There is only one statement that is true: B. The graph of the function is a parabola.
How to study and interpret the characteristics of quadratic equations
In this question we have a quadratic equation, whose characteristics have to be inferred and analyzed. We need to prove each of the five choices presented in the statement:
Choice A:
If we know that x = - 10, then we evaluated it at the function:
f(- 10) = (- 10)² - 5 · (- 10) + 12
f(- 10) = 162
False
Choice B:
By analytical geometry we know that all functions of the form y = a · x² + b · x + c always represent parabolae.
True
Choice C:
The quadratic function opens up as its leading coefficient is greater that 0.
False
Choice D:
If we know that x = 20, then we evaluate it at the function:
f(20) = 20² - 5 · (20) + 12
f(20) = 312
False
Choice E:
If we know that x = 0, then we evaluate it at the function:
f(0) = 0² - 5 · (0) + 12
f(0) = 12
There is only one statement that is true: B. The graph of the function is a parabola.
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1. If x = 1 and y = 7, evaluate x+y/4
Answer:
2
Step-by-step explanation:
given x=1 and y=7
now, given expression ,
x+y/4
by putting the values of the x and y ,we get
x+y/4
= 1+7/4
= 8/4
= 2 (Ans.)
How many positive 3-digit numbers are divisible by 11?
Answer:
81
Step-by-step explanation:
If a number is divisible by 11, then you can make those numbers by multiplying 11 by any number. Like 33 is divisible by 11 because 3×11 is 33.
Of course, 33 is too small, we are looking for 3-digit numbers...
see image.
Here are yesterday's high temperatures (in Fahrenheit) in 12 U.S. cities. 48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80 Notice that the temperatures are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:
The five number summary and interquartile range for the data-set is given by:
Minimum: 48Lower quartile: 54.Median: 63.5.Upper quartile: 74Maximum: 80.Interquartile range: 20How to find the five number summary and interquartile range of the data-set?The five number summary is composed by the minimum and maximum value, and the first quartile, median and third quartile. As for each of these data, they are explained below.
The minimum value is the smallest value from the data-set, as the maximum value is the greatest value of the data-set.The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.The first quartile is the median of the first half of the data-set.The third quartile is the median of the second half of the data-set.The interquartile range is the difference of the third quartile and the first quartile.In this problem, we have that:
The minimum value is the smallest value, of 48.The maximum value is the smallest value, of 80.The data-set has even cardinality, hence the median is the mean of the middle elements, which are 63 and 64, hence the median is of 63.5.The first quartile is the median of the five elements of the first half, hence it is of 54.The third quartile is the median of the five elements of the second half, hence it is of 74.The IQR is the difference between the quartiles, hence 74 - 54 = 20.More can be learned about five number summaries at brainly.com/question/17110151
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A father and his son decide to sum their age. The sum is equal to sixty years. Six years ago, the age of the father was five times the age of the son. Six years from now the son’s age will be?
Answer:
20
Step-by-step explanation:
To solve this you have to make a system of equations.
Since the father and son's age sum up to 60, the first equation will be:
f + s = 60
Secondly, since the father's age is 5 times the age of the son 6 years ago the equation will be:
6 - (5s) = f
Now, you have to solve the first equation to let it equal to s
f + s = 60
f = 60 - s
Plug in
6 - 5s = 60 - s
+s +s
6 - 4s = 60
-6 -6
---------------------
-4s = 54
----- -----
-4 -4
s ≅ 14
14 + 6 = 20
Answer:
20.
Step-by-step explanation:
x = father's age and y = son's age,
x + y = 60
x - 6 = 5(y - 6)
x - 5y = -24
Subtract this from first equation:
6y = 84
y = 14
So the son's age is 14.
Six years time son will be 20.
Given that and are supplementary angles and that , explain how to find the measure of the complement of .
The measure of the complement is 25°.
What is supplementary and complementary angles?If the sum of two angles is 180 degrees then they are said to be supplementary angles, which form a linear angle together. Whereas if the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right angle together.
Given that, [tex]A_{1}[/tex] = 115°
sum of two angles [tex]A_{1}+A_{2} = 180[/tex]°
[tex]A_{2} = 180- A_{1}[/tex]
[tex]A_{2} = 180- 115[/tex]
[tex]A_{2} = 65[/tex]°
Since, [tex]A_{1}[/tex] and [tex]A_{2}[/tex] are supplementary angles.
Now,
Complementary angles add to 90, so the complement of [tex]A_{2}[/tex] is 90 - [tex]A_{2}[/tex] .
Then,
90-65
= 25°
Hence, The measure of the complement is 25°.
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Alonso brings \$21$21dollar sign, 21 to the market to buy eggs and avocados. He gets eggs that cost \$2.50$2.50dollar sign, 2, point, 50. Then, he notices that the store only sells avocados in bags of 333 for \$5$5dollar sign, 5. He wants to buy as many avocados as he can with his remaining money.
How do u get 3 bags of avacodes or 9 avacadoes ??
Based on Alonso's budget, he can get 3.7 bags of avocados and the cost of 3 bags of avacodes or 9 avacadoes is $15.
EquationAmount Alonso brings to the market = $21Cost of an egg = $2.50Cost of avocados in bags of 3 = $5Number of avocados bought = x21 = 2.50 + 5x
21 - 2.50 = 5x
18.50 = 5x
x = 18.50 / 5
x = 3.7 bags of avocados
To get 3 bags of avocados or 9 avocados
= $5 × 3
= $15
Therefore, Alonso can get 3.7 bags of avocados and the cost of 3 bags of avacodes or 9 avacadoes is $15.
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A repeated-measures study comparing two treatments with n = 4 participants produces md = 2 and ss = 75 for the difference scores. what is the estimated standard error for the sample mean difference?
The estimated standard error for the sample mean difference is 2.5 .
According to the question
A repeated-measures study comparing two treatments
n = 4
MD(mean difference) = 2
SS (sum of square) = 75
Now,
error for the sample
Formula for standard error
[tex]S^{2} = \frac{SS}{n-1}[/tex]
by substituting the value
[tex]S^{2} = \frac{75}{4-1}[/tex]
[tex]S^{2} = \frac{75}{3}[/tex]
S² = 25
S = 5 (s is never negative)
Standard error of the estimate for the sample mean difference
As
The standard error of the estimate is the estimation of the accuracy of any predictions.
The formula for standard error of the mean difference
standard error of the mean difference =[tex]\frac{standard\\\ error}{\sqrt{n} }[/tex]
standard error of the mean difference = [tex]\frac{5}{\sqrt{4} }[/tex]
standard error of the mean difference = 2.5
Hence, the estimated standard error for the sample mean difference is 2.5 .
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Given f(x)=abx+c. How would increasing the value of a change the graph?
Increasing the value of a increases the initial value of our exponential, and also increases the rate of growth of the function.
How would increasing the value of a change the graph?
Y assume we have an exponential equation of the form:
y = a*b^x + c
In this case, a is what we know as the "initial value" of the exponential.
Notice that when we evaluate in x = 0, we get:
y = a*b^0 + c
y = a + c
So increasing a will increase the initial value of what we are representing, but it will also increase the "rate" at which our function increases when x increases.
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solve the equation
14x+7y=28
Find the missing length indicated.
The missing length indicated on the right triangle is 120 units
How to determine the missing length?To start with:
The missing length in the right triangle can be represented with the variable x
Next, we have the following equivalent ratio from the given triangle
64 : x = x : 289 - 64
Express the ratio as a fraction
64/x = x/(289 - 64)
Evaluate the difference on the right-hand side
64/x = x/225
Cross multiply in the above equation
x * x = 64 * 225
This gives
x^2 = 64 * 225
Take the square root of x^2 (do not approximate)
x = 64 * 225
Take the square root of 64 and 225 (do not approximate)
x = 64 * 225
Evaluate the product of 8 and 5
x = 120
Based on the given parameters, the missing length indicated on the right triangle is 120 units
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Hello, I need help with this. Giving brainiliest
9^(a) = (sqrt(3))^(a +2)
Answer:
2/3
Step-by-step explanation:
Let's solve your equation step-by-step.
9a=(√3)a+2
9a=1.732051a+2
Solve Exponent.
9a=1.732051a+2
log(9a)=log(1.732051a+2)(Take log of both sides)
a*(log(9))=(a+2)*(log(1.732051))
a=(log(1.732051)/log(9))*(a+2)
a=0.25*(a+2)
a=0.25a+0.5(Simplify both sides of the equation)
a−0.25a=0.25a+0.5−0.25a(Subtract 0.25a from both sides)
0.75a=0.5
0.75a/0.75=0.5/0.75
(Divide both sides by 0.75)
a=0.666667
a=2/3
0.666667=2/3
Hope this helps :)
Answer:
2/3
Step-by-step explanation:
9^a = sqrt(3)^a * sqrt(3)^2
9^a = 3^((a/2)+1)
3^(2a) = 3^((a/2)+1)
2a = (a/2)+1
1.5a=1
a=1/(3/2) = 2/3
Combine the like terms to create an equivalent expression. 9+a-5b-2=
❄ Hi there,
let us combine the like terms and create an equivalent expression –
[tex]\large\begin{gathered} \sf{9+a-5b-2} \\\sf{9-2+a-5b}\\\sf{7+a-5b} \end{gathered}[/tex]
That's as far as we can go.
❄
PLEASE HELP ITS MATH
Answer:
y = 4x + 3
Step-by-step explanation:
as the line is parallel to the given equation, the gradient (4x) must stay the same, and as it must pass through the point (-2, -5), we can solve for the y intercept:
to calculate for the y intercept, it is best to express the equation in slope intercept form:
y = mx + b
in this equation, mx stands for the gradient, which ive already highlighted remains 4x, and b stands for the y intercept (which we don't know yet).
y = 4x + b
what we have been given instead is the coordinates for the point this line crosses through (-2,-5) meaning when x = -2, y = -5.
Using this information, we can replace x and y in the equation:
-5 = 4(-2) + b
with consideration to the order of operations, it is important to solve the brackets first
-5 = -8 + b
now to get b by itself add 8 to both sides of the equation:
-5 + 8 = -8 + 8 + b
3 = b
now we remember from the slope intercept equation, b = the y intercept, so we can now solve the equation.
y = 4x + b
replace b with the number we solved for (3).
y = 4x + 3
this is the equation of the line that is parallel to y = 4x + 1, and passes through the point (-2, -5)
hope this helps :)
THIS IS REALLY IMPORTANT I NEED IT DONE BY TODAY PLEASE
Answer:
15. 155°
16. 115°
Step-by-step explanation:
15.
Use the big triangle.
At the top, the supplement of 60° is 120°.
The angle measuring 120° and the angle measuring 35° are the remote interior angles to exterior angle x.
120° + 35° = x
x = 155°
16.
See picture below.
x = 115°
Answer:
15) x = 155°
16) x = 115°
Step-by-step explanation:
The theorem that relates an exterior angle of a triangle to the opposite (remote) interior angles is helpful for these problems. It says the exterior angle is equal to the sum of the remote interior angles.
15)
Remove the altitude line and consider the interior angle of the triangle next to the exterior angle marked 60°. That interior angle will be ...
180° -60° = 120°
Then the angle we just found and the one marked 35° are "remote" to the exterior angle marked x. The theorem cited at the beginning tells us ...
x = 35° +120°
x = 155°
16)Extend the left side of the "parallelogram" (the side with the arrow) upward until it meets the top horizontal line. This cuts off a triangle with an exterior angle marked x, an interior angle marked 50°, and another remote interior angle at the top edge of that triangle.
The opposite angles of a parallelogram are congruent, so the external angle to the triangle at the top edge will be x, and the adjacent interior angle in the triangle will be (180° -x).
The exterior angle (x) is equal to the sum of the remote interior angles (50° and (180° -x)), so we have ...
x = 50 +(180 -x)
2x = 230 . . . . . . add x, simplify
x = 115 . . . . . . . divide by 2
The measure of the angles marked x is 115°.
A soap company started a promotion in which each packet of detergent powder will have 20% extra powder at the
same price, Jenna buys a 2 kg packet of the detergent powder. How much total detergent powder will be in the packet?
2.4kg.,
..
hope it helps
7. If F is a right angle, find the slope of line FH.
Answer:
1/2
Step-by-step explanation:
Find the slope, m, between E and F m = (7-3)/(2-4) = -2
perpindicular = - 1/m = 1/2 = slope FH
Suppose thirteen people qualify for a college cheerleading squad, eight are men and 5 are women. If a 6 member squad is selected, what is the probability that the squad will have exactly two male members.
The probability that the squad will have exactly two male members is; 0.0816
How to solve probability combinations?We are given;
Total number of people in cheerleading squad = 13
Number of Men = 8
Number of Women = 5
We are told that a 6 member squad is selected and now we want to find the probability that the squad will have exactly two male members.
Thus;
P(exactly 2 male members) = (8C2 * 5C4)/(13C6)
P(exactly 2 male members) = 140/1716
P(exactly 2 male members) = 0.0816
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(8x2-4x-8)(2x2+3x+2)
Answer: 12x squared + 2x + 96
Step-by-step explanation: We first simplify the parentheses. 8x2 = 16 - 4x - 8 = 16-8-4x = 8-4x. 2x2 = 4 +3x+2 = 4+2+3x = 6+3x. So, we are left with (16-4x)(6+3x). We rearrange the problem so it looks like this: (-4x + 16)(3x + 6). -4x(3x+6) + 16(3x+6). Now we just multiply. And, we get 12 x squared + 2x + 96
Susan drove 4 hours. Her average speed was 60 mph. Finish the chart below to give her an average speed of 60 mph.
║hour ║ speed║
______________
║1st ║ 65 ║
║2nd ║ 70 ║
║3rd ║ ____ ║
║4th ║ 55 ║
Answer:
Its 50
Step-by-step explanation:
60 times 4 it gives you 240.
Now minus all the numbers on the table like this
240 - 55 - 70 - 65 which equals to 50
240 would be the miles
1 + 7x = 5x + 25 solve for X
Answer:
x = 12
Step-by-step explanation:
1 + 7x = 5x + 25 ( subtract 5x from both sides )
1 + 2x = 25 ( subtract 1 from both sides )
2x = 24 ( divide both sides by 2 )
x = 12
Answer:
12
Step-by-step explanation:
Start by subtracting both sides by 5x:
[tex]1+7x-5x=25\\1+2x=25[/tex]
Subtract 1 from both sides
[tex]2x=24[/tex]
Divide both sides by 2
[tex]x=12[/tex]
Check[tex]1+7(12)=5(12)+25\\1+84=60+25\\85=85[/tex]
Therefore x = 12
What is a sample statistic give examples give examples. (select all that apply.)
A sample statistic is a numerical descriptive measure of a sample.
What is a sample statistic?A sample statistic is a numerical metric that describes a sample. A statistic (plural) or sample statistic is any quantity generated from values in a sample for statistical purposes. Estimating a population parameter, characterizing a sample, or testing a hypothesis are all statistical goals. A statistic is the average (or mean) of sample values. The term statistic refers to both the function and the function's value on a particular sample. When a statistic is utilized for a certain purpose, it may be given a name that indicates that purpose.The three examples are - x bar, s, s^2, p hatTherefore, a sample statistic is a numerical descriptive measure of a sample.
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The complete question is given below:
What is a sample statistic?
A _____descriptive measure of a _____.
Give three examples. (Select all that apply.)
The projected worth (in millions of dollars) of a large company is modeled by the equation w = 241(1.06) t. the variable t represents the number of years since 2000. what is the projected annual percent of growth, and what should the company be worth in 2011?
Answer:
6%- 457 Million
Step-by-step explanation:
w=241(1.06)^11=457 million
Select the correct answer.
Which function does this graph represent?
A downward open parabola rises from (negative 2 point 4, negative 4) to (negative 1, 2) and declines through (0 point 4, negative 4) on the x y coordinate plane.
A.
f(x) = 3(x + 1)2 + 2
B.
f(x) = -3(x + 1)2 + 2
C.
f(x) = -3(x + 1)2 − 2
D.
f(x) = 3(x − 1)2 + 2
The parabola represented by this graph has the following equation:
y = -16.67(x + 1)² + 2
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
A downward open parabola rises from (-2.4, 4) to (-1,2), and declines through (0.4, -4) on the coordinate plane, hence the vertex is given by:
(-1,2), hence the coefficients are h = -1 and k = 2, and the equation is:
y = a(x - h)² + k
y = a(x + 1)² + 2
We have that when x = -0.4, y = -4, hence the leading coefficient is found as follows:
y = a(x + 1)² + 2
-4 = a(-0.4 + 1)² + 2
a = -6/0.6²
a = -16.67
Hence the equation is:
y = -16.67(x + 1)² + 2
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The high school athletics department is installing a new rectangular addition to their current practice field. the length of the new addition will be at least 10 meters more than twice the width of the new addition. the original field has an area of 300 square meters. the area of the entire practice field, with the addition, must be no more than 1,200 square meters. if a represents the area of the entire practice field, including the new addition, and x represents the width of the new addition, in meters, which system of inequalities can be used to represent this situation?
The system of inequalities that best describes this situation provided A represents the area in which the entire field exists:
[tex]$\left \{ {{A \geq x^{2} +10x+300} \atop {A \leq 1200}} \right.[/tex]
What are word problems?Word problems in mathematics exist methods we can utilize variables, algebra notations, and arithmetic operations to solve real-life cases.
We have a new addition to the current rectangular field,
Let that new addition to the current rectangular field be x
Length of the new addition = 10x
Twice the width of the new addition = 2x²
Original area of the field = 300
From the above information, we can derive a quadratic equation:
2x² + 10x + 300
Also, we exist given a constraint that the total area of the practice field should be no more than 1200.
It can be less than 1200 or equivalent to 1200.
Therefore, the system of inequalities that best describes this situation provided A represents the area in which the entire field exists:
[tex]$\left \{ {{A \geq x^{2} +10x+300} \atop {A \leq 1200}} \right.[/tex]
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Find the average rate of change of the function a(x) = πx2 where a is the area of a circle with radius x as the radius changes from x=4 to x=6.
The average rate of change of the given function is 10π.
Given function
a = πx^2
Where a is the area of a circle with radius x
The radius changes from x = 4 to x = 6.
Calculating the average rate of change of function:
The method of finding the average rate between the function value over a certain interval is called the average rate of change.
The formula is given by :
Average = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
Where f(a) and f(b) are the function value over the limit a and b.
Average = [tex]\frac{f(6)-f(4)}{6-4}[/tex]
= [tex]\frac{\pi (6)^{2} -\pi (4)^{2} }{6-4}[/tex]
= [tex]\frac{\pi (36-16)}{2}[/tex]
= [tex]\frac{20\pi }{2}[/tex]
= 10π
The average rate of change of the given function is 10π.
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Suppose we flip four coins simultaneously: a penny, a nickel, a dime, and a quarter. What is the probability that at least $15$ cents worth of coins come up heads
The probability that at least $15$ cents worth of coins come up heads is
P(H)=1/16
This is further explained below.
What is the probability that at least $15$ cents worth of coins come up heads?Generally, We are doing a simultaneous toss of four coins. How likely is it that every coin will land with the head side facing up?
It has been established by everyone who has participated so far that the solution is 116, which can be written as
(1/2)4=1/16.
On the other hand, a person who is just starting out can benefit from another method to see things.
I'm going to go ahead and make the assumption that each coin is balanced and that each side has an equal chance of facing up.
Each coin has the potential to exist in either of two states (heads or tails). Therefore, there are
2^4 = 16 different permutations (states) that the four coins may be in together as a group.
Only one of these possible permutations results in all heads. This results in the correct value of 1/16.
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A data value is considered _______ if its z-score is less than 2 or greater than 2.
A data value is considered significantly low or significantly high if its z-score is less than -2 or greater than 2.
What does it mean if z-score is 2?
A positive z-score indicates the raw score is higher than the mean average.For example, if a z-score is equal to +1, it is 1 standard deviation above the mean.A negative z-score reveals the raw score is below the mean average.For example, if a z-score is equal to -2, it is 2 standard deviations below the mean.What does a standard deviation of 2 mean?
Standard deviation tells you how spread out the data is. It is a measure of how far each observed value is from the mean.In any distribution, about 95% of values will be within 2 standarddeviations of the mean.
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The correct question is -
A data value is considered _______ if its z-score is less than minus−2 or greater than 2.
A line has a slope of 2 and passes through the point -3, 6 what is the equation in slope intercept form
Answer:
y=2x+12
Step-by-step explanation:
what expression is equivalent to 6+3(n-4)-8+2n
Answer:
Step-by-step explanation:
Comment
Begin by removing the brackets.
6+3(n-4)-8+2n
6 + 3n - 12 - 8 + 2n Collect like terms
3n + 2n + 6 - 12 - 8 Combine
5n - 14
Answer
5n - 14
Solve for all values of xx by factoring.
x^{2}+5x-3= −4x−3
Answer:
x=0, x= -9
Step-by-step explanation:
First we simplify the equation into the form
ax^{2}+bx+c=0
By adding 4x+3 on both sides, we form the equation
x^{2}+9x=0
Now, we factor out the common factor: x.
x(x+9)=0
The only values that allow x(x+9) to be equal to 0 are:
x=0 or
x+9=0
The solutions are x=0 or x= -9
