Given three points of a quadratic function, find the equation of the function: (-1, -3), (0, -4), (2, 6)
A) f(x)=2x^2+2x−4f
B) f(x)=x^2+2x−4f
C) f(x)=x^2+x−4f
D) f(x)=2x^2+x−4f
The quadratic function has an equation of f(x) = 2x²+ x - 4
How to determine the equation of the functionFrom the question, the ordered pairs are given as
(-1, -3), (0, -4), (2, 6)
A quadratic function is represented as
f(x) = ax²+ bx + c
Using the point (0, -4), we have
a(0)²+ b(0) + c = -4
So, we have
c = -4
This gives
f(x) = ax²+ bx - 4
Using the point (-1, -3), we have
a(-1)²+ b(-1) - 4 = -3
So, we have
a - b = 1
Using the point (2, 6), we have
a(2)²+ b(2) - 4 = 6
So, we have
4a+ 2b = 10
So, we have
a - b = 1
This gives
a = b + 1
Substitute a= b + 1 in 4a+ 2b = 10
4(b + 1) + 2b = 10
This gives
4b + 4 + 2b = 10
Evaluate
6b = 6
Divide
b = 1
So, we have
a = 1 + 1
a = 2
So, we have
f(x) = 2x²+ x - 4
Hence, the equation is f(x) = 2x²+ x - 4
Read more about quadratic function at
https://brainly.com/question/1214333
#SPJ1
the number of students in the school went from 1028 down to 755 what is the percent decrease?
Step-by-step explanation:
100% = 1028
1% = 100%/100 = 1028/100 = 10.28
the decrease was
1028 - 755 = 273
these 273 were how many % ?
as many % as how often 1% fits into 273 :
273 / 10.28 = 26.55642023... %
this was a 26.55642023...% decrease.
PLease help it’s due tomorrow morning
Explain the step that is used to solve the equation
-x = -16
Answer:x=16
Step-by-step explanation:
just divide both sides by negative 1
WILL GIVE BRAINLEIST
Which steps show how to use distributive property to evaluate 5 x 38
Answer:
The answer is most definitely A. It is the only answer that reaches the correct value of 190, which is what 5 * 38 equals. However, to put it into perspective...
Step-by-step explanation:
When we use the distributive property we are breaking down something sometimes, and in this case, very simple into a more extended form.
5 * 38 is the same as saying 5(40 - 2). We also know that if we subtract the sum of 5 * 2 from 5 * 40, it will end up the same as 5 * 38 because you are multiplying 5 two times less.
5 * 40 = 200
5 * 2 = 10
200 - 10 = 190
The answer is A
;)
2 is subtracted from twice a number.
early beginner in geometry
Answer:
2x-2 (x is your number)
Step-by-step explanation:
Not sure if this is what you mean lol
:]
ANSWER QUICK I WILL GIVE BRAINLIEST
Solve k over negative 1.8 is less than negative 4.9 for k.
k < −8.82
k > 8.82
k < −6.7
k > −6.7
The solution of the inequality is k > 8.82
How to solve inequality?The expression is in words so we have to convert it to an inequality to be able to solve for k.
An inequality is an expression that has the following symbols: <, >, ≤ and ≥.
Therefore, the inequality can be solved as follows:
k / - 1.8 < - 4.9
Therefore, let's solve for the variable k.
k / - 1.8 < - 4.9
multiply both sides of the inequality by - 1.8
Hence,
k / - 1.8 (-1.8) < - 4.9 (-1.8)
k / 1 > 8.82
Note the sign had to change after we multiply both side of the inequality with a negative number.
Therefore,
k > 8.82
learn more on inequality here: https://brainly.com/question/12690999
#SPJ1
i need help ASAP show your work
Answer:
a=5
Step-by-step explanation:
1/3(6a-15)=(a-2)+2
1/3(6a-15)=a
6a-15=3a
3a=15
a=5
:]
Step-by-step explanation:
1.multiply in first bracket
[tex]2a - 5 = a + 0[/tex]
2.Take unknowns to left and constants to the right
[tex]2a - a = 5[/tex]
3.solve for a
[tex]a = 5[/tex]
Fill in the blanks with the correct angle measure.
For example:
Measure of angle 1 = 110 degrees. You only need to type 110.
Answer:
1:110
2:70
3:110
4:70
5:110
6:70
7:110
8;70
Step-by-step explanation:
lol i think its pretty simple
The value of y varies directly with x. If y = 8, when x = 4, what is y when x = 48?
Answer:
96
Step-by-step explanation:
If Y is directly proportional (or in this case varies directly) then whatever you do to one value you do to the other.
So in this case, when Y = 8 and X = 4 that means that Y is double of X (cause 8 is double 4).
So when X = 48 all you need to do is double X which will give you 96.
A model of a famous statue is 3 1/2 inches tall. The actual statue is 5 1/4 feet tall. What is the ratio of the height of the model to the height of the actual statue in simplest form?
A model of a famous statue is [tex]3\frac{1}{2}[/tex]inches tall. The actual statue is [tex]5\frac{1}{4}[/tex] feet tall, the ratio of the height of the model to the height of the actual statue in simplest form is [tex]3\frac{1}{2}[/tex]:63
What is a ratio mean?A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of the lemons to oranges is 6:8 (or 3:4). (or 4:7).
A ratio can have any number of quantities, such as counts of people or things or measurements of the length, weight, time, etc. Both the numbers must be positive in most situations.
You can specify a ratio by either writing out both of the integers that make it up, "a to b" or "a:b", or by giving just the value of their quotient a/b. Equal quotients correspond to the equal ratios.
A ratio can therefore be thought of as an ordered pair of integers, a fraction with first number in the numerator and the second in the denominator, or as the value represented by this fraction. Ratios of the counts that are expressed in terms of (non-zero) natural numbers are rational numbers and occasionally natural numbers as well. The ratio of the two numbers is a dimensionless number when they are measured using the same unit, which happens frequently. A rate is product of two quantities that are divided by their respective units of measurement.
Given,
A model of a famous statue is [tex]3\frac{1}{2}[/tex] inches tall.
The actual statue is [tex]5\frac{1}{4}[/tex] feet tall
1 feet = 12 inches
21/4 ft = 12*21/4 inches = 63 inches
Therefore the ratio is
[tex]3\frac{1}{2}[/tex]:63
To know more about ratio visit: https://brainly.com/question/13419413
#SPJ9
identify the y-intercept: 6 - 2y = -6
We know that the equation of a line is given by
y = mx + b, where m and b are numbers:
m is the slope of the line and b is the y intercept.
In this case we have the equation:
6 - 2y = - 6
We clear y so we can identify m and b
6 - 2y = -6
6 = -6 + 2y
6 + 6 = 2y
12 = 2y
12/2 = y
6 = y
In this case
y = 6
Then m=0 and b = 6
Then, the y-intercept is b =6Circle the two subtraction problems that have a difference of 10.2.
The problems with a difference of 10.2 are:
16.29 - 6.09 = 10.236.1 - 25.9 = 10.2We are given some subtraction problems for which we need to find the ones with a difference of 10.2.
The problems are:
12.05 - 2.03
16.29 - 6.09
36.1 - 25.9
22.09 - 21.07
10.82 - 9.8
We find the difference for each of them one-by-one after subtraction.
12.05 - 2.03 = 10.0216.29 - 6.09 = 10.236.1 - 25.9 = 10.222.09 - 21.07 = 1.0210.82 - 9.8 = 1.02The question is incomplete. Find the complete question below:
Circle the two subtraction problems that have a difference of 10.2.
12.05 - 2.03
16.29 - 6.09
36.1 - 25.9
22.09 - 21.07
10.82 - 9.8
Learn more about subtraction at https://brainly.com/question/17301989
#SPJ1
Which of the following is equivalent to 2.68?
2.68%
two and seventeen twenty fifths
twenty five seventeenths
26.8%
The expression that is equivalent to the number 2.68 is (b) two and seventeen twenty fifths
How to determine the equivalent number/expression?From the question, we have the following parameters that can be used in our computation:
Number = 2.68
Expand the number using the addition operator
So, we have the following representation
Number = 2 + 0.68
Express 0.68 as a fraction
This gives
Number = 2 + 68/100
Simplify the fraction
So, we have the following representation
Number = 2 + 17/25
This implies that
Number = two and seventeen twenty fifths
Hence, the equivalent of 2.68 is (b) two and seventeen twenty fifths
Read more about equivalent expression at
https://brainly.com/question/2972832
#SPJ1
(last question) but does anyone know the answer (s)??!?!
Answer:
MN = 3
Step-by-step explanation:
MN = 3
Similar triangles :)
1,1.8,3
2,3.6,6
Triangle AMN is half the size of triangle ABC :)
hope this helps
:]
Shaquira is baking cookies to put in packages for a fundraiser. Shaquira has made 868686 chocolate chip cookies and 424242 sugar cookies.
Shaquira wants to create identical packages of cookies to sell, and she must use all of the cookies.
What is the greatest number of identical packages that Shaquira can make?
Camryn practiced both the trumpet and the flute today.
How many days until Camryn practices the trumpet and flute again in the same day
The greatest number of identical packages that Shaquira can make is 2.
Given data:
Shaquira has made 86 chocolate chip cookies and 42 sugar cookies.
Shaquira wants to create identical packages of cookies to sell, and she must use all of the cookies.
To find:
The greatest number of identical packages that Shaquira can make
In order to find the greatest number of packages, we find the HCF of 86 and 42.
Write down this part from the attached image.
Here, 86 = 1 × 2 × 43, 42 = 1 × 2 × 21
Thus HCF = 1 × 2 = 2
So, Shaquira can make 2 identical packages the most.
Each package will have
(86 ÷ 2) = 43 chocolate chips and
(42 ÷ 2) = 21 sugar cookies.
For questions like these you would need to find out the Least Common Multiple, or L.C.M
If Camryn plays the trumpet and the flute today, and they both are in intervals of 11 and 3 days, you would need to find the LCM for 11 and 3.
LCM:
11 = 11, 1
3 = 3, 1
As they both have no common factors, and are prime numbers, multiply 11 x 3 = 33.
So, the least amount of days required for the trumpet and the flute to be played together is 33 days. And the interval between practising them both on the same day is 33 days.
Hence, the number of days until Camryn practices the trumpet and the flute on the same day is 33 days.
To learn more about factors visit:https://brainly.com/question/24182713
#SPJ9
Cuanto es 3/8+-3/4
………..
How many permutations can be formed from all of the letters of the word houston?.
The word "Houston" can have a maximum of 2520 permutations using all it's letters.
As per the question statement, we are provided with a word: HOUSTON.
And we are required to calculate the total number of permutations that can be formed using all the letters of it.
To solve this question, first we will need to determine the number of letters in our concerned word, which in this case is 7, and then number of repeated letters, which is 2, since the letter "O" is repeated once.
Therefore, the total number of permutations that can be formed using all the letters of the word HOUSTON = [(7!)/(2!)]
= (7 * 6 * 5 * 4 * 3)
= 2520
Permutation: In Mathematics, a permutation is a technique to determines the number of possible arrangements of the elements in a set, in a definite order.To learn more about Permutations, click on the link below.
https://brainly.com/question/9411802
#SPJ4
In 1924, the temperature in St. Louis, Missouri, dropped from 53 degrees to −11 degrees in 8 hours. What was the average hourly change in temperature?
(pls this is for a test rn)
Answer: -8°
Step-by-step explanation: the temperature dropped by 64 degrees over the span of 8 hours. 64/8 = 8.
7x - 7; x = 4................
Answer:
21
Step-by-step explanation:
7x - 7
=> substituting x = 4
=> 7(4) - 7
=> 28 - 7
=> 21
HELPPPPPP!!!!! PLEASEEEEE FAST!!!!!!!
Given the function f(x)=2.5xsquared+3, find the average rate of change over the interval 0 ≤ x ≤ 4. What does the average rate of change tell you about the function?
The average rate of change over the interval is 10 and it tells us about the slope
How to determine the average rate of changeThe definition of the function is given as
f(x) = 2.5xsquared + 3
Rewrite the function properly
So, we have the following equation
f(x) = 2.5x² + 3
The interval to calculate the average rate of change is given a
0 ≤ x ≤ 4
This can be represented as
[0, 4]
Further, rewrite as
[a, b] = [0, 4]
Where a = 0 and b = 4
Calculate f(a) and f(b)
So, we have
f(0) = 2.5(0)² + 3 = 3
f(4) = 2.5(4)² + 3 = 43
The average rate of change is then calculated as
Average rate = [f(b) - f(a)]/[b - a]
Substitute the known values in the above equation
So, we have
Average rate = [43 - 3]/[4 - 0]
Evaluate
Average rate = 10
What the average rate tells usThe average rate is the slope of the function
This means that it represents the amount of change in the function with respect to the change in the input variables
Read more about average rate of change at
https://brainly.com/question/16349477
#SPJ1
Write an equivalent expression for -3(7+5g)
Answer:
-3(12g)
Step-by-step explanation:
Because if we simplify the 7+5g to 12g because 7+5=12.
Therefore,
-3(7+5g)= -3(12g)
In a right triangle ABC, < B = 90°. If AC=13cm, BC= 5cm, find AB
Answer:
AB = 12cm
Step-by-step explanation:
ABC is the right triangle, that means we can use theorem: AC²=AB²+BC²
AB²=AC²-BC²=13²-5²=169-25= 144
AB=√144
AB=12cm
15. what are the coordinates of point u, point v, and point w
Answer:
is there a picture because this can't be solved without a picture
a=3p+1
Solve for p
please help me solve this
Answer:
Step-by-step explanation:
p= a/3 - 1/3
Please help me!!!!!!!!!
Answer:
m∠TQS = 137°
m∠RQS = 43°
Step-by-step explanation:
It is given that ∠RQT is a straight angle
That means that this angle is 180° and RQT is a straight line
Therefore m∠TQS + m∠RQS = m∠RQT = 180°
Given
m∠TQS = (6x + 20)° and m∠RQS = (2x + 40)°
adding the two angles together will imply
(6x + 20)° + (2x + 40)° = 180°
=> 6x + 20 + 2x + 4 = 180
=> 6x + 2x + 20 + 4 = 180
=> 8x + 24 = 180
=> 8x = 180 - 24= 156
=> x = 156/8 = 19.5
Substitute for x in the angle expressions
m∠TQS = 6x + 20 = 6(19.5) + 20 = 117 + 20 = 137°
m∠RQS 2x + 4 = 2(19.5) + 4 = 39 + 4 = 43°
(or we could subtract m∠TQS from 180 to get 180 - 137 = 43°)
Check if they add up to 180°
137° + 43° is indeed 180°
don’t know what to do
A power function has the formula f(x) = kxⁿ,
A power function is a function that has a single term that is the product of a real number, a coefficient, and a variable raised to a fixed real value. (A coefficient is a value that increases an exponent by a variable.)
A power function has the formula f(x) = kxⁿ, where k and n are both real numbers. You can change the appearance of a power function's graph by changing the values of k and n. As a result, in this graph, n is greater than zero.The Power function produces an integer that has been raised to a particular power. Power is an alternative for the exponent operator in a mathematical equation (^). The Power function only takes two arguments: number and power. Number must be a numeric value that is either a hardcoded constant or a cell reference.Monomial functions:
Linear: y=3x+5
Quadratic: y = x²
Constant: y = 6
Cubic: y = x³+5
Quartic : y = x⁴
Quantic : y = x⁵
Therefore the function with a power function is given by y = k xⁿ
To learn more about power function visit:
https://brainly.com/question/24364138
#SPJ1
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
7b + 6
Step-by-step explanation:
Given expression,
→ 5b + 10 + 2b - 4
Let's solve the expression,
→ 5b + 10 + 2b - 4
→ (5b + 2b) + (10 - 4)
→ 7b + 6
Hence, answer is 7b + 6.
Translate the sentence into an equation or formula.
25 less than the cube of x is equal to four times the sum of y and five
Answer:
x + y y added to 7. 7+ y. The sum of a and b a + b m more than n n + m ... y. 5 or y ÷ 5. The ratio of u to v u v or u ÷ v u separated into 4 equal parts.
Step-by-step explanation im just guessing so if its incorrect sorry:(
Gas mileage is the number of miles you can drive on a a gallon of gasoline. A test of a new car results in 525 miles on 25 gallons of gas. How far could you drive on 40 gallons of gas? What is the car's gas mileage?
40 gallons
[tex]\frac{525}{25} \times 40=840[/tex] miles
Gas Mileage
[tex]\frac{525}{25}=21[/tex] miles per gallon
What is a hour and how manyyyy
Answer:
An hour is a unit of time.
Step-by-step explanation:
An hour is a period of 60 minutes.
1 hour = 60 minutes.
Answer:
an hour is the si unit of time
1 hour = 60 minutes
1 minutes = 60 seconds
pls mark as brainliest
Step-by-step explanation: