The quadratic equation with the given conditions is:
[tex]f(x) = \frac{3}{16}(x^2 + 2x - 24)[/tex]
The standard form of a quadratic equation with roots [tex](x_1,0)[/tex] and [tex](x_2,0)[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2)[/tex]
In which a is the leading coefficient.
In this problem, the roots are [tex]x_1 = -6, x_2 = 4[/tex], thus:
[tex]f(x) = a(x - (-6))(x - 4)[/tex]
[tex]f(x) = a(x + 6)(x - 4)[/tex]
[tex]f(x) = a(x^2 + 2x - 24)[/tex]
It passes through point (2,-3), which means that when [tex]x = 2, f(x) = -3[/tex], and this is used to find a.
[tex]a(2^2 + (2)(2) - 24) = -3[/tex]
[tex]-16a = -3[/tex]
[tex]a = \frac{3}{16}[/tex]
Thus, the equation is:
[tex]f(x) = \frac{3}{16}(x^2 + 2x - 24)[/tex]
A similar problem is given at https://brainly.com/question/17987697
wins some money on the lottery. She uses 1/3 of her lottery win to buy a house
and she gives 1/8 of her lottery win to charity. Molly then shares the remainder of her
lottery win equally among her four children. Work out the fraction of Molly's lottery
win that each of her four children receives.
Answer:11/96
Step-by-step explanation:
1-(1/3)=2/3=14/24
(2/3)-(1/8)=(14/24)-(3/24)=11/24
11/24 divided into 4 again is 11/96
A certain substance in an experiment was being stored at −1.7°F. It was then placed on a table where the temperature was raised by 3.1F
What was the new temperature of the substance?
the answers are
-4.8F
-1.4F
1.4F
4.8F
1.4F. When you add 3.1 to -1.7 you get 14F
Answer:
The answer is 1.4.
Step-by-step explanation:
The school colors at Mission Middle School are green and white. Kendra volunteered to make cupcakes
for the school bake sale. To make the right shade of green frosting, she uses 7 drops of blue food
coloring for every 3 drops of yellow food coloring.
the sum of two numbers is 6 and the sum of their squares is 28. Find the exact values of these numbers
Answer:
The highest value I could get, without going over, is 5+1=6 and 25+1=26
Step-by-step explanation:
Please help with this question
y=-2/3x + 7 what is the slope?
Answer:
Lucky for you i'm good at algebra:)
Step-by-step explanation:
Slope: -2/3
Y-intercepts: (0,7)
Answer:
Slope = -1.333/2.000 = -0.667
x-intercept = 21/2 = 10.50000
y-intercept = 21/3 = 7
Step-by-step explanation:
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
y-(-2/3*x+7)=0
Step 1:
Simplify 2/3
Equation at the end of step 1:
y - ((0 -(2/3• x)) + 7) = 0
Step 2: Rewriting the whole as an Equivalent Fraction
Rewrite the whole as a fraction using 3 as the denominator :
7 = 7/1 = 7 · 3 /3
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
-2x+7·3/3 = 21-2x/3
Equation at the end of step 2:
y-(21-2x)/3=0
Step 3:
Rewriting the whole as an Equivalent Fraction :
Subtracting a fraction from a whole
Rewrite the whole as a fraction using 3 as the denominator :
y=y/1=y·3/3
Adding fractions that have a common denominator :
Adding up the two equivalent fractions
y • 3 - ((21-2x)) 3y + 2x - 21
————————————————— = ————————————
3 3
Equation at the end of step
3
:
3y + 2x - 21
———————————— = 0
3
STEP
4
:
When a fraction equals zero :
4.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
3y+2x-21
———————— • 3 = 0 • 3
3
Now, on the left hand side, the 3 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
3y+2x-21 = 0
Equation of a Straight Line
4.2 Solve 3y+2x-21 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 3y+2x-21 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 7/1 so this line "cuts" the y axis at y= 7.00000
y-intercept = 21/3 = 7
Calculate the X-Intercept :
When y = 0 the value of x is 21/2 Our line therefore "cuts" the x axis at x=10.50000
x-intercept = 21/2 = 10.50000
Calculate the Slope :
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 7.000 and for x=2.000, the value of y is 5.667. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 5.667 - 7.000 = -1.333 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = -1.333/2.000 = -0.667
Geometric figure: Straight Line
Slope = -1.333/2.000 = -0.667
x-intercept = 21/2 = 10.50000
y-intercept = 21/3 = 7
solve please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
it is very easy solve I will tell you if u follow me we should help each other
6. Write the statements "If you take away 6 from 6 time a number, you get
60” in the form of equations:
(a) 6x + 6 = 60
(b) 6x6 = 60
(c) X-6 = 60
(d) none of these
Answer:
6x-6=60 so if you correctly typed the question its none of them
The Candela brothers own two pizza restaurants, one on Park Street and one on Bridge Road.
The computer output below summarizes the distribution of weekly revenues at each
restaurantâ€"26 weeks for Park Street and 40 weeks for Bridge Avenue.
The mean, median and mode are measures of central tendency, that is they tend to indicate the location middle of the data
Required values;
(a) The performance for the week for Park Street
Revenue is Q₂ < $7,500 < Q₃The sales for the week is better than 72.91% of all salesThe performance for the week for Bridge Road
Revenue; Q₂ < $7,100 < Q₃The sale for the week is better than 59.87% of all sales(b) The mean is $3611
The median is $3,600
The standard deviation is $3250
The Interquartile range is $6075
Reason:
The table of values that maybe used to find a solution to the question is given as follows;
[tex]\begin{array}{|l|l|l|}\mathbf{Variable} &\mathbf{Park}&\mathbf{Bridge}\\N&36&40\\Mean&6611&5989\\SE \ Mean&597&299\\StDev&3580&1794\\Minimum&800&1800\\Q_1&3600&5225\\Median&6600&6000\\Q_3&9675&7625\\Maximum&14100&8600\end{array}\right][/tex]
(a) Park Street revenue = $7,500
Bridge Road's revenue = $7,100
The two stores sold close to but below the 75th percentile
Bridge Road revenue;
The z-score is given as follows;
[tex]Z = \dfrac{x - \mu }{\sigma }[/tex]
[tex]Z = \dfrac{7100 - 5,989 }{1794 } \approx 0.6193[/tex]From the Z-Table, we have;
The percentile= 0.7291
Therefore, the sale for the week for Park Street is better than 72.91% of all the salesPark Street revenue;
The z-score is given as follows;
[tex]Z = \dfrac{7500 - 6611}{3580} \approx 0.25[/tex]From the Z-Table, we have;
The percentile = 0.5987
Therefore, the sale for the week is better than 59.87 % of all the sales(b) Given that the operating cost is $3,000, frim which we have;
The subtracted value is subtracted from the mean and median to find the new value
Profit = The revenue - Cost
New mean = 6611 - 3000 = 3611
The new mean = $3,611The new median = 6600 - 3000 = 3600
The new median = $3,600The standard deviation and the interquartile range remain the same, therefore, we have;
The standard deviation = $3,580The interquartile range = 9675 - 3600 = 6075
The interquartile range = 6075Learn more here:
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yis inversely proportional tox.Wheny=50,x=4Work outywhenx=8
Answer:
55555
Step-by-step explanation:
Solve for c. 2a + 3b = c
Please help as soon as possible. Thanks! =D
Answer:
a = c - 3b/2
Step-by-step explanation:
2a + 3b - 3b = c - 3b
2a = c - 3b
2a/2 = c/2 - 3b/2
therefore your answer is a = c - 3b/2
The value of the digit in the thousands place is_______ times as much as the digit in the hundredths place
Don’t understand I’ll give u a brainly
The answer is the second one
Which is the better buy?
A 450 g box of cereal for $4.69 or a 600 g box of cereal for $6.49?
Please show ALL of your work.
hint: convert each to a unit rate using "cost / gram", then compare each to see which is cheaper.
Answer: The first box (the 450 g box for $4.69)
===========================================================
Explanation:
To get the unit cost, we'll divide each price by the weight
The first box has a unit cost of (4.69)/450 = 0.010422 approximately which rounds to 0.01; so this unit cost is approximately $0.01 per gram or 1 cent per gram.
For the second box, its unit cost is (6.49)/600 = 0.0108167 approximately. When we round to the nearest cent, we get the same unit cost as before. Without rounding, we see that the first box has a slightly lower unit cost. Therefore box 1 is the better buy.
20% of what number is 75?
Answer:
15
Step-by-step explanation:
Answer: 375
Step-by-step explanation:
NEEDS TO BE CORRECT PLZ HELP
Step-by-step explanation:
Linear pairit's hope it helpful to you
Answer:
c
Step-by-step explanation:
its a pair
209
У.
Х
120°
y = [ ? 1°
Answer:
140
Step-by-step explanation:
one exterior = the sum of two interior
Find the exact value of each variable that represents its side length in a right triangle. Please help me with this ASAP!
Answer:
[tex]h=6[/tex]
[tex]k=2.5[/tex]
[tex]m=\sqrt{21}[/tex]
[tex]n=3\sqrt{10}[/tex]
[tex]p=\sqrt{17}[/tex]
Step-by-step explanation:
We can use the Pythagorean Theorem in each case.
Pythagorean Theorem:
[tex]a^{2} +b^{2} =c^{2}[/tex]
Where [tex]a[/tex] and [tex]b[/tex] are two sides of a right-angle triangle and [tex]c[/tex] is Hypotenuse (the longest side opposite to the right angle)
For [tex]h[/tex]:
[tex]h^{2} +8^{2} =10^{2}[/tex]
[tex]h^{2} +64=100[/tex]
Subtract 64 from both sides:
[tex]h^{2} =100-64[/tex]
[tex]h^{2} =36\\[/tex]
[tex]h=\sqrt{36}[/tex]
[tex]h=6[/tex]
We follow the same process to find [tex]k,m,n[/tex] and [tex]p[/tex].
answerrrrrrrrrrrrrrrrrr plzzzzzzz
Answer:
X=24
Step-by-step explanation:
55-31 is 24
Answer:
x+31°=55°[alternate angle]
x=55°-31°
x=24°
answer
what is the square root of 9 and 4
Answer:
3/2
Step-by-step explanation :
Square root of 9 and 4 is 3/2 because it just is
Ian's car can go 231 miles on 7 gallons of gas. During a drive last weekend, Ian used 5 gallons of gas. How far did he drive? Use pencil and paper. Explain how the problem changes if you were given the distance Ian drove last weekend instead of how much gas he used.
Answer:
165 miles
Step-by-step explanation:
part 1
231/7= 33 mpg
33x5 = 165 miles
part 2
distance/mpg = gas used
for example: if you were told he went 200 miles,
200/33 = 6.06 gallons of gas
Given :
Ian's car can go 231 miles on 7 gallons of gas.
During a drive last weekend, lan used
5gallons of gas.
To find :-
How far did he drive?
Solution :-
According to Question ,
Car can go 231 mi on 7 gallons of gas.
Using Unitary Method ,
On 1 gallon of gas it will go 231/7mi
On 5 , it will go 231/7*5 = q65 miles
Hence the required answer is 165 miles
Subtraction of integers
-70 --25 =
Answer:
-45
Step-by-step explanation:
-70 --25
-×-=+
-70 +25
-45
−4 + 20 > −8 what the answers
Answer: -20
Step-by-step explanation: plz mark me brainliest please?
2. Ms. De Los Santos bought 5 3/7 gallons of ice cream for the 6th grade Wakanda Day celebration. If each scholar is served 1/16 gallon of ice cream, what is the greatest number of scholars that can be served?
HELPPP PLEASEEE!!!!!!!
Answer:
CFX, ADC
Step-by-step explanation:
CFX is just a larger version of AEX. Same thing with CFX.
find the midpoint and distance between (5,1) and (-15,11)
Answer:
look i think is -5.005 I don't really know but I hope you get it right. Have a good day
A list of numbers is given below. If x is a number in this list, which inequality could represent x? {-5, -12, -2, -9}
Answer:
x<-1
Step-by-step explanation:
All of the numbers on/in the set are below -1. That means for that any of them to be x, the inequality would be x<-1.
636/526 pls answer and you get points
Answer:
1.20912547529
Step-by-step explanation:
please help me due soon
Answer:
- 7.2
Step-by-step explanation:
it is division and we need to take the reciprocal and multiply it will be -9/5. we need to simplify leaving us -7.2
A Bike rental place rents bikes for $22 plus $8 per hour. Mary paid $67 to rent a bike. Write and solve an equation to represent how many hours she rented the bike.
Answer:
8x+22=67
Step-by-step explanation: