A parabola with focus of (-5, -1) and a directrix of y=7 has the equation of the parabola as: (x + 5)² = 8 (y - 3)
How to write the equation of parabola with directrix of y = 7 and focus of (-5, -1)Quadratic equation = parabolic equation, when the directrix is at y direction is of the form:
(x - h)² = 4P (y - k)
OR
standard vertex form, y = a(x - h)² + k where a = 1/4p
The focus
F (h, k + p) = (-5,-1)
h = -5
k + p = -1
P in this problem, is the midpoint between the focus and the directrix
P = (-1 - 7) / 2 = -4
p = -4
the vertex
v(h, k)
h = -5
k + p = -1, k = 3
v(h, k) = v(-5, 3)
substitution of the values into the equation gives
(x - h)² = 4P (y - k)
(x - -5)² = 4 * 2 (y - 3)
(x + 5)² = 8 (y - 3)
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Marco charges $42.99 for a
repair that takes 2 hours.
Marco charges $87.99 for a
repair that takes 5 hours.
for the slope and y intercept
Answer:
y-intercept= 12.99 slope= 15.00x+12.99
Step-by-step explanation:
The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is a divisor of 6". Find P(A). Outcome Probability 1 0.044 2 0.065 3 0.194 4 0.304 5 0.103 6 0.003 7 0.102 8 0.004 9 0.095 10 0.086
P(A) = P(6) = 0.003
answer: 0.003
An architect plans to buy 5 stone spheres and 3 stone cylinders. For the same amount, he can buy 2 stone spheres and 7 stone cylinders. If one stone cylinder costs $32.73 how much does
each stone sphere cost?
Answer:
Each stone sphere costs $43.64Step-by-step explanation:
Let the cost of stone sphere is s and stone cylinder is c.
According to question we have equation:
5s + 3c = 2s + 7cSolve it for s:
5s - 2s = 7c - 3c3s = 4cSubstitute the value of c:
3s = 4*32.733s = 130.92s = 130.92/3s = 43.64How do you write out the sum of 2 consecutive even intergers
Let's call x to an unknown even integer. The next (consecutive) even integer will be x + 2. For instance, if x = 6, then the next even integer will be 6 + 2 = 8.
In consequence, the sum of two consecutive even integers is:
x + (x + 2)
What does it mean (to the process of finding all factors) that I have found 2 PRIME factors as a factor pair?
Answer:
It means that you are done.
Step-by-step explanation:
When you are trying to find factors of a number or an algebraic expression, you must keep on factoring until you have all PRIME factors. PRIME factors cannot be further factored. So that means you are done factoring.
example: (a number)
6
factors: 2 and 3
2 and 3 are prime they can't be factored anymore so you have completely factored 6.
example: 20
factors: 4 and 5
5 is prime but 4 is not, so you can factor it more.
4 is 2×2
So 20 factored is 2×2×5
Or algebra example:
Factor x^4 - 81
factors: x^2 - 9 and x^2 + 9
x^2 + 9 cannot be factored more (prime) but x^2-9 can. Its x-3 and x+3.
Tanya is training a turtle for a turtle race. For every 1/2 of an hour that the turtle is crawling, he can travel 1/20 of a mile. At what rate is the turtle crawling in miles per hour
If Tanya is training a turtle for a turtle race. For every 1/2 of an hour that the turtle is crawling, he can travel 1/20 of a mile. The rate that the turtle is crawling in miles per hour is: 0.2 miles /hour .
Determining the Unit rate per mileGiven data:
1/2 of an hour = 1/20 of a mile
Now let determine the unit rate
Unit rate that the turtle is crawling is: (1/20)/(1/2)
Hence,
Unit rate = (1/20)×(2/1)
Unit rate = 2/20 miles/hour
Unit rate = 0.2 miles /hour
Therefore the rate is 0.2 miles per hour.
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If for every 1/2 of an hour that the turtle is crawling, he can travel 1/20 of a mile. then 0.1mile/ hour is the rate at which turtle travel per hour.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that,
A turtle is trained by Tanya,
For every 1/2 of an hour that the turtle is crawling, he can travel 1/20 of a mile.
We need to find at what rate the turtle is travelling per hour.
Let x be the distance travelled by turtle in hour.
1/20/1/2=x/1
Apply cross multiplication
x/2=1/20
x=2/20
x=0.1 miles / hour
Hence 0.1 miles per hour is the turtle travelling per hour.
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Rewrite one fourteenth times x cubed times y plus three fourteenths times x times y squared using a common factor.
The equation that represents the sentence will be (1/14)xy ·[x² + 3y].
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The act of converting a specified statement into an expression or equation is known as a sentence-to-equation transformation.
The sentence is given below.
One-fourteenth times x cubed times y plus three-fourteenths times x times y squared.
Convert the sentence into an expression. Then we have
⇒ (1/14)x³y + (3/14)xy²
Simplify the expression, then we have
⇒ (1/14)x³y + (3/14)xy²
⇒ (1/14)xy ·[x² + 3y]
The equation that represents the sentence will be (1/14)xy ·[x² + 3y].
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Solve for x and y in the problem below. Then, find m
Given the Cyclic Quadrilateral Theorem,
Opposite angles of a Cyclic Quadrilateral are supplementary(that is, they add up to 180°).
Therefore,
[tex]\begin{gathered} 17x+78^o=180^o \\ 17x=180^o-78^o \\ 17x=102^o \\ x=\frac{102^o}{17} \\ x=6^o \end{gathered}[/tex]To obtain y,
[tex]\begin{gathered} 9y+6y=180^o \\ 15y=180^o \\ y=\frac{180^o}{15} \\ y=12^o \end{gathered}[/tex]Thus,
[tex]\begin{gathered} m\angle X=9y \\ =9\times12 \\ =108^o \end{gathered}[/tex][tex]\begin{gathered} m\angle V=6y \\ =6\times12 \\ =72^o \end{gathered}[/tex][tex]\begin{gathered} m\angle W=17x \\ =17\times6 \\ =102^o \end{gathered}[/tex]Therefore, the values are
m
m
m
What is the end behavior of the polynomial function? Drag the choices into the boxes to correctly describe the end behavior of the function. f(x)=6x9−6x4−6 f(x)=−3x4−6x+4x−5
As x→−∞
As x→∞
The end behavior of the polynomial function is as shown in the attached picture.
What is polynomial function?Polynomial functions refers to equation that consists of variables that have non negative exponents or powers. The when there is only one term in the equation it is referred to as monomial
What is end behavior of polynomial function?The end behavior refers to the behavior of the function at the extremes of the x direction.
The end behavior of a polynomial function is controlled by the term that has the leading terms
In the given question,
The first question has 6x^9 as the term that controls the end behavior hence substituting the -∞ and +∞ gives the end behavior as attachedSimilarly, the second function has -3x^4 as the leading term substituting the -∞ and +∞ gives the end behavior as attachedLearn more on end behavior at: https://brainly.com/question/1365136
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PLS
Natasha has a photo of a lasagna dish she made, which she wants to post to various
websites. The original image has a width of 300 pixels and a height of 450 pixels.
Consider each set of new dimensions or scale percents that show adjustments to this
original image. Describe how the image changed and whether the new image is
similar to the original. Show your work and explain your reasoning.
New image: 35% width, 35% height
As both the width and height of the new image are 35% of the width and height of the original image, the aspect ratio is maintained and the new image is similar to the original image.
What is a Scale Factor?A scale factor is defined as the ratio of an object's original scale to that of a new one, considering the different depictions of that object (bigger or smaller)
Given:
The dimensions of the original image are a width of 300 pixels and a height of 450 pixels.
The dimensions of the New image have 35% width and 35% height.
Width = 0.35 × 300 = 105
Height = 0.35 × 450 = 157.5
Scale factor = New Dimension/Original Dimension
Scale factor of Height = 157.5/450 = 0.35
Scale factor of width = 105/300 = 0.35
Therefore, the new image is neither scaled down nor scaled up and is the same as the original image.
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twelve hungry teenagers can devour a very large pizza in $20$ minutes. how many teenagers would it take to finish a very large pizza in $15$ minutes? (assume that all teenagers eat pizza at the same rate.)
It would take 9 Teenagers to finish a very large pizza in $15$ minutes.
From the knowlegde of Propotional method/ subject formular in mathematics;
From the questions:
12 Teens finished a very large pizza in $20$ minutes.
The number of teens to finish a very large pizza in $ 15 minutes would calculate thus,
12 Teens=$20$ minutes.
x Teens=$15$ minutes.
then we cross multiply:
x Teens × $20$ minutes =$15$ minutes × 12 Teens
making x Teens subject of the formula we have;
x Teens=$15$ minutes × 12 Teens/$20$ minutes
x Teens=9 Teens
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what expression can be used to add 1/2 plus 5/6?
Step-by-step explanation:
You can add the two fractions by turning 1/2 and 5/6 to have the same denominator. Turn 1/2 into a fraction with a denominator of 6. That simplifies to 1 1/3. Hope this helps yo
Kaitlin sold t-shirts at a festival and made a profit of $71 . She made $4 for each t-shirt she sold. Her total expenses were $25 . How many t-shirts did she sell?
The t-shirts she sell is 24.
What is profit and selling price?
Profit is considered as the gain amount from any business activity. Whenever a shopkeeper sells a product, his motive is to gain some benefit from the buyer in the name of profit.
The selling price is the price that the buyer pays to buy a product or goods. This is a price above cost and includes a profit ratio.
According to Question, Christine sold the t- shirts at $4 each and she earned a profit of $71 and his total expenses were $25
Let the total number of t- shirts sold by Christine be "x"
Profit = Selling price – Expenses
Selling price is given as:
selling price = total number to t-shirt sold ×price of each t shirt
selling price = n ×4
71 = (n×4) -24
71 + 25 = n×4
96/4 = n
n = 24
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Find the value of x in each case.
Not rlly sure how to make the equation, i tried it a couple times and got the answer wrong
Pls help and ill reward Brainly thing
You don't need to explain if you don't want.
Answer:
1
Step-by-step explanation:
The absolute value of x is the black line, therefor the absolute value of x-1 is the blue line
Hope that helps
The length and with of rectangle are consecutive odd integers. the perimeter of the rectangle is 48 meters . find the length and width of the rectangle
The dimensions width and length are 11 cm and 13 cm, respectively .A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter.
What is perimeter?A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations.
Perimeter: 48 cm
The dimensions width and length are consecutive odd integers:
Width: x
Length: x+2
Equation:
2 [(x+2) + x] = 48
Find the width x:
2 [2x + 2) = 48
4x + 4 = 48
4x = 48 - 4
4x/4 = 44/4
x = 11 Width
Find the lenght x+2:
x+2 ⇒ 11+2 = 13 Length
The dimensions:
Width: 11 cm
Length : 13 cm
11 and 13 are consecutive odd integers.
Check:
2 (length + width) = 48
2 (13 + 11) = 48
2 (24) = 48
48 = 48
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the admission fee at a local zoo is $ 1.50 for children and $ 5.00 for adults. on a certain day, 2000 people enter the zoo and $ 7 , 550.00 is collected. how many children and how many adults attended?
There are [tex]700[/tex] children and [tex]1300[/tex] adults.
What is system of linear equations?
A System of Linear Equations is when we have two or more linear equations working together.
Let [tex]x[/tex] be number of children and [tex]y[/tex] be number of adults.
Since [tex]2000[/tex] people enter the zoo then [tex]x+y=2000.[/tex]
The admission fee at a local zoo is $ [tex]1.50[/tex] for children and $ [tex]5.00[/tex] for adults and $[tex]7550.00[/tex] collected then [tex]1.5x+5y=7550[/tex].
Thus there are two linear equations to solve.
Substitute [tex]x=2000-y[/tex] in [tex]1.5x+5y=7550.[/tex]
[tex]1.5(2000-y)+5y=7550[/tex]
[tex]3000-1.5y+5y=7550[/tex]
[tex]3000+3.5y=7550[/tex]
[tex]3.5y=7550-3000[/tex]
[tex]3.5y=4550[/tex]
[tex]y=\frac{4550}{3.5}[/tex]
[tex]y=1300[/tex]
So [tex]x=2000-y=2000-1300=700.[/tex]
Therefore there are [tex]700[/tex] children and [tex]1300[/tex] adults.
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Which set of ordered pairs (x, y) could represent a linear function?
A = {(-3,5), (0, 2), (3,-1), (7,-4)}
B = {(0,3), (1,5), (2,7), (4,9)}
C= {(-3,8), (-1,7), (1,6), (3,5)}
D = {(-5, -1), (-2,2), (1,4), (4,7)}
OA
C
B
D
Submit Answer
The graph of a linear function is a straight line. The following is the form of a linear function. a + bx = y = f(x). One independent variable and one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.
How is a linear function written?The equation y = mx + b, where y is the y-coordinate, denotes a linear function. m represents the line's slope, or how steep it is. The coordinate for x is x.
The equation y = mx + b, where y is the y-coordinate, denotes a linear function.
m represents the line's slope, or how steep it is.The coordinate for x is x.the point where the line intersects the y-axis, or b.To learn more about Linear function refer to:
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Twenty years ago a small town in texas had a population of 10,000. the population has increased 8% each year since then. what equation would be used to solve this population growth problem? a. p = 20 (10,000) superscript .08 b. p = 10,000 (8) superscript 20 c. p = 10,000 (20) superscript 1.08 d. p = 10,000 (1.08) superscript 20
The correct answer for the given problem is option (D) .
growth rate in the initial population of 1.08.. So, the equation for solving this population growth problem is 10,000(1.08) ²⁰
Before twenty years, the actual population was 10,000.
Population growth per year = 8% = ((100+8)10,000)/100=10,800.
So, there will be an addition of 800 people to the population every year.
After a period of twenty years, the total population was 10,000 + 19×(800) = 25,200.
Population for t years = (Initial Population)× (Growth or Decay Rate)×time
Using the above population increment formula,
Time( in years) ----->Population
0------>10000
1------->10000 (1.08)
2------->10000(1.08)(1.08)
3------->10000(1.08)(1.08)(1.08)
------------------
n ----->10000(1.08)
Here, we are required to have a population after 20 years, i.e., n= 20. The required equation, which is used for solving population growth problem, is 10000(1.08)²⁰
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The measures of the angles of a triangle are shown in the figure below. Solve for x.
x°
27°
Answer:
153
Step-by-step explanation:
x+27=180
x=180-27
x=153
What is the answer to this question
The angles are which alternate exterior angles include the following: A. ∠XWY and ∠STR.
What are parallel lines?Parallel lines can be defined as two (2) lines that are cut through by a transversal and they always have the same (equal) distance apart and never meet.
What is the alternate exterior angle theorem?The alternate exterior angle theorem states that when two (2) parallel lines are cut through by a transversal, the alternate exterior angles that are formed lie outside the two (2) parallel lines, are located on opposite sides of the transversal, and are congruent angles.
In conclusion, we can logically deduce that both ∠XWY and ∠STR are alternate exterior angles because they lie outside the two (2) parallel lines and are located on opposite sides of the transversal.
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Find the union, AUB, for of the following pair of sets. Enter "DNE" for the empty set.A = (-∞, - 5], B = [5, ∞)
Given
Two sets A = (-∞, - 5], B = [5, ∞)
Find
union, AUB
Explanation
Union of two sets A and B is the set of all elements that are present in A or in B
so , here A = (-∞, - 5], B = [5, ∞)
then union of set A and B is given by
[tex]A\cup B=(-\infty,-5]\cup[5,\infty)[/tex]Final Answer
Therefore., the union of A and B is (-∞, - 5] U [5, ∞)
Help please! Some friends go to an amusement park in one car. They must pay a 6.00 parking fee plus 29.99 per person for tickets. The algebraic equation is C=6.00+29.99. Use the equation to calculate the number of tickets purchased for the group if the total cost was 215.93. Show all work
Answer:
7 # there were 7 people in the group
Step-by-step explanation:
C = 6.00 + 29.99x # the equation given
215.93 = 6.00 + 29.99x # 215.93 is the total so substitute it for C. Now we solve for x
209.93 = 29.99x # We subtracted 6 from both sides
7 = x # We divided 29.99 from both sides
7 is our answer
s\\line t find the measure of each angle HELP ME NOWWW
The values of the angles for the two parallel lines will be ∠1 = 115°, ∠2=115°, ∠3=148°, and ∠4 = 148°.
What are lines and angles?Straight lines with little depth or width are present. You will learn about a number of lines, including transversal, intersecting, and perpendicular lines. A figure called an angle is one in which two rays originate from the same point.
Given that the lines s and t are parallel to each other. The values of the different angles will be:-
∠1 = 115° Exterior angle property
∠2 = 115° Vertically opposite angle
The value of angle ∠3 will be calculated by the supplementary angle property.
∠3 = 148°
The value of angle ∠4 is 148 by vertically opposite angle property.
∠4 = 148°
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pls help me asap! due in 30 minutes :(
Answer:
(x+6)+x=20 Andy
Step-by-step explanation:
X represents Andy
X+6 represents juana who did 6 more problems
(X+6)+x=20
2x+6=20
2x=14
X=7
Cristian bought a new electronic tablet on sale 1/4 off the original Price.
A.What is the amount of the discount if the original price was $755
B.What is the scales price of the Tablet
Answer:
A: $188.75
B: $566.25
Step-by-step explanation:
To find the amount of the discount you can either multiply the original price ($755) by 1/4 or you can divide by 4.
Either way will get you $188.75. This is a quarter of the original price and is what is subtracted from the original sale price ($755). To find the sale price after the discount you do:
755-188.75=$566.25.
To check this you can do 755 × 3/4.
Hope this helps.
Please Mark Brainliest!!!
Answer:
What he said
Step-by-step explanation:
8) A bank pays interest of 11%. Mamuru puts $5000 in the bank.
How much money does he have after:
a) one year?
b) three years?
c) five years?
Answer:
Assuming that the interest Is paid out yearly After one year he would have $5550 After 3 years he would have $6838.16 After 5 years he would have $8425.29
I need help if you don't mind. I have to graph the linear equation using intercepts.
We want to find the places where the line
2x - 3y = 12
intercepts y-axis and x- axis
y- interceptWhen the line intercepts y axis, we know that x=0, we replace it in the equation so we can find y value:
2x - 3y = 12
↓
2 · 0 - 3y = 12
↓
0 - 3y = 12
-3y = 12
y = 12 / -3
y = -4
x - interceptIn the same way, we find the interception with x- axis when y = 0. We find the value of x replacing y by 0 in the equation:
2x - 3y = 12
↓
2x - 3 · 0 = 12
↓
2x - 0 = 12
2x=12
x = 12 / 2
x = 6
GraphWe locate both points: y = -4 and x = 6:
Finally, we join the points with a straight line
Lauren needed to get her computer fixed. She took it to the repair store. The
technician at the store worked on the computer for 3.75 hours and charged her $119
for parts. The total was $400.25. Write and solve an equation which can be used to
determine a, the cost of the labor per hour.
Answer:
3.75x + $119 = $400.25
x = $75
Step-by-step explanation:
Lauren needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 3.75 hours and charged her $119 for parts. The total was $400.25. Write and solve an equation which can be used to determine a, the cost of the labor per hour.
3.75x + parts = $400.25
so:
3.75x + $119 = $400.25
subtract $119 from both sides:
3.75x + $119 - $119 = $400.25 - $119
3.75x = $281.85
divide both sides by 3.75
3.75x/3.75 = $281.85/3.75
x = $75
so the tech charged $75 per hour.
Which statement is true about the equations –3x + 4y = 12 and One-fourthx – One-thirdy = 1?
The system of the equations has exactly one solution at (–8, 3).
The system of the equations has exactly one solution at (–4, 3).
The system of the equations has no solution; the two lines are parallel.
The system of the equations has an infinite number of solutions represented by either equation.
Answer: The answer is c) The system of the equations has no solution; the two lines are parallel.
Step-by-step explanation: edge 2022
Answer: C
Step-by-step explanation: