The factors in the factored form represents the value of the function when x = 0.
What are Quadratic Functions?Quadratic functions are defined as the polynomial functions consisting of variables and exponents with the degree of the variable being 2.
The general form of a quadratic function is f(x) = ax² + b x + c.
Given is a quadratic function,
y = x² + 2x - 15
This can be factorized as (x + p)(x + q) such that p × q = -15 and p + q = 2.
Two such numbers are -3 and 5.
-3 × 5 = -15 and -3 + 5 = 2
y = x² + 2x - 15
y = (x - 3) (x + 5)
Factors are x - 3 and x + 5
Here, the numbers 3 and -5 represents the input values of the function when the output value or the value of the function equals 0 or they are the x intercepts of the function.
Hence the factors in the factored form are the x intercepts of the function.
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The complete question is as follows :
What do the factors in the factored form represent?
y = x² + 2x - 15
Selecting from millimeter, meter, and kilometer, determine the best unit of measure to express the given length.
Millimeter is the best unit to define the radius of the pencil.
What is a radius?The distance from a circle's centre to any point on its periphery is known as the radius. The radius of a circle is also known as the distance separating any two points on the circle from its centre. The radius of a circle is the separation between its centre and circumference. Always, the diameter is twice the radius. As a result, the formula is created by multiplying the diameter by two.
Define millimeter.The smallest unit of measurement is the millimetre. There are a thousand millimetres in a metre, and a dime is somewhat thicker than a millimetre. When measuring anything's length in metric units, you'll be working with meters and variants on meters, including millimeters.
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Translate the sentence into a mathematical equation.
Power equals current times voltage.
Let P represent power, current, and V voltage. Write the equation.
P=
On solving the Power equals Current times voltage as an equation we get power is P = VI
What is equation?A mathematical equation is a fοrmula that joins twο statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of twο mathematical expressions is knοwn as an equation in algebra. For instance, in the equatiοn 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the twο sentences οn either side of a letter is described by a mathematical fοrmula. Often, there is only οne variable, which also serves as the symbol. fοr instance, 2x – 4 = 2.
Given to write
Power equals current times voltage
in mathematical equation, i.e.
P = V × I
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Maria is renting kayaks from a local shop that charges a $7 fee, plus an hourly rate of $5. 50. For how long can maria rent the kayak if she pays a total of $40?.
The number of hours Maria rent the kayak for the paid amount of $40 when hourly rate is $5.50 is equal to 6 hours.
Fees of renting charges paid for kayaks from a local shop = $7
Hourly rate = $5.50
Let 't' be the number of hours Maria rent kayak.
Total fees paid by Maria for renting kayak for 't' hours is equal to $40
Required equation to represents the above condition is
$40 = $7 + $5.50t
Simplify the expression to get the value of 't'
⇒ 5.50t = 40 - 7
⇒ t = 33 / 5.50
⇒ t = 6 hours
Therefore, for the number of hours Maria rent kayak by paying total of $40 is equal to 6 hours.
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Leager
Assessment Items
Question
A researcher found that for the years 2013 to 2019, the equation, y=-0.4(2-3)² + 42,
models the average gas mileage of new vehicles sold in Switzerland, where z is the
number of years since 2013 and y is the average gas mileage, in miles per gallon (mpg).
During what year was the average gas mileage for new vehicles sold in Switzerland the
greatest?
2016 is the year in which the average gas mileage is the greatest.
What is an equation?An equation contains one or more variables connected by an equal sign.
Example:
1x + 2 = 99 is an equation.
We have,
y = -0.4 (x - 3)² + 42
where x = the number of years since 2013.
y = average gas mileage
Now,
In 2016,
x = 3
y = -0.4 (3 - 3)² + 42
y = 0 + 42
y = 42
This is the greatest value for any x value.
Thus,
In 2016, the average gas mileage for new vehicles sold is the greatest.
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In fall 2006, Pace University in New York raised its annual tuition from $25,000 to $29,750. Freshman enrollment declined from 1,475 in fall 2005 to 1,130 in fall 2006. Assuming that the demand curve for places in the freshmen class at Pace did not shift between 2005 and 2006, use this information to calculate the price elasticity of demand LOADING... . Use the midpoint formula in your calculation.
Answer:The answer is 20000
Step-by-step explanation:
When she subtracts 4 from both sides, 1/2x = -1/2x
results. What is the value of x?
Answer: 0
Step-by-step explanation:
1/2x = -1/2x cannot be true for any other value of x except when x equals 0. In other words, we need the left and right sides to equal each other, but that would only happen when x=0.
e 1.5 Checkpoint: Rational and irrational numbers SNE
Select all the numbers that are irrational.
√55
36
39
√40
L
√√49
√55 and √40 are the irrational numbers.
What is Number system?A number system is defined as a system of writing to express numbers.
A rational number is the one which can be represented in the form of P/Q where P and Q are integers and Q ≠ 0.
But an irrational number cannot be written in the form of simple fractions.
√55 is an irrational number
√40 is an irrational number
√49 value is 7 which is a natural number
Hence, √55 and √40 are the irrational numbers.
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Need help quick with this problem!!! [tex]\frac{6x^{-1} y^{-1}}{\sqrt[4]{xy^{4}} }[/tex]
[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hfill \begin{array}{llll} \textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{6x^{-1}y^{-1}}{\sqrt[4]{xy^4}}\implies \cfrac{6}{x^1 y^1 \left( xy^4 \right)^{\frac{1}{4}}}\implies \cfrac{6}{x^1 y^1 \left( x^{\frac{1}{4}}y^1 \right)}\implies \cfrac{6}{x^1x^{\frac{1}{4}} y^1 y^1} \\\\\\ \cfrac{6}{x^{1+\frac{1}{4}} y^{1+1}}\implies \cfrac{6}{x^{\frac{5}{4}} y^2}\implies {\Large \begin{array}{llll} \stackrel{a\quad b \quad ~~ c}{6x^{-\frac{5}{4}}y^{-2}} \end{array}}[/tex]
On a partagé une somme entre trois personnes: la première en a reçu les deux tiers, la deuxième 300dirhams de moins que la deuxième. Chercher la somme et les trois parts
5 redused to lowest terms make it easy kid friendly for my 10 year old equation please
Sure! To reduce the fraction 5 to its lowest terms, we need to find the greatest common factor of 5 and divide both the numerator and denominator by it.
The greatest common factor of 5 and 5 is 5, so we divide both the numerator and denominator by 5 to get:
5 / 5 = 1
So, 5 reduced to its lowest terms is 1.
To make it kid-friendly, you could explain it like this: "We can simplify the fraction 5 by dividing the top and bottom by the biggest number that they both share. In this case, 5 is the biggest number that 5 and 5 share, so we divide both 5 and 5 by 5 to get 1."
The sum of two numbers is 42. The smaller number is 16 less than the larger number. What are the numbers?
Larger number:
Smaller number:
Answer:
Larger number: 29
Smaller number: 13
Step-by-step explanation:
29 + 13 = 42
29 - 16 = 13
Answer:
Larger number: 29
Smaller number: 13
Step-by-step explanation:
x = larger number
y = smaller number
x+y=42
29-13 = 16
29+13=42
Find the angle of elevation
from point C to point A.
590
m
402 m
2
nm
B
Angle of elevation = [ ? ]0
The required angle of the elevation at point C to A is given as ∠C = 31°.
What is the angle of elevation?The angle of elevation is the angle between a horizontal line of sight and a line of sight that is directed upwards to an object or point. In other words, it is the angle between the horizontal and an observer's line of sight to an object above the observer
Here,
A figure has been shown, Consider triangle ABC, where ∠A = 59, ∠B = 90°,
Since the sum of the angle in the triangle should be 180°.
∠A + ∠B + ∠C = 180
∠C + 90 + 59 = 180
∠C = 90 - 59
∠C = 31°
Thus, the required angle of the elevation at point C to A is given as ∠C = 31°.
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One cubic foot holds 7.48 gallons of water, and 1 gallon of water weighs 8.33 pounds. How much does 2.2 cubic feet of water weigh:
In pounds?
In tons?
So far I Havn't received the correct answer yet.
(ej a number is divisible by 2 and 3, it is divisible by 6. 64 is divisible by 2 but no Sh
What can be concluded from this?
64 is also divisible by 3
54 s dvisible only by 2
() 64 is also divisible by 6
(v) 64 is not divisite by 6
Answer:
64 is not divisible by 6 because although it is divisible by 2, it is not divisible by 3 so it is not divisible by 6.
Step-by-step explanation:
Erica built a fort out of big foam blocks that are 1 /4 of a foot tall. She is adding a 5-foot tower to one side of the fort. How many blocks tall will the tower be?
By the equation formed by the relation to build 5 feet tall tower, Erica will need 20 bricks.
What is an equation?
An equation is a mathematical statement consisting of two expressions joined by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation gives the value of the variable x as x = 7.
According to the information given in the question:
1 brick = 1/4 Feet
Which means, 4 bricks = 1 feet
As Erica wants to make 5 feet tall tower,
5 feet tower = 5 x 4
= 20 bricks
Hence, Erica will need 20 bricks to build 5 feet tower.
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A passenger train traveled 240 miles in the same amount of time it took a freight train to travel 160 miles. The rate of the freight train was 20 miles per hour slower than the rate of the passenger train. Find the rate of the passenger train.
The rate of the passenger's train is given as follows:
60 miles per hour.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence the following equation is built to model the relationship between these variables:
v = d/t.
For the passenger train, the equation is given as follows:
v = 240/t.
vt = 240
t = 240/v.
For the freight train, the velocity is 20 miles slower than for the passenger train, hence:
v - 20 = 160/t
v = 160/t + 20.
Replacing the first equation into the second, the rate of the passenger train is obtained as follows:
v = 160v/240 + 20
v = 2v/3 + 20
v/3 = 20
v = 60 miles per hour.
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If AB = 12 and BC = 19,
then what does AC equal?
The value of length AC is,
⇒ AC = 31
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
Given that;
The lengths are,
AB = 12 and BC = 19
Now, If the points A, B and C are colinear.
Then, The value of length AC is,
⇒ AC = AB + BC
⇒ AC = 12 + 19
⇒ AC = 31
Thus, We get;
⇒ AC = 31
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the frame of a bike weighs16 pounds. each tire weighs 9 ounces. the seat weighs 12 ounces. the handlebars weigh 24 ounces. how punds does the bike weigh
19.375 pounds is the weight of bike.
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
Given that the frame of a bike weighs16 pounds.
each tire weighs 9 ounces.
In a bike there are 2 tires, so total weight of tires is 2×9=18 ounces.
The seat weighs 12 ounces
The handlebars weigh 24 ounces.
Convert the ounces to pounds.
We know that 1 pound=16 ounces
So The total number of weight in ounces is 18+12+24=54 ounces
Divide by 16 to convert 54 ounces to pounds
54/16=3.375
Now total weight=16+3.375 pounds
=19.375
Hence, 19.375 pounds is the weight of bike.
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How can credit cards be safer than cash? a. It is harder to lose a single credit card than a large number of bills. b. A credit card requires a signature, so it is impossible for anyone other than you to use. c. If a merchant does not hold up their end of an agreement, you can call the credit company and dispute the charges. d. Cash can be miscounted, but credit cards cannot.
If a merchant does not hold up their end of an agreement, you can call the credit company and dispute the charges. This way, credit cards can be safer than cash.
What is credit card?
A credit card is a small plastic payment card that is provided by a person's bank and enables the cardholder to pay a merchant for products and services depending on the cardholder's accumulated debt.
To be on the safe side in the event that a merchant breaches an agreement, a cardholder may contact the credit bureau to resolve the disputed charges.
So, this way credit cards can be safer than cash.
Hence, option C is the correct solution.
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Graph the function y=x/4
Answer:
Step-by-step explanation:
need help pls Choose ALL answers that describe the quadrilateral
Answer: A. Parallelogram
Step-by-step explanation: A parallelogram is a four-sided polygon with opposite sides that are parallel and equal in length.
Write the sentence as an equation.
242 fewer than the quantity 193 times n equals 131
The equation that we want to write is:
193n - 242 = 131
How to write the equation?Here we want to write the sentence:
"242 fewer than the quantity 193 times n equals 131"
As an equation.
The first part means that we need to take a number n, multiply it by 193, and then subtract 242.
193n - 242
And that must be equal to 131, then the equation is:
193n - 242 = 131
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Help MEEE I HAVE UNTIL TOMORROW
The actual width and length of the bedroom are respectively; 9 ft and 12 ft
How to interpret Scale Drawing?The parameters are given as;
Width of house = 30 feet = 360 inches
Length of house = 45 feet = 540 inches
Scale drawing width of house = 4 inches
Scale drawing length of house = 6 inches
Thus;
Scale factor width = 360/4 = 90
Scale factor length = 540/6 = 90
Scale drawing width of bedroom = 1.2 inches
Scale drawing length of bedroom = 1.6 inches
Thus;
Actual width of bedroom = 1.2 inches * 90 = 108 inches or 9 ft
Actual length of bedroom = 1.6 inches * 90 = 144 inches or 12 ft
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How do I simplify this into a radical?
Answer:
Step-by-step explanation:
To simplify the expression X^(12/7) * Y^(35/7) into its simplest form, we need to find the greatest common divisor (GCD) of the exponents 12/7 and 35/7 and divide both exponents by the GCD. Here's the step-by-step process:
Find the GCD of 12/7 and 35/7. To do this, we'll use the Euclidean algorithm method:
a. Divide the larger number, 35, by the smaller number, 12, and get the remainder: 35 ÷ 12 = 2 with a remainder of 11.
b. Divide the smaller number, 12, by the remainder, 11, and get the quotient and remainder: 12 ÷ 11 = 1 with a remainder of 1.
c. The last non-zero remainder, 1, is the GCD of 12/7 and 35/7.
Divide both exponents by the GCD, 1:
a. X^(12/7) becomes X^(12/7 ÷ 1) = X^12.
b. Y^(35/7) becomes Y^(35/7 ÷ 1) = Y^35.
Replace the original exponents in the expression with the simplified exponents: X^12 * Y^35.
So, the expression X^(12/7) * Y^(35/7) is simplified as X^12 * Y^35, which is written as a single radical in its simplest form.
[tex]~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill\\\\ x^{\frac{12}{7}}y^{\frac{35}{7}}\implies \left( x^{12} y^{35} \right)^{\frac{1}{7}}\implies \sqrt[7]{x^{12} y^{35}}\implies \sqrt[7]{x^{7+5} (y^5)^7} \\\\\\ \sqrt[7]{x^7 x^5 (y^5)^7}\implies {\Large \begin{array}{llll} x y^5\sqrt[7]{x^5} \end{array}}[/tex]
Which number line best represents the solution to the inequality 3x+2≤4x+5≤9
?
The number line of the inequality is (d)
How to determine the number line of the inequalityfrom the question, we have the following parameters that can be used in our computation:
3x+2≤4x+5≤9
When this is expanded, we have
3x + 2 ≤ 4x + 5 and 4x + 5 ≤ 9
Evaluate the like terms
So, we have the following representation
-x ≤ 3 and 4x ≤ 4
Divide by the coefficient of x
x ≥ -3 and x ≤ 1
When combined, we have
-3 ≤ x ≤ 1
So x is between -3 and 1, inclusive.
This is represented by the number line (d)
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An investment of $65,000 is increasing at a rate of 3.2% per year. Which function represents how to find the value of the investment after t years?
Answer:
I honestly don't know I just need points
what is the solution to | x | -2 <= -3
Help!!
Write an equation to show the total cost, y, for x months.
Please help with this equation
Answer:
Step-by-step explanation:
Adjacent angles is defined as
Opposite,congruent angles formed when two lines intersect.
A set contains the numbers 0,6,12 and 15. 2 different numbers are selected randomly from this set. What is the probability that the sum is greater than 12
Answer:
Step-by-step explanation:
To find the probability of the sum of two randomly selected numbers from a set being greater than 12, we need to first find the total number of possible combinations of two numbers and then count the number of combinations that result in a sum greater than 12.
The set contains four numbers, so there are 4 choose 2 possible combinations of two numbers, which is equal to (4! / (2! * (4 - 2)!)), or 6 combinations. These combinations are:
(0,6), (0,12), (0,15), (6,12), (6,15), (12,15)
Next, we'll count the number of combinations that result in a sum greater than 12. These combinations are:
(6,15), (12,15)
There are 2 combinations that result in a sum greater than 12.
Finally, to find the probability, we'll divide the number of favorable outcomes (combinations with a sum greater than 12) by the total number of outcomes (all possible combinations of two numbers), and express the result as a fraction:
probability = 2 / 6
Reducing the fraction, we get:
probability = 1 / 3
So, the probability that the sum of two randomly selected numbers from the set is greater than 12 is 1/3.
That's how you find the probability of the sum of two randomly selected numbers from a set being greater than a certain value. By counting the number of favorable outcomes and dividing by the total number of possible outcomes, you can find the probability of a certain event.
