The quadratic function which has zeros −3 and 5 and contains the point (4, 14) is 2x²+4x+30 and the vertex points are (-1,28).
What is a quadratic equation?A quadratic equation is the equation in which the unknown variable is one and the highest power of the unknown variable is two.
The standard form of the quadratic equation is,
ax²+bx+c=0
Here,(a,b, c) is the real numbers and (x) is the variable.
A quadratic function has zeros −3 and 5 and contains the point (4, 14). The factored form of quadratic equation is,
f(x)=a(x-z₁)(x-z₂)
Here, z₁ and z₂ are the zeros. Thus,
f(x)=a(x-z₁)(x-z₂)
f(x)=a(x-(-3))(x-5)
f(x)=a(x+3)(x-5)
This equation contains the point (4,14). Thus,
14=a(4+3)(4-5)
14=a(7)(-1)
a=14/-7
a=-2
Put the value in above equation and solve it further:
f(x)=-2(x+3)(x-5)
f(x)=-2(x²-5x+3x-15)
f(x)=-2x²-4x-30
Change the sign,
f(x)=2x²+4x+30
The equation of the quadratic function in standard form is,
f(x)=2(x+1)²+28
Thus, the vertex point are -1 and 28. Similarly, the section equation which contains the point (1, −48) can be solved.
Hence, the quadratic function which has zeros −3 and 5 and contains the point (4, 14) is 2x²+4x+30 and the vertex points are (-1,28).
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The hundred meter dash is marked with a blue line the 400 meter dash is marked with a red line how much further is the red line
Answer:
the red line is 300 meters further
Step-by-step explanation:
since you have 100 meters as the blue line you add 300 meters th get to the 400 meters red line
The cost in dollars of making x
items is given by the function C(x)=10x+900
.
a. The fixed cost is determined when zero items are produced. Find the fixed cost for this item.
Fixed cost =$
b. What is the cost of making 25
items?
C(25)=$
c. Suppose the maximum cost allowed is $1900
. What are the domain and range of the cost function, C(x)
?
When you enter a number in your answer, do not enter any commas in that number. In other words if you want to enter one thousand, then type in 1000 and not 1,000. It's not possible to understand what the interval (1,000,2,000) means, so you should write that as (1000,2000).
The cost in dollars of making x items is given by the function C(x) = 10x + 900. The fixed cost is 900 dollars. C(25 ) = $1150. The Range is 250.
What is a function?The function is a type of relation, or rule, that maps one input to specific single output.
The cost in dollars of making x items is given by the function
C(x) = 10x + 900
a. The fixed cost is determined when zero items are produced. Find the fixed cost for this item.
The fixed cost
C(0) = 10(0) + 900
= 0 + 900
= $900
b. What is the cost of making 25 items?
C(25) = 10(25) + 900
= 250 + 900
= $1150
Therefore, C(25 ) = $1150
c. Suppose the maximum cost allowed is $1900. What are the domain and range of the cost function, C(x)?
The domain is the set of values for which the given function is defined.
Range = Maximum value of the data set - Minimum value of the dataset
Range = C(25 ) - C(0)
= 1150 - 900
= 250
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2. Faith opens a credit card with an APR of 16.50% compounded monthly. How much is charged in interest this month if her
balance is $1,050? (4 points)
$173.25
$87.50
$16.50
$14.44
Answer:
14.44 (Letter D)
Step-by-step explanation:
The answer is 14.44
Hopefully its correct!!!
What is the measure of the unknown angle?
Image of a full circle divided into two angles. One angle is fifty degrees and the other is unknown
Group of answer choices
300°
305°
310°
Answer:
its C 305
Step-by-step explanation:
ik this i got a 100 rofl
Multiply
y^2-9/-2y*-5y/y+3
Answer:
-5(y - 3)/-2
Step-by-step explanation:
y² - 9/-2y × -5y/y + 3
Multiply Rewrite
Simplify the expression
(y - 3)×(y + 3)/2 × 5/y + 3
Simplify the expression
y - 3/2 × 5
Calculate
5(y - 3)/2
HOPE THIS HELPS :)
Answer:
[tex]\huge\boxed{\dfrac{-5(y-3)}{-2}}[/tex]
Step-by-step explanation:
[tex]\dfrac{y^2-9}{-2y}\cdot\dfrac{-5y}{y+3}=\dfrac{y^2-3^2}{-2y}\cdot\dfrac{-5y}{y+3}[/tex]
use: a² - b² = (a - b)(a + b)
[tex]=\dfrac{(y-3)(y+3)}{-2y}\cdot\dfrac{-5y}{y+3}[/tex]
simplify fractions
(y + 3) and y
[tex]=\dfrac{y-3}{-2}\cdot\dfrac{-5}{1}=\dfrac{-5(y-3)}{-2\cdot1}=\dfrac{-5(y-3)}{-2}[/tex]
N
VOLUME OF TRIANGULAR PRISMS
8.9 cm
8 cm
14 cm
8 cm
Answer:
448 cm³
Step-by-step explanation:
Finding volume :
V = LWH/2V = 1/2 x 14 x 8 x 8V = 7 x 64V = 448 cm³Answer: 448 cm³
Step-by-step explanation:
Volume of a triangle prism can be found with;
V = [tex]\frac{1}{2}[/tex] * W * L * H
V = [tex]\frac{1}{2}[/tex] * W * L * H
V = [tex]\frac{1}{2}[/tex] * 8 cm * 14 cm * 8 cm
V = [tex]\frac{1}{2}[/tex] * 8 cm * 14 cm * 8 cm
V = 448 cm³
The triangle prism has an area of 448 cm³
What is the lowest common multiple of 24,36 and 40
Step-by-step explanation:
Here...
2 × 2 × 2 × 3 × 3 × 5 = 360..
hence the LCM is 360...
[tex]..[/tex]
( There is also another method to solve this but I choose this one cause this one is easy to understand....)
solve the matrix equation below. What is the value of x in the new matrix?
The new matrix that is formed by the 3A + B is given below. Then the value of x is 102.
[tex]\begin{bmatrix} w & z \\y & z \\\end{bmatrix} = \begin{bmatrix} 46 & 102 \\15 & -2 \\\end{bmatrix}[/tex]
What is the matrix?A matrix is a specific arrangement of items, particularly numbers. A matrix is a row-and-column mathematical structure. The [tex]a_{ij }[/tex] element in a matrix, such as M, refers to the i-th row and j-th column element.
The matrices are given below.
[tex]\rm A = \begin{bmatrix}9 & 27 \\0 & 6 \\\end{bmatrix}\\\\\\B = \begin{bmatrix}19 & 21 \\15 & -20\\\end{bmatrix}[/tex]
Then the new matrix is given as 3A + B. Then we have
[tex]\rm 3A + B =\begin{bmatrix} w & z \\y & z \\\end{bmatrix}\\\\\\3A + B =3 \times \begin{bmatrix}9 & 27 \\0 & 6 \\\end{bmatrix} + \begin{bmatrix}19 & 21 \\15 & -20\\\end{bmatrix}\\\\\\3A + B = \begin{bmatrix}27& 81\\0 & 18\\\end{bmatrix} + \begin{bmatrix}19 & 21 \\15 & -20\\\end{bmatrix}\\\\\\3A + B = \begin{bmatrix} 46 & 102 \\15 & -2 \\\end{bmatrix}[/tex]
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find x
S
T
43
(9x -14)
U
Answer:
x = 12°
Welcome to concept of Inscribed Angle theorem
In the diagram shown above, the inscribed angle m∠SUT intercepts the diameter ST.
Then,
m∠SUT = 90°
In Δ SUT,
m∠S + m∠U + m∠T = 180°
Substitute.
m∠S + 90° + 43° = 180°
m∠S + 133° = 180°
Subtract 133° from each side.
m∠S = 47°
m∠UST = 47°
By Inscribed Angle Theorem,
m∠arc UT = 2 ⋅ m∠UST
Substitute.
(9x - 14)° = 2 ⋅ 47°
(9x - 14)° = 94°
9x - 14 = 94
Add 14 to each side.
9x = 108
Divide each side by 9
x = 12
Hence, we get as x = 12°
Adrian's computer cost 20% less than Jocelyn's computer. Adrian's computer cost $640. Adrian's computer cost 15% more than Corbin's computer. (50 Points)
Answer:
640 = .8j
640 = 1.15c
Step-by-step explanation:
Let j = cost of Jocelyn's computer
c = cost of Corbin's computer
We know that Adrian's computer costs $640.
Since Adrian's computer costs 20% less than Jocelyn's computer, the cost of Adrian's computer is 80% of (.8 times)the cost of Jocelyn's computer, so 640 = .8j
Since Adrian's computer costs 15% more than Corbin's computer, the cost of Adrian's computer is 115% of (1.15 times) the cost of Corbin's computer, so 640 = 1.15c
Answer:
640 = .8j
640 = 1.15c
Step-by-step explanation:
Find the Mean Absolute Deviation for the following data: 6, 1, 3, 8, 5, 11, 1, 5 (Remember to find the mean first and then use the positive value when subtracting the numbers from the mean. Average that total and you will get your MAD)
The Mean Absolute Deviation for the following data: 6, 1, 3, 8, 5, 11, 1, 5 is 2.5
What is mean absolute deviation?The mean absolute deviation of a dataset is the average distance between each data point and the mean.
mean absolute deviation = [tex]\frac{summation|x-mean|}{n}[/tex]
where
n = number of termsTherefore, let's calculate the mean first.
Arrange the data in ascending order.
1, 1, 3, 5, 5, 6, 8, 11
mean = 1 + 1 + 3 + 5 + 5 + 6 + 8 + 11 / 8 = 40 / 8 = 5
Therefore, let's calculate the distance between each dat point and mean.
|1 - 5| + |1-5| + |3-5| + |5-5| + |5-5| + |6-5| + |8-5| + |11-5|
4 + 4 + 2 + 0 + 0 + 1 + 3 + 6 = 20
Hence,
mean absolute deviation = 20 / 8 = 2.5
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What shape has at least one right angle but is not a square
(2 + 3i) + (3 – 4i)
(3 – 5i) – (–2 – i)
(2 − 4i)(1+ 3i)
2i(−1+ 3i)
Answer:
(5-i)
(5-4i)
(-12i^2+2i+2)
(6i^2-2i)
Read the following actions and decide if they are risks or costs.
fire:
employee salaries:
theft:
health insurance for your employees:
losing important data from the computer network:
taxes:
employee injury:
Answer:
fire: risk
Employee salaries: cost
theft: risk
health insurance for employees: cost
losing important data from computer: cost
taxes: cost
employee injury: cost
A store is having 10% off all pairs of shoes do you want a pair of shoes that normally cost $75 what is the sale price of the pair of shoes you want
Answer:
You pay 67.5 for the shoes.
Step-by-step explanation:
10% of 75 is 7.5.
75 - 7.5 = 67.5
Please Mark Brainliest!
Answer:
Here ya go! Hope it helps
11) Differentiate implicitly if y² = x.
Answer: x2 + y2. − 4x + 5y − 8=0.
Step-by-step explanation:
Answer:
[tex]\dfrac{dy}{dx}=\dfrac{1}{2y}[/tex]
Step-by-step explanation:
Given equation:
[tex]y^2=x[/tex]
Differentiate:
[tex]\implies y^2\:\dfrac{d}{dx}=x\:\dfrac{d}{dx}[/tex]
[tex]\implies 2y\:\dfrac{dy}{dx}=1[/tex]
[tex]\implies \dfrac{dy}{dx}=\dfrac{1}{2y}[/tex]
Which is the graph of the line with equation y−4=2(x+1)?
Number graph ranging from negative three to three on the x axis and negative seven to one on the y axis. A line is drawn on the graph that passes through the points (zero, negative six) and (three, zero).
Number graph ranging from negative four to three on the x axis and negative five to two on the y axis. A line is drawn on the graph that passes through the points (zero, negative four) and (one, zero).
Number graph ranging from negative three to three on the x axis and negative two to four on the y axis. A line is drawn on the graph that passes through the points (negative one, zero) and (zero, four).
Number graph ranging from negative three to three on the x axis and negative one to six on the y axis. A line is drawn on the graph that passes through the points (negative three, zero) and (zero, six).
Answer:
Number graph ranging from negative three to three on the x axis and negative one to six on the y axis. A line is drawn on the graph that passes through the points (negative three, zero) and (zero, six).
Step-by-step explanation:
Simplified y-4 = 2(x + 1) ⇒ y = 2x + 6
Graphed function on desmos graphing calculator
Matched the through points of option #4, (-3, 0) and (0 ,6) to the graph.
Answer: D. "Number graph ranging from negative three to three on the x axis and negative two to four on the y axis. A line is drawn on the graph that passes through the points (negative one, zero) and (zero, four)."
Step-by-step explanation:
We know that our graph passes through two given sets of points, therefore we can plug in those points to find the correct answer.
Let's test it with choice A. It gives us the points (0,-6) and (3,0). We can plug these into the equation to see if it is true. y-4 = 2(x+1) becomes
-6-4 = 2(3+1), or -10 = 8 which is not true, so we can eliminate it.
Choice B gives us (0,-4) and (1,0) -4-4 = 2(0+1) or -8 = 2, this one is wrong.
Choice C gives us (-1,0), so 0-4 = 2(-1+1) or -4 = 0, this one is also wrong.
Choice D gives us (-3,0) so 0-4 = 2(-3+1) or -4 = -4. This is the only option which has a correct solution, and therefore it is your answer.
can I have detailed explanation please
Answer:
Pls refer
Step-by-step explanation:
I hope you understand
Feel free to ask any doubts
+ C:/Users/pertunia/Desktop/IQTT5111A1_FT.pdf 2022 21; 22 Q.3.1 Determine the % marks that the students obtained for each of the modules, given that: Q.3.1.1 The total number of marks available for the Statistics module was 600. (4) Determine this by entering an appropriate formula in cells C2 to C12
The question is an illustration of Excel formulas, and the formula to enter in cell C2 is: =(B2/600)
How to determine the % marks that the students obtained?To enter a formula in Microsoft Office Excel, we make use of the following syntax:
= (Formula)
From the question, the total score is 600.
So, the formula to enter in cell C2 is:
=(B2/600)
Next, drag the content of cell B2 through cell C12.
This is to ensure that all cells C2 to C12 have the appropriate formula.
Lastly, following the highlighted steps to show the result as percentage
Go to the home tabSelect the number groupClick the Percent Style button Increase the number of decimal places, as desired.Read more about Excel formulas at:
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Which expression is Equivalent to the problem in the photo?
Step-by-step explanation:
when given similar terms sometimes its easier to work the problem out before sinplifying
Simplify using the distributive property. 5 Marks
1/5(4m+20)
9(5/9 y-1/3)
Answer+Step-by-step explanation:
[tex]\frac{1}{5} \left( 4m+20\right) =\frac{4}{5}m + \frac{20}{5} = \frac{4}{5}m + 4[/tex]
[tex]9\left( \frac{5}{4} y-\frac{1}{3} \right) =\frac{9\times5}{9} y-\frac{9}{3} = 5y - 3[/tex]
Please i really need help pelase
The quotient is 4x+2 and remainder is +6
What is long division?In math, long division is a method used for dividing large numbers into groups or parts.
The long division helps in breaking the division problem into a sequence of easier steps.
Just like all division problems, a large number, which is the dividend, is divided by another number, which is called the divisor, to give a result called the quotient and sometimes a remainder.
The long division of
(4x²-2+4)÷(x+1), is attached below.
Hence, The quotient is 4x+2 and remainder is +6.
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The function g is related to one of the parent function g(x)=-(x-2)^3
Answer:
(2,0)
Step-by-step explanation:
Please help asap i really want to finish this
It is a Part A and Part B Question
Note: please add the answer next to what part it's from so I can know which part was answered
The general form of a circle is given as x^2+y^2+4x - 12y + 4 = 0. A) What are the coordinates of the center of the circle? B) What is the length of the radius of the circle? ( Please Do Not Repost Someone Else's Answers On Brainly Or Any Other Websites Please If So You'll Be Reported). Will Mark Brainliest if answered correctly and please be honest .
Answer:
center = (-2, 6)
radius = 6
Step-by-step explanation:
Equation of a circle
[tex](x-a)^2+(y-b)^2=r^2[/tex]
(where (a, b) is the center and r is the radius)
Therefore, we need to rewrite the given equation into the standard form of an equation of a circle.
Given equation:
[tex]x^2+y^2+4x-12y+4=0[/tex]
Collect like terms and subtract 4 from both sides:
[tex]\implies x^2+4x+y^2-12y=-4[/tex]
Complete the square for both variables by adding the square of half of the coefficient of [tex]x[/tex] and [tex]y[/tex] to both sides:
[tex]\implies x^2+4x+\left(\dfrac{4}{2}\right)^2+y^2-12y+\left(\dfrac{-12}{2}\right)^2=-4+\left(\dfrac{4}{2}\right)^2+\left(\dfrac{-12}{2}\right)^2[/tex]
[tex]\implies x^2+4x+4+y^2-12y+36=-4+4+36[/tex]
Factor both variables:
[tex]\implies (x+2)^2+(y-6)^2=36[/tex]
Therefore:
center = (-2, 6)radius = √36 = 6Help! Please explain I have a test tomorrow !
base= 10 ft
height= 12 ft
to find:the surface area of the given pyramid.
solution:[tex]s.a = {a}^{2} + 2a \sqrt{ \frac{ {a}^{2} }{4} + {h}^{2} } [/tex]
[tex]s.a = {10}^{2} + 2 \times 10 \times \sqrt{ \frac{ {10}^{2} }{4} { \times 12}^{2} } [/tex]
[tex]s.a = 360 \: {ft}^{2} [/tex]
therefore, the surface area of the given pyramid is 360 square feets.
answer= option D
Please HELP me don’t BE RUDE IM WASTING MY PTS
Based on the information in the table, it can be inferred that the values with two dots are 28 1/2 and 25 1/2.
What is a dot plot?A dot plot is a type of graph that is characterized by representing the frequency of an event by means of points on a line that has the values.
According to the information in the table, it can be inferred that two values have a frequency of 2, these values are:
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Christine runs 5 miles in 46 minutes. How many minutes does she take per mile.
Answer:
9.2 Minutes
Step-by-step explanation:
46 minutes divided by 5 miles is equal to 9.2 minutes per mile
Answer:
9.2
Step-by-step explanation:
To find minutes per mile, divide minutes by miles:
(46 min)/(5 mi) = 9.2 min/mi
On average, it takes 9.2 minutes for Christine to run a mile.
A) find the value of x
B) find the value of y
Answer:
a) x = 9.
b) y = 61.
Step-by-step explanation:
As the 2 weighing scales balance:
4 + 4x = 31 + x
3x = 31 - 4 = 27
x = 9.
Also 4 + 4x + x + 31 = y + 2x + 1
Substituting for x:
4 + 4(9) + 9 + 31 = y + 2(9) + 1
80 = y + 19
y = 80 - 19 = 61.
Answer:
x = 9
y = 61
Step-by-step explanation:
The main scales are balanced.
The left side of the main scales comprises another scale, which is also balanced.
From this and the values given, we can construct two equations.
Equation 1
Balancing the scales on the left of the main scales:
⇒ 4 + 4x = 31 + x
Solving this for x:
⇒ 4 + 4x - 4 = 31 + x - 4
⇒ 4x = 27 + x
⇒ 4x - x = 27 + x - x
⇒ 3x = 27
⇒ 3x ÷ 3 = 27 ÷ 3
⇒ x = 9
Equation 2
Balancing the main scales:
4 + 4x + 31 + x = y + 1 + 2x
Rearranging to make y the subject:
⇒ 5x + 35 = y + 1 + 2x
⇒ 5x + 35 - 1 = y + 1 + 2x - 1
⇒ 5x + 34 = y + 2x
⇒ 5x + 34 - 2x = y + 2x - 2x
⇒ 3x + 34 = y
Substituting the found value of x (from Equation 1) and solving for y:
⇒ y = 3(9) + 34
⇒ y = 27 + 34
⇒ y = 61
Therefore:
x = 9y = 61Write the algebraic equation for the following: The sum of 4 and another number is 22.
Answer:
[tex]4+x=22[/tex]
Step-by-step explanation:
Hope this helps