Using it's concept, the domain of the function is given as follows:
{x| –2 ≤ x <= 5}
What is the domain of a function?The domain of a function is the set that contains all possible input values for the function.
The function described is defined for x between -2 and 5, hence the domain is given by the following interval:
{x| –2 ≤ x <= 5}
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Answer:
{x| –2 ≤ x < 5}
Step-by-step explanation:
In the diagram below, EF || HG, EF = 5, HG = 12, FI = 1 4x + 3
and HI= 6.1x - 6.5.
What is the length of HI?
The length of HI in the similar triangles is: (4) 24.
What are Similar Triangles?The corresponding sides of triangles that are similar to each other have ratios that are equal to each other, thus, they are proportional.
Triangle EFI and triangle GHI are similar to each other. Therefore, their corresponding sides have ratios that are equal. Thus, we will have the following:
HI/FI = HG/EF
Given:
EF = 5,
HG = 12,
FI = 1.4x + 3
HI = 6.1x - 6.5
Plug in the values
6.1x - 6.5/1.4x + 3 = 12/5
Cross multiply
5(6.1x - 6.5) = 12(1.4x + 3)
Open the bracket
30.5x - 32.5 = 16.8x + 36
30.5x - 16.8x = 32.5 + 36
13.7x = 68.5
Divide both sides by 13/7
13.7x/13.7 = 68.5/13.7
x = 5
HI = 6.1x - 6.5
Plug in the value of x
HI = 6.1(5) - 6.5
HI = 30.5 - 6.5
HI = 24
The length of HI in the similar triangles is: (4) 24.
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The table shows the first five terms for two number sequences with different rules. Select the coordinate plane that has the ordered pairs properly plotted. (4 points)
A table with three columns, with the first column titled Sequence One, the second column titled Sequence Two, and the third column titled Ordered Pair. There are five rows below the heading row. Under Sequence One is the numbers six, eight, ten, twelve, fourteen. Under Sequence Two is the numbers sixteen, thirteen, ten, seven, and four. Under Ordered Pairs is the ordered pairs six and sixteen, eight and thirteen, ten and ten, twelve and seven, and fourteen and four.
The linear function of the table of values is y = -1.5x + 25
How to plot the ordered pairs?The table of values is given as:
Sequence One Sequence Two Ordered Pair
6 16 (6, 16)
8 13 (8, 13)
10 10 (10, 10)
12 7 (12, 7)
14 4 (14, 4)
From the above table of values, we can see that:
As x constantly increases by 2 i.e. +1y constantly decreases by 3 i.e. -3This means that the table represents a linear function, and the slope of the function is
m = -3/+2
This gives
m = -1.5
A linear function is represented as:
y = mx + c
This gives
y = -1.5x + c
Using the table of values, we have
16 = -1.5 * 6 + c
Evaluate the product
16 = -9 + c
Add 9 to both sides
c = 25
Substitute c = 25 in y = -1.5x + c
y = -1.5x + 25
Hence, the linear function of the table of values is y = -1.5x + 25
See attachment for the graph of the table
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What is the area of the shape?
The area of the shape is 35 square units
How to determine the area of the shape?The given shape is a trapezoid, and it has the following side lengths
Parallel bases = 6 and 8
Height = 5
The area of the shape is then calculated as:
A = 0.5 * (sum of parallel bases) * height
Substitute the known values in the above equation
A = 0.5 * (6 + 8) * 5
Evaluate the product
A = 35
Hence, the area of the shape is 35 square units
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The area of the given trapezoid is given as 35 square units
How to determine the area of a trapezoid?The given shape is quadrilateral known s a trapezoid. The formula for calculating the are of the trapezoid is expressed as;
A = 1/2(a+b)*h
where
a and b are parallel sides
h is the height of the trapezoid.
Given the following parameters
a =6units
b = 8 units
h - 5 units
Substitute to have:
A = 1/2(6 + 8) * 5
A = 1/2(14) *5
A = 7 * 5
A = 35 square units
Hence the area of the given trapezoid is given as 35 square units
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Use the recursive formula to find the first five terms in the arithmetic sequence.
The first five terms of the sequence are 1/5, 2/5, 3/5,4/5, 1
Recursive functionsRecursive functions are functions that is used to determine the next term of a given sequence giving the common difference.
Given the recursive function shown below;
f(1) = 1/5
f(n) = f(n-1) + 1/5
For the second term;
f(2) = f(1) + 1/5
f(2) = 1/5 + 1/5
f(2) = 2/5
For the third term;
f(3) = f(2) + 1/5
f(3) = 2/5 + 1/5
f(3) = 3/5
For the fourth term;
f(4) = f(3) + 1/5
f(4) = 3/5 + 1/5
f(4) = 4/5
For the fifth term;
f(5) = f(4) + 1/5
f(5) = 4/5 + 1/5
f(5) = 5/5 = 1
Hence the first five terms of the sequence are 1/5, 2/5, 3/5,4/5, 1
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Choose the equation that satisfies the data in the table.
-1 0 1
0
3
6
X
Y
OA. y = 3x +3
B.y = -x +9
Oc.y=x+9
OD. y=-3x +3
Answer:
A
Step-by-step explanation:
Based on the given table:
(x, y ) values are
(-1, 0)
(0, 3)
(1, 6)
A.
y = 3x+3, substitute each x and y pair in the equation to see if it checks
(x= -1, y= 0) (x= 0, y= 3) (x= 1, y= 6)
0 = -1·3+3 3 = 0·3 +3 6 = 1·3 + 3
0 = 0✅ 3 = 3✅ 6 = 6✅
I need help with this
Example 1 Find 6 – 9. 6 – 9 = 6 + ( – 9) To subtract 9, add – 9. = – 3 Simplify
Answer:
Step-by-step explanation: This example is saying that adding a negative number is the same as subtracting a positive number. For example 2-3 = 2 + (-3).
Determine which of the following graphs does not represent a function.
Answer:
Graph b.
Step-by-step explanation:
B is not a function because it fails the vertical line test.
To be a function any vertical line drawn must pass through the graph at one point only. That is not true for graph B - a line can pass through 2 points on this graph.
look at the graph below. what is the slope of the line a. -3 b.-1/3 c.1/3 d. 3
Answer:
-1/3
Step-by-step explanation:
Slope is rise over run. Every 3 units to the left, it rises 1 unit, so the slope is -1/3.
Find the value of each variable.
one of the properties of a cyclic quad (four sided shape in eucliean geometry) is that the opposite sides add up to 180°
So in this case to get x we= 180°-105°=285°
therefore x is 285°
Find the next two terms in this
sequence.
1, -3, 9, -27, 81, [ ? ], [ ? ]
Answer:
the answers are -243 and 729
Step-by-step explanation:
you multiply each by -3. 1x-3 gives you -3. -3x-3 gives you 9. -3x9 gives you -27. -27x-3 gives you 81. 81x-3 gives you -243 and -243x-3 gives you 729. i hope this helps.
What is the area of the following polygon?
I have tried 24, 25 and 26 and none of worked and I am at a loss.
The area of the polygon is 25.5 square units
How to determine the area of the polygon?From the figure, we have the following coordinates
A = (-2, 1)
B = (3, 2)
C = (5, -3)
D = (-1, -3)
The area of the polygon is then calculated as:
A = 0.5 * |(x1y2 - x2y1) + (x2y3 - x3y2) + (x3y4 - x4y3) + (x4y1 - x1y4)|
Substitute the known values in the above equation
Area = 0.5 * |(-2 * 2 - 3 * 1) + (3 * -3 - 5 * 2) + (5 * -3 + 1 * -3) + (-1 * 1 + 2 * -3)|
Evaluate the sum of products
Area = 0.5 * |-51|
Remove the absolute bracket
Area = 0.5 * 51
Evaluate the product
Area = 25.5
Hence, the area of the polygon is 25.5 square units
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HELPP!!!!! PLSSSS!!!!
Consider functions f and g. Select the correct answer.
f(x)=(x^4)+9x²-3
g(x)=(1/2)^(x-2)
Using a table of values, what are the approximate solutions to the equation f(x)=g(x) to the nearest quarter of a unit?
A.) x congruent to -0.25 and x congruent to 2.5
B.) x congruent to -1 and x congruent to 0.75
C.) x congruent to -0.5 and x congruent to 0.5
D.) x congruent to -0.25 and x congruent to 1.5
PLEASE HELP IM STUCK
Step-by-step explanation:
2 equations with 2 variables.
the most common approach is
1. use one equation to express one variable by the other.
2. use this expression in the second equation and solve for the second variable.
3. use that solution in the original first equation and solve for the first variable.
the end.
0.05N + 0.10D = 2.20
N + D = 23
1. N = 23 - D
2. 0.05(23 - D) + 0.10D = 2.20
1.15 - 0.05D + 0.10D = 2.20
0.05D = 1.05
D = 1.05/0.05 = 21
3. N = 23 - D = 23 - 21 = 2
2 Nickels, 21 Dimes
I need help here’s a picture can somone explain what I need to do??
The total area of the composite figure is 176 ft
How to find the area of a composite figure?The area of a composite figure can be found as follows;
Therefore,
Total area = area of rectangle + area of triangle
area of rectangle = lw
where
l = lengthw = widthTherefore,
area of a rectangle = 16 × 8
area of a rectangle = 128 ft²
area of triangle = 1 / 2 bh
where
b = baseh = heightTherefore,
area of triangle = 1 / 2 × 12 × 8
area of triangle = 48 ft²
Total area of the composite figure = 48 + 128 = 176 ft
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A circle has a radius of 9. An arc in this circle has a central angle of 120°. What is the length of the arc?
Answer:
6pi
Step-by-step explanation:
First, find the circumference of the circle with radius 9. The formula is C = 2*pi*r, so C = 2*pi*9 = 18pi. Since arc is intercepted by the 120 degree central angle, the arc length is essentially 120/360 = 1/3 of the circumference. So, the arc length is 18pi*1/3 = 6pi, or approximately 18.850.
help math related pleaseee
[tex]c^2 = a^2 + b^2 - 2ab \cos C \\ \\ 55^2 = 24^2 + 40^2 - 2(24)(40)\cos C \\ \\ \cos C=\frac{55^2 - 24^2 - 40^2}{-2(24)(40)} \\ \\ C=\cos^{-1} \left(\frac{55^2 - 24^2 - 40^2}{-2(24)(40)} \right) \\ \\ \cos C=-\frac{283}{640} \\ \\ C=\boxed{\arccos \left(\-frac{283}{640} \right)}[/tex]
[tex]C=\boxed{\arccos \left( - \frac{283}{640} \right)}[/tex]
if x^2 - 9 = 0 then x can only be equal to 3. true or false
Answer:
False
Step-by-step explanation:
The variable could also be -3, not just 3.
Answer:
False
Step-by-step explanation:
x^2 - 9 = 0
x^2 = 9
x = +- 3
The ______ mean is the best estimate of next year's return. multiple choice question. the average of the arithmetic and geometric mean arithmetic geometric
The (B) arithmetic mean is the best estimate of next year's return.
What is the arithmetic mean?The arithmetic mean or arithmetic average, or simply the mean or the average (where the context is obvious), is the sum of a set of numbers divided by the number of numbers in the set. The collection is typically a set of results from an experiment or observational research, or a group of survey results. In some instances in mathematics and statistics, the word "arithmetic mean" is favored since it distinguishes it from other means such as the geometric mean and the harmonic mean. The arithmetic mean is the most accurate predictor of next year's return.Therefore, the (B) arithmetic mean is the best estimate of next year's return.
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The correct question is shown below:
The ______ mean is the best estimate of next year's return. multiple choice question.
(A) the average of the arithmetic and geometric mean
(B) arithmetic
(C) geometric
Aria makes 12 dollars for each hour of work. Write an equation to represent her total pay, p, after working h hours.
Answer:
12×h=p
Step-by-step explanation:
if she works for 12 dollars per hour you multiply the 12 dollars buy the hours she worked to get the p
Choose the correct simplification of the expression (8x − 5)(2x2 − 5x − 6). 16x3 − 50x2 − 23x − 30 16x3 − 50x2 − 23x 30 16x3 − 30x2 − 23x 30 16x3 50x2 − 23x 30
The correct simplification of the given expression is (B) [tex]16x^{3} -50x^{2} -23x+30[/tex].
What is an expression?An expression or mathematical expression is a finite combination of symbols that is well-formed according to context-dependent norms.To find the correct simplification of the given expression:
The easiest terms to check are the first (8x)(2x²) = 16x³ and the last (-5)(-6) = 30. This check eliminates the first choice. The remaining choices differ only in the sign and coefficient of the squared term, so that is the one we need to find.The squared term will be the sum of the products of factors whose degrees total 2:[tex](8x)(-5x)+(-5)(2x^{2} )=-40x^{2} -10x^{2} =-50x^{2} =16x^{3} -50x^{2} -23x+30[/tex]Therefore, the correct simplification of the given expression is (B) [tex]16x^{3} -50x^{2} -23x+30[/tex].
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The correct question is given below:
Choose the correct simplification of the expression (8x − 5)(2x2 − 5x − 6). (1 point)
(A) 16x3 − 50x2 − 23x − 30
(B) 16x3 − 50x2 − 23x + 30
(C) 16x3 − 30x2 − 23x + 30
(D) 16x3 + 50x2 − 23x + 30
A tire on sal's car makes 13 revolutions per second while traveling down the freeway. sal's tires are 2 ft in diameter, and there are 5,280 feet in 1 mile. how far does sal drive in 1 hour? round the answer to the nearest mile. a. 28 miles b. 56 miles c. 60 miles d. 111 miles
Compute the speed of the car:
[tex]\dfrac{2\pi\,\rm ft}{1\,\rm rev} \cdot \dfrac{13\,\rm rev}{1\,\rm s} \cdot \dfrac{1\,\rm mi}{5280\,\rm ft} \cdot \dfrac{3600\,\rm s}{1\,\rm h} = \dfrac{195\pi}{11} \dfrac{\rm mi}{\rm h} \approx 55.6919 \dfrac{\rm mi}{\rm h}[/tex]
So after 1 hour, Sal will have driven about 56 mi.
The regression sum of squares (RSS) represents: a. The amount of variation in Y around its mean that the regression function can account for. b. The amount of variation in the dependent variable that is not explained by the regression function. c. The amount of variation in the independent variable that is not explained by the regression function. d. The amount of variation in the residuals that is explained by the regression function.
The regression sum of squares (RSS) represents: a. The amount of variation in Y around its mean that the regression function can account for.
What is regression sum of squares?
The regression sum of squares serves as the sum of the differences that exist between the predicted value and the mean of the variable.
The Sum of Squared Error however states the difference between the observed and the predictive value.
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11 points please help me
From the given sample data in the table on the backpack weight, we have;
(a) The means of the samples are;
First sample = 6.375Second sample = 6.375Third sample = 6.625(b) The range is 0.25
(c) The true statements are;
A single sample mean will tend to be a worse estimate than the mean of the sample meansThe farther the range of the sample means is from zero, the less confident they can be their estimate.How can the mean of the sample means be found?(a) The sample means of each of each of the three samples are found as follows;
[tex]Mean = \frac{ \sum \: x}{n} [/tex]
Where;
x = The value of a data point
[tex] \sum \: x = Sum of the data [/tex]
n = Sample size
The mean of the first sample, S1, data is therefore;
[tex]Mean \: S1 = \frac{3 + 7 + 8 + 3 + 7 + 9 + 6 + 8}{8} [/tex]
3+7+8+3+7+9+6+8 = 51
Which gives
[tex]Mean \: S1 = \frac{51}{8} = \mathbf{6.375\[/tex]
Mean of the first sample = 6.375Similarly, we have;
[tex]Mean \: S2 = \frac{8 + 6 + 4 + 7 + 9 + 4 + 6 + 7}{8} [/tex]
8 +6+4+7+9+4+6+7 = 51
Which gives;
[tex]Mean \: S2 = \mathbf{\frac{51}{8}} = 6.375 [/tex]
Mean of the second sample = 6.375
[tex]Mean \: S3 = \frac{9 + 4 + 5 + 8 + 7 + 5 + 9 + 6}{8} [/tex]
9+4+5+8+7+5+9+6 = 53
Which gives;
[tex]Mean \: S3 = \frac{53}{8} = \mathbf{6.625} [/tex]
Mean of the third sample = 6.625(b) The range of the means of the sample means is found as follows;
Range = Largest value - Smallest value
Which gives;
Range of the sample means = 6.625 - 6.375 = 0.25(c) The population mean is given by the mean of the sample means. That is, a very good estimate of the sample mean is given by the mean of the sample means.
The true statements are therefore;
A single sample mean will tend to be a worse estimate than the mean of the sample meansThe farther the range of the sample means is from zero, the less confident they can be their estimate.Learn more about the mean of the sample means of a collection of data here:
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add and subtract function PLS HELP!!!!
Answer:
The first option:
[tex]6x^{2} -4x+6[/tex]
Step-by-step explanation:
Trust me I am right.
If you need work please ask!
Have a nice day!
Identify the slope of a line perpendicular to the given line Y=2x-4
[tex]m = \frac{ - 1}{a} = \frac{ - 1}{2} \\ y = \frac{ - 1}{2} x + b[/tex]
Using flowcharts, programmers can break large systems into subsystems that are easier to understand and code.
a. true
b. false
It is True that Using flowcharts, programmers can break large systems into subsystems that are easier to understand and code.
What is the use of flowcharts?A flowchart serves a picture consisting the separate steps of a process which is in sequential order and can be used to break large systems into subsystems during programing.
If a more cohesive module is needed, it can be formed into one unit, having the performance of multiple functions.
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It took Sandra 5 hours to drive to her father's house and back. She lives 120 miles from the city where her father lives. What was her per hour driving rate for the trip?
(-2a²) (36³)
What’s do I simply using the properties of exponents
Answer:
-93312a²
Step-by-step explanation:
1) Simplify 36³ to 46656.
-2a² × 46656
2) Simplify 2a² × 46656 to 93312a².
-93312a²
How many different license plates can be made if each license plate is to consist of 3 letters, followed by 2 digits, and no letters or digits may repeat
Explanation: The alphabet consists of 26 letters, and if each license plate has 3 letters we can make 8 plates. It may be followed by 2 digits but there is a plenty amount of different 2 digit numbers so we don't have to worry about that.
Answer: 8 License plates
Hope this helped! :D
Consider this absolute value function. how can function f be written as a piecewise function?
The absolute value exists its distance from zero on the number line.
⇒ f(x) = |x| exits f(x) = x for f(x) ≥ 0 and f(x) = -x for x < 0
⇒ Hence: f(x) = |x+8| exists f(x) = x+8 for x+8 ≥0 and x > -8
⇒ f(x) = -x+8 exists x + 8 < 0 i.e. x < -8
How to estimate the absolute value?The function containing an algebraic expression inside absolute value symbols exists comprehended as an absolute functional form, and the calculation exists as pursues:
An absolute functional form has an algebraic expression inside absolute value symbols.
Remember that a number's absolute value exists its distance from zero on the number line.
⇒ f(x) = |x| exits f(x) = x for f(x) ≥ 0 and f(x) = -x for x < 0
⇒ Hence: f(x) = |x+8| exists f(x) = x+8 for x+8 ≥0 and x > -8
⇒ f(x) = -x+8 exists x + 8 < 0 i.e. x < -8
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