|5-2x|+1≤10 absolute value equations or inequalities and graph the solution set on the number line
Answers
The given inequality is
[tex]|5-2x|+1\leq10[/tex]First, we subtract 1 on each side
[tex]\begin{gathered} |5-2x|+1-1\leq10-1 \\ |5-2x|\leq9 \end{gathered}[/tex]Now we use the property of inequalities with absolute values, which states
[tex]|x|\leq a\rightarrow-a\leq x\leq a[/tex]Using this property, we have
[tex]|5-2x|\leq9\rightarrow-9\leq5-2x\leq9[/tex]We solve the compound inequality now
[tex]\begin{gathered} -9\leq5-2x\leq9 \\ -9-5\leq-2x\leq9-5 \\ -14\leq-2x\leq4 \\ \frac{-14}{-2}\ge\frac{-2x}{-2}\ge\frac{4}{-2} \\ 7\ge x\ge-2 \\ -2\leq x\leq7 \end{gathered}[/tex]Therefore, the solution is the interval [-2,7], and the graph of it would be
Related Questions
Write the slope-intercept form equation for a line that contains point (0, 5) and has a slope of 5/4
Answers
The slope-intercept form equation for a line that contains point (0, 5) and has a slope of 5/4 is y = (5/4)x + 5
In this question, we have been given a point (0, 5) and a slope 5/4
We need to write the slope-intercept form equation for a line that contains point (0, 5) and has a slope of 5/4
Using the formula for the point-slope form equation of a line:
(y - y1) = m(x - x1)
y - 5 = (5/4)(x - 0)
y - 5 = (5/4)x
y = (5/4)x + 5
which is slope-intercept form of line.
here slope = 5/4 and y-intercept = 5
Therefore, the slope-intercept form equation for a line that contains point (0, 5) and has a slope of 5/4 is y = (5/4)x + 5
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Please Answer Fast
Write down the next two terms in these quadratic sequences:
9, 13, 19, 27, ___, ___
-5, 0, 9, 22, ___, ___
Answers
The next two terms of the first quadratic sequences are 37 and 49.
The next two terms of the second quadratic sequences are 39 and 60.
What are the next two terms?A quadratic sequence is a sequence in mathematics where the second difference between consecutive terms in the sequence is the same
The first step is to determine the relationship between the terms in the quadratic sequence.
The difference between 9 and 13 = 13 - 9 = 4
The difference between 19 and 13 = 19 - 13 = 6
The difference between 27 and 19 : 27 - 19 = 8
It can be seen that the first difference between the terms in the sequence quadratic sequence increases by 2.
The difference between the fourth term and the fifth term would be 8 + 2 = 10
Fifth term = 27 + 10 = 37
The difference between fifth term and the sixth term would be 10 + 2 = 12
37 + 12 =49
The first step is to determine the relationship between the terms in the quadratic sequence.
The difference between 0 and -5 : 0 - -5 = 5
The difference between 0 and 9 = 9 - 0 = 9
The difference between 9 and 22 = 22 - 9 = 13
Based on the first difference between the consecutive terms in the digit, it can be seen that the first difference increase by a value of 4.
The difference between the fourth term and the fifth term would be : 13 + 4 = 17
Fifth term = 22 + 17 = 39
The difference between fifth term and the sixth term would be 21 ( 17 + 4)
39 + 21 = 60
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If x=|9|what are the possible values of x?
Answers
Answer:
9
Step-by-step explanation:
the absolute value function always delivers only the positive value of anything inside the absolute function.
therefore, x is 9 and only 9.
What is the volume of this container? 4 in.
4 in.
1 in.
4 in.
2 in.
64 in²
56 in³
56 in²
64 in³
Answers
An object's capacity is expressed in terms of volume.
The container's volume is 56 in3.
How to find the container's volume?The capacity of an object is expressed in terms of volume.
A cup's capacity is said to be 100 ml, for instance, if it can hold 100 ml of water in its brim.
The quantity of space a three-dimensional item takes up can also be referred to as volume.
The figure's volume is equal to Bh.
V = Bh
where
B is the base's region.
h is the figure's height.
h = 4 in
The area of the base B is
B = (4*4) - (1*2) = 14 in
V = 14*4 = 56 inch cube.
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contains (1,1) and has a shape of f(x)=2x^2 vertex is on the y axis
Answers
ANSWER
| x=0
Step-by-step explanation:
f(x) = 2x²
Rewrite the function by completing the
square
f(x)
= 2x²
Find the symmetry
X = 0
How to calculate mode and media
Answers
Place the data points in descending order of size to find the center number. The median is as shown. The median is the average of the two numbers if there are two of them. The number that appears the most frequently in a piece of data is the mode.
The middle value in a list that is arranged from smallest to greatest is called the median. The value that appears the most frequently on the list is the mode. Organize the numbers in a set in whatever order—from lowest to highest or highest to lowest—and then tally the frequency with which each number appears in the group. The mode is the one that shows up most frequency
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5
6
Z
1
23
4.
75°
7
y
13 16
14 15
9 12
11
10
x
w
What is mZ2?
What is m1?
Answers
Answer: [tex]m\angle 2=75^{\circ}, m\angle 1=105^{\circ}[/tex]
Step-by-step explanation:
By the alternate interior angles theorem, [tex]m\angle 2=75^{\circ}[/tex].
Using linear pairs, [tex]m\angle 1=105^{\circ}[/tex].
All of the triangles below have a base to height ratio of 5:2. Label the missing dimensions
Answers
ANSWER:
1. b = 5
2. h = 6
3. b = 30
STEP-BY-STEP EXPLANATION:
We know the ratio between height and base.
By means of the following proportions we can determine the missing dimensions in each case:
[tex]\begin{gathered} \frac{5}{2}=\frac{b}{h} \\ \\ \text{ 1st triangle} \\ \\ \frac{5}{2}=\frac{b}{2}\rightarrow b=5 \\ \\ \text{ 2nd triangle} \\ \\ \frac{5}{2}=\frac{15}{h}\rightarrow h=\frac{15}{5}\cdot2\rightarrow h=6 \\ \\ \text{ 3rd triangle} \\ \\ \frac{5}{2}=\frac{b}{12}\rightarrow b=12\cdot\frac{5}{2}\rightarrow b=30 \end{gathered}[/tex]How is this shape not a parallelogram?
There one pair of congruent sides and a bisected diagonal, we can draw two tringles then by using CPCTC, we can conclude that we have 2 pairs of congruent sides, and thus a parallelogram.
Answers
Answer:
SSA is not a valid congruence theorem
Step-by-step explanation:
Given a figure with opposite sides the same length, and their ends joined by a line through the midpoint of the segment joining their other ends, you want to know why the shape is not a parallelogram.
SSA congruenceThe recognized congruence theorems are ...
AAS, ASA, SAS, SSS
The "would be" SSA theorem is not included, because the case where the angle is opposite the shortest of the two sides does not uniquely specify the triangle.
In this diagram, the sides marked with 2 and 1 hash marks are sequential with the vertical angle where the diagonals cross. Hence the only basis for claiming the triangles congruent is SSA.
The basis for claiming congruence is not a recognized congruence theorem, so we cannot conclude the triangles are congruent. (CPCTC does not apply.)
__
Additional comment
As we noted, the SSA criterion for congruence fails if the given angle cannot be demonstrated to be opposite the longest side. The attachment shows the case where the single-hash segment is longer than the double-hash segment, so there are two ways to draw the figure. One is a parallelogram, the other is not.
The HL congruence theorem is essentially SSA, where the A is the right angle. If the angle can be demonstrated to be the largest in the triangle, then the SSA theorem can be used (as for right- or obtuse triangles).
As the attachment shows, there is nothing in this geometry that requires the vertical angle(s) opposite the double hash be the largest.
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you want to use a spoon section of your yard for a chicken pen. you have at most 50 feet of fencing to form the fun. Find the possible length of each side of the chicken pen
Answers
The sum of the length around a square is known as the perimeter thus the possible length of each side of the chicken pen assuming it to be square is 12.5 feet.
What is the perimeter?Perimeter is the addition of an external measure of sides it will always positive.
A perimeter is a length and has a degree of the unit as one.
Perimeter of square = side + side + side + side
Let's assume the chicken pen to the square in order to find the length of each side.
Now since fencing is fitted around the sides so it will be the same as the perimeter of the square.
Perimeter of square = 4 × side
4 × side = 50
Side = 50/4 = 12.5 feet.
Hence "The sum of the length around a square is known as the perimeter thus the possible length of each side of the chicken pen assuming it to be square is 12.5 feet".
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how would i rewrite the polynomial in the form ax^2+bx+c and then identify the values of a,b, and c1/3x^2+7-6x
Answers
Answer:
a=1/3, b=-6, c=7
Explanation:
Given the polynomial:
[tex]\frac{1}{3}x^2+7-6x[/tex]We reorder it to rewrite the polynomial in the form ax²+bx+c:
[tex]\frac{1}{3}x^2-6x+7[/tex]Next, by comparing:
• a is the coefficient of x²: a=1/3
,• b is the coefficient of x: b=-6
,• c is the constant: c=7
[tex]a=\frac{1}{3},b=-6,c=7[/tex]please can you help me to solve an equation ?Determine whether the statement is true or false : The slope of the line y = 1 is zero
Answers
The given line equation is y=1.
The general form of the line equation is
[tex]y=mx+b[/tex]Comparing this equation with y=1, we get
[tex]mx+b=1[/tex][tex]mx+b=(0)x+1[/tex]Compare coefficient of x and constant term, we get
[tex]m=0\text{ and b=1}[/tex]Here m=0 is the slope of the line y=1.
Hence the slope of the line y = 1 is zero.
This statement is true.
anwser? please i need this to pass my test and i dont understand
Answers
Based on the conversion rate between kilometers and miles, the data to complete the table is:
8 miles : 12.88 kilometers 0.93 miles : 1.5 kilometers 5.58 miles : 9 kilometers 3.1 miles : 4.991 kilometersHow to convert miles to kilometers?For every given mile, there will be 1.61 kilometers. To convert miles to kilometers therefore, you have to multiply the number of miles by the number of kilometers in a mile.
If given 8 miles, the number of kilometers is:
= 8 x 1.61
= 12.88 kilometers
If given 3.1 miles, the number of kilometers is:
= 3.1 x 1.61
= 4.991 kilometers
If given 1.5 kilometers, then the number in miles is:
= 1.5 x 0.62
= 0.93 miles
If given 9 kilometers, then the number in miles is:
= 9 x 0.62
= 5.58 miles
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in the conditional statement “If the temperature of water is between the temperatures of ice and steam, then ice is colder than water and steam is hotter than water.” write the given statement and the to prove statement.
Answers
Ice is colder than water due to its more heat absorbing capacity then water and steam is hotter than water due to high heat transfer rate then water.
What is specific heat capacity ?
In scientific terms, a specific heat capacity is the quantity of heat (J) absorbed by a material every time its temperature goes up 1 K (or 1 °C), given in J/(kg K) or J/(kg °C) per unit mass. formulae for specific heat capacity is given by :
Q = mCΔT
Here the given statement is :
If the temperature of water is between the temperatures of ice and steam, then ice is colder than water and steam is hotter than water.
The above statement is justified below :
The steam exhibit more energy than water at the same temperature that is 100° C. The steam uses the latent heat of vaporization so as to get vaporized and water do not exhibit energy and also, The arrangement of molecules in substances is widely influenced by the state of the matter of the substance. In this way, in solids the molecules have a fix organization and are closely packed due to this, solids have both a defined shape and volume; in liquids the molecules are still close to each other but there is no a defined structure and therefore liquids have a defined volume but not a defined shape; finally, in gases molecules do not follow an orderly arrangement and there is more space between them which makes them not have a define volume or shape.
According to this, we can say that Ice is colder than water due to its more heat absorbing capacity then water and steam is hotter than water due to high heat transfer rate then water.
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Find the value of X. If ur answer is not an integer
Answers
Answer: x = (5√2)/2
The last option
Explanation:
The given triangle is a right triangle. Taking angle 45 as the reference angle,
hypotenuse = 5
opposite side = x
We would find x by applying the sine trigonometric ratio which is expressed as
sin θ = opposite side/hypotenuse
By substituting the given values into the equation,
sin45 = x/5
Recall,
[tex]sin45\text{ = }\frac{\sqrt{2}}{2}[/tex]Thus,
[tex]\begin{gathered} \frac{\sqrt{2}}{2}\text{ = }\frac{x}{5} \\ By\text{ crossmultiplying,} \\ x\text{ = }\frac{5\sqrt{2}}{2} \end{gathered}[/tex]x = (5√2)/2
The last option
Can someone please help me with this (there is a part two)
Answers
Part A)
Let x be a number of horses that Sunshine Acre Farm can support. Since each horse needs 1.75 acres of pasture, and the farm has at most 35 acres of pasture available, then we can set the following inequality:
[tex]1.75x\le35.[/tex]Answer Part A)
[tex]1.75x\le35.[/tex]How can you solve, write and graph inequalities on a number line?
Answers
Let's use the following inequation as an example:
[tex]2y>6[/tex]First let's simplify it dividing the inequation by 2:
[tex]y>3[/tex]Now, let's draw a number line, and include the point 3 in it:
We want the values of y that are greater than 3, that is, the numbers to the right of the number 3 in the number line. So we mark the area that corresponds to the values of y that satisfies the inequation:
The number 3 is not part of the answer, because 3 is not greater than 3, so we draw a small empty circle on the number 3. If the number 3 was part of the answer, the circle would be filled.
True or false?
A supply shock is a sudden shortage of a good.
Answers
The following statement "A supply shock is a sudden shortage of a good" is true.
A supply shock is an unexpected incident that abruptly affects the supply of a product or commodity, resulting in an unanticipated change in price. Supply shocks can be negative, resulting in a fall in supply, or positive, resulting in an increase in supply.
Assuming that aggregate demand remains constant, a negative (or unfavorable) supply shock causes a product's price to rise, whereas a positive supply shock causes the price to fall.
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A six -sided fair number cube is rolled once . What is the probability that the result is a 2 or a 5? Select one :1/61/32/55/6
Answers
total number of sides = 6
sides that are 2 or 5 = 2
Divide the sides thata re 2 or 5 (2) by the total sides:
2 /6 = 1/3
If (fg)(x) = h(x) such that h of x is equal to the square root of the quantity 4 times x plus 8 end quantity which of the following could accurately represent f and g?
Answers
The representation of the composite functions f(x) and g(x) are f(x) =√x and g(x) = 4x + 8
How to determine the possible equations of the composite functions f(x) and g(x)From the question, we have the following parameters
(fg)(x) = h(x)
Such that
h(x) = √4x + 8
The given parameter implies that
(fg)(x) =√4x + 8
Let g(x) = 4x + 8
Substitute g(x) for 4x + 8 in the above equation (fg)(x) =√4x + 8
So, we have
(fg)(x) =√g(x)
Substitute g(x) for x in the above equation (fg)(x) =√g(x)
f(x) =√x
This means that
f(x) =√x and g(x) = 4x + 8
Hence, the possible equations are f(x) =√x and g(x) = 4x + 8
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Which expressions can be used to find m∠ABC? Select two options.
cos−1(StartFraction 9.8 Over 6.3 EndFraction)
cos−1StartFraction 6.3 Over 9.8 EndFraction)
cos−1(StartFraction 7.5 Over 9.8 EndFraction)
sin−1(StartFraction 9.8 Over 7.5 EndFraction)
sin−1(StartFraction 7.5 Over 9.8 EndFraction)
]
Answers
The expressions which can be used to find m∠ABC and from the task content are;
cos−¹(StartFraction 6.3 Over 9.8 EndFraction).sin−¹(StartFraction 7.5 Over 9.8 EndFraction).Which expressions can be used to find m∠ABC among the answers choices?It follows from the task content that the expressions which can be used to find m∠ABC are to be identified among the answer choices.
Since, it follows from trigonometric ratios that;
Sin theta = opposite/hypothenuse
Cos theta = adjacent/hypothenuse
It therefore follows that;
Cos(m∠ABC) = 6.3/9.8Sin(m∠ABC) = 7.5/9.8Therefore, the measure of angle ABC can be determined using any of the formulas above;
m∠ABC = cos-¹(6.3/9.8)m∠ABC = sin-¹(7.5/9.8)Therefore the two expressions which can be used to find m∠ABC are;
cos−¹(StartFraction 6.3 Over 9.8 EndFraction).sin−¹(StartFraction 7.5 Over 9.8 EndFraction).Read more on trigonometric ratios;
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Answer: the answer is B [tex]cos^{-1}(\frac{6.3}{9.8}) sin^{-1}(\frac{7.5}{9.8})[/tex]
Step-by-step explanation: it will be show below.
The table shows the total distances of four trails. You want to complete a trail in $1\frac{1}{2}$ hours with an absolute deviation of at most 15 minutes. You hike at a rate of 3 miles per hour. Which trails can you hike? Select all that apply. Trail Miles $A$ $B$ $C$ $D$ $5\frac{1}{4}$ $4\frac{3}{4}$ $3\frac{1}{2}$ $4$ response - correct Responses A A B B C C D D Question 2 Use an absolute value inequality to justify your answer. Inequality : Question 3 Explain.
Answers
Using proportions, the trails that you can hike are given as follows:
Trail A.Trail B.What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using operations such as multiplication or division.
Two examples of proportions are used in this problem:
Relations between hours and minutes -> one hour = 60 minutes.Conversion of mixed numbers to decimal: a and b/c = a + b/c.The time you want to complete a trail is:
1 and 1/2 hours with an absolute deviation of at most 15 minutes.
1 and 1/2 hours = 1.5 hours, as 1 + 1/2 = 1 + 0.5 = 1.5 hours.
1.5 hours = one hour and 30 minutes with a deviation of 15 minutes, the time lengths are:
Lower bound: one hour and 15 minutes = 1.25 hours.Upper bound: one hour and 45 minutes = 1.75 hours.Considering the rate of 3 miles, the distances are between:
1.25 x 3 = 3.75 miles.1.75 x 3 = 5.25 miles.The times for each trail, converting the mixed numbers to decimals, and the decimals to hours and minutes, are given as follows:
Trail A: 5 and 1/4 miles = 5.25 miles -> Yes.Trail B: 4 and 3/4 miles = 4.75 miles -> Yes.Trail C: 3 and 1/2 miles = 3.5 miles -> No, too short.More can be learned about proportions at https://brainly.com/question/24372153
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112Calculate and simplify as much as possible theperimeter and area of the largest figure. All four-sided figures are rectangles.9Perimeter =рArea =
Answers
SOLUTION:
Step 1:
In this question, we are meant to solve the following:
Step 2:
The perimeter of the largest figure is:
[tex]\begin{gathered} Length\text{ + Width + Length + Width} \\ =\text{ ( 12 + p ) + q + ( 12 + p ) + q} \\ =\text{ 24 + 2p + 2q} \\ =\text{ 24 + 2 ( p + q)} \end{gathered}[/tex]On the other hand, the area of the largest figure is:
[tex]\begin{gathered} \text{Length x Width} \\ =\text{ ( 12 + p ) x q} \\ =\text{ ( 12 + p )q} \end{gathered}[/tex]Complete the following truth table. Use T for true and F for false.You may add more columns, but those added columns will not be graded.
Answers
Given,
The equation of table is
[tex]\urcorner p\wedge\urcorner q^{}[/tex]Here,
[tex]\begin{gathered} p\text{ q }\urcorner p\text{ }\urcorner q\text{ }\urcorner p\wedge\urcorner q \\ T\text{ T F F F} \\ T\text{ F F T F} \\ F\text{ T T F F} \\ F\text{ F T T T} \end{gathered}[/tex]Hence, the output of the table is F, F, F, and T
Which equation shows the inverse property of multiplication?
Answers
Answer:
What are the outstanding traditional Chinese culture?
1. Drama is a general term for stage performing arts that achieve narrative purposes in the form of language, movement, dance, music and puppets.
2. Chinese painting, originated in the Han Dynasty, mainly refers to the scroll painting painted on silk, rice paper and silk and mounted.
3, Calligraphy, calligraphy is a unique form of artistic expression of the beauty of Chinese characters in China and the surrounding countries and regions that have been deeply influenced by Chinese culture.
4, Shadow Puppets, also known as "Shadow Puppets" or "lantern Puppets", is a kind of folk drama made of animal skins or cardboard silhouettes to perform stories.
5. Pingju, which is popular in northern China, is one of the traditional operas of the Han nationality and one of the most popular operas among the people. It ranks among the five kinds of operas in China.
Factor the expression 54x2-6y^2?
Answers
Evaluate the expression a-5 -b, when a= 10 and b=4
Answers
Given the expression:
a - 5 - b
we want to evaluate it when a = 10 and b = 4. To do it, we have to replace these values into the equation as follows:
10 - 5 - 4 = 1
help help help help help help help
Answers
The total capacity of her tank would be; 21 gallons.
What is the fundamental principle of multiplication?If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
Given that Leslie makes a stop at a gas station. she put 14 gallons into her tank. if the tank is now 2/3 full.
Let c be the total capacity of the tank.
Then, we can find the capacity of her tank;
c x 2/3 = 14
Cross multiplication;
c = 14 x 3/2
c = 7 x 3
c =21
Hence, the total capacity of her tank would be; 21 gallons.
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Solve. Richard Saltwood's car averages 270 miles on its 18-gallon tank of gas. If Richard runs out of gas and a mechanic comes to his rescue with 2 3/10 gallons of gas, determine how far his car can go. Round to the nearest mile.
Answers
ANSWER:
35 miles
STEP-BY-STEP EXPLANATION:
We can make a proportion, since we know the number of miles per 18 gallons, so for 2 3/10 gallons we can calculate the number of miles proportionally
[tex]\begin{gathered} 2\frac{3}{10}=\frac{23}{10} \\ \text{The proportion is} \\ \frac{270}{18}=\frac{x}{\frac{23}{10}}\rightarrow\frac{270}{18}=\frac{10x}{23} \end{gathered}[/tex]solving for x:
[tex]\begin{gathered} 18\cdot10x=270\cdot23 \\ 180x=6210 \\ x=\frac{6210}{180} \\ x=34.5\cong35 \end{gathered}[/tex]Therefore you can travel a total of 35 miles.
d. Bottom: summary 5. Complete the Coached Example on page 285 - fill in the blanks Upload the Cornell Notetaking Guide and the Coached Example ACHED EXAMPLE number of text messages that Aimee sent on each of the past 7 days is shown 24, 19, 11, 15, 11, 28, 20 t are the first quartile, third quartile and interquartile range of this data set? the numbers from least to greatest. - IL 15 19. 20. 24.29 the median. The median is the 19 Median: _19 value of an ordered data set. 1 is the median of the half ofa data set
Answers
The first quartile (Q1) is defined as the middle number between the smallest number (minimum) and the median of the data set. The first quartile is the median of the first half of a data set.
First QuartileQ1 =11
The third quartile (Q3) is the middle value between the median and the highest value (maximum) of the data set. The third quartile is the median of the second half of a data set.
Third QuartileQ3 = 24
The interquartile range (IQR), is equal to the difference between 75th and 25th percentiles. IQR = Q3 − Q1
IQR = 13