The length of a rectangle is 3 more than 4timesthe width . If the length of the rectangle is 27 feet what is the width

Answers

Answer 1
To answer this question, you need to translate the description into a formula. The formula that can be made should be: length of rectangle= 3+ (4* rectangle width). You already know the length, so you can find the width by inserting it to the formula. The calculation would be:

Length= 3+ 4*width
27ft= 3ft+ 4*width
4*width= 27ft-3ft= 24ft
width= 6ft

Related Questions

Solve for c. a(b − c)=d

Answers

a(b - c) = d
ab - ac = d
-ac = -ab + d
ac = ab - d
ac/a = (ab - d)/a
c = (ab - d)/a

Your answer will be A. c = (ab - d)/a. Hope this helps!
Hello there!

a(b - c) = d
ab - ac = d
We need to add -ab to both sides
ab - ac - ab = d - ab
-ac = d - ab
To get c, we must divide both sides by -a
-ac/-a = (d - ab)/-a
c = (ab - d)/a

The correct answer is the first option.

Good luck!

Two thirds of a number is no more than -10

Answers

Let x be the number in the problem. When it states that x is "no more than -10", it means than it is less than or equal to -10. So, we have

[tex] \frac{2}{3} [/tex]x≤-10

In order to cancel out the [tex] \frac{2}{3} [/tex] on the left and isolate x, we multiply both sides by [tex] \frac{3}{2} [/tex] (since [tex] \frac{3}{2}[/tex]·[tex] \frac{2}{3} [/tex]=1). Thus, we have

x≤-10·[tex] \frac{3}{2} [/tex]=-15

Therefore, x≤-15

Is 0 prime odd or even prime or composite?

Answers

0 is a unique case. It is neither prime nor composite, and is neither odd nor even. Zero is an absence of value case which is not made from other numbers...and didn't appear in numbering systems until the past couple of thousand years...it's a weird concept!

Answer:

0 is nor prime or composite

Step-by-step explanation:

The definition of a prime number is a positive integer that has exactly two positive divisors. Therefore, the simplest reason why 0 is not prime is that 0 is not a positive integer, and the axiom says that all whole numbers greater than 1 are either prime or composite.

Long Division for a quadratic polynomial and binomial, please show your work!
Quadratic polynomial: x^2-x-6=f(x)
Binomial: (x-3)

Answers

answer is given above

[tex]\(x^2 - x - 6\)[/tex] can be expressed as the product of [tex]\((x - 3)\) and \((x - 2)\)[/tex]. The long division image is given below.

Long division for polynomials is similar to long division for numbers. We'll divide the quadratic polynomial [tex]\(f(x) = x^2 - x - 6\)[/tex] by the binomial [tex]\((x - 3)\)[/tex].

Here's a step-by-step breakdown of the process:

1. Start by dividing the highest-degree term of the dividend (in this case, [tex]\(x^2\)[/tex]) by the highest-degree term of the divisor (in this case, [tex]\(x\))[/tex]. This gives us [tex]\(x\)[/tex].

2. Multiply the divisor [tex]\((x - 3)\)[/tex] by the result from step 1, which is [tex]\(x\),[/tex] and write the result below the dividend, aligning like terms. So, [tex]\(x \cdot (x - 3) = x^2 - 3x\)[/tex].

3. Subtract the result from step [tex]2 (\(x^2 - 3x\))[/tex] from the dividend ([tex]\(x^2 - x - 6\)[/tex]). This gives us [tex]\(x^2 - x - 6 - (x^2 - 3x)\)[/tex], which simplifies to [tex]\(-x + 3x - 6\),[/tex] resulting in [tex]\(2x - 6\)[/tex].

4. Now, we repeat the process with the new expression [tex]\(2x - 6\)[/tex]. We divide the highest-degree term ([tex]\(2x\)[/tex]) by the highest-degree term of the divisor [tex](\(x\)),[/tex] which gives us [tex]\(2\).[/tex]

5. Multiply the divisor [tex]\((x - 3)\)[/tex] by the result from step 4, which is [tex]\(2\)[/tex], and write the result below the previous result: [tex]\(2 \cdot (x - 3) = 2x - 6\)[/tex].

6. Subtract the result from step [tex]5 (\(2x - 6\))[/tex] from the previous expression [tex](\(2x - 6\))[/tex], which results in [tex]\(0\)[/tex].

Since we have a remainder of [tex]\(0\),[/tex] this means that [tex]\(x^2 - x - 6\)[/tex] is evenly divisible by [tex]\((x - 3)\)[/tex], and the quotient is [tex]\(x - 2\).[/tex] The final result is:

[tex]\[ \frac{x^2 - x - 6}{x - 3} = x - 2 \][/tex]

This tells us that [tex]\(x^2 - x - 6\)[/tex] can be expressed as the product of [tex]\((x - 3)\) and \((x - 2)\)[/tex].

How do you solve this ?

Answers

The length is w+8 and the width is w.
Perimeter= 2(w+l)

256= 2(w+8+w)
256= 2(2w+8)
256= 4w+16
240= 4w
60= w

Final answer: Width= 60 ft, Length= 68 ft

width = w

 length = w+8

perimieter = 256 feet


formla for perimeter is p=2L+2w

so you have: 256 =2(w+8) +2w =

256 = 2w+16 +2w

256= 4w+16

240=4w

w=240/4 = 60

 width is 60 feet

length = 60+8 = 68 feet

Four times the difference of a number and seven is 32

Answers

as a formula, you're saying 4*(n-7)=32

This solves to n-7 = 8, so n=15

I NEED HELP ASAP

Definition: This is an expression that includes monomials, binomials and more. There is no limit to the number of terms.

Example: 2x+ 3y+ 4xy+ 5xyz What is the term?

Answers

I believe they mean polynomials. Monomials, binomials, trinomials, etc. are all examples of polynomial expressions similar to the example.

Y = -27x + 577, where x represents the number of weeks and y represents the amount of money left in her account. After how many weeks will Alma have $145 left in her account?

Answers

To solve this problem, plugin 145 where the y is located and then solve for x
y = -27x +577
145 = -27x +577
145 -577 = -27x
-432 = -27x
-432/-27 = -27x/-27
16 = x
x = 16
After 16 weeks she will have $145 dollars in her account.

Can someone help me with these maths questions? I totally don't get them.

Do the following coordinates lie on the following graphs?

1) y=2x+4 (7,20)
2) y=4x-14 (-1,-18)
3) y=5x-1 (0.5,2.5)
4) y=-2x+6 (0.8,5.4)
[tex] 5) y=\frac{1}{2}x+2 (0.7,1.6) [/tex]

Answers

1. 2(7) +4 = 18, does not = 20, does not lie on graph

2. 4(-1) -14 = -18, equals -18, does lie on the graph

3. 5(.5)-1 = 1.5, does not = 2.5, does not lie on the graph

4. -2(0.8)+6 = 4.4, does not = 5.4 does not lie on graph

5. 1/2(0.7) +2 = 2.35, does not = 1.6, does not lie on graph

A kennel owner needs 4 1/2 feet of wall space for each crate. How many crates can she fit along a 27 foot wall?

Answers

6 /////////////////////////////////////

The sum of the first and third of three consecutive even integers is 128. find the three even integers.

Answers

62, 64, and 66. 62+66=128

Final answer:

The three even integers are 62, 64, and 66.

Explanation:

The sum of the first and third of three consecutive even integers is 128. To find the three even integers, we start by letting the first integer be x. Because the integers are consecutive even numbers, the second integer will be x + 2 and the third will be x + 4. The sum of the first and third integers gives us the equation:

x + (x + 4) = 128

Solving this equation:

Combine like terms: 2x + 4 = 128.

Subtract 4 from both sides: 2x = 124.

Divide both sides by 2: x = 62.

So, the first even integer is 62. Consequently, the second is 62 + 2 = 64, and the third is 62 + 4 = 66. Therefore, the three consecutive even integers are 62, 64, and 66.

Find f(x) and g(x) so the function can be expressed as y=f (g (x)).
y=2/x^2 +3

Answers

Since f(g(x)) essentially means that we plug f(x) into what g(x) already is (e.g. if g(x) is x^2 and f(x) is x+1, then f(g(x)) is x^2+1). If g(x) is 2/x^2 (the first part of y) and f(x) is x+3, in f(g(x)) g(x) essentially replaces x to be (2/x^2)+3

An exhibit at Tabu World Square in Japan includes a scale model of the Empire State Building. The model was built using a scale of 1 m : 25 m. The height of the actual Empire State Building is 443.2 meters. What is the height of the model? Round your answer to the nearest thousanths place.

Answers

The scale is 1 m : 25 m.
The actual height = 443.2 m

Therefore the scaled height is 443.2/25 = 17.7280 m

Answer: 17.728 m (nearest thousandth)

PLEASE HELP?!

Both trapezoids are similar. The area of the larger trapezoid is 61 ft2. Which is the best approximation for the area of the smaller trapezoid?

39 ft2
34 ft2
49 ft2
44 ft2

Answers

39ft^2 is the answer

The best approximation for the area of the smaller trapezoid is 39 [tex]ft^2[/tex].

Since the trapezoids are similar, the ratio of their corresponding side lengths is constant. We know the base of the larger trapezoid is 30 ft and the smaller one is 24 ft. Therefore, the ratio of their bases is:

ratio of bases = [tex]\frac{30 ft}{24 ft}[/tex] = [tex]\frac{5}{4}[/tex]

The area of a trapezoid is given by:

Area = [tex]\frac{1}{2}[/tex] * base * height

For similar shapes, the ratio of their areas is proportional to the square of the ratio of their corresponding side lengths. In this case, the ratio of areas will be:

Ratio of areas = [tex](Ratio \ {of \ { bases)^2[/tex] = [tex]({\frac{5}{4} })^2[/tex] = [tex]\frac{25}{16}[/tex]

We know the area of the larger trapezoid is 61 [tex]ft^2[/tex]. Applying the ratio of areas:

Area of smaller trapezoid = (61 [tex]ft^2[/tex]) * [tex]\frac{16}{25}[/tex]

Area of smaller trapezoid ≈ 38.91 [tex]ft^2[/tex] ≈ 39[tex]ft^2[/tex]

What is the 100th term in the following arithmetic number pattern: 2,7,12

Answers

So the change in between terms is 5 so you would put 5x, then for the first term, which is 2, 5*1(x)(because it's first term) then the difference between 5-2(because it's the 2nd term) So you would plug 100 in for x so 5(100)-3=497. Hope this helped!

which ordered triple is a solution of this system 2x+y-z=7
-x-2y+4z=-15
x+2y-5z=17

Answers

We want to solve
2x + y - z = 7                (1)
-x - 2y + 4z = -15          (2)
x + 2y - 5z = 17             (3)

Add (2) and (3).
-x - 2y + 4z + (x + 2y - 5z) = -15 + 17
-z = 2
z = - 2

Therefore, (1) and (2) become
2x + y - (-2) = 7
2x + y = 5                          (4)
-x - 2y + 4(-2) = -15
-x - 2y -8 = -15
-x - 2y = -7
Multiply by 2.
-2x - 4y = -14                    (5)

Add (4) and (5).
2x + y + (-2x - 4y) = 5 - 14
-3y = -9
y = 3

From (4), obtain
2x + 3 = 5
2x = 2
x = 1

Answer: x = 1, y = 3, z = -2.

Graph the image of the given triangle after the transformation with the rule (x, y)→(y, x) .

Answers

See the attached figure. The original triangle is shown in red (triangle ABC). The line of reflection is the blue dashed line. This is the equation y = x. Reflecting triangle ABC over the line y = x results in the purple triangle A'B'C'. 

Note how the x and y values swap places. 
We have...
point A = (5,1) turn into point A' = (1,5)
point B = (8,1) turn into point B' = (1,8)
point C = (8,6) turn into point B' = (6,8)
The swap occurs because the rule (x,y) --> (y,x) tells this to happen. 

The purple triangle is the final answer.

Add the following military times: 0645 + 0745

Answers

14:30 is the answer.
(Aka 2:30 PM)

The perimeter of a rectangle is 44 inches, and its area is 105 square inches. find the length and width of the rectangle.

Answers

Perimeter = (Length + Width)x2
Area = LengthxWidth

P=(L+W)x2
P/2=L+W
L=P/2 - W

Area=(P/2 - W)(W)
A=WP/2-W^2
105=W(44)/2 - W^2
105=22W - W^2
W^2-22W+105=0
(W-7)(W-15)=0
Width= 7 or 15

A=LxW
105=Lx7
105/7=L
L=15

Length is 15 inches, Width is 7 inches.

What is the area of a circle with a radius of 14 feet? use 22/7 for π?

Answers

So the formula is pi*r^2 and if you plug that in it is 22/7* 14^2 and you get 616

There were three concerts in Lakeside. The first concert had 935 people in attendance. The second and third concerts each had a full house of 1,100. What was was the average number of people at the three concerts?

Answers

To find the average we need to sum the number of people in all the concert and divide it by the number of concert. Average = (935+1100+1100) / 3 = 3135 / 3 Average number of people in the three concerts = 1045 people

Solve the following problem for the roots by completing the square

3x^2 -12x = 9

Answers

3(x^2+3) is the answer you are looking for. :)
3x^2 - 12x = 9
Divide both sides by 3
x^2 - 4x = 3
To make a square with "x^2 - 4x", you need to have a "+ 4" after it so it can be simplified as (x-2)^2.  So add 4 to both sides.
x^2 - 4x + 4 = 7
(x-2)^2 = 7
x - 2 = (square root) of 7
x = 2 (+/-) (square root) of 7.
x = {-0.65, 4.65}

The solutions are -0.65 and 4.65.

If you like this answer, please give it Brainiest medal reward, thank you.

Amber has 4/5-pound bag of colored sand. She uses 1/2 of the bag for the project. How much sand does she use for the project?


Answers

3/10
4/5 - 1/2= 8/10-5/10

Answer:

[tex]\frac{2}{5}[/tex]-pound of sand

Step-by-step explanation:

We have been given that Amber has [tex]\frac{4}{5}[/tex]-pound bag of colored sand. She uses 1/2 of the bag for the project.

We need to find 1/2 'of' the 4/5 as:

[tex]\frac{4}{5}\times \frac{1}{2}[/tex]

[tex]\frac{4\times1}{5\times2}[/tex]

[tex]\frac{2\times1}{5\times1}[/tex]

[tex]\frac{2}{5}[/tex]

Therefore, Amber used [tex]\frac{2}{5}[/tex]-pound of sand for the project.

How do I do these only need to do 1 I just need to see how to do it!

Answers

Lets do the first one(7). Fist change 10x -2y = 3,which is in standard form to point slope form so you can see the slope.


10x - 2y = 3

-2y = -10x + 3

-2y/-2 = -10x / -2 + 3/-2

y = 5x - 3/2

The slope is the m in y = mx + b so our slope is 5x, well it wants you to find the equation of a line that passes through (0,1) that is parallel to the equation this (Parallel) mean has the same slope.The slope is 5. Now that we know the slope is 5 we can find the equation by using the point slope form of an equation of a line.

point slope form =  y – y1 = m(x – x1)

Remember m = slope = 5. Now plugin our x and y cord  from the point (0,1) and our slope of 5

y - y1 = m(x - x1)

y - 1 = 5(x - 0)

y - 1 = 5x - 0

y - 1+1 = 5x + 1

y= 5x + 1

So the point (0,1) passes through y = 5x + 1


Number 8 is already in slope intercept form so you don't have to do anything to find the slope. You can see that the slope is 7 so just plug your point into y - y1 = m(x - x1) and then put it into slope intercept form.

8) 

Point = (5,8)

Slope = 7

y - y1 = m(x - x1) 

y - 8 = 7(x - 5) 

y =  7x - 27

So for number 8 the point (5,8) passes through y = 7x - 27


(9) For nine they want an equation that is perpendicular, which means to flip the slope. For instance, if you have a slope of 2/5 the perpendicular slope would be 5/2. For 9 we see that the slope is 2/5 so its perpendicular slope would be 5/2. Now just plug your point into the point slope form equation.

Point = (-4, 6)

Slope = 2/5 

perpendicular slope = 5/2

y - 6 = 5/2(x - (-4))

y = 5/2 x + 16

So point (-4, 6) passes through y = 5/2 x + 16


(10) Point (4,1) passes through y = 7/5 x - 23/5









first off, let's keep in mind something, two lines that are parallel to each other, have the same slope, and two lines that are perpendicular to each other, have negative reciprocal slopes.

7)

so is parallel to 10x-2y=3... now, let's solve that for "y", to put it in slope-intercept form 

[tex]\bf 10x-2y=3\implies 10x-3=2y\implies \cfrac{10x-3}{2}=y \\\\\\ \stackrel{\textit{slope-intercept~form}}{\cfrac{5}{2}x-\cfrac{3}{2}}=y\impliedby \textit{slope is }\frac{5}{2}[/tex]

so then, we're looking for a line whose slope is 5/2 and passes (0,1)

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 0}}\quad ,&{{ 1}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{5}{2} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-1=\cfrac{5}{2}(x-0)\implies y-1=\cfrac{5}{2}x \\\\\\ \boxed{y=\cfrac{5}{2}x+1}[/tex]

8)

now, is parallel to  [tex]\bf y=\stackrel{slope}{7}x-6[/tex]  , now, that's already in slope-intercept form, so the slope we can see is just 7, so then.

we are looking for a line whose slope is 7 passes (5,8)

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 5}}\quad ,&{{ 8}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies 7 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-8=7(x-5)\implies y-8=7x-35 \\\\\\ y=7x-35+8\implies \boxed{y=7x-27}[/tex]

9)

well, this function is also already in slope-intercept form, so we can tell the slope is 2/5.

now, the line we're looking for, is perpendicular to it, so it has a negative reciprocal slope, let's check

[tex]\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{2}{5}\\\\ slope=\cfrac{2}{{{ 5}}}\qquad negative\implies -\cfrac{2}{{{ 5}}}\qquad reciprocal\implies - \cfrac{{{ 5}}}{2}[/tex]

so, we're looking for a line whose slope is -5/2 and passes (-4,6)

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ -4}}\quad ,&{{ 6}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies -\cfrac{5}{2} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-6=-\cfrac{5}{2}[x-(-4)] \\\\\\ y-6=-\cfrac{5}{2}(x+4)\implies y-6=-\cfrac{5}{2}x-10\implies \boxed{y=-\cfrac{5}{2}-4}[/tex]

10)

let's solve for "y" first

[tex]\bf 5x-7y=44\implies 5x-44=7y\implies \cfrac{5x-44}{7}=y \\\\\\ \stackrel{slope}{\cfrac{5}{7}}x-\cfrac{44}{7}=y[/tex]

now, let's find the negative reciprocal of that

[tex]\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{5}{7}\\\\ slope=\cfrac{5}{{{ 7}}}\qquad negative\implies -\cfrac{5}{{{ 7}}}\qquad reciprocal\implies - \cfrac{{{ 7}}}{5}[/tex]

so, we're looking for a line whose slope is -7/5 and passes (4,1)

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 4}}\quad ,&{{ 1}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies -\cfrac{7}{5} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-1=-\cfrac{7}{5}(x-4)\implies y-1=-\cfrac{7}{5}x+\cfrac{28}{5} \\\\\\ y=-\cfrac{7}{5}x+\cfrac{28}{5}+1\implies \boxed{y=-\cfrac{7}{5}x+\cfrac{33}{5}}[/tex]

If you only have a 1/3 measuring cup and a recipe calls for 8 2/3 cups of flour, how many 1/3 cups would you need to use?

Answers

(8+2/3) cups divided by 1/3 = 26 cups
8*3=24=24/3
24/3+2/3= 26/3
you are going to need 26 1/3 cups

Do you know the answer to this question

Answers

Answer:  [C]:  " f(x) = log₃ (x − 3) " .
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How to draw a grid of area of 12 square centimeters and a perimeter of 16 centimeters?

Answers

Alright, so if w is the width and l is the length, we have 2w+2l=16 (for the perimeter) and w*l=12. For 2w+2l=16 , we can subtract 2l from both sides to get 2w=16-2l, and then divide both sides by 2 to get w=8-l. Substituting that into w*l=12, we get (8-l)*l=12 and -l^2+8l=12. Subtracting 12 from both sides, we get -l^2+8l-12=0. Using the quadratic formula, we get
l=(-8+-sqrt(64-(4*-1*12))/-2=(-8+-sqrt(16))/-2= (-8+-4)/2=either 2 or 6. Plugging them into 8-l=w, we get that w is either 2 or 6 too, meaning that you just have to draw the grid with one side being the length of 2 and the other with the length of 6

Mason deposited $763.21 in a savings account that earns 1.7% simple interest. What is Mason's account balance after nine years?

Answers

The formula is
A=p (1+rt)
A future value?
P present value 763.21
R interest rate 0.017
T time 9 years

A=763.21×(1+0.017×9)
A=879.98

Hope it helps!

Explain why the following statement are equivalent 4(x+y)=4x+4y

Answers

They are equivalent because they are showing the Distributive Property....The Distributive Property shows that you can Distribute one number into another one, and still get the same answer.....So, you would have to do 4x+4y!!! I hope this helps!!!

The equation 4(x+y)=4x+4y represents the same value after solving.

What is Distributive Property?

This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.

Given:

We have 4(x+y)=4x+4y.

We have the Distributive Property

a x ( b+ c )= a x b + a x c

let x= 2 and y = 5

So, 4 (x+ y) = 4 (2+ 5)= 4(7) = 28

and, 4x+ 4y= 4(2)+ 4(5) = 8+ 20 = 28

Learn more about Distributive Property here:

https://brainly.com/question/5637942

#SPJ2

The minute hand of a clock is 4 inches long. how far does the tipof the minute hand move in 20 minnutes?

Answers

This is an arc length question, but it's a little hidden. The minute hand is the radius of the circle, so r=4. Next we need to know how much of the circle the tip of the minute hand will move through. Since there are 60 minutes in an hour, the minute hand will pass through 20/60=1/3 of the clock. Then we just use the circumference formula scaled by the amount of the clock we have:
[tex]l=2\pi(4)(\frac{1}{3})[/tex]
Final answer:

The tip of the minute hand moves approximately (8/3)π inches in 20 minutes, using the circumference of the circular path it follows and the proportion of the path covered in that time.

Explanation:

The student is asking about the distance traveled by the tip of the minute hand of a clock over a 20-minute period. To find the distance, we'll consider the movement of the minute hand as part of a circular path, which is described by the arc length of the circle segment.

The length of the minute hand, which is 4 inches, acts as the radius (r) of the circle. The minute hand completes one full rotation around the clock face in 60 minutes, so in 20 minutes, it covers one-third of a full rotation. We can find the arc length of the minute hand's path using the formula for the circumference of a circle (C = 2πr), multiplied by the fraction of the rotation:

Circumference: C = 2π(4 inches) = 8π inches

Arc Length for 20 minutes: (1/3) × 8π inches = (8/3)π inches

Therefore, the tip of the minute hand moves approximately (8/3)π inches in 20 minutes.

Other Questions
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