Matt's den is 10 feet longer than it is wide. If the dents area is 231 square feet, what are the dimensions of the room?
The dimensions of the room are
ft.
(Use a comma to separate answers as needed.)

Answers

Answer 1

Answer:

[tex]21\: \mathrm{feet\: by}\: 11 \: \mathrm{feet}[/tex]

Step-by-step explanation:

(Assuming the den is a rectangle)

Let [tex]x[/tex] be the length of the den. Because the length is 10 feet longer than the width, the width of the den can be represented as [tex]x-10[/tex].

The area of a rectangle is given as [tex]l\cdot w[/tex], therefore we can form the following equation:

[tex]x(x-10)=231[/tex]

Expanding this, we have:

[tex]x^2-10x=231, \\\\x^2-10x-231=0[/tex]

This factors into [tex](x-21)(x+11)=0[/tex], therefore [tex]x=21, \: -11[/tex].

Because -11 is extraneous, the length of the den is [tex]21[/tex] feet and the width is [tex]21-10=11[/tex]. Thus, the dimensions of the den are [tex]\fbox{$21\: \mathrm{feet\: by}\: 11 \: \mathrm{feet}$}[/tex].


Related Questions

The regular price of a skateboard is p. Which expression represents the price of the skateboard when it is on sale for 25% off? Select all that apply.

Answers

Answer:   The expression represents the price of the skateboard when it is on sale for 25% off = 0.75p

Step-by-step explanation:

Given: Regular price of a skateboard is p.

Discount = 25% off = 0.25p

Now, the  price of the skateboard when it is on sale for 25% off = p - Discount

= p -0.25p

= (1-0.25)p

= 0.75p

Hence, the expression represents the price of the skateboard when it is on sale for 25% off = 0.75p

Answer: The expression represents the price of the skateboard when it is on sale for 25% off = 0.75p

Step-by-step explanation:

This pack of Pokemon cards is currently selling on Amazon for $3.90. If there are 10 cards in the pack, how much money are you paying per card?
A. $39.00
B. $13.90
C. $6.10
D. $0.39

Answers

the answer is D. $0.39. explanation: if you divide $3.90 by 10 you get 0.39.
The answer is D, it’s simple, you divide 3.90 by 10 and get .39 :) hope this helps!

hey, i wanna ask you an interesting question if you know the answer give it in comments okay !!

the question is :

what is the HCF / GCD
of 0 (zero) and 5

let me know the answer ..​

Answers

Answer:

it will 5 because 0 has all factor other than 0 and 5 has two factor 1 and 5 So hcf of 0 and 5 will 5

Find 80% of 14,236.
Enter the correct answer in the box.

Answers

Answer:

11388.8

Step-by-step explanation:

Answer:

11,388.8

Step-by-step explanation:

if 14,236 = 100℅

X. = 80℅

14,236*80℅ divided by 100℅

X= 11,388.8

Find the area of each geometric figure or product of the polynomial.

(-6r + 3) (-3r - 3)

A) 18r2 + 9r - 9
B) -30r2 - 38r + 16
C) 40r2 + 20r - 20
D) 40r2 + 60r + 20​

Answers

Answer:

Step-by-step explanation:

Nose

Need help plsssss !!!!

Answers

Answer: The answer is C

URGENT
which number produces a rational number when multiplied by 0.53?
A: π
B: 0.2645751311
C: √5
D: 5/7

Answers

Answer:

B

Step-by-step explanation:

Find the value of x. Round to the nearest tenth.

Answers

Answer:

14.86854, or 15

Step-by-step explanation:

The slope formula can be used to find the slope, m, of a line with points (L1, y1) and (22, 42).
Y2 - Yi
22 - 21
m
Which is an equivalent equation?
O Y1 = -m (22 – x1) + y2
yı = -m (x2 – 21) – Y2
Oyı = m (22 – 21) + y2
Oyı = m (22 – 21) – Y2

Answers

Answer: [tex](y-y_1)=m(x-x_1)\ or \ (y-y_2)=m(y-y_2)[/tex]

Step-by-step explanation:

Point slope form: [tex](y-b)=n(x-a)[/tex] , where n=slope , (a,b) is the point through which line passes.

If slope of the line = m and line passes through [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] :-

[tex](y-y_1)=m(x-x_1)\ or \ (y-y_2)=m(y-y_2)[/tex]

So, the equivalent equations are :

[tex](y-y_1)=m(x-x_1)\ or \ (y-y_2)=m(y-y_2)[/tex]

hiii please help! i’ll give brainliest if you give a correct answer tysm!

Answers

Answer:

B) 3 1/3

Step-by-step explanation:

To divide the fractions, simply follow these steps.

First, flip the second fraction, so that the numerator is the denominator, and the denominator is the numerator. Change the division sign into a multiplication:

(2/3)/(1/5) = (2/3) * (5/1)

Next, multiply straight across:

(2/3) * (5/1) = (2 * 5)/(3 * 1) = 10/3

Finally, simplify. Change the improper fraction into a mixed:

10/3 = 3/3 + 3/3 + 3/3 + 1/3 =  3 1/3

B) 3 1/3 is your answer.

~

Answer:

I got 3 1/3

Step-by-step explanation:

Also to divide fractions do.  Keep Change and Flip

Keep the first fraction, flip the divide sign to the multiply sign.  Then flip the other fraction.  Then multiply

Point R is located on segment QS. If QR = 10 and RS = 7, what is the measure of QS?

Answers

Answer:

QS = 17 units

Step-by-step explanation:

Given:

R located at QS

QR = 10

RS = 7

Find:

Measure of QS

Computation:

QS = QR + RS

QS = 10 + 7

QS = 17 units

The equation kx² + px + 5 = 0 has repeated real roots. Find k in terms of p

Answers

Answer:

k= -50/p

Step-by-step explanation:

Answer is worked out in the photo above.

Posted this question 1000times. Plz some answer plz plz i beg. Plz show all working, thank you sir

Answers

Answer:

[tex]\approx 26.16\:\mathrm{m}[/tex]

Step-by-step explanation:

Let [tex]h[/tex] be the height of the tree. In reference to the tree and bird, a right triangle is formed. We can write the following trig function for that right triangle:

[tex]\tan28^{\circ}=\frac{h}{15},\\h=15\tan28^{\circ},\\h\approx 7.98\:\mathrm{m}[/tex].

Now we can use this to find the hypotenuse of this triangle (the distance between the cat and the bird):

Let the distance between the cat and bird be [tex]k[/tex]. Then,

[tex]7.98^2+15^2=k^2,\\k\approx 16.99\:\mathrm{m}[/tex]. This is one side of the triangle that is formed by the cat, bird, and mouse.

The right triangle formed by the tree, cat, and mouse shares the height [tex]h[/tex] with the other right triangle, as we found earlier. Let [tex]l[/tex] represent the hypotenuse of this triangle or the distance between the cat and mouse. We then have the following trig function:

[tex]\sin 40^{\circ}=\frac{7.98}{l},\\l=\frac{7.98}{\sin40^{\circ}}\approx 12.41\:\mathrm{m}[/tex]. This is another side of the triangle that is formed by the cat, bird, and mouse.

The triangle that is formed by the cat, bird, and mouse has shares an angle of [tex]125^{\circ}[/tex] with the base of the auxiliary pyramid. The other angles, however, are not shared.

Since we have two sides and the angle between these two sides, we can use the Law of Cosines to find the other side (the distance between the mouse and bird). The Law of Cosines is given by:

[tex]m^2=k^2+l^2-2kl\cos M[/tex], where [tex]m[/tex] is the distance between the bird and the mouse and the other variables are defined above.

Plugging in values, we get:

[tex]m^2=16.99^2+12.41^2-2\cdot16.99\cdot12.41\cdot\cos 125^{\circ}[/tex]

Solving, we get:

[tex]m\approx \fbox{$26.16\:\mathrm{m}$}[/tex].

find the total surface area of the triangular prism

Answers

Answer:

[tex]1,008\:\mathrm{cm^2}[/tex]

Step-by-step explanation:

The total surface area of this triangular prism consists of three rectangles and two triangles. Adding the areas of each of these shapes allows us to find the total surface area of this 3D figure:

Area of both triangles:

[tex]2\cdot \frac{1}{2}\cdot12\cdot 14=168\:\mathrm{cm^2}[/tex]

Area of all three rectangles:

[tex]15\cdot 20 +13\cdot 20+14\cdot 20=840\:\mathrm{cm^2}[/tex]

Therefore, the total surface area of this figure is:

[tex]840+160=\fbox{$1,008\:\mathrm{cm^2}$} \: \checkmark[/tex]

where do you find the answers at

Answers

Answer:

Step-by-step explanation:

I find the answer at the search bar :)

Search bar was this a trick question lol

Distribute -5(m-2)

Help

Answers

Answer:

(-5*m)-(-5*2)

Step-by-step explanation:

Here, we want to use the distributivity property to evaluate the expression

We have this as;

(-5*m)-(-5*2)

Each of 3 bags contains x pencils. Tyler adds 2 more pencils to each bag. Altogether, the gift bags contain 12 pencils.

Please draw the tape diagram for the problem above

Answers

Answer:

Below

Step-by-step explanation:

ZX and zy or supplementary angles. zy measures 49 degrees what is the measure of ZX

Answers

Answer:

131˙

Step-by-step explanation:

Supplementary angles are angles that add up to 180˙. If you subtract 49 from 180, you get 131.

Brainliest? Maybe?

Explain how to find the constant rate of change from the verbal description below.

Joe can drive his motorcycle 124 miles in 2 hours. If he goes at a constant speed what is the constant rate of change? (solve it but also explain how you would solve it)

Answers

Answer:

62miles/1hr

Step-by-step explanation:

In order to get the rate of change I divided 124 miles by 2 hours to get 62 miles.

A breakfast menu liste 3 eggs with 2 sausage for $4.15 or 4 eggs with 1 sausage for $4.30 . What is the cost of 1 egg, and what is the cost for 1 sausage?

Answers

Answer:

Cost of 1 egg = x = $0.89

Cost of 1 sausage = y = $0.74

Step-by-step explanation:

Let the:

Cost of 1 egg = x

Cost of 1 sausage = y

A breakfast menu lists:

3 eggs with 2 sausage for $4.15

3x + 2y = 4.15......Equation 1

4 eggs with 1 sausage for $4.30 .

4x + y = 4.30...... Equation 2

y = 4.30 - 4x

We substitute 4.30 - 4x for y in Equation 1

3x + 2(4.30 - 4x) = 4.15

3x + 8.6 - 8x = 4.15

3x - 8x = 4.15 - 8.6

-5x = -4.45

x = -4.45/-5

x = $0.89

Solving for y

y = 4.30 - 4x

y = 4.30 - 4(0.89)

y = 4.30 - 3.56

y = $0.74

Therefore,

Cost of 1 egg = x = $0.89

Cost of 1 sausage = y = $0.74

19. If 1:3=4:x, then what is the value of x
9
12
4/3

15​

Answers

Answer:

Step-by-step explanation:

1 : 3 : : 4: x

Multiply 1 and x and multiply 3 and 4

x = 12

(-5/7-11/7 x=-y, 2y=7+5x)

Answers

Answer:

Solve the system of equations:

x= -3

y= -4

Step-by-step explanation:

This is right if x went with 11/17:

11/17x

I didn't know if they were separated or not

Find the missing slant height

Answers

Answer:

[tex]\ell=\frac{77}{4}[/tex]

Step-by-step explanation:

Because these two cones are similar, we can set up the following proportion:

[tex]\frac{11}{4}=\frac{\ell}{7}[/tex]

Solving, we get:

[tex]\ell=\frac{7\cdot11}{4},\\\ell=\fbox{$\frac{77}{4}$}[/tex].

X - 5 = -11

Solve the value of x.

Answers

X=-6 that should be the correct answer

Drag the labels to the table to solve the equation and plot the solution as a point on a number line. Not all labels will be used.

4x − 3 = 21

Answers

Answer:

First one is 4x = 24

Second one is x = 6

This one is 6

Answer:

Add 3 to both sides of the equation:

4x − 3 + 3 = 21 + 3

4x = 24

Divide both sides of the equation by 4:

4x/4 = 24/4

x = 6

The number line represents x-values, so the solution is at 6.

The line with the red colour dotted 6

Step-by-step explanation:

If it takes eight men ten hours to build a wall, how long would it take four men?

Answers

Answer:

20 bc if 8 men took 10 hours then 4 men would take double the time

Answer:

ha ha is it math question seriously or riddle if riddle the wall is already built by men they non time is taken by men.

Question 6 Multiple Choice Worth 5 points)
(04.07A LC)
Which equation does the graph below represent?
20
16
12
8
4
1
2
3
5
-5 -4 -3 -2 -1 0
4
-8
-12
-16
-20
y = a + x
y = 1 X
y = 4 + x
y = 4x

Answers

Answer:

The equation of the graph is;

y = 4·x

Step-by-step explanation:

The coordinates of two points, (x₁, y₁), and (x₂, y₂) respectively on the straight line graph are;

(-3, 12), and (2, 8)

The slope, m, of the straight line graph is given as follows;

[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Therefore, by substitution of the values, we have;

[tex]Slope, \, m =\dfrac{8-(-12)}{2-(-3)} = \dfrac{8 + 12}{2 + 3} =\dfrac{20}{5} = 4[/tex]

The equation of the graph in point slope form is therefore;

(y - 8) = 4×(x - 2)

y = 4·x - 8 + 8 = 4·x

y = 4·x.

what is the maximum value of f(x)=−4x2+4x−2?

Answers

Answer: -1

Step-by-step explanation: A typical quadratic equation is [tex]ax^{2} +bx+c[/tex] and the maximum value formula is -b/2a, so let plug it in -4/2(-4) which equals 1/2. Then let plug 1/2 into the equation,

-4(1/2)^2+4(1/2)-2=

    -1+2-2=

          -1

What is the domain of the function shown on the graph?

Answers

Domain is the input value, The x value)

The arrows on the graphed line mean the line continues in that direction,

There is arrows on both ends so the domain would be negative infinity to infinity.

The answer is B.

100 points! Will mark brainliest! Only answer if u know it. Random answers will be reported

Answers

Step-by-step explanation:

Hey there!

According to the question, you need to find out the distance from your friend's house to school.

Firstly figure out the coordinate of your school and school. Then use formula of distance.

So, we find the coordinates as (7,7) and (5,0).

So, x 1 = 7 y1= 7

x 2 = 5 y2 = 0

~ Use distance formula.

[tex]d = \sqrt{( {x2 - x1)}^{2} + ( {y2 - y1)}^{2} } [/tex]

~ Put all values.

[tex]d = \sqrt{ {(5 - 7)}^{2} + ( {0 - 7)}^{2} } [/tex]

~ Simplify it.

[tex]d = \sqrt{ {( - 2)}^{2} + {( - 7)}^{2} } [/tex]

[tex]d = \sqrt{4 + 49} [/tex]

[tex]d = \sqrt{53} [/tex]

D= 7.280

Therefore, the distance between your friend's house and your school is 7.3 units.

Hope it helps....

you need to find out the distance from your friend's house to school.

Firstly figure out the coordinate of your school and school. Then use formula of distance.

So, we find the coordinates as (7,7) and (5,0).

So, x 1 = 7 y1= 7

x 2 = 5 y2 = 0

~ Use distance formula.

~ Put all values.

~ Simplify it.

D= 7.280

Therefore, the distance between your friend's house and your school is 7.3 units

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