Answer:
8 cm.
Step-by-step explanation:
Area = length × width
Use the variable w instead of width.
Area = w × (w+3)
Substitute 40 for the Area
40 = w × (w + 3)
Create a table to find the greatest common factors of 40.
1 × 40, not it because 40 is 39 units greater than 1, not 3
2 ×20, not it because 20 is 18 units greater than 2, not 3
4 × 10, not it because 10 is 6 units greater than 4, not 3
5 × 8, correct because 8 is 3 units greater than 5
Now substitute 5 for w to check your answer
40 = 5 × (5 +3 )
40 = 5 × 8
40 = 40
The answer is correct.
Hope this helps!!!
A rectangle is a quadrilateral with 4 sides. In a rectangle, one side is longer than the other. The longer side is called the width and the shorter side is called the length.
The length of the rectangle is 8cm.
The formula for the area of a rectangle is given as :
Length x Width
From the question, the length is 3 more than its width. We can represent this mathematically as:
L = W + 3
Area of the rectangle = 40 sq. cm
Inputting this into the formula
(W + 3) x W = 40
W² + 3W = 40
W² + 3W - 40 = 0
Factorise
W² +8W - 5W - 40 = 0
W(W + 8) - 5(W + 8) = 0
(W + 8)(W - 5) = 0
To find W
W + 8 = 0
W = - 8 or
W - 5 = 0
W = 5 cm
Therefore, the width is 5cm.
To find the length, L = W + 3
L = 5 + 3
L = 8 cm
Therefore, the length is 8 cm.
To learn more, visit the link below:
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what is the equation of the line that is parallel to the given line and passes through the point (2, 3)?
Given problems:
Line parallel that passes through (2,3);
Solution:
To solve this problem, we need to first understand what parallel lines are.
A parallel line is any two line that does not meet at any point.
In order to achieve this, both lines must have the same slope.
So, we find the slope of the given line and write in the form for a straight line.
Slope of line = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
let x₁, y₁ = (-2, -1)
x₂, y₂ = (2 , -3)
Now input the parameters and solve for the slope;
Slope of line = [tex]\frac{-3-(-1)}{2- (-1)}[/tex] = [tex]\frac{-2}{3}[/tex]
Any line that would be parallel to this must have the same slope.
Equation of a straight line;
y = mx + c;
y and x are the coordinates;
m is the slope
c is the y-axis intercept;
From (2, 3);
y = 3 and x = 2; m = [tex]\frac{-2}{3}[/tex]
3 = [tex]\frac{-2}{3}[/tex] x 2 + C
3 = [tex]-\frac{4}{3}[/tex] + C
C = [tex]\frac{13}{3}[/tex]
So the equation of the line is;
y = [tex]\frac{-2}{3} x[/tex] + [tex]\frac{13}{3}[/tex]
Multiply through by 3;
3y = -2x + 13
The equation of the line is 3y = -2x + 13
Answer:
x + 2y = 8
Step-by-step explanation:
What would be the profit when the price is $35?
Step-by-step explanation:
The total expenses stay the same at $92,039.
The income changes to 12,000 × $35 = $420,000.
So the profit is $420,000 − $92,039 = $327,961.
2.1÷6 long division
Answer:
0.35
Step-by-step explanation
6 ) 2.1 ( 0.35 <------- Quotient.
18
30
30
...
2. A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. If the dean wanted to estimate the proportion of all students receiving financial aid to within 3% with 99% reliability, how many students would need to be sampled?
Answer:
The number of students to be sampled is [tex]n = 1789 [/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is E = 0.03
Generally the proportion of students that receive financial aid is mathematically represented as
[tex]\^ p = \frac{118 }{200}[/tex]
=> [tex]\^ p = 0.59[/tex]
From the question we are told the confidence level is 99% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 2.58 [/tex]
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p ) [/tex]
=> [tex]n = [\frac{2.58}{0.03} ]^2 * 0.59(1 - 0.59) [/tex]
=> [tex]n = 1789 [/tex]
Using the margin of error, it is found that 1033 students would need to be sampled.
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The dean randomly selects 200 students and finds that 118 of them are receiving financial aid, hence, the estimate is:
[tex]\pi = \frac{118}{200} = 0.59[/tex]
99% confidence level
So [tex]\alpha = 0.99[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so [tex]z = 2.575[/tex].
The sample size needed is n when M = 0.03, hence:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.59(0.41)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96\sqrt{0.59(0.41)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.59(0.41)}}{0.03}[/tex]
[tex]\sqrt{n}^2 = \left(\frac{1.96\sqrt{0.59(0.41)}}{0.03}\right)^2[/tex]
[tex]n = 1032.5[/tex]
Rounding up, it is found that 1033 students would need to be sampled.
A similar problem is given at https://brainly.com/question/25420216
According to Siri every 5 inches of the map represents 3 miles of trails in the park how many inches on the map represents 9 miles on the park trails
Answer:
15 inches
Step-by-step explanation:
If 3 miles represents 5 inches and you want to know what represents 9 miles Just multiply 5*3 to get 15
define Standard form of a linear equation in ur own words
Standard form of a linear equation is an equation that shows the form a straight line. It has three constants which are A,B, and C. The two variables being X and Y.
Here is the linear equation.
Ax+By=C
The ages of three siblings are all consecutive integers. The sum of their ages is 39. How old is the youngest sibling?
could anyone explain this in a 2 part answer
Answer:
Let x = the age of the youngest child
Let x + 1 = the age of the middle child
Let x + 2 = the age of the oldest child
x + x + 1 + x + 2 = 39
3x + 3 = 39
3x = 36
x = 12 years
Can someone please help. I'm offering a lot of points because this answer needs an explanation. Statement proof style would be helpful, but it's not totally needed
Answer:
See below
Step-by-step explanation:
Given∠A ≅ ∠B and CD⊥ABTo prove CD bisects ∠ACBSolutionAs CD⊥AB, ∠BDC = ∠ADC = 90°
∠BDC ≅ ∠ADC
∠BCD = 180 - (∠BDC + ∠DBC)and
∠ACD = 180 - (∠ADC + ∠DAC)We can substitute ∠ADC with ∠BDC and ∠DAC with ∠DBC
Then we get same equation for ∠BCD and ∠ACD
Therefore ∠BCD = ∠ACD = 1/2∠ACB
It proves that CD bisects ∠ACB
please do 10 and 11
20 points!!!
Answer:
10. It will take 14 minutes for the balloon's elevation to change by -315 feet
11. mm I'm not sure but this answer was on Brainly before and they got 4 1/2 hours
Step-by-step explanation:
Hope this helps sorry I took long lol
f(x)=-5x-4x^-3 Please Help!
Answer:
-:3"5'6:7;8\4-4-4-4✓
The value of the the expression:
50 times the sum of 64 and 36?
3,236
2,354
4,104
5,000
Answer:
5000
Step-by-step explanation:
Let's start by evaluating what we are given. 50 times the sum of 64 and 36. Ok, so 50 times which is the way to write x (multiply) and the sum of 64 and 36 is another way to write 64 + 36.
Lets put this together now!
50 x ( 64 + 36 ) = 50 x ( 100 )
= 5000
Bits are items of ________.
A. Biannual data
B. Bimodel data
C. Binary data
D. Binomial data
Answer:
C. Binary Data
Step-by-step explanation:
What would the phrase "three times the sum of a number and 4" look like as a
variable expression?
3x +4
O3(3x +4)
O3(x + 4)
3x -4
Determine the intercepts of the line
X-intercept: (__ , __)
Y-intercept: (__, __)
Answer:
x-int: (-1.2, 0)
y-int: (0, -0.7)
Step-by-step explanation:
The x-intercept is the x value when y = 0.
Another way to reword that is when the graph crosses the x-axis.
The y-intercept is the y value when x = 0.
Another way to reword that is when the graph crosses the y-axis.
According to the graph, when y = 0 and when the line crosses the x-axis, the x-value is -1.2. Therefore, our x-intercept is (-1.2, 0).
According to the graph, when x = 0 and when the line crosses the y-axis, the y-value is -0.7. Therefore, our x-intercept is (0, -0.7).
Please answer this correctly I only have a little bit of time
Answer:
1.Commutative
2.Associative
3.Distributive
4.Double Negative
Step-by-step explanation:
Hope this helps! :)
Answer:
1.commutative2.associative3.distributive4.double negetiveWhat is the distance between 2 and 3 on the number line? Write the integer only. *
Answer:
1
Step-by-step explanation:
The distance between any two numbers on the number line is their difference:
3 - 2 = 1
_____
Any two consecutive integers have a distance between them of 1 on the number line.
What is the answer to -5x-10<20
Answer:
your answer is x< -2.... because 1st we have to take common between 5x and 10.
(2t - 4)(3t + 3)
Find the product. Simplify for answer
✽ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ✽
[tex](2t-4)(3t+3)[/tex]
[tex]= (2t + -4) (3t + 3)[/tex]
[tex]= (2t) (3t) + (2t) (3) + (-4) (3t) + (-4) (3)[/tex]
[tex]= 6t^2 + 6t - 12t - 12[/tex]
[tex]= 6t^2 - 6t - 12[/tex]
➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ May ♡
Find the slope of each line.
Answer:
It is 1/2
Step-by-step explanation:
the rise is 2
the run is 4
2 over four simplifies to one half
The length of a rectangle is 3 inches more than it’s width. if the perimeter is 42 inches, find the dimensions of the rectangle
Answer:
Length = 9 in Width = 12 inStep-by-step explanation:
Length L = 3 + W
Perimeter P = 42 in
Perimeter = 2L + 2W
plugin values:
42 = 2(3 + W) + 2W
42 = 6 + 2W + 2W
42-6 = 4W
W = 36 / 4
W = 9
solve L by substituting the value of W=9 into the equation:
L = 3 + W
L = 3 + 9
L = 12
therefore, the dimensions of the rectangle:
Length = 9 in
Width = 12 in
The dimensions for the rectangle are 12 in and 9 in if the length of a rectangle is 3 inches more than its width. if the perimeter is 42 inches.
What is rectangle?It is defined as the two-dimensional geometry in which the angle between the adjacent sides are 90 degree. It is a type of quadrilateral.
It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
It is given that:
The length of a rectangle is 3 inches more than its width. if the perimeter is 42 inches.
Let l be the length and w be the width of the rectangle.
Length l = 3 + w
Perimeter P = 42 in
Perimeter = 2l + 2w
42 = 2(3 + w) + 2w
w = 36/4
w = 9 in
solve for l by substituting the value of w = 9 into the equation:
l = 3 + w
l = 3 + 9
l = 12 in
Thus, the dimensions for the rectangle are 12 in and 9 in if the length of a rectangle is 3 inches more than its width. if the perimeter is 42 inches.
Learn more about the rectangle here:
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Solve 2x+3y-z=-4
3x+2y+2z=14
x -3z=-13
Answer:
1. x = -3/2 y+ 1/2z - 2
2. x = -2/3y + -2/3z + 14/3
3. x = 3z - 13
Step-by-step explanation:
solve for x
Eva is reading a book that is 400 pages.She has read 336 pages so far.What percentage of the book does she have left to read?
Plz tell me the answer I need helpp
Answer:
Eva has 16% of the book left to read
Step-by-step explanation:
Answer:
16%
Step-by-step explanation:
400-336=64
64÷400= 0.16
0.16x100=16
16% is your answer
Find the number such that the sum of that number and 25 is 48
Answer:
x = 23
Step-by-step explanation:
x + 25 = 48
x = 23....
Answer:
23
Step-by-step explanation:
You subtract 25 from 48
48 - 25 = 23
Which of the following coordinates exists on the line y = 2x - 4?
O A. (1,-2)
O B. (-1,2)
O C. (-3,-5)
O D. (2,-4)
(1, -2) is the coordinates that exists on the line y = 2x - 4
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given is an equation of a line, we need to find that on which of the given points it lies,
So, we will put the points one by one, the point which stratify the equation will be the answer.
The equation :- y = 2x-4
1) (1, -2)
Put x = 1, y = -2 in the equation,
2(1)-4
= 2-4 = -2
LHS = RHS
Since, point (1, -2) satisfy the equation therefore, the line will pass through it.
Hence, (1, -2) is the coordinates that exists on the line y = 2x - 4
Learn more about equations, click;
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Original Function and Transformed function. what is the transformation?
Answer:
A function transformation takes whatever is the basic function f (x) and then "transforms" it (or "translates" it), which is a fancy way of saying that you change the formula a bit and thereby move the graph around. ... Moving the function down works the same way; f (x) – b is f (x) moved down b units.
your thinking
2. A shipping box should weigh 1.0 pound. If
there is a 10% error on the weight, what is the
range of acceptable weight?
Answer:
.9 pounds to 1.1 pounds
Step-by-step explanation:
10% of 1.0 is .1, so it allows for a .1 addition or subtraction to the weight of the box
Answer:
the answer is 0.9-1.0
Step-by-step explanation:
the answer is that because my teacher gave me the answer
PLZ HELP FAST
Which is closest to the area of a circle with a diameter of 6 inches?
Select one:
108 square inches
36 square inches
27 square inches
54 square inches
Jason left home for school at 7:30 a.m. and arrived at school at 8:35 a.m. how long did
The cost of an Uber ride can be modled by y = 3x + 5, where x is the number of miles driven. You paid $44 in a
cab fare, how many miles did you drive?
Answer:
13
Step-by-step explanation:
44=3x+5
44-5=39
39/3=13
Answer:
13 miles driven
Step-by-step explanation:
y = 3x + 5
Y is the amount we paid, so we insert 44 into the equation.
44 = 3x + 5
Any thing you do to one side of the equation, you do to the other side, so -5 from both sides.
44-5 = 39
5-5 = 0
So you are left with:
39 = 3x + 0 (So you can ignore the 0)
Like I said earlier, anything you do to one side of the equation you do to the other so divide both sides by 3:
39 divided by 3 = 13
3 divided by 3 = 1
So now you have:
13 = 1x
So x = 13 and that is how many miles you drove.
If this is confusing let me know
If a polynomial has four terms, 3x³ + 5x + 6x² + 10, which factoring method can be considered?
