Answer:
y = (1/4)x² - (5/4)x + 1
Step-by-step explanation:
The x-intercepts of the quadratic equation are simply it's roots.
Thus, we have;
(x + 1) = 0 and (x - 4) = 0
Now, formula for quadratic equation is;
y = ax² + bx + c
Where c is the y intercept.
At y-intercept: (0,1), we have;
At (-1,0), thus;
0 = a(1²) + b(1) + 1
a + b = -1 - - - (1)
At (4,0), thus;
0 = a(4²) + b(4) + 1
16a + 4b = -1
Divide both sides by 4 to get;
4a + b = -1/4 - - - (2)
From eq 1, b = -1 - a
Thus;
4a + (-1 - a) = -1/4
4a - 1 - a = -1/4
3a - 1 = -1/4
3a = 1 - 1/4
3a = 3/4
a = 1/4
b = -1 - 1/4
b = -5/4
Thus;
y = (1/4)x² - (5/4)x + 1
Which of the following is an even function?
Answer:
thats right
Step-by-step explanation:
odd functions are ones you flip 180 degrees and get same thing but basically everything else (unless of course it has no symmetry such as sqrt x) should be even (even can also be thought of as bilateral symmetry)
Find a solution to the following system of equations –5x + 2y = 9 3x + 5y = 7
Answer: (-1, 2)
Step-by-step explanation:
Let's start by solving for x in
[tex]-5x+2y=9\\-5x+2y+-2y=9+-2y\\-5x=9+-2y\\\frac{-5x}{-5} =\frac{9+-2y}{-5} \\x=\frac{2}{5} y+\frac{-9}{5}[/tex]
We can now sub this value of x in 3x+5y=7 and solve
[tex]3x+5y=7\\3(\frac{2}{5} y+\frac{-9}{5})+5y=7\\(3)(\frac{2}{5} y)+(3)(\frac{-9}{5})+5y=7\\\frac{6}{5} y+\frac{-27}{5}+5y=7\\\frac{6}{5} y+\frac{25}{5}y +\frac{-27}{5}=7\\\frac{31}{5} y+\frac{-27}{5}=7\\\frac{31}{5} y+\frac{-27}{5}+\frac{27}{5}=7+\frac{27}{5}\\\frac{31}{5} y=\frac{62}{5} \\\frac{\frac{31}{5} y}{\frac{31}{5}} =\frac{\frac{62}{5} }{\frac{31}{5}} \\y=2[/tex]
Now we can sub in 2 for y in one of the equations
[tex]3x+5(2)=7\\3x+10=7\\3x+10-10=7-10\\3x=-3\\\frac{3x}{3} =\frac{-3}{3} \\x=-1[/tex]
x=-1 and y=2 giving us the point (-1, 2)
An on-demand movie company charges 52.95 per movie plus a monthly fee of $39.95. Which expression represents
the yearly cost for x movie rentals?
295x+39.95
39.95x295
2958-39 95(12)
295x3995(12)
Hurry I'm being timed !
Answer:
52.95x + 39.95(12)
Step-by-step explanation:
Answer:
52.95 x + 39.95 (12)
Step-by-step explanation:
cost per movie = 52.95
a monthly subscription is 39.95 and there are 12 months in a year so it would be 39.95 x 12
the x would be dependent on the amount of movie rentals and therefore the cost of the rentals = 52.95 x
Roger has 50 ounces of water. If he drinks 30% of it, how
much water will he have left?
Answer:
35 ounces
Step-by-step explanation:
If Roger drinks 30% of the water, that means there will be 70% of it left. We can turn percentages into decimals by dividing them by 100. If we multiply 50 by 0.7, we get 35 ounces.
use abc to find the value of sin b
Answer:
12/37
Step-by-step explanation:
We know ,
=> sin B = p/h
=> sin B = 12/ 37
Answer:
Step-by-step explanation:
[tex]Sin \ B = \frac{opposite \ side }{hypotenuse}\\\\Sin \ B = \frac{35}{37}\\\\[/tex]
I need help
Please
I hate math
Create 5 examples of gains and losses using positive and negative numbers. Explain your examples.
Answer:
Look below...
Step-by-step explanation:
Losing 7 cards in a deck: -7. Losing means negative.
Saving $102 in your wallet: 102. You are saving, that means you gain.
336 feet below sea level: -336. Below indicates less than 0, which is negative.
Depositing $43 into your bank account: 43. Depositing means putting. If you put $43 in YOUR bank account, the bank account gains money. So you gain money. Making it positive.
1,000 feet above sea level: 1,000. Above indicates more than zero. Anything more than zero on a number line is positive.
Hope this helps :)
Pencils cost $0.30 each and pads of paper cost $1.25 each. You have $3.30 to spend and you need 6 pencils. How many pads of paper can you purchase?
Answer:
6 x 0,30 = $1,80
$3,30 - $1,80 = $1,50
$1,50 - $1,25 = $0,25 (not enough money)
you can buy 1 pad of paper
hope it helps.
Also, I think that Brainly is an awesome app, but there's an app which is doing great work for me in maths, named Gauthmath. I will suggest it. Video concepts and answers from real tutors.
HELP WILL GIVE BRAINLIEST
Answer:
A. hexagonal prism
Step-by-step explanation:
The box has 2 congruent hexagons as bases, and 6 congruent rectangles as sides.
Answer: hexagonal prism
find the sum or difference of the following ( simplify all answers)
a) 1/5 + 3/5=
b) 5/8-1/8=
c) 8/9 + 4/9 =
d) 3/5+ 1/10=
e) 2/3 +3/4=
f) 4/5- 1/3=
How much would $500 invested at 5% interest compounded continuously be worth after 4 years? Round your answer to the nearest cent
Answer:
$610.70
Step-by-step explanation:
[tex]a = pe^{rt}[/tex]
a = 500 [tex]e^{.05 * 4}[/tex]
a = $610.70
A sweater is on sale for $45.00, down from $75.00. What is the
percent of discount of the sweater?
A. 50%
B. 30%
C. 55%
D. 40%
Answer:
D
Step-by-step explanation:
The percentage of discount on the sweater will be 40%. The correct option is D.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that a sweater is on sale for $45.00, down from $75.00. The percentage discount will be calculated as:-
Percentage discount = (75 - 45) / 75
Percentage discount = ( 30 / 75 )
Percentage discount = 0.4 x 100 = 40%
Therefore, the percentage of discount on the sweater will be 40%. The correct option is D.
To know more about percentages follow
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which of the following give the highest future value is 6000000 is invested at 6% for 3 years
Answer:
$5084745.76271
Step-by-step explanation:
Given data
Final amount= $6000000
Rate=6%
Time= 3 years
Now let us find the initial amount which is the principal
using the simple interest formula we have
6000000 = P(1+0.06*3)
6000000 =P(1+0.18)
6000000 =P*1.18
P= 6000000 /1.18
P=$5084745.76271
Hence the initial deposite is $5084745.76271
if x = 3 and y = 2, then the value of ( x - y )(x² + xy + y²) is
(a) 31 (b) 19 (c) 1 (d) 25
Answer:
19
Step-by-step explanation:
(3-2)(3^2+3x2+2^2)
(1)(9+6+4)
(1)(19)
[tex]\displaystyle\bf \underbrace{ (x-y)(x^2+xy+y^2)}}_{x^3-y^3}=3^3-2^3=19\\\\Answer: b)19[/tex]
Get three real world examples of a rectangle prism
Answer:
a shipping container ,the ones they use in large cargo ships
[tex]\text{Solve for 'x'.}\\\\3x + 15 = 33\\\\\\text{Thank you.}[/tex]
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]x=6[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Solving for 'x'...}}\\\\3x + 15 = 33\\--------------\\\rightarrow 3x + 15 - 15 = 33 - 15\\\\\rightarrow 3x = 18\\\\\rightarrow \frac{3x=18}{3}\\\\\rightarrow \boxed{x = 6}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Answer:
x=6
Step-by-step explanation:
3x+15=33
or as, 3x=33-15
or as, 3x=18
x=18/3=6
so we got 6 is the answer
If you vertically compress the absolute value parent function, (x) = |X|, by a
factor of 4, what is the equation of the new function?
O A. g(x) = |4x|
O B. g(x) = 1/4 |x|
O C. g(x) = 4|x|
O D. g(x) = |x-4|
pls mark me as brainlist
thanks a lot
Ava’s gross pay is $2,500 per month. Her deductions include the following:
Federal income tax $290
State income tax $85
Social Security $112
Medicare $35
What is Ava’s net pay each month?
what is the equation of the line shown?
Answer:
y=1/2x+1/2
Step-by-step explanation:
the line intercepts at (0,0.5) which makes the y-intercept 1/2 and if you look at the slope, it increases 1 unit up and 2 units to the right so the slope is also 1/2
The equation of line is y= 1/2x+ 1/2.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
Take points from the graph as (-1, 0) and (3, 2).
So, slope of line = (2 - 0)/ (3 -(-1))
= 2/4
= 1/2
Now, slope- intercept form
y- 0 = 1/2 ( x-(-1))
y= 1/2x + 1/2
Hence, the equation of line is y= 1/2x+ 1/2
Learn more about slope here:
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Find the measure of the missing angle using the triangle angle sum theorem
Answer:
m∠60
Step-by-step explanation:
30 + 90 = 120
180-120=60
Answer:
x = 60°
Step-by-step explanation:
A triangle is equal to 180°
Make an equation and solve:
30° + 90° + x = 180°
120° + x = 180°
x = 180° - 120°
x = 60°
ℎ = 6 + 11 − 22
calculation path
Answer:
[tex]h = 6 + 11 - 22 \\ h = 17 - 22 \\ h = - 5[/tex]
Answer:
-5
Step-by-step explanation:
6+11 = 17↓
17-22 = -5
or
11-22 = -11↓
-11+6 = -5
Complete the equation: 2^2 – 14x + __ = (_)^2
A. –14; 2 + 14
B. -14; 2 – 14
C. 49; 2 +7
D. 49; r - 7
Help me please guys
Answer:
1st box is -4
2nd box is -4
3rd box is 3
4th box is -1
Answer: 15x squared -4x-3
rewrite the expression
15x squared + 5x-9x-3
factor the expressions
5x × (3x+1)-3(3x+1)
factor the expression
solution
(3x + 1) × (5x - 3)
Which of the following are square roots of the number below? Check all that
apply.
196
A. -14
B. 196^1/2
C. 14
D. 98
E. 7
F. -196^1/2
Answer:
B. 196^1/2
C. 14
Step-by-step explanation:
Square root of 196=14
196^1/2=14
If (2,1) is the midpoint of the line segment ST and the coordinates of S are (5,4), find the coordinates of T.
Answer:
Step-by-step explanation:
The formula to find the midpoint of a segment is
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex] and we have the midpoint and we also have a coordinate of (5, 4). Let's let x₁ = 5 and y₁ = 4. Filling in what we have:
[tex](2,1)=(\frac{5+x_1}{2},\frac{4+y_2}{2})[/tex] and we'll deal with the x terms first. The x coordinate of the midpoint is 2, so:
[tex]2=\frac{5+x_2}{2}[/tex] and multiply both sides by 2 to get rid of the denominator to get:
4 = 5 + x₂ so
x₂ = -1. Going on to the y coordinate. The y coordinate of the midpoint is 1, so:
[tex]1=\frac{4+y_2}{2}[/tex] and again multiply both sides by 2 to get rid of the denominator to get:
2 = 4 + y₂ so
y₂ = -2
The coordinates of T are (-1, -2)
Helpppppp and explain toooo thankyouuuu
Step 1: Distribute
5x + 10 - 3x > 7 - 4x + 12
Step 2: Combine like terms
2x + 10 > -4x + 19
Step 3: Move all variable terms to one side, and all constants to the other
6x + 10 > 19
6x > 9
Step 4: Divide
x > 9 / 6
x > 1.5
Hope this helps!
Any help is appreciated!!!!
Answer:
D
Step-by-step explanation:
because 3x - 12y = 15 has only numbers that are divisible by 3 leaving just one single x term, and the other terms simply reduce their used numbers to still integer numbers (4 and 5).
this makes it easier to be used in the other equation.
Graph each equation by using the y-intercept and slope
y=-x-4
Y-int=______
Slope=_____
whats the y-intercept and slope for this equation?
Answers:
y intercept = -4
slope = -1
==========================================
Explanation:
The given equation is the same as y = -1x + (-4)
Compare this to y = mx+b form, and we see that
m = -1 is the slope
b = -4 is the y intercept
To graph y = -x-4, you could plot the two points (0,-4) and (1,-5) and draw a straight line through them. Extend the line as far as you can in either direction.
Notice how going from (0,-4) to (1,-5) follows the process "down 1, right 1" which is directly pulled from the slope = -1 = -1/1.
An amount of 25,000 is borrow for 15 years at 5.5% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back?
Answer: [tex]55,811.91[/tex]
Step-by-step explanation:
Given
Principal amount is 25,000
Time Period is [tex]t=15\ yr[/tex]
Rate of interest [tex]r=5.5\%[/tex]
Amount in compound interest is given by
[tex]\Rightarrow A=P\left(1+r\%\right)^t[/tex]
Insert the values
[tex]\Rightarrow A=25,000(1+\dfrac{5.5}{100})^{15}\\\\\Rightarrow A=25,000(1.055)^{15}\\\Rightarrow A=55,811.91[/tex]
Therefore, [tex]55,811.91[/tex] must be paid back
Helppppp
A. 8/15
B. 8/17
C. 15/8
D. 15/17
Answer:
D
Step-by-step explanation:
sin theta is equal to perpendicular by hypotenuse
here perpendicular is equal to 15 and base is equal to 8 therefore hypotenuse will be equal to 17
on putting on putting the value of perpendicular by hypotenuse we get 15 by 17 as sin theta
Answer:
Step-by-step explanation:
hypotenuse = √(15²+8²) = √289 = 17
sinθ = (leg opposite θ)/hypotenuse = 15/17
