Example:
[tex](f+g)(x)=f(x)+g(x)[/tex]
To add this, we can substitute in the functions and combine like terms.
Solving the QuestionWe're given:
[tex]k(x)=5x-6[/tex][tex](k+k)(4)=?[/tex]Add k to k:
[tex](k+k)(x) = k(x)+k(x)\\(k+k)(x) = 5x-6+5x-6\\(k+k)(x) = 10x-12[/tex]
Input x as 4:
[tex](k+k)(4) = 10x-12\\(k+k)(4) = 10(4)-12\\(k+k)(4) = 40-12\\(k+k)(4) = 28[/tex]
Answer[tex](k+k)(4)=28[/tex]
(k+k)(4) is equivalent to 28.
What is function ?If we have two non-empty sets X & Y, then each element of X is relative to at least one element of Y. This relation between elements of two sets is called function.
Addition of two functions : If f(x) & g(x) be two functions, then
(f+g)(x) = f(x)+g(x)
What is the required result ?Given, k(x) = 5x-6
Now, Adding function k with k we get,
(k+k)(x) = k(x)+k(x)
= (5x-6)+(5x-6)
= 5x-6+5x-6
= 10x-12
We have to find, (k+k)(4)
∴ (k+k)(4) = (10×4)-12
= 40-12
= 28
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what are the coordinates of this point help plssssssssssssssss
Answer:
(-2, -4)
Step-by-step explanation:
Use the (x,y) thing:
x = -2
y = -4
therefore, (-2, -4)
Which expression is equivalent to...
Answer:
p^2/r
Step-by-step explanation:
so I have shown every work in the picture attached
please let me know if this doesn't help
Which is the equation of the line with slope 0 passing through the point (-3, -1)?
I'm a kid. and I'm starting 4th grade so I lied to the computer, Anyhoo. Can anyone PLS help me comvert 6/7.
6/7 converted to a decimal is 0.8571
Conversion to decimalsFrom the question, we are to convert the given fraction to a decimal
The given fraction is
6/7
6/7 = 0.8571
Thus,
6/7 expressed as a decimal is 0.8571
Hence, 6/7 converted to a decimal is 0.8571
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manual spent 4.56 on a sandwich and 2.98 on a drink How much did he spend in all? If he paid with a 10$ bill how much change did he get
Manual paid with a $10 bill and he got $2.46 as a change.
What is subtraction?Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. Subtraction is signified by the minus sign, −.
Money spent on sandwich=$4.56 and money spent on drink=$2.98.
We need to find out how much did he spend in all.
That is, the total money spent=4.56+2.98=$7.54
He paid with a $10 bill, he gets change as 10-7.54=$2.46
Hence, he paid with a $10 bill and he got $2.46 as a change.
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the volume of a cube depends on the length of its sides.this can be written in function notation as v(s). what is the best interpretation of v(4) =64
Answer:
Interpretation: A cube with sides of 4 units each has a volume of 64 units³.
Explanation:
As v(s) represents the volume of the cube, s represents the length of the sides.
∴ v(4) represents the volume of a cube with sides of units, and the volume is 64 units³
(x-8)^2 i need step by step please like eveyone gets x2 -16x +64 i dont get
how
Answer:
x²-16x+64
use formula =a²-2ab+b²x²-2.x.8+8² (for knowledge 2 × 8 = 16)x²-16x+64Answer:
(x -8)² = x² -16x +64
Step-by-step explanation:
A lot of math is about pattern recognition. For many of the patterns you are asked to recognize, it is helpful to be very familiar with basic math facts: addition facts, multiplication facts, and the squares and cubes of small integers.
All of algebra is based on a few properties of arithmetic and equality. One that is important here is the distributive property.
__
expanding a product of binomialsOne of the patterns that is used with quadratics is the square of a binomial.
(a - b)² = a² -2ab +b²
This is the result of applying the distributive property several times.
First of all, the exponent indicates repeated multiplication:
(a -b)² = (a -b)×(a -b)
The distributive property tells you each term outside parentheses multiplies each term inside:
= a×(a -b) -b×(a -b)
= a·a -a·b -b·a +b·b . . . . . and again
Now, we collect terms, recognizing that ab=ba.
= a² -2(a·b) +b² . . . . . . . using exponents for repeated multiplication
So, the pattern for the square of a binomial is ...
(a -b)² = a² -2ab +b²
__
using the patternFor your specific case, ...
a = xb = 8(x -8)² = x² -2(x)(8) +8² . . . . . . using the above pattern
(x -8)² = x² -16x +64
_____
Additional comment
If you want to do this without using the pattern, just make use of the distributive property:
[tex](x-8)^2=(x-8)(x-8)\\\\=x(x -8) -8(x-8)\\\\=x^2-8x-(8x-64)\\\\=x^2-8x-8x+64\\\\\boxed{(x-8)^2=x^2-16x+64}}[/tex]
__
While the distributive property is the fundamental property involved, some find it helpful to remember a mnemonic that gets you to the same result for the product of binomials: FOIL. The letters refer to First, Outer, Inner, Last, and they remind you of the terms that make up the expansion of the product:
(x -8)(x -8) -- First: x·x = x²(x -8)(x -8) -- Outer: x·(-8) = -8x(x -8)(x -8) -- Inner: (-8)·x = -8x(x -8)(x -8) -- Last: (-8)(-8) = 64Then the product is ...
(x -8)² = x² -8x -8x +64 = x² -16x +64
__
Of course, the distributive property is involved in what we call "collecting terms."
-8x -8x = (-8-8)x = -16x
The variable is factored out using the distributive property, then the coefficients are added to simplify the expression in parentheses.
4. Use the formula for the area of a circle to derive the formula for the area of a sector.
The area of a circle to derive the formula for the area of a sector will be (θ/2π) x (area of the circle).
What is the area of the sector?Let r be the radius of the circle. Then the area of the circle will be
Area = πr²
Let r is the radius of the sector and θ be the angle subtends by the sector at the center. Then the area of the sector of the circle will be
Area = (θ/2π) πr²
Area = (θ/2π) x (area of the circle)
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if 300 equals 9 and 500 equals 16 what is the pattern? and what will 7 and 18 equal?
Step-by-step explanation:
hope you can understand
Which is the graph of f(c)=1/4(4)^x?
Answer: The graph shown
Step-by-step explanation:
Another graph of the function is attached in this answer.
y=2x^2-4x-3
Solve quadratic questions
By applying the quadratic formula we conclude that the roots of the quadratic equation y = 2 · x² - 4 · x - 3 are 1 + 0.5√10 and 1 - 0.5√10, respectively.
How to find the roots of a quadratic equation
All quadratic equations of the form a · x² + b · x + c = 0 have two roots that can be found by using the quadratic formula:
[tex]x = \frac{-b \pm \sqrt{b^{2}-4\cdot a \cdot c}}{2\cdot a}[/tex] (1)
If we know that a = 2, b = - 4 and c = - 3, then the roots of the quadratic equations are:
[tex]x = \frac{4 \pm \sqrt{(-4)^{2}-4\cdot (2) \cdot (- 3)}}{2\cdot (2)}[/tex]
[tex]x = 1 \pm \frac{\sqrt{40}}{4}[/tex]
[tex]x = 1 \pm \frac{\sqrt{10}}{2}[/tex]
By applying the quadratic formula we conclude that the roots of the quadratic equation y = 2 · x² - 4 · x - 3 are 1 + 0.5√10 and 1 - 0.5√10, respectively.
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What is the solution to this system of equations?
Negative 3 x + 5 y = negative 2. 3 x + 7 y = 26.
(4, 2)
(2, 3 and one-third)
no solution
infinitely many solution
The solution to the system of equation is (-4 , 2) , Option A is the right answer.
What are System Of equation ?A set of equation whose factors are common are called system of equations.
It is given in the question
3x +5y = -2
3x +7y = 2
On solving this we get
-2y = -4
y = 2
On substitution in any equation
x = -4
Therefore solution to the system of equation is (-4 , 2) , Option A is the right answer.
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Answer:
A.
Step-by-step explanation:
took tha quiz
The value of the expression 2x2/x+(100-15x) when x=5 is
Answer:
27
Step-by-step explanation:
Equations Of Parabolas (Conics) Unscramble
The match is shown in the picture for the function of a parabola and the graph of a parabola.
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
As we know the standard form of the parabola is:
y = a(x - h)² + k
If a > 0 (parabola opens upwards)
If a < 0 (parabola opens downwards)
or
x = a(y - h)² + k
If a > 0 (parabola opens right side)
If a < 0 (parabola opens left side)
Here (h, k) is the vertex of the parabola and a is the leading term.
Thus, the match is shown in the picture for the function of a parabola and the graph of a parabola.
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The volume of a tree stump can be modeled by considering it as a right cylinder. Jin measures its radius as 11 in and its volume as 13685 cubic inches. Find the height of the stump in inches. Round your answer to the nearest tenth if necessary.
If the radius of tree stump is 11 inches and volume is 13685 cubic inches then the height will be equal to 36 inches.
Given Radius of tree stump is 11 inches and volume is 13685 cubic inches.
We know that the volume of cylinder will be equal to π[tex]r^{2} h[/tex].
Volume which is given as 13685 cubic inches.
13685=π[tex]r^{2}h[/tex]
π=22/7
13685=π[tex](11)^{2}[/tex]h
h=13685*7/22*121
h=95795/2662
h=35.98
if we round it to nearest tenth then the value of h be 36 inches.
Hence if radius is 11 inches, volume is 13685 cubic inches then the height of tree stump will be 36 inches.
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Answer:36
Step-by-step explanation:
3
cky has a board that is 2 feet long. She needs to cut the board into 11 pieces of equal length. How long
ould each piece be?
0.223 feet
0.25 feet
0.5 feet
0.75 feet
ase select the best answer from the choices provided
A
В
C
D
Answer:
0.223 is the answers for the question but I got this answer 0.181
Step-by-step explanation:
please mark me as brainlest
Each serving of a cereal is 80 calories.which expression can be used to find the number of calories In 3 servings
Answer:
[tex]80\times3[/tex]
Step-by-step explanation:
Based on the given conditions, formulate: [tex]80\times3[/tex]
Calculate the product or quotient: 240
get the result: 240
Answer: 240
To find this answer, we had to use the expression 80 * 3, therefore making it the answer.
Answer:
240
Step-by-step explanation:
80*3=240
so u multiply the equation
Use the graph to write the inequality that represents the shaded region
Answer:
4/2 is the wrong answer
Step-by-step explanation:
because it is
-750 DEGREE TO RADIAN
2 more than product of a number and 9 is 8. variable w
Answer:
w (number) = 2/3
Step-by-step explanation:
Variable w means use the letter w as the unknown number :
This is the equation made from the question :
2+(9w) = 8
Let's subtract 2 from both sides :
9w = 6
Divide both sides by 9 :
w = 6/9
Simplify fraction :
w = 2/3
Hope this helped and have a good day
Which statement is true about this equation Y=-3x2+4x+-11
Answer:
For plato users, the answer would be letter C.
Step-by-step explanation:
A.
It represents neither a relation nor a function.
B.
It represents a relation only.
C.
It represents both a relation and a function.
D.
It represents a function only.
This equation represents both a relation and a function.
Took the test, hope this helps!
Step-by-step explanation:
Renate launched an object vertically from a point that is 58.9 meters above ground level with an initial velocity of 21.6 meters per second. This situation can be represented by the equation h=−4.9t2+21.6t+58.9, where h is the height of the object in meters and t
is the time in seconds after the object is launched.
What is the maximum height of the object?
The maximum height of the object is 82.7034 from the ground
What is Velocity ?Velocity is the measure of movement of an object with respect to time.
It is measured in m/sec
h = -4.9t²+21.6t +58.9
dh/dt = -9.8t +21.6
At maximum height , velocity = 0
therefore
-9.8t +21.6 = 0
9.8t = 21.6
t = 2.204 sec
h = -4.9 (2.204)²+ 21.6 * 2.204 +58.9
h = -23.803 +47.606 +58.9
h = 82.7034 from the ground
h = 23.80 from the point it is launched.
The maximum height of the object is 82.7034 from the ground
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What is the solution of
x²-1
2
x2 +5X+4
<0?
Answer:
Step-by-step explanation:
Find the x- and y-intercepts of the parabola y=x2+10x+4
Answer:
x-intercepts: -5 +/-[tex]\sqrt{21}[/tex]. y-intercept: 4
Step-by-step explanation:
For x-intercepts use the quadratic equation
[tex]x= (-b +/-\sqrt{b^2-4ac} )/2a[/tex]
Fill in your values:
[tex]x= (-10 +/-\sqrt{100-16} )/2[/tex]
And solve
[tex]x=-5 +/- \sqrt{21}[/tex]
For y-intercepts set x=0 and solve. In this case, setting x= 0 gives you y=4.
URGENT 30 points I need help
Answer:
- 112 + 100 n
Step-by-step explanation:
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1 )d
~~~~~~~
[tex]a_{1}[/tex] = - 12
d = 100
[tex]a_{n}[/tex] = - 12 + 100( n - 1 )
[tex]a_{n}[/tex] = - 12 + 100n - 100
[tex]a_{n}[/tex] = - 112 + 100 n
The weight of corn chips dispensed into a 24-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 25 ounces and a standard deviation of 0.8 ounce. What proportion of the 24-ounce bags contain more than the advertised 24 ounces of chips?
The percentage of 24-ounce bags containing more than the advertised 24 ounces of chips will be -1.25.
What is the z score?The z-score is a numerical assessment of a value's connection to the mean of a set of values, expressed in terms of standards from the mean, that is used in statistics.
Given data;
Mean,μ = 25
Standard deviation,σ=0.8
The Z score is found as;
[tex]\rm Z = \frac{x-\mu}{ \sigma } \\\\ Z = \frac{24-25}{0.8} \\\\ Z= -1.25[/tex]
The P-value for the obtained z score is .2113.
Hence the percentage of 24-ounce bags containing more than the advertised 24 ounces of chips will be -1.25.
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Find the time diffrence.
If u click there will be pic (very easy im just lazy lol)
Step-by-step explanation:
2 hours and 45 minutes.
8:45am + 2 hours = 10:45am
10:45am + 45 minutes = 11:30 am
Find the inverse of the function.
y = -3x - 9
Write your answer in the form ax + b. Simplify any fractions.
y =
Answer: [tex]y=-\frac{1}{3} x-3[/tex]
Step-by-step explanation:
To find the inverse of a function you must first swap the places of x and y
[tex]x=-3y-9[/tex]
Now solve for y
Step 1: Flip the equation.
[tex]-3y-9=x[/tex]
Step 2: Add 9 to both sides.
[tex]-3y-9+9=x+9\\-3y=x+9[/tex]
Step 3: Divide both sides by -3.
[tex]\frac{-3y}{-3} =\frac{x}{-3} +\frac{9}{-3} \\y=-\frac{1}{3} x-3[/tex]
I’m so confused on what numbers l should put into the boxes
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The lines for the given statements can be plotted as shown below.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is y-intercept.
The lines for the given statements can be plotted as shown below.
The coordinate grid can be filled as,
1)
x 0 3 1
y 3 0 2
2.)
x 0 1 -1
y 1 0 2
3.)
x 0 4 -1
y -2 0 2
4.)
x 0 1 1
y -2 0 -2
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Question 7 of 10 Which system of inequalities is graphed below? 10 -10 -8- 8 10 OA. y > X - 4 y < x +6 OB. VS X - 4 y < x +6 O c. y2 x -4 y > x + E OD. VS X - 4 y > x2 + 6
Because in both graphs the shaded region is above the curve, the correct option is C.
Which pair of inequalities is graphed?
On the graph we can see two parabolas, such that the y-intercepts of these are:
y = 6
y = -4
So we just need to find the pair of options with these y-intercepts, and noticing that for both cases, we must have:
y > parabola.
Because both shaded regions are above the parabolas.
The only option that meets these requirements is option C. Where there is a mistake, as you can see both curves have dashed lines, and always when we have dashed lines we should use the symbols > or <, while in that option we have a ≥ symbol
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