Answers
a) The quadratic equation behind the parabola is y = (4 / 5) · x² - (8 / 5) · x - 1.
b) There are two x-intercepts: x₁ = - 0.5, x₂ = 2.5.
How to derive a quadratic equation and find its x-intercepts
Mathematically speaking, parabolas are represented by quadratic equations, whose standard form is introduced below:
y = a · x² + b · x + c
Where a, b, c are real coefficients.
The values of the three coefficients are found from the knowledge of three distinct points on Cartesian plane. First, choose the three points:
(x₁, y₁) = (- 0.5, 0), (x₂, y₂) = (2.5, 0), (x₃, y₃) = (0, - 1)
Second, construct the system of linear equations with all the given points and the standard form of the quadratic equation:
0.25 · a - 0.5 · b + c = 0
6.25 · a + 2.5 · b + c = 0
c = - 1
Third, solve the system by numerical methods:
(a, b, c) = (4 / 5, - 8 / 5, - 1)
Fourth, write the quadratic equation:
y = (4 / 5) · x² - (8 / 5) · x - 1
The x-intercepts of the quadratic equation are the points of the curve that pass through the x-axis. Then, the x-intercepts are x₁ = - 0.5 and x₂ = 2.5.
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Related Questions
Stevenson’s Market is selling 3 packs of toothpicks for $0.87. How much will 10 packs of toothpicks cost at this price? Round your answer to the nearest cent.
Answers
Answer:
$2.90
Step-by-step explanation:
87 cents / 3 packs = 29 cents per pack
$0.29 × 10 = $2.90
what is the value of X? 16X = 156.8
Answers
the given expression is,
16x = 156.8
x = 156.8/16
x = 9.8
thus, the answer is 9.8
Answer:
x = 9.8
Step-by-step explanation:
16x=156.8
x = 156.8/16
x = 9.8
What is the equation for this please help
Answers
Answer:
the equation would be 1.67x+0
PreviousWhich of the following sampling methods would most likely have the largest margin of error?OA. Roll a die 100 times and estimate the proportion of 3's that result.OB. Sample 10 adults and ask them if they regularly smoke cigarettes and use this data to represent the proportion of adults who smoke in a community.OC. Sample 500 registered voters in a large city and ask them their political preference and use the results to estimate the breakdown by party of all registered voters in the citOD. Flip a coin 1000 times and estimate the proportion of "heads" that result.Reset SelectionNextacer
Answers
have the largest margin of error
The more trials or samples that occur, the greater the chance of making mistakes. or increasing the margin error,
then the sample with a largest margin of error is
flip a coin 1000 times
What is the equation of a line that passes through (1,4) and (3, -6)?l
Answers
The equation of the line is that passes through (1,4) and (3, -6) is
y = -5x + 9
First, write the equation in slope-intercept form:
y = mx + b
(the m is the slope, and b is the y-intercept)
Now, Lets find the slope(m) of the line by using the formula:
y2-y1/x2-x1
(-6 - 4)/ (3 - 1) = -10/2 = -5
Next, find the y-intercept (b) by using the slope-intercept form equation and substituting -5 in for m and one of the ordered pairs in for x and y:
4 = (-5)(1) + b
b = 9
-OR-
-6 = (-5)(3) + b
b = -6 + 15 = 9
b = 9
Now, we can write the full equation of the line:
y = -5x + 9 is the answer
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4. Find each amount:
3.8% of 25
0.2% of 50
180.5% of 99
how do I find and explain this??
Answers
The result of each part is
Part 1
3.8% of 25 is 0.95
Part 2
0.2% of 50 is 0.1
Part 3
180.5% of 99 is 178.695
Part 1
The given expression is
3.8% of 25
Here we have to find the 3.8 percentage of 25
Then the mathematical expression will be
25 × 3.8% = 25 × 3.8/100
= 25 × 0.038
= 0.95
Part 2
The given expression is
0.2% of 50
The mathematical expression will be
50 × 0.2% = 50 × 0.2/100
= 50 × 0.002
= 0.1
Part 3
The expression is
180.5% of 99
The mathematical expression will be
99 × 180.5% = 99 × 180.5/100
= 99 × 1.805
= 178.695
Hence, the result of each part is
Part 1
3.8% of 25 is 0.95
Part 2
0.2% of 50 is 0.1
Part 3
180.5% of 99 is 178.695
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please help!!!
A handicapped ramp is being constructed for the front entrance of First National Bank in Springfield. ADA guidelines requires a rise angle from the foot of the ramp (point furthest from the entrance) not to exceed 4.8 degrees. This means the vertical to horizontal ratio cannot exceed 1:12. If the handicapped ramp must start 15 feet away from the front entrance, contractors estimate the rise to be about 3 feet.
Part A: Explain thoroughly whether or not these ramp dimensions meet the ADA guidelines.
Part B: If the rise estimate does not meet ADA requirements, provide a measurement that would meet the guidelines.
Answers
Part A; The vertical to horizontal ratio of the ramp in the question of 3:15 does not meet the ADA guideline of a vertical to horizontal ratio of 1:12
Part B; The measurement of the ramp that would meet ADA guideline is a vertical to horizontal ratio of 3 feet to 36 feet.
The front entrance of the ramp should therefore be 36 feet away
What is a ratio in mathematics?A ratio is an indication of the number of times one quantity is contained in another quantity.
The ADA guidelines requires that the rise angle ≤ 4.8°
The vertical ratio of the ramp ≤ 1:12
The distance the handicapped ramp must start = 15 feet from the front entrance
The rise of the ramp estimated by the contractors = 3 feet
Part A; The vertical to horizontal ratio of the ramp in the question = 3/15, which is 1:5
Therefore, the ramp does not meet ADA guidelines that requires a vertical to horizontal ratio of less than or equal to 1:12
Part B:
The ramp can be made to meet ADA guideline, whereby the horizontal distance from the entrance can be be adjusted as follows;
Let d represent the required horizontal distance of the front entrance, we get;
3:d = 1:12
From which we get;
[tex]\dfrac{3}{d} =\dfrac{1}{12}[/tex]
3 × 12 = 1 × d
d = 36
The horizontal distance of the front entrance of the ramp should be 36 feet away.
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Determine the exact surface area of the cylinder in terms of π.
cylinder with radius labeled 1 and one fourth centimeters and a height labeled 2 and three fourths centimeters
6 and 9 over 16 times pi square centimeters
10 times pi square centimeters
15 and 15 over 16 times pi square centimeters
19 and three eighths times pi square centimeters
Answers
A right circular cylinder is a three dimensional geometric figure with its top and bottom as circle. The exact surface area for the given cylinder is 10π square cm.
What is a cylinder?A cylinder is a three dimensional geometric figure.
The volume of a cylinder is given as πr²h, where r is the radius and h is the height of the cylinder.
Given that,
The radius of cylinder r = 1 and one fourth cm
= 1 + 1 / 4 cm
= 5 / 4 cm
The height of cylinder h = 2 and three fourth cm
= 2 + 3 / 4 cm
= 11 / 4 cm.
Since the exact surface area of cylinder is given by 2πr(h+ r), the exact surface area for the given cylinder is given as,
= 2π × (5 / 4 ) × ((11 / 4) + ( 5 / 4))
= 2π × (5 / 4 ) × 4
= 10π
Hence, the exact surface area for the given cylinder is 10π square cm.
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Hello I got this wrong will you help me solve
Answers
Solve for y
[tex]4x+3y=-21[/tex]Subtract 4x both sides
[tex]\begin{gathered} 4x+3y-4x=-21-4x \\ 3y=-21-4x \\ \end{gathered}[/tex]Divide by 3 into both sides
[tex]\begin{gathered} \frac{3y}{3}=-\frac{21}{3}-\frac{4x}{3} \\ y=-7-\frac{4}{3}x \\ by\text{ reordering} \\ y=-\frac{4}{3}x-7 \end{gathered}[/tex]Answer:
[tex]y=-\frac{4}{3}x-7[/tex]3. the mean lifetime for cardiac stents is 8.7 years. a medical device company has implemented some improvements in the manufacturing process and hypothesizes that the lifetime is now longer. a study of 100 new devices reveals a mean lifetime of 9.3 years with a standard deviation of 3.8 years. is there statistical evidence of a prolonged lifetime of the stents?
Answers
There is no statistical evidence of a prolonged lifetime of the stents.
Given data,
n (sample size) = 100
X (sample mean) = 9.3
s (sample standard deviation) = 3.8
Next, we need to define the null hypothesis and alternative hypothesis
Null hypothesis
[tex]H_{o}[/tex] : u (mu) = 8.7
Alternative hyptohesis
[tex]H_{o}[/tex] : u (mu) > 8.7
Next, we need to do hypothesis testing to get the claim about a population mean is tested under the null and the alternative hypotheses by using t-test and p-value.
t-test is a sampling test statistic and used when the population standard deviation is unknown.
the t-test can be calculated as follows:
= [tex]\frac{X-u}{s/\sqrt{n} }[/tex]
= [tex]\frac{9.3-8.7}{3.8/\sqrt{100} }[/tex]
= 1.578
Next, we need to calculate the p-value using Microsoft excel function. The p-value helps decide whether to reject the null hypothesis.
Enter the function below in excel to calculate p-value:
=TDIST(1.578,40-1,1)
= 0.061322.
The p-values is greater than the common threshold ( p<0.05), which means We can conclude that there is no statistical evidence of a prolonged lifetime of the stents.
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Jacob is buying pizza dough at the store to make pizzas for his family.
For every 15 pizza doughs he buys, he pays $20.
What is the price per pizza dough?
Answers
Answer: $1.33
This can be worked out as a simple algebra problem: 15x=20, x being 1 pizza dough. In order to find the value of one pizza dough (x) you need to isolate it. To do that, divide 15 from both sides and you'll be left with x=1.33
15x=20
/15 /15
x=1.33
ZEFH = 127°. Solve for mzGFH.
E
F
mZGFH =
(8x - 4)º
(5x + 14)°
G
H
Answers
The value of ∠GFH=59°, in the given question.
What do you mean by angle?
Two straight lines or rays intersect at a same terminus to make an angle. The vertex of an angle is the point at which all points meet.
According to the data in the given question,
We have :
∠EFH=127°
∠EFG=(8x-4)°
∠GFH=(5x+14)°
Now, we have to solve the value of ∠GFH,
∠EFG+∠GFH=∠EFH
Putting the values given and solve for x,
(8x-4)°+(5x+14)°=127°
8x°-4°+5x°+14°=127°
13x°+10°=127°
13x°=127°-10°
13x°=117°
x=9
Then, putting the value of x in ∠GFH,
∠GFH=(5x+14)°
=(5(9)+14)°
=(45+14)°
=59°
Therefore, the value of ∠GFH=59°.
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how do i solve each system for these equations
x-y=4 2x+y=5
Answers
Answer:
x = 3
y = -1
Step-by-step explanation:
x-y=4 [1]
2x+y=5 [2]
rearrange [1] and label it [3]
x = 4 + y [3]
substitute [3] into [2]
2(4 + y) + y = 5
8 + 3y = 5
3y = -3
y = -1
substitute y = -1 into [1]
x - (-1) = 4
x = 3
Can someone help with these two pages if possible?
Answers
The rules of the transformations using the translation notation are;
11) [tex]T_{(2, \,-1)}[/tex]
12) [tex]T_{(-5, \,2)}[/tex]
13) [tex]T_{(-1, \,3)}[/tex]
14) [tex]T_{(0, \,-1)}[/tex]
15) [tex]T_{(3, \,4)}[/tex]
16) [tex]T_{(-3, \,1)}[/tex]
17) [tex]T_{(1, \,0)}[/tex]
18) [tex]T_{(6, \,-5)}[/tex]
19) [tex]T_{(4, \,0)}[/tex]
20) [tex]T_{(2, \,4)}[/tex]
21) [tex]T_{(1, \,-5)}[/tex]
22) [tex]T_{(5, \,-1)}[/tex]
23) [tex]T_{(0, \,-1)}[/tex]
24) [tex]T_{(-2, \,-1)}[/tex]
25) [tex]T_{(-3, \,-2)}[/tex]
What is a translation transformation?A translation transformation is a rigid transformation in which the location of the image obtained from the pre-image is different, but the dimensions are the same.
11) The transformation is similar to a rigid transformation
The change in coordinate is from (2, 2), to (4, 1), which is a translation 2 units to the right and -1 unit down
12) The shape is preserved and the length of the sides are also preserved, therefore, the transformation is a rigid transformation, with a change from (5, 3) to (0, 5), which is a translation 5 units to the left and 2 units up.
13) The change in the coordinates from the pre-image to the image are from V(-3, 2) to V(-4, 5), which is a transformation of 1 unit to the left and 3 units up
14) The coordinates of a point on the pre-image is T(-5, 2), and the coordinates of the corresponding point on the image is T'(-5, 1), which is a translation of one unit downwards, [tex]T_{(0, \,-1)}[/tex]
15) A point on the pre-image is T(-3, -1), the corresponding point on the image is T'(0, 3), which indicates that the rule for the transformation is a translation of 3 units to the right and a vertical translation of 4 units upwards
16) The difference between the x and y values are;
Δx = 0 - 3 = -3
Δy = -3 - (-4) = 1
The transformation is therefore of the form [tex]T_{(-3, \,1)}[/tex], which is a translation of 3 units to the left and 1 unit upwards
17) The change in the x and y values are;
Δx = -2 - (-3) = 1
Δy = -3 - (-3) = 0
The rule of the transformation is therefore of the form [tex]T_{(1, \,0)}[/tex], which is a translation one unit to the right.
18) The change in the x and y values of the transformation are;
Δx = 1 - (-5) = 6
Δy = -4 - 1 = -5
The rule of the transformation is therefore, [tex]T_{(6, \,-5)}[/tex], which is a translation of 6 units to the right and 5 units down
19) The transformation of J(-5, 3), K(-3, 5), L(0, 1) to J'(-1, 3), K'(1, 5), L'($, 1) is a transformation of the form [tex]T_{(4, \,0)}[/tex] which is a horizontal translation 4 units to the right
20) H(-4, -3), I(-5, 0), J(-3, 0), K(-2, 1) to H'(-2, 1), 'I(-3, 4), J'(-1, 4), K'(0, 5) The transformation rule is [tex]T_{(2, \,4)}[/tex], which is a translation 2 units to the right and 3 units up
21) E(0, 1), F(-1, 5), G(0, 5), H(3, 2), to E'(1, -4), F'(0, 0), G'(1, 0), H'(4, -3), which is a transformation with the rule, [tex]T_{(1, \,-5)}[/tex], which is a translation one unit to the right and five units down
22) B(-4, -2), C(-3, 3), D(-2, 1) to B'(1, -3), C'(2, 2), D'(3, 0), which is a transformation of the form [tex]T_{(5, \,-1)}[/tex], which is a translation of 5 units to the right and 1 units down
23) I(2, 1), H(4, 4), G(5, 0) to I'(2, 0), H'(4, 3), G'(5, -1), which is a transformation with the rule [tex]T_{(0, \,-1)}[/tex], which is a translation of one unit down
24) X(1, -4) W(3, 0), V(3, -4) to X(3, -5) W(5, -1), V(5, -5), which is a transformation with the rule, [tex]T_{(-2, \,-1)}[/tex], which is a translation of 2 units to the left and 1 units down
25) G(1, -1), F(2, 3), E(4, 2), D(4, -3) to G'(-2, -3), F'(-1, 1), E'(1, 0), D'(1, -5) which is a transformation with the rule, [tex]T_{(-3, \,-2)}[/tex], which is a translation of 3 units to the left and 2 units down
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true or false? the solutions for y>x+3 are all in the points in the shaded half plane but does not include points on the line y=x+3
Answers
When we have an inequality with the symbols < or >, the boundary line of the solution area will not be included in the solution of the inequality, then in this case that we have y>x+3 the solution set are all the points in the shaded half-plane but does not include points on the line y=x+3, and the answer is true
kinda due now pls help
Answers
The function describes the motorboat's distance from the shore
y = -4x+50
Given,
In the question:
A motorboat moves across a lake as a constant speed. when it begins, it is 50 km from the shore
After 9 minutes, it is 14 km from the shore.
So, The rate of change =
= [tex]\frac{Final Distance - initial distance}{time} \\\\\frac{14-50}{9} = -4[/tex]
Negative sign shows that there is decrease in distance per minute
The rate of change of distance is 4 km / minutes
General equation : y = mx+ c
Where m is the slope and c is the constant
Substitute the values in the equation :
y= -4x +50
Where y is the final distance and x is the minutes
So, Option C is true
Hence, The function describes the motorboat's distance from the shore
y = -4x + 50.
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What is the midpoint of the line segment with the endpoint (3.5,2.2) and (1.5,-4.8)?
Answers
Given
A = (3.5, 2.2)
B = (1.5, -4.8)
Procedure
A midpoint is a point on a line segment that divides the segment into two equal segments.
A travel agency charges $64 for each bus ticket and $82 for each train ticket. How much does it cost for 3 bus tickets and 4 train tickets?
Answers
Cost of 3 bus tickets is $ 192 and cost of 4 train tickets is $ 328.
Explain the use of multiplication?
The process of finding the sum of two or more numbers is known as multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. We can rapidly determine the total number of things by multiplying.
When multiplying, we'll consider the number of groups with similar sizes and the number of items in each group.
It is given ,
Cost of each bus ticket = $ 64
Cost of each train ticket = $ 82
Number of bus ticket = 3
Number of train ticket = 4
Total cost of bus ticket = 3 × 64 = $ 192
Total cost of train ticket = 4 × 82 = $ 328
Hence , cost of 3 bus tickets is $ 192 and cost of 4 train tickets is $ 328.
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Landyn's brother is five years older than Landyn. Their combined ages add up to 23. How old is Landyn?
The variable y represents: []
Equation: [] (Make sure to simplify this!)
Landyn is 9 years old.
Answers
Answer:
X = 9
Landyn is 9 and his brother is 14
Step-by-step explanation:
X + Y = 23
Y = X + 5
X + X + 5 = 23
2x + 5 + 23
- 5 - 5
2x / 2 = 18 / 2
Simplified = 9 / 1
Y = 9 + 5
Y = 14
a population of amoebas in a petri dish will triple in size every hour .at the start of an experiment the population is =800x^3 where x is the number of hours models the population growth how amoebas are in the perri dish after 9 hours
Answers
From the given information, we know that the expression that models the population of amoebas with respect to time is:
[tex]P=8x^3[/tex]Where x is the number of hours. by replacing 9 for x, we can find the population after 9 hours, like this:
[tex]\begin{gathered} P=8\times9^3 \\ P=8\times729 \\ P=5832 \end{gathered}[/tex]Then, the population of amoebas after 9 hours is 5832.
through -4,-5 parrelel to y=1/2x-4
Answers
The equation of the line that passes through the point (-4, -5) and is parallel to y = 1/2x -4 is y = 1/2x - 3
Equation of a straight line passing through a given pointFrom the question, we are to determine the equation of the line that passes through the given point and is parallel to the given equation.
The given point is (-4, -5)
The given equation is y = 1/2x - 4
NOTE: If two lines are parallel, then their slopes are equal
Now, we will determine the slope of the given line '
y = 1/2x - 4
Compare to the general form of an equation of a straight line
y = mx + b
Where m is the slope
and b is the y-intercept
Therefore, m = 1/2
That is, the slope of the line is 1/2
Now, we will determine the equation of the line that has a slope of 1/2 and that passes through the point (-4, -5)
Using the point-slope form of the equation of a straight line
y - y₁ = m(x - x₁)
Then,
y - (-5) = 1/2(x - (-4))
y + 5 = 1/2(x + 4)
y + 5 = 1/2x + 2
y = 1/2x + 2 - 5
y = 1/2x -3
Hence, the equation of the line is y = 1/2x - 3
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explain the error a problem states that Ursula earns $9 per hour to write an expression that tells you how much money that Ursula earns for H hours. Joshua 9 / h and Sarah wrote 9h who's expression is correct and why
Answers
We will have that Sarah's function is the correct one, since each hour she will get $9, then when we multiply will give us the amount of money she makes in the number of hours.
H = 9h
13. Suppose you live in a state that collects 18.2c excise tax on a gallonof gasoline. If you buy 18.5 gallons of gasoline, how much state excise taxis collected?a, $3.06b 83.37$2.99C
Answers
The excise tax on 1 gallon of gasoline = 18.2 cents
You will buy 18.5 gallons
We need to find the excise tax you should pay
At first let us change the cent to dollar
1 cent = 1/100 dollars
18.2 cents = 18.2 * 1/100 = 0.182 dollars
Now you will buy 18.5 gallons
You will pay = 18.5 * 0.182 = 3.367 Dollars
The state excise tax = $3.367
Round the number to the nearest cent, then it will be $3.37
On a road map, the distance from City A to City B is 4 inches. The map scale is 1 inch = 20 miles. What is the actual distance, in miles, between City A and City B? A. 5 miles B. 24 miles C. 48 miles D. 80 miles
Answers
Answer: D. 80 miles
Step-by-step explanation:
if 1 inch is 20 miles, then 4 inches is 4 x 20 = 80 miles what is real distance between City A and City B
1 inch = 20 miles4 inch = 4 x 1 inch = 4 x 20 miles = 80 milesAnswer:
D. 80 miles
Step-by-step explanation:
If the map distance between Cities A and B is 4 in, and the map scale is 1 in = 20 mi, then the actual distance between Cities A and B is:
[tex]\frac{4\text{ in}}{1}\times\frac{20\text{ mi}}{1\text{ in}}=\frac{80\text{ mi}}{1}=80\text{ mi}[/tex]
In other words, every one inch on the map equates to 20 miles in actual distance. Therefore, 4 inches equates to 80 miles.
May you please help me solve the answer to this problem step by step, please?
Answers
Given:
As angle N is 90 degree.
[tex]\begin{gathered} \angle N=44^{\circ}+\angle n \\ \angle n=90^{\circ}-44^{\circ} \\ \angle n=46^{\circ} \end{gathered}[/tex]To find the bearing of flight from Elgin to Canton.
Use the sin ratio,
[tex]\begin{gathered} \frac{\sin c}{510}=\frac{\sin n}{720} \\ \frac{\sin c}{510}=\frac{\sin46^{\circ}}{720} \\ \sin c=\frac{\sin46^{\circ}}{720}\times510 \\ \sin c=0.4995 \\ c=\sin ^{-1}(0.5095) \\ c=30.63^{\circ} \end{gathered}[/tex]The bearing angle ( clockwise from north ) can be calculated by subtracting the above angle from the west bearing angle of 270 degree.
[tex]270^{\circ}-30.63^{\circ}=239.37^{\circ}[/tex]Answer: 239.37 degree
1. A roll of ribbon contains 5 yards of ribbon, Janet cuts 1 yards of ribbon from the roll. How much ribbon is left on the roll? 4įyards 3ş yards 6 yards 4ş yards
Answers
Given that the total length of the ribbon on the roll is 5 yards.
Janet cuts 1 (1/3) yards of ribbon from the roll, then the remaining length of ribbon on the roll is calculated as,
[tex]\begin{gathered} \text{Remaining Ribbon length=Total Length-Length cut out} \\ \text{Remaining Ribbon length=}5\text{ yards-1}\frac{1}{3}\text{ yards} \\ \text{Remaining Ribbon length=}(5-\frac{4}{3})\text{ yards} \\ \text{Remaining Ribbon length=(}\frac{15-4}{3})\text{ yards} \\ \text{Remaining Ribbon length=(}\frac{11}{3})\text{ yards} \\ \text{Remaining Ribbon length=3}\frac{2}{3}\text{ yards} \end{gathered}[/tex]Thus, the length of the ribbon left on the roll is 3 (2/3) yards.
So the second option is the correct choice.
Vector v has an initial point at (9, 3) and a terminal point at (16, 12). Which of the following represents the linear form of v?
Answers
Answer:
The coordinate of the initial point is given below as
[tex](x_1,y_1)\Rightarrow(9,3)[/tex]The coordinate of the terminal point is
[tex](x_2,y_2)\Rightarrow(16,12)[/tex]Concept:
The formula below will be used to calculate a linear form of v
[tex]\Rightarrow(x_2-x_1)i+(y_2-y_1)j_{}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \Rightarrow(x_2-x_1)i+(y_2-y_1)j_{} \\ \Rightarrow(16-9)i+(12-3)j \\ \Rightarrow7i+9j \end{gathered}[/tex]Hence,
The final answer is
[tex]v=7i+9j[/tex]The FIRST OPTION is the right answer
If a graph includes the points (2,5) and (8,5) which of the following must be true ? 1.it is the graph of a linear function 2.it is not the graph of a function 3.it is the graph of an increasing function 4.none of the above
Answers
Answer
Option 1 is correct.
The graph could easily be the graph of a linear function.
Explanation
The points (2, 5) and (8, 5) can be seen to lie on the same line of y = 5
So, we can conclude that the graph could be a simple linear function, or a curve that passes this point twice.
So, option A is the only correct option here.
Hope this Helps!!!
A new streaming service sent out a survey to 250 households to see who would be interested in its service. The company found that it could charge $45 per month, with a margin of error of ±1.5. If 1,000 people signed up for the service, what is the least amount of monthly revenue the company should expect?
$43,500
$45,250
$46,500
$47,000
Answers
Answer:
$43,500
Step-by-step explanation:
Charge for the month - margin of error
= 45 - 1.5
= $43.50
= 43.50 x 1,000
= $43,500
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Answers
Answer:
length = 12 miles
width = 6 miles
Step-by-step explanation:
Framing algebraic expression and solving:length = x miles
width = (x - 6) miles
Area of rectangle = 72 square miles
length * width = 72
x * (x - 6) = 72
x*x - 6*x = 72
x² - 6x - 72 = 0
Sum = -6
Product = -72
Factors = 6 , (-12) { 6 + (-12) = -6 and 6*(-12) =-72 }
Rewrite the middle term using the factors.
x² + 6x - 12x - 72 = 0
x(x + 6) -12(x + 6) =0
(x + 6)(x - 12) = 0
{x + 6 = 0 is rejected as length will not have negative value}
x - 12 = 0
[tex]\sf \boxed{\bf x = 12 \ miles}[/tex]
length = 12 miles
Width = 12 - 6 = 6 miles