Well, we know standard form of quadratic equation : ax² + bx + c where,
a = Coefficient of x²
b = Coefficient of x
c = Constant term
We also equation for determinant :
⇒ b² - 4ac
Here, if value of determinant i.e. (b² - 4ac) = A perfect Square, then we can understand that the givdn equation is factorisable.
But, if the value of (b² - 4ac) ≠ A perfect square, then it will be considered as "Not factorisable"
Now let's calculate whether the equation is factorisable or not :
Comparing the given equation with ax² + bx + c, we get :
a = 1
b = -3
c = -54
Putting values in the determinant equation :
⇒ (-3)² - 4(1 × -54)
⇒ 9 + 216
⇒ 225
⇒ 15²
So, determinant = A perfect square
That means the given equation is factorisable.
Now let's factorize with by middle term splitting :
⇒ x² - 3x - 54
⇒ x² -(9 - 6)x - 54
⇒ x² - 9x + 6x - 54
⇒ x(x - 9) + 6(x - 9)
⇒ (x + 6)(x - 9) [Required Solution]
Hence, we get our required solution.
Hope this Helps (✿◡‿◡)
Ava bought 2 1/4 pounds of ham for $7.65 at ShopRite last week. This week she bought 3 1/2 pounds of the same ham for $12.60 at Stop & Shop. Which store has the better price per pound for ham? How much less expensive is the ham at the store with the better price?
Answer:Ava bought 2 1/4 pounds of ham for $7.65 at ShopRite last week. This week she bought 3 1/2 pounds of the same ham for $12.60 at Stop & Shop. Which store has the better price per pound for ham? How much less expensive is the ham at the store with the better price?
Step-by-step explanation:
Ava bought 2 1/4 pounds of ham for $7.65 at ShopRite last week. This week she bought 3 1/2 pounds of the same ham for $12.60 at Stop & Shop. Which store has the better price per pound for ham? How much less expensive is the ham at the store with the better price?
I need help cause I’m lazy to do it myself it’s 4 in the morning
Answer:
C. Mario should have multiplied the x-values by $6.50 to get the y values.
Step-by-step explanation:
Let's do it the way they said. If we were to multiply 1 by 65, it would be $65. If we did the same thing for 2, 2 x 65 is $130. This is incorrect because these values do not match up with the ones on the graph.
Decimal points are important in this case because it completely changes your answer. When you multiply 1 by 6.50, you get 6.50. Which is what's on the graph. Multiply 2 by 6.50 and you'll get $13, and so on.
So now we can conclude that the mistake Mario made was that he multiplied x by the wrong value (65), when it should have been $6.50.
Note: Hope this helps! Good luck on your test. :)
Four deep-sea divers reported the depths they went below sea level on their last dive. Which depth is the farthest from sea level?
A. -54
B.-80
C.-82
D.-67
Answer: C. -82
Step-by-step explanation:
-82 is the depth which is the farthest from sea level.
What is the depth of a sea?The deep ocean is generally defined as the depth at which light begins to dwindle, typically around 200 meters (656 feet).
Given that, Four deep-sea divers reported the depths they went below sea level on their last dive.
The farthest point in sea among the given options, is -82, this is because, the distance down the sea is marked as a negative, and 82 is the greatest in the options, therefore, -82 is the greatest distance.
Hence, -82 is the depth which is the farthest from sea level.
Learn more about depth of the sea, click;
https://brainly.com/question/6459494
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PLEASE HELP ASAP!! Will give BRAINLIEST for the first correct answer!
Dr. Hammer noticed that the distribution of scores for his psychology class's last unit test was
not normal. In fact, the class results were positively skewed. According to this, which of the
following would be true?
OPTIONS:
A. The mean, median, mode would all be the same
B. The mean would be higher than the median and mode
C. The mean and median would be the same, but the mode would be higher
D. The mode and median would be higher than the mean
Answer:
E
Step-by-step explanation:
Answer:
B. The mean would be higher than the median and mode
Step-by-step explanation:
Write an algebraic expression for the phrase. Six times a number h plus seven.
Answer:
6 x h + 7
Step-by-step explanation:
pls help will give brainisest.
Find the length of A.
Answer:
If i'm correct I think that the length of a would be 4 because it shorter then five just by a minuscule measure .
Step-by-step explanation:
(1 + 2/3)*(1+2/5)*(1+2/7)*(1+2/9)
Answer: 11/3 or 3.6 or 3 2/3
Step-by-step explanation:
All you have to do is simplify the expression
Jeremiah plans on building a 5 meter long garden walkway that is paved with square stones that measure LaTeX: \frac{5}{6}5 6 meter on each side. There will be no spaces between the stones. How many stones will be needed to complete the garden walkway?
Answer:
Example 1
A backyard farmer wants to enclose a rectangular space for a new garden. She has purchased 80 feet of wire fencing to enclose 3 sides, and will put the 4th side against the backyard fence. Find a formula for the area enclosed by the fence if the sides of fencing perpendicular to the existing fence have length
L.
In a scenario like this involving geometry, it is often helpful to draw a picture. It might also be helpful to introduce a temporary variable,
W, to represent the side of fencing parallel to the 4th side or backyard fence.
Since we know we only have 80 feet of fence available, we know that
L + W + L = 80, or more simply, 2L + W = 80. This allows us to represent the width, W, in terms of L: W = 80 – 2L
Now we are ready to write an equation for the area the fence encloses. We know the area of a rectangle is length multiplied by width, so
A = LW = L(80 – 2L)
A(L) = 80L – 2L2
This formula represents the area of the fence in terms of the variable length
L.
Example 2
Returning to our backyard farmer from the beginning of the section, what dimensions should she make her garden to maximize the enclosed area?
Earlier we determined the area she could enclose with 80 feet of fencing on three sides was given by the equation
A(L) = 80L – 2L2. Notice that quadratic has been vertically reflected, since the coefficient on the squared term is negative, so the graph will open downwards, and the vertex will be a maximum value for the area.
In finding the vertex, we take care since the equation is not written in standard polynomial form with decreasing powers. But we know that
a is the coefficient on the squared term, so a = -2, b = 80, and c = 0.
Finding the vertex:
h
=
−
80
2
(
−
2
)
=
20
,
k
=
A
(
20
)
=
80
(
20
)
−
2
(
20
)
2
=
800
The maximum value of the function is an area of 800 square feet, which occurs when
L = 20 feet. When the shorter sides are 20 feet, that leaves 40 feet of fencing for the longer side. To maximize the area, she should enclose the garden so the two shorter sides have length 20 feet, and the longer side parallel to the existing fence has length 40 feet.
Example 3
A ball is thrown upwards from the top of a 40 foot high building at a speed of 80 feet per second. The ball’s height above ground can be modeled by the equation
H(t) = –16t2 + 80t + 40.
What is the maximum height of the ball?
When does the ball hit the ground?
To find the maximum height of the ball, we would need to know the vertex of the quadratic.
h
=
−
80
2
(
−
16
)
=
80
32
=
5
2
,
k
=
H
(
5
2
)
=
−
16
(
5
2
)
2
+
80
(
5
2
)
+
40
=
140
The ball reaches a maximum height of 140 feet after 2.5 seconds.
To find when the ball hits the ground, we need to determine when the height is zero—when
H(t) = 0. While we could do this using the transformation form of the quadratic, we can also use the quadratic formula:
t
=
−
80
±
√
80
2
−
4
(
−
16
)
(
40
)
2
(
−
16
)
=
−
80
s
q
r
t
8960
−
32
Since the square root does not simplify nicely, we can use a calculator to approximate the values of the solutions:
t
=
−
80
−
s
q
r
t
8960
−
32
a
p
p
r
o
x
5.458
The second answer is outside the reasonable domain of our model, so we conclude the ball will hit the ground after about 5.458 seconds.Step-by-step explanation:
[WILL GIVE BRAINLIIEST! PLEASE HELP!!] In the first week of July, a record 1,040 people went to the local swimming pool. In the second week, 105 fewer people went to the pool than in the first week. In the third week, 145 more people went to the pool than in the second week. In the fourth week, 196 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
Answer:
13
Step-by-step explanation:
I'm just here for da points can I still get brainliitest?
Jane paid $40 for an item after she received a 20% discount. Jane's friend says this means that the original price of the item was $48. a. How do you think Jane's friend arrived at this amount?
Answer:
The discount is $8
Step-by-step explanation:
Step one
Given data
Jane paid $40 for an item after she received a 20% discount.
Required
The initial cost of the item
Now in other to check whether Jane's friend is correct, let us solve for the initiai cost as follows
Let the initial cost be x
so
20% of 40
20/100*40
=0.2*40= $8
Therefore the discount is $8
hence the original price is
discount+ discounted sale(amount paid)
=8+40
=$48
2.1.PS-14
Error Analysis A contractor purchases 7 dozen pairs of padded work gloves for $97.44. He
incorrectly calculates the unit price as $13.92 per pair for the expense report. What is the correct
unit price? What is the error?
The correct unit price is $
per pair
Answer:
Unit price = $1.16
His error was he divided $97.44 by 7 when in fact he should have divided 97.44 by 84
Step-by-step explanation:
7 dozen pairs
1 dozen = 12
7×12 = 84
97.44 ÷ 84 = 1.16
ASAP PLEASE HELP! THANK YOUU
math , help plss thnx
Answer:
The answer is
[tex]y = \frac{1}{4} x - 2[/tex]
Step-by-step explanation:
Remmeber:
[tex]Slope = \frac{rise}{run} [/tex]
Please hurry. I will give brainliest. :)
Answer: Am thinking it is B because am only 11 and I don't know if this is right. Hope this helps, or not...
Step-by-step explanation:
What is the length of AB? 4 units 5 units 6 units 7 units
Answer:
the answer is 6 units
Step-by-step explanation:
find point A and point B and then just count the units over from
A to B and you will get AB is 6 units
Answer c
Step-by-step explanation: bc its 6 units
I need help on this PLEASE!!
Answer:
I can't solve this completely for you, but I'll help you figure it out.
Step-by-step explanation:
All you need to do is choose a number to plug in for x, I'd start with zero and work my way up. Do this for all equations to solve for solutions to your problem.
Please helpppp I want to go to sleep xD (There's a screenshot)
Answer:
Step-by-step explanation:
2n-8 :) zzzzzzzzzzzzzzzzzzzzz :P
Answer:
2n - 8
Step-by-step explanation:
Combine like terms in the parenthesis 2(1n - 4)
The distribute (multiple both of the terms inside by 2)
It gives 2n - 8
ay someone help me out please?
Answer:
a, c, and d
Step-by-step explanation:
Simplify the following expression (2x⁴y⁻³)⁻¹
Answer:
please make sure the input is complete.
Step-by-step explanation:
I need help with a math question
An angle measures 3.8° more than the measure of its complementary angle. What is the measure of each angle?
Answer: 41.2 degrees
Step-by-step explanation:
Complementary angles are angles that add to 90 degrees, so if they were equal, they would be 45 and 45, but since one is 3.8 more, it is 45+3.8 = 48.8 and the other, to add to 90 degrees is 90-48.8 = 41.2
What is the y-intercept?
(0, 8)
(8, 0)
2/1
4/1
Answer:
8 and 0
Step-by-step explanation:
Factor this polynomial.
-3x^2-16x- 5
Answer:
B. [tex]-(3x+1) (x+5)[/tex]
Step-by-step explanation
factored the equation to solve. Hope this helps!
solve each inequality and graph the solution
5+ x <12
Answer:
Inequality Form:
x<7
Interval Notation:
(−∞,7)
Step-by-step explanation:
plz give brainlyest
Which angle number is adjacent to angle to MNJ?
Answer:
I think it is ACB
Step-by-step explanation:
Please don't come after me if i'm wrong
Find the value of c x 8 when c=9.
Answer:
72 hope it helps............
Answer:
72
is you answer because 8×9=72
who has the ps5 i do
Answer:
im from da fam round herrrr u either got the ps3 or the x box 3-60
lm.ao.
Are the ratios 1:5 and 4:20 equivalent?
Answer:
yes they are
Step-by-step explanation:
4:20 can be simplified till 1:5
Answer:
Yes
Step-by-step explanation:
If you simplify 4:20 by dividing both sides by 4, you'll end up with 1:5, meaning they are equivalent.
BRAINLEST TO WHOEVER
X= ?
Answer:
11.4
Step-by-step explanation:
15 divided by 5= 3 so ABC is 3 times bigger than EFD. you times 3.8 by 3 to get your answer. I hope this helps!!
please help! 30 points !!
Answer:
1. C
2. C
Step-by-step explanation:
1. 5x+12=57
Subtract 12 from both sides
5x=45
Divide both sides by 5
x=9
2. 7-4x=12-3x
Combine like terms =
-4x+3x=-12-7
x=-12-7
x=19
