Algebra 3, in the excercise size the graphs to determine the functions domain and range, x and y intercepts if any, and the functions values indicated below the graphs
Answers
Answer:
Read Explanation
Step-by-step explanation:
The domain is a list of all possible x-values, this graph starts at 0 and proceeds to positive infinity, making the domain:
[0,∞)
The range is a list of all possible y-values, this graph starts at -1 and proceeds to positive infinity, making the range:
[-1,∞)
x-intercepts Are where the line crosses the x-axis, in this graph the line only crosses the x-axis at x of 2. Making its only x-intercept 2.
y-intercepts Are where the line crosses the y-axis, in this graph the line only crosses the y-axis at y of -1. Therefore its y-intercept is -1.
In function notation when a question asks for f(x) its asking for the y values at the given x-values. At x of 3 the y value equals 1.
Related Questions
Given u=2i-9j and v=-5i+7j, what is u•v?
Answers
The value of the vector will be -53. The correct option is C.
What are vectors?In mathematics and physics, the term "vector" is used informally to describe certain quantities that cannot be described by a single number or by a set of vector space elements.
The dot product, also known as the scalar product, is an algebraic operation that takes two sequences of integers of equal length and outputs a single number.
The given vectors are u=2i-9j and v=-5i+7j, the dot product of the vectors will be calculated as below:-
u.v = ( 2i-9j ).( -5i+7j)
u.v = -10i² + 17 (i.j) -45(i.j) -63j²
Substitute i² = 1, j² = 1 and (i.j) = 0 in the above equation.
u.v = -10 + 63
u.v = 53
Therefore, the value of the vector will be -53. The correct option is C.
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Solve:
4(2 + a) = 24
A =
Answers
Answer:
a=4Step-by-step explanation:
Simplify both sides of the equation:
4 (2 + a) = 24
( 4 )( 2 ) + ( 4 )( a ) = 24 (Distribute)
8 + 4a = 24
4a + 8 = 24
subtract 8 from both sides:
4a + 8 − 8 = 24 − 8
4a = 16
Divide both sides by 4:
4 a/4 = 16/4
a = 4
Multiple bracket out first:
4 x 2 =8
4 x a = 4a
8 +4a = 24
-8
4a. = 16
÷4
a = 4
Hope this helps!
Can you help me solve this, please?
Answers
Answer:
Step-by-step explanation:
A school dance committee has 14 volunteers. Each dance requires 3 volunteers at the door, 5 volunteers on the floor, and 6 floaters. If two of the volunteers, Christine and Samuel, cannot work together since they are new, in in how many ways can the volunteers be assigned?
Answers
There are 91 such ways in whih the volunteers can be assigned if two of them cannot be assigned from 14 volunteers.
Given that a school dance committee has 14 volunteers and each dance requires 3 volunteers at the door, 5 volunteers on the floor and 6 on floaters.
We are required to find the number of ways in which the volunteers can be assigned.
Combinations means finding the ways in which the things can be choosed to make a new thing or to do something else.
n[tex]C_{r}[/tex]=n!/r!(n-r)!
Number of ways in which the volunteers can be assigned is equal to the following:
Since 2 have not been assigned so left over volunteers are 14-2=12 volunteers.
Number of ways =14[tex]C_{12}[/tex]
=14!/12!(14-12)!
=14!/12!*2!
=14*13/2*1
=91 ways
Hence there are 91 such ways in whih the volunteers can be assigned if two of them cannot be assigned.
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Estimate each of these square roots.
a) √80
b) √27
c) √110
d) √0.03
e) √0.12
Answers
Answer:
a) √80 ≈ 9
b) √27 ≈ 5
c) √110 ≈ 10
d) √0.03 ≈ 0.2
e) √0.12 ≈ 0.3
Step-by-step explanation:
a) √8080 is close to 81
Therefore, √80 can be estimated as √81
√81 = 9
[tex]\Large\boxed{\sqrt{80}\approx9 }[/tex]
b) √2727 is close to 25
Therefore, √27 can be estimated as √25
√25 = 5
[tex]\Large\boxed{\sqrt{27}\approx5 }[/tex]
c) √110110 is close to 100
Therefore, √110 can be estimated as √100
√100 = 10
[tex]\Large\boxed{\sqrt{110}\approx10 }[/tex]
d) √0.030.03 is close to 0.04
Therefore, √0.03 can be estimated as √0.04
√0.04 = 0.2
[tex]\Large\boxed{\sqrt{0.03}\approx0.2 }[/tex]
e) √0.120.12 is close to 0.09
Therefore, √0.12 can be estimated as √0.09
√0.09 = 0.3
[tex]\Large\boxed{\sqrt{0.12}\approx0.3 }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
The half life of a substance is defined as the time required for the substance to decrease by half. If the weight of a substance begins at 128 grams, and the half life is 7 years, what will be the weight of the substance after 28 years?
Answers
the weight of the substance after 28 years is 8 grams.
How to determine the amountWe have that the half life of a substance is defined as the time required for the substance to decrease by half
The formula for calculating the half - life of a material is given as;
[tex]N(t) = N0 (\frac{1}{2} )^\frac{t}{t^\frac{1}{2} }[/tex]
Where
N(t) is final amountNo is the initial amount = 128 gramst1/2 is the half life = 7 yearst is the time elapsed = 28 yearsSubstitute into the formula
N(t) = 128 × (0. 5) ^28/ 7
N (t) = 128 × ( 0. 5) ^ 4
N(t) = 128 × 0. 0625
N(t) = 8 grams
Thus, the weight of the substance after 28 years is 8 grams.
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what is the measure of an angle if it is 660 less than 6 times its own supplement
Answers
Answer:
60
Step-by-step explanation:
Since this angle is unknown, let's just represent it with the variable "x". So the supplement angle of "x" is essentially, the value of the angle that we need to add to "x" to get 180. In other words let's just say that the supplement angle is "y". This means that: [tex]x+y=180[/tex]. If we subtract x from both sides we can represent "y" or the supplement angle as: [tex](180-x)[/tex].
Since it's 660 less than 6 times it's own supplement let's first multiply the supplement by 6
[tex]6(180-x) = 1,080-6x[/tex]
Now let's subtract 660 from it, since it's 660 less
[tex](1,080 - 6x) - (660) = 420 - 6x[/tex]
This value should be equal to the angle, which is represented as "x". So let's set it equal to x
[tex]420-6x=x[/tex]
Add 6x to both sides
[tex]420=7x[/tex]
Divide both sides by 7
[tex]60 = x[/tex]
Can someone help me with this? I cannot figure it out
Answers
Answer:
Step-by-step explanation:
To graph by hand I would first convert both equations into y=mx+b.
We start with:
[tex]\left \{ {{2x-2y=4} \atop {x+2y=8}} \right.[/tex]
Solve for y for 2x-2y=4
[tex]2x+2y=4\\2y=4-2x\\y=2-x[/tex]
Solve for y for x+2y=8
[tex]x+2y=8\\2y=8-x\\y=4-\frac{x}{2}[/tex]
Giving the new but equal system of equations:
[tex]\left \{ {{y=2x-x} \atop {y=4-\frac{x}{2} }} \right.[/tex]
From this point on you can graph the two functions to find where the two lines intersect, thats your solution.
I've gone ahead and graphed it on desmos for you
Finding the area of a regular polygon
Answers
360° ÷ 10 ÷ 2 = 18°
So the length of the decagon side is:
10 × tan18° × 2 = 20 × tan18°
The area is: ½ × 20 × tan18° × 10 × 10 = 1000 × tan18°
≈ 324.9
.: 324.9 is the final answer.
I hope this helps.
The following two points are on a line: (2,3), (-2,5). What is the slope of the line?
Answers
Answer:
D
Step-by-step explanation:
slope = rise / run
slope = (5 - 3) / (-2 - 2)
slope = 2 / -4
slope = -2 / 4
slope = -1/2
find the perimeter of parallelogram PORS when side PQ=12cm and QR =7cm (with solution)
Answers
The answer is 38cm.
The formula used is perimeter of rectangle so in this case it will be 2(PQ+QR).
So,
=2×(12+7)
=2×19
=38cm
Plot the axis of symmetry and the point where the maximum value occurs for this function: h(x) = -(x 2)2 8.
Answers
See attachment for the axis of symmetry and maximum point.
What is a function?A function from a set X to a set Y allocates exactly one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain. Originally, functions were the idealization of how a variable quantity depends on another quantity.To plot the axis of symmetry:
The given function is: [tex]h(x) = -(x+2)^{2} +8[/tex]This function is in the form: [tex]g(x) = a(x-h)^{2} +k[/tex]Where the axis of symmetry is given by, x = h.y comparison, we have -h=2.This implies h=-2Therefore the axis of symmetry is x = -2.
Therefore, the maximum value occurs at the vertex, given by (h,k)=(-2,8).
So, see attachment for the axis of symmetry and maximum point.
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Which of the following scatter plots does not have a zero correlation?
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The following are the distances (in miles) to the nearest airport for 11 families. 9, 11, 11, 16, 16, 24, 28, 30, 34, 42, 45 Notice that the numbers are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set.
Answers
Here is the five-number summary, range and interquartile range:
Minimum: 9
Lower quartile: 11
Median: 24
Upper quartile: 34
Maximum: 45
Interquartile range: 23
What is the five-number summary?The minimum number is the smallest number in the data. The minimum number is 9. The maximum number is the biggest number in the dataset. The maximum number is 45.
The first quartile, third quartile and the interquartile range are used to measure dispersion.
The first quartile : 1/4(n + 1)
1/4 x (12) = 3rd term = 11
The third quartile : 3/4 x (n + 1)
3/4 x (12) = 9th term = 34
Interquartile range = third quartile - first quartile
34 - 11 = 23
Median can be described as the number that is at the center of the dataset when the number is arranged in either ascending or descending order.
Median = 25
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Using Euler's formula, how many
edges does a polyhedron with 9
faces and 14 vertices have?
[?] edges
Euler's Formula: F+ V=E+2
Answers
Answer:
Euler's Formula = F+V=E+2
F=9
V=14
So, 9+14=E+2
23=E+2
23-2=E
21=E
Hence, E (edges) = 21
Step-by-step explanation:
What is the tenth term in the sequence 9, 13, 17, 21, 25…?
Answers
Step-by-step explanation:
its 29 9x4=29 9+4=13 13+4=17
3² +4² = 5²,
6² + 8² = 10² and
9² + 12² = 15²
Can you prove,using algebraic method,that this relationship will be true for any multiple of the triple,
3, 4, 5?
Prove that the statement
5² +12² =13² will hold true for any multiple of this triple.
Answers
Answer:
They are all true
Step-by-step explanation:
1. 3² +4² = 5²
3x3 + 4x4 = 5x5
9 + 16 = 25
25 = 25
-----------------------
2. 6² + 8² = 10²
36 + 64 = 100
100 = 100
------------------
3. 9² + 12² = 15²
81 + 144 = 225
225 = 225
-------------------
4. 5² +12² =13²
25 + 144 = 169
169 =169
-------------------
I’m stuck on this problem
Answers
The value of the f(-8) from the given f(x) is 1/53.
According to the statement
we have given that the value of f(x) and with the value of this we hav eto find the value of f(-8).
So, For this purpose,
The given value of f(x) :
The function f(x) is
f(x) = 1 / x^2 -11
Now we find the value of the f(-8) then
For this put Put x is -8 in the f(x) then the equation become
f(x) = 1 / x^2 -11
f(-8) = 1 / (-8)^2 -11
f(-8) = 1 / 64 -11
f(-8) = 1 / 53.
here the value becomes 1/53.
So, The value of the f(-8) from the given f(x) is 1/53.
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Charlie is watching hot air balloons. balloon a has risen at a 50° angle. balloon b has risen at a 78° angle. if the distance from balloon a to the ground is 1,000 feet, how far is balloon b from balloon a? round your answer to the nearest whole number.
Answers
The distance from Balloon A to Balloon B, d ≈ 1,052 feet
What is distance ?
Distance is defined to be the magnitude or size of displacement between two positions. Note that the distance between two positions is not the same as the distance traveled between them. Distance traveled is the total length of the path traveled between two positions. Distance traveled is not a vector.The given parameters are;
The angle at which Balloon A rises, x° = 50° above horizontal
The angle at which Balloon B rises, y° = 78° above horizontal
The (vertical) distance of Balloon A to the ground, h = 1,000 ft.
The required parameter;
The distance from Balloon A to Balloon B, d
We find the distances of the balloons from Charlie and the angle between the balloon strings, θ, then apply cosine rule
Let,
The height of the balloon strings are equal
The distance of Balloon A to the ground, h₁ = The distance of Balloon B to the ground, h₂ = 1,000 ft.
The distance of the Balloon A from Charlie, l₁, is given as follows;
l₁ × sin(x°) = h₁
∴ l₁ = h₁/(sin(x°))
Which gives;
l₁ = 1,000 ft./(sin(50°)) ≈ 1,305.41 ft.
l₁ ≈ 1,305.41 ft.
For Balloon B, we get;
h₁ = h₂ = 1,000 ft.
∴ l₂ = 1,000 ft./(sin(78°)) ≈ 1,022.34 ft.
l₂ ≈ 1,022.34 ft
The angle between the balloon strings, θ = 180° - (x° + y°)
∴ θ = 180° - (50° + 78°) = 52°
The angle between the balloon strings, θ = 52°
By cosine rule, we have;
d = √(l₁² + l₂² - 2 × l₁ × l₂ × cos(θ))
∴ d = √(1,305.41² + 1,022.34² - 2 × 1,305.41×1,022.34 × cos(52°)) ≈ 1,052 feet
Therefore, the distance from Balloon A to Balloon B, d ≈ 1,052 feet
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PLS HELP LOTs OF POINTS!!!!What is the difference of….
Answers
[tex]\frac{-2x^{2} +25 }{(x-2) (x-5)} ,x\neq 2,x\neq 5[/tex] is the difference.
What is an expression?
⇒ An expression is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.)
Calculation :
⇒ [tex]\frac{3x^{2} }{(x^{2} -7x+10)}- \frac{5x} {x-2}[/tex]
⇒ [tex]\frac{3x^{2} }{(x-2)(x-5)}- \frac{5x} {x-2}[/tex]
⇒1/(x-2) [(3x²-5x{x-5})/(x-5)]
⇒1/(x-2) [(3x²-5x²+25x)/(x-5)]
⇒1/(x-2) [ (-2x²+25x)/(x-5)]
⇒[tex]\frac{-2x^{2} +25x }{(x-2)(x-5)}[/tex]
at x=2 and x=5 the denominator becomes zero If the denominator of a fraction is zero, the expression is not a legal fraction because its overall value is undefined.
⇒ [tex]\frac{-2x^{2} +25 }{(x-2) (x-5)} ,x\neq 2,x\neq 5[/tex] is the difference
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The figure below is made of 222 rectangular prisms.
What is the volume of this figure?
A shape made up of two rectangular prisms. The first rectangular prism has a base that measures 9 inches length by 6 inches width, and has a height of 3 inches. The second rectangular prism sits behind the first rectangular prism. It has a base that measures 10 inches length by 7 inches width and has a height of 3 inches.
please help its a khan question and i have a timer :'D
Answers
Answer:
372 in^3.
Step-by-step explanation:
The volume of the first prism = 9*6*3
= 162 in^3.
Volume of second prism
= 10*7*3
= 210 in^3.
Total vol = 162 + 210
= 372 in^3.
The required volume of the composite prism is 372 cubic inches,
Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
here,
To determine the volume of the composite prism,
As we can see there is two rectangular prisms,
Calculate the volume of two individual prisms and add their volume to the composite volume of the figure.
The volume of the first prism
= lenght × width × height
= 9 × 6 ×3 = 162 in³
The volume of the second prism
= lenght × width × height
= 10 × 7 ×3 = 210 in³
The total volume of the composite figure = 162 + 210 = 372 in³.
Thus, the required volume of the composite prism is 372 cubic inches,
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for f(x)=7x and g(x)=x+1, find the following functions. a.(fog)(x); b.(gof)(x); c.(fog)(4); d.(gof)(4)
Answers
Answer:
[tex]a.(fog)(x) = 7x + 7 \\ b.(gof)(x) = 7x + 1 \\ c.(fog)(4) = 35 \\ d.(gof)(4) = 29[/tex]
Step-by-step explanation:
Greetings !
a. (fog)(x)= f[g(x)] = 7(x+1)
(fog)(x)= 7x+7b. (gof)(x) = g[f(x)] =7x+1
c. (fog)(4)=7(4)+7=28+7=35
d. (gof)(4)= 7(4)+1=28+1=29
(fog)(x)
f(g(x))f(x+1)7x+7(gof)(x)
g(f(x))g(7x)7x+1(fog)(4)
7(4)+735(gof)(4)
7(4)+129What is the equation of a line in point-slope form passing through (-4,6) and (2, 3)?
Answers
The answer is y - 3 = -1/2 (x - 2).
First, let's find the slope.
m = y₂ - y₁ / x₂ - x₁m = 3 - 6 / 2 + 4m = -3/6m = -1/2Then, the point slope form will be :
y - 3 = -1/2 (x - 2)Answer: y=-0,5x+4.
Step-by-step explanation:
[tex]A(-4;6)\ \ \ \ B(2;3)\\Straight \ line\ equation\ is:\\\displaystyle\\\boxed {\frac{x-x_1}{x_2-x_1} =\frac{y-y_1}{y_2-y_1}} \\\frac{x-(-4)}{2-(-4)}=\frac{y-6}{3-6} \\ \frac{x+4}{2+4}=\frac{y-6}{-3} \\\frac{x+4}{6}=\frac{y-6}{-3} \\ Multiply\ the\ left\ and\ right\ sides\ of\ the\ equation \ by\ -3:\\\frac{-(x+4)}{2} =y-6\\-0,5x-2=y-6\\y=-0,5x+4.[/tex]
What is the solution to the inequality 3x - 12| ≥ 6?
0-6
02
Ox<-6 or x> 18
Ox≤2 or x ≥6
Answers
========================================
Work Shown:
|3x-12| ≥ 6
3x-12 ≥ 6 or 3x-12 ≤ -6 ..... see note below
3x ≥ 6+12 or 3x ≤ -6+12
3x ≥ 18 or 3x ≤ -6+12
3x ≥ 18 or 3x ≤ 6
x ≥ 18/3 or x ≤ 6/3
x ≥ 6 or x ≤ 2
x ≤ 2 or x ≥ 6
----
Note: if |A| ≥ B, then A ≥ B or A ≤ -B where B is some positive number.
Example: |x| ≥ 5 means either x ≥ 5 or x ≤ - 5
A boat takes 10 hours to sail a distance of 100 nautical miles with the current.
Against the current, it takes the boat 25 hours to sail the same distance. Find
the rate of the current.
Answers
The rate of the current is 6 mile/hour.
What does a rate mean ?In this context, the rate is tantamount to speed o velocity in a linear motion. The S.I unit will be mile per hour.
Given that a boat takes 10 hours to sail a distance of 100 nautical miles with the current. The rate at which the boat move will be
The rate R1 = 100/10
R1 = 10 mile/hour
And when it moves against the current, it takes the boat 25 hours to sail the same distance. The rate at which the boat move will be
The rate R2 = 100/25
R2 = 4 mile/hour
The rate of the current R will be the difference between the two calculated rate. That is,
R = R1 - R2
R = 10 - 4
R = 6 mile/hour
Therefore, the rate of the current is 6 mile/hour.
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If you have 66 data observations in a sample, how many classes (bins) does the sturges' rule recommend for you to construct a frequency distribution?
Answers
According to Sturge's rule, number of classes or bins recommended to construct a frequency distribution is k ≈ 7
Sturge's Rule: There are no hard and fast guidelines for the size of a class interval or bin when building a frequency distribution table. However, Sturge's rule offers advice on how many intervals one can make if one is genuinely unable to choose a class width. Sturge's rule advises that the class interval number be for a set of n observations.
Given,
n = 66
We know that,
According to Sturge's rule, the optimal number of class intervals can be determined by using the equation:
[tex]k=1+log_{2} n[/tex]
Here, n is equal to 66 and by substituting the value to the equation we get:
[tex]k=1+log_{2} (66)[/tex]
k = 7.0444
k ≈ 7
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The temperature during a day can be modeled by a sinusoid. Answer the following question given that the low temperature of 7 degrees occurs at 5 AM and the high temperature for the day is 45 degrees.
Find the temperature, to the nearest degree, at 9 AM.
Answers
The temperature at 9 AM is approximately 10 degrees. Neither of the answers are correct. (Correct choice: E)
What is the temperature of a place at a given time?
Sinusoids are expressions with trascendent functions, to be more specfic, trigonometric functions, whose form is described below:
T(t) = A · sin (2π · t / T + C) + B (1)
Where:
A - Temperature amplitude, in degrees.B - Middle temperature, in degrees.T - Period, in hours.C - Angular phase, in radians.The temperature amplitude and the middle temperature can be found by the following expressions:
A = (t' - t'') / 2 (2)
B = (t' + t'') / 2 (3)
Where t' and t'' are maximum and minimum temperatures, in degrees.
Then, we proceed to find each constant of the sinusoidal model:
A = (45 - 7) / 2
A = 38 / 2
A = 19
B = (45 + 7) / 2
B = 52 / 2
B = 26
We assume a period of 24 hours (T = 24).
If we know that t = 0, T = 24, A = 19, B = 26, T(t) = 7, then the angular phase is:
7 = 19 · sin [(π / 12) · 0 + C] + 26
- 19 = 19 · sin C
sin C = - 1
C = π
T(t) = 19 · sin (π · t / 12 + π) + 26
Then, the temperature at 9 AM is: (t = 4)
T(4) = 19 · sin (π · 4 / 12 + π) + 26
T(4) ≈ 9.545
The temperature at 9 AM is approximately 10 degrees. Neither of the answers are correct. (Correct choice: E)
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Cross-multiplication is helpful in: a. quadratic equations c. linear equations b. solving proportions d. word problems please select the best answer from the choices provided a b c d
Answers
Correct option is B)
Cross-multiplication is helpful in Solving proportions.
What is Solving Proportions?Solving proportions is simply a matter of stating the ratios as fractions, setting the two fractions equal to each other, cross-multiplying and solving the resulting equation.
What are the 2 methods for solving proportions?Method I: Draw a double-sided number line, label the parts, set up a proportion and solve.
Method II: Using any method, calculate unit rate and then calculate how many pounds you can get for $30. Method III: Graph a point to represent the original ratio.
What is the rule for solving proportions?The product of the means is equal to the product of the extremes.
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I understand the the question you are looking for is :
Cross-multiplication is helpful in:
a. quadratic equations
b. solving proportions
c. linear equations
d. word problems
please select the best answer from the choices provided a b c d
The variable used to predict another variable in a regression analysis (usually x) is called the?
Answers
The variable used to predict another variable in a regression analysis (usually x) is called the independent variable.
The regression analysis is used to determine the effect on the dependent variable with every one unit change in the independent variable.
The dependent variable is also known as response.
and the independent variable is also known as predictor.
In case of simple linear regression there is only one independent variable and in cases of multiple linear regression there are more than one independent variables.
The general form of simple linear regression is:
[tex]y=mx+c[/tex]
The general form of multiple linear regression is:
[tex]y=c+m_1x_1+m_2x_2+...+m_nx_n[/tex]
The dependent variable are usually denoted by the letter "y" and the independent variables are usually denoted by the letter "x".
Therefore, the variable used to predict another variable in a regression analysis (usually x) is called the independent variable.
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guys pls make it fast [tex]3^{3x-2\\} =\sqrt[3]{9}[/tex]
Answers
Explanation
3^3x-2=3^2/3
3x-2=2/3
3x=2/3+2
3x=8/3
x=8/9
