Answer:
[tex]\Large \boxed{\mathrm{f(-5) = 20, \ f(0) = 10}}[/tex]
Step-by-step explanation:
The function is given:
f(x) = 2|x - 5|
Solve for f(-5).
x = -5
f(-5) = 2|-5 - 5|
f(-5) = 2|-10|
f(-5) = 2(10) = 20
Solve for f(0).
x = 0
f(-5) = 2|0 - 5|
f(-5) = 2|-5|
f(-5) = 2(5) = 10
solve for x 3(x+2) = 12
Answer:
x=2
Step-by-step explanation:
3(x+2) = 12
Divide by 3
3/3(x+2) = 12/3
x+2 = 4
Subtract 2 from each side
x+2-2 = 4-2
x =2
Answer:
The value of x is equal to 2.
Step-by-step explanation:
3(x + 2) = 12
Distribute 3 to (x + 2)
3x + 6 = 12
Subtract 6 from both sides of the equation.
3x = 6
Divide 3 on both sides of the equation.
x = 2
The value of x is 2
Diana made a recipe that yields 6 and 1 over 2 cups. If each serving is 1 over 4 cup, which expression will help Diana determine the number of servings her recipe will yield? 6 and 1 over 2 ⋅ 1 over 4 6 and 1 over 2 ÷ 1 over 4 6 and 1 over 2 + 1 over 4 6 and 1 over 2 − 1 over 4
Answer:
6 1/2 divided by 1/4SOMEONE PLZ HELP ME!!!! I WILL GIVE BRAINLIEST!!!
Answer:
Step-by-step explanation:
Let the quadratic equation of the function by the points in the given equation is,
f(x) = ax² + bx + c
If the points lying on the graph are (-3, -10), (-4, -8) and (0, 8),
For (0, 8),
f(0) = a(0)² + b(0) + c
8 = c
For a point (-3, -10),
f(-3) = a(-3)² + b(-3) + 8
-10 = 9a - 3b + 8
9a - 3b = -18
3a - b = -6 --------(1)
For (-4, -8),
f(-4) = a(-4)² + b(-4) + 8
-8 = 16a - 4b + 8
-16 = 16a - 4b
4a - b = -4 ------(2)
Subtract equation (1) from equation (2)
(4a - b) - (3a - b) = -4 + 6
a = 2
From equation (1),
6 - b = -6
b = 12
Function will be,
f(x) = 2x² + 12x + 8
= 2(x² + 6x) + 8
= 2(x² + 6x + 9 - 9) + 8
= 2(x² + 6x + 9) - 18 + 8
= 2(x + 3)² - 10
By comparing this function with the vertex form of the function,
y = a(x - h)² + k
where (h, k) is the vertex.
Vertex of the function 'f' will be (-3, -10)
And axis of symmetry will be,
x = -3
From the given graph, axis of the symmetry of the function 'g' is; x = -3
Therefore, both the functions will have the same axis of symmetry.
y-intercept of the function 'f' → y = 8 Or (0, 8)
y-intercept of the function 'g' → y = -2 Or (0, -2)
Therefore, y-intercept of 'f' is greater than 'g'
Average rate of change of function 'f' = [tex]\frac{f(b)-f(a)}{b-a}[/tex] in the interval [a, b]
= [tex]\frac{f(-3)-f(-6)}{-3+6}[/tex]
= [tex]\frac{-10-8}{3}[/tex]
= -6
Average rate of change of function 'g' = [tex]\frac{g(b)-g(a)}{b-a}[/tex]
= [tex]\frac{g(-3)-g(-6)}{-3+6}[/tex]
= [tex]\frac{7+2}{-3+6}[/tex]
= 3
Therefore, Average rate of change of function 'f' is less than 'g'.
Evaluate. Write in standard form.
Answer:
-i
Step-by-step explanation:
(-i)^0 = 1
(-i)^1 = -i
(-i)^2 = -1
(-i)^3 = -i
(-i)^4 = 1
(-i)^5 = -i
etc.
From this pattern, you see that when the exponent is a multiple of 4, you get 1. When the exponent is a multiple of 4 plus 1, you get -i, etc.
213 = 4 * 53 + 1
213 is 1 more than a multiple of 4.
(-i)^213 = (-i)^1 = -i
How to do this question plz.
plz work out for me in your notebook or sheet if you can plz the question so I can understand more plzz
Answer:
[tex]3\pi[/tex]
Step-by-step explanation:
The circumference of a circle is [tex]2\pi r[/tex].
If we want to find the circumference of this semi-circle, we can find the circumference if it was a whole circle then divide by 2.
[tex]2 \cdot \pi \cdot r\\2 \cdot \pi \cdot 3\\6 \cdot \pi\\ 6\pi[/tex]
Now we know the circumference of the whole circle.
To find the circumference of half the circle we divide by 2.
[tex]6\pi \div 2 = 3\pi[/tex]
Hope this helped!
Simply. If the solution is not a real number enter not a real number rotate picture answer all 3 please
Answer:
13. [tex]\frac{\sqrt[5]{x^4} }{x}[/tex].
14. [tex]v = \pm3\sqrt{5}[/tex]
15. 2.
Step-by-step explanation:
13. [tex]x^{1/5} * x^{-2/5}[/tex]
= [tex]x^{1/5 + (-2/5)}[/tex]
= [tex]x^{1/5 - 2/5}[/tex]
= [tex]x^{-1/5}[/tex]
= [tex]\frac{1}{x^{1/5}}[/tex]
= [tex]\frac{x^{4/5}}{x^{1/5 + 4/5}}[/tex]
= [tex]\frac{x^{4/5}}{x}[/tex]
= [tex]\frac{\sqrt[5]{x^4} }{x}[/tex].
14. [tex]v^2 - 45 = 0[/tex]
[tex]v^2 = 45[/tex]
[tex]\sqrt{v^2} = \pm\sqrt{45}[/tex]
[tex]\sqrt{v^2} = \pm\sqrt{3^2 * 5}[/tex]
[tex]v = \pm3\sqrt{5}[/tex].
15. [tex]\sqrt[3]{2} * \sqrt[3]{4}[/tex]
= [tex]\sqrt[3]{2 * 4}[/tex]
= [tex]\sqrt[3]{2 * 2 * 2}[/tex]
= [tex]\sqrt[3]{2 ^3}[/tex]
= 2.
Hope this helps!
10 points :) Graph this for me :P
Answer:
-2≤x≤2 f(x)=[x+3]
first the sign is ≤ it means the point is solid point and the interval is x+3
plz ans asap i havd limited time ill give brainliest
Answer:
C. $128
Step-by-step explanation:
320 x 0.5 = 160
320 - 160 = 160
160 x 0.20 = 32
160 - 32 = 128
23-[12+{16-(12÷3)}] simplify
Answer:
23-[12+{16-(12÷3)}] = - 1Step-by-step explanation:
23 - [12 + {16 - (12÷3)}] =
= 23 - [12 + {16 - 4}] =
= 23 - [12 + 12] =
= 23 - 24 =
= - 1
Answer:
The Answer to 23-[12+{16-(12/3)}]=-1
Step-by-step explanation:
To answer this question you must follow the order of operations.
PEDMAS
23-[12+{16-(12/3)}]
23-[12+{16-4}]
23-[12+12]
23-24=-1
The lines on a 2-cup liquid measuring cup divide each cup into eighths If you measure 1 3/4 cups of water between which two quantities can you be certain that your exact measurement will be
Answer:
The line between 1 5/8 and 1 7/8 is exactly 1 3/4.
Step-by-step explanation:
1 3/4 = 1 6/8
Since the lines are every 1/8 of a cup, there are a total of 16 lines indicating 1/8 of a cup for a total of two full cups.
1/8 less than 1 6/8 is 1 5/8.
1/8 more than 1 6/8 is 1 7/8.
The line between 1 5/8 and 1 7/8 is exactly 1 3/4.
Jonas needs a cell phone. He has a choice between two companies with the following monthly billing policies. Each company’s monthly billing policy has an initial operating fee and charge per text message. Sprint charges $29.95 monthly plus .15 cents per text, AT&T charges $4.95 monthly plus .39 cents per text. Create equations for the two cell phone plans.
Answer:
Since both companies have a different plan, two equations are created to determine which company Jonas should choose with respect to the number of messages sent.
Step-by-step explanation:
- Sprint = $ 29.95 * X (0.15)
- AT & T = $ 4.95 * X (0.39)
One dollar equals 100 cents, so 0.15 cents equals $ 0.0015 dollars.
- Sprint = $ 29.95 * X (0.0015)
- AT & T = $ 4.95 * X (0.0039)
Si Jonas envía 500 mensajes de texto el valor mensual de cada empresa sería de:
- Sprint = $ 29.95 * 500 (0.0015) = 22.46 dollar per month.
- AT & T = $ 4.95 * 500 (0.0039) = 9.65 dollar per month.
The company Jonas should choose is AT&T.
AT&T also charges a little more per number of text messages, but since the phone's value is so low it would take thousands of text messages to compare to Sprint's monthly value.
In Exercise 4, find the surface area of the solid
formed by the net.
Answer:
3. 150.72 in²
4. 535.2cm²
Step-by-step Explanation:
3. The solid formed by the net given in problem 3 is the net of a cylinder.
The cylinder bases are the 2 circles, while the curved surface of the cylinder is the rectangle.
The surface area = Area of the 2 circles + area of the rectangle
Take π as 3.14
radius of circle = ½ of 4 = 2 in
Area of the 2 circles = 2(πr²) = 2*3.14*2²
Area of the 2 circles = 25.12 in²
Area of the rectangle = L*W
width is given as 10 in.
Length (L) = the circumference or perimeter of the circle = πd = 3.14*4 = 12.56 in
Area of rectangle = L*W = 12.56*10 = 125.6 in²
Surface area of net = Area of the 2 circles + area of the rectangle
= 25.12 + 125.6 = 150.72 in²
4. Surface area of the net (S.A) = 2(area of triangle) + 3(area of rectangle)
= [tex] 2(0.5*b*h) + 3(l*w) [/tex]
Where,
b = 8 cm
h = [tex] \sqrt{8^2 - 4^2} = \sqrt{48} = 6.9 cm} (Pythagorean theorem)
w = 8 cm
[tex]S.A = 2(0.5*8*6.9) + 3(20*8)[/tex]
[tex]S.A = 2(27.6) + 3(160)[/tex]
[tex]S.A = 55.2 + 480[/tex]
[tex]S.A = 535.2 cm^2[/tex]
what are the squares from 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20 answer when multiplied by itself
Answer:
I hope it helps :)
Step-by-step explanation:
[tex] {1}^{2} = 1 \times 1 = 1\\ {2}^{2} = 2 \times 2 = 4\\ {3}^{2} =3 \times 3 = 9\\ {4}^{2} = 4 \times 4 = 16 \\ [/tex]
[tex]{5}^{2} = 5 \times 5 = 25 \\ {6}^{2} = 6 \times 6 = 36 \\ {7}^{2} = 7 \times 7 = 49\\ {8}^{2} = 8 \times 8 = 64[/tex]
[tex] {9}^{2} = 9 \times 9 = 81 \\ {10}^{2} = 10 \times 10 = 100 \\ {11}^{2} = 11 \times 11 = 121 \\ { {12}^{2} } = 12 \times 12 = 144[/tex]
[tex] {13}^{2} = 13 \times 13 = 169 \\ {14}^{2} = 14 \times 14 = 196 \\ {15}^{2} = 15 \times 15 = 225 \\ {16}^{2} = 16 \times 16 = 256[/tex]
[tex] {17}^{2} = 17 \times 17 = 289 \\ {18}^{2} = 18 \times 18 = 324 \\ {19}^{2} = 19 \times 19 = 361 \\ {20}^{2} = 20 \times 20 = 400[/tex]
Step-by-step explanation:
Is this the answer you want? If nope inform me.i hope you just ignore my handwriting ☺️
In 2002, the population of a district was 22,800. With a continuous annual growth rate of approximately 5% what will the population be in 2012 according to the exponential growth function?
Answer:
37,139
Step-by-step explanation:
Given the following :
Population in 2002 = Initial population (P0) = 22,800
Growth rate (r) = 5% = 0.05
Growth in 2012 using the exponential growth function?
Time or period (t) = 2012 - 2002 = 10years
Exponential growth function:
P(t) = P0 * (1 + r) ^t
Where P(t) = population in t years
P(10) = 22800 * (1 + 0.05)^10
P(10) = 22800 * (1.05)^10
P(10) = 22800 * 1.62889
P(10) = 37138.797
P(10) = 37,139 ( to the nearest whole number)
percent increase formula
A = old value
B = new value
C = percent change
C = [ (B-A)/A ] * 100%
---------------------
Example:
Lets say we start at A = 10 and increase to B = 15. The percent change would be...
C = [ (B-A)/A ] * 100%
C = [ (15 - 10)/10] * 100%
C = (5/10) * 100%
C = 0.5 * 100%
C = 50%
The positive C value means we have a percent increase. Going from 10 to 15 is a 50% increase.
Part of the graph of the function f(x) = (x + 4)(x - 6) is
shown below.
Which statements about the function are true? Select
two options.
py
The vertex of the function is at (1.-25).
6
4
The vertex of the function is at (1,-24).
The graph is increasing only on the interval -4< x < 6.
The graph is positive only on one interval, where x <-
4.
2-
-6
2
4
6
х
-2
-2
The graph is negative on the entire interval
4
4
6
Answer:
x-intercept(s):
( − 4 , 0 ) , ( 6 , 0 )
y-intercept(s):
( 0 , − 24 )
Step-by-step explanation:
The graph of the function f ( x ) = ( x + 4 ) ( x - 6 ) is plotted
What is a Parabola?A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line
The equation of the parabola is given by
( x - h )² = 4p ( y - k )
y = a ( x - h )² + k
where ( h , k ) is the vertex and ( h , k + p ) is the focus
y is the directrix and y = k – p
The equation of the parabola is also given by the equation
y = ax² + bx + c
where a , b , and c are the three coefficients and the parabola is uniquely identified
Given data ,
Let the parabolic equation be represented as A
Now , the value of A is
f ( x ) = ( x + 4 ) ( x - 6 ) be equation (1)
On simplifying , we get
The graph of the function is plotted and it is increasing only on the interval -4< x < 6
And , the vertex of the function is at P ( 1 , -25 )
Therefore , the function is f ( x ) = ( x + 4 ) ( x - 6 )
Hence , the function is f ( x ) = ( x + 4 ) ( x - 6 )
To learn more about parabola click :
https://brainly.com/question/24042022
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(t)What is the difference between
{2, 3} and {{2, 3}}?
Answer:
[tex]\boxed{\mathrm{view \ explanation}}[/tex]
Step-by-step explanation:
{2, 3} is a set consisting of two elements. The two elements are the numbers 2 and 3.
{{2, 3}} is a set consisting of one element. That one element is the set {2, 3}.
LaShawn solved the equation below to the determine the solution.
3 x minus 8 = negative x + 4 (x minus 2)
Answer:
x = all real numbers.
Step-by-step explanation:
3 x minus 8 = negative x + 4 (x minus 2)
3x - 8 = -x + 4(x - 2)
3x - 8 = -x + 4x - 8
3x - 8 = 3x - 8
3x - 3x = -8 + 8
0 = 0
Since the result is a true statement, but 0 = 0, x is equivalent to all real numbers.
Hope this helps!
Answer:
Step-by-step explanation:
identify the terms of each expression 7 + 5 p + 4r + 6 s
Find the distance across the lake. Assume the triangles are similar.
80 m
х
у
20 m
60 m
Answer:
a
Step-by-step explanation:
Answer:
A. L = 240 m
Step-by-step explanation:
use similar triangle
L / 60 = 80 / 20
L = (80 * 60) / 20
L = 240 m
Farmer Green sent his two children out to count the hens and sheep. His daughter counted 40 hens, and his son counted 100 legs. How many of each animal is on the farm?
Answer:
40 hens, 5 sheep
Step-by-step explanation:
40 x 2 = 80 (hens have 2 legs)
100 - 80 = 20 ----> 20 legs left for sheep,, sheep have 4 legs
20/4 = 5 so there are 5 sheep
Answer:
40 hens, 5 sheep
Step-by-step explanation:
40 x 2 = 80 (hens have 2 legs)
100 - 80 = 20 ----> 20 legs left for sheep,, sheep have 4 legs
20/4 = 5 so there are 5 sheep
Gretchen made a paper cone to hold a gift for a friend. The paper cone was 11 inches high and had a radius of 5 inches. Find the volume of the paper cone to the nearest tenth. Use 3.14 for π.
Answer:
91.67inch^3
Step-by-step explanation:
The volume of a cone can be calculated using below formula
V= 1/3 π.r^2h
Where h= height of the cone
r= radius of the cone
V= volume of the cone
Given :
height= 11inches
radius= 5inches
π= 3.14
Then substitute into the formula we have
V= 1/3 × 3.14× 5^2 ×11
V= 91.67inch^3
Therefore volume of the cone is 91.67inch^3
What is the greatest common factor of 30, 90 and 75?
Please solve, -7x+8=-4(x+1)
Answer: [tex]x=4[/tex]
Simplify both sides of the equation.
[tex]-7x+8=-4(x+1)\\-7x+8=(-4)(x)+(-4)(1)(Distribute)\\-7x+8=-4x+-4[/tex]
Add 4x to both sides
[tex]-7x+8+4x=-4x-4+4x\\-3x+8=-4[/tex]
Subtract 8 from both sides
[tex]-3x+8-8=-4-8\\-3x=-12[/tex]
Divide both sides by -3
[tex]-3x/-3=-12/-3\\x=4[/tex]
Answer:
x=4
Step-by-step explanation:
Let's first simplify the equation.
-7x+8= -4x-4
You get -4x-4 by distributing the -4 into the numbers in the parenthesis because -4 is right outside the parenthesis.
-4 times x= -4x
-4 times 1= -4
-7x+8= -4x-4
Next, move the -4x to where the -7x is because we want to combine like terms. When a number moves to the opposite side, it changes from positive to negative or negative to positive. Like here: -4x moves to a different side, so it becomes +4x.
-7x+4x+8= -4
Do the same for 8. Since -4 is on the other side, move 8 to that side. It turns from +8 to -8.
-7x+4x= -4-8
Combine like terms and solve.
-7x+4x= -3x
-4-8= -12
So we have this now: -3x= -12
Since 12 divided by 3 is 4, and negative with negative is positive, it becomes positive 4. :)
The Ross family and the Russell family each used their sprinklers last summer. The water output rate for the Ross family's sprinkler was 35L per hour. The water output rate for the Russell family's sprinkler was 30L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in a total water output of 1725L. How long was each sprinkler used?
Answer:
Ross = 15 hours
Russel = 40 hours
Step-by-step explanation:
Let Ross have used their sprinklers for x hours
Let Russell have used their sprinklers for y hours
Together they used 55 hours
x+y = 55 hours
The output of Ross is 35 liters per hour and Russell is 30 liters per hour for a total of 1725
35x + 30y = 1725
Multiply the first equation by -30
-30(x+y=55)
-30x -30y = -1650
Add this to the second equation to eliminate y
-30x -30y = -1650
35x + 30y = 1725
-----------------------------
5x =75
Divide each side by 5
x = 15
Now find y
x+y = 55
y = 55-15
y = 40
Evaluate the expression for the given value of the variable. −9x − 8, when x = −6
Answer:
46
Step-by-step explanation:
The expression is:
● -9x - 8
Replace x by -6 to evaluate the expression when x = -6
● -9 ×(-6) - 8
● 54-8
● 46
Answer:
[tex]\huge\boxed{46}[/tex]
Step-by-step explanation:
-9x - 8, when x = -6
Substitute in -6 for x in the expression
-9x - 8
-9(-6) - 8
Multiply -9 * -6
54 - 8
Subtract
[tex]\huge\boxed{46}[/tex]
Hope this helps :)
What is the length of LM? (Question and answer choices provided in picture.)
Answer:
24√3
Step-by-step explanation:
cos∅ = adjacent over hypotenuse
Step 1: Use cos∅
cos30° = LM/48
Step 2: Multiply both sides by 48
48cos30° = LM
Step 3: Evaluate
LM = 24√3
Answer:
[tex]\large \boxed{24 \sqrt{3} }[/tex]
Step-by-step explanation:
The triangles are right triangles. We can use trig functions to solve.
cos θ = adj/hyp
Take the triangle KLM.
cos 30 = LM/KL
cos 30 = LM/48
Multipy both sides by 48
(48) cos 30 = LM/48 (48)
Simplify.
48 cos30 = LM
24√3 = LM
which of the following statements are true? check all that apply. check all that apply. the volume of a cube depends on the lenght of its sides. a cube with a side length of 10 feet has a volume of 1,000 cubic feet. a cube with a side length of 2 feet has a volume of 8 cubic feet.
A. volume(2)=8
B. volume (8)=2
C. volume (10)=1,000
D. volume (1,000)=10
Answer:
Option A and Option C
Step-by-step explanation:
Solve 2(x - 5) = 48 - 4(x + 1)
Answer:
x = 9
Step-by-step explanation:
first remove the brackets
2x - 5 = 48 - 4x + 1
then take numbers to the opposite sides
2x + 4x = 48 + 5 + 1
I have used addition because since your taking-5 to the other side it becomes+5 and -4 becomes +4
now solve
2x + 4x= 6x
48+5+1= 54
6x = 54
now solve for x
divide both sides by 6x
x = 9
Solve the simultaneous equation
X+3y=13
X-y=5
Answer:
x = 7
y = 2
Step-by-step explanation:
In the above question, we are given 2 equations which are simultaneous. To solve this equation, we have to find the values of x and y
x + 3y = 13 ........ Equation 1
x - y = 5...........Equation 2
From Equation 2,
x = 5 + y
Substitute 5 + y for x in Equation 1
x + 3y = 13 ........ Equation 1
5 + y + 3y = 13
5 + 4y = 13
4y = 13 - 5
4y = 8
y = 8/4
y = 2
Since y = 2, substitute , 2 for y in Equation 2
x - y = 5...........Equation 2
x - 2 = 5
x = 5 + 2
x = 7
Therefore, x = 7 and y = 2
