Answer:
The x-intercepts of the function are [tex]x = 3[/tex] and [tex]x = -5[/tex].
Step-by-step explanation:
We are given the function [tex]\displaystyle f(x) = x^2 + 2x - 15[/tex].
In order to find the x-intercepts of the equation, we need to solve this quadratic. We can use factoring methods to solve it.
The parent function for a quadratic is [tex]f(x) = ax^2 + bx + c = 0[/tex].
We can use this information to determine what factoring technique we want to use.
There are several different methods, including using the quadratic formula, but because this is easily factorable, we can avoid using it.
We see that our a is equal to 1 (there is no coefficient in front of x²), so we can use the easier of the techniques:
Find what factors of c add up to give you b.Add to x if positive or subtract from x if negative and set it equal to zero.Solve for x - these are your x-intercepts.Therefore, let's determine what our c is: 15.
Now, let's label the factors for 15.
15 cannot be divided by 2 evenly.15 can be divided by 3 evenly: 15/3 = 515 cannot be divided by 4 evenly.15 can be divided by 5 evenly: 15/5 = 3Therefore, our two factors are 3 and 5 since they cannot be broken down any further (they are prime numbers - we just performed prime factorization).
Now, we need to pay attention to the sign for c. It's negative, so one of our factors needs to be negative. Therefore, we can test this out:
[tex]5 + -3 = 2[/tex][tex]-5 + 3 = -2[/tex]Now, we check for which one matches the sign for b. This is positive 2, so our two factors are 5 and -3.
Finally, to factor, we add or subtract the factors from x depending on the sign. If the factor is positive, we add it. If the factor is negative, we subtract it. Therefore, we can set up our equations.
[tex]x + 5 = 0\\\\x = -5[/tex]
[tex]x - 3 = 0\\\\x = 3[/tex]
Therefore, for when x = 3 or x = -5, the line crosses the x-axis. These are the x-intercepts of the function.
Our answers are x = -5 and x = 3.
A ball is thrown from the top row of seats in a stadium. The function h(t)=-16t^2+64t+80 gives the height, in feet, of the ball t seconds after it is thrown. How long will it be before the ball hits the ground?
I already found the maximum height, it's at 144 feet
A. 5
B. 16
C. 2
D. 9
Answer:
5 seccsStep-by-step explanation:
Given the modeled function of the height expressed as;
h(t)=-16t^2+64t+80
The ball hits the ground when h(t) = 0 (when the height is zero)
Substitute into the function and find t;
0 =-16t^2+64t+80
divide through by -16
0 = t²-4t-5
Factorize;
t²-4t-5 = 0
t²-5t+t-5 = 0
t(t-5)+1(t-5) = 0
(t+1)(t-5) = 0
t + 1 = 0 and t-5 = 0
t = -1 and t = 5
Time can't be negative
Hence it will take the ball 5secs before it hits the ground
can someone help me please :( it’s stressing me out
20x+6+9x=180
add the values of x together
29x+6=180
subtract 6 from each side
29x=174
divide each side by 29
x=6
1
A bag contains 100 marbles. Some are red and the rest are black. There
are 3 red marbles for every 1 black marble. How many red marbles are in
the bag?
Answer:
there are 33 marbles
Step-by-step explanation:
100÷3
Jessica earns 2,000 per month as a saleswomen. In addition to the salary she earns 80 per product that she sells. If her goal is to earn 10,000 per month, how many products does she need to sell
Answer:
100 products
Step-by-step explanation:
Jessica earns 2,000 per month as a sales woman
In addition to the salary she earns 80 per product that she sells
Her goal is to earn 10,000 per month
Therefore the number of products that will be sold to attain 10,000 can be calculated as follows
= 80×100
= 8,000
= 8,000+2,000= 10,000
Hence she needs to sells 100 products to attain 10,000
Solve x to the power of 2 = 4 where x is a real number. Please help fast
Answer:
It's 2
Step-by-step explanation:
X is 2 because if you multiply two by two you get 4
Convert the following point-slope form equation to slope-intercept form: y-2 = 3(x-2)
Answer:
y = 3x - 4
Step-by-step explanation:
Uhh........ I got to go walk my fish
What is the greatest common factors or 45 and 100
Answer:
5
Step-by-step explanation:
5 is the gcf of 45 and 100
the answer is 5,,,,,,,,,,,,
Please can you help me
9514 1404 393
Answer:
x = 5
Step-by-step explanation:
In a parallelogram, the diagonals bisect each other. This means ...
PQ = PS
2x +15 = 5x
15 = 3x . . . . . . subtract 2x
5 = x . . . . . . . divide by 3
5x^2+3x-3=0 using equation method
9514 1404 393
Answer:
x = (-3±√69)/10
Step-by-step explanation:
Perhaps you want to find the solutions using the quadratic formula.
For the equation ...
ax² +bx +c = 0
The solution is given by the formula ...
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Here, we have a=5, b=3, c=-3, so the values of x are ...
[tex]x=\dfrac{-3\pm\sqrt{3^3-4(5)(-3)}}{2(5)}\\\\\boxed{x=\dfrac{-3\pm\sqrt{69}}{10}}[/tex]
The perimeter of a kite is 50 mm. The length of one of its sides is 1 mm more than twice the length of another. Find the length of the LONGEST side of the kite. Only write the value of the longest side.
Answer:
The length of the longest side is 13mm
Step-by-step explanation:
Represent the two sides with a and b, where a is the longest
[tex]Perimeter = 50[/tex]
[tex]a=b + 1[/tex]
Required
Determine the length of the longest side
Perimeter of a kite is calculated as thus:
[tex]Perimeter = 2(a + b)[/tex]
Make b the subject in [tex]a=b + 1[/tex]
[tex]b = a -1[/tex]
Substitute a - 1 for b and 50 for Perimeter in [tex]Perimeter = 2(a + b)[/tex]
[tex]50 = 2(a + a - 1)[/tex]
Divide through by 2
[tex]25 = a + a - 1[/tex]
[tex]25 = 2a- 1[/tex]
Add 1 to both sides
[tex]25 + 1 = 2a - 1 +1[/tex]
[tex]25 + 1 = 2a[/tex]
[tex]26 = 2a[/tex]
Solve for a
[tex]a = 26/2[/tex]
[tex]a = 13[/tex]
Hence, the length of the longest side is 13mm
Use a table, an equation, and a graph to represent the relationship below.
Ty is 6 years younger than Bea.
Answer:
UkwkwkwStep-by-step explanation:
Answer:
b-6=t
Step-by-step explanation:
X + 2x + 12y + x Apply the properties of operations by combining like terms to produce an equivalent expression. Prove your answer by showing your work.
Answer:
4(x+3y)
Step-by-step explanation:
Given the expression X + 2x + 12y + x
First thing to do is combine the like terms;
X + 2x + 12y + x
= x+x+2x+12y
Add the like terms(Addition property)
= 4x + 12y
Then factor out the like terms
= 4(x+3y)
Hence the equivalent expression is 4(x+3y)
What is the slope of the line through ( 3.3) and ( 1.1)?
Answer:
slope = -2
Step-by-step explanation:
slope = m = y2-y1/x2-x1
given points (-3,3) and (-1,-1)
plug in to slope formula
m = -1 - 3 / -1 - (-3)
m = -4 / 2
m = - 2
Please help asap.xxx
Answer:
3,4
Step-by-step explanation:
(3,4)
Step-by-step explanation:
An online company offers a package that includes 2 games for $11.98 they also offer a package that includes 5 games for $24.95 Which package is a better deal?
FIND UNIT RATES!!!!!
Answer:
the package that has five games
Step-by-step explanation:
divide both
4.99
and 5.99 4.99 is btter
If the turkey says gobble, gobble, gobble, and a peach says cobbler, cobbler, cobbler, what would a computer say?
Answer: error
Step-by-step explanation:
Answer:
goog le goo gle go ogle
Step-by-step explanation:
sorry but the problem is that brainly thinks Goo gle is too inappropriate of a word
divide the polynomial 3x^4-6x^2-x/x=
Answer: 3x^3-6x-1
Step-by-step explanation:
Take out an x from everything. Numbers that have powers will just go down a power (ex- 3x^4 would go to 3x^3) and if you have just an x then it turns into one.
The polynomial by the division is equal to [tex]3x^3-6x-1[/tex]
What is a polynomial?They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.
We are given the polynomial
[tex]3x^4-6x^2-x/x[/tex]
We need to divide the polynomial by x.
[tex]3x^4-6x^2-x/x[/tex]
Then we need to factor out x
[tex]x(3x^3-6x- 1)/x[/tex]
The answer is [tex]3x^3-6x-1[/tex]
Learn more about polynomials here:
https://brainly.com/question/27343162
#SPJ2
When Sarah passes a ball on a sidewalk to her friend, the ball bounces off at the same angle that it was thrown. Use the figure below to find the angle at which the ball hits the sidewalk
and bounces to her friend.
1000
a. 40 if you dont believe me just look at a 40 degree triangle then the pic
find the slope of a line parallel to each given line y = -2x - 5
Answer:If we have a line given by the equation y=5x−1, what would be the equation of a line parallel to it? A line parallel to this will have the same slope and a different intercept. Since, the slope in the equation is m=5 the slope for the parallel line will be m=5.
Step-by-step explanation:
Answer:
m= -2
Step-by-step explanation:
Joey Road his new bike around his block he traveled a total of 375 m it took him a total of 97 seconds what was his average speed
Answer:
I think his average speed is approximately 3.87 for every 1 second. I just divided 375 divided by 97 to see his average speed per second. I could be wrong tho
What's your favorite color and why?
have to create graph for math class
Answer:
blue
Step-by-step explanation:
love the sky
Answer:
Pink
Step-by-step explanation:
Because it’s pretty and makes me feel at ease
How many times greater is the 6 in the thousands place than the 6 in the hundreds place
Given h(x) = -2 – 1, find h(6).
Which value is the solution to the equation 42 ÷ j = 6?
Answer:
[tex]j = 7[/tex]hope that helps!
The value which is the solution to the equation 42 ÷ j = 6 is; j =7
One variable equation:
According to the question;
The equation given is; 42 ÷ j = 6.To solve the equation; we can do Cross-product as follows;
42 = 6jj = 42/6
j = 7.
Read more on one variable equation:
https://brainly.com/question/21528555
Your Benz Wagon has (f) gallons of gas. Your Benz Wagon uses (g) gallons of gas
for every mile traveled. Enter an equation for the amount of gas remaining, (r), in
the tank after (m) miles.
4) Use ONLY the variables (f. g, m, r) used in the situation above. DO NOT put
space in your answer.
*
Your answer
This is a required question
Back
Next
Answer:
r=f-(gm)
Step-by-step explanation:
Benz wagon has f gallons of gas
We are now told that Benz Wagon uses (g) gallons of gas for every mile traveled
Thus, amount of gas used after "m" miles is; gm
We are given r as the amount of gas remaining.
Thus;
r=f-(gm)
What is f(x)=2x^2-8 ?
Find the discriminant of
Answer:
76
Step-by-step explanation:
Substitute in the values of a, b, and c.
[tex](-10)^2-4(3*2)[/tex]
Evaluate the result to find the discriminant.
[tex]76[/tex]
Answer:
76
Step-by-step explanation:
im shmaht
There are 2.54 centimeters in 1 inch. There are 100 centimeters in 1 meter.
To the nearest inch, how many inches are in 13 meters? Enter the answer in the box.
inches
Answer:
Answer: 512 inches
Step-by-step explanation:
Unit Conversion
We need to recall two basic unit conversions for length:
1 inch = 2.54 cm
1 meter = 100 cm
We are given a length of 13 meters. Converting to centimeters:
13 * 100 = 1300 cm
Now convert to inches dividing by 2.54:
[tex]1300 / 2.54 \approx 512[/tex]
Answer: 512 inches
Answer:
512 inches
Step-by-step explanation:
on piece of paper,graph the system of equatons. Then determine which answer choice matches the graph you drew and indetify the solution to the system y=2x-1 y= -x+5
Answer:
Idisisisos9191929929293938kdidif8c8c8c87c7c7c7c7c
What is the value of 3 - 14?
Answer:
The answer is -11 .