In the xy-plane, a line that has the equation y = c for some constant c intersects a parabola at exactly one point . If the parabola has the equation y=-x^ 2 +5x. what is the value of c?
Answer:
c=6.25
Step-by-step explanation:
If a line that is flat (has a slope of zero) hits only one point of the parabola, it means that point is the vertex of the parabola.
In this case your equation is ---
y= –x^2 + 5x
--- and you just need to write in vertex for the equation:
y=a(x–h)^2 + k
y= –(x–2.5)^2 + 6.25
The vertex is (h,k) or (2.5,6.25)
Since the equation is "y=", k=c
or c=6.25
Thank You.
In this question:
We have to find the point of intersection of the line and the parabola.To do this, we have to apply concepts needed to solve a quadratic equation.Doing this, we find that the value is: [tex]c = \frac{25}{4}[/tex]
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
Line: y = c
Parabola: y = -x^ 2 +5x.
The intersection is at the point:
[tex]-x^2 + 5x = c[/tex]
[tex]-x^2 + 5x - c = 0[/tex]
[tex]x^2 - 5x + c = 0[/tex]
Which is a quadratic equation with [tex]a = 1, b = -5[/tex].
The line and the parabola intersect at exactly one point, which means that the quadratic equation has one solution, that is, [tex]\Delta = 0[/tex].
Since:
[tex]\Delta = b^{2} - 4ac[/tex]
It means that:
[tex]b^2 - 4ac = 0[/tex]
We use this to find the value of c.
[tex](-5)^2 - 4(1)(c) = 0[/tex]
[tex]4c = 25[/tex]
[tex]c = \frac{25}{4}[/tex]
The value is: [tex]c = \frac{25}{4}[/tex]
A similar question is found at https://brainly.com/question/15211279
Which defines a line segment?
two rays with a common endpoint
a piece of a line with two endpoints
a piece of a line with one endpoint
all points equidistant from a given point
B. A piece of a line with two endpoints
The definition that defines a line segment is
piece of a line with two endpoints.
What is line segment?Line segment refer to line on a piece which comprises of two points that are extreme to each other.
Therefore, The definition that defines a line segment is piece of a line with two endpoints.
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2nd Option : a piece of a line with two endpoints
What is line ?
A figure formed by joining two points and whose ends are extended to the infinity is called line.
What is line segment ?A line segment is the finite length between two points, which can be measured. A line segment is a small part of a line.
What is the correct option ?A line segment is defined as a piece of a line with two endpoints.
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Select the correct answer. Identify the axis of symmetry of the function graphed below. A. x = -3 B. x = -1 C. x = 1 D. x = -4
Answer:
B
Step-by-step explanation:
The vertex of the parabola is (-1,-4)
So the axis of symetry is x=-1
15−x+y=14−(−x−y) help plz
Answer:
[tex]x=0.5[/tex]
[tex]y=anything[/tex]
Step-by-step explanation:
15−x+y=14−(−x−y)
15-x+y=14+x+y
Subtract 14 from both sides
1-x+y=x+y
Subtract y from both sides
1-x=x
Add x to both sides
1=2x
2x=1
Divide both sides by 2
x=0.5
There were 70 employees working at a rental company. This year the number of employees increased by 10 percent. How many employees work for the rental company this year?
Classify the following triangle?
Answer:
B.
Step-by-step explanation:
The triangle is obtuse because there only has to be one obtuse angle for it to be obtuse.
Answer:obtuse
Step-by-step explanation: it’s 180 degrees
plz help me by complete the steps to solve for x
Answer:
30
Step-by-step explanation:
5/6x-1/5x=19
19/30x=19
30/19(19/30x)= 30/19(19)
x= 30
Translate the sentence into an equation.
The sum of 8 times a number and 9 is 2.
Use the variable for the unknown number.
Answer:
x=-0.875
Step-by-step explanation:
Into an equasion it would be: 8•x+9=2
Let's solve for x:
1. 8x+9=2
2. 8x=2-9
3. 8x=-7
4. x=-0.875
10 years ago, the ratio of Jeremy's age to randy's age to Kadens's age was 4:3:1. The sum of their present age is 102. Find Randy's age now.
Answer:
Randy: 38.25
Step-by-step explanation:
J 4×12.75= 51
R 3×12.75= 38.25
K 1×12.75= 12.75
51+38.25+12.75=102
Answer: 37
Step-by-step explanation: TEN years ago : 4+3+1 = 8 TEN years ago (102-30) = 72 72/8 = 9
Randy was 3 * 9 = 27 ten years ago now he is 37 y/o
Can someone help me with number 8 plz
Answer:
7/23
Step-by-step explanation:
Multiples of 4 are 4 and 8
4 was spun 4 times
8 was spun 3 times
total spins = 2+3+2+4+5+3+1+3=23
P( 4 or 8) = number of times spun / total
= (4+3) / 23
=7/23
solve for y in this equation
Answer:
y= -1 1/3
Decimal form: -1.3
Which equation in the form y = mx + cs models Emma's situation?
O y = 20x + 0.15
O y = 20x + 15
O y = 20x + 0.15s
y = 20x + 15s
Help!!!!
Answer:
the answer would be y = 20x + 0.15s
Step-by-step explanation:
In this problem you would just plug in your facts. 20 would plug in for m, 15% would change to 0.15 then you would plug 0.15 into c.
The equation represents Emma's situation is y = 20x + 0.15s. The correct option is C.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The equation in the form y = mx + cs models Emma’s situation is
y = 20x + 0.15s
She makes $20 per hour, so for x hours, she makes 20x. The slope-intercept of the line y= mx+c
Where y coordinate, x- x co-ordinate
m=slope of the given line
C-y intercept.
She makes a 15% commission on the sales, s. 15% = 0.15,
So for the sales, she makes
15% * s = 0.15s.
The total she makes is 20x + 0.15s
y = 20x + 0.15s
The complete question is given below:-
Emma has just started a new sales job. She makes $20 an hour. On top of her hourly wages, she’ll be paid a commission of 15% on all sales she makes. Use this information to answer the following questions.
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Which type of science is economics? A. physical science B. social science C. life science D. applied science
Answer:The answer is B
Step-by-step explanation:
Is it true or false ...help please
Answer: TRUE
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
A^2+B^2=C^2
On their first dive, researchers explore a part of the ocean floor that is 60 feet
below sea level. This depth can be represented by the integer -60. On their
second dive, researchers explore a deeper depth.
Write an inequality that represents the possible depth, d, of the researchers'
second dive.
Answer:
d < -60
Step-by-step explanation:
Let d represent the depth of the researchers' second dive.
Given;
Depth of First dive = -60 ft
It was stated that in their second dive, the researchers explore a deeper depth, That is depth deeper than 60 ft.
Since the depth of 60ft is represented by the integer -60,
Deeper depth would be represented by integers less than -60.
So, d can be represented as;
d < -60
Answer:
d < -60
Step-by-step explanation:
Let d represent the depth of the researchers' second dive.
Depth of First dive = -60 ft
It was stated that in their second dive, the researchers explore a deeper depth, That is depth deeper than 60 ft.
Since the depth of 60ft is represented by the integer -60,
Deeper depth would be represented by integers less than -60.
So, d can be represented as;
d < -60
PLEASE HELP ME!
How can I figure out the length of the short leg on a 30-60-90 right triangle without measuring it. And how can I determine the hypotenuse of the same triangle without measuring it.
Antonio wants to build a cube-shaped storage container that holds 216 cubic inches of water for some frogs he recently purchased.
Using the formula,V=s3, where V represents the volume of the container andsrepresents its side length, find the length of one side of the container.
Answer: a = 6 inches
Step-by-step explanation:
a = V^1/3
Need help with this pls
(Show work pls!!)
Answer:
46
Step-by-step explanation:I know this because I have done this before!
Complete the rule:
positive + positive =
Answer:
Positive
Step-by-step explanation:
Positive plus positive is positive. For example, 3+3. That will be 6. 3 is positive both times. And six is positive.
Use the graph of g to solve.
Find g(-16)
Answer:
g(-16) = 6
Step-by-step explanation:
We want the value of the function when x = -16
The function is constant from x = -8 to the left. The value is 6
g(-16) = 6
Answer:
g(-16) = 6
Step-by-step explanation:
The upper horizontal line with an arrow to the left means that the value of function g remains at 6 from x = -8 as it approaches negative infinity. Since -16 is in the interval from -8 to -infinity, then
g(-16) = 6
The ordered pair below is a solution to which equation?
(4,12)
Answer:
C.
Step-by-step explanation:
x= 4, y = 12
A . y = 6x
12 = 6*4
12 = 24 false
C. y = 3x
12 = 3*4
12 = 12 true
Given: F(x) = x + 2 and G(x) = 3x + 5
(F*G) (x) =
Answer:
[tex] \boxed{(f \times g)(x) = 3 {x}^{2} + 11x + 10} [/tex]
Given:
[tex]f(x) = x + 2 \\ \\ g(x) = 3x + 5[/tex]
To Find:
[tex] (f \times g)(x) = f(x) \times g(x)[/tex]
Step-by-step explanation:
[tex]= > f(x) \times g(x) = (x + 2)( 3x + 5) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =x( 3x + 5) + 2(3x + 5) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =3 {x}^{2} + 5x + 6x + 10\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =3 {x}^{2} + 11x + 10[/tex]
Answer:
[tex]\boxed{(f \times g)(x) = 3 {x}^{2} + 11x + 10}[/tex]
Step-by-step explanation:
Foil:
x times 2x
2 times 3x
x times 5
2 times 5
then add them all up
Students were asked to write 6x^5 + 8x - 3x^3 + 7x^7 in standard form.
Shown below are four student
responses.
Anne: 7x^7 + 6x^5 – 3x^3 + 8x
Bob: -3x^3 + 6x^5 + 7x^7 + 8x
Carrie: 8x + 7x^7 + 6x^5 – 3x^3
Dylan: 8x - 3x^3 + 6x^5 + 7x^7
Which student is correct?
Anne: 7x^7 + 6x^5 – 3x^3 + 8x
A can contains 414 mL of chicken broth. Roland poured 4 cans of broth into a pot for a soup recipe. How many liters of broth did Roland pour into the soup?
Answer:
1.656 litres
Step-by-step explanation:
1 can = 414ml
4 cans = 414 x 4
4 cans = 1,656ml
1,656ml = 1.656 litres
The amount of broth poured into the soup is 1.656 L.
Given data:
To determine the number of liters of broth Roland poured into the soup, we need to convert the volume of the broth from milliliters (mL) to liters (L).
Given that each can contains 414 mL of chicken broth, and Roland poured 4 cans of broth into the pot, we can calculate the total volume in milliliters:
414 mL/can * 4 cans = 1656 mL
On simplifying the equation:
To convert milliliters to liters, we divide by 1000 since there are 1000 milliliters in a liter:
1656 mL / 1000 = 1.656 L
Hence, Roland poured 1.656 liters of broth.
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Combine like terms to find the expression to −6(14b+10)+4(910b+3).
Answer:
3556b - 48
Step-by-step explanation:
−6(14b+10)+4(910b+3)=
-84b-60+3640b+12=
(3640-84)b+(12-60)=
3556b - 48
What is the probability of spinning a 5 or a 6? select the fraction and the percent
1/5
1/2
1/4
2/9
20%
50%
25%
22.2%
Answer:
1/5 or 20%
Step-by-step explanation:
There are 10 total options
P( 5 or6) = number of 5's or 6's / total
=2/10
= 1/5
1/5 = 20%
Answer:
1/5, 20%
Step-by-step explanation:
Since there are 10 numbers in all from 1-10, the probability of spinning a 5 or a 6 is 2/10 which simplifies to 1/5. This also equals 20%.
What is the factorization of 729x^15 + 1000?
729x¹⁵ + 1000
This is a case of a sum of cubes.
729 is the cube of 9
1000 is the cube of 10
x¹⁵ is the cube of x⁵
A sum of perfect cubes can be factored into
(a + b) (a² - ab + b²)
(9x⁵+ 10) ((9x⁵)²-(9x⁵)(10) + 10²)
(9x⁵ + 10) (81x¹⁰ - 90x⁵ + 100) THIS IS THE FACTORIZATION
9x⁵ (81x¹⁰ - 90x⁵ + 100) + 10(81x¹⁰ - 90x⁵ + 100)
729x¹⁵ - 810x¹⁰ + 900x⁵ + 810x¹⁰ - 900x⁵ + 1000
729x¹⁵ - 810x¹⁰ + 810x¹⁰ + 900x⁵ - 900x⁵ + 1000
729x¹⁵ + 1000
Simpson deposits $1,200 in a savings account that earns simple interest at the rate of 5% per year. What interest does he earn at the end of 1 year?
-must haves :)..
right answer.
makes sense.
step by step.
^I will mark someone the brainliest when someone answers this, thank youuu:)
Answer:
$60
Step-by-step explanation:
1200*0.05 = $60
Does anyone know the answers please help!
Answer:
I am sick
Step-by-step explanation:
The solution of [tex]\frac{1}{3}[/tex]x + 2 = 7x is
A. 1
B. 3/10
C. 1/2
D. 1/10
Answer:
B)
Step-by-step explanation:
[tex]\frac{1}{3}x+2=7x[/tex]
Subtract (1/3)x form both sides
[tex]\frac{1}{3}x+2-\frac{1}{3}x=7x-\frac{1}{3}x\\\\2=7x-\frac{1}{3}x\\\\2=\frac{7*3}{1*3}x-\frac{1}{3}x\\\\2=\frac{21}{3}x-\frac{1}{3}x\\\\2=\frac{20}{3}x\\\\\frac{20}{3}x=2\\\\x=2*\frac{3}{20}\\\\x=\frac{3}{10}[/tex]
