Answer:
The zeros are the points where the parabola intercepts the x-axis.
[tex]\sf x = 7 \implies x - 7 = 0[/tex]
[tex]\sf x = 1 \implies x - 1 = 0[/tex]
[tex]\sf \implies y = a(x - 7)(x - 1)[/tex] where a is some constant
If the parabola passes through point (3, 4) then:
[tex]\sf \implies a(3 - 7)(3 - 1) = 4[/tex]
[tex]\sf \implies a(-4)(2) = 4[/tex]
[tex]\sf \implies -8a = 4[/tex]
[tex]\sf \implies a = -\dfrac12[/tex]
So the equation of the parabola is:
[tex]\sf y = -\dfrac12(x - 7)(x - 1)[/tex]
Or in standard form:
[tex]\sf y = -\dfrac12x^2+4x-\dfrac72[/tex]
Spot the quadratic equation:-
(x-1)(x-7)x(x-7)-1(x-7)x²-7x-x+7x²-8x+7Find a through (3,4)
a(x²-8x+7)=4a(9-24+7)=4a(-8)=4a=-1/2Equation:-
y=-1/2(x-7)(x-1)I sold 853 raffle tickets at 5 for $20. How much money did I make?
Answer:
17,060$
Step-by-step explanation:
#CarryOnLearning Free to ask
If y varies inversely as x and y=37 when x=33, find y if x=5
Answer: y=6
Explanation:
I need help please give explanation as well thank you
The rate of decay in the mass, M, of a radioactive substance is given by the differential equation dM dt equals negative 1 times k times M , where k is a positive constant. If the initial mass was 150g, then find the expression for the mass, M, at any time t
Using separation of variables, it is found that the expression for the mass, M, at any time t, is given by:
[tex]M(t) = 150e^{-kt}[/tex]
What is separation of variables?In separation of variables, supposing a differential equation in the format [tex]\frac{dy}{dx}[/tex], we place all the factors of y on one side of the equation with dy, all the factors of x on the other side with dx, and integrate both sides.
In this problem, the differential equation is:
[tex]\frac{dM}{dt} = -kM[/tex]
Then, applying separation of variables:
[tex]\frac{dM}{M} = -k dt[/tex]
[tex]\int \frac{dM}{M} = \int -k dt[/tex]
[tex]\ln{M} = -kt + C[/tex]
[tex]M(t) = M(0)e^{-kt}[/tex]
The initial mass is of M(0) = 150, hence:
[tex]M(t) = 150e^{-kt}[/tex]
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ABC is an equilateral triangle .Three distinct points are marked on each sides of the triangle. (not on the vertices). (i) How many lines can be drawn joining 2 of these nine points? [3 marks] (ii) Find the number of different triangles that can be formed using of 3 of these nine points as vertices. [3 marks]
The number of lines and triangles illustrates combination
36 lines can be drawn to join the nine points84 triangles can be drawn using the nine pointsThe number of lines that can be drawn
The given parameters are:
Total points, n = 9
Total points on each line, r = 2
The number of lines that can be drawn is then calculated using the following combination formula
Lines = nCr
This gives
Lines = 9C2
Evaluate the combination expression
Lines = 36
Hence, 36 lines can be drawn to join the nine points
The number of triangles that can be drawnThe given parameters are:
Total points, n = 9
Total points on each triangle, r = 3
The number of triangles that can be drawn is then calculated using the following combination formula
Triangles = nCr
This gives
Triangles = 9C3
Evaluate the combination expression
Triangles = 84
Hence, 84 triangles can be drawn using the nine points
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Find the product of (x - 5)2
-
O x2 + 10x + 25
O x2 - 10x + 25
O x2 - 25
-
O x2 + 25
Simplify the exponential expression.
ANSWER QUICK FOR A. AND B. !
Answer: a=4
b=1600x
Step-by-step explanation:
At the popular restaurant fire wok 55% of guests order the signature dish what fraction of guests order the signature dish?
Answer:
The simplest fraction is 11/20
Step-by-step explanation:
Given that,
Guests order the signature dish is 55%.
We need to find simplest fraction of guests who order signature dish.
Let the fraction be X.
According to above information, calculation of data are as follows,
x=55/100
x=11/20
So, the simplest fraction of guests is 11/20
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PLEASE I’LL MARK BRAINIEST
Simplifying expressions by combining like terms
2t - t - t + 5t + 6t + 10t
Explanation:
[tex]\dashrightarrow \sf \ \ 2t-t-t+5t+6t+10t[/tex]
combine similar terms
[tex]\dashrightarrow \sf \ \ 5t+6t+10t[/tex]
addition
[tex]\dashrightarrow \sf \ \ 21t[/tex]
Answer:
21t
Step-by-step explanation:
2t-t-t+5t+6t+10t
=2t-t-t=0
Then,
5t+6t+10t = 21t ans.
Ticket for football final selling well, on Thursday 4/7 of the tickets are sold, on Friday 1/4 of the tickets are sold, What fractions of tickets are available on Saturday?
Answer:
5/28
Step-by-step explanation:
1/1 represents the whole amount of tickets.
4/7 are sold on Thursday.
an additional 1/4 are did on Friday.
fraction of available tickets on Saturday are therefore
1/1 - 4/7 - 1/4 = 4/1 - 16/7 - 1/1 = 28/1 - 16/1 - 7/1 = 5/1
that means out of 28 equal parts of the total number of tickets 16+7 = 23 parts have been sold.
so, there are only 5 out of the total 28 parts available on Saturday, and the fraction of available tickets is therefore 5/28.
we could have also tried to bring both fractions to the same denominator, and found that this is 28.
and then
4/7 + 1/4 = 4/4 × 4/7 + 7/7 × 1/4 =
= 16/28 + 7/28 = 23/28
and the whole is 28/28.
so we have 28/27 - 23/28 = 5/28 left.
surprise, surprise, it is the same result ...
why do the leaves drop?
Why do the leaves drop:
Dropping them gives the plant a fresh start in the spring (naturally)environmental stress, diseaseHope that helps!
Please help EDGINUITY 2022
if z=-1-v3i and 26 = a +bi, then a =
and =
Please help :) (its for my friend)
If your friend has 7 apples, you take 3. How much do you have?
My sister needs help
Answer:
» 15
Step-by-step explanation:
» 5*3=15
hope this helps.
Which of the following is a person who supports or believes in the philosophy of communism?
A. Communist
B. Nihilist
C. Fascist
Answer:
ITS DEFINITELY AStep-by-step explanation:
an athletic director pays $90 for 12 visors, how much will the athletic director pay to buy 15 visors?
Answer:
sample What is the length of a rectangle if the width is
10 centimeters and the diagonal is 16 centimeters?
Step-by-step explanation:
There are 100 patients in a hospital with a certain disease. Of these, 10 are selected to undergo a drug treatment that increases the percentage cured rate from 50 percent to 75 percent. What is the probability that the patient received a drug treatment if the patient is known to be cured?
Answer:
1/7
Step-by-step explanation:
hope this helps x have a great day
Triangle DEF has side lengths d= 7.1 and f= 26.5. The measure of angle E is 13°. What is the length of side e? 31.9 19.6 4.7 162.3
Answer:
19.6
Step-by-step explanation:
According to the
Cosine Theorem
e² = d² + f² - 2dfcos /_E
°Cos 13° = 0.974
e² = (7.1) 2 + (26.5) 2-2 × 26 = 5 × 7.1 × 0.974
=752.66 - 366.516
= 386.14
e = 386.14 = 19.6
Which linear line equation has no solution?
Answer:
4x+7=3x+7
Step-by-step explanation:
-3(2x-5)=15-6x is infinite solution
top left is x=-3
top right is x=5 5x
In a particular city, 21 in 1.5 million people have been struck by lightning. What is the experimental probability of being struck by lightning in this city?
21/(1.5 million) = 0.0014%
Simplify the expression. –(3)–4
a)12
b)[tex]-\frac{1}{81}[/tex]
c)81
d)[tex]\frac{1}{81}[/tex]
Answer:
Answer is {C}
Step-by-step explanation:
Find the value of x, if C is on line AE
Answer:
x = 11°
Step-by-step explanation:
Linear Pair
Two angles adjacent to each other that form a straight line.
The sum of angles of a linear pair is always equal to 180°.
⇒ m∠C = 180° - 33° = 147°
Alternate Interior Angle Theorem
When two parallel lines are cut by a transversal, the alternate interior angles are congruent.
From inspection of the diagram, we can see that AB ║ DC.
Therefore, AE is the transversal.
So m∠A = 33°
Sum of interior angles of a triangle is 180°
Therefore, the top angle of the triangle = 180° - m∠A - 2x
= 180° - 33° - 2x
= 147° - 2x
Angles around a point add up to 360°
⇒ 33° + m∠C + 5x + (147° - 2x) = 360°
⇒ 33° + 147° + 5x + 147° - 2x = 360°
⇒ 327° + 3x = 360°
⇒ 3x = 33°
⇒ x = 11°
Answer:
x = 11°
Explanation:
m∠C = m∠A = 33°m∠B = 2(x)m∠I = 180° - 5(x)============ [ total interior angle in a triangle is 180° ]
solve for x
33° + 2(x) + 180° - 5(x) = 180°-3(x) = 180° - 213°-3(x) = -33°x = 11°Help me pls math and will make brainless
Answer 7. Pls !!!
if x+y = -10 and x-y = 2 what is the value of x
Answer:
x= -4
Step-by-step explanation:
adding the two equations,
x+x+y-y=-10+2
2x= -8
x=-4
2. Lisa can buy orange juice in 0.24-liter cartons or 0.48-liter cartons. Which is closest to the
number of 0.48-liter cartons she would need to completely fill a pitcher that holds 3.58 liters?
(A. 1.7
B. 5.0
C.1.5
D. 15.0
Answer:
i think its 1.7 if this is correct can u mark me brainliest
Step-by-step explanation:
In the graph z1 and z2 are complex numbers represented as vectors from the origin. What is z2-z1?
Finding the complex numbers and subtracting them, it is found that z2 - z1 = (0, -4).
What are complex numbers?They are in the format:
z = a + bi.
In which:
a is the real part.b is the imginary part.In a graph, the real part is the horizontal axis, while the imaginary part is the vertical axis. Hence, the numbers are given by:
z1 = (2,5).z2 = (2,1).What is the subtraction?To find the result of the subtraction, we subtract each part, hence:
z2 - z1 = (2,1) - (2,5) = (2 - 2, 1 - 5) = (0, -4).
More can be learned about complex numbers at https://brainly.com/question/25572463
A person invests 4000 dollars in a bank. The bank pays 5.75% interest compounded
quarterly. To the nearest tenth of a year, how long must the person leave the money
in the bank until it reaches 5900 dollars?
nt
A = P(1+)
The time required to get a total amount of $5,900.00 with compounded interest on a principal of $5,000.00 at an interest rate of 5.75% per year 2.899 years
Compound InterestGiven Data
Principal P = $4000Rate r= 5.75%Final Amount A = %5900Calculation Steps:
First, convert R as a percent to r as a decimal
r = R/100
r = 5.75/100
r = 0.0575 per year,
Then, solve the equation for t
t = ln(A/P) / n[ln(1 + r/n)]
t = ln(5,900.00/5,000.00) / ( 4 × [ln(1 + 0.0575/4)] )
t = ln(5,900.00/5,000.00) / ( 4 × [ln(1 + 0.014375)] )
t = 2.899 years
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A sales representative is paid a commission of N5 on every N100 sale he makes. If his commission for the week is N10,000.00, how much sales has he made
