-16\right)\right][/tex] is 165.

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PLEASE ANSWER ASAP FOR BRAINLEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
You ask the students in class two questions. Which question is statistical and which is non-statistical? Explain.
What time does the first period begin?
What time do you leave home to go to school?

Answers

Answer:

the first is non-statistical and the second one is statistical

Step-by-step explanation:

when it is statistical it is asking in general (like a yes or no question) and when it's non-statistical it is asking something specific.

Put some air in your tires: Let X represent the number of tires with low air pressure on a randomly chosen car. The probability distribution of X is as follows.

x 0 1 2 3 4
Px 0.2 0.1 0.4 0.2 0.1
Compute the standard deviation σX. Round the answer to at least three decimal places.

Answers

Step-by-step explanation:

sorry po hindi ko po alam sagot

What is the gradient?

Answers

Answer:

Gradient = 2

Step-by-step explanation:

Gradient of a line = Slope of the line

Since, slope of a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,

Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Given line in the graph passes through two points (1, 0) and (2, 2)

Therefore, slope or gradient of the line = [tex]\frac{2-0}{2-1}[/tex]

                                                                  = 2

Gradient = 2 will be the answer.

The gene for black coat color (B) is dominant over the gene for brown coat color (b) What percent of the offspring are expected to have brown coat color as a result of a cross between a dog with black coat color (Bb and a dog with brown coat color (bb)? A:25 B:50 c:75 d:100 answer quick please!

Answers

Answer:

errrr- I dont know but good luck !

Step-by-step explanation:

Answer:

Most likely A

Step-by-step explanation:

Considering at the beginning it says the gene for back coat color is dominant, it makes brown coat color less dominant

Problem 5 Statement: 1. Andre received and spent money in the following ways last month. For each example write a positive or negative number to represent the change in money from his perspective. a. His uncle gave him $25 as a present. b. He earned $18 dollars tutoring. c. He spent $10 on a book. 2. What does 0 mean in this situation?

Answers

Answer:

$48

Step-by-step explanation:

Other Questions
Can someone please help me with this its really important match the term to the definition! MARKING BRAINLIEST!!! Is it better to be a child, a teenager, or an adult? What are the benefits of each age? What are the drawbacks? Choose the period of life that you think is best and write an essay arguing why it is the best time of life. Support your position with anecdotes from your own life as well as facts and details drawn from the lives of others. what is the fear of hell what surface does a rolling ball traveled faster and longerA.rough roadB.rocky roadC.smooth roadD.grassy road What is the equation that you get when you put together the twoequations below? what is the solution to the problemx + 8.63 = 11.001 Find the erea of the trapezoid. which vector is the sum of vectors a and b Plz help me well mark brainliest if correct! An object is in motion if ___ When warm, moist air rises, it _____________________ as atmospheric pressure decreases at higher altitudes. Air's ability to hold water vapor is decreased as pressure is reduced and cools adiabatically and eventually reaching its saturation level. As a result, rising air becomes unable to hold water vapors (air is saturated), leading to condensation and then followed by ________________________. which of the following equations has no solutions? Which of the following items will you need in order to complete the PROFILE?A.Medicaid informationB.Educational backgroundC.Student and parent W-2 formsD.Medical history If sin x=3/4,then cos x Pls help me Ill mark brainliest if correct The Gettysburg Address"Fourscore and seven years ago our fathers brought forth on this continent a new nation, conceived in liberty and dedicated to the proposition that all men are created equal. Now we are engaged in a great civil war, testing whether that nation or any nation so conceived and so dedicated can long endure. We are met on a great battlefield of that war. We have come to dedicate a portion of that field as a final resting-place for those who here gave their lives that that nation might live. It is altogether fitting and proper that we should do this. But in a larger sense, we cannot dedicate, we cannot consecrate, we cannot hallow this ground. The brave men, living and dead who struggled here have consecrated it far above our poor power to add or detract. The world will little note nor long remember what we say here, but it can never forget what they did here. It is for us the living rather to be dedicated here to the unfinished work which they who fought here have thus far so nobly advanced. It is rather for us to be here dedicated to the great task remaining before us-that from these honored dead we take increased devotion to that cause for which they gave the last full measure of devotion-that we here highly resolve that these dead shall not have died in vain, that this nation under God shall have a new birth of freedom, and that government of the people, by the people, for the people shall not perish from the earth."Which of the following is the best summary of the line in bold? (5 points)Question 4 options:1) The battle fought at this particular location was unimportant.2) Patriotic citizens have the right to rebel against government.3) War is pointless and should be used only as a last resort.4) Our purpose is to see this war through and to win it for justice 3. What is the scientific term for a group of interacting individuals of the same type, living in the same area at the same time? Question 4 of 10Which story element most clearly shows direct characterization?A. A character's private thoughts and feelings while aloneO B. How other characters act when a specific character is aroundC. The narrator's comments about a character's true natureD. The way a character dressesSUBMIT Pleaseeeeee helppppp