the formula for the parabola that passes through the points, y = ax2 + bx + c. The values of a, b, and c are -9, -19,32 respectively.
What exactly does parabola mean?The intersection of a right circular cone with a plane parallel to an element of the cone creates a plane curve, which is equivalent to a point moving so that its distance from a given point equals its distance from a fixed line.
based on the available facts;
Parabola fundamental: y = ax2 + bx + c
We can plug in three locations for (x, y) to get three equations at once.
(-4, -40): 40 = 4a - 2b + c {equation 1}
(-3, -13): -13 = 9a + 3b + c {equation 2}
(-2,4): 4 = a - b + c {equation 3}
Solve this system to find the values of a, b, c
Let's first eliminate variable c:
4a - 2b + c = -40 {equation 1}
a - b + c = 4 {equation 3}
--------------------- subtract
3a - b = -44
9a + 3b + c = -13 {equation 2}
a - b + c = 4 {equation 3}
-------------------- subtract
8a + 4b = -17
We now have two equations with 2 unknowns we can use to find a, b
3a - b = -44 {equation 4}
8a + 4b = -4 {equation 5}
Multiply equation 4 through by 4 and add equations
12a - 4b = -176
8a + 4b = -4
----------------- add
20a = -180
a = 180/20
a = -9
8a + 4b = -4
4b = -76
b = -19
Plug these 2 values into one of the original equations and solve for c
4 = a - b + c {equation 3}
4 = -9-19 + c
4 = -28 + c
4+28= c
c = 32
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Find all zeros of the function: s(x) = x^2 - 7x - 60.
The zeros are x =
Find the lowest common denominator for 5. 11 and 10
In ΔJKL, m ∠ L=71°, j=11 m , and m ∠ K=46° . Find k .
Step-by-step explanation:
first : the sum of all angles in a triangle is always 180°.
second : the law of sine
a/sin(A) = b/sin(B) = c/sin(C)
a, b, c are the sides, A, B, C are the the corresponding opposite angles.
therefore,
angle J = 180 - 71 - 46 = 63°
j/sin(J) = k/sin(K)
11/sin(63) = k/sin(46)
k = 11×sin(46)/sin(63) = 8.880673249... m
How many passes were completed in the NFL for the 2018 season?
2 1/5 divided by 3/5
if you make 2 1/5 a improper fraction it would be 6/5
6/5÷3/5 is easy because 6÷3=2
the answer is 2.
Answer:
3 2/3
Step-by-step explanation:
2 1/5 ÷ 3/5
Convert 2 1/5 to an improper fraction
2 1/5 -- > 5 × 2 + 1 = 11/5
= 11/5 ÷ 3/5
Change the operator to multiplication
= 11/5 × 5/3
Cross multiply
= 11/3
Convert improper fraction to a mixed number
= 3 2/3
what is 15 equal pieces shaded 2/3
Answer: Shade 10 of the pieces.
Step-by-step explanation: To figure this out, divide 15 by 3(5) and then multiple 5 by two and you will get 10!
Answer: You need to shade 10 of the pieces.
Take 15/3 and get 5
Then take 5 * 2 and get 10
Step-by-step explanation:
Write an expression using fractions to show how to determine the amount that each person will pay. Then calculate each person's contributions showing all steps in long division.
my chart:
#1 $36.87
#2 $29.37
#3 $26.27
#4 $35.27
The required solution of each person's contributions showing all steps in long division is 3687/100, 2937/100, 2627/100 and 3527/100.
What is expression?An expression is a set of terms combined using the operations +, – , x or ÷. An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An expression is in simplest form when no terms can be combined.
Given:
The given expression is
#1 $36.87
#2 $29.37
#3 $26.27
#4 $35.27
According to given question we have
By the long division method we get
1. $36.87 =36+0.87
$36.87 = 36+87/100
GCD( 87,100)=1
$36.87 = 36+87/100=36+1
$36.87 = 36+87/100
$36.87=3687/100
2. $29.37 =29+0.37=29+37/100
GCD( 37,100)=1
$29.37 =29+37/100
$29.37 =2937/100
3. $26.27 =26+0.27 =26+27/100
GCD( 27,100)=1
$26.27 =26+27/100
$26.27 =2627/100
4. $35.27 =35+0.27=35+27/100
GCD( 27,100)=1
$35.27 =35+27/100
$35.27 =3527/100
Therefore, the required solution of each person's contributions showing all steps in long division is 3687/100, 2937/100, 2627/100 and 3527/100.
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−4k + 6 − 2k= −3 (4k − 10)?
Sorry, I got perplexed about how I was doing this.
Answer:
k=4
Step-by-step explanation:
−4k+6−2k=−3(4k−10)
−4k+6−2k=−3(4k−10)
−4k+6+−2k=(−3)(4k)+(−3)(−10)
−4k+6+−2k=−12k+30
(−4k+−2k)+(6)=−12k+30
−6k+6=−12k+30
−6k+6=−12k+30
−6k+6+12k=−12k+30+12k
6k+6=30
6k+6−6=30−6
6k=24
6k/6=24/6
k=4
(sorry if this was confusing)
Answer:
-3.5
Step-by-step explanation:
-4k+ 6 - 2k= -3(-6k)
-4k+ 4k= 18k
-4k = 18k-4k
-4k = 14
-4k/-4 = 14/-4
K= -3.5
f(x)=10 x-10 . Find each value.
(f ⁰ f⁻¹)(d)
Function composition exists a mathematical procedure where two functions, f and g, are taken and a function, h = g ⁰ f, exists produced such that h(x) = g(f(x)).
If the function be f(x) = 10x - 10 then the value of (f ⁰ f⁻¹)(d) is 99.
What is meant by composition?Function composition exists a mathematical procedure where two functions, f and g, exists taken and a function, h = g ⁰ f, exists produced such that h(x) = g(f(x)). The function g is used in this operation on the outcome of applying the function f to x.
Let the function be f(x) = 10x -10
We want to find (f ⁰ f⁻¹)(d)
To differentiate with respect to X, then we get
[tex]F^{-1}[/tex](x) = 10
To find the value of (f ⁰ f⁻¹)(d)
F([tex]f^{-1}[/tex](x)) = F(10)
F([tex]f^{-1}[/tex](x)) = 10x - 10
substituting the values in the above equation, then
F([tex]f^{-1}[/tex](x)) = 10(10) - 10
simplifying the above equation, we get
F([tex]f^{-1}[/tex](x)) = 100 -10
F([tex]f^{-1}[/tex](x)) = 99
Therefore, the value of (f ⁰ f⁻¹)(d) = 99
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How many zeros does 7.185629 x 102985 have?
Answer:
3
Step-by-step explanation:
3
Answer:
4
Step-by-step explanation:
7.185629 x 102985 = 740,012.002565 which has 4 zeros
Zen design a character for a video game he just three sizes of the character on grid paper then uses the expression 6+ X to the power of two to find the number of grid squares in a character of any size S find the number of grade squares in a character of size 7 show your work
If Zen design a character for a video game he just three sizes of the character on grid paper then uses the expression 6+ X to the power of two. the number of grid squares in a character of size 7 is 55.
Number of grid squareGiven:
Expression=6+x²
Now using the expression to determine the number of grid square in a character of size 7.
Expression=6+x²
Where:
x=7
Hence,
6+7²
=6+49
x=55
Therefore If Zen design a character for a video game he just three sizes of the character on grid paper then uses the expression 6+ X to the power of two. the number of grid squares in a character of size 7 is 55.
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Tristian says that 9.32 is a rational number Barry says that 9.32 is a terminating decimal who is correct
Tristian and Barry both are correct as 9,32 is a rational and terminating decimal.
A rational number is one that can be written as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively.
A terminating decimal is a decimal number with a finite number of digits after the decimal point. The repeating decimal 5.6500000000... can be used to represent a terminating decimal like 5.65, however, when it is zero, the value is typically referred to as terminating.
A decimal number having a limited number of digits following the decimal point is referred to as a terminating decimal. Therefore, all decimal numbers that terminate are rational numbers.
Hence both are correct.
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Jodi wants to visit her extended family in barbados next summer, and the flight costs $450. how much does she need to save each month if she wants to buy the flight in exactly 9 months?
If Jodi wants to visit her extended family in Barbados next summer, and the flight costs $450, then she needs to save 50$ each month if she wants to buy the flight in exactly 9 months.
If the flight costs $450, then the amount of money Jodi needs to save each month can be determined by using division.
Division is one of the four basic operations of arithmetic and involves the separation into equal parts.
By dividing the cost of the flight by the number of months, the money Jodi needs to save each month can be calculated.
Considering x to be money Jodi needs to save each month,
x = flight cost / number of months
x = 450 / 9
x = 50
Hence, the money Jodi needs to save each month if she wants to buy the flight in 9 months is calculated to 50$.
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Find the quotient of 30 x 10^-24 / 5 x 10^-24. Write the final answer in scientific notation.
6 x 10^48
6 x 10^24
6 x 10^0
6 x 10^−48
The quotient of 30 × 10⁻²⁴/5 × 10⁻²⁴ in scientific notation is equal to: C. 6 x 10^0.
What is quotient?Quotient can be defined as a mathematical expression that is simply used to represent the division of a number by another number.
What are the laws of indices?In Mathematics, laws of indices can be defined as the standard principles and rules that are used for simplifying a mathematical equation or expression that involves powers of the same base.
By applying the laws of indices, the quotient is given by:
Quotient = 30 × 10⁻²⁴/5 × 10⁻²⁴
Quotient = 30/5 × 10⁽⁻²⁴ ⁺ ²⁴)
Quotient = 6 × 10⁰
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Your sports drink bottle is 56 full. After practice, the bottle is 38 full. Write the difference of the amounts after practice and before practice. Write your answer as a fraction in simplest form.
The difference of the amounts after practice and before practice is 18 full.
The difference as a fraction in simplest form will be 9/28.
How to calculate the value?The sports drink bottle is 56 full and after practice, the bottle is 38 full, the difference of the amounts after practice and before practice will be:
= 56 - 38
= 18
The difference as a fraction in simplest form will be:
= Difference / Original value
= 18 / 56
= 9 / 28
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Solve each equation. Check for extraneous solutions. 4(3 x-3)²/₃=36
The solutions of the equation [tex]4(3x-3)^{\frac{2}{3} } = 36[/tex] are x = 10 and x = - 8.
An extraneous solution is one that results from the process of addressing the problem but is not a legitimate solution to the problem, such as the answer to an equation.
A formula known as an equation uses the equals sign (=) to express how two expressions are equal.
Consider the equation,
[tex]4(3x-3)^{\frac{2}{3} } = 36[/tex]
Now, divide each side of the equation by 4.
[tex]\frac{4(3x-3)^{\frac{2}{3} }}{4}=\frac{36}{4}[/tex]
[tex](3x-3)^{\frac{2}{3} } = 9[/tex]
Cubing the above equation.
[tex]((3x-3)^{\frac{2}{3} })^{3}=(9)^{3}[/tex]
( 3x - 3 )² = 729
3x - 3 = ( √729 )
3x - 3 = ± 27
Now,
3x - 3 = 27
3x = 30
x = 10
and;
3x - 3 = - 27
3x = - 24
x = - 8
Checking for extraneous solutions,
x = 10
[tex]4(3x-3)^{\frac{2}{3} }=36\\4(3(10)-3)^{\frac{2}{3} }=36\\4(27)^{\frac{2}{3} }=36\\27^{\frac{2}{3} }=9\\(3^{3})^{\frac{2}{3} } = 9\\3^{2}=9\\9=9[/tex]
When x = - 8,
[tex]4(3x-3)^{\frac{2}{3} }=36\\4(3(-8)-3)^{\frac{2}{3}}=36\\(-27)^{\frac{2}{3}}=9\\(-27)^{2}=(9)^{3}\\729=729[/tex]
The solutions for the equation are x = 10 and x = - 8.
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MODELING REAL LIFE Bowling alley A charges $3.75 to rent shoes and $4 per game. Bowling alley B charges $2.50 to
rent shoes and $4.50 per game.
a. For what numbers of games is the total cost, including a pair of rental shoes, less at bowling alley A? at bowling alley B?
Bowling alley A:
Bowling alley B:
or more games
or
games
b. Bowling alley A increases the cost per game by $0.50. How does this affect your answer in part (a)? Explain.o
Using linear functions, it is found that:
a) The cheaper costs are given as follows:
Bowling alley A: 3 or more games.Bowling alley B: 1 or 2 games.b) Due to the same cost per game and higher cost for the pair of shoes, bowling alley A will never be cheaper than bowling alley B.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, we have that:
The cost to rent shoes is the intercept.The cost per game is the slope.Hence the cost functions are given as follows:
A(x) = 3.75 + 4x.B(x) = 2.5 + 4.5x.The costs are equal when:
A(x) = B(x)
3.75 + 4x = 2.5 + 4.5x
0.5x = 1.25
x = 1.25/0.5
x = 2.5.
Hence the cheaper costs are given as follows:
Bowling alley A: 3 or more games.Bowling alley B: 1 or 2 games.Alley B has the lower initial cost due to the lower cost for the pair of shoes.
For item b, if we increase the cost per game by $0.50 for alley A, we have that:
A(x) = 4.5x + 3.75.
Hence:
Due to the same cost per game and higher cost for the pair of shoes, bowling alley A will never be cheaper than bowling alley B.
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Point D(−1, 5) is reflected across the x-axis. Which statements about D′ are true? Select each correct answer. Responses The y-coordinate is 5. The , y, -coordinate is 5. The y-coordinate is −5. The , y, -coordinate is , negative 5, . The x-coordinate is −1. The , x, -coordinate is , negative 1, . The x-coordinate is 1.
The correct option is (A) The y-coordinate is -5. If point D(-1, 5) is reflected across the x-axis then the coordinates of D’ are (-1, -5).
What does it mean to reflect coordinates?Geometry. The x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the x-axis as (x, -y).
Determine the location of the mirror line before reflecting an object on a coordinate plane. Simply multiply the coordinate of the point by -1 to reflect over the axis. Use the symbols. Simply multiply the coordinate of the point by -1 to reflect over the axis.
Given coordinates of D= (-1, 5)
While reflecting any points across the x-axis with coordinates as (x, y) becomes, (x, -y). i.e sign of y-coordinate changes.
The rule is: (x, y) arrow (x, -y)
Applying so, after reflecting point D, its reflection D' will have coordinates as (-1, -5)
Therefore, the y-coordinate is -5.
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Match each addition expression on the left with an equivalent expression on the right. 4(8 + 3) 10 + 14 25 + 10 32 + 12 6+9 Intro K 8 of 12 3(2 + 3) 5(5 + 2) 2(5 + 7) Do
The match is
10 + 14 -------> 2(5 +7)25 + 10 --------> 5(5 +2)32 + 12 --------->4(8 + 3)6 + 9-----------> 3(2 +3)What is number system?A number system is defined as a system of writing to express numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner.
Given:
10 + 14
=2(5 +7)
25 + 10
=5(5 +2)
32 + 12
=4(8 + 3)
6+9
=3(2 +3)
So, the matching is
10 + 14 -------> 2(5 +7)
25 + 10 --------> 5(5 +2)
32 + 12 --------->4(8 + 3)
6 + 9-----------> 3(2 +3)
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Can some one help me it’s too difficult
please help!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: where's the question?
Step-by-step explanation:
Answer:
your question please
Step-by-step explanation:
(2x)²y; x = 4, y = 8
[Mathematical Problem]
[tex](2x)^2y; x=4,y=8[/tex]
Solution:
Substitute the value of the variable into the expression, then simplify.
[tex](2(4))^2[/tex] × [tex]8[/tex]
↓
[tex](8)^2[/tex]
↓
[tex](8)^2[/tex] × [tex]8[/tex]
↓
[tex]64[/tex]
↓
[tex]64[/tex] × [tex]8[/tex] = 512
Hence, our solution is 512.
Hope this helps! It's been a while since I've done this, but this should be correct. Lmk if it helps! Thanks and good luck!
Write as an expression using an negative exponent 1/16
The negative exponent of 1/16 is 2⁻^{4}.
What is an expression?A statement is considered to be an expression if it has a minimum of two numbers or variables as well as at least one mathematical action.
Wha at is negative exponent?The multiplicative inverse of the base raised to the power opposite to the provided power is the definition of a negative exponent. In plain English, we write the number's reciprocal and solve it just like positive exponents. For instance, (2/3)-2 may be represented as (3/2)2.
1/16 = 16⁻¹
1/16 = 16⁻¹ = 4⁻²
1/16 = 16⁻¹ = 4⁻² = (2^2)⁻² = 2⁻^{4} .
1/16 = 2⁻^{4} .
Hence, the negative exponent of 1/16 is 2⁻^{4}.
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EVERY ONE PLEASE GO ON MY PAGE AND HELP ME, PLEASE
Answer:With what?
Step-by-step explanation:there is no page
Answer:
I helped you on your first question, I wasn't too sure about the others because their answer options are mostly inaccurate from what I know.
Grant can buy 6-packs of table-tennis balls for $2.10 or 9-packs of table-tennis balls. for $2.88. Grant wants to buy 18 table- tennis balls. How much more will he spend if he buys only 6-packs of table-tennis balls? Show work
Order the numbers below from least to greatest.
Answer:[tex]\sqrt 7,2.8,\pi ,\sqrt{17, 4.6[/tex]
Step-by-step explanation:
15/48
The graph below describes the journey of a train between two cities.
a) Work out the
acceleration, in km/h²,
in the first 15 mins.
1201
100
80
b) Work out the distance
between the two cities. 60
a)
8
40
c) Work out the average
speed of the train during 20
the journey.
9am
10am
Time
11am
a)The acceleration, in km/h², in the first 15 mins = 200 km/h².
b) The distance between the two cities = 125 km.
c) The average speed during 20 the journey = 62.5 km/hr.
What is defined as the acceleration?Acceleration is the rate during which velocity changes over time, both in terms of speed and direction. A point or takes place in a straight line is sped up if it quickens or decelerates. Even if the speed is constant, motion on such a circle is accelerated because the direction is constantly changing.For the given question;
Every horizontal block is 1/8 hour = 7.5 minutes long.
Each vertical block has a speed of 10 km/hr:
The table drawn as per the data given in the table:
Time Velocity km/hr
0 Min ( 0 hr) ---> 0
15 Min (1/4 hr) --> 50
45 Min (3/4 hr) --> 50
60 MIn ( 1 hr) --> 100
90 Min ( 3/2 hr) ---> 100
120 Min ( 2hr) ---> 0
The formula for acceleration:
Part a: Acceleration = final velocity - initial velocity / final time - initial time
Acceleration in the first 15 minutes: (1/4 hr) = (50 - 0)/(1/4 - 0)
= 50/(1/4)
=200
Thus, acceleration in the first 15 minutes is 200 kmph.
Part b: Distance among two cities:
= (1/2)(0 + 50)(1/4 - 0) + 50 * (3/4 - 1/4) + (1/2)(50 + 100)(1 - 3/4) + 100 * (3/2 - 1) + (1/2)(100 + 0)(2 - 3/2)
= 25/4 + 25 + 75/4 + 50 + 25
= 125
The difference distance for two cities is 125 kilometers.
Part c: Average speed = distance/2
Average Travel Speed = 125/2 = 62.5 km/hr
Therefore,
a: Acceleration in the first 15 minutes = 200 km/h²
b: The distance between two cities is 125 kilometers.
c: The average speed of the journey is 62 miles per hour.
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Lola went to the hardware store and bought 6 yellow ropes. The total length of the ropes was 8.1 meters. How long was each rope?
The length of each rope is 1.35 meters
How to calculate the length of each rope ?Lola went to the hardware store and bought 6 yellow ropes
The total length of the rope was 8.1 meters
Therefore the length of each rope can be calculated as follows
= 8.1/6
= 1.35
Hence the length of each rope at the hardware store is 1.35 meters
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Simplify each expression. (-8x³)⁻⁴/₃
The solution for the expression ( -8x³) ⁻ ⁴/₃ = 1 / 16x⁴
Given expression is ( -8x³) ⁻ ⁴/₃
= ( -8x³) ⁻ ⁴/₃
It can be written as
We know that 8 = 2³ then
= ((-2x)³) ⁻ ⁴/₃
= ((-2x)³* ⁻ ⁴/₃
On the exponents '3' will be canceled then we get
= (-2x) ⁻ ⁴
We know that x ⁻ ¹ can be written as 1/x, then
= 1/(-2x)⁴
= 1 / 16x⁴
∴ ( -8x³) ⁻ ⁴/₃ = 1 / 16x⁴
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Solve using the Quadratic Formula. x²-9 x+15=0
The answer to the question is 9±√21/2
By using the quadratic formula x=-b±√b²-4ac/2a
By comparing x²-9 x+15=0 with ax²+bx+c
we get a=1 b=-9 c=15
x=-(-9)±√(-9)²-4×1×15/2×1
x=9±√81-60/2
x=9±√21/2
So the answer to the question is x=9+√21/2
and x=9-√21/2
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