The value of a and b in the function f(x) = √ x+2 and g(x) = ax + b , is a = 0 and b = 2 .
In the question ,
it is given that ,
the function f(x) = √(x+2) and the function g(x) = ax + b
also given that
fog(1) = 2
f(g(1)) = 2
f(a + b) = 2 .... because g(1) = a + b
√(a + b +2) = 2
Squaring both the sides
a + b + 2 = 4
a + b = 2 .......(1)
also given that
g(-1) = 2
a(-1) + b = 2
-a + b = 2 .....(2)
Adding equation (1) and (2) , we get
2b = 4
b = 2
Substituting b = 2 in the a + b = 2 , we get
a + 2 = 2
a = 2 - 2
a = 0
Therefore , The value of a and b in the function f(x) = √ x+2 and g(x) = ax + b , is a = 0 and b = 2 .
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1. Find the y-intercept of the line passing through the points A (3, -2) and B (-1, 3). (5 pts)
Answer:
-1.25
Step-by-step explanation:
m=
[tex]y2 - y1 \div x2 - x1[/tex]
3- (-2)÷ -1-3
5/-4
m=-1.25
A square with sides length x are cut out of each corner of a rectangular piece of cardboard measuring 5ft by 8ft. The resulting piece of cardboard is then folded into a box without a lid. Find the volume of the largest box that can be formed this way.
The volume of the largest box that can be made from the rectangular cardboard obtained by using the value of the derivative of the function for the volume at the extremum point is 18 cubic feet
What is an extremum point in mathematics?An extremum of a function is the point where the value of the function is a maximum or a minimum.
The side length of the cut out squares = x
The width of the rectangular cardboard = 5 feet
The length of the rectangular cardboard = 8 feet
The length of the side of the cut square = 8 - 2·x
Width of the side of the cut square = 5 - 2·x
Height of the cut square = x
Volume of the cut square, V = (8 - 2·x) × (5 - 2·x) × x = 4·x³ - 26·x² + 40·x
When the volume of the box is largest, we have;[tex]V' = \dfrac{d}{dx} \left(4\cdot x^3 - 26\cdot x^2 + 40\cdot x\right) = 12\cdot x^2 - 52\cdot x + 40=0[/tex]
12·x² - 52·x + 40 = 0
3·x² - 13·x + 10 = 0
Which gives;
(3·x - 10)·(x - 1) = 0
The dimensions of the cut square that gives the maximum volume are therefore;
x = 1 or x = 10/3
When x = 10/3, we have;
V = (8 - 2×(10/3)) × (5 - 2×(10/3)) × (10/3) ≈ -200/27 < 0
When x = 1, we have;
V = (8 - 2×1) × (5 - 2×1) × 1 = 18
The value of x that gives the maximum volume is therefore, x = 1
The dimensions of the box that give the maximum volume are therefore;
Height = x = 1
Length = 8 - 2×1 = 6
Width = 5 - 2 × 1 = 3
The dimensions of the box that gives the maximum volume are;
Height = 1 ft
Length = 6 ft
Width = 3 ft
The volume of the largest box that can be formed is 18 cubic feet
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which expressions are equivalent to 3^4/9/3^2/9? select all that apply
Answer:
Two correct answers: subtracting exponents and
3^ 2/9
Step-by-step explanation:
To divide, subtract exponents. To subtract fractions keep the bottom number the same and subtract the top number. See image.
Shayla is tracking the weight of the smallest puppy in a liter. use the table to write a linear function that model’s the puppy’s growth
The linear function that models the puppy's growth is written as: y = 3x + 3.
How to Write the Equation of a Linear Function?The values we need to find before we can write he linear function that models a situation, are:
The slope = mThe y-intercept = bThe linear function would be expressed as y = mx + b, which is in the slope-intercept form.
The table of the puppy's growth that Shayla is tracking is shown below. Using two points on the table, say, (0, 3) and (1, 6):
Slope (m) = change in y / change in x = (6 - 3)/(1 - 0)
Slope (m) = 3/1 = 3
Substitute m = 3 and (0, 3) into y = mx + b to find b:
3 = 3(0) + b
3 = 0 + b
3 = b
b = 3
To write the linear function, substitute m = 3 and b = 3 into the equation, y = mx + b:
y = 3x + 3
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Answer: A
Step-by-step explanation: FLVS question the answer is A
compare 5.9 and 152 using <, > or =
Answer:
Step-by-step explanation:
please help me ..............................!!!
Answer:
I hope this will be helpful for you.
0 (zero)
Step-by-step explanation:
[tex]{ \blue{ \sf{ {5}^{ - 3} \times {2}^{4} \times {5}^{3} \times {2}^{ - 5}}}} [/tex]
Arrange the like terms in order
[tex]{ \blue{ \sf{ {5}^{ - 3} \times {5}^{3} \times {2}^{4} \times {2}^{ - 5}}}} [/tex]
This is in the form of [tex]{ \red{ \sf{ {a}^{m} \times {a}^{n} = {a}^{m + n}}}} [/tex]
[tex]{ \blue{ \sf{ {5}^{ - 3 + 3} \times {2}^{4 + ( - 5)}}}} [/tex]
[tex]{ \blue{ \sf{ {5}^{0} \times {2}^{4 - 5}}}} [/tex]
[tex] { \blue{ \sf{0 \times {2}^{ - 1}}}} [/tex]
[tex]{ = \blue{ \sf{0}}}[/tex]
Any number which is multiplied with zero is zero itself.
A giant tortoise moves at a slow but steady
pace. It takes the giant tortoise 1 hour to travel
2 miles. ¿How many miles (mi) a tortoise
travels in ¼ hour? Use the bar diagram to help
you.
According to the information, it can be inferred that the turtle travels 0.5 miles in a quarter of an hour (1/4 hours).
How to find the distance that the tortoise travels in a quarter of an hour (1/4 hours)?To find the distance that the tortoise travels in a quarter of an hour we must perform the following operations and take into account the information provided.
1 hour = 2 miles1/2 hour = 1 mile1/4 hour = 0.5 miles1/8 hour = 0.25 milesTo verify that the turtle takes 1/4 of an hour to travel 0.5 miles, we must divide the total number of miles it travels in one hour by 4, because we want to identify how much distance it travels in a quarter of the time, as shown below:
2 miles / 4 = 0.5 miles
Based on the above, we can infer that the tortoise travels 0.5 miles in 1/4 hour.
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I need help in answering this question
Answer:
2 6 12 20,000
6 18 36 60,000
Step-by-step explanation:
The bottom number is 3 times the top number.
Given the equation F=95C+32 where C is the temperature in degrees Celsius and F is the corresponding temperature in degrees Fahrenheit, and the following ordered pairs:
(25,F1), (−30,F2)
The corresponding values of F1 and F2 in the ordered pairs are 77 degrees Fahrenheit and -22 degrees Fahrenheit
How to use the equation to convert from degrees Celsius to degrees Fahrenheit?
Given: the equation F=9/5C+32 and ordered pairs: (25, F1), (−30, F2)
In order to convert the given values to degrees Fahrenheit, substitute the given values into the equation to get F1 and F2 respectively:
For (25, F1):
F = 9/5 C+32 (put C= 25 in the equation)
F1 = 9/5(25) + 32
F1 = 45 +22
F1 = 77 degrees Fahrenheit
For (−30, F2):
F = 9/5 C+32 (put C= -30 in the equation)
F2 = 9/5(-30) + 32
F2 = -54 + 32
F2 = -22 degrees Fahrenheit
Therefore, the values of F1 and F2 are 77 degrees Fahrenheit and -22 degrees Fahrenheit respectively
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To find the local extrema of a polynomial function f(x) = anxn + an-1xn-1 + … + a2x2 + a1x + a0 (or any other function), you would apply the equation f ’(x) = 0. Consider the basic form of a quadratic equation: f(x) = ax2 + bx + c. Apply the equation above to this quadratic function and solve for x. The resulting equation should be familiar from algebra/pre-calculus. What did you call this equation and how is it related to the location of a local extrema on a quadratic function?
The resulting equation is the x-coordinate of the point of local extrema of a quadratic function.
To find the local extrema of a polynomial function f(x), we apply the equation f'(x) = 0. We are given the basic form of a quadratic equation. The equation is given below.
f(x) = ax² + bx + c
We need to find the differentiation of the above equation.
f'(x) = 2ax + b
Now, we will equate the obtained equation to zero and solve for the value of the variable "x".
f'(x) = 0
2ax + b = 0
2ax = -b
x = -b/2a
This resulting equation is familiar from algebra/pre-calculus. This is the x-coordinate of the point of local extrema of a quadratic function.
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What is the standard form of the quadratic function y=ax^2+bx+c shown in the graph below? a=_ b=_ c=_
The standard form of the quadratic function y=ax² + bx + c = a (x - h)² + k
How to find the standard for of a quadratic function?By definition, quadratic function is a function in the form f(x) = ax² + bx + c, where a, b, and c are numbers with a not equal to zero.
ax² + bx + c = a (x² - 2xh + h²) + kax² + bx + c
= ax² - 2ah x + (ah² + k)
Comparing the coefficients of x on both sides,b = -2ah ⇒ h = -b/2a .............................................(i)
Comparing the constants on both sides,c = ah² + kc = a (-b/2a)² + k (From (1))
c = b²/(4a) + kk = c - (b²/4a)k = (4ac - b²) / (4a)
Therefore, we can use the formulas h = -b/2a and k = (4ac - b²) / (4a) to convert the standard form to its vertex form.
the vertex form of the parabola is y = a (x - h)² + k
The standard form of the parabola is y = ax² + bx + c
The standard form of the quadratic function y=ax²+bx+c is x=-b± [tex]\frac{\sqrt{b^{2}- } 4ac}{2a}[/tex]
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Okay I think I'm going on to see if ur in
Answer:
21y-7/11
Step-by-step explanation:
First you would multiply everything outside of the prhthises to the inside. Second multiply 7 times 3y that would equal 21y. Third multiply 7 times - 1/11 that would equal to 21y-7/11
How many more white squares are there than black squares in the 47th term? Explain how you know.
Expression (White Squares):
Expression: (Black Squares):
There are 9216 more white squares than black squares in the 47th term with it's an odd number of 97
How to calculate the 47th termThe terms are generated with the square of odd numbers with the black squares being the addition of the odd number and one subtracted from it.
For the 47th term:
Given that the first term is consists of 25 squares with 9 black and 16 white squares
first term has odd number 5
the square of 5; 5² = 25
black squares = 5 + (5-1) = 9
white squares = 25 - 9 = 16
Therefore, for the 47th term:
47th term has odd number 97
the square of 97; 97² = 9409
black squares = 97 + (97-1) = 193
white squares = 9409 - 193 = 9216
Hence, the 47th term has an odd number 97 with 9216 more black squares than the white squares,
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it Question 3 Sandra draws a graph representing the relationship between time and distance on her morning run. She wants to show her coach that her rate in minutes per mile was the same for the entire run. Sandra chose two points on the line and drew vertical line segments from the points to the x-axis. How can she use these segments to prove that her speed was constant? Explain your reasoning.
Using the two points on the graph, Sandra can prove that her speed was constant using: Slope (m) = (18 - 6) / (3 - 1).
What is the Slope of a Graph?The slope of a graph is the ratio of the vertical distance along the line to the horizontal distance across the line, which is given as, m = change in y / change in x.
For a proportional graph, the slope is always constant, for whichever points we choose to use on the line.
Given two points on the line that Sandra chose, (3, 18) and (1, 6), therefore:
Slope (m) = change in y / change in x
Slope (m) = (18 - 6) / (3 - 1)
Slope (m) = 12/2
Slope (m) = 6
Therefore, to show her speed, which is the slope of the line, is constant, she can use the equation below:
Slope (m) = (18 - 6) / (3 - 1).
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The function
h
(
x
)
=
(
x
+
3
)
5
can be expressed in the form
f
(
g
(
x
)
)
where
f
(
x
)
=
x
5
, and
g
(
x
)
is defined below:
The auxiliary function used in the composition between the two functions f(x) and g(x) is equal to linear function g(x) = x + 3.
How to derive the auxiliary function in a composition function
Herein we find the result of a composition between two functions, where the variable x of the parent function f(x) is substituted by the auxiliary function g(x). The composition between the two functions is defined below:
h(x) = f ° g (x) = f [g (x)]
If we know that the parent function f(x) = x⁵, then the auxiliary function within the composition is the linear function g(x) = x + 3.
Remark
The statement is poorly formatted, the correct form is shown below: The function h(x) = (x + 3)⁵ can be expressed in the form f[g(x)] where f(x) = x⁵ and g(x) is defined below.
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HELP PLS AND HURRY!!!
Answer:
1. 5√7
2. (√15)/6
Step-by-step explanation:
1. √175
= √(25) * √(7)
= 5√7
2. √(5/12)
= (√5)/(√12)
= (√5)/(√(4) * √(3))
= (√5)/(2√3)
Radicals can't be in the denominator:
(√5)/(2√3)
(√5 * 2√3)/(2√3 * 2√3)
(2√15)/12
(√15)/6
Write a linear function $f$ with $f\left(0\right)=7$ and $f\left(3\right)=1$ .
A linear function will have the form f(x) = mx + b.
f(0)=7 means the point (0,7) is on this line.
f(3)=1 means the point (3,1) is on the line as well.
Using those two points, we can find the slope:
m = (1-7)/(3-0) = -6/3 = -2
Since we were given f(0)=7, we also know the y-intercept.
So our function is f(x) = -2x+7
Darren planted sunflowers in the community garden. During his last visit to the garden, the plants were 60 inches tall. Today, Darren found them to be 10% taller. How tall are the sunflowers now?
please due tommroe
Answer:
66 inches
Step-by-step explanation:
60 + .1(60)
60 + 6
66
Answer:
66 inches
Step-by-step explanation:
60 x .10 = 6
60 +6 =66
The length of one parallel side of a trapezium measures 24 m and the distance between parallel sides measures 28 m. The area of the trapezium is 756 m2. What is the measure of the other parallel side?
Answer:
30 m
Step-by-step explanation:
Given a trapezium with area 756 m², height 28 m, and one base of length 24 m, you want to know the length of the other base.
Area formulaThe formula for the area of a trapezium is ...
A = 1/2(b1 +b2)h
ApplicationUsing the given values, we have ...
756 = 1/2(24 +b2)(28)
54 = 24 +b2 . . . . . . . . . . . divide by 14
30 = b2 . . . . . . . . . . . . subtract 24
The measure of the other parallel side is 30 m.
Let f(x) = 1 / 2+3x and point P = (2 , 1/8)
a.) Use the following definition of the slope of the tangent line at x = a to find the slope of the line tangent to the graph of f at P.
m = lim f(a+h) - f(a) / h
tan h --> 0
b.) Determine an equation of the tangent line at P.
The slope is -3/(2+3a)² and the equation of the line is y - 1/8 = [-3/(2+3a)²](x - 2).
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
f(x) = 1 / 2+3x and point P = (2 , 1/8)
f(x+h) = 1/(2 + 3a + 3h)
f(a) = 1/(2 + 3a)
m(tan) = [1/(2 + 3a + 3h) - 1/(2 + 3a)]/h
After simplifying:
m(tan) = -3/[(2+3a)(2+3a+3h)]
h = 0
m(tan) = -3/(2+3a)²
The equation of the line:
y - 1/8 = [-3/(2+3a)²](x - 2)
Thus, the slope is -3/(2+3a)² and the equation of the line is y - 1/8 = [-3/(2+3a)²](x - 2).
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Assume the radius of a certain planet is 4790 km and the planet is a sphere. What is its surface area?
Answer:
A ≈ 2.88×108km²
Step-by-step explanation:
A= 4 π r² = 4·π· 47902 ≈ 2.88324×10 power 8 km²
PLEASE HELP MEEE!!!
Which point is located on the line represented by the equation y+8=3/7(x-5)
a. (3/7, 5)
b. (-5, 8)
c. (8, -5)
d. (5, -8)
e. (-8, 5)
Answer:
D, (5,-8)
Step-by-step explanation:
On the graph in the image, you can see option D's only point on the line.
Answer: D
Step-by-step explanation:
You will plug every value into the equation; if they are true, that is the correct option.
A.
5+8=3/7(3/7-5)
13=3/7(-32/7)
13=(-96/49)
A is INCORRECT
B.
8+8=3/7(-5-5)
16=3/7(-10)
16=-30/7
B is INCORRECT
C.
-5+8=3/7(8-5)
3=3/7(3)
3=9/7
C is INCORRECT
D.
-8+8=3/7(5-5)
0=3/7(0)
0=0
D IS CORRECT
subtract -2x^2+5x+10 and -7x-3
The difference of the given algebraic expressions is -2x²+12x+13.
The given algebraic expressions are -2x²+5x+10 and -7x-3.
What is the subtraction of expressions?To subtract an algebraic expression from another, we should change the signs (from '+' to '-' or from '-' to '+') of all the terms of the expression which is to be subtracted and then the two expressions are added.
The subtraction of given expressions is as follows
-2x²+5x+10-(-7x-3)
= -2x²+5x+10+7x+3
= -2x²+12x+13
Hence, the difference of the given algebraic expressions is -2x²+12x+13.
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A rectangular sheet of metal measures 8 inches by 10 inches. The metal is worth $2.00 per square inch. How much is the sheet of metal worth?
The cost of the 80 square inches metal sheet is $160
The length of the rectangular sheet = 8 inches
The width of the rectangular sheet = 10 inches
The area of the rectangular sheet = The length of the rectangular sheet × The width of the rectangular sheet
Substitute the values in the equation
= 8 × 10
= 80 square inches
The cost of metal per square inch = $2
Then the cost of metal sheet = The area of the rectangular sheet × The cost of metal per square inch
Substitute the values in the equation
= 80 × 2
= $160
Hence, the cost of the 80 square inches metal sheet is $160
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i need help what is the ancer to 7+7
Answer: 14 is the ancer
Step-by-step explanation:
Answer:
its 14
Step-by-step explanation:
3, 12, 27, 64, 75, 108
a) give the next number in this pattern
b) what is the rule to find the nth term?
c) what is the 20th term?
Please help + explain!
The third term from the sequence should be 48 so that (a) the next term is 147 (b) the rule to find the nth term is 3×n² and (c) the 20th term is 1200.
How to find the next term of the sequenceFrom the question, 3, 12, 27, 64, 75, 108 the third term 64 is supposed to be 48. hence the terms are derived as follows:
1st term; 3 × 1² = 3
2nd term;3 × 2² = 12
3rd term; 3 × 3² = 27
4th term; 3 × 4² = 48
5th term; 3 × 5² = 75
6th term; 3 × 6² = 108
Therefore, the next term which the 7th term is 3 × 7² = 147, the rule for the sequence is 3×n² and the 20th term is 3 × 20² = 1200.
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what is the volume of the recycling box shown in the diagram , 20cm, 40cm, 60cm can someone please help asap
write answers and working out.
Answer:
i got 48000
Step-by-step explanation:
20x40x60
when solving volume you multiply the length times width times height.
3 to the second power times 3 to the third power
Solve the equation 32 = v + 27 for v.
−5
5
−59
59
Answer:
Step-by-step explanation: 32=v + 27
V= 5
how:
32-27=5
v=5
I don"t know what you meant for at the bottom, if that is included please explain what you mean.
Answer:
5
Step-by-step explanation:
32 = v + 27
Subtract 27 from both sides and make v the subject.
32 - 27 = v
5 = v
Judging by the appearance, name a acute angle, an obtuse angle, and a right angle
Answer:
acute angle - UVW
obtuse angle - VWX
right angle - UYX