The vertex form of the equation y = -z² + 12z -4 is y = -(z - 6)² + 32.
What is a parabola?A parabola's vertex is the location where the curve turns steepest. If a parabolic function has the shape of a 'U', it has a minimum value; otherwise, it has a maximum value. The parabola's axis of symmetry intersects with the parabola at its vertex.
For any parabola Ax² + Bx + C, the x-coordinate of the vertex is given by -B/(2A).
So, according to our question
A = -1
B = 12
C = -4
So, z = - 12/2(-1)
z = - 12/- 2
z = 6
Plug the value in the equation
y = - (6)² + 12(6) -4
y = -36 +72 -4
y = 32
So, the vertex of the parabola will be at (6, 32) and the vertex form of the equation y = -z² + 12z -4 is y = -(z - 6)² + 32.
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fill in the table using this function rule y=-2x-5
For given equation y = -2x - 5,
x y
-4 3
-2 -1
0 -5
2 -9
In this question we have been given an equation y = -2x - 5
We need to complete the table using given function rule.
for x = -4,
y = -2(-4) - 5
y = 8 - 5
y = 3
for x = -2,
y = -2(-2) - 5
y = 4 - 5
y = -1
for x = 0,
y = -2(0) - 5
y = -5
for x = 2,
y = -2(2) - 5
y = -4 - 5
y = -9
Therefore, for given equation y = -2x - 5,
x y
-4 3
-2 -1
0 -5
2 -9
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The ratio of cats to dogs in a shelter is 3:8.
Check all statements that must be true based on the statement above.
If none of the statements is true, check "None of the above".
There are 8 cats to every 3 dogs in the shelter.
O For every 8 cats in the shelter, there are 3 dogs.
There are 3 dogs to every 8 cats in the shelter.
There are 8 dogs to every 3 cats in the shelter.
None of the above
Answer:
Step-by-step explanation:
no
Which function ha real zero at x = –8 and x = 5?
g(x) = x2 3x – 40
g(x) = x2 3x 40
g(x) = x2 14x – 40
g(x) = x2 14x 40
The function which has real zero at x = –8 and x = 5 is x² + 3x - 40
Given the real zeroes at x = -8 and x = 5.
Factor theorem states that (x-r) is a factor of the polynomial function f(x) if and only if r is a root of the function f(x).
Since, we know that the root of the function i.e g(x) are -8 and 5 then the function has the following factor:
(x+8) = 0 and (x-5) =0
Zero product property states that if ab = 0 if and only if a =0 and b =0.
By zero product property,
(x+8)(x-5) = 0
Now, distribute each terms of the first polynomial to every term of the second polynomial we get;
x(x - 5) + 8(x - 5)
Now, when you multiply two terms together you must multiply the coefficient (numbers) and add the exponent.
x² + 8x - 5x - 40
Combine like terms;
x² + 3x - 40
therefore, the function has real zeros at x = -8 and x =5 is x² + 3x - 40
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Write the equation of the line
that is perpendicular to y=-2x
and passes through (-2, -1)
A) y = 1/2x + 1
B) y = -3x - 7
C) y = -2x - 5
D) y = 1/2x
E) y = 1/2
2 Which ordered pairs represent vertices of the
polygon?
Circle THREE correct answers.
(-11, 13)
(1, -1)
(1/4 , 2 2/1)
(1,-3)
The ordered pairs representing the vertices of a polygon are
(-11, 13) , (1, -1) and (1,-3).
Given, the ordered pairs representing the vertices of the polygon.
as, the given ordered pairs are
(-11, 13) , (1, -1) , (1/4 , 2(2/1)) , (1,-3).
Now, from the given ordered pairs
the pairs which are representing the vertices of a polygon are
(-11, 13) , (1, -1) and (1,-3).
So, the ordered pairs representing the vertices of a polygon are (-11, 13) ,
(1, -1) and (1,-3).
Hence, the ordered pairs representing the vertices of a polygon are
(-11, 13) , (1, -1) and (1,-3).
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a raft left port a and traveled toward port b. at the same time, a motorboat left port b and traveled toward port a. how many hours after departure will the two meet if the raft travels the distance between ports a and b after 30 hours and the motorboat travels the same distance in 6 horus?
If the raft travels the distance between ports a and b after 30 hours and the motorboat travels the distance in 6 hours. After the departure the two boats will after 5 hours 4 minutes.
Given that,
After leaving the port,
Raft travels the distance between a and b ports = 30 hours
Motorboats travels the distance between a and b ports = 6 hours
The triangle formed by their tracks and the line joining their current positions in a right angled triangle.
According to the Pythagoras Theorem,
a² + b² = c²
⇒ (30)²+ (6)² = c²
⇒ 900 + 36 = c²
⇒ 936 = c²
⇒ c = √936
⇒ c = 30.59
Rounding up 30.59 in 30.6.
Therefore, the boats will the two meet by 30 hours and 6 minutes after they leave the port.
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Write a linear equation that has m=-4 and passes through (5,9)!
Answer:
[tex]y=-4x+29[/tex]
Step-by-step explanation:
Using point-slope form,
[tex]y-9=-4(x-5) \\ \\ y-9=-4x+20 \\ \\ y=-4x+29[/tex]
Joelle is working on a school report in a word processor. She wants to place an oversized image which is 30.51 cm wide so that it appears centered on the page. The width of the page is 21.59 cm In the program, horizontal positions to the right of the leftmost edge of the page are positive.
What horizontal position for the left edge of the image should Joelle use to center the image?
The horizontal position for the left edge of the image should Joelle use to center the image is -4.46 cm .
In the question ,
it is given that ,
the length of the over sized image = 30.51 cm and
the length of the page = 21.59 cm
to find the margin , we subtract the width of the word processor page from the width of the oversized image.
that is
margin = 30.51 - 21.59 = 8.92 cm
Since , we have margin on two side ,that is horizontal positions to the left most side and horizontal positions to the right of the left most edge of the page . we divide 8.92 by 2 .
= 8.92/2
= 4.46 cm
it is given that the horizontal positions to the right of the leftmost edge of the page are positive,
So , horizontal position for the left edge of the image which Joelle should use to center the image would the negative .
the horizontal position is -4.46 cm .
Therefore , The horizontal position for the left edge of the image should Joelle use to center the image is -4.46 cm .
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Jess has to spend 12000 on expenses each year. If that amount of money is 30 percent of her salary, then how much much does jess make as an administrador per year? Round your answer to the nearest whole number if necessary
Jess makes $40000 per year as an administrator .
What is an administrator?
Administrators support the efficient operation of offices by carrying out clerical jobs and initiatives. You can be planning project meetings in the construction business as an administrator.
Main Body:
Expenses incurred by Jess = $12000
According to the question , 30% of his annual salary is his expenses
Let his annual salary be x.
so,
⇒30% of x = 12000
⇒ (30/100)*x = 12000
⇒x = 12000*100/30
⇒x= 40000
Hence the salary made by Jess in a year is $40000.
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there are 6 circles and 9 triangles what is the simplest ratio of circles to triangles?
A student club plans to buy food for a soup kitchen. A case of vegetables coats $10.68. The club can spend at most $50 for this project. What are all the possible numbers of cases c that the club can buy?
Answer:
0,1,2,3,4
Step-by-step explanation:
[tex]\frac{50}{16.68}[/tex] = 4.68 rounded to the nearest hundredths.
Please help! ASAP!! i really don't understand
Answer: B
Kyler earns more money in one week. Kyler earns $1,150 and Xiang earns $685 in one week.
Step-by-step explanation:
Have A Good Day!
Joe bought 5 1/4-pounds of trail mix for $24.94. What is the price per pound of the trail mix?
Answer:
Step-by-step explanation:
probably close to 5$
karen buys four movie tickets for $\$10.50$ each and two buckets of popcorn for $\$5.50$ each. how many dollars does she spend for the movie tickets and the popcorn? express your answer as a decimal to the nearest hundredth.
Karen spent $42.00 on movie ticket and $11.00 on popcorn.
Firstly calculating the amount spent on movie tickets
Cost of one movie ticket = $10.50
Cost of four movie tickets = 4×10.5
Performing multiplication on Right Hand Side of the equation
Cost of four movie tickets = $42.00
Now calculating the amount spent on popcorn
Cost on one bucket of popcorn = $5.50
Cost of two buckets of popcorn = 2 × 5.50
Performing multiplication on Right Hand Side of the equation
Cost of two buckets of popcorn = $11.00
Hence, the cost spent on movie tickets and popcorn is $42.00 and $11.00 respectively.
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What would be the compound interest obtained on an amount of $4800 at a rate of 5% per annum for 3 years?
A $448.7
B) $817.8
C)$623.5
D $756.6
The total compound interest obtained is $756.6.
We are given an initial amount equal to $4,800. This is the principal amount that is denoted by the variable "P". The rate of interest is 5% per annum and is denoted by "r". The interest is compounded annually and denoted by "I". The time duration is 3 years, denoted by the variable "t". Let the final amount be represented by the variable "A". We can use the given formula.
A = P(1 + r)^t
A = $4,800*(1 + 0.05)³
A = $4,800*(1.05)³
A = $4,800*1.157625
A = $5,556.6
The compound interest earned is the difference between the initial and the final amount.
I = A - P
I = $5,556.6 - $4,800
I = $756.6
Hence, the interest amount is $756.6.
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Eve is organizing a race to raise money for a local children's hospital. She makes $20 for each 5K participant and $45 for each 10K participant. Her goal is to raise $9,500.
If x represents the number of participants in the 5K race and y represents the number of participants in the 10K race, the linear equation for the given scenario is
x + y = . If Eve raises exactly $9,500, is it possible for there to be 220 participants in the 5K race?
(yes/no)
No It is not possible to have 220 participants in the 5k race.
How to determine the number of participants in the racesInformation from the question
She makes $20 for each 5K participant
$45 for each 10K participant.
x represents the number of participants in the 5K race
y represents the number of participants in the 10K race
Eve raises exactly $9,500, is it possible for there to be 220 participants in the 5K race = ?
From the question
$20 for each 5K participant and x represents the number of participants in the 5K race. = 20x
$45 for each 10K participant and y represents the number of participants in the 10K race = 45y
Eve raises exactly $9,500 means the sum of amount from 5k and 10k is 9500 = 20x + 45y = 9500
if Eve raise 220 participants in the 5k race then the equation will be
20 * 220 + 45y = 9500
4400 + 45y = 9500
45y = 9500 - 4400
45y = 5100
y = 113.333
The participants are human being and cannot be represented as fractions hence 220 is impossible for the 5k race
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an airplane flying at an elevation of 3,500 ft., directly above a straight highway. two motorists are driving cars on the highway on opposite sides of the plane. the angle of depression to one car is 31 degrees and to the other is 53 degrees. how far apart are the cars?
The first and second cars are 7724 feet apart from each other.
The angle of depression is the angle we have to move your eyes downwards to look at the car from the plane. Let's start with the first car, with the 31° angle of depression. Draw an upside-down right triangle with vertices at the plane, the car, and the point 3500 feet in the air above the car (level with the plane). The vertex at the plane is 31° and the right angle is the vertex in the air above the car. The length of the leg from the car to the point in the air above the car is 3500 feet. We like to find the length of the leg from the plane to the point in the air above the car. Since the two sides involved are the legs of the triangle, use tangent:
tan = opposite/ adjacent
⇒ tan(31°) = 3500/x
⇒ 0.60086 = 3500/x
⇒ 0.67 x = 3500 [ rounding up 0.60086 = 0.67]
⇒ x = 5223.88
That means the first car is 5223.88 feet from the point on the highway below the plane.
We can do something similar with the second car, which has an angle of depression of 53° from the plane. Again, the leg from the car to the point in the air above the car (level with the plane) is 3500 feet, the right angle is at the vertex at the point in the air above the car, and the 53° angle is at the vertex at the plane. We are looking for the length of the other leg, which runs from the plane to the point in the air above the car. Use tangent:
tan(53°) = 3500/x
⇒ 1.327 = 3500/x
⇒ 1.4x = 3500 [ rounding 1.327 = 1.4]
⇒ x = 3500/1.4
⇒ x = 2500
That means the second car is 2500 feet from the point on the highway below the plane.
Add the two distances together to get the total distance from car to car:
5223.88 + 2500.00 = 7723.88
So, rounded to the nearest foot, the cars are 7724 feet apart.
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please help and show steps please
Answer:
Step-by-step explanation:
f(x)=3x
2
+9x−16
Quadratic polynomial can be factored using the transformation ax
2
+bx+c=a(x−x
1
)(x−x
2
), where x
1
and x
2
are the solutions of the quadratic equation ax
2
+bx+c=0.
3x
2
+9x−16=0
All equations of the form ax
2
+bx+c=0 can be solved using the quadratic formula:
2a
−b±
b
2
−4ac
. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
x=
2×3
−9±
9
2
−4×3(−16)
Square 9.
x=
2×3
−9±
81−4×3(−16)
Multiply −4 times 3.
x=
2×3
−9±
81−12(−16)
Multiply −12 times −16.
x=
2×3
−9±
81+192
Add 81 to 192.
x=
2×3
−9±
273
Multiply 2 times 3.
x=
6
−9±
273
Now solve the equation x=
6
−9±
273
when ± is plus. Add −9 to
273
.
x=
6
273
−9
Divide −9+
273
by 6.
x=
6
273
−
2
3
Now solve the equation x=
6
−9±
273
when ± is minus. Subtract
273
from −9.
question is on image
Answer:
y= -3/4 x + 8
Step-by-step explanation:
y-2 = -3/4 (x-8)
y-2 = -3/4 x + 6
y = -3/4 x + 6 + 2
y = -3/4 x + 8
[50 Points help!] A circle graph shows that an office supply store spends a total of $1200 per month on expenses. If the company spends $300 on paper, what would be the measure of the central angle for paper in the circle graph?
A. 75 degrees
B. 90 degrees
C. 120 degrees
D. 150 degrees
E. 175 degrees
Answer:
B. 90 degreesStep-by-step explanation:
The circle represents a 360° angle.
Total spending corresponds to full circle and part of it spent on paper.
The ratio of paper over total is:
300/1200 = 1/4This is the part of circle which is:
360°*1/4 = 90°Correct choice is B.
Answer:
b) 90 degrees
Step-by-step explanation:
Forming the expression,
→ 360° × (300/1200)
Let's solve given expression,
→ 360° × (300/1200)
→ 360° × (1/4)
→ (360°/4)
→ 90°
Hence, the answer is 90°.
I need help please!!!!!
A circle has a radius of 16 ft. What is the area of the circle in terms of π?
Responses
A. 256π ft2
B. 128π ft2
C. 64π ft2
D. 32π ft2
The area of the circle in terms of π if the circle has a radius of 16 ft is 256 π ft^2. Option A is correct.
First, let us understand the circle:
A circle is nothing more than a round form with no corners or line segments. In geometry, it is a closed curve shape.
Some formulas related to circle:
Area of the circle = πr^2
Circumference of the circle = 2πr
where, r = radius of the circle.
We are given;
A circle has a radius of 16 ft.
We need to find the area of the circle in terms of π.
Area of the circle = πr^2
Put the value of r in the above formula:
Area of the circle = π 16^2 * ft^2
Area of the circle = 256 ft^2
Thus, the area of the circle in terms of π if the circle has a radius of 16 ft is 256 π ft^2. Option A is correct.
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Answer:
option A
Step-by-step explanation:
a college believes that 28% of applicants to that school have parents who have remarried. how large a sample is needed to estimate the true proportion of students who have parents who have remarried to within 6 percentage points with 95% confidence?
The sample size required for the true proportion of students who have parents who have remarried is 607.
What is termed the Confidence Interval?
The confidence interval is indeed the range of values within which you expect your forecast to fall a certain proportion of the time if you repeat your experiment or re-sample a population in the same manner.
The alpha value determines the confidence level, which is the percentage of times you anticipate reproducing an approximate between both the upper and lower limits of the confidence interval.
The above problem is based on the use of determining sample size to estimate the true percentage of students given the constraints.
We may also need to consult the table to determine the Z value.
For the given question,
α = 0.5
Consider the Z-table,
Zα/2 = Z (0.1/2)
Z (0.025) = 1.96
Let 'n' be the sample size required for the true proportion of students who have parents who have remarried.
For calculating the margin error 'E' is given 3%.
n = Z² (α/2) / E² × (P°(1 - P°))
Put the given values.
n = (1.96)² / (0.03)² × (0.28(1 - 0.28))
On solving,
n = 4268.444(0.2016)
n = 860.51
n ≈ 860.51
Thus, the sample size required for the true proportion of students who have parents who have remarried is 860.
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HELP! I WILL NAME YOU THE BRAINLIEST. Solve the system by graphing.
y = x + 4
-x + y = -3
in a parking lot with 200 cars, 50 cars are white, 30 cars are red, and 20 cars are silver. one car will be selected at random from the parking lot. if each car in the parking has only one color, which of the following cannot be the probability that the selected car will be green?
If each car in the parking has only one color , then the option which cannot be the probability that the selected car will be green is 0.6 , the correct option is (c) .
In the question ,
it is given that ,
total numbers of car in the parking lot = 200 cars
number of white cars = 50
number of red cars = 30
number of silver cars = 20
let the number of green cars be "x" ,
So , the number of green cars possible = 200 - 100 = 100
that means x ≤ 100 .
So , P(green) = x/200
Option(a)
p = 0.2 ,
So , x/200 = 0.2
x = 40
Option(b)
p = 0.1 ,
So , x/200 = 0.1
x = 20
Option(c)
p = 0.6 ,
So , x/200 = 0.6
x = 120
Option(d)
p = 0.5 ,
So , x/200 = 0.5
x = 100 ,
We can see that only option(c) gives the number of green cars as 120 , which is not possible .
Therefore , If each car in the parking has only one color , then the option which cannot be the probability that the selected car will be green is 0.6 , the correct option is (c) .
The given question is incomplete , the complete question
In a parking lot with 200 cars, 50 cars are white, 30 cars are red, and 20 cars are silver. one car will be selected at random from the parking lot. if each car in the parking has only one color, which of the following cannot be the probability that the selected car will be green ?
(a) 0.2
(b) 0.1
(c) 0.6
(d) 0.5
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Distribute to create an equivalent expression with the fewest symbols possible.
4(x - 2 + y) =4(x−2+y)
The equivalent expression of the given expression 4(x - 2 + y) is 4x-8+4y.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given expression is 4(x - 2 + y). The equivalent expression will be solved as,
E = 4(x - 2 + y)
E = 4x - 8 + 4y
Therefore, the equivalent expression of the given expression 4(x - 2 + y) is 4x-8+4y.
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what is the ratio of james wins to james play
Answer:
Step-by-step explanation:
If the expression [tex]\sqrt{25x^5y^5}/xy^4[/tex] is written in the form ax^by^c. then what is the product of a, b and c?
The product of a, b, and c is -45/4.
What is multiplication?Multiplication is the process of adding a number up to a given number.
The given expression is [tex]\frac{\sqrt{25x^5y^5}}{xy^4}[/tex].
Rewrite the expression as follows,
[tex]\frac{\sqrt{25x^5y^5}}{xy^4}[/tex]
[tex]=\frac{5x^{\frac{5}{2}}y^{\frac{5}{2}}}{xy^4}\\=5x^{\frac{5}{2}-1}y^{\frac{5}{2}-4}\\=5x^{\frac{3}{2}}y^{-\frac{3}{2}}[/tex]
The values of a, b, and c are 5, 3/2, -3/2.
The product of a, b, and c is,
5 × 3/2 × (-3/2)
= -45/4
Hence, the product of a, b, and c is -45/4.
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Given the exponential growth function †(x) = 75(1.0025)*
What is the initial value of the function?
What is the growth factor, or growth rate of the function (as a percent)?
The initial value of the function is 75.
The growth factor or growth rate of the function as a percent is 0.25%
An exponential growth model is defined as :
F(x) = A( 1 + r)^x
Where;
A = Initial amount,
r = rate of increase
x = time
Comparing the exponential growth function with the exponential growth model given;
f(x)=75(1.0025)ˣ
A = 75 = Initial amount
The growth rate of the model expressed as a percentage :
Taking :
(1 + r) = 1.0025
1 + r = 1.0025
r = 1.0025 - 1
r = 0.0025
Expressing r as a percentage:
r = 0.0025×100
= 0.25%
Hence we get the required answers.
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QUESTION 9/10 HELP ASAPP
Answer:
y = 3x + 8Step-by-step explanation:
GivenThe y-intercept b = 8,Slope m = 3.The equation is y = mx + by = 3x + 8