Answer:
1) f(x) = 0.5*(x + 3)*(x - 4)
2) f(x) = -2*x^2 - 2*x + 12
Step-by-step explanation:
Wen we have a quadratic function like:
f(x) = a*x^2 + b*x + c*x
And it has roots at x1 and x2, we can write the function in the factored form as:
f(x) = a*(x - x1)*(x - x2)
then:
1) we have x-intercepts at: (-3, 0) and (4, 0) (then the roots of this function are x = -3 and x =4) and we know that f(1) = -6
we have:
x1 = -3
x2 = 4
then we can write f(x) as:
f(x) = a*(x - (-3))*(x - 4)
f(x) = a*(x + 3)*(x - 4)
Where a is a real number.
and now we can use the fact that f(1) = -6
then:
f(1) = a*(1 + 3)*(1 - 4) = -6
a*4*(-3) = -6
a*-12 = -6
a = -6/-12 = 1/2 = 0.5
Then the function is:
f(x) = 0.5*(x + 3)*(x - 4)
2) Now we have roots x = 2 and x = .3
Then:
x1 = 2
x2 = -3
Then this function is something like:
f(x) = a*(x - 2)*(x - (-3))
f(x) = a*(x - 2)*(x + 3)
Now we know that f(0) = 12.
then:
f(0) = a*(0 - 2)*(0 + 3) = 12
a*(-2)*3 = 12
a*(-6) = 12
a = 12/-6 = -2
f(x) = -2*(x - 2)*(x + 3)
And we do not want this one written in factored form, so we can just distribute the multiplications to et:
f(x) = -2*(x - 2)*(x + 3) = (-2*x + 4)*(x + 3) = -2*x^2 + 4*x - 6*x + 12
f(x) = -2*x^2 - 2*x + 12
I need help with this question
Answer:
a) 2.5 x 10^5
b) 8.1 x 10^4
c) 9.06 x 10^8
d) 1.034 x 10^10
A storekeeper increased the price of hats by 5%.
Write an equation to calculate the increase of the total
cost, c, when the price of a hat is p dollars.
Select all that apply.
A c 1.50p
BC-,95p
cc 1.05p
Dc-1 + 05p
Ec-(1 + .05)p
Answer: c = 1.05p
Step-by-step explanation:
Price of the hat = p
Percentage increase in the price of the hat = 5%
The equation to calculate the increase of the total cost, c, of the hat will be:
c = p + (5% × p)
= p + (5/100 × p)
= p + (0.05 × p)
= p + 0.05p
c = 1.05p
The measure of the second angle is 15 degrees more then the measure of the 1st angle. The measure of the 3rd angle is 45 degrees more than the measure of the 1st angle. Find the measures of the interior angles in the triangle.
Let the first angle be x
So, second angle = (x+15)°
and third angle= (x+ 45)°
Now,
x+ (x+15) + (x+45)= 180°. ( Triangle sum property)
x+x+x+15°+45° = 180°
3x+ 60° = 180°
3x= 180°-60°
3x= 120°
x= 120°/3
x= 40°
Now,
first angle=x= 40°
second angle = (x+15)°= 40°+15° = 55°
third angle= (x+45)° = 40°+45° = 85°
Hope it helps you. Please mark as brainliest if it does.
(6,3) -> (-3/2x , 2/3y) -> (x + 6 , y - 4) -> (2/3x , -3/2y)
After these series of transformations, what will the final point be?
Answer:
Please refer to the attached image.
LeBron bought a 8-pack of Powerade for $7.68. What is the unit rate for one bottle of Powerade?
what is the length of line segment FH?
Choose all the fractions that are in simplest form. 4/26 8/21 6/19 9/10 10/22
Answer:
8/12, 6/19 and 9/10!
Step-by-step explanation:
All of them cannot be simplified.
but the rest can like
4/26 can be simplified by 2
and 10.22 can be simplified by 2
The masses of four vehicles and the net forces acting on them as they enter a highway are recorded in the table below. Vehicle Mass (kg) Force (N) Sedan 1400 5250 SUV 1900 5250 Truck 2100 5250 RV 2500 5250 Which vehicle has the greatest acceleration as it enters the highway?
Answer:
if you use Newton's 2nd rule:
F = m* a (force = mass * acceleration)
you can rearrange the terms to:
a = F/m (acceleration = Force/mass)
which will let you solve for acceleration.
Leslie purchased a new bar of soap. Three days after she originally used
the soap, she was curious how much soap per day she was using. She
decide to weigh her soap and that the bar was 103 grams. Four day later
she re-measured the same bar of sop and record a weight of 80 grams.
Assuming that Leslie uses the same amount of soap daily (and that she
used soap daily), write an equation that shows that amount of soap
remaining after d days of use. *Hint: slope intercept form and you will
need the slope formula
Answer:
The equation is:
y= 103 --23d
Step-by-step explanation:
The initial amount was 103 grams.
After one day of use the remaining amount of soap was 80 grams.
So the amount of time he spent in one day was:
Each day Leslie spends 23 grams of soap.
if d represents the number of days elapsed then, the amount of soap "y" that Leslie spends after days is:
y= 103 --23d
HELP!!!!
Given that x=6 and y=-4, evaluate each of the following expressions:
A. 5x/3y+x
B. 2x (square) - y (cube)
Answer:
A. 5x/3y+x=5×6/(3×-4)=30/-12=-10/4=-5/2
B. 2x (square) - y (cube)=2×6²-(-4)³=72--64=72+64=136
brainliest give an explanation to
Answer:
70 caps, 72 hotdogs, 50 paintings, 8 scouts
Step-by-step explanation:
BRAINLIEST FOR ANSWER PLEASE HURRY
Answer:
11.3
Step-by-step explanation:
Pythagorean theorem is a^2+b^2=c^2
8^2+8^2=128
the square root of 128 is 11.3137085
then you round to the nearest tenth and get 11.3
Whats the opposite of 8x
Answer:
-8x
Step-by-step explanation:
Answer:
x/8
Step-by-step explanation:
To find the inverse, interchange the variables and solve for y.
Which of the following could be the side measures of a right triangle?
Answer:
c
Step-by-step explanation:
if you use the Pythagorean Theorem and take the sum of the square of the legs, it will equal the square of the hypotenuse in answer (c)
8² + 6² = 10²
64 + 36 = 100
100 = 100
Answer:
Step-by-step explanation:
C
A type of fish for your aquarium costs $9 each. You can spend at most $45. How many
of these fish can you buy? Write an inequality to model the problem. Then solve the
inequality to find the number of fish.
7a + 4- 2a = 7a +- 2a + 4=
. 5a
. 0
. -5
. 5a+4
Step-by-step explanation:
0 would be your answer
first you combine like terms and get 5a+4 on each side then you have to solve the equation.
Kaylin buys a greeting card for $3.79. She then buys 4 postcards that all cost the same amount. The total cost is $5.11. How much is each postcard?
Answer:
$0.33
Step-by-step explanation:
5.11-3.79=1.32 1.32/4
Hope this helps :)
Answer:
each postcard cost .33 or 33 cent
Step-by-step explanation:
5.11(total cost)-3.79(greeting card)= 1.32
1.32(cost of all postcards)/4= .33
need help please thanks
Answer:
6x-y = -18
Step-by-step explanation:
Washington Middle School is painting a circle on their playground with a radius of 12 feet. What will be the total area of the circle, in square feet?
Answer: circle
A=452.39ft2
R radius 12
A=πr 2=π. 12 ‘2=452.38934ft’2
Alvin is 15 years younger than Elga. The sum of their ages is 49. What is Elga's age?
Answer:
32
Step-by-step explanation:
Suppose Alvin is x years old. Then Elga is x+15 years old.
x+x+15=49
2x=34
x=17
17+15=32
The square below has an area of x^2-10x+25 square meters
what expression represents the length of one side of the square?
Answer:
Answer: Expression that represents the length of one side of the square is x - 5.
Match each of the equations with their corresponding graph
Answer:
equation a and graph E
equation b and graph a
equation c and graph b
equation d and graph D
Step-by-step explanation:
6.37x10^-2
Thanks to anyone who answers this.
Answer:
6.37 x 10^-2 =0.0637
Rosie has £m in her pocket she is given £4 pocket money write an expression for how much money she has now
Answer:
m+4
Step-by-step explanation:
She currently has a variable "m" in her pocket which we don't know, BUT we know how much she is getting, which is 4.
Square root of -8 multiplied by the square root of -32
The midpoint of RS is point T. What are the coordinates
of point S?
5
4
3
R (-2,3)
01 - 3
0 1 )
2
1
45 -4 -3 -2 -1
2
3
4
5
X
O (8,4)
(10,-7)
-2
T(4-2)
-3
Answer:
( 10,-7)
i didn't understand what u wrote in choice
The coordinates of the point S of the line RS having midpoint T are found to be (10, -7).
What is mid point?In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.
here, we have,
The points that are given to us are R(-2,3) and T(4, -2).
The point T is the mid point of the line segment RS.
If A(a, b) and B(c, d) are the two points then the mid point M of the two points will be,
M = ((a+c)/2), ((b+d/2))
So, using the above modified form of section formula we can find the coordinates of the point S.
Assuming point S to be x and y.
So, putting all the values,
(4, -2) = ((-2+x)/2), ((3+y/2))
Now, solving further, we get,
-1+x/2 = 4
-2+x = 8
x = 10
And,
3 + y = -4
y = -7
So, the coordinates are (10, -7).
To know more about mid point formula, visit,
brainly.com/question/30276996
#SPJ7
Which function matches the graph?
-2
a. f(x) = -2(x - 3)2 + 1
b. f(x) - 2(x+3)2 - 1
c. f(x) = (x+3)²+2
d.
A(x) = 1/(x - 3)² - 1
Answer:
Its a or c sorry if im wrong
(hope this helps :D hehe)
Step-by-step explanation:
Answer:
Please insert a graph.
Step-by-step explanation:
If you submit a picture of the graph on here, I will see how how I can help.
Calculating Algebraic expressions and stuff. (See Attachment) Plz explain if you can.
Answer:
no it is not correct
Step-by-step explanation:
it's kind of hard to explain in words so I'm sorry about that
hope it helps
What is the smaller angle formed by the minute and hour hands at 3:30pm?
[asy]
unitsize(50);
draw(Circle((0,0),1),black+1);
dot((0,0));
for(real i=0;i<360;i+=6){
draw(0.96*(cos(i*pi/180),sin(i*pi/180))--(cos(i*pi/180),sin(i*pi/180)),black+0.5);
};
for(real i=30;i<390;i+=30){
draw(0.93*(cos(i*pi/180),sin(i*pi/180))--(cos(i*pi/180),sin(i*pi/180)),black+0.5);
label(string(i/30),0.83*(sin(i*pi/180),cos(i*pi/180)));
};
real h=3.5; real m=30;
draw(0.65*(sin(pi/6*(h)),cos(pi/6*(h)))--(0,0)--0.9*(sin(pi/30*m),cos(pi/30*m)),black+1,Arrows(TeXHead));
draw(anglemark(dir(-90),origin,dir(-15),5));
[/asy]
Answer:
75 degrees
Step-by-step explanation:
At 3:30, the hour hand is halfway between the 3 and the 4. The minute hand is exactly on the 6.
There are 360/12 = 30 degrees between each of the marked hours. The angle between the hands covers 2.5 of these gaps, so the angle between the hands is 2.5(30) = 75 degrees.
Hope this helps!
The angle between the hands at 3:30 pm is 90°.
What is the angle between the hands of a clock at 3:30 pm?
At that time, one hand points at the 3, and the other hand points at the 6.
Now, there is a rule to transform time into angles.
We know that a clock has 12 hours in a full revolution, and a circle has 360° in a complete revolution.
Then we know that:
12 hours = 360°
Then:
1 hour = (360°/12) = 30°
So each between each number in the clock we have an angle of 30°.
Then, between 3 and 6 (3 hours) we have:
3*30° = 90°
The angle between the hands at 3:30 pm is 90°.
If you want to learn more about angles, you can read:
https://brainly.com/question/17972372
Solve the system below.
y = x2
y = –2x + 15
Answer:
since,
y = 2x and y = –2x + 15
then,
2x = –2x + 15
or, 4x = 15
or, x = 15/4
or, x = 3.75
Also,
y= 2x
= 2*3.75
= 7.5
Hope it helped
All the best!!
Answer:
Step-by-step explanation:
[tex]x^{2} = -2x^{2} +15[/tex]
add [tex]2x^{2}[/tex] to both sides
[tex]3x^{2} = 15[/tex]
divide each side by 3
[tex]x^{2} =5[/tex]
square root each side [tex]\sqrt{x^2} =\sqrt{5}[/tex]
[tex]x= 2.23606794[/tex] or rounded to the nearest hundredth [tex]x=2.24[/tex] or x = ±[tex]\sqrt{5}[/tex]