Using translation concepts, it is found that the equation for function g(x) is given by:
[tex]y = -\frac{2}{3}|x|[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The parent function is given by:
f(x) = |x|.
Researching the problem on the internet, function g(x) was reflected over the x-axis, and compressed by a factor of 2/3, hence it is multiplied by -2/3(negative due to the reflection), and the equation for function g(x) is given by:
[tex]y = -\frac{2}{3}|x|[/tex]
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Abag contains 8 red marbles, 3 blue marbles, and 1 green marble. Find P(not blue).
a. 9 b. 4/3 c. 1/4 d. 3/4
Answer:
A: 9
Step-by-step explanation:
if p is red and green
Answer:
--------------------------HeyA-------------------------
GiveN :
Total no.of marbles : 12Total no.of red marbles : 8 Total no.of blue marbles : 3Total no.of green marbles : 1To FinD :
P ( not blue )SolvinG :
- First step is to find out P( blue )
P ( blue ) = 3 / 12 = 1/4- Now , find out P ( not blue )
P ( not blue ) = 1 - 1/4 = 3/4- Option D [ 3/4 ] is the right option.
--------------------HappY LearninG <3 --------------
Please hurry!
The diagram shows two squares constructed on the sides of a rectangle. What is the area of C?
Square A=6 ft2
Rectangle B=5 ft2
Don’t mind the writing
Answer:
25/6
Step-by-step explanation:
a²=6 -> a=✓6 (a must be positive so reject negative solutions)
ab=5 -> b = 5/✓6
thus area of C is b² = 25/6
The members of the Math Club need to elect a president and a vice president. They determine that there are a total of 272 ways that they can fill the positions with two different members. How many people are in the Math Club
Answer:
544
Step-by-step explanation:
EASY JUST MULTIPLY!!!
multiply your total of ways to fill the position, by how many members!
so... 272 x 2 = 544 hopes this helps!!
Which of the following points on the number line would be the plotted point for √5
Answer:
Point C
Step-by-step explanation:
The correct answer would be about 2.2 so C is the closest.
3 Najid paid $10 000 income tax in a year. What was his salary that year?
Answer:
income tax=13% of total salary
Step-by-step explanation:
Here,
let salary be 'x'
Now,
13%of x = $10 000
13/100 × x = $10 000
13x = 1000000
x=10 00000/13
Therefore x =76,923.0769
His salary that year was 76,923.0769
Help me pls answer pls I’m pls
1 litre is approximately 1.75 pints,
1 gallon = 8 pints
calculate the approximate number of gallons that are equal to 48 000 cm3
Answer:
10.5 gallons are equal to 48000 cm3
Step-by-step explanation:
What is Limit of StartFraction StartRoot x + 1 EndRoot minus 2 Over x minus 3 EndFraction as x approaches 3?
Answer:
[tex]\displaystyle \lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} = \boxed{ \frac{1}{4} }[/tex]
General Formulas and Concepts:
Calculus
Limits
Limit Rule [Variable Direct Substitution]:
[tex]\displaystyle \lim_{x \to c} x = c[/tex]
Special Limit Rule [L’Hopital’s Rule]:
[tex]\displaystyle \lim_{x \to c} \frac{f(x)}{g(x)} = \lim_{x \to c} \frac{f'(x)}{g'(x)}[/tex]
Differentiation
DerivativesDerivative NotationDerivative Property [Addition/Subtraction]:
[tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Derivative Rule [Basic Power Rule]:
Derivative Rule [Chain Rule]:
[tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify given limit.
[tex]\displaystyle \lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3}[/tex]
Step 2: Find Limit
Let's start out by directly evaluating the limit:
[Limit] Apply Limit Rule [Variable Direct Substitution]:When we do evaluate the limit directly, we end up with an indeterminant form. We can now use L' Hopital's Rule to simply the limit:
[Limit] Apply Limit Rule [L' Hopital's Rule]:∴ we have evaluated the given limit.
___
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___
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
Without using l'Hopitâl's rule, we can instead rationalize the numerator.
[tex]\dfrac{\sqrt{x+1} - 2}{x-3} = \dfrac{\left(\sqrt{x+1}-2\right)\left(\sqrt{x+1}+2\right)}{(x-3)\left(\sqrt{x+1}+2\right)} = \dfrac{(x+1)-4}{(x-3)\left(\sqrt{x+1}+2\right)} = \dfrac1{\sqrt{x+1}+2}[/tex]
We've removed the discontinuity at [tex]x=3[/tex], so the limand is continuous and
[tex]\displaystyle \lim_{x\to3} \frac{\sqrt{x+1}-2}{x-3} = \lim_{x\to3} \frac1{\sqrt{x+1}+2} = \frac1{\sqrt{3+1}+2} = \boxed{\frac14}[/tex]
if someone in 2022 is now 89, how old were they in 1971?
Answer:38
Step-by-step explanation:
they were born in 1933 and 1971 minus 1933 is 38.
Please help, I can’t do this and it’s due tomorrow
Answer:
a) 11/100
b) 60 times
Step-by-step explanation:
a)
We want to find the probability that a 3 will be rolled.
Probability = # of favorable outcomes / total # of outcomes.
Here the number of favorable outcomes will be the number of times a 3 was rolled and the total number of outcomes will simply be the # of times that the dice was rolled which can be calculated by finding the sum of the frequencies of each number.
So # of favorable outcomes = 11 ( as the dice was rolled on a 3 11 times.)
And the total number of outcomes would be 100 ( the sum of the frequencies , 12 + 35 + 11 + 23 + 7 + 12 = 100 )
So the probability of rolling a 3 would be 11/100
b)
For this part we want to find the expected times that a 6 would be rolled if we rolled the die 500 more times.
To calculate this we simply find the probability of rolling a 6 and then multiply that by 500.
So again probability = # of favorable outcomes / total # of outcomes.
Here # of favorable outcomes is frequency of rolling a 6 which would be 12 and the total number of outcomes is 100 as we found out during the last part.
So the probability of rolling a 6 is 12/100 or 3/25
We then multiply this by 500 to find the expected number of times a 6 would be rolled if the dice was rolled 500 more times
So our answer = 3/25 × 500 = 60 times
A right circular cone is intersected by a plane that passes through the cone's
vertex and is perpendicular to its base, as in the picture below. What is
produced from this intersection?
A. A single line
B. A pair of intersecting lines
C. A point
D. A pair of parallel lines
When a circular cone is intersected by a plane that passes through the cone's vertex and is perpendicular to its base, a pair of intersecting lines is formed.
How to know what is formed from a line intersecting a cone?The right circular cone is intersected by a plane that passes through the cone's vertex and is perpendicular to its base.
This means the intersecting line forms a right angle with the base of the right circular cone.
Therefore, what is produced from this interaction is a pair of intersecting lines. The intersecting lines also have a point.
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Find the value of x.
135°
(7x + 2)°
x = [?]°
The required value of the x in the expression of angle is 19.
An expression of angle is given as 7x + 2 = 135°, the value of the x is to be determined.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
7x + 2 = 135
Simplifying,
7x = 135 - 2
7x = 133
x = 133 / 7
x = 19
Thus, the required value of the x in the expression of angle is 19.
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Y-intercept: (0,
y=-2x2 – 16x – 34
What is the y intercept?
Answer: Solve for Y
y = -16x - 38
And then y intercept is
(0, -38)
Step-by-step explanation:
pleasee help me! One circle has a circumference of 12 cm. Another circle has a circumference of 32 cm. What is the ratio of the radius of the smaller circle to the radius of the larger circle? 3:8 8:3 1:3 3:1
Answer:
A: 3;8
Step-by-step explanation:
12/2 = 6
32/2 = 16
6/2 = 3
16/2 = 8
3:8
Time Left:1:32:30
Ryan Harris: Attempt 1
(06.07 MC)
The cost and customer rating of 15 cars is shown on the scatterplot. The cars are
rated on a scale of 0 to 100.
120
100
80
Rating
60
Based on the relationship between the ratings and cost, the association is a positive correlation. The data point that affects the appropriateness of using linear regression is $4,200 and 15 rating.
A car that is cost effective and rated highly is the data point (3,500,100).
What does the scatterplot show on cost and customer rating?In general, the cost of cars shown is higher when the customer reviews are high as well. This shows a positive correlation between cost and customer ratings.
The car at (4,200, 15) is an outlier because it is expensive and yet has low ratings. It would therefore affect a linear regression model if one is used to fit the data shown.
The car at (3,500, 100) is cost-effective and rated high because it is not as expensive as a lot of other cars, and yet has the highest customer rating of 100.
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The fabric store is having a sale the price of every item in the store has been reduced 30% which equation show the proportional relationship between the regular price of an item at the fabric store and its sale price, s?
what is the slope of the line that contains the points (-2,6) and (2,-2)
Answer:
[tex]-\frac{8}{4}[/tex]
Step-by-step explanation:
To find slope from 2 points: [tex]\frac{y2-y1}{x2-x1}[/tex]
[tex]\frac{-2-6}{2-(-2)} =-\frac{8}{4}[/tex]
1) x2 + 5x + 4 = 0
a =
b=
C =
vb2 - 4ac =
-
Answer:
9
Step-by-step explanation:
given a quadratic equation in standard form
ax² + bx + c = 0 ( a ≠ 0 ) then the discriminant is
Δ = b² - 4ac
x² + 5x + 4 = 0 ← is in standard form
with a = 1, b = 5 , c = 4 , then
b² - 4ac = 5² - (4 × 1 × 4) = 25 - 16 = 9
35 is what percent of 150
[tex]~~~~~~150\times x\% = 35\\\\\implies 150 \times \dfrac{x}{100} = 35\\\\\implies \dfrac{3x}{2}=35\\\\\implies 3x = 35\cdot 2\\\\\implies 3x = 70\\\\\implies x = \dfrac{70}{3}\\\\\implies x =23.\overline{3}\\\\\text{So, 35 is}~ 23.\overline{3}\%~ \text{of} ~150.[/tex]
does someone mind helping me with this question? Thank you!
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: a = \pi {r}^{2} [/tex]
where, r = d/2 = 6/2 = 3 ft[tex]\qquad \sf \dashrightarrow \: a = 3.14 \times {3}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: a = 3.14 \times 9[/tex]
[tex]\qquad \sf \dashrightarrow \: a = 13.26 \: \: ft {}^{2} [/tex]
Answer: 28.26
Step-by-step explanation:
D = 6
R = 3
3.14 x 3 x 3 = 28.26
urgent help with a geometry assignment!!
Answer: 480 and 253.2
Step-by-step explanation:
For the first one we want to do (12 x 5 / 2) x 16 which equals 480.
For the next question, the answer is 253.2 because 2πrh is the formula of lateral area. If we just plug in the numbers it's (2 x 3.14 x 4.8 x 8.4) = 253.2cm
The diameter of the circle above is 86 cm. What is the circumference of the circle? (Use = 3.14.)
A. 135.02 cm
B. 5,805.86 cm
C. 11,611.72 cm
D. 270.04 cm
Answer:
D
Step-by-step explanation:
Circumference = pi × diameter
(-3c+6) + (-c+8) simplify with a step by step please
Step-by-step explanation:
[tex] = ( - 3c + 6) + ( - c + 8)[/tex]
[tex] = - 3c + 6 - c + 8[/tex]
[tex] = - 3c - c + 6 + 8[/tex]
= -4c + 14
hence -4c + 14 is the answer ...
hope it helped !!
What is the slope of the line passing through the points (4, 5) and (0, -7)? Show all your work.
Answer:
slope = 3
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, 5 ) and (x₂, y₂ ) = (0, - 7 )
m = [tex]\frac{-7-5}{0-4}[/tex] = [tex]\frac{-12}{-4}[/tex] = 3
rise over run
you can also use the y2-y1/x2-x1 but these numbers where small enough where graphing can help visually
Lindsey bought supplies for a class project and brought the receipt to school. The 6 items cost:
$5.00$3.00$8.00$5.00$4.00$5.00
What was the mode of the prices of the items?
Answer:
$5
Step-by-step explanation:
$5 appeared more in the prices
Answer:
5 dollars
Step-by-step explanation:
cuz I just know
5) Find the x-intercept and the y-intercept of the equation: 8x - y = -24.
Answer:
First we have to turn it into slope intercept form which is y = mx + b.
we need to isolate y. To do this, we have to subtract 8x from both sides to get
-y = -8x - 24
-25 is the y intercept and -8 is the slope.
Step-by-step explanation:
Question 5 (1 point)
(07.07)
Find the product of (x + 3). (1 point)
o a
x2 + 6x + 9
x2 - 6x + 9
Ос
x2-9
d
x2 + 9
Answer:
a) x² + 6x + 9
Step-by-step explanation:
When we square something, we multiply it by itself:
⇒ (x + 3)² = (x + 3)(x + 3)
Using the FOIL method: (a + b)(c + d) = ac + ad + bc + bd
⇒ (x + 3)(x + 3) = x² + 3x + 3x + 9
= x² + 6x + 9
a.
[tex]\huge{{x}^{2} + 6x + 9}[/tex]
Step-by-step explanation:
Using Binomial Theorem:
[tex]\boxed{{(a+b)} ^n= \sum_{k=0}^{n}\binom{n}{k} a^{n-k}b^{k}}[/tex]
.
.
.
[tex](a+b) ^2 =a^{2} + 2ab +b^{2} [/tex]
The answer seems to be [tex]x^{2} + 6x + 9[/tex]...
All 6 members of a family work. their hourly wages (in dollars) are the following.
18, 14, 35, 34, 11, 26
assuming that these wages constitute an entire population, find the standard deviation of the population. round your answer to two decimal places.
The standard deviation of the population dataset is 9.35
How to determine the standard deviation?The dataset is given as:
18, 14, 35, 34, 11, 26
Start by calculating the mean using:
Mean = Sum/Count
This gives:
[tex]\bar x = (18+ 14+ 35+ 34+ 11+ 26)/6[/tex]
Evaluate
[tex]\bar x = 23[/tex]
The standard deviation is then calculated using:
[tex]\sigma = \sqrt{\frac{\sum (x - \bar x)^2}{n}}[/tex]
This gives
[tex]\sigma = \sqrt{\frac{(18 - 23)^2 + (14- 23)^2 + (35- 23)^2 + (34- 23)^2 + (11- 23)^2 + (26- 23)^2}{6}}[/tex]
Evaluate
[tex]\sigma = \sqrt{\frac{524}{6}}[/tex]
This gives
[tex]\sigma = 9.35[/tex]
Hence, the standard deviation of the population is 9.35
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How much is a $99 top hat at 1/3 off
Answer:
66$
Step-by-step explanation:
1/3 of 99 is 33
so 99 - 33 = 66
A microscope shows you an image of an object that is 80 times the object's actual size. So the scale factor of the enlargement is 80. An insect has a body length of 9 millimeters. What is the body length of the insect under the microscope?
Answer:
80
Step-by-step explanation:
