If
x
=
4
and
y
=
6
, evaluate the following expression:
2
(
x
+
y
)
[tex]x=4 , ~y = 6\\\\2(x+y) = 2(4+6) = 2(10) = 20[/tex]
if(4x + 20) , (3x+10)^ and (2x+30)^ are angles of a triangle then the value
A) 13°
B) 13 1 3 ^
C) 13 2 3 ^
D) 14°
Using angle sum property
[tex]\\ \sf\longmapsto 4x+20+3x+10+2x+30=180[/tex]
[tex]\\ \sf\longmapsto 9x+60=180[/tex]
[tex]\\ \sf\longmapsto 9x=120[/tex]
[tex]\\ \sf\longmapsto x=13.2[/tex]
Help me with questions please
Question 1 of 10
f (2) = y + 10. Find the inverse of f(x).
O A f-'(x) = (x + 10)
O B. f-1(x) = 73 + 10
O C. f-1(x) = (x – 10)3
O D. f-'(x) = x3 – 10
Option D
step by step explanation:
[tex] \sf f(x) = \sqrt[3]{x + 10} \\ \sf y = \sqrt[3]{x + 10} \\ \sf y = \sqrt[3]{y + 10} \\ \sf y = {x}^{3} - 10 \\ \sf {f}^{ - 1} (x) = {x}^{3} - 10[/tex]
The inverse of the given function is represented as f' ( x ) = x³ - 10
What is Function Rule?A function is a mathematical object that takes an input (or several inputs) and produces an output. The rule of a function describes how the input is transformed to produce the output. It can be written using mathematical notation, words, or a combination of both.
Functions are used in many areas of mathematics, science, engineering, and other fields to model relationships between variables, make predictions, and solve problems.
Given data ,
Let the function be represented as A
Now , the value of A is
Now , the function is depicted as f ( x ) = ∛( x + 10 )
Simplifying results in
The function's inverse is obtained by swapping the x and y variables.
So ,
y = ∛( x + 10 )
x = ∛( y + 10 )
On solving for y , we get
y = x³ - 10
And , the inverse is f' ( x ) = x³ - 10
The function is therefore f' (x) = x³ - 10.
Go here to read more about the function rule.
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22-2x when x = to -5
Answer:
5
Step-by-step explanation:
22-2x ... (equation-1)
(x=-5)
Substituting the value of x in equation 1
22-2(x-5)
20(x-5)
20x-100
20x=100
x=100/20
x=5
Hope it helps
A 5 pound bag of potatoes costs $2.77 while the store also sells individual potatoes for $0.59 per pound to make enough mashed potatoes to feed everyone at thanksgiving dinner you will need 7 pounds of potatoes
Which system of inequalities is shown?
[tex]\huge\green{\tt MathSolution:}[/tex]
C. y < × y < 4
The graph of y = b is a horizontal line passing through the point (0, b) on the y-axis. To graph an equation of this form, such as y = 4, plot the point (0, b) on the y-axis and draw a horizontal line through it (see Example 4). If the equation is not in the form y = b, solve the equation for y. Vertical Lines: x = a.^^what is 4a-6b+9c + 5a+9b-3c
Answer:
9a + 3b + 6c
Step-by-step explanation:
4a-6b+9c + 5a+9b-3c
4a + (-6b) + 9c + 5a + 9b + (-3c)
(4a + 5a) + (-6b+9b) + (9c-3c)
9a + 3b + 6c
Answer:
the person below is correct I believe
Step-by-step explanation:
hope this helped have a good rest of your night :)❤
Raju wants to buy a storybook. The price of the storybook is divisible by 4, 6 and 8. What is the lowest possible price of the storybook?
Answer:
24
Step-by-step explanation:
take theL.C.M. of 4,6,8.
4=2×2
6=2×3
8=2×2×2
L.C.M.=2×2×2×3=24
I need this done, FAST! EMERGANCY! 20 4 this!
The account balance of each of three children at the end of a month is shown below: John has −$2.75 Cheryl has −$3.00 Andrew has as much savings in his account as the amount John owes the bank. Part A: On a blank paper, draw a number line from −4 to +4. Plot points on the number line to show the account balances of the three children. Label the points using the name of each child. Describe in detail how you created and labeled this number line, and what it looks like in detail. (5 points) Part B: Determine whether John or Cheryl owes the bank more. Use absolute values and inequalities to write statements that justify your conclusion. (5 points)
Answer:John has −$2.75
Cheryl has −$3.00
Andrew has as much savings in his account as the amount John owes the bank.
: On a blank paper, draw a number line from −4 to +4. Plot points on the number line to show the account balances of the three children. Label the points using the name of each child. Describe in detail how you created and labeled this number line, and what it looks like in detail. (5 points)
: Determine whether John or Cheryl owes the bank more. Use absolute values and inequalities to write statements that justify your conclusion. (5 points)
Step-by-step explanation:
Time went scuba diving and descended at a rate of 35 feet every 20 min. If Tim was diving from 11:00AM to 12:00PM. What was Tim's altitude at 11:40AM?
Answer:
70 feet
Step-by-step explanation:
35 x 2 = 70
Solve the problem using a system of equations: Donnette found a widescreen TV at a garage sale, but she isn't sure if it will fit in her entertainment center. The TV is 50". The size of a TV is measured on the diagonal of the screen, and a widescreen has a length that is larger than the width. The screen also has an area of 1,200 square inches. What are the length and width of the TV screen?
length=___inches, width=___ inches
Check the picture below.
[tex]\begin{cases} L^2+w^2=50^2\\ Lw = 1200\\[-0.5em] \hrulefill\\ L^2+w^2=2500\\ L=\sqrt{2500-w^2} \end{cases}\qquad \stackrel{\textit{substituting on the 2nd equation}}{\sqrt{2500-w^2}~w=1200} \\\\\\ \stackrel{\textit{squaring both sides}}{w^2(2500-w^2) = 1200^2}\implies 2500w^2-w^4=1440000 \\\\\\ 0=w^4-2500w^2+1440000\implies 0=\stackrel{\textit{tis a quadratic}}{(w^2)^2-2500w^2+1440000}[/tex]
[tex]0=(w^2-900)(w^2-1600)\implies \begin{cases} 0=w^2-900\\ 900=w^2\\ \sqrt{900}=w\\ \boxed{30=w}\\[-0.5em] \hrulefill\\ 0=w^2-1600\\ 1600=w^2\\ \sqrt{1600}=w\\ \boxed{40=w} \end{cases} \\\\\\ \stackrel{\textit{we know that}}{L = \sqrt{2500 - w^2}}\implies \begin{cases} L=\sqrt{2500-30^2}\\ \boxed{L=40}\\[-0.5em] \hrulefill\\ L=\sqrt{2500-40^2}\\ \boxed{L = 30} \end{cases}[/tex]
The length of the given TV is 40 inches and width of the given TV is 30 inches.
What is the area of a rectangle?The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.
The area of rectangular shape TV is 1,200 square inches.
The TV is 50".
Now, L²+W²=50² ----------(I)
L×W=1200 ----------(II)
L²+W²=2500
⇒ L²=2500-W²
⇒ L=√(2500-W²)
Substitute L=1200/W in L=√(2500-W²), we get
1200/W=√(2500-W²)
Squaring on both the sides we get
1440000/W² =2500-W²
⇒ 1440000=2500W²-[tex]W^4[/tex]
⇒ [tex]W^4[/tex]-2500W²+1440000=0
⇒ (W²)²-2500W²+1440000=0
⇒ (W²)²-900W²-1600W²+1440000=0
⇒ W²(W²-900)-1600(W²-1600)=0
⇒ (W²-1600)(W²-900)=0
⇒ W²-1600=0 and W²-900=0
⇒ W²=1600 and W²=900
⇒ W=±40 and W=±30
So, W=40, -40, 30, -30
Length =1200/W =40 or 30
Therefore, the length of the TV is 40 inches and width is 30 inches.
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"HKA
Erloka borrowed money from her brother to buy a new phone, and is paying off a fixed amount
each week
Answer:
$76
Step-by-step explanation:
X to the third power equals 512
Answer:
8
Step-by-step explanation:
5. The coordinate increments from (4, 3) to (9, 7) are :
6. The coordinate increments from (- 6, - 4) to (12, - 9) are:
7. The coordinate increments from (10, - 7) to (14, - 9) are: are:
8. The coordinate increments from (- 47, - 10) to ( 17 , 8) are:
Answer:
the correct answer is 8
Step-by-step explanation:
Answer:
5. Is "+" 6. is "-" 7. is "+" 8. is "-"
Step-by-step explanation:
9.091 as a mixed number
Select the correct answer.
In the graph, what does A represent?
A.
foci
B.
minor axis
C.
major axis
D.
vertices
Answer:
B minor axis..................:)
Select the correct answer.
When graphing an inequality, the boundary line needs to be graphed first. Which graph correctly shows the boundary line of the inequality?
y <1/3x+ 1
Answer:
C (Top Right)
Step-by-step explanation:
First things first, the line is dotted which makes it one of the answers since it's less than, instead of equal to or less than. Both numbers are positive, the bottom left graph goes into the -x while the top right graph keeps the slope increasing positively by 1/3 + 1.
The boundary line of the inequality y <1/3x+ 1 is represented by the graph C.
Let us find two points on the line.
You can choose any x-values you like and calculate the corresponding y-values using the equation.
When x=0 then y=1.
When x=3, then y=2
Now let us find the graph in which the line passes through (0, 1) and (3, 2).
The boundary line should be dotted because it is less than and doesnot have equal symbol.
When we observe these two criteria's the graph C is the graph for inequality y <1/3x+ 1.
Hence, Graph c correctly shows the boundary line of the inequality y <1/3x+ 1.
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Wind forms dunes through ___.
A. evaporation
B. deposition
C. sublimation
D. condensation
Answer: I think it would have to be c) Sublimation
Please help!!!! ive been trying to get help for almost 2 days and I have yet to get an actual answer :(. Please try to show some work if you can, thank youu
49. [tex]x = \dfrac{1}{a}[/tex] and [tex]y = 3[/tex]
50. [tex]x = \dfrac{1}{2a}[/tex] and [tex]y = \dfrac{1}{b}[/tex]
Step-by-step explanation:
We are going to solve these systems of equations using the elimination method.
49. Given:
[tex]5ax + 4y = 17[/tex] (1)
[tex]\:\:ax + 7y = 22[/tex] (2)
Multiply Eqn(1) by 7 and multiply Eqn(2) by -4 to get
[tex]\:\:35ax + 28y = 119[/tex]
[tex]-4ax - 28y = -88[/tex]
Adding the two equations above, we get
[tex]31ax = 31 \Rightarrow x = \dfrac{1}{a}[/tex]
Substituting this value for a into Eqn(2), we get
[tex]y = 3[/tex]
50. Given:
[tex]4ax + \:\:by = 3[/tex] (3)
[tex]6ax + 5by = 8[/tex] (4)
Multiplying Eqn(3) by -5, we get
[tex]-20ax - 5by = -15[/tex]
[tex]\:\:\:\:\:\:6ax + 5by = \:\:8[/tex]
Adding the two equations above, we get
[tex]-14ax = -7 \Rightarrow x = \dfrac{1}{2a}[/tex]
Plugging in the value of x into Eqn(3), we get the value for y as
[tex]4a(\frac{1}{2a}) + by = 3[/tex]
or
[tex]2 + by = 3 \Rightarrow y = \dfrac{1}{b}[/tex]
Anyone able to help with this?
Answer:
20.1°
Step-by-step explanation:
Put the given numbers into the given formula and do the arithmetic.
∆L = 1050/(60·cos(29.5°)) ≈ 20.1°
The change in longitude is about 20.1 degrees.
__
Additional comments
A degree is 60 minutes: 1° = 60', so 30' = 0.5°.
This formula is accurate when the distance units are nautical miles.
A survey 3,000 who bought a new car showed that 900 had problems. What is the relative frequency of the people that had problems. show steps for me
Answer:
30%
Step-by-step explanation:
Presuming that "survey 3,000" is the total and "900" is the factor who had problems then dividing the total amount by the amount of problems like equal the relative frequency of people that had problems
Math:
Amount of people you had problems / Amount of people who bought the new car.
900 / 3000 = 0.3
Now you need to multiply by 100% (because % in this case is a unit/measurement)
0.3 * 100% = 30%
1) Trent made a scale drawing of the elementary school. The schoolyard, which is 85
meters wide in real life, is 102 millimeters wide in the drawing. What scale did Trent use?
6 millimeters:
The scale Trent used for his elementary school which has a school yard of 85
meters wide in real life and 102 millimetre wide in drawing is 51 : 42500
Firstly, let's do the conversion of the units
1 meters = 1000 millimetres
85 meters = ?
cross multiply
length in millimetres = 85 × 1000 = 85000 millimetres
Since the schoolyard width is 85000 millimetres in real life but it's 102 millimetres wide in drawing , the scale will be as follows:
= 102 / 85000
= 51 / 42500
Therefore, the scale is as follows:
51 : 42500
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A scale is chosen to plot the large graphs on smaller paper representing each unit by a supposed unit.
1.2 mm is used to represent 1 meter.
In the scale given the 102 mm is drawn to represent 85 meters.
So dividing the graph line with the original length the scale Trent has used can be found.
102/85= 1.2
This shows that 1.2 mm is used to represent 1 meter.
Multiplying 85 with 1.2 gives 102 .
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The price of a scarf is reduced by $2.19. The price is now $8.40. What was the original price of the scarf? Enter your answer in the box. $WHOEVER ANSWER GETS BRAINLESS NEED HELP
If the price was reduced by $2.19, the original price of the scarf would be $2.19 + $8.40 which is $10.59
Answer:
The original price of the scarf was $10.59.
Step-by-step explanation:
"The price of a scarf is reduced by 2.19. The price is now 8.40."
Let X be the original price of the scarf.
That can be written as an equation like this:
x - 2.19 = 8.40
Now, just solve for x. Add 2.19 to both sides:
x = 10.59
The original price of the scarf was $10.59.
NEED HELP I DONT REMEBER DIS
Answer:
a. ΔMNK =Δ [tex]PRT[/tex]
b. TR=MN
c. [tex]x=7[/tex]
Step-by-step explanation:
I hope this help you
Please help! Grade 7 math
Answer:
6 apple pies
Step-by-step explanation:
A circular garden has a diameter of 10 feet approximately how much edging trim is needed to surround the garden by placing the trim all along the gardens circumference
The amount of edging trim needed will be equal to the circumference of the given circle, so it will be 31.4ft
We know that the circumference of a circle of diameter D is given by:
C = 3.14*D
Here, we have a circular garden with a diameter of 10ft, and we want to place edging trim along its circumference, so the amount of edging trim that we need is given by:
C = 3.14*10ft = 31.4 ft
You need 31.4ft of edging trim to surround the garden by placing the trim all along the garden's circumference.
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Eighteen greater than a number is 159. Find the number. Check your solution
The number is___
Answer:
let the number be x.
[tex]x + 18 = 159 \\ x = 159 - 18 = 141[/tex]
the number is 141
hope helpful <3
Solve the following system using the elimination method
y+3x=−2
2y−3x=14
Answer:
x = -2-y/3
Step-by-step explanation:
4z-2 when z=3
plz help
Answer:
10
Step-by-step explanation:
4 times 3 = 12
12-2=10