The area of a rectangle is 65 m2 , and the length of the rectangle is 3 m less than twice the width. find the dimensions of the rectangle.

Answers

Answer 1

x = width
2x-3 = length

[tex]x(2x-3) = 65\\ 2x^2 - 3x - 65 = 0 \\ D=b^2-4ac=(-3)^2-4*2*(-65)=529\\ x_{1,2}= \frac{-bб \sqrt{D} }{2a}= \frac{3б 23}{4} \\ x_1=-5 \ \ \O \\ x_2=6.5 \ \ [/tex]

width = 6.5 m
length = 2x-3 = 2*6.5 - 3 = 10 m

Answer 2

The dimensions of the rectangle are 10 meters and 6.5 meters

Let the width of the rectangle be represented by w.

The length of the rectangle will then be:

= 2w - 3

Area of the rectangle = 65m²

Note that length × width = Area

Therefore, w × (2w - 3) = 65

2w² - 3w = 65

2w² - 3w - 65 = 0

2w² - 13w + 10w - 65 = 0

2w(w - 6.5) + 10(w - 6.5) = 0

Therefore, w - 6.5 = 0

w = 0 + 6.5

w = 6.5

Width = 6.5 meters

Length = 2w - 3

Length = 2(6.5) - 3

Length = 13 - 3

Length = 10 meters.

The dimensions of the rectangle is 10 meters and 6.5 meters

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Related Questions

The area of a certain rectangle is 288 yd2. the perimeter is 68 yd. what are the dimensions of the rectangle?

Answers

P = 2(L + W)
P = 68
68 = 2(L + W)
68/2 = L + W
34 = L + W
34 - L = W

A = L * W
A = 288
W = 34 - L

288 = L(34 - L)
288 = 34L - L^2
L^2 - 34L + 288 = 0
(L - 16)(L - 18)

L - 16 = 0
L = 16

L - 18 = 0
L = 18

not exactly sure which (length or width) , but one is 16 yds and one is 18 yds

The dimensions of the rectangle are a length of 16 yds and a width of 18 yds.

What is the area of the rectangle?

The area of a rectangle is defined as the product of the length and width.

The area of a rectangle = L × W

Where W is the width of the rectangle and L is the length of the rectangle

Given that the perimeter is 68 yd

We know that the perimeter of a rectangle is:

P = 2(L + W)

∴ P = 68

68 = 2(L + W)

68/2 = L + W

34 = L + W

34 - L = W ....(i)

The area of a rectangle is:

A = L × W ....(ii)

∴ A = 288

Substitute the value W = 34 - L in equation (ii), and solve for L

288 = L(34 - L)

288 = 34L - L²

L² - 34L + 288 = 0

(L - 16)(L - 18)

L - 16 = 0 and L - 18 = 0

L = 16 and L = 18

Take L = 16 and substitute the value in the equation (i)

So, W = 34 - 16 = 18

Therefore, the rectangle's length is 16 yds and its width is 18 yds.

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Generally, how would one work out the surface area of a frustum?

Answers

see the formula in the picture

R is larger diameter, r is smaller diameter

The cost of painting a circular traffic sign is $3.50 per square foot. How much, to the nearest dollar, will it cost to paint the sign if its diameter measures 36 INCHES.

Answers

area of a circle = pi x r^2

using 3.14 for pi

radius = 36/2 =18

area = 3.14 x 18^2 = 1017.36 square inches

1 sq ft = 144"

1017.36/144 = 7.065 sq ft

7.065*3.50 = $24.73 to the nearest dollar = $25

An isosceles trapezoid has bases of 4 and 10. If the base angle is 45°, find the area.

A: 42 sq. units
B: 21√2 sq. units
C: 21 sq. units

Answers

Draw this trapezoid, let it be ABCD, where AB is the smaller base (=4) and
DC, the larger one (=10)
From A & B draw the altitude AA' & BB'. You notice that ABA'B' is a rectangle and A'B' = 4,. You conclude that DA' = B'C = 3 .
Now let's calculate the altitude AA'.
The right triangle ADA' is also an isosceles right triangle:
( angle DA'A=90, angle ADA' = 45 and angle DAA' =45) , then
DA' = AA' (altitude) = 3 units. Now we can calculate the area of the trapezoid:
Area = (B+b).H/2

Area = (4+10)x3/2 = 14x3/2 = 42/2 = 21 sq.unit

Answer:

21 sq. units

Step-by-step explanation:

a gas-filled balloon rises 40 feet in the 1st minute, 60 feet in the 2nd minute, and 80 feet in the 3rd minute, how many feet will the balloon rise during the 15th minute?

Answers

Let [tex]g_n[/tex] represent the number of feet that the balloon rises in the [tex] n^{th} [/tex] minute.

so

[tex]g_1=40[/tex] ft , means that in the 1st minute, the balloon rose 40 feet

[tex]g_2=60[/tex] ft, means : in the 2nd minute the balloon rose 60 feet

[tex]g_3=80[/tex]

we notice that each minute, the balloon rises a multiple of 20, feet:

[tex]g_1=40=2*20[/tex]

[tex]g_2=60=3*20[/tex]

[tex]g_3=80=4*20[/tex]

so it is clear that [tex]g_n=(n+1)*20[/tex]

during the 15th minute the balloon rises [tex]g_1_5=16*20=320[/tex](feet)

Answer: 320

A survey asked 30 people what their favorite genre of television broadcasting was, and the results were tabulated above. Find the probability that a person chosen at random was female, given that they like comedy. Round the answer to the nearest hundredth.

Answers

The probability that a person chosen at random is female, given they like comedy, is approximately 0.53 or 53% .

Next, we need to determine the total number of females. There are 16 females who like drama, and 4 females who like sports. Adding these together, we get 20 females in total.

Now, we can calculate the conditional probability that a female likes comedy given that she was chosen at random. The formula for conditional probability is P(A|B) = P(AnB) / P(B). In this case, event A is "being female" and event B is "liking comedy."

P(A|B) = (Number of females who like comedy) / (Total number of people who like comedy)

P(A|B) = 8 / 15

To express this as a percentage, multiply by 100:

P(A|B) * 100 ≈ 0.5333

Rounded to the nearest hundredth, the probability is 0.53 or 53%.

The probability that a person chosen at random is female, given they like comedy, is approximately 0.53 or 53% .

First, let's find the total number of females who like comedy. In the Venn diagram, there are 8 females who like comedy. There are also 7 males who like comedy. So, there are 15 people who like comedy in total.

Next, we need to determine the total number of females. There are 16 females who like drama, and 4 females who like sports. Adding these together, we get 20 females in total.

Now, we can calculate the conditional probability that a female likes comedy given that she was chosen at random. The formula for conditional probability is P(A|B) = P(AnB) / P(B). In this case, event A is "being female" and event B is "liking comedy."

P(A|B) = (Number of females who like comedy) / (Total number of people who like comedy)

P(A|B) = 8 / 15

To express this as a percentage, multiply by 100:

P(A|B) * 100 ≈ 0.5333

Rounded to the nearest hundredth, the probability is 0.53 or 53%.

Suppose you toss a coin 100 times and get 76 heads and 24 tails. based on these results, what is the probability that the next flip results in a head?

Answers

If it is a fair coin, the probability of the next flip resulting in "heads" is 50-50 or .5

The probability that the next flip results in a head is 50% or 0.5.

We have,

Total number of coins tossed = 100

Number of heads outcome = 76

Number of tails outcome = 24

Now,

The probability of getting heads in the tossing of coins 100 times.

= 76/100

= 0.76

= 76%

Now,

Generally for an unbiased coin.

The probability of getting a head in tossing a coin is 50%.

So,

Based on the results of the first 100 coin tosses, even if the probability of getting a head is 76% the probability that the next flip results in a head is still 50%.

Thus,

The probability that the next flip results in a head is 50% or 0.5.

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How can x2 = x2 + 2x + 9 be set up as a system of equations?

Answers

Final answer:

To set up x^2 = x^2 + 2x + 9 as a system of equations, we would have x^2 = x^2 + 2x + 9 and x = -4.5.

Explanation:

To set up x2 = x2 + 2x + 9 as a system of equations, we can separate it into two separate equations:

Equation 1: x2 = x2 + 2x + 9

Equation 2: 0 = 2x + 9

By rearranging Equation 2, we can rewrite it as:

x = -4.5

Therefore, the system of equations for x2 = x2 + 2x + 9 is: x2 = x2 + 2x + 9 and x = -4.5.

A number is chosen at random from the integers between 11 and 99, inclusive. what is the probability that the number contains the digit 2?

Answers

18 out of 88 or 20% chance

There are 26.2 in a marathon .Write the number of miles using a fraction.

Answers

Partitioning the value 26.2

26.2 = 20+6+0.2

The decimal value 0.2 is read two tenth = 2/10

Writing 26.2 as mixed numbers

[tex]26.2=26 \frac{2}{10} [/tex]

If we want to write this as an improper fraction, multiply 26 by 10 then add the 2 to get the numerator

[tex]26.2 = 26 \frac{2}{10}= \frac{262}{10}= \frac{131}{5} [/tex]

It doesn't matter which of the two points on a line you choose to call (x1, y1) and which you choose to call (x2, y2) to calculate the slope of the line.

A. True
B. False

Answers

ANSWER

A. True

EXPLANATION

Let

[tex](x_1,y_1) = (1,2)[/tex]

and

[tex](x_2,y_2) = (2,3)[/tex]

be two points on the straight line.

Then the slope is given by

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

This implies that,

[tex]m = \frac{3 - 2}{2 - 1} = \frac{1}{1} = 1[/tex]

Let us now choose it the other way round,

[tex](x_1,y_1) = (2,3)[/tex]
[tex](x_2,y_2) = (1,2)[/tex]

Then the slope is,

[tex]m = \frac{2 - 3}{1 - 2} = \frac{ - 1}{ - 1} = 1[/tex]

We still had they same result. Hence it doesn't matter which one you choose to call

[tex](x_1,y_1)[/tex]
and which to call

[tex](x_2,y_2) [/tex]

Answer:

the answer is true

Step-by-step explanation:

it's what I got

Branliest and 30 points to who answers first
To make one dose chispa put 2 drops of a herbal remedy into a 30 ml bottle and adds spring water he has now used 54 drops of the 120 that the full bottle contained how many more times can chispa use his herbal remedy

Answers

Assuming that the bottle contained only herbal remedy, we have 120-54=66. 66/2=33 uses left

Find the equation of the line specified.
The slope is 3, and it passes through ( -4, -7).

a.
y = 6x + 5
c.
y = 3x - 7
b.
y = 3x + 5
d.
y = 3x - 19

Please select the best answer from the choices provided

A
B
C
D

Answers

If slope is 3 then A answer is wrong for sure, and if the graph passes (-4; -7) point it means that when we put -4 instead of x we should get -7, if you try this method you will get the following answer:

B. y = 3x + 5

Answer:

Step-by-step explanation:

Edge 2021

What is the value of
x/3y, when x = 18 and y = 3?

Answers

assuming ya meant [tex]\frac{x}{3y}[/tex]

x=18 and y=3

[tex]\frac{18}{(3)(3)}=\frac{18}{9}=2[/tex]

this has been asked at least 3 times so far today

18/3*3 = 18/9 = 2

answer is 2

Let f(x) = 16x5 − 48x4 − 8x3 and g(x) = 8x2. Find f of x over g of x.

Answers

The correct answer is
2x^3-6x^2-x

It is given in the question that

[tex]f(x) = 16x^5 -48x^4-8x^3 \ and \ g(x) = 8x^2[/tex]

And we have to find the value of

[tex]\frac{f(x)}{g(x)}[/tex]

Substituting the values of two functions, we will get

[tex]=\frac{16x^5 -48x^4 -8x^3}{8x^2}[/tex]

8x^3 is common in the numerator, and on taking it out, we will get

[tex]= \frac{8x^3(2x^2 -6x-1)}{8x^2} = x(2x^2 -6x-1)[/tex]

And that's the required answer .

What is the slope of the line shown below?

Answers

Answer:

correct option is B) 2

Step-by-step explanation:

Slope of line is calculated by formula :-

Suppose two points on line are [tex](x_1, y_1) and (x_2 ,y_2)[/tex] then slope 'm' is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex].

We can see two points on line of graph are :- (-1, -4) and (2,2)

then slope will be calculated as,

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

since [tex]x_1 = -1, x_2 =2, y_1=-4\;and\; y_2=2[/tex]

now, put in formula

[tex]m=\frac{2-(-4)}{2-(-1)}[/tex]

[tex]m=\frac{2+4}{2+1}[/tex]

[tex]m=\frac{6}{3}[/tex]

[tex]m=2[/tex]

Hence, slope is 2 of the provided graph.

Therefore, correct option is B) 2

if two triangles share a common side what else must be true for the SAS triangle congruence theorem to apply

Answers

They must share the same angle postion

The conditions to be added are:

The two triangles have congruent angles between the sides that are not the common side.

The two triangles have congruent lengths for the sides adjacent to the congruent angles.

What is a triangle?

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

The SAS (Side-Angle-Side) triangle congruence theorem states that if two triangles have two sides and the included angle of one triangle is congruent to two sides and the included angle of the other triangle, then the two triangles are congruent.

Therefore, in addition to sharing a common side, the two triangles must have congruent angles between the sides that are not the common side. Specifically, the angle opposite the common side must be congruent in both triangles.

To summarize, for the SAS triangle congruence theorem to apply, the following conditions must be met:

The two triangles share a common side.

The two triangles have congruent angles between the sides that are not the common side.

The two triangles have congruent lengths for the sides adjacent to the congruent angles (the "included" side).

Thus,

The conditions to be added are:

The two triangles have congruent angles between the sides that are not the common side.

The two triangles have congruent lengths for the sides adjacent to the congruent angles.

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PLEASE HELP!!!! Solve the equation. Check for extraneous solutions. Type your answers in the blanks. Show your work.

x = _____ or _____

Answers

|4x+3|=9+2x if we square both sides, we can eliminate the absolute values signs...

16x^2+24x+9=81+36x+4x^2 subtract the right side from both sides

12x^2-12x-72=0 now we can factor

12(x^2-x-6)=0

12(x^2+2x-3x-6)=0

12(x(x+2)-3(x+2)=0

12(x-3)(x+2)

So:

x= -2 or 3

Answer:

-3

Step-by-step explanation:

The standard form of the equation of a parabola is x=y^2+6y+1. What is the vertex form of the equation?
A. X=(y+3)^2-8
B. X=(y+3)^2-5
C. X=(y+6)^2-35

Answers

A. x = (y+3)^2-8 is the correct answer.
What you want to do is get the quadratic (y^2+6y+1) into it's root factor form, in other words, the quantity of (y+what) squared will equal y^2+6y+1. Well it's not a perfect square so we'll have to play around with it a little.
In the format ay^2 + by + c, completing the square first requires finding out what value would do that: c = (b/2)^2 = (6/2)^2 = 3^2 = 9
So we need y^2+6y+1 to have the last number (c) to equal 9 to have (y+b/2)^2, or (y+3)^2
How do we get 9 down to the 1 that we have for c?? 9-1=8, so just subtract 8.
That means that y^2+6y+1 is the same as (y^2+6y+9)-8, and y^2+6y+9 = (y+3)^2, so now we have: y^2+6y+1 = (y+3)^2-8, which is answer [A]

what is the vaule of 3.85+0.004+0.117 ?

Answers

3.85+0.004+0.117=3.971

HELPPPPPP make sure your right !:)

Answers

To find your constant of variation, you just need to figure out what you multiply the x by in order to get f(x). In other words, what do you multiply the 3 by to get 6? What do you multiply the 7 by to get 14? Another way to think of it is to divide f(x) by the x to get your constant.

what is the greatest integer that satisfies the inequality 3x-4≤8 ?
A.4
B.5
C.6
D.7

Answers

3x - 4 ≤ 8
3x ≤ 12
x ≤ 4

answer

A.4

To figure this out, we need to solve for the inequality. A quick way is to plug in an answer choice for x.
For example, answer choice "A.)";
3(4) -4 <_ 8
We plugged in 4 for x.
Let's see if A.) is correct.
3(4) -4 <_ 8
12 - 4 <_ 8
8 <_ 8

This is the GREATEST possible integer, as the question asks for what the highest possible number would match the inequality.

Your correct answer choice is "A.)"

I hope this helps!

you invest 2,600 in an account that pays an interest rate of 8.5% compounded continuously. Calculate the balance of your account after 5 years

Answers

The formula is
A=p e^rt
A future value?
P present value 2600
R interest rate 0.085
T time 5years
E constant
A=2,600×e^(0.085×5)
A=3,976.94

Express the sum of 8.79 m and 6.0 m using the correct number of significant digits.

Answers

6.0 has only one digit, the least. Now 8.78 has two, but can't be written as 8,7, one needs to round it to one digit:

8.8 in this cas, so

8.79 + 6.0 = 8.8 + 6.0 = 14.8

14.8 is the answer

Answer:

The sum of the numbers is [tex]8.79+6.0=14.79[/tex]

Step-by-step explanation:

To find : Express the sum of 8.79 m and 6.0 m using the correct number of significant digits.

Solution :

Writing the sum of the numbers according to significant digits by writing in their place value,

8 . 7 9

+6 . 0 0

----------

14 . 7 9

Therefore, The sum of the numbers is [tex]8.79+6.0=14.79[/tex]

1 oz of walnuts were mixed with 4 oz of peanuts which cost $4/oz to make mixed nuts which cost $5/oz. what is the price per oz of walnuts

Answers

Call w the unknwon price of the walnuts, then:

total cost of walnuts = 1oz * w

Total cost of peanuts = 4 oz * $4/oz = $16

Total cost of nuts = 5oz * $5 /oz = $25

=> 1oz*w + $16 = $25 => w = ($25 - $16) /1oz = $9/oz

Verfify:

1oz * $9/oz + 4oz * $4/oz = $9 + $16 = $25, which is equal to 5oz * $5/oz.

Answer: $9 per oz.

(04.02 LC)

The graph represents function 1 and the equation represents function 2:

Function 2
y = 3x + 1

How much more is the rate of change of function 2 than the rate of change of function 1?
1
2
3
4

Answers

The graph is the horizontal line:

y=3 it has a slope of zero.

Function 2 is

y=3x+1, it is in slope-intercept form, y=mx+b where m is the slope and b is the y=intercept so in this case it has a slope of 3.

So the difference in slopes is 3-0=3

Final answer:

The rate of change of function 2 is 3 times greater than the rate of change of function 1.

Explanation:

The rate of change of a function measures how much the output of the function changes when the input changes by 1 unit. In function 1, since the graph is a straight line, the rate of change is constant. We can find the rate of change of function 1 by finding the slope of the line, which represents the rate of change. In function 2, the equation is y = 3x + 1, so the rate of change is 3. Therefore, the rate of change of function 2 is 3 times greater than the rate of change of function 1.

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Find the area of the triangle with the given measurements. round the solution to the nearest hundredth if necessary. b = 107°, a = 10 cm, c = 22 cm

Answers

Answer:

105.19 cm²

Step-by-step explanation:

The applicable area formula is ...

area = (1/2)ac·sin(B) = (1/2)(10)(22)sin(107°) ≈ 105.19 cm²

Solve the problem by writing an inequality. A club decides to sell T-shirts for $12 as a fund-raiser. It costs $20 plus $8 per T-shirt to make the T-shirts. Write and solve an equation to find how many T-shirts the club needs to make and sell in order to profit at least $100. Show your work.

Answers

An algebraic equation containing an inequality may contain symbols such as <, >, ≤ and ≥. You should know the concept of profit first. Profit is the net income you acquired by getting the total revenue, and subtracting from it all the fixed and variable costs. So, in equation, that would be

Profit = Revenue - (Fixed Cost + Variable Cost)

You should note that the limit for profit is at least $100. So that means it can be more than $100 but can't be less than. Therefore, the symbol to be used is greater than or equal to, symbolized by ≥. Then the equation is

12x - (20 + 8x) ≥ 100, where x represents the minimum number of t-shirts to reach a profit of at least $100. Solving the equation,

12x - 20 - 8x ≥ 100
12x - 8x ≥ 100 + 20
4x ≥ 120
x ≥30

Therefore, the club needs to sell at least 30 shirts.

Which is the best approximation for the value of √102?
A.10
B.11
C.50
D.51

Answers

10, because when you use a scientific calculator you get 10.09950494
which would be round to 10 because after the decimal the number is 0 below 5 so 10 stays as 10

We know that √100 = 10,
so √102 is approximately 10

A researcher wishes to find out whether giving a student $1 million in cash will improve or ruin the student's grades in school. A high school class consists of the 8 students numbered in the following list. 0 Juanita 1 Tuan 2 Harry 3 Greta 4 William 5 Hiroshi 6 Betty 7 Jane Help the researcher by using the line from a table of random numbers (shown below) to assign 4 of these students to the treatment group. 39661 55832 02589 52612 25414 19879 60880 30641 55259 35324 Which students go in the treatment group?

Answers

Answer:

Greta, Betty, Tuan and Hiroshi

Step-by-step explanation:

Start from the beginning:

3 - Greta

Then, continue with the next numbers:

9 - skip (there is no student numbered with a 9)

6 - Betty

6 - skip (Betty is already chosen)

1 - Tuan

5 - Hiroshi

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