a rectangle has a width that is 7 centimeters less than its length, and it’s area is 330 square centimeters. what are the dimensions of the rectangle?

Answers

Answer 1

Answer:

The dimensions of the rectangle are 22cm of length and 15cm of width

Step-by-step explanation:

To solve this we first have to know the formula to calculate the area of ​​a rectangle

a = area = 330 cm²

L = length  =

w = width = L - 7cm

a = l * w

we replace with the known values

330 cm² = L * (l - 7cm)

330 cm² = L² - 7Lcm

0 = L² - 7Lcm - 330 cm²

when we have an equation like this we can use bhaskara

a = 1

b = -7Lcm

c = -330cm²

ax² + bx + c = 0

x = -b(±)√(b² - 4ac)/2a

we replace with the known values

L = -(-7cm)(±)√(7² - 4(1)(-330cm²)) / 2(1)

L = 7cm(±)√(49 + 1320cm²)) / 2

L = 7cm(±)√(1369cm²)) / 2

L1 = (7cm + 37cm) / 2

L1 = 44cm / 2 = 22cm

L2 = (7cm - 37cm) / 2

L2 = -30cm / 2 = -15cm

The positive represents the unknown with which we work (L) and the negative with which we do not work (W)

The dimensions of the rectangle are 22cm of length and 15cm of width


Related Questions

What type of sequence is 0,12,24,36,48 geometric or arithmetic?

Answers

Answer:

Arithmetic

Step-by-step explanation:

Since each number is 12 larger than the last, this is an arithmetic sequence. A geometric sequence is one in which each next number in the sequence is the previous one multiplied by a certain set coefficient, while in an arithmetic sequence it's a certain number added. Hope this helps!

Answer:

It is arithmetic because to get from one term to the next, you add 12, and in an arithmetic sequence, you add/subtract a common difference to get from one term to the next. Hope this helps!

Which is the correct way to model the equation-+8 = 7x+(-8) using algebra tiles?
1 positive x-tile and 8 positive unit tiles on the left side; 7 positive x-tiles and 8 positive unit tiles on the right side
8 positive unit tiles on the left side; 7 positive x-tiles and 8 negative unit tiles on the right side
1 negative x-tile and 8 positive unit tiles on the left side; 7 positive x-tiles and 8 negative unit tiles on the right side
8 positive x-tiles and 1 negative unit tile on the left side; 8 negative X-tiles and 7 positive unit tiles on the right side
VX

Answers

Answer:

Step-by-step explanation:

1 negative x-tile and 8 positive unit tiles on the left side; 7 positive x-tiles and 8 negative unit tiles on the right side

Answer:

the answer is c

Step-by-step explanation:

The line plot shows the number of bags of grapes,grouped by weight, to the nearest 1/8 pound. How many bags of grapes had a weight of 3/8 pound or less

Answers

Answer:

2.25 pounds

Step-by-step explanation:

The diagram showing the weight of bags with grapes is shown in the attached file below.

From the diagram; number of  bags of grapes that had a weight of [tex]\dfrac{3}{8}[/tex] pounds or less is:

[tex]\dfrac{3}{8}[/tex] pounds  = 3

[tex]\dfrac{1}{4}[/tex] pounds = 4

[tex]\dfrac{1}{8}[/tex] pounds = 1

Thus; the total is = 3+4+1 = 8

However, The total weight of the grapes in the bag that had a weight of  [tex]\dfrac{3}{8}[/tex] pounds or less is :

= [tex]\dfrac{3}{8}(3) + \dfrac{1}{4}(4) + \dfrac{1}{8}(1)[/tex]

= [tex]\dfrac{9}{8} + 1 + \dfrac{1}{8}[/tex]

= [tex]\dfrac{9+8+1}{8}[/tex]

= [tex]\dfrac{18}{8}[/tex]

= 2.25 pounds

The probability that Shruti succeeds at any given free-throw is 80%, percent. She was curious how many free-throws she can expect to succeed in a sample of 12 free-throws.


She simulated 25 samples of 12 free-throws where each free-throw had a 0.8, point, 8 probability of being a success.


Shruti counted how many free-throws were successes in each simulated sample. Here are her results:


Use her results to estimate the probability that she succeeds at 10 or more free-throws in a sample of 12 free-throws.

Give your answer as either a fraction or a decimal.

Answers

Answer:

0.5584 probability that she succeeds at 10 or more free-throws in a sample of 12 free-throws.

Step-by-step explanation:

For each free throw, there are only two possible outcomes. Either she makes it, or she does not. The probability of making a free throw is independent of other free throws. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The probability that Shruti succeeds at any given free-throw is 80%, percent.

This means that [tex]p = 0.8[/tex]

Sample of 12 free throws:

This means that [tex]n = 12[/tex]

Use her results to estimate the probability that she succeeds at 10 or more free-throws in a sample of 12 free-throws.

[tex]P(X \geq 10) = P(X = 10) + P(X = 11) + P(X = 12)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 10) = C_{12,10}.(0.8)^{10}.(0.2)^{2} = 0.2835[/tex]

[tex]P(X = 11) = C_{12,11}.(0.8)^{11}.(0.2)^{1} = 0.2062[/tex]

[tex]P(X = 12) = C_{12,12}.(0.8)^{12}.(0.2)^{0} = 0.0687[/tex]

[tex]P(X \geq 10) = P(X = 10) + P(X = 11) + P(X = 12) = 0.2835 + 0.2062 + 0.0687 = 0.5584[/tex]

0.5584 probability that she succeeds at 10 or more free-throws in a sample of 12 free-throws.

Answer:0.8

Step-by-step explanation:in 5 of the 25 stimulated trials, scrutiny continued federal than 10 successes

Which reason best describes why you can divide any number by 10 by moving the decimal point one place to the left?

1.Dividing a number by 10 is the same as subtracting the number ten times.

2. Dividing by 10 is the same as removing a zero.

3. Moving the decimal point left makes the number smaller.

4. Moving the decimal point one place to the left makes the number 1/10 of its original value.

Answers

4 is the answer

The next best is 3

Mark has invested $300 at age 16 into a money market account earning 6%. How many times will Mark's investment double before age 52? What will his investment be worth? What would Mark's investment be if he had invested at age 28?

Answers

Answer:

A.3times

B.$1214.68

Step-by-step Explanation

A

Using compound interest formula

A=P(1+I)^n

A is the amount

P is the principal=$300

I is the interest=0.06

n is the time ( between 52 and 16years)=36years

A=300(1+0.06)^36

A=$2444.175

Which means 300 would have become

$2444.175 which is 8 folds.

That means it would have doubled 3times(2×2×2) at age of 52.

B. The time would change to (52-28)=24

Using compound interest formula

A=300(1+0.06)^24

A=$1214.68

Therefore his investment would have been $1214.68.

Sarah is buying plants and soil for her garden! The soil Sarah wants costs $3.50 per bag, and the plants she wants are $8 each. Sarah can buy at most 20 items, as this is all she can fit in her car, and she cannot spend more than $150. Let x represents the number of bags of soil and y represents the number of plants:

Answers

Answer:

x+y ≤20

3.50 x +8 y ≤150

Step-by-step explanation:

Hi, the rest of the question is:

How do you write a system of linear inequalities to model the situation?

So, for the first inequality:

The sum of the number of soil bags (x) and plants(y) bought must be less or equal to 20.

x+y ≤20

For the second inequality:

The product of the number of soil bags (x) and the price of each bag (3.50) ; plus the number of plants bought(y) and the price of each plant (8) must be less or equal to 150.

3.50 x +8 y ≤150

In conclusion, the system is:

x+y ≤20

3.50 x +8 y ≤150

100 POINTS!!!!!! the following stem and leaf plot shows the number of hours that mrs. dixon's students spent on their pre calc work last week. what is the mean absolute deviation for the data

Answers

Answer:

11.2467

Step-by-step explanation:

First we need to find the mean

Add up all the data and divide by number of points)

(6+7+8+10+12+13+14+17+17+17+18+19+21+23+24+24+25+27+31+31+32+36+36+39+41+45+45+46+49+50)/30

261/10

26.1

Then to find the mean absolute deviation take each value and find the absolute value from the mean and sum it and then divide by the number of points

((26.1 -6)+(26.1-7)+(26.1-8)+(26.1-10)+(26.1-12)+(26.1-13)+(26.1-14)+(26.1-17)+(26.1-17)+(26.1-17)+(26.1-18)+(26.1-19)+(26.1-21)+(26.1-23)+(26.1-24)+(26.1-24)+(26.1-25)+(27-26.1)+(31-26.1)+(31-26.1)+(32-26.1)+(36-26.1)+(36-26.1)+(39-26.1)+(41-26.1)+(45-26.1)+(45-26.1)+(46-26.1)+(49-26.1)+(50-26.1))/30

11.2467

Answer:

11 16/75

Step-by-step explanation:

Find the mean: sum/n

783/30

26.1

Find individual |x - 26.1| and add them:

|6-26.1| + |7-26.1| + ...... + |50-26.1|

= 20.1 + 19.1 + .... + 23.9

= 336.4

M.A.D = 336.4/30

11 16/75

A sample space consists of 80 separate events that are equally likely. What is the probability of each? A sample space consists of 80 separate events that are equally likely. What is the probability of each?

Answers

Answer:

1/80

Step-by-step explanation:

The probability of selecting each of the event in the sample space is; 1/80

How to Find the Probability?

We are given;

Sample Space = 80 separate events

Now, we are told that each event is equally likely to be selected.

Thus;

Probability of selecting each event = 1/80

Read more about Probability at; https://brainly.com/question/251701

#SPJ2

I need answers asap​

Answers

Answer:

22/24

Step-by-step explanation:

Isaiah was given a gift card for a coffee shop. Each morning, Isaiah uses the card to buy one cup of coffee. Each cup of coffee costs $2.50 and after buying 16 cups of coffee, the card had a $5 remaining balance. Write an equation for A(x),A(x), representing the amount money remaining on the card after buying xx cups of coffee.

Answers

Answer:

$45-$2.50xx

Step-by-step explanation:

Let first of all determine the original amount on the gift card as follows

amount utilized=$2.50*16=$40

balance left after utilizing $40=$5

original amount on the gift card=amount utilized+balance left=$40+$5=$45

if xx cups of coffee is purchased ,the amount utilized would be xx*$2.50

i.e $2.50xx

The equation for the amount left would total amount on the gift card minus the $2.50xx

equation for amount remaining =$45-$2.50xx

If the questioner has duplicated x,which means he or she meant just x

equation of the amount remaining would=$45-$2.50x

if anyone know probability stuff pls help w this!!

Answers

Answer:

A - 9/34

B - 7/34

Step-by-step explanation:

A girl grabs a lollipop - 9/34 (Event A)

A boy grabs a fruit chew - 7/34 (Event B)

Because there are 34 possibilities in total....

Thanks!

If the point (a,1) lies on the line y = 3x - 5, what is the value of a?

Answers

Answer:

a = 2

Step-by-step explanation:

Note that a point uses (x , y).

y = 1

x = a

Plug in 1 for y in the equation, and a for x:

y = 3x - 5

1 = 3a - 5

Isolate the variable, a. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

First add 5 to both sides:

1 (+5) = 3a - 5 (+5)

1 + 5 = 3a

6 = 3a

Next, divide 3 from both sides:

(6)/3 = (3a)/3

a = 6/3

a = 2

2 is your value for a.

~

two integers that multiply to 18 and add to -11

Answers

Answer:

-9 and 2

Step-by-step explanation:

i need the missing blanks .

Answers

Answer:

K, (-3.5,-5), E, (3.5, 3)

Step-by-step explanation:

A company is designing a new cylindrical water bottle. The volume of the bottle will be 187 cmcubed. The height of the water bottle is 7.3 cm. What is the radius of the water​ bottle? Use 3.14 for pi.

Answers

Answer:

2.86cm

Step-by-step explanation:

Step 1:

Data obtained from the question. This includes the following:

Volume (V) = 187cm3

Height (h) = 7.3cm

Pi (π) = 3.14

Radius (r) =..?

Step 2:

Determination of the radius of the cylindrical water bottle.

The radius of the cylindrical water bottle can be obtained as follow:

V = πr^2h

187 = 3.14 x r^2 x 7.3

Divide both side by 3.14 x 7.3

r^2 = 187 / (3.14 x 7.3)

Take the square root of both side

r = √[187 / (3.14 x 7.3)]

r = 2.86cm

Therefore, the radius of the cylindrical water bottle is 2.86cm

What is equivalent to -1/4y -2 1/4y + 1/2 (4-2y) a) -3y + 2 b) -3 1/2y + 2 c) -4y + 4
d) -4 1/2y + 2

Answers

Answer:

B. -3 1/2y + 2

Step-by-step explanation:

Our expression is: [tex]\frac{-1}{4} y-2\frac{1}{4} y+\frac{1}{2} (4-2y)[/tex].

Let's first distribute out that parentheses. Remember that distribution is simply taking the sum of the product of the outside term with each of the inside terms. Here, the outside term is 1/2 and the inside terms are 4 and -2y:

[tex]\frac{1}{2} (4-2y)=\frac{1}{2} *4+\frac{1}{2} *(-2y)=2-y[/tex]

Now, we have:

[tex]\frac{-1}{4} y-2\frac{1}{4} y+2-y[/tex]

We want to combine like terms, which means combining all the terms with y in them:

[tex]\frac{-1}{4} y-2\frac{1}{4} y-y+2=\frac{-1}{4} y-\frac{9}{4} y-\frac{4}{4} y+2=\frac{-1-9-4}{4} y+2=\frac{-14}{4} y+2=\frac{-7}{2} y+2[/tex]

Remember that -7/2 can be written as the mixed number -3 1/2, so our final answer is:

-3 1/2y + 2

The answer is thus B.

~ an aesthetics lover

easy geometric shapes question!

Answers

Answer:

Cylinder

Step-by-step explanation:

The given geometric shape is of a cylinder.

Answer:

Cylinder

Step-by-step explanation:

The shape will make a cylinder if put together.

Find the smallest number to be Find the smallest number to be added to 2345 to get the nearest perfect square.

Answers

Answer:

48^2 =2304 < 2345 < 2401 = 49^2

=> Smallest number should be: 2401 - 2345 = 56

Hope this helps!

:)

Answer:

56

Step-by-step explanation:

sqrt(2345) = 48.425...

Nearest integer is 49

So, the nearest perfect is 49²

49² = 2401

To be added:

2401 - 2345

56

What is the mean and median of 25,50,58,54,55

Answers

Answer:

median = 58

mean= 48.4

Step-by-step explanation:

to find the mean you add all of the numbers and divide it by 5 in this case

the mean is 48.2
the median is 54

8y=4x-32/2 slope intercept form

Answers

Answer:

y=0.5x-2

Step-by-step explanation:

8y=4x-32/2

First thing you are going to do is solve for 32/2=16 and then enter it into the equation.

8y=4x-16

Second thing you are going to do is divide everything by 8 to get rid of 8y.

8y=4x-16

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

   8

4/8=0.5 and 16/8=2

y=0.5x-2

Reduce the following mixed number 2 2/8

Answers

Answer:

2 1/4

Step-by-step explanation:

2 2/8

The top and bottom of the fraction can be divided by 2

2 1/4

State the slope and y-intercept of the graph of the equation y = 3x + 2

The slope is _________.

The y-intercept is ____________-

Answers

Slope 3
Intercept is 2

What is 13 - 4 x = 1 - x?

Answers

Answer:

x=4

Step-by-step explanation

Answer:

x = 4

Explanation:                                                                                                                  

You start with a penny which doubles each day for 30 days. How much money would you have after 30 days?



Answers

Answer:

$5,368,709.12

Step-by-step explanation:

Kono Dio Da!!

Answer:

5368709.12

Step-by-step explanation:

i just did this earlier

You spin the spinner below once. What is the probability that the arrow will land on 3

Answers

Answer:

how many numbers are there and if there is more of the same number then that will be ur probability

Step-by-step explanation:

2x² - x-6=0 resuelve

Answers

Answer:

x = -3/2          x=2

Step-by-step explanation:

2x² - x-6=0

Factor

(2x     ) (x      ) =0

6 = 2*3

2*-2 +3 = -1

(2x  +3   ) (x  -2    ) =0

2x+3 =0      x-2 =0

2x = -3            x=2

x = -3/2          x=2

Find the exact value of sin 300°.

Answers

Answer:

-0.86602540378 or -√3/2

3x-2y=2 in slope intercept form

Answers

Answer:

y= - 3/2x + 1

how do you write 2x - 2y = 8 in slope-intercept form ?

Answers

Answer:

y=x-4

Step-by-step explanation:

The general scaffold for the slope intercept form is y=mx+b, where m is the slope and b is the y intercept. You can rearrange the equation that you are given like this:

2x-2y=8

-2y=-2x+8

y=x-4

Hope this helps!

Answer:

Rearrange the equation so that it is written in slope intercept form:

y=mx+b.

2x+2y=8.

2y=−2x+8.

y=−x+4.

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