Answers
The value of f(1) is 3.
An estimate of the value of f(-1) is -0.2.
The values of x for which f(x) = 1 are: x = (0, 3).
The value of x such that f(x) = 0 is x = -0.5.
The domain of f is {-2, 4}.
The range of f is {-1, 3}.
The interval over which f is increasing is {-2, 1}.
What is a domain?In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.
Furthermore, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph of the function shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-2, 4}.
Range = {-1, 3}.
In conclusion, we can logically deduce that this function is increasing over the [-2, 1] and decreasing over the interval [1, 4].
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Related Questions
3
Q
The diagram shows three shapes that are mathematically similar.
The heights of the shapes are in the ratio small: medium: large = 1:5:8.
Find the ratio shaded area : total unshaded area.
Give your answer in its simplest form.
NOT TO
SCALE
Answers
The ratio of the shaded area to the total unshaded area can be found to be 5 : 9.
How to find the ratio ?The three shapes are similar to each other which means that their areas must be similar as well.
The only shape that is shaded is the second largest shape and it has the value of 5 in the ratio. This means that the other two shapes are not shaded and their ratio values are 1 and 8.
This then means that the ratio of shaded area to unshaded area can be written as :
Shaded area : Unshaded area
5 x width : ( 1 x width) + ( 8 x width )
5 : 1 + 8
5 : 9
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Select the correct answer. Which statement correctly describes this expression?\left|x^3\right|+5 A. the sum of the absolute value of three times a number and 5 B. 5 more than the absolute value of the cube of a number C. the cube of the sum of a number and 5 D. the absolute value of three times a number added to 5
Answers
The expression |x³| + 5 is 5 more than the absolute value of the cube of a number.
Option B is the correct answer.
We have,
The expression |x³| represents the absolute value of the cube of a number x.
This means that no matter what value x takes (positive, negative or zero), the result of the expression will always be positive.
For example, if x = 2, then |x³| = |2³| = |8| = 8.
If x = -2, then |x³| = |-2³| = |-8| = 8.
Adding 5 to the absolute value of the cube of x means adding 5 to the positive number that resulted from |x³|.
So, if we take the examples from above, if x = 2, then the expression becomes |2³| + 5 = 8 + 5 = 13.
If x = -2, then the expression becomes |-2³| + 5 = 8 + 5 = 13.
Therefore,
The expression |x³| + 5 is 5 more than the absolute value of the cube of a number.
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What is the value of z in the triangle?
Enter your answer in the box. Round your final answer to the nearest hundredth.
Answers
Answer:
z = 12.52 in.
Step-by-step explanation:
Because this is a right triangle, we can solve for z using on the trigonometric ratios.
If we allow 37° to be our reference angle, the 10 in. side is the adjacent side and z (directly across from the right angle) is the hypotenuse.
Thus, we can use the cosine ratio which is
[tex]cos(angle)=\frac{adjacent}{hypotenuse}[/tex]
Now, we can plug everything into the formula and solve for z, the hypotenuse:
[tex]cos(37)=10/z\\z*cos(37)=10\\z=10/cos(37)\\z=12.52135658\\z=12.52[/tex]
What is the value of Q3 of the data represented by the box plot?
Enter your answer in the box.
Answers
The value of Q₃ of the data represented by the box plot is,
⇒ Q₃ = 30
Given that;
A box plot is shown in figure.
Now, We have been given an image of a box plot and we are asked to find the value of third quartile represented by our given box plot.
Since, we know that the upper or 3rd quartile is represented by the last line of the box.
We can see that 1st line of our box is at 20 ,so it will be 1st or lower quartile.
And, The middle line is at 25, so median for our given box plot is 25.
The last line of the box is at 30, which is representing the upper or third quartile of our given box plot.
Therefore, the third quartile, is 30 for our given box-plot.
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Shane is 61 feet high on a ride at an amusement park. The angle of depression to the park entrance is 42°, and the angle of depression to his friends standing below is 80°. How far from the entrance are his
friends standing? Round to the nearest foot.
Answers
tan(42) = 61 / x
tan(80) = 61 / y
Solving for y, we get:
y = 61 / tan(80)
y ≈ 12.2 feet
Therefore, Shane's friends are standing approximately 12.2 feet away from him.
solvesolveslvesolbesolve
Answers
The maximum value of z = 28. I occurs at (x, y) = 4
How to go about this ?To solve thhis linear programming problem, we can use the graphical method..
Graph the feasible region defined by the constraints.....
x >= 0 and y >= 0 represent the non-negative quadrants.
x + y < = 8 represents the area below the line passing through ( 8, 0) and (0, 8).
x + y >= 2 represents the area above the line passing through ( 2 , 0) and (0 , 2).
Identify the corner points of the feasible region .....
(0, 2)
( 2, 0)
( 4, 4)
( 8, 0 )
Calculate tthe objective function at each corner point....
z(0, 2 ) = 3(0) + 4(2) = 8
z (2, 0 ) = 3(2) + 4(0) = 6
z(4, 4 ) = 3(4) + 4(4) = 28
z ( 8, 0) = 3(8) + 4(0) = 24
Determine the maximum value of the objective function and the values of x and y that give this maximum value
The maximum value of z is 28, which occurs at the corner point (4, 4).
So we c can be stated as follows --
Maximum value of z = 28
x = 4
y = 4
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Write a polynomial function with the given zeros and their correspond possible answers. f(x) = Zeros 0 -6 -7 Mult. 1 3 1
[tex] - 13(t - 7) {6(t + 1) {8(t - 2)}^{?} }^{?} [/tex]
Answers
The value of a polynomial function with the given zeros would be,
⇒ f (x) = x (x + 7) (x + 6)³
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
Functions have zeroes 0, - 6, - 7 with multiplicity 1, 3, 1
Hence, We can formulate;
The value of a polynomial function with the given zeros would be,
⇒ f (x) = (x - 0)¹ (x - (- 6))³ (x - (- 7))¹
⇒ f (x) = x (x + 6)³ (x + 7)
⇒ f (x) = x (x + 7) (x + 6)³
Thus, The value of a polynomial function with the given zeros would be,
⇒ f (x) = x (x + 7) (x + 6)³
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What the answer for radius huryyyyyyyyyy pleaseeee
Answers
Answer: 12.6
Step-by-step explanation:
150/360*2*pi*r=10.
divide to get r alone
How many permutations do I have it I select 4 things from a total of 9 with replacement? (9P4)
Answers
There are 3024 possible arrangements of 4 items selected from a total of 9 with replacement.
It is required to find the number of permutations when 4 things are selected from a total of 9 with replacement.
Use the formula for permutations with replacement, which is:
= [tex]^np_r[/tex]
Here n is the total number of items and r is the number of selections.
As per the question, n = 9 and r = 4.
So, the number of permutations is:
= ⁹p₄
= 9!/5!
= 9 x 8 x 7 x 6
= 3024
Thus, there are 3024 possible arrangements of 4 items selected from a total of 9 with replacement.
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Write an explicit formula for an, the nth term of the sequence 36, 32, 28, ....
WORTH 20
Answers
Answer:
an = 36 + -4(n - 1)
Step-by-step explanation:
Explicit formula:
[tex]a_n=a_1+(n-1)d[/tex]
Where:
an = nth terma1 = first termd = common differenceHere, we are given the following:
Sequence: 36, 32, 28The first term is 36
To get to the next term, 4 is subtracted from the previous term so the common difference is -4.
So we have:
First term(a1) = 36Common difference = -4By plugging this into [tex]a_n=a_1+(n-1)d[/tex]
We acquire : [tex]a_n=36+(n-1)(-4)[/tex]
Assignment Active
The Economic Effect of Snowsheds
With so many snowsheds along the line, annual
maintenance soared. By 1910 many of the original
wooden structures needed replacing, and heavy snows in
the winter of 1912-13 crushed others. That year the
railway hired 1,800 workers to make shed improvements
along just 8 miles of track, and the need for additional
sheds was clear....
While making repairs on the Cascade Mountain
snowsheds in 1917, the Great Northern Railway used over
35 million board feet of timber that cost triple what it had
just eight years earlier. By this time, snowsheds and
tunnels covered 6.7 of the 9 track miles between
Wellington and Scenic.
According to this passage, how did snowsheds affect
the railroad in the long term?
O They decreased delays, which lowered the railroad
costs.
They required frequent repairs, which added to the
railroad costs.
They reduced the need for bridges, which lowered
the railroad costs.
O They required many workers to operate them,
which added to the railroad costs.
Answers
What is the slope of the line that passes through the points (2,-4) and (5,2)
Answers
Answer:
2.
Step-by-step explanation:
To find the slope of the line that passes through the points (2,-4) and (5,2), we can use the slope formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) = (2,-4) and (x2, y2) = (5,2)
slope = (2 - (-4)) / (5 - 2)
slope = 6 / 3
slope = 2
Therefore, the slope of the line that passes through the points (2,-4) and (5,2) is 2.
Can someone explain how to get the answer to…if 7p-4=8 what is the value of p?
Answers
The value of p in the equation 7p - 4 = 8 is p = 12/7
Solving for what is the value of p?From the question, we have the following parameters that can be used in our computation:
7p - 4 = 8
Add 4 to both sides
So, we have
7p = 12
Divide both sides by 7
So, we have
p = 12/7
Hence, the solution is p = 12/7
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perimeter of a tabe is 228 inches and the length is 18 inches which is more than twice the width. How do I find the length and width of the worktable
Answers
The width of the worktable is 32 inches, and the length of the worktable is 82 inches.
Let's assume that the width of the worktable is "w" inches.
We are given that the length is 18 inches more than twice the width, which can be expressed as:
Length = 2w + 18
The perimeter of the worktable is the sum of the lengths of all four sides.
We know that the perimeter of the worktable is 228 inches, so we can write an equation:
Perimeter = 2 × (Length + Width)
228 = 2 × (2w + 18 + w)
228 = 2 × (3w + 18)
Dividing both sides by 2:
114 = 3w + 18
Subtracting 18 from both sides:
96 = 3w
Dividing both sides by 3:
w = 32
So, the width of the worktable is 32 inches.
Now we can use this value to find the length:
Length = 2w + 18
Length = 2 × 32 + 18
Length = 82
So, the length of the worktable is 82 inches.
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In a roll of 50 pennies, 15 were made before 1985. What percent of the pennies in the roll were made before 1985?
Answers
The percentage of pennies in the roll is A = 30 %
Given data ,
Let the percentage of pennies in the roll made before 1985 be A
Now , the total number of pennies be = 50 pennies
And , the number of pennies made before 1985 is = 15 pennies
So , the percentage is A = ( 15 / 50 ) x 100
On simplifying the equation , we get
A = 3/10 x 100
A = 30 %
Hence , the percentage is 30 %
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help help help help help
Answers
have a good day
What is the measure of angle b?
A
90o
B
180o
C
43o
D
47o
Answers
Answer:
b
Step-by-step explanation: makes sense
The radius of a circle with area A is approximately $\sqrt{\frac{A}{3}}$
. The area of a circular mouse pad is 45 square inches. Estimate its radius to the nearest tenth.
in.
Answers
The radius of the circular mouse is 3.7 inches.
How to find the radius of a circle?The area of the circular mouse pad 45 square inches. Therefore, the radius of the circle can be found as follows:
area of the circle = πr²
where
r = radiusTherefore,
area of the circular mouse = 3.14 × r²
45 = 3.14r²
divide both sides by 3.14
r² = 45 / 3.14
r² = 14.3312101911
square root both sides
r = √14.331210911
r = 3.78565714243
r = 3.7 inches
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Triangle A and B are similar. Triangle A is shown below. The shortest side of triangle B is 10cm. What is the length of the other two sides?
Answers
Using the concept of similar triangles, the length of the other two sides of triangle B are: 20 cm and 25 cm
How to find the lengths of similar triangles?Similar triangles are defined as triangles that possess the same shape, but then their sizes may very well vary. This means that, if two triangles are similar, then we can say that their corresponding angles are congruent and corresponding sides are in equal proportion.
Since the shortest side of triangle B is 10cm, it means that it corresponds to the shortest side of triangle A which is 8 cm.
Thus:
Ratio of corresponding sides of B:A = 10/8
Thus:
Second side of triangle B: (10/8) = (x/16)
x = 160/8
x = 20 cm
Third side of triangle B: 10/8 = y/20
y = 200/8
y = 25 cm
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Pls help thanks!!!!!!!!!!!
Answers
Answer:
Put your calculator in degree mode.
sin(13°) = 500/x
x sin(13°) = 500
x = 500/sin(13°) = 2,222.7 miles
Using a trigonometric relation we can see that x = 2,222.7 ft
How to find the value of x?We can see a right triangle, there we can see that one of the angles has a measure of 13°.
The opposite cathetus has a measure of 500ft, and we want to find x, which is the hypotenuse.
Then we can use the relation:
sin(a) = (opp cathetus)/hypotenuse
Replacing what we know, we will get:
sin(13°) = 500/x
Solving that for x:
x = 500/sin(13°) = 2,222.7 ft
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What are the angles of rotation for a regular
pentagon? (Select all that apply)
a) 60
B) 72
c)90
d) 144
e) 180
f)216
g) 360
Answers
Answer:
c,,e,b,f
Step-by-step explanation:
what’s the answer? To solve the law of cosine I don’t understand this math I rly need help.
Answers
The length of u to the nearest centimeter is about 30 cm.
We are given that;'
s = 730 cm, t = 270 cm and U=125°.
Now,
The Law of Cosines states that for any triangle with sides a, b and c and angle C opposite to side c, we have:
c2=a2+b2−2abcosC
To find c = u. Plugging in the values, we get:
u2=7302+2702−2×730×270×cos125°
Using a calculator, we get:
u2≈912.9
Taking the square root of both sides, we get:
u≈30.21
Rounding to the nearest centimeter, we get:
u≈30cm
Therefore, by the law of cosine the answer will be 30 cm.
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Ellie is going to see a movie and is taking her 2 kids. Each movie ticket costs $13 and there are an assortment of snacks available to purchase for $5 each. How much total money would Ellie have to pay for her family if she were to buy 4 snacks for everybody to share? How much would Ellie have to pay if she bought x snacks for everybody to share?
Total cost with 4 snacks:
Total cost with x snacks:
Answers
The total cost that Ellie would pay with 4 snacks is $59.
The total cost that Ellie would pay with x snacks is $29 + $5x.
What is the total cost?The first step is to determine the total number of people going to the movies. There are 3 people going to the movies.
The total cost spent by Ellie is the sum of the tickets and the total cost of the snacks.
Total cost = total cost of the tickets + total cost of the snacks
= (cost of one ticket x number of people going to the movie) + (number of snacks bought x price of one snack)
= (13 x 3) + ($5 x 4)
$39 + $20 = $59
Total cost if x snacks is bought: (13 x 3) + ($5 x x) = $39 + $5x
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This is the graph of a function in the form f(x)=a•b^x what’s the function
Answers
Answer:
Step-by-step explanation:
The function f(x) = a * b^x represents exponential growth or decay. The value of a represents the starting value or y-intercept, while the value of b represents the growth or decay factor. If b is greater than 1, the function represents exponential growth, while if b is between 0 and 1, the function represents exponential decay.
To determine the values of a and b from a graph, we need to look for specific features. The y-intercept represents the value of a, so we can read it directly from the graph. The growth or decay factor b can be found by examining the slope of the graph. If the graph is increasing, then b is greater than 1, and if it is decreasing, then b is between 0 and 1.
El 60% de número de hombres es igual al 40% de mujeres. ¿qué tanto por ciento del total representa las mujeres?
Answers
The percentage of the total that women represent, would be 60% of the total.
How to find the percentage ?Given that 60 % of men is equal to 40 % of women, we have :
0. 6 M = 0. 4 W
Solving for women in terms of Men gives:
W = ( 0.6 x M) / 0.4
= 1.5 x M
We can then find the percentage of women to be:
= (W / Total ) x 100
= ((1.5 x M) / (2.5 x M)) x 100
= (1.5 / 2.5) x 100
= 0.6 x 100
= 60%
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Find the area of this semi-circle with diameter, d = 20cm.
Give your answer rounded to 2 DP.
Answers
The area of the semicircle is 157. 00 cm
How to determine the area of the semi-circleTo determine the area of the semi-circle, we need to consider the formua.
the formula for calculating the area of a semi-circle is expressed with the equation;
A = 1/2π²
Such that the parameters of the formula are;
A is the area of the semi-circler is the radius of the semi-circleπ takes the constant value of 3.14It is important to note that
Formula for diameter is expressed as
Diameter = 2radius
Radius = 10cm
Substitute the values
Area = 1/2× 3.14 × 100
Multiply the values
Area = 157 cm²
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Kevin wants to save $600 to buy a TV. He saves $17 each week. The amount, A (in dollars), that he still needs after w weeks is given by the following function.
A (w)=600-17w
Answer the following questions.
(a) If Kevin still needs $277, how many weeks has he been saving?
weeks
(b) How much money does Kevin still need after 5 weeks?
$?
Answers
Answer:
A) Kevin has been saving money for 19 weeks.
B) Kevin still needs $515.
Step-by-step explanation:
A) 277=600-17x /-600
-17=-323 /÷(-17)
x=19
B) x=600-17×5
x=600-85
x= 515
An hourglass is 6ft wide and 4 ft tall on top. On bottom the hourglass is 6ft wide and 2 feet tall. It can hold 2000 pounds. if the water takes exactly one year to pass through the hourglass, how much water pass through to the bottom each day? What is the linear function of the water passing through the hourglass?
Answers
The linear equation outlining the entire volume of water (y) which has coursed through the hourglass following x days. is
y = 5.48xThe volume of water passed each which is the slope is
5.48How to find the amount of water passing through the glass each dayTo ascertain the amount of water that is passing through the hourglass daily:
where:
Total water capacity: 2000 pounds
Time: 365 days
Water transpiring every day = Total water capacity / Time
Water pervading each day ≈ 200 / 365
Water pervading each day ≈ 5.48 pounds/day
the linear function of the water traveling through the hourglass.
Making x the number of days and y being the total quantity of water which has crossed through the hourglass after x days--as the fluid fluxes at a constant velocity--thus a linear relationship between x and y can be determined.
Every single day (x), the hourglass moves 5.48 pounds of water. This reveals the linear representation of:
y = 5.48x
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A positive real number is 1 less than another. When 2 times the larger is added to the square of the smaller, the result is 13. Find the numbers. (If applicable, write your answers in the form p±q√r)
Answers
From the problem, we know that:
2(x + 1) + x^2 = 13
Simplifying and rearranging:
x^2 + 2x - 11 = 0
Using the quadratic formula:
x = (-2 ± sqrt(2^2 - 4(1)(-11))) / (2(1))
x = (-2 ± sqrt(48)) / 2
x = (-2 ± 4sqrt(3)) / 2
x = -1 ± 2sqrt(3)
Since the problem states that the numbers are positive, we can ignore the negative solution. Therefore, the smaller number is:
x = -1 + 2sqrt(3)
And the larger number is:
x + 1 = 2sqrt(3)
So the two numbers are -1 + 2sqrt(3) and 2sqrt(3).
Write the inductive hypothesis for this statement
Answers
The inductive hypothesis is P₍ₐ₊₁₎ : 7 + 13 + 19 + ... + {6(a +1) +1} = (a + 1) {3(a + 1) + 4} is true for all (a+1) = n for the statement Pₙ : 7 + 13 + 19 + ... + (6n +1) = n(3n +4)
The statement is given as,
Pₙ : 7 + 13 + 19 + ... + (6n +1) = n(3n +4)
For n =1 we get,
P₁ : 6(1) + 1 =7
and, 1{3(1) + 4} = 7
Hence, 6n+ 1 = n(3n + 4) is true for n= 1.
Therefore assume that Pₐ is true for some a = n, we get,
Pₐ : 7 + 13 +19 +... + (6a +1 ) = a(3a + 4)
Let, n =a+1 , we get,
P₍ₐ₊₁₎ : 7 + 13 + 19 + ... + (6a +1) + {6(a +1) +1}
= Pₐ + (6a+ 7)
= a(3a + 4) + 6a + 7
= 3a² + 4a + 6a + 7
= 3a² +10a + 7
= 3a² + 7a + 3a + 7
= a( 3a + 7) + 1(3a + 7)
= (a + 1) ( 3a + 7)
= (a + 1) {3(a + 1) + 4}
Hence, (a +1) is true for all (a+1) = n by mathematical induction principle. Thus, the inductive hypothesis is true.
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