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]
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Given: 22 and 24 are vertical angles
Prove: Z2 Z4
Answer:
Where is the picture? Also, Im kinda confused
Step-by-step explanation:
A Student takes exam containing 18 true or false questions What is the probability that he will get exactly 14 questions right?
Answer:
1.5442%
Step-by-step explanation:
Which formula could be used to find the volume of a cube with side length equal to s?
s cubed
(6) (s squared)
s squared
(6) (s cubed)
Answer:
s cubed
Step-by-step explanation:
Formula for volume of a cube is side ^3
The volume of cube with side length s is s cubed.
What is cube?
A cube is a region of space formed by six identical square faces joined along their edges.
What is the formula for the volume of cube?The volume of cube is defined as the total number of cubic units occupied by a cube.
The Formula for the volume of cube is given by
[tex]v = a^{3}[/tex]
Where, v is the volume of cube
and, a is the side of cube.
According to the given question we have
The side length of cube is s.
Therefore, the formula for finding the volume of cube is given by
volume of cube = [tex]s^{3}[/tex]
Hence, the volume of cube with side length s is s cubed.
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At a cafe
2 teas + 1 coffee cost= £3.40
1 tea and 4 coffees cost=£7.30
Work out the cost of 1 tea and the cost of 1 coffee?
Step by step explanation, pleaseeeee
Answer:
cost of 1 tea= £1.08
cost of 1 coffee= £1.24
Step-by-step explanation:
Please see the attached picture for full solution
HI CAN I PLEASE GET SOME HELP PLEASE THANK YOU I WOULD APPRECIATE IT HOW MANY SOLUTIONS ARE THERE TO THIS NONLINEAR SYSTEM!!!! A)no solutions B)one solution C)two solutions
Answer:
B) one solution
Step-by-step explanation:
The blue line and the red line cross at only one point so there is one solution. It would be no solution if the blue line never crossed the red line and it would be two or possibly more solutions if the lines crossed more than once.
If 40 people buy lemonade while at the
food stand, what percent of the people
bought lemonade? Illustrate on the
number line.
Answer: transforms
Step-by-step explanation:
Please use a system of equations to solve this problem. I already know how to solve this, but I want to know how to solve it using a system of equations!!! A writing workshop enrolls novelists and poets in a ratio of 5:3. There are 24 people at the workshop. How many novelists are there and how many poets are there?
Answer:
[tex]\boxed{\sf \ \ \ 15 \ \ novelists \ \ and \ \ 9 \ \ poets \ \ \ }[/tex]
Step-by-step explanation:
hello,
let's note a the number of novelists and
b the number of poets.
we know that a = 5/3 b as "enrolls novelits and poets in a ratio of 5:3"
it comes 3a=5b which is the first equation
and we know that a + b = 24 "there are 24 people"
we we have two equations
(1) 3a - 5b = 0
(2) a + b = 24
let's multiply (2) by 3 it comes 3a + 3b = 24*3 = 72
let's do 3*(2) - (1) it comes
3a + 3b -3a + 5b = 72 - 0 = 72
so 8b = 72
so b = 9
and then we replace b in (2) it comes
a = 24-9 = 15
hope this helps
Please help with this
Answer:
The answer would be D
Step-by-step explanation:
Answer:
D
The triangle moved 6 units right and one unit up.
B-CR-SLHv2
How many ideas should be on each note card in the index-card method of note-taking?
zero
one
two
as many as you can fit
Answer:
1 or 2
Step-by-step explanation:
2 if you write really small but otherwise 1 idea on 1 side of a notecard.
Which of the following are solutions to the equation below?
Check all that apply.
6x2 - 2x + 36 = 5x2 + 10x
O A. 18
B. 4
C. 6
D. -6
O E. -3
F. -4
Answer:
B. 4
Step-by-step explanation:
Rearrange the equation so that is in the form (ax² + bx + c = 0).
6x² - 3x + 36 = 5x² + 10x
x² - 3x + 36 = 10x
x² - 13x + 36 = 0
Now, factor the equation and solve for x.
x² - 13x + 36 = 0
(x - 4)(x - 9) = 0
x - 4 = 0
x = 4
x - 9 = 0
x = 9
The solutions to the equation are 4 and 9. The correct answer choice is B.
Answer:
The answer B.4
Step-by-step explanation:
Arrange the equation so that is in the form
(ax² + bx + c = 0).
6x² - 3x + 36 = 5x² + 10x
x² - 3x + 36 = 10x
x² - 13x + 36 = 0
the equation and solve for x.
x² - 13x + 36 = 0
(x - 4)(x - 9) = 0
x - 4 = 0
x = 4
x - 9 = 0
x = 9
NEED ASAP !!! helppppp
Answer: 960
Step-by-step explanation: all you have to do to find the volume is 10*8*12, which would be 960, so the cubic volume is 960.
A scientist is running an experiment with
two species of bacteria that grow exponentially.
If species A doubles in population every
two days, species B doubles in population
every five days, and each species began the
experiment with a population of 50 bacteria,
what will the difference be between the
populations of the two species after ten days?
(A) 200
(B) 800
(C) 1,200
(D) 1,400
Answer:
D 1,400
Step-by-step explanation:
Species A doubles every 2 days and species B doubles every 5 days, so in 10 days, species A will double 10/2 = 5 times and species B will double 10/5=2 times. After 10 days from an initial population of 50 in each species, species A will have 50 x 2 ^5= 50 x 32 = 1,600 population while species B will have 50 x 2 ^2 = 200 population. Their difference is 1,600-200 = 1,400.
(1.3 x 10-2) (0.05) = ?
Answer:
=0.065x10−0.1
Step-by-step explanation:
(1.3x10−2)(0.05)
=(1.3x10+−2)(0.05)
=(1.3x10)(0.05)+(−2)(0.05)
=0.065x10−0.1
Answer: 0.55
Step-by-step explanation:
1.3 x 10= 13
13-2= 11
11 x 0.05= 0.55
BOOM! math.
The pieces on a chessboard are either white or black. Of the pieces remaining on a chessboard, the probability of randomly picking a white piece is 5/12 What is the probability of randomly picking a black piece?
A. 5/12
B. 1/2
C. 7/12
D. 2/3
7/12
12/12 is the total
So 12/12 minus 5/12 is 7/12
Correct me if I am wrong
90°
30
==
Help me please
Answer:
90
Step-by-step explanation:
If there is a straight line and 1 angle is 90 degrees, the angle next to it is also 90 degrees.
Answer:
x = 90°
Step-by-step explanation:
Since x and 90° share the same straight line, they are supplementary, meaning they must add up to 180°. Hence x must be 180-90 = 90.
Solve for X (BRAINLIEST)
Answer:
x = 24
Step-by-step explanation:
The triangles are similar so we can use ratios to solve
x 6
------ = -----------
x+8 8
Using cross products
8x = 6*(x+8)
8x = 6x+48
Subtract 6x from each side
8x-6x = 48
2x = 48
Divide by 2
2x/2 = 48/2
x = 24
Answer:
x = 24
Step-by-step explanation:
Very similar to the previous problems of this type, these two triangles have a shared angle A and both have a right angle, prove AA similarity.
From there, we can set up a ratio:
(x+8)/x = 8/6
Multiply both sides by x:
x+8 = 8x/6
Multiply both sides by 6:
6x+48 = 8x
Move the 6x to the right:
48 = 2x
Divide both sides by 2:
x = 24
Complete each step in the following solution.
10x + 8 = 3(x – 2)
10x + 8 = 3x ___
7x = ___
x = -2
A: 10x + 8 = 3(x – 2)
10x + 8 = 3x – 6
7x = – 14
x = -2
Step 1 : Multiplying 3 with -2, we get -6
Step 2 : Subtract -6 and 8 , we get -14
Step 3 : We get x = -2
What is an equation?"An equation is a formula that expresses the equality of two expressions, by connecting them with the equal sign. Solving an equation containing variable consists of determining which values of the variables make the equality true."
Given equation
10x + 8 = 3(x – 2)
In this step by multiplying 3 with -2, we get -6
10x + 8 = 3x - 6
Subtract the variables
Subtract -6 and 8 , we get -14
7x = -6 - 8
7x = -14
Divide with 7 on both sides, we get
x = -2
Hence these are the following steps to get x = -2
Step 1 : Multiplying 3 with -2, we get -6
Step 2 : Subtract -6 and 8 , we get -14
Step 3 : We get x = -2
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Find the slope and y-intercept of the line. y =1/5x – 8 1/5; –8 –8;1/5 8; 1/5 5; 8
Answer:
Slope = 1/5 y intercept=-8
Step-by-step explanation:
We can use sloper intercept form to find the answer
Answer:
Step-by-step explanation:
Slope = 0.400/2.000 = 0.200
x-intercept = 40/1 = 40.00000
y-intercept = -40/5 = -8
What is being constructed based on the markings in the following diagram?
Line AB with two points C and D on each side of the line; a circle is created with center C passing through point D, and the intersection of circle C with line AB creates points E and F such that point A is between points E and F and point F is between points A and B. Point G is not located on line AB and is on the same side as point D. A circle is created with center F and a radius of FG, and another circle is created with the same radius from point E. Points H and I are intersecting points of circles E and F, and a line is drawn through points H and I.
Inscribed regular hexagon
Inscribed equilateral triangle
Perpendicular line through a point off a line
Perpendicular line through a point on a line
Answer:
The correct option is;
Perpendicular line through a point off a line
Step-by-step explanation:
Based on the markings in the diagram, we have;
Marking points E and F along AB extended forms two points equidistant from the point C on the line AB
Construction of the line HI by using equal arc lengths from E and F creates two points equidistant from E and F on either side of the line AB such that HI passes through C forming a perpendicular bisector from C to AB.
Therefore, a perpendicular line has been constructed from the point C off the line AB to the line AB
Hence the correct option is the construction of a perpendicular line through a point off a line.
Zoe and Hannah share tips in the ratio 3:7 . Last week Zoe received £24 . How much did Hannah receive last week?
Answer:
56 euros
Step-by-step explanation:
3=24
7=x
7 x 24=56
Let a and b be real numbers where a b 0. Which of the following functions could represent the graph below?
Answer:
C. f(x) = x4(x – a)(x – b)2
Step-by-step explanation:
just took the test on edge
A function which could represent the above graph is: C. f(x) = x⁴(x - a)(x - b)².
How to interpret the graph?In Mathematics, the nature of the intercept on a polynomial graph highlights the nature of its multiplicity. Also, the polynomial graph has no single zero (factor) but bounced off the x-axis at three (3) different locations.
This ultimately implies that, the polynomial graph has an even multiplicity at these three (3) points:
x⁴x - a(x - b)²In conclusion, a function which could represent the above graph is f(x) = x⁴(x - a)(x - b)².
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h = -162 +64t +960.
What is the maximum height?
Answer:
2 seconds to reach maximum height
Step-by-step explanation:
When dividing complex numbers, why do you need to multiply the numerator and denominator by the complex conjugate of the denominator?
Answer:
Step-by-step explanation:
So that the denominator is a real number. I know that doesn't sound like a good reason, but it is the reason mostly by convention. You don't want complex i's floating all over the answer. There should be just one i.
Answer:
You have to multiply by the complex conjugate because the denominator has to be a real number. By multiplying the complex conjugate you can transform the denominator in to a real number.
Is (0,0) a solution to this system?
Answer:
D.
Step-by-step explanation:
If you substitute (0,0) then the inequality is not true in both cases. This accounts for answer D.
Solve the inequality for x. –8x + 16 > –72 A) x 7 D) x > 11
Answer:
x < 11
Step-by-step explanation:
–8x + 16 > –72
Let's transfer the components which do not contain x to the right side and change sign of these components
-8x > -72 - 16
Now, we simplify the right side
-8x > -88
We then multiply both sides by (-1/8) and change the greater symbol to smaller symbol
(-1/8)*(-8)x < (-1/8)*(-88)
Finally, we simplify both sides to solve this inequality
x < 11
Hope this helps!
Which expression can be used to convert 100 USD to Japanese yen?
100usd[99.30487yen/1usd]
100usd[1usd/99.30487yen]
100usd[0.01007yen/1usd
100usd[99.30487usd/1yen]
Answer:
a. 100usd{99.30487yen/1usd}
The equations of three lines are given below.
Line 1: 10x - 4y= -4
Line 2: 5y = –2x+3
2
Line 3: y = -7X-4
5
fx-4
For each pair of lines, determine whether they are parallel, perpendicular, or neither.
Answer:
3
Step-by-step explanation:
Which equation matches the following graph?
Options:
y = x^2
y = -x^2
x = y^2
x = -y^2
The answer is: [tex]y=-x^2[/tex].
Hope this helps.
A function has a discriminant of 25.
How many x-intercepts does it have?
Answer:
2
Step-by-step explanation:
If the value of the discriminant is positive, there are two real solutions for x, meaning the graph of the solution has two distinct x-intercepts
Here 25 is positive discriminant, hence the function will have 2 x - intercepts
Tia measured the daily high temperature in Kats, Colorado for each of the 30 days in April. She then created both a dot plot and a box plot to display the same data (both diagrams are shown below). Which display makes it easier to see that the third quartile is 14 degrees C
Answer:
A box plot would make it easier to see that the third quartile is 14 degrees C.
Step-by-step explanation:
On a box plot, the right end of the box gives the exact value of the third quartile. On a dot plot, you would have to identify the value based on the number of dots shown.
Answer:
Box plot and dot plot
Step-by-step explanation:
Because I checked.
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