The range of the function is x∈[(-8 ,16)]
It is required to find the range.
What is function?A function is defined as a relation between a set of inputs having one output each. function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.
Given:
Since f(x) = -2x + 4 is linear, its limit values correspond to the limits imposed by the domain (in this case x∈[(-6 ,6)]
By put the value of x in the given function we get,
f(-6) = -2(-6) + 4
=12+4
=16
f(6) = -2*6 + 4
=-12+4
=-8
So the range is -8<x<16.
Therefore, the range of the function is x∈[(-8 ,16)]
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A. Independent Activity 1 Identify whether the following equations are quadratic equations or not? m( 2m + 3) =0 11t2 (t - 4 ) = 0 5h + h2 = - 7 4b (b - 2 ) = - 8 y2 + 7y - 6 = 0 please answer
1, 3, 4,5
The polynomial equations of degree two in one variable of type f(x) = ax² + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x). The roots of the quadratic equation are the values of x that fulfill the equation (α, β).
It is a given that the quadratic equation has two roots. Roots might have either a real or imaginary nature.
1)m( 2m + 3) =0
2m²+3m=0
Yes it is a quadratic equation.
2) 11t² (t - 4 ) = 0
11t³-44t²=0
NO
3) 5h + h² = - 7
Yes it is a quadratic equation.
4)4b (b - 2 ) = - 8
4b²-8b +8 =0
Yes, it is a quadratic equation.
5) y² + 7y - 6 = 0
Yes it is a quadratic equation.
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Can ya'll help me? This problem has stumped me for a few days.
is the point with coordintaes (-2,-9) on the line whose equation is y=4x - 1?
Answer:
Yes
Step-by-step explanation:
If you have a graphing calculator or something similar, that could really help because all you would have to do is plug in the equation and look up the table and it would show that coordinate in there.
Brook went bowling with her friends she bowled 3 games and her average score for those games was 121 she had 117 her first game and 108 on her second game write an equation to find g the score of her third game
Answer:
121 x 3 = 363
117 + 108 = 225
363 - 225 = 138
138 is the third game
I'm not very sure how to write an equation for this, I guess it would look something like
117 + 108 + x = 363
Step-by-step explanation:
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!
What’s the GCF of 42, 70, 84
Answer: 14
Step-by-step explanation:
First. take the prime factorization of all three numbers:
42: 21*2 ==> 3*7*2
70: 35*2 ==> 5*7*2
84: 42*2 ==> 21*2*2 ==> 3*7*2*2
Notice any common factors? That's the GCF.
GCF: 7*2=14
GCF: 14
Answer:
14
Step-by-step explanation:
The greatest number that divides 42, 70, and 84 exactly is their greatest common factor.
Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42
Factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70
Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The GCF of 42, 70, and 84 is 14.
The greatest number that divides 42, 70, and 84 is 14.
What is GCF?
The biggest positive integer that divides evenly into all the numbers with no remainder is the greatest common factor (GCF, GCD, or HCF) of a set of whole numbers. For instance, the GCF is equal to 6 for the set of numbers 18, 30, and 42.
How do I get the GCF of something?
The greatest common factor among numbers can be discovered in a number of ways.
Factoring:
List each number's factors in order to calculate the GCF by factoring. The factors that evenly divide into the number with no remainder are known as whole numbers. The GCF is the largest number that appears on each list of common factors for each number.
Example: Find the GCF of 18 and 27
The factors of 18 are 1, 2, 3, 6, 9, 18.
The factors of 27 are 1, 3, 9, 27.
The common factors of 18 and 27 are 1, 3 and 9.
The greatest common factor of 18 and 27 is 9.
Prime Factorization:
List all of each number's prime factors to determine the GCF by prime factorization. List the prime factors that each of the original numbers has in common. Include the most instances of each prime factor that each original number has in common. To find the GCF, multiply these by one another.
You'll observe that the prime factorization approach may be simpler than straight factoring as numbers grow larger.
Example: Find the GCF (18, 27)
The prime factorization of 18 is 2 x 3 x 3 = 18.
The prime factorization of 27 is 3 x 3 x 3 = 27.
The occurrences of common prime factors of 18 and 27 are 3 and 3.
So the greatest common factor of 18 and 27 is 3 x 3 = 9.
There is another method but it focuses on more complex numbers.
Hope this helps!
Jackie makes $11.75 an hour and worked for 14 hours this week.
How much more money did she make?
Answer: $164.5
Step-by-step explanation:
11.75*14=$164.5
Find values of m so that the function y xm is a solution of the given differential equation. x^2y''-7xy' 15y=0
If [tex]y=x^m[/tex] is a solution to the ODE
[tex]x^2 y'' - 7xy' + 15y = 0[/tex]
then substituting [tex]y[/tex] and its derivatives
[tex]y' = mx^{m-1} \text{ and } y'' = m(m-1)x^{m-2}[/tex]
gives
[tex]m(m-1)x^2x^{m-2} - 7mxx^{m-1} + 15x^m = 0[/tex]
[tex]m(m-1)x^{m} - 7mx^{m} + 15x^m = 0[/tex]
[tex](m(m-1) - 7m + 15)x^{m} = 0[/tex]
We ignore the trivial case of [tex]y=x^m=0[/tex]. Solve for [tex]m[/tex].
[tex]m(m-1) - 7m + 15 = 0[/tex]
[tex]m^2 - 8m + 15 = 0[/tex]
[tex](m - 3) (m - 5) = 0[/tex]
[tex]\implies \boxed{m=3} \text{ or } \boxed{m=5}[/tex]
Math's Question. Please answer
Answer:
i think 15.84 is right
Step-by-step explanation:
bcz Ian all there is 99 4/5 paper towels and tere were 5 rolls. so, to calculate meters of each roll of paper towels we should divide the given value by 5
99 4/5 /5
Given T(1,5), U(-2,-8), V(7,-9), and W(-6, y). Find y such that
TU VW
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of TU
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-8}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{1}}} \implies \cfrac{-13}{-3}\implies \cfrac{13}{3}[/tex]
hmmmm, well, if that's so, then the slope of VW will be the negative reciprocal of that only if both are really perpendicular, so
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{13}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{13}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{13}}}[/tex]
since now we know the slope if VW, let's use it
[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{-9})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{y}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{y}-\stackrel{y1}{(-9)}}}{\underset{run} {\underset{x_2}{-6}-\underset{x_1}{7}}} \implies \cfrac{y +9}{-13}~~ = ~~\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{3}{13}}\implies y+9=\cfrac{3(-13)}{-13} \\\\\\ y+9=3\implies {\LARGE \begin{array}{llll} y = -6 \end{array}}[/tex]
The base of a triangle is 3 inches more than 2 times the height. If the area of the triangle is 76 square inches, find
the base and height.
Height is h = 8 and base = 19 inch in triangle .
What Does a Triangle's Area Mean?
The space bounded by a triangle's three sides is known as the area of a triangle. Depending on the type of triangle, it is computed using a variety of methods and expressed in square units like cm2, inches2, and so forth.Area of a triangle whose base is b and height is h is =1/2 * b * h
Let the height of given triangle be h inch and as base of a triangle is 3 inch greater than the height, base is ( 2h + 3)
b = 2h + 3
Hence, its area is 1/2 × h × (2h + 3 ) = 76 inch²
So, 1/2 × h × (2h + 3) = 76
2h² + 3h = 76 × 2
2h² + 3h - 152 = 0
2h² + 19h - 16h - 152 = 0
h( 2h + 19 ) -8 (2h + 19) = 0
(h-8) ( 2h - 19)
now h = 8 and h = -19/2 but height of triangle cannot be negative.
Hence height is h = 8 and base = 2 * 8 + 3 = 19 inch
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work out the area of the shape
Answer:
88 [tex]cm^{2}[/tex]
Step-by-step explanation:
We need to find the area of the rectangle and the triangle.
Area of the rectangle:
a = length x width
a = 11 x 6 = 66
Area of the triangle:
a = [tex]\frac{ b x h}{2}[/tex] We need to find the base and height of the triangle. The base is the same length as the length of the rectangle: 11 and the height is 10 - 6 or 4
a = [tex]\frac{11 x 4}{2}[/tex]
a = [tex]\frac{44}{2}[/tex]
a = 22
Add the area of the rectangle and the triangle together. 66 + 22 = 88
greg can eat 1/8 of a hamburger in 1/12 of an hour how many hamburgers can greag eat in one hour
Answer: 1.5 Burgers an hour
1/8 x 12 = 1.5
Multiply 1/8 by 12 to get and hour because 12/12ths = 1 hour
find the value of sqrt 361
why is this so got dam fake
Answer:
Not sure, is there a problem or only the rant? lol. I'd appreciate my first brainliest though.
Step-by-step explanation:
Which shows ray C A?
In exercises 19 and 20, find the indicated angle measure. (See photo)
Answer:
See below to complete
Step-by-step explanation:
ABC = 37 +21 °
LMN = 85 +23 °
Evaluate the function.
f(x) = x² - 4x – 12
Find f(-7)
Answer:
Your answer is 65
Step-by-step explanation:
f(x) = x² - 4x - 12
f(-7) = (-7)² - 4 x (-7) - 12
= 49 - (-28) - 12
= 49 + 28 - 12
= 77 - 12
= 65
n+2.1 - 12
what is it
Perform the indicated operation and express the result as a simplified complex number.
6 + 7i
6-7i
The value of complex number 6 + 7i / 6-7i is -13 / 85 + 84i/85
What are complex numbers?Complex numbers are those that are represented as a+ib, where a and b are actual numbers and I is a fictitious number termed a "iota." I has the value (-1). As an illustration, the complex number 2+3i is made up of the real number 2 (Re) and the imaginary number 3i (Im).
Given the complex number is -
6 + 7i / 6-7i
⇒ 6 + 7i / 6 - 7i × 6 + 7i / 6 + 7i
⇒ (6+7i)² / 6² - 7²(i²)
Using (a+b)² = a² + b² + 2ab
⇒ 6² + (7i)² +2(6)(7i) / 36 - 49(-1)
⇒ 36 - 49 + 84i / 36 + 49
⇒ -13 + 84i / 85
⇒ -13 / 85 + 84i/85
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Suppose that you are playing blackjack against a dealer. in a freshly shuffled deck, what is the probability that neither you nor the dealer is dealt a blackjack?
The probability that neither you nor the dealer is dealt a blackjack will be 1/26.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
Suppose that you are playing blackjack against a dealer. In a freshly shuffled deck.
Then the total number of the event will be
Total events = 52
Then the probability that neither you nor the dealer is dealt a blackjack will be
Favorable event = 2 {Spade of Jack and Club of Jack}
Then the probability of that events will be
P = 2 / 52
P = 1 / 26
The probability that neither you nor the dealer is dealt a blackjack will be 1/26.
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if f(x) = mx +c, f(4) = 11 and f(5) = 13, find the value of f(2).
Answer:
7
Step-by-step explanation:
[tex]f(4)=4m+c=11 \\ \\ f(5)=5m+c=13[/tex]
Subtracting the equations yields that m=2, and thus c=3.
[tex]\implies f(2)=2(2)+3=7[/tex]
-4x-3=-2x-2 solving for x
Answer:
x = 1/2
Step-by-step explanation:
4x -3 = 2x - 2 There are many ways to approach this problem. I am going to start by subtracting 2x from both sides of the equation.
2x -3 = -2 I am going to add 3 to both sides of the equation
2x = 1 Divide both sides of the equation by 2
x = 1/2
What’s the answer to the question attached
(a) The third term of the sequence is 19.
(b) The term-to-term rule of the new sequence is "subtract 13 and then divide by 6".
The first term is given to be -2.The term-to-term rule is to multiply by 6 and then add 13.(a) The second term is equal to (-2)*6 +13The second term equals -12 +13The second term is 1The third term equals (1)*6 +13The third term equals 6 +13The third term is 19(b) The order of the three terms of the sequence is reversed.This means the term-to-term rule will be the inverse of the current term-to-term rule.We will now first subtract 13 and then divide by 6.To learn more about sequence, visit :
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A county has 225 acres of vacant land.
Residents voted to turn some of the vacant land.
into parks. Now, there are 36% less acres of
vacant land. How many acres of vacant land
does the county have now?
The acres of vacant land that the county have now will be 144 acres.
How to calculate the value?Since 36% has been used, the remaining percentage will be:
= 1 - 36%
= 64%
Therefore, the acres of vacant land that the county have now will be:
= 64% × 225
= 64/100 × 225
= 0.64 × 225
= 144
Therefore, the acres of vacant land that the county have now will be 144 acres.
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A woman went shopping and spent 2/3 of all the money she had. Then she lost 3/5 of what she had left after shopping. How much money did she have in the beginning if she now has $10.00.
The amount of money the women had in the beggining was $75.
Let the total amout of money the women had intially be x.
According to the questio.
A woman went shopping and spent 2/3 of all the money she had. Then she lost 3/5 of what she had left after shopping.
So, the amount of money she spent for shopping = (2/3)x = 2x/3
⇒ The amount of money she had after shopping
= x -2x/3
= 3x -2x/3
= x/3
Now, the amount of money she lost 3/5 × (x/3) = x/5
⇒ Amount of money she have after the lost of money
= x/3 - x/5
= 5x - 3x /15
= 2x/15
It is given that she have $10.
⇒ 2x/15 = 10
⇒ 2x = 150
⇒ x = 150/2
⇒ x = $75
Hence, the amount of money the women had in the beggining was $75.
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the sporting goods store sold 10 balls, 3 bats, and 2 bases for $99 on Monday. They sold 4 balls, 8 bats, and 2 bases for $78 on Tuesday. On Wednesday they sold 2 balls 3 bats and 1 base for 33.60. What is the cost of each individual item?
Answer:
ball: $8.00bat: $5.40base: $1.40Step-by-step explanation:
Given three relations between the costs of balls, bats, and bases, you want to find the cost of each.
10 balls + 3 bats + 2 bases = $994 balls + 8 bats + 2 bases = $782 balls + 3 bats + 1 base = $33.60SolutionSolving three linear equations in three unknowns can be accomplished easily by any number of calculators, apps, or spreadsheets. Here, we'll use an ad hoc solution.
Subtracting twice the third equation from the second, we have ...
(4 balls + 8 bats + 2 bases) -(2(2 balls + 3 bats + 1 base) = 78 -2(33.60)
2 bats = 10.80 . . . . . . . simplify
1 bat = 5.40 . . . . . . divide by 2
Subtracting the second equation from the first, we have ...
(10 balls +3 bats +2 bases) -(4 balls +8 bats +2 bases) = (99) -(78)
6 balls -5 bats = 21 . . . . . simplify
6 balls = 21 + 5(5.40) . . . . . add 5 bats and substitute their cost
6 balls = 48 . . . . . . . . simplify
1 ball = 8.00 . . . . . . . divide by 6
Using the last equation, we can find the cost of 1 base.
1 base = 33.60 -2 balls -3 bats = 33.60 -2(8.00) -3(5.40)
1 base = 1.40
The costs are ...
1 ball: $8.00
1 bat: $5.40
1 base: $1.40
Find the magnitude of the net electric field at the origin (created by charges q1 and q2).
The direction of the net magnetic field is [tex]$167.36^{\circ}$[/tex]
How to find the magnitude?[tex]q_1=-4 \mathrm{nC} \text { at }(0.6,0.8)[/tex]
[tex]$q_2=6 \mathrm{nC}$[/tex] at (0.6,0)
[tex]$r_1=$[/tex]Distance of [tex]$q_1$[/tex] from origin[tex]$=\sqrt{0.6^2+0.8^2}$[/tex]
[tex]$r_2=$[/tex] Distance of [tex]$q_2$[/tex] from origin [tex]$=0.6$[/tex]
[tex]$\mathrm{k}=$[/tex] Coulomb constant[tex]$=9[/tex]times [tex]10^9 \mathrm{Nm}^2 / \mathrm{C}^2$[/tex]
Electric field is given by
[tex]&E_1=\frac{k q_1}{r_1^2} \\[/tex]
[tex]&\Rightarrow E_1=\frac{9 \times 10^9 \times 4 \times 10^{-9}}{\sqrt{0.6^2+0.8^2}} \\[/tex]
[tex]&\Rightarrow E_1=36 \mathrm{~N} / \mathrm{C}[/tex]
[tex]&\theta=\tan ^{-1} \frac{0.8}{0.6} \\[/tex]
[tex]&\Rightarrow \theta=53.13^{\circ} \\[/tex]
[tex]&E_1=36 \cos 53.13^{\circ} \hat{i}+36 \sin 53.13^{\circ} \hat{j} \\[/tex]
[tex]&\Rightarrow E_1=21.6 \hat{i}+28.8 \hat{j}[/tex]
[tex]&E_2=\frac{k q_2}{r_2^2} \\[/tex]
[tex]&\Rightarrow E_2=\frac{9 \times 10^9 \times 6 \times 10^{-9}}{0.6^2} \\[/tex]
[tex]&\Rightarrow E_2=150 \mathrm{~N} / \mathrm{C}[/tex]
The charge [tex]$q_2$[/tex] is on the [tex]$\mathrm{x}$[/tex] axis itself and it is pointing towards the origin (left side) so the sign will be negative
[tex]E_2=-150 \hat{i}[/tex]
Resultant electric field
[tex]&E=E_1+E_2 \\[/tex]
[tex]&\Rightarrow E=21.6 \hat{i}+28.8 \hat{j}+(-150 \hat{i}) \\[/tex]
[tex]&\Rightarrow E=-128.4 \hat{i}+28.8 \hat{j}[/tex]
Magnitude of electric field is given by
[tex]&|E|=\sqrt{(-128.4)^2+28.8^2} \\[/tex]
[tex]&\Rightarrow|E|=121.6 \mathrm{~N} / \mathrm{C}[/tex]
Magnitude of the net electric field is [tex]$121.6 \mathrm{~N} / \mathrm{C}$[/tex]
Direction is given by
[tex]\theta=\tan ^{-1} \frac{128.4}{28.8}=77.36^{\circ}[/tex]
From the -x axis
[tex](90+77.36)^{\circ}=167.36^{\circ}[/tex]
The direction of the net magnetic field is [tex]$167.36^{\circ}$[/tex]
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Which of the following fractions is not equivalent to
Answer:
The third option is right
Step-by-step explanation:
This is because if you have two negative it becomes a positive
40 35 37 40 39 41 39 39 36 38 36 39 36 39 35 39 36 37 41 37 38 36 35 40 40 41 39 38 39 35 35 40 39 39 37 38 38 39 35 35 41 37 40 39 38 37 37. Calculate the mode
The mode of the data is 39 as it's frequency is highest .
Mode is a measure of central tendency . It is the no . which has highest frequency in data .
Data - Frequency
40 - 6
35 - 7
37 - 7
39 - 12 ( max . )
36 - 5
38 - 6
41 - 4
The value of frequency corresponding to 39 is maximum .
Therefore , as 39 occurs most of the time in the data , hence it is the mode of this data .
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Adam is re tilling his rectangular bathroom floor with one-square foot tiles.the bathroom floor is 1,770 square feet and the width is.he wants to know the approximate length of the bathroom show two methods
Answer:
length = area/width
Step-by-step explanation:
The width is missing.
area = length × width
length = area/width
Divide the area by the width to find the length.
