The range of f(x) = (4/5)^x is {y| y > 0}, and the range of g(x) = (4/5)^x + 6 is {y| y > 6}.
Explanation:The range of a function refers to the set of all possible output values of the function. To determine the range of f(x) = (4/5)^x, we need to consider that any positive real number raised to any power will yield a positive result. Therefore, the range of f(x) is {y | y > 0}.
For g(x) = (4/5)^x + 6, we can see that adding a constant term of 6 to the function will shift the entire graph upwards by 6 units. Consequently, the range of g(x) is {y | y > 6}.
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A building lot in a city is shaped as a 30°-60°-90° triangle, like the figure shown.
The side opposite the 30° angle measures 41 feet.
A) find the length of the side of the lot opposite the 60° angle.(show how I know).
B) find the length of the hypotenuse of the triangular lot.(show how I know)
A measure of ________ for a numerical data set describes how its values vary with a single number.
center
tendency
variation
shape @NeedHelpQuick546 @paki @texaschic101 @mjoxprm360,
The measure of variation for a numerical data set describes how the values of a number vary with the single number. This measurement shows the difference in the properties of a certain number to the rest of the numbers in the numerical data set.
The term that describes how values of a numerical data set vary with a single number is 'variation'. It quantifies the spread of data values, helping to add context and meaning to averages in a data set.
Explanation:A measure of variation for a numerical data set describes how its values vary with a single number. Variation is a statistical concept that is used to quantify the spread or dispersion of a set of data values. A low variation indicates that the data points tend to be close to the mean (or expected value), while a high variation indicates that the data points are spread out over a wider range.
For example, if we have a data set of test scores, the variation can help us understand how close or far the scores are from the average test score. This provides more context and meaning to the overall average.
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Explain how to use the figure below and a sequence of similarity transformations to prove that all circles are similar.
I'm not sure what it means by "similarity transformations" unless those are the translations, dilations, etc. If that's what it's referring to, then I think I understand what it's asking. Thanks in advance.
Translation, reflection, rotation and dilation always produces similar shapes, therefore all circles are similar.
What are similar figures?Two figures are said to be similar if they have the same shape and the ratio of their corresponding sides are in the same proportion.
Translation, reflection, rotation and dilation always produces similar shapes, therefore all circles are similar.
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A tree casts a shadow that is about 15ft. long. Javier, who is about 5.5 ft. tall, is standing near the tree. Javier's shadow is about 4.5 ft. long. What is the estimated height, t, of the tree?
A. 9.6 ft.
B. 12 ft.
C. 15 ft.
D. 18 ft.
I got no idea on this! Please help!! 20 points.
What is the sum of the polynomials
Answer:
Option B. 4m - 24n + 3
Step-by-step explanation:
There are two polynomials (17m - 12n - 1) and (4 - 13m - 12n)
We have to add the given tow polynomials
(17m - 12n -1) + (4 - 13m -12n)
Now we will put the similar terms together and add them.
(17m - 12n -1 + 4 - 13m - 12n) = 17m - 13m -12n - 12n -1 + 4 = 4m - 24n + 3
The final answer by adding them is Option B. 4m - 24n + 3
Which piecewise relation defines a function?
Answer:
option c is correct
Step-by-step explanation:
Which of the following functions best represents the graph?
A. f(x) = x3 + 2x2 − 4x − 8
B. f(x) = x3 + 4x2 − x − 4
C. f(x) = x3 + x2 − 9x − 9
D. f(x) = x3 + 3x2 − 3x − 9
Answer:
Option: C is the correct answer.
[tex]f(x)=x^3+x^2-9x-9[/tex]
Step-by-step explanation:
Clearly from the graph we could see that:
3 and -3 are zeros of the function f(x).
since the graph crosses these two points on the x-axis.
i.e. when x=3 or -3 ⇒ f(x)=0
Now when we put x=3 in each of the equation we see that:
A)
[tex]f(x)=x^3+2x^2-4x-8[/tex]
when x=3
[tex]f(x)=3^3+2\times 3^2-4\times 3-8\\\\f(x)=27+18-12-8\\\\f(x)=25\neq0[/tex]
Hence, option A is incorrect.
B)
[tex]f(x)=x^3+4x^2-x-4[/tex]
when x=3
[tex]f(x)=27+36-3-4\\\\f(x)=56\neq0[/tex]
Hence, option B is incorrect.
D)
[tex]f(x)=x^3+3x^2-3x-9[/tex]
when x=3
[tex]f(x)=27+27-9-9\\\\f(x)=36\neq0[/tex]
Hence, option D is incorrect.
Hence all the three options are discarded.
Hence, option C is the correct answer.
The function best represents the graph is:
[tex]f(x)=x^3+x^2-9x-9[/tex]
The wheels on Annie's bicycle are $20$ inches in diameter. If each wheel makes $3$ full revolutions every second, then how many feet does Annie travel in $1$ second? Give your answer as an integer, rounded to the nearest foot.
Final answer:
To calculate the distance Annie travels on a bicycle with 20-inch diameter wheels making 3 revolutions per second, use the formula for calculating distance traveled.
Explanation:
The diameter of the wheels is 20 inches, which means the radius is half of the diameter, so radius = 10 inches = 10/12 feet. Each wheel makes 3 revolutions per second.
To find how many feet Annie travels in 1 second, you can use the formula:
Distance traveled = 2 * pi * radius * number of revolutions per second.
Substitute the values into the formula and then round to the nearest foot to get the answer.
The answer is 0 feet.
HELP! A scale model of an ancient Egyptian pyramid is 29 centimeters high, with a base length of 46 centimeters.
The height of the real pyramid is 145 meters. What is the base length of the real pyramid?
Enter your answer, in simplest form, in the box
The length of a rectangle is 3 times its width. if the width is diminished by 1 inch and the length is increased by 3 inches. the area of the the new rectangle is 72 square inches. find the dimensions of the original rectangle.
The width of the original rectangle is 5 inches and the length is 15 inches.
Explanation:Let's assume the width of the original rectangle is x inches. According to the problem, the length of the rectangle is 3 times its width, so the length of the original rectangle is 3x inches.
When the width is diminished by 1 inch, the new width becomes x - 1 inches. And when the length is increased by 3 inches, the new length becomes 3x + 3 inches.
The area of a rectangle is given by length multiplied by width, so we can set up the following equation:
(x - 1)(3x + 3) = 72
By multiplying out the terms and rearranging the equation, we get:
3x^2 + 6x - x - 3 = 72
Combining like terms and simplifying further:
3x^2 + 5x - 75 = 0
Solving this quadratic equation gives us two possible answers for x: x = -5 or x = 5.
Since the width cannot be negative, we discard the negative value of x. Therefore, the width of the original rectangle is 5 inches and the length is 3 times the width, which is 3 * 5 = 15 inches.
Refer to Explorations in Literature for a complete version of this passage.
Read this excerpt from "Here Is New York."
…each embraces New York with the intense excitement of first love, each absorbs New York with the fresh eyes of an adventurer, each generates heat and light to dwarf the Consolidated Edison Company.
How does the author use imagery in “Here Is New York” to advance his viewpoint?
A: The imagery emphasizes that individual people can find opportunities in New York that they cannot find elsewhere.
B: The imagery expresses the majesty of New York City and illustrates how the writer sees New York.
C: The imagery illustrates his view of what a true New Yorker is and the relationship that a New Yorker should have with the city.
D: Specific references to personal experiences illustrate how the writer felt when he first came to New York.
Answer:
'each embraces New York with the intense excitement of first love, each absorbs New York with the fresh eyes of an adventurer, each generates heat and light to dwarf the Consolidated Edison Company'
The correct answer is C - The imagery illustrates his view of what a true New Yorker is and the relationship that a New Yorker should have with the city.
what ratio is the same as 75 percent
4. The triangles are similar. If QR = 9, QP = 6, and TU = 19, find TS. Round to the nearest tenth.
A. 16
B. 28.5
C. 2.8
D. 12.7
HURRRY QUICK!!!!!!
HELP ME ON THIS!!!!!!!!!!!!!!!!!!!!
Say you own 316 shares of Esti Transport stock, which offers an annual dividend of $8.16 per share. How much will you receive in quarterly dividends?
Answer:
$644.64
Step-by-step explanation:
Total shares=316
Annual Dividend on 1 share =$8.16
Annual Dividend on 316 shares=$8.16*316
=$2578.56
As there are four quarters in a year, the total annual dividend will be divided by 4 to get the quarterly dividend.
Quarterly Dividend for 316 shares= 2578.56/4
=$644.64
Answer:
the answer is c
Step-by-step explanation:
What is measure of angle R?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
What is measure of angle P?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
Both questions use the same pic
Given is a Right triangle PQR with angle Q = 90 degrees.
Given are sides PQ = 8 cm, QR = 15 cm, PR = 17 cm.
Side PR is the hypotenuse.
We can use formula for "sin" given as follows :-
[tex] sin(\theta)=\frac{Opposite}{Hypotenuse} [/tex]
For angle R, opposite side would be PQ.
[tex] sin(R)=\frac{PQ}{PR} \\\\
sin(R)=\frac{8}{17} \\\\
sin(R)=0.470588235 \\\\
R=sin^{-1}(0.470588235) \\\\
R = 28.07248694 \;\;degrees \approx 28.07 \;degrees [/tex]
For angle P, opposite side would be QR.
[tex] sin(P)=\frac{QR}{PR} \\\\
sin(P)=\frac{15}{17} \\\\
sin(P)=0.882352941 \\\\
P=sin^{-1}(0.882352941) \\\\
P = 61.92751306 \;\;degrees \approx 61.93 \;degrees [/tex]
Hence, R = 28.07 degrees and P = 61.93 degrees.
To solve the problem we must know about Trigonometric functions.
Trigonometric functions[tex]\rm {Sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]\rm {Cos \theta=\dfrac{Base}{Hypotenuse}[/tex]
[tex]\rm {tan\theta=\dfrac{Perpendicular}{Base}[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
The value of the ∠R is 28.0724°.The value of the ∠P is 61.9275°.Given to usPR = 17 cmQR = 15 cmPQ = 8 cm1. For ∠RFor ∠R, the opposite side will be PR, therefore, PR will be the Perpendicular,
Substituting the values in the formula of Sine,
[tex]\rm {Sin (\angle R)=\dfrac{PQ}{PR}\\\\ [/tex]
[tex]\rm {Sin (\angle R)=\dfrac{8}{17}\\ [/tex]
[tex]\rm {(\angle R)=Sin^{-1} \dfrac{8}{17}\\ [/tex]
[tex]\rm {(\angle R)=28.0724^o [/tex]
Hence, the value of the ∠R is 28.0724°.
2. For ∠PFor ∠P, the opposite side will be QR, therefore, QR will be the Perpendicular,
Substituting the values in the formula of Sine,
[tex]\rm {Sin (\angle P)=\dfrac{QR}{PR}\\\\ [/tex]
[tex]\rm {Sin (\angle P)=\dfrac{15}{17}\\ [/tex]
[tex]\rm {(\angle P)=Sin^{-1} \dfrac{15}{17}\\ [/tex]
[tex]\rm {(\angle R)=61.9275^o [/tex]
Hence, the value of the ∠P is 61.9275°.
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A car dealership sold one car in its first month of business. The number of cars it sold doubled each month. What was the total number of cars the dealership sold during the first 12 months?
Assuming the number of cars it sold doubled each month. The total number of cars the dealership sold during the first 12 months is: 4095.
Total number of cars soldUsing exponential growth formula
Total number of cars sold=2^N - 1
Where:
N = Number of months=12 months
Let plug in the formula
Total number of cars sold=2^12 - 1
Total number of cars sold=4,096 - 1
Total number of cars sold=4,095
Inconclusion the total number of cars the dealership sold during the first 12 months is: 4095.
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HELP ME PLEASE !
1. What is the solution of n² – 49 = 0? (1 point)
–7
7
±7
no solution
2. What is the solution of x² + 64 = 0? (1 point)
–5
8
±8
no solution
3. What is the side length of a square with an area of 144x²? (1 point)
12
12x
±12x
no solution
5. What is the value of z so that –9 and 9 are both solutions of x² + z = 103? (1 point)
–22
3
22
184
If 300 cubes can fit in the rectangular prism below what is the edge length of each cube
Answer:
Basic common sense just by looking at the dimensions
Step-by-step explanation:
...
A. 1/64in
B. 7/400in
C. 1/4in
D.4 11/16
Please help asap!! 14 points
Answer:
The equation of the line in slope-intercept form is y = 92x + 532.
The equation of the line in standard form is 9x−2y=−53
Explanation:
The slope of the line passing through (−7,−5)and(−5,4) is m=y2−y1x2−x1=4+5−5+7=92
Let the equation of the line in slope-intercept form be y=mx +cory =92x+c The point (-7,-5) will satisfy the equation . So, −5=92⋅ (−7)+corc=632−5=532
Hence the equation of the line in slope-intercept form is y=92x+532.
The equation of the line in standard form is
y=92x+532.or2y=9x+53
or 9x−2y =−53 {Ans]
What is the best way to combine sentences 6 and 7? Answer it and I'll mark you brainliest answer !!
A,b,c, or d let me know ASAP.
Consider the half reactions below for a chemical reaction.
(pictured below)
What is the overall equation for this chemical reaction?
choices below
Answer:
The answer is A
Step-by-step explanation:
In the below system, solve for y in the first equation.
x – 3y = –6
2x – 7y = 10
one thirdx + 2
negative one thirdx + 6
–x + 2
negative one thirdx + 2
PLZ HELP ME WITH THIS
ASAP
BLANK 1 : right, down, left , up
BLANK 2: up, right , left , down
BLANK 3: 2, 6, 9,-1
BLANK 4: -1, -8, 2, -5
Thx
WORTH 30 PTS PLS ANSWER ASAP.
Jordan is a manager of a car dealership. He has two professional car washers, Matthew and Arianna, to clean the entire lot of cars. Matthew can wash all the cars in 14 hours. Arianna can wash all the cars in 11 hours. Jordan wants to know how long it will take them to wash all the cars in the lot if they work together.
Write an equation and solve for the time it will take Matthew and Arianna to wash all the cars together. Explain each step.
Answer:
They will take 6.16 hrs or 6 hrs, 9 minutes and 36 seconds.
Step-by-step explanation:
Consider the provided information.
Let x is the number of cars in a lot.
Matthew can wash all the cars in 14 hours. That means in 1 hr he can wash x/14 cars.
Arianna can wash all the cars in 11 hours. That means in 1 hr Aranna can wash x/11 cars.
Together there rate will be:
[tex]\frac{x}{14}+\frac{x}{11}=\frac{x}{y}[/tex]
Here y represent the time taken by them if they work together.
Divide both sides by x, we get
[tex]\frac{1}{14}+\frac{1}{11}=\frac{1}{y}[/tex]
Thus, the required equation is: [tex]\frac{1}{14}+\frac{1}{11}=\frac{1}{y}[/tex]
Now solve for time, Here time is represents by y.
[tex]\frac{1}{14}+\frac{1}{11}=\frac{1}{y}[/tex]
[tex]\frac{11+14}{154}=\frac{1}{y}[/tex]
[tex]\frac{25}{154}=\frac{1}{y}[/tex]
[tex]y=\frac{154}{25}[/tex]
[tex]y=6.16[/tex]
Hence, they will take 6.16 hrs or 6 hrs, 9 minutes and 36 seconds.
Find the lateral area of a right circular cone whose radius is 6 feet and height is 8 feet.
The lateral area of a right circular cone with a radius of 6 feet and height of 8 feet is 60π square feet. We calculate this by first finding the slant height using the Pythagorean Theorem and then substituting the radius and slant height into the formula for the lateral area of a cone.
Explanation:The lateral area of a cone can be calculated using the formula πrl, where r is the radius and l is the slant height. However, in this question, we're not provided the slant height, but the height. Therefore, we first need to find the slant height using the Pythagorean theorem, since a right circular cone forms a right triangle with the radius and the height. Using Pythagorean theorem, the slant height (l) can be found as
l = √(r² + h²) = √((6ft)² + (8ft)²) = 10ft.
Substitute the values of r and l into the formula for lateral area: πrl = π × 6ft × 10ft = 60π ft².
So, the lateral area of the cone is 60π square feet.
Remember to always use the correct units when solving such problems.
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Please help ASAP!!! 14 points ):
i need help fast thx
Please help me figure this out because everything I've tried doesn't work. I NEED TO FINISH THIS TO GRADUATE PLEASE PLEASE PLEASE HELP ME!
A perpendicular bisector, CD , is drawn through point C on AB.
If the coordinates of point A are (-3, 2) and the coordinates of point B are (7, 6), the x-intercept of CD is ____ . Point ___ lies on CD.
Part 1 options
(3,0)
(18/5,0)
(9,0)
(45/2,0)
Part 2 options
(-52,141)
(-20,57)
(32,-71)
(54,-128)