Answer:
1. Look at the screenshot below.
2. If a line intersects a parabola at a point, the coordinates of the intersection point must satisfy the equation of the line and the equation of the parabola.
Since the equation of the line is y = c, where c is a constant, the y-coordinate of the intersection point must be c.
It follows then that substituting c for y in the equation for the parabola will result in another true equation: c = −x^2 + 5x.
Subtracting c from both sides of c = −x^2 + 5x and then dividing both sides by −1 yields 0 = x^2 − 5x + c.
The solution to this quadratic equation would give the x-coordinate(s) of the point(s) of intersection.
Since it’s given that the line and parabola intersect at exactly one point, the equation 0 = x^2 − 5x + c has exactly one solution.
A quadratic equation in the form 0 = ax^2 + bx + c has exactly one solution when its discriminant b 2 − 4ac is equal to 0. In the equation 0 = x^2 − 5x + c, a = 1, b = −5, and c = c.
Therefore, (−5)^2 − 4(1)(c ) = 0, or 25 − 4c = 0.
Subtracting 25 from both sides of 25 − 4c = 0 and then dividing both sides by −4 yields c = 25/4 .
Therefore, if the line y = c intersects the parabola defined by y = −x^2 + 5x at exactly one point, then c = 25/4 .
Either 25/4 or 6.25
Help please :( !
Compare . Who picked fruit at a faster pace ?
Answer:
Shawn.
Step-by-step explanation:
We can solve for apples per hour and pears per hour. For Shawn, to get the apples per hour, we do 4/2 which is 2 bushels of apples per hour. For pears, we do 5/2 which is 2.5 bushels of pears per hour.
When Carla is picking, we can do:4/3 which is 1 and 1/3, which is her apple bushel picking per hour. For her pears, she picks them at 2 bushels of pears per hour.
Since Shawn picks her apples quicker per hour, and her pears quicker per hour, Shawn picks at a faster fruit pace.
Need a little help with this.
Answer:
a.) not like terms
b.) not like terms
c.) like terms ; 14 yards
Step-by-step explanation:
please help i will mark branliest
Answer:
A. S=3w
Step-by-step explanation:
Hope it helps
Simplify the expression:
4x2 + 9x + 14 + 4x2 - 2x
ASAP PLEASEEEEEEE
Answer:
8x²+7x+14
Step-by-step explanation:
4x²+4x²= 8x²
9x-2x= 7x
14=14
8x²+7x+14
hope it helps! please mark me brainliest
thank you! have a good day ahead
this is for freckle which I hate can someone help?
Answer:
The answer is B. 26 miles per hour.
Step-by-step explanation:
13+13=26
X goes by an hour.
Which triangles are similar?
Answer:
A and c are similar except C is bigger than as so the scaling has gotten higher, so the answer is D
Step-by-step explanation:
Simplify 3^8 x 3^4 divided by 3^2 x 3^8 in index form
The ratio of the perimeter of the rectangle ABCD to the perimeter of rectangle EFGH is 4:7. The value of x is
Answer:
x = ~8.76
Step-by-step explanation:
Since we know that the scale factor is 4:7, we can figure that 5 will be 4/7 the size of x.
4/7 = 0.571
5 / 0.571 = ~8.76
PLS HELP MEEEEEE ( I don’t need to know the first one )
Answer:
k=27
Step-by-step explanation:
Answer:
direct variation is y = kx
k is the slope of the line y = mx + b
i don't know that last one, sorry
Step-by-step explanation:
An investor bought a number of shares of stock for $1600 after Priess dropped by $10 per share she sold all but four of her shares for $1120 how many shares that she originally by?
Answer:
She originally bought either 20 or 32 shares
Step-by-step explanation:
An investor bought a number of shares of stock for $1600 after Price dropped by $10 per share she sold all but four of her shares for $1120 how many shares that she originally by?
Let the number of shares she bought be represented by 1600/x
This is calculated as:
1600/x = 1120/x + 10 + 4
Multiply through by (x)(x - 10)
1600(x-10) = 1120(x) + 4(x)(x - 10)
1600x - 16000 = 1120x + 4x² - 40x
Collect like terms
4x² + 1120x - 1600x - 40x +16000 = 0
4x² - 520x + 16000 = 0
Using the Almighty formula method
= -b ± √b²- 4ac/2a
a = 4, b = -520 , c = 16,000
Hence:
= -(-520) ± √-520² - 4 × 4 × 16000/2 × 4
= 520 ± √14400/8
= 520 ± 120/8
520 - 120/8
= 400/8
= 50
520 ± 120/8
= 520 + 120/8
= 640/8
= 80
Since we have:
1600/x
When x = 50
= 1600/50
= 32
When x = 80
= 1600/80
= 20
Therefore, she originally bought either 20 or 32 shares
Use a calculator to find the trigonometric value to
4 decimal places.
tan 31°
=
Answer:
Approximately 0.6009
The value of tan 31 is 0.6008606.
What is Trigonometry?
The branch of mathematics concerned with specific functions of angles and their application to calculations.
As, the angle 31° lies between 0° and 90° (First quad).
So, tangent function is positive in the first quadrant.
Tan 31 degrees= tan (0.54105 . . .) in radians.
As, using degree to radian conversion,
θ(radians) = θ in degrees × (π/180°)
31 degrees = 31° × (π/180°) rad
= 0.5410
So, tan 31°
= tan(0.5410)
= 0.6008606.
Hence, tan 31= 0.6008606.
Learn more about trigonometry here:
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Bags of flour come in 3 sizes:
Small bag: A 500 g bag costs 90p.
Medium bag: A 2 kg bag costs £3.40.
Large bag: A 4 kg bag costs £7.60.
Calculate the cost of 2 kg for the small and large bags.
Give your answer in pounds to 2 dp.
Write the bag that is the better value in the comments.
Answer:
Ik where u got this q from but:
small bag is £3.60
large is $3.80
Step-by-step explanation:
the 500 grams x 4 to get 2kg then do 90p x 4
then
4kg divided by 2 to get 2kg as the question states, then do £7.60/2
hegarty maths anyone?
help Math 39 points Asap Probability image below
Answer:
1/10
Step-by-step explanation:
There are 3 reds and 2 blues. He picks one and then another with no replacement. ? of getting 2 blues.
There are five marbles altogether.
First is 2/5
The second blue is 1/4
The chance of them both being blue is 2/5 * 1/4 = 2/20 = 1/10
PLEASE HELP
need to know cos(F), sin(F), and tan(F)
WILL GIVE BRAINLIEST
Answer:
Cos(F) = 5/13
Sin(F) = 12/13
Tan(F) = 12/5
Step-by-step explanation:
Soh Sine: Opposite(12) over Hypotenuse(13)
Cah Cosine: Adjacent(5) over Hypotenuse(13)
Toa Tangent: Opposite(12) over Adjacent(5)
Who can help with this question please?
Answer:
Let the sum be x.
Using formula,
I=
100
PRT
=
100
x×
12
15
×
2
15
−
100
x×
12
8
×
2
25
=32.50
⇒
2400
25x
=32.50
⇒x=
25
32.50×2400
=3120
∴ Required sum =Rs.3120
Step-by-step explanation:
Find the value of x in the following figure ( Please hurry)
Answer:
x=9
Step-by-step explanation:
2x+12=5x-15
3x=27
x=9
Answer:
the value of X in the figure is 0 I think
Susan purchased a prepaid phone card for $15. Long distance calls cost 14 cents a minute using this card. Susan used her card only once to make a long distance call. If the remaining credit on her card is $9.26, how many minutes did her call last?
Answer:
41 minutes
Step-by-step explanation:
Step one:
given data
Susan purchased a prepaid phone card for $15
let the number of minutes be x
and let the total be y
per minute call cost = 14 cents = $0.14 per minute
Hence the expression for the situation is given as
y= 15-0.14x
Step two:
given that the balance after a call is 9.26
9.26=15-0.14x
solve for x
9.26-15= -0.14x
5.74=0.14x
divide both sides by 0.14
x=5.74/0.14
x=41 minutes
A (litres)
160
140
120
100
The amount of oil A left in a leaky barrel after
t minutes is shown on the graph alongside.
a Find the gradient and A-intercept of the line.
Interpret your answers.
6 Find the model connecting A and t.
c. How much oil will be left after 15 minutes?
d For what values of t is it reasonable to apply
this model?
80
60
40
20
0
12
6
(minutes)
Answer:
Step-by-step explanation:
Graph attached represents the relation between amount of oil left in the leaky oil tanker and time.
a). Gradient of the line = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
= [tex]\frac{(160-120)}{(0-8)}[/tex]
= -5
A-intercept = 160
b). Linear equation to represent the given relation in the graph will be,
A = (-5)t + 160
c). At t = 15 minutes,
A = (-5)(15) + 160
A = -75 + 160
A = 85 liters
d). This model is applicable till the container gets fully emptied.
For A = 0,
0 = -5t + 160
t = [tex]\frac{160}{5}[/tex]
t = 32 minutes
Therefore, this model is reasonable up to t = 32 minutes.
Hola chicos, solo necesito ayuda con la vida. Solo bromeaba o lo estoy?
Answer:
no sé eres tú
Step-by-step explanation:
Solve the equation.
x/-2-17=-7
A.) 48
B.) –2
C.) 14
D.) –20
hii can someone help with this pls :)
i think it’s (0.6,2.8) but i’m not sure so can someone confirm
Answer:
[tex]R(x,y) = (0.8,-1.2)[/tex]
Step-by-step explanation:
The coordinates of QS are:
[tex]Q(x_1,y_1) = (-2,-6)[/tex]
[tex]S(x_2,y_2) = (5,6)[/tex]
The ratio is represented as:
[tex]R_{m:n} = 2:3[/tex]
Required
Find the coordinates of R
The coordinates of R is calculated by:
[tex]R(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]
Substitute values for m, n, x's and y's
[tex]R(x,y) = (\frac{2 * 5 + 3 * -2}{2+3},\frac{2*6 + 3*-6}{2+3})[/tex]
[tex]R(x,y) = (\frac{4}{5},\frac{-6}{5})[/tex]
[tex]R(x,y) = (0.8,-1.2)[/tex]
None of the options is correct
Easy 3rd grade mathy! ITS 100 POINTS
Answer:
3.5?
Step-by-step explanation:
May I have brainliest please I'm trying to level up!
</3 PureBeauty
Answer:
uhmm 3.2???
Step-by-step explanation:
I barely remember not gonna lie :'(
On a coordinate plane, the center of a circle P is at the point (2, 15) . Point M is located on the circle at (7, 3). Which equation describes circle P?
Answer: (x - 2)^2 + (y - 15)^2 = 13^2
Step-by-step explanation:
We know that the general equation for a circle is:
(x - a)^2 + (y - b)^2 = R^2
Where:
(a, b) is the center of the circle
R is the radius of the circle.
First, we know that the center of the circle is the point P, (2, 15)
Now, we also know that point M, (7, 3), is located at the circle.
Then we know that the radius of the circle will be equal to the distance between point P and point M.
Remember that the distance between two points (a, b) and (c, d) is:
Distance = √( (a - c)^2 + (b - d)^2)
Then in our case, we have:
Distance = √( (2 - 7)^2 + (15 - 3)^2) = √(25 + 144) = 13
This means that the radius of the circle is R = 13.
Now we know the radius of the circle and the center of the circle, then we can write the equation of the circle as:
(x - 2)^2 + (y - 15)^2 = 13^2
Help Asap 15points pic below
Answer:
[tex]\frac{1}{r^{10} }[/tex]
Step-by-step explanation:
Using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] ( with n > m )
= [tex]\frac{1}{a^{(n-m)} }[/tex]
Then
[tex]\frac{r^{2} }{r^{12} }[/tex]
= [tex]\frac{1}{r^{(12-2)} }[/tex]
= [tex]\frac{1}{r^{10} }[/tex]
Find the average rate of change
f(x)=x^2+9x+13 where x2=5 and x1=2
the answer in the picture
Please help! Ralph buys a computer for $675. The sales tax rate is 6%. How much did Ralph pay for the computer?
Answer:
$715.50 my dudeeee
Step-by-step explanation:
..........
Ralph pays a total of $715.5 for the computer including the sales tax amount.
What is Percentage?Percentage is defined as the part of a number in a whole of 100. % is the symbol used to denote the percentage.
Percentage of a number in a whole can be calculated by dividing that number with the whole and then multiply to 100.
Actual price of the computer = $675
Sales tax rate = 6%
Ralph has to pay the actual price and in addition the sales tax to buy the computer.
Amount of sales tax = 6% × 675
= (6/100) × 675
= 0.06 × 675
= $40.5
Ralph should add $40.5 to the actual price.
Total payment made for buying the computer = $675 + $40.5
= $715.5
Hence Ralph pays a total amount of $715.5 for the computer.
To learn more about Percentage, click on the link given below:
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ITS RATIOS
BTW DON'T MIND I ANSWERED IT I CLICKED ONE BY ACCIDENT
Answer: 9:4
Step-by-step explanation:
I think
© ABCD is a rectangle with sides 6 cm and
8 cm. If its diagonals cross at X, the length
of AX is
Answer:
10
Step-by-step explanation:
If the sides of the rectangle is 6cm and 8cm, then we mean that, the length and breadth are 6cm and 8cm
The diagonal which cross at AX will be the hypotenus of the triangle formed by drawing the diagonal.
Hence,
Hypotenus = sqrt (opposite² + adjacent²)
AX = sqrt[(8²) + (6²)]
AX = sqrt(64 + 36)
AX = sqrt(100)
AX = 10
If he starts at 1 and jumps 3 units to the right, then where is he on the number line? How far away from zero is he? (explain how you got the answer)
Answer:
4, he is 4 spaces away from zero.
Step-by-step explanation: I know things
If 5-x=3 then what is 3x^2
• Solution:-
➪ 5 - x - 3 = 0
➪ 5 - 3 - x = 0
➪ 2 - x = 0
➪ 2 = x
Hence, x = 2
Now,
✯ 3x²
➪ 3 × (2)²
➪ 3 × 4
➪ 12Therefore, 3x² will be = 12.