The only function rule that works is A.
Instead of using f(x) - use y
Then place the numbers in for x and see which are true. The answer is A
A new hospital tracked the number of births during its first 6 months of operation, as shown in the table.
A 2-column table with 6 rows. The first column is labeled month with entries 1, 2, 3, 4, 5, 6. The second column is labeled number of births with entries 137, 110, 93, 70, 65, 77.
Find a quadratic function that models the data. Round numerical values to the nearest whole number
Answer:
y = 4x² - 43x + 178
Step-by-step explanation:
Given that data:
1 __ 137
2 __ 110
3 __ 93
4 __ 70
5 __ 65
6 __ 77
Usibg technology, the quadratic regression equation obtained is written in the form:
Ax² + Bx + C
A = 4.34 = 4 ( nearest whole number)
B = - 43.46 = - 43 (nearest whole number)
C = 178.3 = 178 ( nearest whole number)
Hence, the quadratic model is
y = 4x² - 43x + 178
By rounding the coefficients to the nearest whole number, the quadratic function that models the data is[tex]f(x) = 5x^2 - 42x + 174[/tex]
How to Find a quadratic function that models the data.To find a quadratic function that models the data, use a quadratic equation of the form:
[tex]f(x) = ax^2 + bx + c[/tex]
Let's use the given data points to form a system of equations and solve for the coefficients a, b, and c.
Using the first data point (month 1 with 137 births):
[tex]f(1) = a(1)^2 + b(1) + c = 137[/tex]
a + b + c = 137 (Equation 1)
Using the second data point (month 2 with 110 births):
[tex]f(2) = a(2)^2 + b(2) + c = 110[/tex]
4a + 2b + c = 110 (Equation 2)
Using the third data point (month 3 with 93 births):
[tex]f(3) = a(3)^2 + b(3) + c = 93[/tex]
This simplifies to:
9a + 3b + c = 93 (Equation 3)
Solve this system of equations will give us the values of a, b, and c.
Subtract Equation 1 from Equation 2
3a + b = -27 (Equation 4)
Subtract Equation 1 from Equation 3
8a + 2b = -44 (Equation 5)
Now solve Equations 4 and 5 simultaneously.
Multiply Equation 4 by 2 and subtracting it from Equation 5:
8a + 2b - (6a + 2b) = -44 - (-54)
2a = 10
Divide both sides by 2:
a = 5
Now substitute the value of a back into Equation 4:
3(5) + b = -27
15 + b = -27
Subtract 15 from both sides:
b = -42
Finally, substitute the values of a and b into Equation 1
5 + (-42) + c = 137
-37 + c = 137
Add 37 to both sides:
c = 174
Therefore, the quadratic function that models the data is:
[tex]f(x) = 5x^2 - 42x + 174[/tex]
Rounding the coefficients to the nearest whole number, the quadratic function becomes:
[tex]f(x) = 5x^2 - 42x + 174[/tex]
Learn more on quadratic on https://brainly.com/question/1214333
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The side length of the cube is 5 cm. Find the volume of the cube.
Answer:
125 cm³
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Volume of a Cube Formula: V = a³
a is a side lengthStep-by-step explanation:
Step 1: Define
Identify variables
a = 5 cm
Step 2: Find Volume
Substitute in variables [Volume of a Cube Formula]: V = (5 cm)³Evaluate exponents: V = 125 cm³Answer:
[tex]\huge\boxed{V=125cm^3}[/tex]
Step-by-step explanation:
The formula of a volume of a cube with edge [tex]a[/tex]:
[tex]V=a^3[/tex]
We have [tex]a=5cm[/tex].
Therefore the volume is:
[tex]V=(5cm)^3=5cm\cdot5cm\cdot5cm=125cm^3[/tex]
2. A rectangle has length 13 and width 10. The length and the width of the rectangle are each
increased by 2. By how much does the area of the rectangle increase? *
50
20
38
35
FACTOR....
x^2 + 10× - 2400 = 0
Answer:
x= -5 + 5[tex]\sqrt{97}[/tex], x= -5 - 5[tex]\sqrt{97}[/tex]
Step-by-step explanation:
Since this quadratic is set to zero, we can use the quadratic formula to solve this.
x^2 + 10x - 2400 = 0
Quadractic formula = x= -b +- [tex]\sqrt{b^2 - 4ac}[/tex] /2a
For this equation:
a= 1, b=10, c=-2400
Plug these numbers into the equation and solve.
x= -10 +- [tex]\sqrt{10^2 - 4(1)(-2400}[/tex])/2(1)
x= -10 +- [tex]\sqrt{100 + 9,600}[/tex]/2
x= -10 +- [tex]\sqrt{9,700}[/tex]/2
x= -10 +- [tex]\sqrt{2^2 * 5^2 * 97}[/tex]/2
x= -10 +- 5 * 2[tex]\sqrt{97}[/tex]/2
x= -10 +- 10[tex]\sqrt{97}[/tex] / 2
Divide by 2.
x= -5 +- 5[tex]\sqrt{97}[/tex]
Answer:
x= -5 + 5[tex]\sqrt{97}[/tex] or x= -5 - 5[tex]\sqrt{97}[/tex]
Find the TWO integers whos product is -12 and whose sum is 1
Answer:
[tex] \rm Numbers = 4 \ and \ -3.[/tex]
Step-by-step explanation:
Given :-
The sum of two numbers is 1 .
The product of the nos . is 12 .
And we need to find out the numbers. So let us take ,
First number be x
Second number be 1-x .
According to first condition :-
[tex]\rm\implies 1st \ number * 2nd \ number= -12\\\\\rm\implies x(1-x)=-12\\\\\rm\implies x - x^2=-12\\\\\rm\implies x^2-x-12=0\\\\\rm\implies x^2-4x+3x-12=0\\\\\rm\implies x(x-4)+3(x-4)=0\\\\\rm\implies (x-4)(x+3)=0\\\\\rm\implies\boxed{\red{\rm x = 4 , -3 }}[/tex]
Hence the numbers are 4 and -3
Answer:
Step-by-step explanation:
If the product of 2 integers is -12, then that equation looks like this:
xy = -12
If the sum of those same 2 integers in 1, then that equation looks like this:
x + y = 1
Let's solve the second equation for x and plug it into the first equation. Solving the second equation for x gives us
x = 1 - y and plug that into the first equation in place of x to get:
(1 - y)y = -12 and
[tex]y-y^2=-12[/tex] Now move everything over to one side and factor to find y:
[tex]-y^2+y+12=0[/tex] and the 2 values for y are
y = -3 and y = 4. Let's see what happens when we solve for x.
If xy = -12 and y is -3:
x(-3) = -12 so
x = 4
If xy = -12 and y is4:
x(4) = -12 so
x = -3
So it looks like the 2 integers are -3 and 4
PLEASE HELP !!!!! Which type of conic section is described by the following equation?
(y - 3)2/4^2- (x+2)^2/6^2=1
A. Circle
B. Parabola that opens up
C. Parabola that opens down
U O
D. Hyperbola opening left and right
E. Ellipse
E Hyperbola opening up and dow
Answer:
F
Step-by-step explanation:I just took the test
Determine the solution on the following equation
Answer:
x = 3
Step-by-step explanation:
Step-by-step explanation:
3(8x-8)/2=64
3(8x-8)=64×2
24x-24=128
24x=128+24
24x=152
24x/24=152/24
x=6.3
Two cars started from a point and traveled in opposite directions; each
car has traveled some miles as shown on the number line. Find the
distance between the two cars.
Answer:
Hey, could you please add the number line to the question too
What is the scale factor from ABC to DEF?
Within similar triangles, the angles are the same. So, we need to look at the side lengths then.
72 to 12
66 to 11
42 to 7
In each pair of corresponding side lengths, the original side length from triangle ABC is divided by 6 (or multiplied by 1/6) to get the smaller side length on triangle DEF.
The scale factor from ABC to DEF is 1/6.
Hope this helps!
For what value of b will f(x) = x^2 + bx + 400 have -20 as its only zero? Record your answer and fill in the bubbles on your answer document.
The polynomials f(x) = x^2 + bx + 400 have -20 as its only zero then the value of b is 40.
The polynomials f(x) = x^2 + bx + 400 have -20 as its only zero
Then x=-20
What is the zero of a polynomial?The zeros of a polynomial p(x) are all the x-values that make the polynomial equal to zero.
x=-20 is the zero of the given polynomial
Therefore it satisfies the given polynomial
[tex]f(-20)=(-20)^2+b(-20)+400[/tex]
[tex]0=400-20b+400\\800-20b=0\\-20b=-800\\b=\frac{-800}{-20} \\b=40[/tex]
Therefore the value of b is 40.
To learn more about the zeros of the polynomials visit:
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HELP ASAP 10 POINTS AND BRAINLIST AND 5 STAR AND THANKS BUT IF CORRECT
Step-by-step explanation:
hope it helps you..........
Answer:
[tex](\frac{2}{5} )^{3}[/tex] = [tex]\frac{8}{125}[/tex] [tex]cm^{3}[/tex]
Step-by-step explanation:
Three consecutive odd integers have a sum of 27. Find the integers.
[tex]\sf \bf {\boxed {\mathbb {GIVEN:}}}[/tex]
Sum of three consecutive odd integers = [tex]27[/tex]
[tex]\sf \bf {\boxed {\mathbb {TO\:FIND:}}}[/tex]
The values of the three integers.
[tex]\sf \bf {\boxed {\mathbb {SOLUTION:}}}[/tex]
[tex]\sf\purple{The\:three\:consecutive \:odd\:integers\:are\:7,\:9\:and\:11.}[/tex]
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}[/tex]
Let us assume the three consecutive odd integers to be [tex]x[/tex], [tex](x+2)[/tex] and [tex](x+4)[/tex].
As per the condition, we have
[tex]Sum \: \: of \: \: the \: \: three \: \: consecutive \: \: odd \: \: integers = 27[/tex]
[tex]➺ \: x + (x + 2) + (x + 4) = 27[/tex]
[tex]➺ \: x + x + 2 + x + 4 = 27[/tex]
Now, collect the like terms.
[tex]➺ \: (x + x + x) + (2 + 4) = 27[/tex]
[tex]➺ \: 3x + 6 = 27[/tex]
[tex]➺ \: 3x = 27 - 6[/tex]
[tex]➺ \: 3x = 21[/tex]
[tex]➺ \: x = \frac{21}{3} \\[/tex]
[tex]➺ \: x = 7[/tex]
Therefore, the three consecutive odd integers whose sum is [tex]27[/tex] are [tex]\boxed{ 7 }[/tex], [tex]\boxed{ 9 }[/tex] and [tex]\boxed{ 11 }[/tex] respectively.
[tex]\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}[/tex]
[tex]⇢ 7 + 9 + 11 = 27[/tex]
[tex]⇢ 27 = 27[/tex]
⇢ L. H. S. = R. H. S.
[tex]\sf\blue{Hence\:verified.}[/tex]
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35ヅ}}}}}[/tex]
In an indirect proof, you prove an "if-then" statement is true by assuming the statement is false (stating the inverse or converse), and then disproving the false statement. You want to prove the statement shown below in an indirect proof. What statement should you prove is false?
Statement to Prove True: If a figure has exactly three sides, then it is a triangle.
Statement to Prove False:
Answer:
Step-by-step explanation:
Triangle ABC is congruent to LMN. Find the value of x. Please and thank you!
Warning: if you give an answer that is NOT related to the question at all then I will report you - FIND THE VALUE OF X
Answer:
x = 9
Step-by-step explanation:
The ratios of corresponding sides are equal, that is
[tex]\frac{BC}{MN}[/tex] = [tex]\frac{AB}{LM}[/tex] , substitute values
[tex]\frac{x}{15}[/tex] = [tex]\frac{6}{10}[/tex] ( cross- multiply )
10x = 90 ( divide both sides by 10 )
x = 9
15 years from now Renu will be four times her present age. What is Renu's present age?
Answer:
5 years
Step-by-step explanation:
(x+15)=4x
15=4x-x
15=3x
5=x
2(4+2x)≥5x+5 solve inequality
Answer:
x ≤ 3
Step-by-step explanation:
2(4+2x)≥5x+5
8+4x≥5x+5
4x-5x≥5-8
-x≥-3
x ≤ 3
[tex]\tt\displaystyle\2(4+2x)\geq 5x+5\\\\8+4x\geq 5x+5\\\\4x-5x\geq 5-8\\\\-x\geq -3\\\\x\leq 3 \\\\Answer: x\leq 3 \quad or \quad x\in(-\infty;3][/tex]
The two
triangles are similar.
What is the value of x?
Enter your answer in the box:
Answer:
x = 5
Step-by-step explanation:
Sides of large triangle: 4x and 15
Corresponding sides of small triangle: 3x + 1 and 12
[tex] \dfrac{4x}{15} = \dfrac{3x + 1}{12} [/tex]
[tex] 60 \times \dfrac{4x}{15} = 60 \times \dfrac{3x + 1}{12} [/tex]
[tex] 16x = 15x + 5 [/tex]
[tex] x = 5 [/tex]
What is 6 1/3 divied by 1/6
Answer:
38
Step-by-step explanation:
6⅓÷⅙
change 6⅓ to improper fraction
19/3÷1/6
keep the first fraction, change the division sign to multiplication and reciprocate/flip the second fraction
19/3× 6/1
the denominator 3 and numerator 6 will simplify/cancel each other
the new fraction is now: 19/1 × 2/1
there is no need to multiply the denominators because it will still be equal to 1 so we just need to multiply the numerators by each other
19×2=38 OR 38/1 (both answers are the same)
if f(x)= 3^x+10x and g(x)= 2(x) = 2x - 4 find (f+g)(x)
Answer:
(f + g)(x) = 3^x + 12x -4
Step-by-step explanation:
Here, we want to get the value of (f + g)(x)
Mathematically, we have this as;
(f + g)(x) = f(x) + g(x)
= 3^x + 10x + 2x-4
= 3^x + 12x -4
Printed Pages in Color Time (min), x 2 6 8 18 Number of pages, y 3 9 12 27 What is the constant of variation?
Answer:
3/2
Step-by-step explanation:
formula k = y/x
comes from
y = kx
k = constant of variation
when y = 3 , x = 2
k = 3/2
There are five students standing in a line with their hats. Suddenly the wind picks up the hats and randomly assigns each hat to a student. What is the probability that no student will get his or her own hat
Answer:
The probability of a person getting their own hat is 1/5 or 20%.
Step-by-step explanation:
If each person has one hat the chances (the probability) of them getting their own hat would be 20%. The chances (the probability) of them getting a hat that belongs to one of the other four students would be 80%. Due to there being 5 hats each person owns 1 hat so there would be a 1 out of 5 chance of them getting their own hat.
What is the mean from the frequency conceded goals frequency 0 2 1 8 2 4 3 10 4 6
Answer:
Mean = 2.33
Step-by-step explanation:
Given that,
conceded goals : 0 1 2 3 4
Frequency : 2 8 4 10 6
Mean,
[tex]M=\dfrac{\Sigma fx}{\Sigma f}\\\\M=\dfrac{0\times 2+1\times 8+2\times 4+3\times 10+4\times 6}{2+8+4+10+6}\\\\=\dfrac{70}{30}\\\\M=2.33[/tex]
So, the required mean is 2.33.
Please help I will mark brainliest- I already know it’s not the last two- please help!
Answer:
Traversable because it has exactly two odd nodes
Step-by-step explanation:
There is a rule that says it is traversable if it has exactly 2 odd nodes. The are other rule where it can be traversable is if has no odd nodes.
Also if we let the starting point be D and the ending point be B we can travel the network in such way that each edge is only traveled once which is the definition that the network is traversable.
So I will do this by starting at D, then travel to A using the outside edge, then travel to back to D using inside edge, then travel to C, then travel to B, then travel to A using outside edge, and then back to B from A using inside edge.
the quadratic function f(x) = ax² + bx + c has tge minimum point (-2,-9) ans f(-1) = -7 Find (a) values of a,b and c
i'll mark u brainliest pls,help
Hello again,
"katie deleted your answer to the question Hello,a=2, b=8, c=-1Indeed,y=f(x)=ax...
You've been warned"
Answer is a=2, b=8 and c=-1
Indeed:
y=f(x)=ax²+bx+c
Since (-2,-9) is the vertex,
y=k*(x+2)²-9
Or f(-1)=-7 ==> -7=k*(-1+2)²-9 ==> k=2
f(x)=2(x+2)²-9=2*(x²+4x+4)-9=2x²+8x+8-9
f(x)=2x²+8x-1
A proof: the picture is following.
Which of these is an example of a literal equation?
A. 4x + 7 = 22
B. 5+ 20 = 52
C. ax - by = k
D. 2x + 7y
Help, someone please lol
Answer:
2x+5x^2=1
2x+5x*5x=1
2x+25x=1
27x=1
1/27=x
Hope This Helps!!!
Answer:
D. 24
Hope it helps!
Help me please
I will mark you as brainliest
Answer:
In picture
Step-by-step explanation:
Brainliest please~
[tex](0,3)[/tex] and [tex](1,-2)[/tex]
Equation: (refer the image below)
Slope:
[tex]m=\frac{3+2}{0-1}[/tex]
[tex]m=-5[/tex]
Equation:
[tex]y=5x-b[/tex]
[tex]3=b[/tex]
Substitute (0,3)
Point: [tex](1,-2)[/tex]
For the function y=log(x-2)+1 which of the following statements is true? (see picture) (WILL GIVE BRAINLIEST)
Answer:
B.
Step-by-step explanation:
Question
The quotient of a number and 5 has a result of 2. What is the number
Answer:
Probably 10
Step-by-step explanation:
10/5=2
Solve the qn in attachment .
Answer:
[tex]\implies \dfrac{ -4x+7}{2(x-2) }[/tex]
Step-by-step explanation:
The given expression to us is ,
[tex]\implies \dfrac{\frac{ 3}{x-1} -4 }{ 2 -\frac{2}{x-1}}[/tex]
Now take the LCM as ( x - 1 ) and Simplify , we have ,
[tex]\implies \dfrac{\frac{ 3 -4(x-1) }{x-1} }{ \frac{2-2(2x-1)}{x-1}}[/tex]
Simplifying further , we get ,
[tex]\implies \dfrac{ -4x+7}{2(x-2) }[/tex]
Hence the second option is correct.
Answer:
[tex] \frac{ \frac{3}{x - 1} - 4}{2 - \frac{2}{x - 1} } \\ = \frac{ \frac{3 - 4(x - 1)}{x - 1} }{ \frac{2(x - 1)}{x - 1} } \\ = \frac{3 - 4x + 4}{2x - 2} \\ \frac{ - 4x + 7}{2(x - 1)} \\ option \: b \: is \: your \: answer \\ thank \: you[/tex]
