Answer:
[tex] \boxed{\sf (f-g)(x) = -{x}^{2} + 3x + 7} [/tex]
Given:
[tex] \sf f(x) = 3x + 1 \\ \sf g(x) = {x}^{2} - 6 [/tex]
To find:
[tex] \sf (f - g)(x) = f(x) - g(x)[/tex]
Step-by-step explanation:
[tex] \sf \implies(f - g)x = f(x) - g(x) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (3x + 1) - ( {x}^{2} - 6) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (3x + 1) + (- {x}^{2} + 6) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3x + 1 - {x}^{2} + 6 \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - {x}^{2} + 3x + 1 + 6 \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = -{x}^{2} + 3x + 7 [/tex]
What’s the equation to (–5, –2), (–5, 7) ?
Answer:
x=-5
Step-by-step explanation:
Since the y value goes from -2 to -7 while the x value stays constant, no matter what y value you plug in x will be -5. Therefore, the equation of this line is x=-5. Hope this helps!
Share £15 in 2:3
Please help me put
Here are two similar rectangles. Work out the area of the larger rectangle
Answer:
take the picture please or give the measurements of the rectangles
Answer:
see attachment for measurements
Step-by-step explanation:
What is the Q1 and Q3?
4,6,8,9,13,21,31
The data is already sorted for us. If it wasn't, then you would have to write the values from smallest to largest.
The median is the middle most value 9 (in slot 4)
The median separates the data into two halves, which I'll call the lower and upper half
lower half = {4,6,8}
upper half = {13,21,31}
The median of the lower half is 6, and this is the value of Q1.
The median of the upper half is 21. This is the value of Q3
Find the area of the following kite. Please help me
Answer:
56
Step-by-step explanation:
The larger half is 4*10=40
The smaller half is 4*4=16
40+16=56
The area of the given kite is 56 square units and it has two diagonals of lengths 14 and 8 units.
The are of kite is product of diagonals by two.
Area of kite = (Diagonal 1 × Diagonal 2)/2.
Diagonal 1= 10+4
=14 units.
Diagonal 2= 4+4
=8 units.
Now plug in these values in above formula:
Area of kite = (14×8)/2
=112/2
=56 square units.
To learn more on Area click:
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what is the equation of the circle that is centred at the origin and passes through the point (-3,4)
Answer:
The correct answer is (x)² + (y)² = r².
Step-by-step explanation:
The standard equation for a circle is (x - h)² + (y - k)² = r². Since our circle is centered at the origin, or (0, 0), our values for h and k are simply 0 and 0, so there is no need to list these values within the equation.
Now, it is time to determine r, or the radius of the circle. The circle passes through the point (-3, 4), so (-3)² + (4)² = 25², so r = 25.
Therefore, your equation is x² + y² = 25.
Help
Two distinct number cubes are rolled together. Each number cube has sides numbered 1 through 6.
What is the probability that the outcome of the roll is an even sum or a sum that is a multiple of 3?
Enter your answer, in simplest fraction form, in the box.
Answer:
The probability is 2/3
Step-by-step explanation:
The first thing to write here is the sample space.
I have shown this in the attachment.
Kindly note that the number of expected outcome is 36
The outcome we are looking at is either an even sum or a multiple of 3
These are what i have circled in the addition results
The number of circles is 24
The probability is thus 24/36 = 2/3
Write each polynomial in standard form. What is the name of the polynomial based on its degree and number of terms?
a. 3 + 5x − 4x2
b. 8x + x + 5 + x3
Answer:
Step-by-step explanation:
(a) 3 + 5x − 4x^2 should be written as −4x2 + 5x + 3. This is a QUADRATIC function.
(b) 8x + x + 5 + x^3 should be re-written first as 9x + 5 + x^3 and then as
x^3 + 9x + 5. This is a CUBING function.
Find the midpoint of the line segment.
Could someone explain how to solve these aswell?
Answer:
(-2, -3)
Step-by-step explanation:
The middle of the point. It covers two blocks so find the middle.
Or you can use the midpoint formula
[tex](x_m, y_m) = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]
(-2,-3) because it is in the middle of the line segment, between the two marked points
Describe fully the single transformation that maps triangle a onto triangle b
Answer:
reflection y=x
Step-by-step explanation:
The single transformation that maps triangle a onto triangle b is the reflection of y=x.
What is single transformation?This is known to be the mix up or the combination of transformations that is said to be seen as one transformation.
Note that in the image attached, when reflection of y axis is said to be cast on the x - axis, one can see that triangle a can be maps onto triangle b and thus:
The single transformation that maps triangle a onto triangle b is the reflection of y=x.
Learn more about reflection from
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help me find AD in degrees
Answer:
43°
Step-by-step explanation:
In circle with center P, AB is diameter. Hence, [tex] \widehat{ACB} [/tex] is a semicircular arc.
[tex] \therefore \widehat{ACB}= 180\degree.... (1)\\
\because \widehat{ACB}= \widehat{AD} + \widehat{DC}+ \widehat{CB}.... (2)\\
From\: (1)\: \&\: (2)\\
\widehat{AD} + \widehat{DC}+ \widehat{CB} = 180\degree \\
\therefore (7x + 1)\degree + 90\degree + (9x-7)\degree = 180\degree \\
\therefore (16x - 6)\degree = 180\degree- 90\degree\\
\therefore (16x - 6)\degree = 90\degree\\
\therefore 16x - 6 = 90\\
\therefore 16x = 90 +6\\
\therefore 16x = 96\\\\
\therefore x = \frac{96}{16}\\\\
\huge \red {\boxed {\therefore x = 6}} \\
\therefore \widehat{AD} = (7x+1)\degree \\
\therefore \widehat{AD} = (7\times 6+1)\degree \\
\therefore \widehat{AD} = (42+1)\degree \\
\huge \orange {\boxed {\therefore \widehat{AD} = 43\degree}} \\
[/tex]
I really need help please :(
Answer:
0≤y≤5
Step-by-step explanation:
The range is the values of the output, or in this case the y values
The y values go from 0 to 5
0≤y≤5
The answer is C.
You can see visually that the function's domain lies within range from -5 to 5 on the x axis.
i think of a number, take away 1 and multiply it by 3
Answer:
X-3, not sure. Try that.
Answer:
[tex]3(x - 1)[/tex]
Step-by-step explanation:
Thinked number = x
take away = -1
[tex]x - 1[/tex]
multiply it by 3
[tex]3(x - 1)[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
ill give Brainliest!!
Answer:
A
Step-by-step explanation:
1st graph is the same for all choices.
3d graph is horizontal line y=50 or C(x) = 50.
It is A or B choices.
We have white circle , that means value of x is not included x > 6.
It is A.
We can check the 2d line. By continuing line we can see that y -int = 10, and we can see slope= rise/run = 5. Also, 2<x≤ 6.
Answer:
It's the first option.
Step-by-step explanation:
Note that the filled circles means that the value is included in the inequality and the clear circle means it is not.
For the first 2 Gb ( 0 to 2 inclusive) used, the cost is $15.
Then for x > 2 up to and including x = 6 ( that is 6 Gb used) it rises at a rate of 5 dollars per Gb + $10, so its 5x + 10 for 2 < x <= 6.
Then the cost stays at $50.
PLS HELP will give brainliest
If a graph is symmetric with respect to the x-axis, then it cannot be symmetric with respect to the y-axis.
A. FALSE
B. TRUE
Answer:
False, it could be.
Work out the percentage change to 2 decimal places when a price of £189 is decreased to £150.
Answer:
The percentage change is -21%
Step-by-step explanation:
The percentage change can be expressed by the formula;
(new price -old price)/old price * 100%
New price = £150
old price = £189
Inputing these values in the formula, we have;
(150-189)/189 * 100%
-39/189 * 100%
= -20.63% and that is approximately -21%
Please help ASAP! Correct answer only! This assignment is due today.
A student has to choose an elective class for the last semester of high school. His counselor suggested 8 electives, 5 of which were dance classes.
If the student randomly chose to read about 4 of the electives, what is the probability that all of them are dance classes?
Write your answer as a decimal rounded to four decimal places.
Answer:
Probability ≈ 0.0714
Step-by-step explanation:
Consider permutation and combination;
[tex]Total Combinations - 8C4,\\8C4 = 8! / 4! * ( 8 - 4 )!,\\8 * 7 * 6 * 5 / 4!,\\\\Total Combinations = 70,\\\\Combinations of Dance Classes - 5C4,\\5C4 = 5! / 4! * ( 5 - 4 )!,\\5 * 4 * 3 * 2 * 1 / 4 * 3 * 2 * 1,\\\\Dance Classes = 5,\\\\Probability - 5 / 70 = 0.0714,\\Conclusion; Probability = ( About ) 0.0714[/tex]
PLEASE HELP ME WITH THIS IT'S TIMED I WILL GIVE BRAINLIEST-
1. A right triangle has side lengths 15 centimeters, 20 centimeters, and 25 centimeters. How can you use the Pythagorean Theorem to write an equation the describes how the side lengths are related?
2. How do you know that the geometric proof of the Pythagorean Theorem in question 1 can be applied to all right triangles?
Step-by-step explanation:
1)
In a right triangle longest side is hypotenuse and the remaining two sides represent the perpendicular legs.
Hence, from the given question it is obvious that 25 is hypotenuse and 20 and 15 are perpendicular legs.
Now, by Pythagorean theorem:
[tex] (one\: side) ^2 +(other \: side) ^2 = (hypotenuse) ^2
\\\\\therefore 20^2 +15^2 =25^2[/tex]
2)
Because all right triangles have one hypotenuse and two perpendicular legs.
Need help with this please
Answer:
The third side is sqrt(77)
Step-by-step explanation:
Since this is a right triangle we can use the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
2^2 + b^2 = 9^2
4+ b^2 = 81
Subtract 4 from each side
b^2 = 81-4
b^2=77
Take the square root of each side
sqrt(b^2) = sqrt(77)
b = sqrt(77)
The third side is sqrt(77)
Pls help me ASAP! Thanks a lot!
Answer:
E) 32
Step-by-step explanation:
Square sheet of paper is folded 4 times into half.
Holes in the paper = 2(4)(4)
= 32 Holes
P.S. Also did it practically
Which number is irrational?
-4
2/9
8.26
11
Answer:
C. Square Root of 11
Edg 2020
Answer:
C
Step-by-step explanation:
edge 2020
A runner moves west with an initial velocity of 4 m/s. She accelerates 3 m/s2 for 30 seconds. The runner’s final velocity is m/s.
Answer:94m/s
Step-by-step explanation:
Using the formula:
v=u+at
Where v= final velocity (the unknown)
u= initial velocity (4m/s)
a= acceleration (3m/s)
t= time (30seconds)
v=4+(3*30)
= 4+90
= 94m/s
4x+3=-10x+ 3 in simples form
Answer:
14x=0
Step-by-step explanation:
Answer
14x+3=3
add 10x to both sides
What is 9^-53 × 9^37
Answer: 9⁵³ ₓ 9³⁷ = 9⁹⁰
Explanation: 53 + 37 = 90
So our answer: 9⁹⁰
A brick weighs w
kg. Write an expression for the weight of 2 bricks
Answer:
2w
Step-by-step explanation:
weight of 1 brick = w
so to find the weight of 2, times it by 2, which leaves you with 2w
plz help!! i believe it's a but i'm not 100% sure
Answer:
its a
Step-by-step explanation:
Find the value of z and
simplify completely.
Answer:
z = 6√2 = 8.49
Step-by-step explanation:
In this question, we are to find the value of the length z.
Mathematically, using Pythagoras’s theorem we can do this.
The Pythagoras’ theorem states that the square of the length of the hypotenuse equals the sum of the length of the squares of the two other sides.
Kindly note that the hypotenuse is the side that faces the angle 90
These are the points needed to solve for z
Using Pythagoras,
z^2 = y^2 + 4^2
z^2 = y^2 + 16 •••••••(i)
x^2 + z^2 = 20^2
x^2 + z^2 = 400 •••••••••(ii)
z^2 + 16^2 = x^2. ••••••••(iii)
Substitute iii into ii
z^2 + 16^2 + z^2 = 400
2z^2 + 256 = 400
2z^2 = 400-256
2z^2 = 144
z^2 = 72
z = √(72)
z = 6√2
Answer:
4[tex]\sqrt{5}[/tex]
Step-by-step explanation:
I would really appreciate if someone help me I need help please help me thank you it’s geometry
Answer:
< 3 and < 5
Step-by-step explanation:
Others are not
Please help me with my question!!
[tex](5^3)^7[/tex]
[tex]5^{3 \times 7}[/tex]
[tex]5^{21}[/tex]
Answer:3*7=21 not 10
You have to multiply the number outside brackets with the inner number
Step-by-step explanation:
Find the term to term rules for the following sequence 2 6 18 54 162
Answer:
486
Step-by-step explanation: