Answers
.. (-3/2)x^2 +0x +3
to the pattern of
.. ax^2 +bx +c
and you can see that
.. a = -3/2 . . . b = 0 . . . c = 3
____
Because a is negative, the parabola opens down. Because it opens down, the vertex is the high point, the maximum.
____
The y-intercept is always c. Here c=3, so the y-intercept is (0, 3).
____
The axis of symmetry is given by
.. x = -b/(2a)
.. x = -0/(2*(-3/2)) = 0
____
Because the y-intercept is on the axis of symmetry, it is the vertex.
.. vertex = (0, 3)
____
Put x=±2 in the equation and evaluate.
.. y = (-3/2)*(±2)^2 +3
.. = (-3/2)*4 +3
.. = -6 +3 = -3
The two points are (-2, -3) and (2, -3).
Related Questions
Mark has 36 drawings of horses and 4 drawings of spaceships. write and solve an equation to find how many times as many drawings of horses he has as spaceships.
Answers
4x = 36
Dividing both sides by 4:
x = 9
Hope this helps!
(I need 20 letters)
Find the percent of increase from 4.5 inches to 13.5 inches.
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Final answer:
To calculate the percent of increase from 4.5 inches to 13.5 inches, subtract the original value from the new value, divide by the original value, and then multiply by 100, resulting in a 200% increase.
Explanation:
To find the percent of increase from one number to another, you can use the formula: (New Value - Original Value) / Original Value × 100%. Applying this to the question, the original value is 4.5 inches, and the new value is 13.5 inches.
Calculate the increase: 13.5 - 4.5 = 9 inches.Divide the increase by the original number: 9 / 4.5 = 2.Convert this to a percentage by multiplying by 100: 2 × 100% = 200%.Therefore, the percent of increase from 4.5 inches to 13.5 inches is 200%.
one method of estimating is to
Answers
Hope this helps!
1. Solve the equation. -4x = 0
X = -4
X = 4
X = 0
X = 1
2. decide whether the given number is a solution of the given equation. Is 8 a solution of y + 9 = 17 ?
Yes or no
3. simplify the expression by combining like terms. 10x - x - 2x - x
8x
x² + 8x
6x
-x2 + 8x
4. Name the property shown. 12x( y ) = 12(xy)
Answers
2. is yes
3. is 6x
4. is associative property of multiplication
Match each correlation coefficient with the type of association it indicates between the variables x and y.
r = 0.9
r = -1.0
r = -0.6
r = 0.1
a perfect linear association in which y increases as x increases
a perfect linear association in which y decreases as x increases
a strong linear association in which y increases as x increases
a strong linear association in which y decreases as x increases
a moderate linear association in which y increases as x increases
Answers
A value of 0.9 would indicate that the correlation is positive. Since it's also close to the value 1, it would also tell us that the correlation of y and x is strong. Therefore, r = 0.9 would be a strong linear association in which y increases as x increases.
r = -1.0
Since the value of r is negative, this would mean that the correlation is also negative. Furthermore, the value of r is also at the minimum point which is -1.0 thus this would tell us that the correlation is a perfect linear association in which y decreases as x increases.
r = -0.6
Likewise, this r value is also negative thus allowing us to know that y will decrease as x increases. The value of r, which is -0.6, is also close to -1.0. This allows us to tell that it is a strong relationship. Therefore, r = -0.6 is a strong linear association in which y decreases as x increases.
r = 0.1
For this correlation, the r value is positive. This would indicate that the value of y will increase as x increases. Since the r value is only 0.1, we cannot say that it is a strong relationship since it is far from the maximum value for a perfect relationship which is 1. Therefore, r = 0.1 is a moderate linear association in which y increases as x increases.
r = 0.9 (a strong linear association in which y increases as x increases)
r = -1.0 (a perfect linear association in which y decreases as x increases)
r = -0.6 (a moderate linear association in which y decreases as x increases)
r = 0.1 (no linear association or a very weak association)
PLZ HELP ASAP WILL GIVE BRAINLIEST ANSWER!!!!!
What do you predict the current will be in the absence of sunlight?
Answers
Given: ΔABC ≅ ΔFDE. . What is the length of segment DE rounded to the nearest tenth?. . 3.2. . 4.2. . 2.2. . 3.6. .
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[tex]d= \sqrt{( x_{2}- x_{1})^2 + ( y_{2}- y_{1})^2 } [/tex]
[tex]d= \sqrt{(1)^2 + (-3)^2 } [/tex]
[tex]d= \sqrt{1+9 } [/tex]
[tex]d= \sqrt{10 } [/tex]
[tex]d= 3.2[/tex]
The length of segment DE is 3.2
Answer:
The length of segment DE is 3.2 (A)
Step-by-step explanation:
Find a rational number that is between 9.5 and 9.7
Answers
I think a rational number between 9.5 and 9.7 could be 9.6.
Enjoy.
~Isabella
Answer:
9.6
Step-by-step explanation:
It is a rational number as it has terminating decimal expansion
The expanded form 700,000 + 10,000+9 represents the whole number. 701,309. 713,009. 710,309. 713,090.
Answers
A light bulb manufacturing machine produces 72 light bulbs per minute. How much time would it take to make 5400 light bulbs?
Answers
It would take 75 minutes for the machine to make 5400 light bulbs.
The ordered pairs below represent a function
(-2,-17.5),(5,8.75),(0,-10),(-1,-13.75),(3,1.25)
What is the rate of change of the function?Round to the nearest hundreth if necessary. PLEASE HELP ASAP WILL AWARD BRAINLIEST!!!
Answers
If you plot the points, you will see that they are linear. The rate of change is equal to the slope between the points. Since the slope is the same between all of them, pick two points and find the slope.
(8.75 - (-17.5) / ( 5 - (-2))
26.25 / 7
3.75
Answer:
The answer is 3.75.
Step-by-step explanation:
I did this before
Carpet sells for $3 per square foot and will cost you $810 to recarpet your rectangular room. if your room is 18 feet long, how many feet wide is it?
Answers
Area of the room is 270 square feet.
Area = 270 square feet, length = 18 feet
Area = Length x Width
270 = 18 x width
Width = 280 ÷ 18
Width = 15 feet
The room is 15 feet wide.
In the figure, line TU is tangent to the circle at point U. Use the figure to answer both of the questions. Show all of your work.
(a) Describe the relationship among the lengths of the segments formed by the secant, RT , and the tangent segment, TU. You may use words and/or an equation to describe.
(b) Suppose RT= 9 in. and ST = 4 in. Is it possible to find the length of TU ? If so, show how to find the length. If not, explain why not.
Answers
RT×ST = TU²
b) Using the above relationship, fill in the given values and solve for TU.
(9 in)×(4 in) = TU²
TU = √(36 in²) = 6 in
Answer:
(a) The relation is RT × ST = TU²
(b) TU = 6
Step-by-step explanation:
(a) There is a secant law for circles that says the following: "if two secants are drawn to a circle from one exterior point, then the product of the external segment and the total length of each secant are equal". Applying this for the mentioned question, we have that RT × ST = TU x TU = TU² (considering that for TU case, the tangent is also a secant).
Then RT × ST = TU²
(b) Let's apply the equation in (a). RT × ST = TU² means 9 × 4 = TU²
Solving that equation, we have TU = √36 = 6
Thus TU = 6
PLEASE ANSWER THIS EASY MATH QUESTION!!
WILL PROVIDE THE ANSWERS BELOW!!!
Answers
Analyze the graph of the quadratic function that contains the points (0,-2), (1,0) and (3,10). Create the equation of the function given the three points.
Answers
Which graph represents the function on the interval [−3, 3] ?
Answers
floor(0.1) -3 = -3 . . . . only the lower-left graph has this point.
The lower-left selection is appropriate.
Carolina is mowing lawns for a summer job. For every mowing job, she charges an initial fee plus $6 for each hour of work. Her total fee for a 4-hour job, for instance, is $ 32.
Answers
Carolina's charges can be represented by the linear equation y = 8 + 6x, where x represents hours worked and y represents the total fee charged for the service.
Explanation:The subject this question pertains to is Mathematics, specifically linear equations. Carolina's job can be modelled by a linear equation, where the independent variable is the number of hours worked and the dependent variable is the total fee charged.
In this case, Carolina charges an initial flat fee plus $6 per hour worked. Her total charge for a 4-hour job is $32, which means her initial fee can be deduced by subtracting four times her per-hour fee from the total fee, that is $32 - 4*$6 = $32 - $24 = $8. Therefore, the linear equation that models Carolina's job is y = 8 + 6x, where x is the number of hours worked and y is the total fee charged.
This is similar to the linear equation that represents Svetlana's tutoring job in Example 12.4, where each tutoring session earns her a one-time fee of $25 plus $15 per hour of tutoring, modeled by the equation y = 25 + 15x.
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PLEASE HELP ME ON THIS
Answers
The number of hours it will take is :
22h = 221-45
22h = 176
h = 176/22
h=8
so it takes them 8 more hours to finish learning the song.
If tan x=a/4 and cos x=4/b what is the value of sin x?
Answers
The value of sin x is sqrt(b^2 - 16)/16.
Explanation:
To find the value of sin x, we can use the trigonometric identity: sin^2(x) + cos^2(x) = 1.
Given that tan x = a/4 and cos x = 4/b, we can use the Pythagorean identity (1 + tan^2(x) = sec^2(x)) to find the value of sin x:
1 + (a/4)^2 = (4/b)^2
Simplifying the equation, we get: 1 + a^2/16 = 16/b^2Multiplying both sides by 16, we get: 16 + a^2 = 256/b^2Substituting the value of cos x, we get: 16 + a^2 = 256/(16/b^2)Further simplifying, we get: 16 + a^2 = 16b^2/16Cross multiplying, we get: 16 + a^2 = b^2Substituting the value of tan x, we get: 16 + (4a)^2 = b^2Simplifying the equation, we get: 16 + 16a^2 = b^2Subtracting 16 from both sides, we get: 16a^2 = b^2 - 16Taking the square root of both sides, we get: 4a = sqrt(b^2 - 16)Dividing both sides by 4, we get: a = sqrt(b^2 - 16)/4Substituting the value of a in the equation sin x = a/4, we get: sin x = sqrt(b^2 - 16)/16
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What is the domain of y = cos θ?
A. [-1, 1]
B. [0, infinity]
C. All real numbers
D. 2pi,
Answers
Answer:
Option C - All real numbers
Step-by-step explanation:
Given : Function [tex]y=\cos \theta[/tex]
To find : The domain of given function ?
Solution :
Domain is defined as the set of values for which function is defined.
We have given the function,
[tex]y=\cos \theta[/tex]
We know, for any value of [tex]\theta[/tex] the function [tex]y=\cos \theta[/tex] is defined.
Which means the set of all real numbers defined the given function i.e. [tex]x\in(-\infty,\infty)[/tex]
Therefore, Option C is correct.
The domain of [tex]y=\cos \theta[/tex] is all real numbers.
Javier bought a 20 oz smoothie that contains 450 total calories how many calories does a smoothie contain per ounce
Answers
1 oz = 450 ÷ 20
1 oz = 22.5 calories
PLEASE HELP ME ON THIS
Answers
After receiving $42, the new domain (that Albert can afford) is from 80 to 147.
Find an nth degree polynomial function with real coefficients satisfying the given conditions. calculator
Answers
To find an nth-degree polynomial function with real coefficients given certain conditions, we can write the polynomial as a product of its linear factors using the given roots.
Explanation:To find an nth-degree polynomial function with real coefficients, we need to use the given conditions. Let's say the conditions include the roots of the polynomial. If we have n distinct real roots, the polynomial will have n factors. So, if the roots are a, b, c, ..., we can write the polynomial as P(x) = (x - a)(x - b)(x - c)...
Example:To find a quadratic polynomial with roots 2 and -3, we can write the polynomial as P(x) = (x - 2)(x - (-3)) = (x - 2)(x + 3) = x² + x - 6.
Similarly, for higher-degree polynomials, we use the same approach. We write the polynomial as a product of its linear factors using the given roots.
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A tour group charges a flat price for a tour of up to 20 people. The cost per person varies inversely with the number of people. If five people pay 135 each, what must 15 people pay per person.
Answers
15 people must pay 45 unit currency each
Explanation:
Assume that the number of people is x and that the price per person is y.
We are given that the cost per person varies inversely with the number of people.
This means that as the number of people (x) increases, the cost per person (y) decreases and vice versa
This can be translated into the following equation:
y = k / x
where k is the constant of proportionality.
Now, we need to get k.
We are given that:
for number of people (x) = 5, the charge per person (y) is 135.
Substitute with this in the above equation to get k as follows:
y = k / x
135 = k / 5
k = 135 * 5 = 675
The equation now became:
y = 675 / x
Finally, we want to get the cost per person (y) when the number of people (x) is 15.
All we have to do is substitute in the above equation to get the y as follows:
y = 675 / x
y = 675 / 15
y = 45
This means that, for a group of 15 people, each one will pay 45 unit currency
Hope this helps :)
Among 320 randomly selected airline travelers, the mean number of hours spent travelling per year is 24 hours and the standard deviation is 2.9. What is the margin of error, assuming a 90% confidence level? Round your answer to the nearest tenth. 0.01
Answers
The Margin of error for a 95% confidence level will be ..
Answer= greater than 0.3
Answer:
The margin of error assuming a 90% confidence level is 0.3
Step-by-step explanation:
Size of the sample: n=320
Mean: m=24
Standard deviation: s=2.9
Confidence interval: 90%
100(1-α)=90
Solving for α: Dividing by 100 both sides of the equation above:
100(1-α)/100=90/100
1-α=0.9
Subtracting 1 both sides of the equation:
1-α-1=0.9-1
-α=-0.1
Multiplying the equation by -1:
(-1)(-α=-0.1)
α=0.1
n= [z(1-α/2) s / E]^2
where E is the margin of error
z(1-α/2)=z(1-0.1/2)=z(1-0.05)=z(0.95)=1.64 (Table standard normal distribution)
z(1-α/2)=1.64
Replacing the known values in the equation above:
320= [(1.64) (2.9) / E]^2
320= (4.756/ E)^2
Solving for E: Square root both sides of the equation:
sqrt(320)=sqrt[ (4.756/ E)^2]
17.88854382=4.756/E
Cross multiplication:
17.88854382 E = 4.756
Dividing both sides of the equation by 17.88854382:
17.88854382 E / 17.88854382 = 4.756 / 17.88854382
E=0.265868486
Rounding tho the nearest tenth:
E=0.3
In circle C, what is the value of X?
X=112 degrees
X=90 degrees
X=68 degrees
X=22 degrees
Answers
Answer:
x=22 degrees
Step-by-step explanation:
We are given a circle C
Centre is at C
A line passes through the centre makes angle x and 68 on either side
A triangle is formed with angles x, 68 and another angle at the circumference.
Since the line passing through the centre is diameter of the circle, we have
the third angle of the triangle = 90 degrees ( BY semi circle angle theorem)
In the triangle sum of three angles
=90+x+68 =180
x =22 degrees
Given f(x) = 3x+4 . What is f(8)
Answers
Comment the correct answer.
f(x)=3x+4
f(8)=3(8)+4
f(8)= 24+4
f(8)=28
hope that helps!!
what is the y- coordinate of the y- intercept of the line that passes through the points (-4,-4) and (4,8)
Answers
[tex]\bf \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}y-(-4)=\cfrac{3}{2}[x-(-4)] \\\\\\ y+4=\cfrac{3}{2}(x+4)\implies y+4=\cfrac{3}{2}x+6\implies y=\stackrel{slope}{\cfrac{3}{2}}x\stackrel{y-intercept}{+2}[/tex]
notice the slope-intercept form, that's the y-coordinate.
Suppose you invest $500 at an annual interest rate of 8.2% compounded continuously. How much will you have in the account after 15 years? (1 point)
$1,671.74
$17,028.75
$1,710.61
$8,140.92
Answers
A=Pe^(rt)
P=$500 r=8.2% n=15
A=500*e^(0.082*15)
=500*e^1.23
= 1710.61476814
Rounding off to the nearest hundredths, we have
A= $1,710.61
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