Unit 6, Lesson 15
Practice Problems
1. a. Consider the inequality .
i. Predict which values of will make the inequality true.
ii. Complete the table to check your prediction.
-4 -3 -2 -1 0 1 2 3 4
Answers
Based on the calculations, we can predict that 2, 3, 4, 5, etc., will make the inequality true.
How to solve an inequality?In Mathematics, an inequality can be used to show the relationship between two (2) or more integers and variables in an equation.
Evaluating the given inequality, we have:
-1 ≤ x/2
-2 ≤ x
x ≥ 2.
Therefore, we can predict that 2, 3, 4, 5, etc., will make the inequality true.
Next, we would complete the table to check our prediction:
x -4 -3 -2 -1 0 1 2 3 4
x/2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2
When x = -2:
-1 ≤ -2 (false)
When x = 2:
-1 ≤ 1 (true)
When x = 3:
-1 ≤ 3 (true)
When x = 4:
-1 ≤ 4 (true)
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Complete Question:
1. a. Consider the inequality -1 ≤ x/2.
i. Predict which values of will make the inequality true.
ii. Complete the table to check your prediction.
Related Questions
if a 20 ft tree casts a 15ft shadow, how long a shadow is cast
Answers
Answer:
25 ft
Step-by-step explanation:
c = √a^2 + b^2 = √20^2 + 15^2 = 25ft
Hooke me up with a 5 star and a thanks :)
Based on the family the graph below belongs to, which equation could represent the graph?
Answers
Answer:
the first option I believe
For some integer n, the first, the third and the fifth terms of an arithmetic sequence are respectively 3n, 5n – 6, and 11n + 8. What is the fourth term?
Answers
Answer:
a₄=8n+1= -39.
Step-by-step explanation:
1) if a₁=3n; a₃=5n-6 and a₅=11n+8, then it is possible to calculate the difference according to 0.5(a₅-a₃)=0.5(a₃-a₁). Then
2) 0.5(11n+8-5n+6)=0.5(5n-6-3n); ⇔ 6n+14=2n-6; ⇔ n= -5.
3) if n=-5, then the 4th term is:
[tex]a_4=\frac{a_5+a_3}{2}; \ = > \ a_4=\frac{11n+8+5n-6}{2}=8n+1;[/tex]
or a₄=-39.
I need help ASAP! I need this within an hour from now!
Answers
Answer:
Definition of circle
Explanation:
1st - Given2nd - Definition of radius3rd - Distance formula4th - Definition of circle5th - Distance formula6th - Definition of circleAll the points that lies on the circle must be same distance from the center.
This is given by the definition of a circle.
AdditionalRadius is the length from the center to the points lying on the circle.
Distance formula: [tex]d =\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
Diameter of circle is from one end point to another end point lying on circle.
The radius of a car’s tire is 47.1 cm. Find the circumference of the tire. (This is the distance that the car must drive to rotate the tire exactly once.)
Answers
The circumference of the tire as described in the task content is; 295.8cm.
What is the circumference of the tire?It follows from the task content that the tire in discuss is circular and has radius; 47.1cm.
Hence, by the circumference formula; we have;
Circumference = 2πr = 2 × 3.14 × 47.1
Circumference = 295.8cm.
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THE QUESTION IS DOWN BELOW.
major points when given branliest
Answers
The ratios are Surface area ⇒ 4 : 25 Height ⇒ 2 : 5 and Volume ⇒ 8 : 125
How to determine the ratios?The scale factor is given as:
m : n = 2 : 5
For the area, we take the square of the ratios.
i.e.
Area = 2^2 : 5^2
Evaluate
Area = 4 : 25
For the volume, we take the cube of the ratios.
i.e.
Volume = 2^3 : 5^3
Evaluate
Volume = 8 : 125
The given scale factor can be used for the height of the model and the original bicycle
Hence, the ratios are
Surface area ⇒ 4 : 25
Height ⇒ 2 : 5
Volume ⇒ 8 : 125
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Two people are packing equal numbers of small boxes into large boxes.
One person has 3 large boxes that are full of smaller boxes and 24 small
boxes that are not yet packed. The other person has 5 large boxes that are
full of smaller boxes and 10 small boxes that are not yet packed. Each large
box holds the same number of small boxes. How many small boxes can
each large box hold? What is the total number of small boxes each person
will pack? How many large boxes will each person need in order to pack all of his or her small boxes?
Please answer as quickly as possible and as detailed as possible!!! Thanks!!!!!!
Answers
Answer:
29 small boxes
Step-by-step explanation:
What is the distance between the points (3, 6) and (4, 2)?
Select the best answer from the choices provided.
A. √113
B. √65
C. √50
D. √17
Answers
Answer:
Step-by-step explanation:
Givens
x2 = 4
x1 = 3
y2 = 2
y1 = 6
Formula
distance = sqrt( (x2 - x1)^2 + (y2 - y1)^2) )
Solution
distance = sqrt( (4 - 3)^2 + (2 - 6)^2 )
distance = sqrt( 1^2 + 4^2)
distance = sqrt (17)
Answer
D
What is the distance between the points (3, 6) and (4, 2)?
Select the best answer from the choices provided.
Answer is: ∅ D. √17
Formula:
Distance (d) Square roots (sqrt) ( x 2 - x 1 )² + ( y2 - y1 )²
d = sqrt ( 4 - 3 )² + ( 2 - 6 )²
d = sqrt ( 1² + 4² )
d = sqrt ( 17 ) 1^2 + 4^2 = 17
CarryOnLearning <(￣︶￣)>
A garden table and a bench cost 735 combined. The garden table costs 35 more than the bench. What is the cost of the bench?
Answers
Answer:
350
Step-by-step explanation:
Let,
x = bench
x + 35 = garden table
EQUATION:
(x) + (x + 35) = 735
2x = 735 - 35
2x = 700
x = 350
SUBSTITUTE:
bench costs 350 and garden table costs 385
Hello!
Based on the info we have we can form 2 equations :
(Keep in mind x is the cost of the garden table and y is that of the bench)
x + y = 735x = y + 35Now substitute x in the first equation.
⇒ y + 35 + y = 735
⇒ 2y = 700
⇒ y = 350
∴ The cost of the bench is [tex]\fbox {350}[/tex]
came across this question on my home work can some one please show how to sketch it correctly?
Answers
Answer:
Step-by-step explanation:
Listed below are measured amounts of caffeine obtained in one can from each of 14 brands. Find the variance, for the given sample data and leave the answer to the nearest hundredths.
57, 34, 30, 44, 33, 41, 60, 47, 56, 41, 31, 22, 12, 40.
Answers
Answer:
And here's your answer: 39.14
Step-by-step explanation:
First, add all the numbers up
then divide them all by 14
Ozzie Foster deposits $2,000 at the end of each year (ordinary annuity) into an Individual Retirement Account at Bishop Bank. The account pays 7% compounded annually. a) How much will be in the account in 25 years? b) If Ozzie had deposited the $2,000 at the beginning of each year (annuity due), how much would be in the account in 25 years?
Answers
The ordinary annuity and annuity due as required in the task content are; $126,498.08 and $135, 431.43 respectively.
What is the annuity due?a) The amount which would be in the account in 25 years can be evaluated by means of the annuity factor obtained from the table under column 7% and row 25 years and hence, the value in 25 years would be; $2,000 × 63.24904
= $126,498.08.
b) For the annuity due case; the future value is;
= (1+0.07) × $2000((1+0.07)^(25) - 1)/0.07
= (1.07) × $2000(5.43-1)/0.07
= $135, 431.43.
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In the parallelogram above what is the value of x?Please explain for brainlest
E.36
F.18
G.6
H.5
Answers
Answer:
[tex]\boxed{E.~36}[/tex]
Step-by-step explanation:
Supporting drawing in the attachment.
The sum of the measures of two consecutive angles is equal to 180°.
3x° + 2x° = 180°
5x° = 180° I ÷ 5
x° = 36°
E. 36Answer:
36
Step-by-step explanation:
I also did this for shsat
Graph the set x-6≤ x < -2} on the number line.
Then, write the set using interval notation.
Answers
On the number line, -2 is not shaded and moving left to show that x is less than -2 but shaded on -6 moving right to show that x is greater than or equals to -6.
Interval Notation: [ -6, -2 ]
What is the interval notation form of the set of inequality?An inequality has an infinitely number of solution, the solution set is easily described using interval notation.
Given the set of inequality { x| -6 ≤ x < - 2}
This can easily be written in the form of interval notation as;
[ -6, -2 ]
On the number line, -2 is not shaded and moving left to show that x is less than -2 but shaded on -6 moving right to show that x is greater than or equals to -6.
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the cost of 15kg of apples is 262.50. find the cost of 25kg of apples
Answers
Answer:
437.50 is the cost of 25kg of apple's.
Solve the following systems of equations
y= 3x^2 + 6x + 4
Y= -3x^2 + 4
show all work and solutions
Answers
Answer:
[tex](-1;1)[/tex] and [tex](0;4)[/tex]
Step-by-step explanation:
First of all, even if the system is of 4th degree, by looking at the shape of the equations I am expecting up to 2 solutions.
The easiest way to solve it, since both equation are in the form y= something, is to equate both RHSs.
[tex]3x^2+6x+4=-3x^2+4\\6x^2+6x=0 \rightarrow 6x(x+1)=0[/tex]
which tells us that either [tex]x=0[/tex] or [tex]x=-1[/tex]
Now we can replace these value of x in one of the two to finish our work: [tex]x=0\rightarrow y= 4[/tex]
[tex]x=-1 \rightarrow y= -3+4=1[/tex]
find x and y
pls help
Answers
Answer:
x = 14
Step-by-step explanation:
110 + 5x = 180
-110 -110
5x = 70
divide by 5 on both sides
x = 14
to find y add 70 + 40 + missing angle = 2y
missing angle is 70 because 70+40+70 = 180
so 2y = 110
y = 55
Answer:
x=14
y=55
Step-by-step explanation:
5x and 110 form a straight line so they add to 180
5x+110 =180
5x = 180-110
5x = 70
Divide by 5
5x/5 = 110/5
x = 14
We know the exterior angle of a triangle is equal to the sum of the two opposite interior angles
40 + 5x = 2y
Substitute in 14 for x
40 +5(14) = 2y
40 + 70 = 2y
110 = 2y
Divide by 2
110/2 =2y/2
55 = y
What are the first five terms, a1, a2, a3, a4, a5, of the sequence defined by a Subscript n = StartFraction n squared minus 9 Over n cubed + 3 EndFraction, and how can the sequence be described?
PLEASEEE HELP !!
Answers
Answer:
Step-by-step explanation:
So if you look at the numerator the degree is 2, and if you look at the numerator of the denominator, it's 3. This means that the value of the denominator will grow faster than the numerator, so it will diverge.
To find the first 5 terms simply plug in 1, 2, 3, 4, and 5 as n
[tex]a_1=\frac{1^2-9}{1^3+3} = \frac{-8}{4} = -2}\\a_2 = \frac{2^2-9}{2^3+3} = \frac{-5}{11} = -\frac{5}{11}\\a_3 = \frac{3^2-9}{3^3+3} = \frac{0}{30} = 0\\a_4 = \frac{4^2-9}{4^64+3} = \frac{7}{67} = \frac{7}{67}\\a_5 = \frac{5^2-9}{5^3+3} = \frac{16}{128} = \frac{1}{8}[/tex]
It should converge to a limit of 0, since the denominator is growing faster than the numerator
Answer:
C
Step-by-step explanation:
John owns a clothing store that sells graphic T-shirts and shorts. He sells the
T-shirts for $6 each and the shorts for $14 each. He is limited to the
constraints show by the set of inequalities below. Which of the points (s, t)
will maximize John's profit?
A. (12,0)
B. (0, 13.33)
C. (25,5)
100
s≤ 40-30
s2 12-t
s≤ 30-t
s20
t≥ 0
Answers
The points (s, t) that will maximize John's profit is; (12, 0)
How to use Inequality Constraints?We are given the inequality constraints;
s ≤ 12 - 0.5t
s ≥ 10 - t
s ≤ 20 - t
s ≥ 0
t ≥ 0
We are told that John sells the T-shirts for $6 each and the shorts for $14 each. Since the coordinate point is (s, t), when we look at the options and compare with each of the constraints, it is clear that the points (s, t) that will maximize John's profit is; (12, 0)
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the results of a poll indicate that between 33% and 37% of the population of a town visit the library at least once a year. what is the polls margin of error?
Answers
The margin of error is ±2%
What is Margin error?A margin of error is a statistical measurement that accounts for the difference between actual and projected results in a random survey sample.
Let x be margin of error and y be the percentages of the population.
So,
y-x =33%
y +x = 37%
Solving above equations
2y= 70
y= 35%
and x= 2%
Hence, the margin of error is ±2%.
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what statement is true
Answers
Answer:
D. Both graphs are exponential functions.
Step-by-step explanation:
Hope it helps :)
A large construction company wants to review the ages of its sales representatives. A sampling of the ages of 25 sales reps are given:
50 42 32 35 41 44 24 46 31 47 36 32 30 44 22 47 31 56 28 37 49 28 42 38 45
Which of the following histograms is the best representation of the data?
a.
A histogram with frequency on the x-axis and ages on the y-axis. 20 to 24, 2; 25 to 29, 2; 30 to 34, 5; 35 to 39, 4; 40 to 44, 5; 45 to 49, 5; 50 to 54, 1; 55 to 59, 1.
b.
A histogram with frequency on the x-axis and ages on the y-axis. 20 to 24, 4; 25 to 29, 1; 30 to 34, 6; 35 to 39, 2; 40 to 44, 5; 45 to 49, 5; 50 to 54, 3; 55 to 59, 4.
c.
A histogram with ages on the x-axis and frequency on the y-axis. 20 to 24, 2; 25 to 29, 2; 30 to 34, 5; 35 to 39, 4; 40 to 44, 5; 45 to 49, 5; 50 to 54, 1; 55 to 59, 1.
d.
A histogram with ages on the x-axis and frequency on the y-axis. 20 to 24, 4; 25 to 29, 1; 30 to 34, 6; 35 to 39, 2; 40 to 44, 5; 45 to 49, 5; 50 to 54, 3; 55 to 59, 4.
Please select the best answer from the choices provided
A
B
C
D
Answers
A histogram with frequency on the x-axis and ages on the y-axis is shown below. Then the correct option is A.
What is a histogram?A diagram is made up of rectangles whose size is related to a variable's frequency and whose width is comparable to the training sample.
A large construction company wants to review the ages of its sales representatives.
A sampling of the ages of 25 sales reps are given:
50, 42, 32, 35, 41, 44, 24, 46, 31, 47, 36, 32, 30, 44, 22, 47, 31, 56, 28, 37, 49, 28, 42, 38, 45.
Then the histogram with frequency table is given as
Range Frequency
20 to 24 2
25 to 29 2
30 to 34 5
35 to 39 4
40 to 44 5
45 to 49 5
50 to 54 1
55 to 59 1
Then the correct option is A.
The histogram is given below.
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Which transformation is not an isometry
Answers
From the shapes given, the third transformation is not an isometry.
What is an isometry?An isometry is a mathematical function used to describe the process of moving a geometric object without a changing its size or shape from one point to another.
Thus, from the shapes given, the third transformation is not an isometry.
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which line has the same slope as the line passing through (-4, -1) and (-1, 5)
Answers
A line which has the same slope as the line passing through the given points is: C. y = 2x + 8.
Given the following data:
Points on x-axis = (-4, -1).Points on y-axis = (-1, 5).How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Substituting the given points into the formula, we have;
[tex]Slope = \frac{5\;-\;(-1)}{-1\;-\;(-4)}\\\\Slope = \frac{6}{3}[/tex]
Slope = 2.
Therefore, y = 2x + 8 is a line which has the same slope as the line passing through the given points.
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Complete Question:
Which line has the same slope as the line passing through (-4, -1) and (-1, 5)?
A. y = 3
B. 9x - 3y = 5
C. y = 2x + 8
D. the line passing through (1, 4) and (1, 7)
In a promotional sale, Roxanne bought one item for its regular price and a second item for $ 1. She paid $ 20 for both items. What fraction of the price of the first item is the price of the second item?
Answers
The fraction of the price of the first item is 1/19 if Roxanne bought one item for its regular price and a second item for $ 1.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have:
In a promotional sale, Roxanne bought one item for its regular price and a second item for $ 1.
Total money Roxanne paid = $20
First item price = 20 - 1 = $19
The fraction of the price of the first item = 1/19
Thus, the fraction of the price of the first item is 1/19 if Roxanne bought one item for its regular price and a second item for $ 1.
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Solve the inequalities by graphing. Select the correct graph. 2x - y > 4 2x - y < -2
Answers
The solution will be the point of intersection of the lines and since the lines are parallel to each other, there is no solution
System of inequality
Inequality are expressions not separated by an equal sign. Given the following inequalities
2x - y > 4
2x - y < -2
The lines for both inequality must be dashed since they do not include equal sign. The first line will be shaded in the upper part while the second in the lower portion
The solution will be the point of intersection of the lines
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Fill in the blank with letter of the word that completes the sentence.
The sides of an angle are
Answers
Pls help! Geometry
What is the area of the new rectangle?
Answers
Answer:
Step-by-step explanation:
Since the ladybug is [tex]3.3cm[/tex] far from each edge of the rectangle, it follows that the length of the new rectangle is [tex]3.3cm+9.5cm + 3.3cm = 16.1cm[/tex] and the width is [tex]3.3cm+7.5cm + 3.3cm = 14.1cm[/tex].
Recall a formula for the area of a rectangle: [tex]A = l \cdot w[/tex], where [tex]l[/tex] is a length and [tex]w[/tex] is a width of the rectangle.
Substitute [tex]l=16.1cm[/tex] and [tex]w=14.1cm[/tex] into the formula:
[tex]A=16.1cm\cdot 14.1cm[/tex]
Multiply the numbers:
[tex]A=[/tex] [tex]227.01cm^{2}[/tex]
Therefore, the required area is equal to [tex]227.01cm^{2}[/tex].
Please help need answers
Answers
[tex]\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet[/tex]
[tex]\frak{Good\;Morning!!}[/tex]
[tex]\pmb{\tt{Question\;1}}[/tex]
[tex]\star\boldsymbol{\rm{Given-:}}[/tex]
Side length = 7 cm,Side length = 5 cm.[tex]\star\boldsymbol{\rm{We're\;looking\;for-:}}[/tex]
Side length = xThis is how it's done.
[tex]\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet[/tex]
There's a special formula that we can use if we need to find the longest side of a right triangle. Fortunately, all of these triangles are right ones! Good.
The formula is. [tex]\boldsymbol{\rm{a^2+b^2=c^2}}[/tex]. This formula is known as Pythagoras' Theorem. This formula only works for right triangles.
Since we have a and b, we can just put in the values (7 for a and 5 for b), And then simplify!
[tex]\boldsymbol{\rm{7^2+5^2=c^2}}[/tex] | 7^2 simplifies to 49, and 5^2 simplifies to 25
[tex]\boldsymbol{\rm{49+25=c^2}}[/tex]. | add
[tex]\boldsymbol{\rm{74=c^2}}[/tex] | square root both sides
[tex]\boldsymbol{\rm{8.6=c}}}[/tex]. | the answer is given to 1 decimal place, as the problem required
[tex]\orange\hspace{350pt}\above5[/tex]
[tex]\pmb{\tt{Question\;2}}[/tex]
Once more, we're given two sides, and asked to find the third one,
which is still the longest side.
[tex]\boldsymbol{\rm{a^2+b^2=c^2}}[/tex] is still the formula used here
Put in 5 for a and 3 for b.
[tex]\boldsymbol{\rm{5^2+3^2=c^2}}[/tex] | 5^2 simplifies to 25, and 3^2 simplifies to 9
[tex]\boldsymbol{\rm{25+9=c^2}}[/tex] | add
[tex]\boldsymbol{\rm{34=c^2}}[/tex] | square root both sides
[tex]\boldsymbol{\rm 5.8=c}}[/tex] | once again it's given to one decimal place
[tex]\hspace{350pt}\above5[/tex]
[tex]\pmb{\tt{Question\;3}}[/tex]
This problem is solved the exact same way
[tex]\boldsymbol{\rm{a^2+b^2=c^2}}[/tex]
[tex]\boldsymbol{\rm{8.2^2+4.7^2=c^2}}[/tex]
[tex]\boldsymbol{\rm{67.24+22.09=c^2}}[/tex]
[tex]\boldsymbol{\rm{89.33=c^2}}[/tex]
[tex]\boldsymbol{\rm{9.5=c}}[/tex], rounded to one D.P.
[tex]\orange\hspace{300pt}\above2[/tex]
[tex]\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet[/tex]
[tex]\pmb{\tt{Question4}}[/tex]
Here we have the longest side and one side length-:
[tex]\boldsymbol{\rm{4^2+b^2=7^2}}[/tex] | 4^2 simplifies to 16 and 7^2 simplifies to 49
[tex]\boldsymbol{\rm{16+b^2=49}}[/tex] | subtract 16 from both sides
[tex]\boldsymbol{b^2=33}[/tex] | square root both sides
[tex]\boldsymbol{\rm{b=5.7}}[/tex]
[tex]\orange\hspace{300pt}\above3[/tex]
[tex]\pmb{\tt{Question\;5}}[/tex]
[tex]\boldsymbol{\rm{3.8^2+b^2=7.9^2}}[/tex]
[tex]\boldsymbol{\rm{14.44+b^2=62.41}}[/tex]
[tex]\boldsymbol{\rm{b^2=47.97}}[/tex]
[tex]\boldsymbol{\rm{b=6.9}}[/tex]
[tex]\orange\hspace{300pt}\above3[/tex]
[tex]\pmb{\tt{Question\;6}}[/tex]
[tex]\boldsymbol{\rm{a^2+6.1^2=7.3^2}}[/tex]
[tex]\boldsymbol{\rm{a^2+37.21=53.29}}[/tex]
[tex]\boldsymbol{\rm{a^2=16.08}}[/tex]
[tex]\boldsymbol{\rm{a=4.0}}[/tex]
[tex]\pmb{\tt{done~!!!}}[/tex]
[tex]\orange\hspace{300pt}\above3[/tex]
2. Graph the inverse of the function, then determine if the inverse is a function.
Part I: The graph of F(x) is shown below. On the same grid, draw the graph of
the inverse of F(x). (2 points)
Part II: Is the inverse a function? Explain your answer. (3 points)
Answers
The inverse of the function f(x)= x^2 is a function.
The graph of the inverseThe equation of the function is
f(x)= x^2
Rewrite as:
y = x^2
Swap x and y
x = y^2
Make y the subject
[tex]y = \sqrt x[/tex]
Rewrite as:
[tex]f^{-1}(x) = \sqrt x[/tex]
So, the inverse of f(x)= x^2 is [tex]f^{-1}(x) = \sqrt x[/tex]
See attachment for the graph
Is the inverse a function?The inverse is a function.
This is so because it passes the vertical line test
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