Diego wrote f(x)=(x+2)(x−4) as an example of a function whose graph has x-intercepts at x=−4, 2. What was his mistake?
Taking into account the factored form, Diego's mistake was to express the opposite signs to those he should have.
The function f(x) = ax² + bx + c
with a, b, c real numbers and a ≠ 0, is a function quadratic expressed in its polynomial form (It is so called because the function is expressed by a polynomial).
The following expression is called discriminant:
Δ= b²- 4*a*c
The discriminant determines the amount of roots of the function. The roots are those values of x for which the expression is 0, so it graphically cuts the x-axis.
Then:
If Δ <0 the function has no real roots and its graph does not intersect the x-axis. If Δ> 0 the function has two real roots and its graph intersects the x-axis at two points .If Δ = 0 the function has a real root and its graph intersects the x-axis at a single point that coincides with its vertex. In this case the function is said to have a double root.Every quadratic function can be factored based on its roots as:
f(x)= a(x-x1)(x-x2)
where x1 and x2 are the roots of the function. This way of expressing the quadratic function is called the factored form.
If the function does not have real roots (Δ <0) it cannot be factored, that is, it does not have a factored form.
If the function has a double real root (Δ = 0) the factored function takes the form:
f(x)= a(x-x1)²
In this case, the function has x-intercepts at x=−4, 2. So, an example of the factored form is:
f(x)=[x-(+2)][x-(-4)]
f(x)=(x-2)(x+4)
Finally, Diego's mistake was to express the opposite signs to those he should have.
Learn more:
https://brainly.com/question/14477557?referrer=searchResults
Multiply (−7)(2)(−2).
−28
−14
28
14
Answer:
28
Step-by-step explanation:
Answer:
Positive 28
Step-by-step explanation:
When We Multiply (-7) With (2) We get -14. That 14 Is negative An Negative number multiplied by a positive number Equals an negative number.
Rule
Pairs of numbers that are the same sign combine to make a positive product.
(Positive) ⋅ (Positive) = Positive
(Negative) ⋅ (Negative) = Positive
Rule
Pairs of numbers that are opposite signs combine to make a negative product.
(Positive) ⋅ (Negative) = Negative
(Negative) ⋅ (Positive) = Negative
After we have (-14) we still need to multiply it by (-2) Which gives us -28 But WAIT. 2 Negative numbers in a problem will result in a positive number being your answer if its the last part of the problem!
Hope this helps!
Alan earns $530 in gross wages. How much is deducted from Alan’s paycheck for Social Security (6.2%) taxes?
Answer:
$32.86 maybe ?
Step-by-step explanation:
Answer:
530-6.2% = 32.86
Step-by-step explanation:
What is 3.9 rounded to the nearest whole number?
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
5 or more round up
4 or less round down
9 is more then 5 so it is rounded up
3.9 is rounded up to 4
The table below shows what 300 Boxer students ate for lunch on Friday. What is the ratio of the number of students who ate soup to the number of students who did not eat soup? Food Soup Pizza Salad Hotdog Number of students
Answer:
A)
[tex] \frac{1}{4} [/tex]
Step-by-step explanation:
120 + 30 + 90 = 240
60/240 = 1/4
x2 − 2x − 4 = 0 quadratic formula
Answer:
x=±1.73205i
Explaination
hiw do I find CD in the problem
Answer:
CD = 7
Step-by-step:
28 - 18 = 10
17 - 10 = 7
CD is 7
Good Luck
( please help ) Find the magnitude of the vector. Write your answer in simplified form
TAY
GO
6
4
NS
-10
-8
-6
-4
-2
0
2
4
6
8
10
-2
-4
-6
-8
-104
Answer:
The magnitude of a vector in Rn
(if you're using dot product as inner product) is given by the square-root of the sum of the square of each coordinate of the vector
Step-by-step explanation:
The image of point F after a rotation of 180° counterclockwise around the origin is located at (8,-10)
What is rotation?Rotation means the circular movement over the object around the center.
Rotation can be done in both directions like clockwise as well as counter clockwise
It requires rotation implies negative magnitude
A counter clockwise turns has a positive magnitude.
here, we have,
to determine the image of F:
The coordinate of point F is given as:
F = (-8,10)
The rule of rotation by 180° counterclockwise around the origin is:
(x,y) -> (-x,-y)
So, we have:
F' = (8,-10)
Hence, the image of point F is located at (8,-10)
Read more about rotation at:
brainly.com/question/4289712
#SPJ7
What are the like terms of 4x+5-8 ?
Answer:
There are no like terms
Step-by-step explanation:
Like terms are when you have the same variable on both sides which you dont have
30kx - 6kx = 8 solve for x
Answer: x= 1/3k
Step-by-step explanation:
21. How many different integers can have the same absolute
value?
Give an example.
1. Le Point Bookbindery
pays a dividend of $1.25
per share every three
months. How many
months would it take to
earn dividends amounting
to $8.75 per share?
Answer:
7 months dawg because take 1.25 x 4 and that's 5.00 + 1.25=6.25+1.25=7.50+1.25=8.75
At its closest distance, the moon is approximately 3.6 × 105 km from Earth. Mars, at its closest distance, is approximately 5.57 × 107 km from Earth. How much farther is the distance from Earth to Mars than from Earth to the moon? Express your answer in scientific notation.
Answer:
The answer is 5.534 x107km
Step-by-step explanation:
the answer is;ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
What is the domain of the set of ordered pairs above?
OA.
{-1, 0, 5, 10}
B.
{-1, 10)
OC.
{1,-1, -11, -21)
D.
{-1, 1)
Answer:
A. {-1, 0, 5, 10}
Step-by-step explanation:
Given:
(-1, 1), (0, -1), (5, -11), (10, -21)
Required:
Domain of the set of the above ordered pairs
SOLUTION:
Domain of any set of ordered pairs includes all the x-values in the set of ordered pairs, while the y-values in the set of the ordered pairs makes up the range.
The first value in an ordered pair is the x-value while the second is the y-values, i.e. (x, y).
Therefore, the domain for the given set of ordered pairs is:
{-1, 0, 5, 10}.
The correct option is A.
Question:
What is the domain of the set of ordered pairs above?
A. {1, -1, -11, -21}
B. {-1, 1}
C. {-1, 0, 5, 10}
D. {-1, 10}
Answer:
C. {-1, 0, 5, 10}
What is the domain of the function represented in the graph?
What will be the area of triangle with base
10 cm and height 4.5 cm?
Answer:
Area of triangle = 1/2*b*h
= 1/2*10*4.5
= 1/2*45
= 45/2
= 22.5
alan bought 3 pencils and a notebook. the notebook cost $6, and he spent a total of $12. how much did each pencil cost?
Answer:
Step-by-step explanation:
3x+6=12
-6. -6
3x=6
Divid three by both sides.
X=2
Each penicillin cost 2 dollars
a teacher has 1/4 gallon of milk he pours the milk into 5 glasses for each children each child receives the same amount of milk and there is no milk left over how much milk in gallons did each child due tomorrow pls answer :)
Answer:
1/20
Step-by-step explanation:
Each child got 1/20 gallon of milk, because 1/20 * 5 is 4/20, which can be simplified to 1/4.
Which point on the number line represents the product (5)(-2)(-1)?
I need it ASAP
Answer:
point D
Step-by-step explanation:
What is 90.125 written in expanded form?
Answer:
90+0.1+0.02+0.005
Step-by-step explanation:
Answer:
Step-by-step explanation:
90+0.1+0.02+0.005
Answer the following questions:
a. How much is $5,500 decreased by 6%?
b. What number is 22% more than $12,787?
c. $225 is what percent more than $50?
Please help me and got more answers
For what value of y must LMNP be a parallelogram?
L
M
68°
680
DO
P
N
Answer:
68°
Step-by-step explanation:
sum of interior angles in a parallelogram is 360. two side must form 180 degrees and the opposite side are equal
3. A car and a truck were travelling in the same direction along the same road. The
car was travelling at a constant speed of 70 km/h and the truck was travelling at
a constant speed of 58 km/h. At 08:00, the truck was 20 km ahead of the car. Half
hour later, the truck broke down.
a) How far was the truck from the car when it broke down?
b) What time did the car pass the truck?
Take 8:00 to be the starting time, t = 0, and the car's starting position 20 km behind the truck to be the origin. Then the car's position at time t is
x = (70 km/h) t
and the truck's position is
x = 20 km + (58 km/h) t
(a) Right before the truck breaks down 0.5 h later, it will cover an additional distance of
(58 km/h) * (0.5 h) = 29 km
from its starting point, while the car will have covered a distance of
(70 km/h) * (0.5 h) = 35 km
from its starting point. So at 8:30, the truck is (20 km + 29 km) - 35 km = 14 km away from the car when it broke down.
(b) If neither vehicles stops, then the car passes the truck when their positions are equal, which would happen after
(70 km/h) t = 20 km + (58 km/h) t
(12 km/h) t = 20 km
t = (20 km) / (12 km/h)
t ≈ 1.7 h
But with the truck breaking down a 8:30, it is stuck 49 km away from the origin, so we need to find when the car travels this distance:
(70 km/h) t = 49 km
t = (49 km) / (70 km/h)
t = 0.7 h = 42 min
or at 8:42.
Each morning librarians place 560 books on a book shelf in the school library. Each student that visits library that day takes exactly 3 books from this shelf. Let s be the number of students which visit library on a particular day. Let b be the number of books left on the shelf at the end of that day.
b
There are 150 students studying in this school. Use this information to find the domain of the function b(s).
Answer:
The domain of the function b(s) is
[tex]s\in[0,150][/tex]
Step-by-step explanation:
Given that, a total of 560 books is added to the book shelf each morning.
[tex]s[/tex] be the number of the students who visit the library on a particular day and takes exactly 3 books from this shelf.
So, the number of books they take from the shelf is 3s.
The number of remaining books the shelf [tex]=560-3s[/tex].
As , given that [tex]b[/tex] be the number of books left on the shelf at the end of that day, so the required function, [tex]b(s)[/tex], is
[tex]b=560-3s\;\cdots(i)[/tex]
As there are 150 students in the school. So, if no one will go to the library, than [tex]s=0[/tex] which is the minimum value, and if all goes to the library , than [tex]s=150[/tex] which is the maximum value of [tex]s[/tex].
So, the possible value of s is:
[tex]0\leq s\leq150\;\cdots(ii)[/tex]
Now, as there is no book left or there are some books left the negative value of [tex]b[/tex] is not possible. So,
[tex]b\geq0[/tex]
[tex]\Rightarrow 560-3s\geq0[/tex] [fron equation (i)]
[tex]\Rightarrow s\leq 560/3[/tex]
[tex]\Rightarrow s\leq 186\frac{2}{3}[/tex]
as s id the number of students which cant be a fractional value, so the possible nearest value is,
[tex]s\leq 186\;\cdots(iii)[/tex]
From the equations (ii) and (iii), the domain of the function [tex]b(s)[/tex] is
[tex]s\in[0,150][/tex]
Help!!!!! plz ill award as brainliest
A piggy bank contains $2.65 in nickels and dimes. If the number of nickels is 7 less than three times the number of dimes, how many of each kind of coin are there?
A traveler covered 4/5 of his journey with bicycle and the rest of the distance on foot. If the whole journey was 160 km, how much distance did he cover on foot?
Answer:
x = 12 dimes and 3x-7 = (3*12)-7 = 29 nickels in the piggy bank
Step-by-step explanation:
Hope this helps
Answer:
see below
Step-by-step explanation:
1.
total = $2.65 = d + n
let d = dimes
n = nickels
nickels = 3d - 7
plugin values into the formula:
2.65 = d + 3d - 7
2.65 + 7 = 4d
d = 9.65
4
d = $2.41
nickels = 3d - 7
= 3(2.41) - 7
n = $0.24
----------------------------------------------------------
2.
since Cindy ate 30, less than Ann and Ben together so, the equation is
7x = 5x + 5x - 30
7x - 10x = -30
x = 30/3
x = 10
ann 5 x 10 = 50
ben 5 x 10 = 50
cindy 7 x 10 = 70
total = 170
It is known that 10% of the items produced by a certain machine end up having a flaw. If we select 7 items from the production line, a) What is the probability that at least one of them has a flaw? Part b) What is the probability that exactly three of them has a flaw?
Step-by-step explanation:
p = 0.1, q = 0.9, n = 7
a) Use complementary probability.
P(at least 1) = 1 − P(0)
P(at least 1) = 1 − (0.9)⁷
P(at least 1) = 0.522
b) Use binomial probability.
P = nCr pʳ qⁿ⁻ʳ
P(3) = ₇C₃ (0.1)³ (0.9)⁴
P(3) = 0.023
Perpendicular lines intersect to form right angles. What is true about the statement? Check all that apply. The hypothesis is “if perpendicular lines.” The hypothesis is “if lines are perpendicular.” The conclusion is “then right angles.” This is a compound statement. This is a conditional statement.
Answer:
1. The Hypothesis is "If lines are perpendicular" 2. This Is a Compound Statement 3. This is a Conditional Statement
Step-by-step explanation:
I just did this and It showed me the answers
The following options are true about given statement.
- The hypothesis is “if lines are perpendicular.”
- This is a compound statement.
- This is a conditional statement.
What is a compound statement?"It is a statement that consists of two or more statements separated by logical connectors such as 'or', 'and', 'if then', 'if and only if'."
What is conditional statement?"It is the if-then statement in which part of the statement after 'if' is called a hypothesis and the part of statement after 'then' is called a conclusion."
For given example,
We have been a statement 'Perpendicular lines intersect to form right angles.'
We can write this statement as 'if the lines are perpendicular then they form right angles.'
This is a conditional statement with hypothesis if the lines are perpendicular and conclusion they form right angles.
Therefore, the following options are true about given statement.
- The hypothesis is “if lines are perpendicular.”
- This is a compound statement.
- This is a conditional statement.
Learn more about the conditional statement here:
https://brainly.com/question/11369777
#SPJ2
Evaluate 4 + (-2)= PLEASE HELP IF YOU KNOW THE ANSWER PLEASE SHOW WORK!? THANK YOU!
Answer:
2
Step-by-step explanation:
4 + -2 = 2
HOPE THIS HELPED!
1kg apple =100 rupee so 200gm apple =?
Answer:
20,000 rupee or 20 rupee
Step-by-step explanation:
if you saying grams then its 20 rupee if your talking about kgs then its 20,000
Eli caught three fish. The weights of the fish were 2lb4oz, 1lb11oz, and 4lb14oz,. What was the total weight of the three fish?
Answer:
The total weight of the three fishes is 8lb and 13oz
Step-by-step explanation:
2lb 4oz + 1lb 11oz + 4lb + 14 = 7lb 29oz
Remember, there are 16 ounces (oz) in a pound (lb).
So 29oz - 16 oz would be 13oz and the answer would be 8lb and 13 oz.
Hope this helps, can you please mark me brainliest because I just need 4 more brainliest to become expert:)
