a rectangle with a diagonal of length x is twice as long as it is wide. what is the area of the rectangle?
Answers
The area of the rectangle whose diagonal is twice its width is (x²√3)/4 square units.
What is the Area of Rectangle?The area of rectangle is defined by the product of its length and width. Mathematically-
Area [A] = Length [L] x Width [W]
Given is a rectangle whose diagonal is twice as long as it's width. From this, we can write -
Width = w
Length of diagonal = x = 2w
Assume that the length of the rectangle is L. Using the Pythagoras theorem in the triangle ΔABC, we get -
AC² = AB² + BC²
x² = L² + w²
(2w)² = L² + w²
4w² = L² + w²
L² = 3w²
L = w√3
Now, the width of rectangle is 'w' and its length is 'w√3'. Its area will be-
Area = length x width
A = w√3 × w
A = w²√3
Now, length of diagonal → x = 2w. So, we can write -
w = x/2
Therefore, the area will be -
A = (x/2)²√3 = (x²√3)/4
Therefore, the area of the rectangle whose diagonal is twice its width is (x²√3)/4 square units.
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Related Questions
For each function, find the vertex, the axis of symmetry, the y-intercept, the x- intercepts (if any), whether the parabola opens upward or downward, the intervals on which the function is increasing or decreasing, the maximum or minimum value, and the range. Then sketch the graph. y = -2(x + 3)² + 8
Answers
Given parabola [tex]y=-2(x+3)^{2} +8[/tex] have vertex (-3,8)
axis of symmetry :x=-3
x intercepts (-1,0),(5,0)
y intercepts (0,-10)
Maximum value (-3,8)
Range is y[tex]\leq 8[/tex] or (-∞,8]
Parabola is increasing in (-∞,-3) and decreasing in (-3,∞)
How to identify parabola type from vertex form and its attributes?
The parabola equation y=ax²+bx+c
The parabola equation in its vertex form is
y = a(x - h)² + k, where
a is same as the a coefficient in the standard form;
(h, k) is coordinates of the vertex of parabola
h and k can be calculated as
h = - b/(2a)
k = c - b²/(4a)
If a is negative the parabola opens downward and if a is positive the the parabola opens upward
Axis of symmetry : x= h
For a parabola y=ax²+bx+c if a<0 then the range is y [tex]\leq k[/tex] and if a>0 then range is y[tex]\geq k[/tex]
For Maximum and minimum value , if a<0 then vertex is the maximum value and if a>0 then vertex is the minimum value.
For given equation [tex]y=-2(x+3)^{2} +8[/tex]
As this equation is in vertex form
h=-3, a=-2, k=8
Therefore, vertex = (-3,8)
For x intercept put y=0
Then [tex]y=-2(x+3)^{2} +8\\y\\=-2x^{2} -12x-10\\y=0\\\\x=-1,-5\\put x=0 \\y= -10[/tex]x intercepts (-1,0),(5,0)
y intercepts (0,-10)
Axis of symmetry : x= -3
[tex]y=-2(x+3)^{2} +8\\y=-2x^{2} -12x-10[/tex]
As a is negative therefore range is y[tex]\leq 8[/tex] or (-∞,8]
As a is negative therefore vertex (-3,8) is the maximum value
f'(x)= -4x-12
f'(x)=0 gives x= -3
f'(x)>0 in (-∞,-3), parabola is increasing in (-∞,-3)
f'(x)<0 in (-3,∞), parabola is decreasing in (-3,∞)
Please find the graph attached.
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gina visits her local farm to buy apples oranges to make a fruit salad. she has 10.00 to spend.
Answers
Based on the fact that Gina has $10.00 to spend, if she only buys oranges, the number of oranges she can buy is 29.41176 oranges.
How to find the number of oranges?The number of oranges that Gina can buy when she visits her local farm to buy apples and oranges for a fruit salad can be found as:
= Amount that Gina has to spend / Price of oranges
Solving for the total amount of oranges gives:
= 10 / $0.34
= 29.41176 oranges.
The full question is:
Gina visits her local farm stand to buy apples and oranges to make a fruit salad. She has $10.00 to spend. If she buys only oranges and oranges are $0.34 how much oranges can she buy
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Cyndee wants to invest $50,000. Her financial planner advises her to invest in three types of accounts: one paying 3%, one
paying 5%, and one paying 6% simple interest per year. Cyndee wants to put twice as much in the lowest-yielding, least-risky
account as in the highest-yielding account. How much should she invest in each account to achieve a total annual return of
$2120?
Answers
Answer:
$25,333.33 at 3%$12000 at 5%$12,666.67 at 6%Step-by-step explanation:
Cyndee invests $50,000 in accounts earning 3%, 5%, and 6% annually, for a total annual return of $2120. She puts twice as much in the first account as in the third. You want to know the amount invested in each account.
SetupLet x represent the amount invested in the third account. Then 2x is the amount invested in the first account, and (50000 -3x) is the amount invested in the second account. The total return is ...
0.03(2x) +0.05(50000 -3x) +0.06(x) = 2120
SolutionSimplifying the equation gives ...
-0.03x +2500 = 2120
380 = 0.03x . . . . . . . . . . add 0.03x-2120
12,666 2/3 = x . . . . . . . divide by 0.03
2x = 25,333 1/3
50000 -3x = 12,000
Cyndee should invest 25,333.33 at 3%, $12,000 at 5%, and $12,666.67 at 6%.
the weight of an organ in adult male has a bell shaped distribution with a mean of 300 grams and a standard deviation of 25 grams. Use the empirical rule to determine the following:
a.) About 95% of organs will be between what weights?
b.) What percentage of organs weighs between 225 grams and 375 grams?
c.) What percentage of organs weighs less than 225 grams or more than 275 grams?
d.) what percentage of organs weighs between 275 grams and 275 grams?
Answers
Using the Empirical Rule, it is found that:
a) About 95% of the organs will be between 250 and 350 grams.
b) 99.7% of organs weighs between 225 grams and 375 grams.
c) 84.15% of organs weighs less than 225 grams or more than 275 grams.
d) 0% of organs weight exactly 275 grams.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.95% of the weights are within 2 standard deviations of the mean, hence:
300 - 2 x 25 = 250 grams.300 + 2 x 25 = 350 grams.About 95% of the organs will be between 250 and 350 grams.
For item b, the amounts are within 3 standard deviations of the mean, hence:
99.7% of organs weighs between 225 grams and 375 grams.
For item c, considering the symmetry of the normal distribution, we have that:
0.5 x 0.003 = 0.15% weigh less than 225 grams.0.5 x 68% + 50% = 84% weight more than 275 grams.Hence:
84.15% of organs weighs less than 225 grams or more than 275 grams.
For item d, considering that the normal distribution is continuous, the percentage of an exact value is 0, hence:
0% of organs weight exactly 275 grams.
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In 1985, there were 326,030 cell phone subscribers in the United States. By 2008, the number of cell phone subscribers increased to 262,359,000. What is the geometric mean annual increase for the period?
Answers
33.7618% is the geometric mean annual increase for the period
Rate of Increase Over Time(GM)=[tex]\sqrt[n]{value end period / value start period }[/tex] -1
In 1985, there were 326,030 cell phone subscribers in the United States. By 2008, the number of cell phone subscribers increased to 262,359,000. we have to find the geometric mean annual increase for the period
from 1885 to 2008 that is (2008- 1885=23 ) in 23 years the GM become
therefore n= 23
value of start period = 326030
value of end period = 262359000
rate of increase over time GM= [tex]\sqrt[23]{262359000/326030} -1[/tex]
= 1.337618 -1
=0.337618
rate of increase is 33.7618% per year
33.7618% is the geometric mean annual increase for the period
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Someone can help me please
Answers
4-3i^2
Step-by-step explanation:
(2-3i)(2-3i)
4-6i-6i+3i^2
3i^2-12i+4
Aisha drove 17 miles in 3 hours. On average, how fast did she drive, in miles per
hour? Enter your answer as a whole number, proper fraction, or mixed number in
simplest form.
Answers
Answer: 5.6 repeating
Step-by-step explanation: No explanation added.
At the arcade, Ryan, Sara, and Tim played video racing games, pinball, and air hockey. Ryan spent $6 for 6 racing games, 2 pinball games, and 1 game of air hockey. Sara spent $12 for 3 racing games, 4 pinball games, and 5 games of air hockey. Tim spent $12.25 for 2 racing games, 7 pinball games, and 4 games of air hockey. How much did each of the games cost?
Answers
Answer: Racing $.50
Pinball $.75
Air Hockey $1.50
How to find the slope of the line that passes through the points (−2,3) and (5,−7)
Answers
Answer:
[tex]\frac{-10}{7}[/tex]
Step-by-step explanation:
Use the formula
m= [tex]\frac{y2-y1}{x2-x1}[/tex]
another way to say this is Δy divided by Δx
Δ means "change in"
m = slope
The y2 value is -7
The y1 value is 3
The x2 value is 5
The x1 value is -2
Plug those values in the formula
m = [tex]\frac{(-7)-3}{5-(-2)}[/tex]
Simplify
m = [tex]\frac{-10}{7}[/tex]
The slope is [tex]\frac{-10}{7}[/tex]
Given the function g(x)=11x^2+28x, solve for g(x)=−12.
Answers
Answer: -2, -6/11
Step-by-step explanation:
[tex]11x^2 +28x=-12\\\\11x^2 +28x+12=0\\\\(11x+6)(x+2)=0\\\\x=-2, -6/11[/tex]
How many bacteria are in the Petri dish after 120 minutes ?
Answers
Answer:
D. [tex]2^9[/tex]
Step-by-step explanation:
[tex]2^6*2^3 = 2^9[/tex]
We can just add the exponents together.
If it were continued another 120 minutes past this, it would be
[tex]2^9*2^3 = 2^1^2[/tex]
write an equation using f(x) notation to show how the numbers in the domain and the range are related {(1,2), (-2,-4), (3,6), (0,0)
Answers
Answer:
f(x) = 2x
Step-by-step explanation:
It is obvious that the relationship between x and y is y = 2x from the numbers given
So equation is f(x) = 2x
Solve the following compound inequality. Graph the solution.
5x2-30 and 5x ≤ 15
What is the solution? Select the correct answer below and, if necessary, fill in the answer boxes within your choice.
OA. xs
OB. xs
OC. x2
OD. SXS (Type integers or decimals.)
E. The compound inequality has no solution.
OF. The solution is all real numbers.
XXXB
or x2 (Type integers or decimals.)
(Type an integer or a decimal.)
(Type an integer or a decimal.)
Answers
The solution to the inequality is x ≤ 3
How to solve the compound inequality and graph the solution?The compound inequality is given as:
5x ≤ -30 and 5x ≤ 15
Divide both sides of the individual inequality in the compound inequality by the coefficient of the variable x
So, we have
x ≤ -6 and x ≤ 3
One of the above inequalities can be true
x ≤ 3 is a proper set of x ≤ -6
So, the solution to the inequality is x ≤ 3
See attachment for the graph of the inequality
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If Cindy shoots a ball at a basket 40 times
and scores 15 times, what is the
experimental probability of Cindy scoring?
Answers
Experimental probability of Cindy scoring=0.375
Probability:
Probability is always a number between 0 and 1, where 0 means an event is impossible and 1 means an event is certain.
The probabilities in a probability model must sum to 1.
When the outcomes of an experiment are all equally likely, we can find the probability of an event by dividing the number of outcomes in the event by the total number of outcomes in the sample space for the experiment.
To find the probability of the union of two events, we add the probabilities of the two events and subtract the probability that both events occur simultaneously.
To find the probability of the union of two mutually exclusive events, we add the probabilities of each of the events.
The probability of the complement of an event is the difference between 1 and the probability that the event occurs.
In some probability problems, we need to use permutations and combinations to find the number of elements in events and sample spaces.
Formula :
probability of an event with equally likely outcomes : [tex]\frac{n( experimental-event )}{n(total no. of event )}[/tex]
Given :
Total no. of event =Cindy shoots a ball at a basket 40 times
experimental event = 15 times
[tex]P(E)= \frac{15}{40} \\P(E)=\frac{3}{8} \\P(E)= 0.375\\[/tex]
experimental probability of Cindy scoring=0.375
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Which of the following expressions is equivalent to 9x-27
Answers
Answer:
3
Step-by-step explanation:
9x-27=0
+27. +27
9x=27
x=3
A5.1 m long ladder is leaning against a
wall. The wall stands perpendicular to the
ground. The base of the ladder is 1.8 m
away from the wall.
Work out the size of the acute angle that
the ladder makes with the ground.
Give your answer in degrees to 1 d.p.
Answers
The acute angle the ladder makes with the ground is 69.3 degrees.
How to find the acute angles formed from the right triangle ?The ladder is 5.1 m and it is leaning against a wall.
The wall is perpendicular to the ground.
This means the ground forms 90 degrees with the wall.
This situation forms a right angle triangle.
Therefore, the acute angle the ladder forms with the ground can be found as follows:
Using trigonometric ratios,
cos ∅ = adjacent / hypotenuse
where
∅ = acute angle
Therefore,
adjacent side = 1.8 m
hypotenuse side = 5.1 m
Hence,
cos ∅ = 1.8 / 5.1
∅ = cos⁻¹ 0.35294117647
∅ = 69.3326835065
∅ = 69.3°
Therefore, the acute angle the ladder makes with the ground is 69.3 degrees.
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6. Reggie went to the grocery
store and purchased several
items. The cereal he bought cost
$2.10, which was twice as much as
the eggs. What was the price of the
eggs?
Answers
eggs = $2.10 divided by 2
2.10/2=1.05
price of eggs = $1.05
need help asap please
Answers
Answer:
3/30 for 66 lo siento I core help you
Which is the mean? a density curve that models the distribution of a quantitative variable shown here. identify the location of the mean and median by letter. justify your answer.
Answers
The location of the mean and median by letter are C and B, respectively
How to identify the location of the mean and median by letter?The given parameter is the density curve that models the distribution of a quantitative variable
From the density curve, we can see that:
The density curve is a right-skewed distribution
In a right-skewed distribution, the median is the middle line and the mean is to the right of the median
This means that
Median = B
Mean = C
Hence, the location of the mean and median by letter are C and B, respectively
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simplify (2^4)^-1. Answer options: 1 over 2^-4, 1 over 2^4, -2^4, and 2^3
Answers
[tex]\frac{1}{2^{4} }[/tex] is simple form of the equation.
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.A linear equation with one variable is one that contains just one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.Simply solve this equation = [tex](2^{4}) ^{-1}[/tex]
multiply the powers = [tex]2^{-4}[/tex]
now right on simple form = [tex]\frac{1}{2^{4} }[/tex]
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I need help I dot understand someone explain it step by step
Answers
Chloe reads 7 pages of a mystery book in 9 minutes. What is her average reading rate in pages per
minute?
Answers
Answer:
1.25
Step-by-step explanation:
you have to take the 9 pages and divide by 7 and then divide that by 60 and u get 1.25
Leah is training to run half marathon Her goal For training is to run 20 miles a week. she ran 3 1/2 Miles on Monday 4. 3/4 miles on Tuesday 5 miles on Wednesday And 4 miles On Thursday. how Many Miles will She Need to run On Friday In Order to meet her goal?
Answers
The number of miles she should run on Friday is 2 3/4 miles.
Given that, Leah is training to run a half marathon her goal training is to run 20 miles a week. she ran 3 1/2 miles on Monday 4 3/4 miles on Tuesday 5 miles on Wednesday and 4 miles on Thursday.
We need to find how many miles will she need to run on Friday in order to meet her goal.
How to add mixed fractions?Follow these steps to add mixed fractions:
Add the whole numbers together. Find the lowest common denominator (LCD) of both fractions. The LCD is the lowest number that is evenly divisible by both numbers.Convert the fractions to have the LCD as their denominator.Once you have a common denominator, the fractions can be added by simply adding the numerators.Now, the number of miles she ran together from Monday to Thursday
=3 1/2 + 4 3/4 + 5 + 4 =(3+4+5+4)(1/2 + 3/4)
=16 (2/4 + 3/4)
=16 5/4
=17 1/4
Remaining miles = 20-17 1/4
=20-69/4
=(80-69)/4
=11/4
=2 3/4
Therefore, the number of miles she should run on Friday is 2 3/4 miles.
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Ruby looks over the edge of her boat and sees fish 0.4 meter below the surface of the water. If Ruby holds a 1-meter long net at 0.5 meter above sea level, What will be the answer?
Answers
It should be noted that Ruby will be able to reach the fish
What is sea level?It should be noted that sea level simply means the sea base level that is used for measuring the elevation and the depth on the Earth.
It should be noted that Ruby looks over the edge of her boat and sees fish 0.4 meter below the surface of the water and Ruby holds a 1-meter long net at 0.5 meter above sea level.
It should be noted that he will be able to each the fish. This will be illustrated as:
=1m - (0.4 + 0.5)
= 1 - 0.9
= 0.1m
Therefore, the long net is enough to reach the fish.
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Ruby looks over the edge of her boat and sees fish 0.4 meter below the surface of the water. If Ruby holds a 1-meter long net at 0.5 meter above sea level. Can she reach the fish?
please help with this one! ASAP
Answers
Answer: 699 m^2
Step-by-step explanation:
What is a sticker price of higher education
Answers
Sticker price refers to the published tuition and fees, whereas net price refers to the amount the student actually pays after financial help which is much lower than the sticker price.
Sticker priceThe sticker price of a college education is the entire annual cost. This cost covers the whole cost of tuition every year, books, lodging, and board, as well as any other charges the campus may levy, such as a parking permit or library card fee.
In this report, there are two prices listed: a sticker price and a net price. The sticker price of a college education is the entire annual cost. Every year's full tuition, books, housing, and board are included in this amount.
Hence sticker price refers to the published tuition and fees
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Polygon B is a scaled copy of Polygon A using a scale factor of 5. Polygon A's area is what fraction of Polygon B's area?
Answers
Polygon A's area is 1/25 times of Polygon B's area.
What do you understand by polygon?In geometry, a polygon is a two-dimensional closed shape with straight sides that is flat or plane. It doesn't have any curved edges.
A polygon's sides are also known as its edges. The vertices (or corners) of a polygon are the points where two sides meet.Polygons are named after the number of sides they have. Polygons are commonly represented by the symbol n-gon, where n indicates the number of sides.A 5-sided polygon is called a 5-gon, a ten-sided polygon is called a 10-gon, and so on.Now, as per the given question;
The formula of the scale factor is given as;
Area of Polygon B = (scale factor)²×(Area of Polygon A).
The scale factor is given as 5.
(Area of Polygon B) = (5)²×(Area of Polygon A)
Further simplifying;
(Area of Polygon B) = (25)×(Area of Polygon A)
or,
Area of Polygon A = (1/25)×Area of Polygon B
Therefore, the area of polygon A is found to be 1/25 times times the area of the polygon B.
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A manufacturer estimates his marginal cost and revenue at various levels of output to be the following. If fixed cost is 500, estimate, using the Simpsons rule, the total profit or loss of producing 100 units is Blank 1. Fill in the blank, read surrounding text.
GHC
q (units)
0
20
40
60
80
100
120
MC
260
250
240
200
240
250
270
MR
410
350
300
250
270
250
300
Answers
If the fixed cost is GHC500, the total profit or loss of producing 100 units is GHC 0.
What is the profit when MC = MR?When the marginal cost (MC) equals the marginal revenue (MR), the company breaks even, and from that point, profit maximization starts.
When MR is more than MC, the tendency is for the firm to produce more and earn more profit, and when MR is less than MC, the firm produces fewer as it incurs losses.
The profit maximization level occurs where the MR and the MC are equal.
Data and Calculations:Total revenue = fixed cost + variable cost (MR x Units)
Total revenue = 500 + (100 x 250)
Total revenue = 500 + 25,000
Total revenue = GHC 25,500
Total profit or loss at 100 units = GHC0 (GHC25,500 - GHC25,500)
GHC
q (units) 0 20 40 60 80 100 120
MC 260 250 240 200 240 250 270
MR 410 350 300 250 270 250 300
Thus, if the fixed cost is GHC500, the total profit or loss of producing 100 units is GHC 0.
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Find the area of the polygon with the given vertices.
K(-3, 4), L(1, 4), M(-4,-2), N(0, - 2)
Answers
Answer: 24.33 units
Step-by-step explanation: If we appropriately measure the distance between the points we can depict a parallelogram with 2 sides measuring 6.083 units and 2 others measuring 4 units. We multiply 4 x 6.083 and get the area: 24.33 units
Answer: 24
Step-by-step explanation: As the formula to solve this equation is A= 1/2 | [(x1y2) - (x2y1)] + [(x2y3) - (x3y2)] + [(x3y4) - (x4y3)] + [(x4y1) - (x1y4)]
Which would be (with the numbers)
[(-3 x 4) - 1 x 4)] + [(1 x -2) - (0 x 4)] + [(10 x 2) - (-4 x -2)] + [(-4 x 4) - (-3 x -2)]
which lowers down too
(-12 - 4) + (-2 - 0) + (0 - -8) + (-16 - 6)
Then that gets us (absolute values) of
|-16| + |-2| + |8| + |-22|
using absolute values that gets us to
16 + 2 + 8 + 22
Which is equal to 48.
Don't forget to divide by 2 because we need half of it as it says in the beginning of the formula (A = 1/2)
So that gives us the answer of 24.
Hope this helped :)
Also, this could help by labeling each coordinate as a (X, Y) Number
[-3(x1) , 4(y1)} (you could write the x and y part above it)
And then you go down the list and label each as either x1 , x2 , x3 , x4 (for the left side of comma) and then y1 , y2, y3 , y4 (for the right side of the comma)
Solve for x.
A=x+y-2
Answers
Answer:
x=1
Step-by-step explanation: