Which of these statements are true? Choose all answers that apply: (Choice A) Greater width relates to greater area as long as the width is less than 10 (Choice B) Greater width relates to greater area as long as the width is more than 10 (Choice C) To get the greatest area, the width should be 10 (Choice D) To get the greatest area, the width should be 20
The true statement about the function of area of by rectangle and width of rectangle are:
Greater width relates to greater area as long as the width is less than 10 To get the greatest area, the width should be 10The correct answer option is options A and D
Which width gives the maximum area of rectangle?A rectangle is a quadrilateral having opposing sides parallel and four right angles.
At point (x, y) = (10, 100) the area is maximum.
This means that the area of the rectangle is maximum when width is 10m.
If the width of the rectangle is more than 10m, the area reduces or decreases.
Therefore, the statement Greater width relates to greater area as long as the width is more than 10 m is false.
The statement "To get the greatest area, the width should be 20" is false.
Complete question:
Simon has a certain length of fencing to enclose a rectangular area. The function A, models give the rectangles area (in square meters) as a function of its width (in meters).
Wlhich of these statements are true?
A. Greater width relates to greater area as long as the width is less than 10.
B. Greater width relates to greater area as long as the width is more than 10.
C. To get the greatest area, the width should be 10
D. To get the greatest area, the width should be 20
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determine the sum of the first 8 terms of the geometric sequence if the first term is 5, the common ratio is -2 and the 8th term is -640
Answer:
-425
Step-by-step explanation:
You want the sum of the first 8 terms of the geometric series with first term 5 and common ratio -2.
Series sumThe sum is given by the formula ...
Sn = a1·(r^n -1)/(r -1) . . . . . . a1 = first term, r = common ratio
The sum of 8 terms of the given series is ...
S8 = 5·((-2)^8 -1)/(-2 -1) = 5(255/-3) = -1275/3 = -425
The sum of 8 terms is -425.
HELP MEE
−5g+(−2)−2g −7
Answer:
-7g - 9
Step-by-step explanation:
Subtract the numbers
-5g -2 -2g -7
-5g - 9 - 2g
Combine like terms
-5g - 9 - 2g
-7g - 9
Solution
-7g - 9
Answer:
-7g -9
Step-by-step explanation:
Just subtract and then combine like terms
Solve for x in the equation 2 x squared 3 x minus 7 = x squared 5 x 39.
After solving the equation for x , we get the solution as x = 1 [tex]+[/tex] √47 and x = 1 - √47 .
In the question ,
it is given that ,
the equation in words is written as "2 x squared plus 3 x minus 7 [tex]=[/tex] x squared plus 5 x plus 39 " .
So , the equation in number can be written as
2x² [tex]+[/tex] 3x - 7 = x² [tex]+[/tex] 5x + 39
Making Like terms together ,
we get ,
2x² - x² [tex]+[/tex] 3x - 5x - 7 - 39 [tex]=[/tex] 0
(2 - 1)x² [tex]+[/tex] (3 - 5)x - 46 [tex]=[/tex] 0
x² - 2x - 46 [tex]=[/tex] 0
Applying quadratic formula in the above quadratic Equation ,
we get ,
x = -b ± √(b² - 4ac)/2a
From the given quadratic equation , we get that a = 1 , b = -2 and c = -46 .
So ,
x = -(-2) ± √((-2)² - 4(1)(-46))/2(1)
= 2 ± √(4 [tex]+[/tex] 4(46))/2
= 2 ± √4(1 [tex]+[/tex] 46)/2
= 2 ± 2√47/2
= 2(1 ± √47)/2
= 1 ±√47
x = 1 + √47 and 1 - √47 .
Therefore , After solving the equation for x , we get the solution as x = 1 + √47 and x = 1 - √47 .
The given question is incomplete , the complete question is
Solve for x in the equation , "2 x squared plus 3 x minus 7 = x squared plus 5 x plus 39 " .
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Given the equation y=78x+15, what is the value of y when x is 4?
Answer:327
Step-by-step explanation:
Because you already have the equation, all you need to do is plug in the value for X. If X is equal to 4, our equation would look like this:
y = 78 * 4 + 15
Because of order or operations (PEMDAS), we do multiplication first.
y = 312 + 15
y = 327
Hope this helped!
Solve the following:-
[tex]\sf \cfrac{x}{11} + 16 = 30[/tex]
Answer:
x = 154
Step-by-step explanation:
[tex]\frac{x}{11}[/tex] + 16 = 30 ( subtract 16 from both sides )
[tex]\frac{x}{11}[/tex] = 14 ( multiply both sides by 11 to clear the fraction )
x = 11 × 14 = 154
Answer:
x = 154
Step-by-step explanation:
Given equation,
→ (x/11) + 16 = 30
Now the value of x will be,
→ (x/11) + 16 = 30
→ x/11 = 30 - 16
→ x = 14 × 11
→ [ x = 154 ]
Hence, value of x is 154.
Find the value of each variable. a,b,c,d,e
Answer:
a - 67
b - 58
c - 125
d - 23
e - 90
Step-by-step explanation:
Solve for b first
90 - 32 = 58
Then you can solve for a
180 - 58 - 55 = 67
Now solve for c
180 - 55 = 125
Now you can solve for d
180 - 125 - 32 = 23
e is equal to 32 + b, so it is 90.
I can text 65 words in 10 minutes. At this rate, how many words could I text in 12 minutes?
Find the original price given each total amount and rate of increase. Round to the nearest cent if necessary. 83.82. 10%
The original amount is $92.202.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is primarily used to compare and determine ratios and is represented by the symbol %.
Given:
Total amount = 83.82
rate of increase = 10%
So, the original amount
= 83.82 + 83.82 x 0.1
= 83.82 + 8.382
= $92.202
Hence, the original amount is $92.202.
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solve the equation 15 < b - 4
Answer:
b>19
Step-by-step explanation:
15<b−4
Rewrite so b is on the left side of the inequality.
b−4>15
Move all terms not containing b to the right side of the inequality.
Add 4 to both sides of the inequality.
b>15+4
Add 15 and 4.
b>19
b>19
The result can be shown in multiple forms.
Inequality Form:
b>19
Interval Notation:
(19,∞)
a pharmaceutical company is interested in comparing four brands of sleep medication to see which brand is best at relieving sleep pattern symptoms, primarily insomnia. the participants are 80 people with sleep pattern symptoms. they are randomly assigned to four groups of 20 participants. each group receives one of the four brands of sleep medication. the improvement in the sleep pattern of the 80 participants is recorded 6 weeks after taking the medication and the average improvement is compared among the four treatment groups. what are the factor(s) and level(s) of this scenario? the factor is the . the levels are the
Answer:
The factor is the sleep medication
The levels are the 4 different treatments, or medications
Step-by-step explanation:
Use the figure below for the following problems (not drawn to scale).
Given: m/1 = 70,
What is m/4?
O a 125⁰
.Ob
70°
Oc
40°
Od
55°
5
6
The measure of angle 4 is 125° for the given triangle.
According to the question,
We have the following information:
A figure is given of triangle and its exterior angles.
m∠1 = 70°
Now, the two sides (with line on them) of the triangle are equal. So, it means that it is an isosceles triangle.
We know that sum of three angles of a triangle is 180°.
Let's take the two equal angles to be x°.
x+x+70 = 180
2x+70 = 180
2x = 180-70
2x = 110
x = 110/2
x = 55°
We know that angles made on a straight line is 180°.
∠4 and angle x will make a straight line.
∠4 = 180-55
∠4 = 125°
Hence, the correct option is A.
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Solve for w.
10 = |w + 9|
Write your answers as integers or as proper or improper fractions in simplest form.
w =
or w =
A cruise ship maintains a speed of 22 knots (nautical miles per hour) sailing from San Juan to Barbados, a distance of 600
nautical miles. To avoid a tropical storm, the captain heads out of San Juan at a direction of 28° off a direct heading to
Barbados. The captain maintains the 22-knot speed for 15 hours, after which time the path to Barbados becomes clear of
storms.
(a) Through what angle should the captain turn to head directly to Barbados?
(b) Once the turn is made, how long will it be before the ship reaches Barbados if the same 22-knot speed is maintained?
(round to one decimal place)
Answer: A cruise ship maintains a speed of 22 knots (nautical miles per hour) sailing from San Juan to Barbados, a distance of 600 nautical miles. To avoid a tropical storm, the captain heads out of San Juan at a direction of
20
∘
off a direct heading to Barbados. The captain maintains the 22-knot speed for 9 hours, after which time the path to Barbados becomes clear of storms. (a) Through what angle should the captain turn to head directly to Barbados? (b) Once the turn is made, how long will it be before the ship reaches Barbados if the same 22-knot speed is maintained? (a) The captain should head through an angle of (Do not round until the final answer. Then round to one decimal place as needed.) (b) The time it will take for the ship to reach Barbados is hours (Do not round until the final answer. Then round to one decimal place as needed.)
what type of statistics has been used in the following: descriptive or inferential the national center for health statistics, part of the centers for disease control and prevention has reported about 60 births per every 1,000 women ages 15 to 44 years.
In the situation, 60 births per every 1,000 women ages 15 to 44 years, the statistics used is descriptive statistics.
What is descriptive statistics?
Suppose there is a population and suppose there is a sample of the population. If the inference is made on the sample alone and not on the whole population, the statistics used is called descriptive statistics.
Here, the sample is 60 births per every 1,000 women ages 15 to 44 years.
And the inference is made only about those 60 births per every 1,000 women ages 15 to 44 years, and not on the whole population of women aged between 15 to 44 years. So the statistics used in this case is descriptive statistics.
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I don't understand this question in my homework
The equation of line passes through the point (-6, -3) will be;
⇒ y = 5/3x + 7
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The point on the line are (-6, -3).
And, The parallel line is,
⇒ 5x - 3y = 9
⇒ y = (5x - 9) / 3
Now,
Since, The equation of line passes through the point (- 6, -3).
So, We need to find the slope of the line.
Since, The slope of the parallel line is same.
Hence, Slope of the line is,
y = 5/3x - 3
m = dy/dx = 5/3
m = 5/3
Thus, The equation of line with slope 5/3 is,
⇒ y - (-3) = 5/3 (x - (-6))
⇒ y + 3 = 5/3 (x + 6)
⇒ y + 3 = 5/3x + 10
⇒ y = 5/3x + 10 - 3
⇒ y = 5/3x + 7
Therefore, The equation of line passes through the point (-6, -3) will be;
⇒ y = 5/3x + 7
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if the numbers in the brackets go together in a certain way, find the missing number.
(1,2) (2,5) (3,10) (?,362)
a. 4
b. 10
c. 15
d. 19
e. none of these
The missing number in the bracket is 19. The correct option is d. 19
Determining the missing numberFrom the question, we are to determine the missing number in the bracket.
The given sequence is
(1,2) (2,5) (3,10) (?,362)
Now, to determine the missing number, we will study the given sequence.
Let the missing number be x
From the sequence, we can observe that
1² + 1 = 2
2² + 1 = 5
3² + 1 = 10
and
x² + 1 = 362
Now, we will solve the equation for x
x² + 1 = 362
Subtract 1 from both sides of the equation
x² + 1 - 1 = 362 - 1
x² = 361
Therefore,
x = √361
x = 19
Hence, the missing number is 19
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Cube A has a mass of 81 g.
Cube B has a mass of 128 g.
Work out
the density of cube A: the density of cube B
Give your answer in the form a: b, where a and b are integers.
The ratio of the density of cube A to the density of cube B as required in the task content is; 81 : 128.
What is the ratio of the density of cube A to the density of cube B?It follows from the task content that the ratio of the density of cube A to cube B is to be determined.
Recall that the density of an object is given as its mass to volume ratio.
Therefore, given that the volumes are equal; it can be inferred that the density and mass are directly proportional.
Ultimately, the required density ratio can be estimated from the given masses as;
Density of A : Density of B = 81 : 128.
Consequently, the required ratio is; 81 : 128.
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Help pls
If a ball is released from a height of about 6 feet, what is the minimum initial velocity needed to throw the ball over 37 feet up?
The ball must be thrown up at an initial velocity of approximately 24.658 feet per second.
What is the initial velocity of a ball to satisfy a free fall motion?
Free fall motion is an uniformly accelerated motion due to gravity. In this question we need to determine the initial velocity of a ball (v), in feet per second, such that the ball reaches a height of 37 feet up. The initial velocity can be found by means of the following equation:
v'² = v² + 2 · g · (h' - h)
Where:
h - Initial height above the ground, in feet.h' - Final height above the ground, in feet.g - Gravitational acceleration, in feet per square second. v - Initial speed, in feet per second.v' - Final speed, in feet per second.If we know that v' = 0 ft / s, g = - 9.807 ft / s², h = 6 ft and h' = 37 ft, then the minimum initial velocity of the ball is:
v² = v'² - 2 · g · (h' - h)
v = √[v'² - 2 · g · (h' - h)]
v = √[(0 ft /s)² - 2 · (- 9.807 ft / s²) · (37 ft - 6 ft)]
v ≈ 24.658 ft / s
The ball must have an initial velocity of approximately 24.658 feet per second.
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A population of beetles grows by 25% every month. If the beetle population starts
with 1, 600 beetles, which equation represents the population, P, after t months?
OP= 1,600(0.25)*
OP= 1,600(1.25)
OP 1,600 +0.25t
OP= 1,600 +1.25t
Answer:
Step-by-step explanation:
When an object (with negligible wind resistance) is dropped, its height, h, in feet at a certain
time is given by the model h = - 16t+s where s is the height from which the object was dropped and t
is the number of seconds it has fallen. Find the number of seconds it takes for such an object to fall to the
ground (height = 0) from a height of 800 feet.
The number of seconds it takes for such an object to fall to the
ground from a height of 800 feet is 50 seconds
According to the question,
When an object (with negligible wind resistance) is dropped, its height, h, in feet at a certain time is given by the model
h = - 16t+s
where s is the height from which the object was dropped
t is the number of seconds it has fallen
We have to find the number of second it takes to reach ground when fall from height 800 feet
given,
s = 800
h = 0 (ground height = 0)
using the model h = - 16t+s
0 = -16t + 800
800 = 16t
t = 800/16
t = 50 seconds
Hence, the object will take 50 seconds to reach ground when drop from 800 feet
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the great pyramid of cheapos is a square based pyramid
The height of the pyramid is 99.1875 meters when the Great Pyramid of Cheops has a square base, 230-meter-long sides, and a height of 147 meters.
Given that,
The Great Pyramid of Cheops has a square base, 230-meter-long sides, and a height of 147 meters.
We have to find what would the height be if you gave the base sides of 280m using the same material.
We know that,
Volume of Great Pyramid of Cheops = Volume of the pyramid with the base sides of 280m
Volume of Great Pyramid of Cheops is 1/3×(side of the base)²×(height of the pyramid)
Side of the base is 230 meters.
Height of the pyramid is 147 meters.
Volume of the pyramid with the base sides of 280m is 1/3×(side of the base)²×(height of the pyramid)
Side of the base is 280 meters.
Height of the pyramid is h meters.
Volume of Great Pyramid of Cheops = Volume of the pyramid with the base sides of 280m
1/3×(230)²×(147)=1/3×(280)²×h
h = 99.1875 meters.
Therefore, the height of the pyramid is 99.1875 meters while the Great Pyramid of Cheops has a square base, 230-meter-long sides, and a height of 147 meters.
The complete question is:
The Great Pyramid of Cheops is a square-based pyramid, the base has sides of 230m, and the height is 147m.
Using the same material, what would the height be if you give the base sides of 280m.
Please give the answer to the nearest meter.
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Beth tells her math teacher that the following set of ordered pairs IS a function. Is Beth correct?
Why or why not?
(2,3) (3,8) (2,4) (5,7)
Answer:
No, Beth is not correct. One of the x-values, 2, corresponds to two y-values.
Joseph takes out a loan that gathers compound interest.
The table below shows the value of the loan over time.
a) What is the rate of interest per annum?
Give your answer as a percentage to 1 d.p.
b) Work out the value of the loan 10 years after it starts.
Give your answer in pounds (£) to the nearest 1p.
Start
£7500.00
After 1 year
£7965.00
After 2 years
£8458.83
Answer:
a) 6.2%
b) £13,687
Step-by-step explanation:
a)
To find the rate of interest, we first find the interest itself.
£7965.00 - £7500.00 = £465.00
Using this, we find the rate of interest in percentage as a fraction of the original loan.
(£7500.00 ÷ £465.0) × 100 = 6.2%
Thus, the rate of interest is 6.2%.
b)
Compound interest is found using the formula
[tex]A = P(1 + \frac{r}{100})^{t}[/tex]
Where
A = final amount
P = initial principal balance
r = interest rate
t = number of time periods elapsed
Thus, with an initial balance of £7500, an interest rate of 6.2% and a time period of 10 years, calculated per annum, we can plug the numbers into the formula, giving us
[tex]A = 7500(1 + \frac{6.2}{100})^{10}[/tex]
[tex]=[/tex] £13,686.94
≈ £13,687 (to nearest £1)
Some things to note: number of time periods elapsed mean the amount of times it is compounded; if the question says compounded quarterly for 3 years, t = 12 as it is compounded 4 times a year for 3 years, giving is 12 time periods. This also applies to monthly, bi-weekly etc.
The gold trophy has 27 racers, she will 12 racers on the racetrack that runs.
How many racers did she have runs?
She will have run a total of 2.25 racers in 27 racers
How to determine the number of racers?From the question, we have the following parameters that can be used in our solution:
Total number of racers = 27 racers
Number of racers in a run = 12 racers
From the above parameter, we can calculate the total number of racers using the following equation
The total number of racers is calculated as
Total number of racers in the run = Total number of racers/Number of racers in a run
Substitute the known values in the above equation
So, we have the following equation
Total number of racers in the run = 27/12
Evaluate the quotient
Total number of racers in the run = 2.25
Hence, the total number of racers in the run is 2.25 racers
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need help with this one
Answer:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Step-by-step explanation:
Point Form:
[tex](\frac{2}{3} ,-\frac{5}{3}) , (-1, -5)[/tex]
Equation Form:
x= [tex](\frac{2}{3}[/tex], [tex]-\frac{5}{3} )\\[/tex] , y= [tex]-\frac{5}{3}[/tex]
x = -1 , y =-5
Hope this answer your question... sorry I couldnt help more, if it didnt.
Find the surface area and volume of each triangular prism (base is a right triangle).
triangle legs are 3 ft and 4 ft, hypotenuse is 5 ft, height of prism is 8 ft
The surface area of the triangular prism be 108 ft²
The volume of the triangular prism be 48 ft³.
Given, a triangular prism (base is a right triangle).
Triangle legs are 3 ft and 4 ft, hypotenuse is 5 ft, height of prism is 8 ft.
Now, the surface area of the triangular prism is,
Surface Area = 2×Area of the base triangle + Side rectangle 1 +Side rectangle 2 + Side rectangle 3
Surface Area = 2×(1/2×3×4) + 5×8 + 3×8 + 4×8
Surface Area = 12 + 40 + 24 + 32
Surface Area = 108 ft²
Now, Volume of the triangular prism be,
Volume = Area of the base triangle × height
Volume = 1/2×3×4×8
Volume = 48 ft³
Hence, the surface area of the triangular prism be 108 ft²
and the volume of the triangular prism be 48 ft³.
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Morgan got a 42 out of 40 points on her American Government quiz due to an extra credit question. What is her grade as a mixed number in simplest form?
Answer: 1 -1/20
Step-by-step explanation:
Based on the given conditions, formulate: 42 divided by 40
Cross out the common factor: 21/20
Convert to mixed fraction: 1- 1/20
A movie theater sends out a coupon for 45% off the price of a ticket. Write an equation for the situation, where y is the price of the ticket with the coupon, and x is the original price of the ticket. Use pencil and paper. Draw a graph of the equation and explain why the line should only be in the first quadrant.
The equation where y is the price of the ticket with the coupon, and x is the original price of the ticket.
y= 0.55 x.
Given:
A movie theater sends out a coupon for 45% off the price of a ticket. Write an equation for the situation, where y is the price of the ticket with the coupon, and x is the original price of the ticket.
If x is the price of the ticket without the coupon, and the theater offers a discount if you have a coupon, then having a coupon means that the price a person ultimately pays (y) is the original price (x) minus a 45% of this price:
y= x -0.45 x
By association: y= (1-0.45) x
and then y= 0.55 x.
The line should be in the first quadrant because the first quadrant allows you to represent a situation in which the dependent variable (y) and the independent variable (x) are both positive. This is the case in this exercise, because both prices, the one without discount (x) and the one with discount (y) are necessary positive (you can not pay a negative price!).
Hence we get the required equation.
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2. Create a graph in the workspace provided to model the relationship that that exists if the school store is selling 5 pens (x) for $2.00 (y). Then find the constant rate of change.
Answer: The constant of variation, k , is 54
Step-by-step explanation: Step 1: Check whether the graph is a straight line. If the graph is not a straight line, it does not represent a proportional relationship. Step 2: Check whether the line goes through the origin. If the graph does not go through the origin, it does not represent a proportional relationship.