the formula for the polynomial is:
p(x) = (-3/10)*(x - 2)^2*(x + 5)
How to find the formula for p(x)?Here we have a polynomial with the following roots:
x = 2, with a multiplicity of 2.x = -5 with a multiplicity of 1.So, if we define A as the leading coefficient, we can write the polynomial as:
p(x) = A*(x - 2)^2*(x + 5)
We know that the y-intercept is -6, so evaluating in x = 0 we should get:
p(0) = -6 = A*(0 - 2)^2*(0 + 5) = A*4*5 = A*20
-6/20 = A = -3/10
Then the formula for the polynomial is:
p(x) = (-3/10)*(x - 2)^2*(x + 5).
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d-6e+4f=-12
2d+5f=-15
d=0
Answer:
What digital/technological features will your futuristic bath/shower time utilize?
Consider the tables created with Fahrenheit and Celsius temperatures. Table A represents the function that models Celsius temperature, C(F), based on the given Fahrenheit temperature, F.
Which table could be used with Table A to verify that the function modeling Fahrenheit temperature, F(C), based on a given Celsius temperature, C, is the inverse of C(F)?
A table which could be used with Table A to verify that the function modeling Fahrenheit temperature, F(C), based on a given Celsius temperature, C, is the inverse of C(F) is: option A.
C -20 -15 -5
F(C) -5 4 23
What is temperature?Temperature can be defined as a measure of either the degree of hotness or coldness of a physical body (object).
In Science, temperature can be measured by using a thermometer and its units of measurement include the following:
Celsius (°C)Kelvin (K) Fahrenheit (°F)What is an inverse function?In Mathematics, an inverse function can be defined as a type of function that is obtained by reversing (undoing) the operation of a given function f(x). In Mathematics, a given function f(x) and its inverse function has the following property f⁻¹(f(x)) = x.
Based on the given function which models the Fahrenheit temperature, F(C) and Celsius temperature, C, the inverse of C(F) is as follows:
C -20 -15 -5
F(C) -5 4 23
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Answer:
A
Step-by-step explanation:
Hope this helps! Pls give brainliest!
5. The circle graph shows last year's ticket
sales with a total of 842 tickets.
4%
17%
55%
24%
Adults
Students
Children Under 12
Seniors
This year 22 more tickets were sold to
seniors. How many senior tickets were
sold this year?
A 36 tickets
B 39 tickets
C 143 tickets
D 165 tickets
The total ticket were sold this year is 39 tickets.
What is arithmetic?
Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
The circle graph shows last year's ticket sales with a total of 842 tickets.
Adults =4%
Students =17%
Children Under 12 =55%
Seniors =24%
This year 22 more tickets were sold to seniors.
According to given question we have
Ticket sold to the senior
=24% *842
= 202.08 tickets.
Tickets were sold this year
= 202.08/12 tickets.
=16.84 tickets.
This year 22 more tickets were sold to seniors
=16.84 tickets+22 tickets
=38.84 ≈39 tickets
Therefore, the total ticket were sold this year is 39 tickets.
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A child is 40 inches tall at age 6. For the next few years, the child grows by 2 inches per year. Explain why the child’s height after age 6 is a linear function of his age. Identify the growth rate and initial value. Using for time in years since age 6 and for height in inches, find a formula for as a linear function of .
1. The child's height after age 6 is a linear function of his age because it grows at a constant rate annually.
2. The child's growth rate is 5% with an initial value of 40 inches.
3. A linear function that represents the scenario is , H(t) = 40 + 2t.
What is a linear function?A linear function is a mathematical expression with variables multiplied by constants appearing in the first degree.
The mathematical operations involved in a linear function are addition and subtraction.
A linear function represents a straight line on the coordinate plane.
Data and Calculations:Initial height at age 6 = 40 inches
The annual growth rate in inches = 2 inches
Growth rate in percentage = 5% (2/40 x 100)
Linear Function for H:H(t) = 40 + 2t
Where t = years after age 6
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Question Completion:Using t for the time in years since age 6 and H for height in inches, find a formula for H as a linear function of t.
Pls help me as fast as possible
Find m∠2
Any help on this would be great!
Finding m∠2 is c. 44°.
Measure of angleFirst step is to find the Measure of angle 1 which is m∠1
Measure of angle 1 = (68° + 68°) or (68°×2)
Measure of angle 1 = 136°
Second step is to find m∠2
Since we have find the measure of angle 1 in order for us to find or determine m∠2 we would have to deduct or subtract m∠1 from 180°
Now let find m∠2
m∠1 = 136°
m∠1 + m∠2 = 180°
136° + m∠2 = 180°
m∠2 = 180° - 136°
m∠2 = 44°
Therefore finding m∠2 is c. 44°.
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Let [tex]F=\ \textless \ 7xy, 2y^2\ \textgreater \ [/tex] be a vector field in the plane, and [tex]C[/tex] the path [tex]y=8x^2[/tex] joining [tex](0,0)[/tex] to [tex](1,8)[/tex] in the plane.
Evaluate the following:
Given that F = <7xy, 2y²> is a vector field in the plane, and C the path y = 8x² joining (0,0) to (1,8) in the plane.the line integral ∫F.dr = 355¹/₃ units
What are line integrals?Line integrals are integrals evaluated along a curve. It is given by I = ∫F.dr
where dr = dxi + dyj
How to find the given integral ∫F.dr?Given that F = <7xy, 2y²> is a vector field in the plane, and C the path y = 8x² joining (0,0) to (1,8) in the plane.
So, we need to find the line integral ∫F.dr
Since
F = <7xy, 2y²> = (7xy)i + (2y²)j and dr = dxi + dyjSo, ∫F.dr = ∫[(7xy)i + (2y²)j.(dxi + dyj)] = ∫(7xydx + 2y²dy)
We integrate y from 0 to 8 and x from 0 to 1 and susbstitute y = 8x² into the equation. So, we have
∫F.dr = ∫(7xydx + ∫2y²dy)
= ∫(7x(8x²)dx + ∫2y²dy)
= ∫56x³dx + ∫2y²dy
= 56∫₀¹x³dx + 2∫₀⁸y²dy
= 56[x⁴/4]₀¹ + 2[y³/3]₀⁸
= 56[1⁴/4 - 0⁴/4] + 2[8³/3 - 0³/3]
= 56[1/4 - 0] + 2[512/3 - 0]
= 56[1/4} + 2[512/3]
= 14 + 1024/3
= (42 + 1024)/3
= 1066/3
= 355¹/₃ units
So, given that F = <7xy, 2y²> is a vector field in the plane, and C the path y = 8x² joining (0,0) to (1,8) in the plane.the line integral ∫F.dr = 355¹/₃ units
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at the beginning of march, michelle had a balane of 887.43 in her checking account. during the month she wrote checks for 435, 58.27 and 127.96 she also deposited a check for 301.68. what was the balance in her account at the end of march
Answer:
$567.88
Step-by-step explanation:
Start with the beginning balance.
Add all the mounts of checks and subtract the total from the beginning balance.
Add the amount of the deposit to the balance.
Beginning balance: $887.43
Withdraw: $435, $58.27, $127.96
Total withdrawals: $435 + $58.27 + $127.96 = $621.23
Deposit: $301.68
Final balance = beginning balance - total of checks + amount of deposit
Final balance: $887.43 - $621.23 + $301.68 = $567.88
Answer: $567.88
-a + 5y
When a=-5 and y=6
Answer:
35
Step-by-step explanation:
-a +5y
-(-5) +5(6)
5 + 30
35
A ball is dropped from a 70-m building. The height (in meters) after t sec is given by h (t) = -4.97 +70.
(a) Find h (2) and h (2.5).
(b) Interpret the meaning of the function values found in part (a).
Part: 0 / 4
Part 1 of 4
(a) h (2) =
X
5
In quartic equation, The player will catch the ball on its way down, at about 4.346 seconds. .
What is the quartic equation's formula?
It might be argued that using this formula makes it possible to solve the quadratic with a pencil. Ax4 + bx3 + cx2 + dx + e = 0 is an analogous formula for the generic quartic equation.h = -16t2 + 70t + 4
We want to know how many seconds it takes for the ball to be 6 feet above the ground.
We want to know the value of t when h = 6 . So plug in 6 for h and solve for t .
6 = -16t2 + 70t + 4 Subtract 6 from both sides of the equation.
0 = -16t2 + 70t - 2 Let's solve this quadratic equation using the quadratic formula.
t = -70 ± √70² - 4( -16)(-2)/2(-16)
t = -70 ± √4900 -128/ -32
t = -70 ± √4772/ -32
t = -70 + √4772/ -32 ≈ 0.029
t = -70 - √4772/ -32 ≈ 4.346
So we know that
(a) at 0.029 seconds, the ball is 6 feet above the ground and on its way up, and
(b ) at 4.346 seconds, the ball is 6 feet above the ground and on its way down.
The player will catch the ball on its way down, at about 4.346 seconds.
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Match each division problem on the left to its quotient on the right.
Answer:Zero-0 divided by 8 3
Step-by-step explanation:
Joel digs a hole at a rate of 3/5 feet every 10 minutes. After digging for 30 minutes, Joel places a bush in the hole that fills exactly 1/2 feet of the hole. Relative to ground level, what is the elevation of the hole after placing the bush in the hole? Enter your answer as a simplified mixed number in the box.
After excavating and inserting bushes, the hole's elevation in feet is 1 1/10 feet.
3/5 feet per 10 minutes are dug up on average.
After 30 minutes, the elevation or depth of the hole:
3/5 × (30/10) = (3/5 × 3) = 9/5 feets
Consequently, after 30 minutes, the hole's height will be 9 1/2 feet.
Elevation after planting bushes in half of the hole:
After 30 / 2 minutes, the hole's elevation was 2/ (9/5)
=2/(9 /5 )
= (9 /5 ) × 1/2
= 9/10 feet.
Consequently, the hole is elevated by 1 1/10 of a foot above the surrounding ground.
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the product of a number and twice that number is 800. what are the numbers
The two numbers are 20 and 40
How to calculate the numbers ?Let n represent the unknown
Next is to find the the products of both numbers
n × 2n= 800
2n²= 800
n²= 800/2
n²= 400
n= √400
n= 20
The first number is 20
The second number 2(20)= 40
Hence the two number are 20 and 40
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Three out of every ten crates of grapes
were spoiled when the shipment arrived.
If the company threw away 24 crates of
spoiled grapes, how many crates were in
the shipment?
WhWhat are the coordinates of the vertex of the function f(x) = x2 − 12x + 5?
(6, 31)
(−6, 31)
(6, −31)
(−6, −31)
Answer:
(6, -31)
Step-by-step explanation:
Answer:
I think (6, -31)
(11) How many students are there all together? In a school result 20% students passed in all three subjects (Maths, English and Dance), 46% failed in Maths, 57% failed in English and 42% failed in Dance, 35% failed in Maths and English, 25% failed in English and Dance, 15% failed in Dance and Maths. What percentage of the students failed in all three subjects?
10 percent of the students failed in all three subjects.
Let the us assume that the total number of students in the school are 100.
Thus, according the the information given-
number of students who passed in all three subjects = 20
⇒ number of students who failed in at least one subject = 100 - 20 = 80
Let the number of people who failed in all three subjects be a
Then, as per the given information, we can make a venn diagram as shown in the figure below.
Now, the sum of all the terms in the venn diagram must be 80 since 80 people failed in at least 1 subject. Thus, we get the following equation-
a -3 + 35 - a + 25 - a + a + a - 4 + 15 - a + 2 + a = 80
a + 32 + 25 + 11 + 2 = 80
a + 70 = 80
a = 80 - 70
a = 10
Thus, the percentage of the students who failed in all 3 subjects will be-
10/100 × 100
= 10%
Hence, 10 percent of the students failed in all three subjects.
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Choose what the expressions below best represent within the context of the word problem.
x best represent the width of the rectangle and x + 12 best represents the length of the rectangle.
How to find the width and length of a rectangle?The length of the rectangle is 12 inches more than it width.
The width of the rectangle can be found as follows:
The perimeter of the rectangle is 42 inches.
Therefore,
perimeter of a rectangle = 2(l + w)
where
l = lengthw = widthHence,
perimeter of a rectangle = 2(l + w)
The length of the rectangle is 12 inches more than it width.
Therefore,
let
x = width
Hence,
length = 12 + x
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what is -9(2)+10 with workout please
The volume of a cone varies jointly as its height, and the square of its radius. If a cone with a height of 8 cm and a radius of 2 cm has a volume of 33.5 cm3 what is the volume of a cone with a height of 6 cm and a radius of 4 cm?
The volume of a cone with a height of 6 cm and a radius of 4 cm is:
V = 100.5 cm³
What is the volume of a cone with a height of 6cm and a radius of 4cm?
If the volume of a cone varies jointly as its height, and the square of its radius, then we can write the equation:
V = R²*H*k
Where:
R = radius
H = height
k = constant of the variation.
Here we know that if R = 2cm and H = 8cm, the volume is 33.5 cm³, then we can replace that to get:
33.5 cm³ = (2cm)²*8cm*k
The value of k is:
(33.5 cm³)/( (2cm)²*8cm ) = k = 1.046875
Then the formula for the volume is:
V = R²*H*1.046875
Now if the radius is 4cm and the height is 6cm, the volume will be:
V = (4cm)²*(6cm)*1.046875 = 100.5 cm³
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What is the order of magnitude for the following number 1.25 x 105 ?
A. 1.25
B. 10
C. 5
The order of the magnitude of the given number is a 5.
According to the statement
We have to find that the order of the magnitude.
So, For this purpose, we know that the
An order of magnitude is an exponential change of plus or minus 1 in the value of a quantity or unit. The term is generally used in conjunction with power-of-10 scientific notation.
From the given information:
The number are 1.25 x 105
To find the order firstly solve it then
1.25 x 105
1.25 x 105 = 131.25
And in this according to the definition of the order of the magnitude:
The order is of the 5 numbers.
So, The order of the magnitude of the given number is a 5.
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The diameter of a human red blood cell is 0.000006 m. write the number using scientific notation, in the form of a x 10b
At which value in the domain does:
Answer:
Step-by-step explanation:
How is 8.67 become 8 2/3 (please help)
Answer:
Step-by-step explanation:
Because 8 2/3 is basically 8.66666666... (you can find this out by doing division 2÷3)
There's an infinite amount of 6's at the end and so the answer got rounded up to 8.67.
Anything above 5 when rounding will be rounded up.
HELP ME OUT PLEASE!!!!
Answer: no
Step-by-step explanation: hope this helps
In a day care center each child takes three classes and either passes or fails each class. The grades are shown in the table below. P represents a passed class, and F represents a failed class. Let X represent the number of classes failed by a child. Construct a probability distribution for X. Arrange x in increasing order and write the probabilities P(x) as simplified fractions. Child Grades Child 1 PFP Child 2 PPF Child 3 FFP Child 4 PPP Child 5 PFP Child 6 PPF Child 7 FPF Child 8 PPP Provide your answer below:
The probability distribution for X in a day care center where each child takes three classes and either passes or fails each class will be:
0 = 1/4
1 = 1/4
2 = 1/4
How to illustrate the information?It should be noted that from the information, the grades are shown in the table below.
P represents a passed class.
F represents a failed class.
X represent the number of classes failed by a child.
The probability that the number of classes failed by a child is 0 will be:
= 2/8
= 1/4.
The probability that the number of classes failed by a child is 1 will be:
= 4/8
= 1/2
The probability that the number of classes failed by a child is 2 will be:
= 2/8
= 1/4.
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Radicals that have the same radicand (inside) and index (kickstand) are?
Niko has a collection of 60 stamps. Of these stamps, 30% are from New York, 25% are from California, and the rest are from countries outside of the United States. How many stamps in Niko’s collection are from countries that are outside of the United States?
Use the zero product property to create a Quadratic Equation if: the x-intercepts are x=-1 and x=3
The quadratic equation is y = x^2 - x - 6
How to use the zero product property to create a quadratic equation?The given parameters are
x-intercepts: x=-1 and x=3
Rewrite properly as
x1 = -2 and x2 = 3
By zero product property, the quadratic equation is
y = (x - x1) * (x - x1)
This gives
y = (x + 2) * (x - 3)
Expand
y = x^2 + 2x - 3x - 6
Evaluate the difference
y = x^2 - x - 6
Hence, the quadratic equation is y = x^2 - x - 6
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Hector earned $2640 through an academic scholarship. He used three-eighths of it to buy books. How much of the
scholarship money was used for books?
The scholarship money used by Hector to purchase books is $990
Hector earned $2640 through an academic scholarship.
Hector used three-eighths of his earned academic scholarship of $2640 to buy books
This is a problem of fractions
In simple words, Fractions means the parts of a whole. The whole can be an object or a group of objects. For example, when we cut a piece of cake from the whole of it, then the portion is the fraction of the cake.
The fraction is also termed as a portion or section of any quantity.
Money used for buying books = 3/8 of $2640
= 3/8 × 2640
= 7920/8
= 990
Hence, the scholarship money used by Hector to purchase books is $990
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Say you are given the graph of the line y x. Write the equation of the line that is perpendicular to the given line and goes through the point (8, 2).
The equation of a line perpendicular to y = x that passes through the point (8,2) is y = -x + 10
How to find the equation of the perpendicular line?The equation of the line is given as
y = x
Rewrite the equation as
y = x
A linear equation is represented as
y = mx + c
Where
Slope = m
So, we have
m = 1
The slopes of perpendicular lines are opposite reciprocals
This means that
m2 = -1/m1
So, we have
m = -1/1
Evaluate
m = -1
The equation of the perpendicular line is then calculated as
y = m(x - x1) + y1
Where
(x1, y1) = (8, 2)
This gives
y = -1(x - 8) + 2
Evaluate
y = -x + 8 + 2
Evaluate the sum and the difference
y = -x + 10
So, the equation of a line perpendicular to y = x that passes through the point (8,2) is y = -x + 10
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