Answers
a The absolute value of ax will be considered while for the second the absolute value of ax + b will be considered.
b The absolute value of ax will be considered while for the second the absolute value of ax + b will be considered.
Given data
a, b, c, and x be real numbers.
How to show the difference in solving |ax| + b = c and |ax + b| = c|ax| + b = c
The equation here contains the modulus sign only for ax hence only the absolute value of ax is considered.
|ax + b| = c
Here the modulus sign covers both ax and b hence the absolute values of ax + b is considered.
How to show the difference in solving |ax| + b ≤ c and |ax + b| ≥ c|ax| + b ≤ c
The equation here contains the modulus sign only for ax hence only the absolute value of ax is considered.
|ax + b| ≥ c
Here the modulus sign covers both ax and b hence the absolute values of ax + b is considered.
Note that absolute values do not consider the signs
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Related Questions
Does anyone understand this?
Answers
Answer: B.
Step-by-step explanation:
the goal of the question is to make <AZB ≈ (around) <AYB. Answer b is the only one that makes sense because in the first answer triangle AYB is obtuse and much wider than triangle AZB. While in answer c, triangle AYB is acute and way too small to be around triangle AZB. In answer b, the angles are around the same even though one triangle is slightly larger than the other.
Determine the amplitude or period as requested.
Amplitude of y = negative one-third sine x
a.
Negative one-third
b.
StartFraction pi Over 3 EndFraction
c.
One-third
d.
3
Answers
The amplitude of the function is 1/3
How to determine the amplitude of the function?The function is given as:
y = negative one-third sine x
Rewrite properly as
y = -1/3sin(x)
A sine function is represented as:
y = Asin(x)
And the amplitude is
Amplitude = |A|
In y = -1/3sin(x), we have
A = -1/3
So, we have
Amplitude = |-1/3|
Evaluate
Amplitude = 1/3
Hence, the amplitude of the function is 1/3
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About what percent of the data are greater than 20?
About what percent of the data are less than 15?
Describe and correct the error in interpreting the box-and-whisker plot.
please answer questions 8-10.
Answers
About 25 percent of the data are greater than 20.(option a)
About 50 percent of the data are less than 15. (option b)
20 is wrongly interpreted as the median. 20 is the third quartile. The data between 11 and 20 is 50%.
How can a box-and-whisker plot be interpreted?A box plot is used to study the distribution and level of a set of scores. The scores are distributed into 4 groups. Each group has a value of 25%
The box plot consists of two whiskers and a box. The first whisker represent the minimum value. The second whisker represents the maximum number.
On the box, the first line to the left represents the lower (first) quartile. 25% of the score represents the lower quartile. The next line on the box represents the median. 50% of the score represents the median. The third line on the box represents the upper (third) quartile. 75% of the scores represents the upper quartile.
20 is the third quartile. Score greater than 20 is 25% (100% - 75%)
15 is the median. Scores less than 15 is 50% (100 - 50%),
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Find an equation of the line perpendicular to 3y=x+3 that passes through the point (5,8). Write the answer in slope-intercept form, y=mx+b, with all fractions written in the lowest terms.
Answers
Let the equation of the line perpendicular to line 3x+2y=16 is:-
2x - 3y = C. ………………(1)
Line (1) passes through the point (9,-2), therefore
2×9 - 3×(-2)= C
or, C = 24.
Thus, the required equation is:-
2x - 3y = 24.
or, 3y = 2y - 24.
or, y = (2/3).x + (-8). Answer.
35/456 long division
Answers
The quotient after the long division of 35/456 is 0.076.
What do we mean by long division?The division is one of the four basic operations of arithmetic, which are the methods by which numbers are combined to form new numbers. Addition, subtraction, and multiplication are the other operations. The division with a remainder or Euclidean division of two natural numbers yields an integer quotient, which is the number of times the second number is completely contained in the first number, and a remainder, which is the part of the first number that remains when no further full chunk of the size of the second number can be allocated during the quotient computation. Long division is a standard division algorithm that is simple enough to perform by hand for dividing multi-digit Hindu-Arabic numerals (Positional notation).So, after the long division:
(Refer to the image given below)Quotient: 0.076(Calculated to 3 decimal places)Therefore, the quotient after the long division of 35/456 is 0.076.
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A company has found that the demand for its product varies inversely as the price of the product. When the price x is 3.5 dollars, the demand is 400 units. Find a mathematical model that gives the demand y in terms of the price x in dollars.
I don't understand how to make this into an equation. Do I have enough variables?
Answers
A mathematical model that gives the demand y in terms of the price x in dollars.
y = 1400/ x
This is further explained below.
What is a mathematical model that gives the demand y in terms of the price x in dollars.?Generally, The following formula would apply in the situation when there is an inverse link between y and x:
y = k/x
where k is constant.
In a relationship with an inverse connection, one variable will tend to decrease as the other variable grows.
y denotes the amount of demand.
x is equivalent to the cost.
400 = k/3.5
k = 400 * 3.5
k = 1,400
The following is the formula for the mathematical model that calculates the demand y based on the price x in dollars:
y = 1400/ x
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How is the word term used to describe a ratio relationship and in the context of an expression?
Answers
It should be noted a term is one of the two numbers that are in the ratio. An example is that in the "ratio of a to b" a is the first term and b is the second term.
How to illustrate the information?It should be noted that it's important to understand ratio and use ratio language to describe the relationship between two quantities.
For example, it van be stated that the ratio of wings to beaks in the bird house at the zoo is 2:1, this implies that b for every 2 wings there is 1 beak.
Therefore, it should be noted a term is one of the two numbers that are in the ratio. An example is that in the "ratio of a to b" a is the first term and b is the second term.
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[tex] \rm\sum_{n = 0}^ \infty \bigg( - \frac{1}2 \bigg)^{n} \frac{ \Gamma ( \frac{1 + n}{2} )}{ \Gamma(1 + \frac{n}2) } \\ [/tex]
Answers
Let [tex]S[/tex] be the sum. Introduce a factor of [tex]\Gamma\left(\frac12\right)=\sqrt\pi[/tex] to rewrite the summand as a beta function integral. Then in the sum, interchange it with the integral, and [tex]S[/tex] reduces to a simple integral.
[tex]\displaystyle S = \sum_{n=0}^\infty \left(-\frac12\right)^n \frac{\Gamma\left(\frac{n+1}2\right)}{\Gamma\left(\frac n2+1\right)}[/tex]
[tex]\displaystyle . ~~ = \frac1{\sqrt\pi} \sum_{n=0}^\infty \left(-\frac12\right)^n \, \mathrm{B}\left(\frac n2+\frac12, \frac12\right) \\\\ ~~~~ = \frac1{\sqrt\pi} \sum_{n=0}^\infty \left(-\frac12\right)^n \int_0^1 \frac{t^{n/2}}{\sqrt t \sqrt{1-t}} \, dt \\\\ ~~~~ = \frac1{\sqrt\pi} \int_0^1 \frac{dt}{\sqrt t \sqrt{1-t}} \sum_{n=0}^\infty \left(-\frac{\sqrt t}2\right)^n \\\\ ~~~~ = \frac2{\sqrt\pi} \int_0^1 \frac{dt}{\sqrt t\sqrt{1-t}\left(\sqrt t+2\right)}[/tex]
Substitute [tex]u=\sqrt t+2[/tex] and [tex]du=\frac{dt}{2\sqrt t}[/tex].
[tex]\displaystyle S = \frac4{\sqrt\pi} \int_2^3 \frac{du}{u\sqrt{-(u-1)(u-3)}}[/tex]
Now substitute [tex]u=1+\frac2{1+t^2}[/tex] and [tex]du=-\frac{4t}{(1+t^2)^2}\,dt[/tex] - this comes from an Euler substitution of the form [tex]\sqrt{a(x-\alpha)(x-\beta)}=(x-\alpha)t[/tex]. [tex]S[/tex] reduces drastically to a trivial arctangent integral.
[tex]\displaystyle S = \frac8{\sqrt\pi} \int_0^1 \frac{dt}{t^2+3} \\\\ ~~~~ = \frac8{\sqrt\pi} \cdot \frac\pi{6\sqrt3} = \boxed{\frac43\sqrt{\frac\pi3}}[/tex]
Someone answer this riddle in the photo
Answers
They still loose 100 dollars
Answer:
The store lost $100....
An advertiser goes to a printer and is charged $38 for 100 copies of one flyer and $50 for 208 copies of another flyer. The
printer charges a fixed setup cost plus a charge for every copy of single-page flyers. Find a function that describes the cost
of a printing job, if x is the number of copies made. C(x) =
4.
Answers
Answer:
C(x) = (1/9)x + 242/9
Step-by-step explanation:
Let x = number of pages.
Let y = cost.
We are given two ordered pairs, (x, y):
(100, 38) and (208, 50)
We must find the equation of the line that passes through these two points.
y = mx + b
m = (y_2 - y_1)/(x_2 - x_1) = (50 - 38)/(208 - 100) = 12/108 = 1/9
y = (1/9)x + b
Use point (100, 38) as x and y to find b.
38 = (1/9)(100) + b
38 × 9 = 100 + 9b
9b + 100 = 342
9b = 242
b = 242/9
The equation is:
y = (1/9)x + 242/9
Answer: C(x) = (1/9)x + 242/9
30 ones, 2 thousands, 4 hundred thousands, 60 tens and 100 hundreds what number am I?
Answers
Answer:
602,630
Step-by-step explanation:
3. Ages of Accountants. The average age of the accountants at Three Rivers Corp. is 25 years,
with a standard deviation of 4 years; the average salary of the accountants is $30,500, with a
standard deviation of $4500. Compare the variations of age and income.
Answers
The age of accountant is more variable than salary.
What is standard deviation ?Standard deviation is the square of difference between the sets of data and mean.
Comparison for variation of data can be determined by coefficient of variation (C.V).
We know C.V = [tex]\frac{\sigma}{|\overline{x|}}[/tex] × 100.
First we are determining C.V for ages.
Where [tex]\sigma[/tex] = standard deviation and [tex]|\overline{x}|[/tex] = arithmetic mean or average.
∴ C.V for ages, where [tex]\sigma[/tex] = 4 and [tex]|\overline{x}|[/tex] = 25 years is
C.V = [tex]\frac{4}{25}[/tex] × 100.
C.V = 16.
[tex]C.V_a_g_e[/tex] = 16%.
Now C.V for salary,
where [tex]\sigma[/tex] = 4500 and [tex]|\overline{x}|[/tex] = 30500.
C.V = [tex]\frac{4500}{30500}[/tex] × 100.
C.V = [tex]\frac{4500}{305}[/tex].
[tex]C.V_s_a_l_a_r_y =[/tex] 14.75 %.
So, the coefficient of variation of age is more than that of salary.
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A scientist had 3/4 of a botttle of solution. She used 1/6 of the solution in experiment. How much of the bottle did she use?
Answers
Answer:
[tex]\frac{1}{8}[/tex]
Step-by-step explanation:
Given : A scientist had [tex]\frac{3}{4}[/tex] of a bottle of a solution.
The part of the solution she used in the experiment : [tex]\frac{1}{6}[/tex]
The part of bottle she used is given by :
[tex]\frac{1}{6} *\frac{3}{4}[/tex]
= [tex]\frac{1*3}{4*6}[/tex]
= [tex]\frac{3}{24}[/tex]
Simplify = [tex]\frac{1}{8}[/tex]
Hence, she used [tex]\frac{1}{8}[/tex] of the bottle .
Two triangles are similar. First triangle has sides of length 6, 8, and 14. The shortest
side of the other has length 12.
a) What is the scale factor going from first to the second triangle?
b) Determine the length of the longest side of the second triangle.
Answers
The scale factor going from the first to the second triangle according to the task content is; 2.
The length of the longest side of.the triangle as required in the task content is; 24.
What is the scale factor going from the first to the second triangle?According to the task content, it follows that the two triangles are similar.
Therefore, the corresponding sides of such triangles must be in proportion.
Therefore the scale factor from the first to the second triangle as required is;
Scale factor = 12/6; since the shortest sides are corresponding sides.
Scale factor = 2.
Hence, since the length of the longest side in the first triangle is 14, the length of the longest side in the second triangle is;
L = 2 × 14
L = 28
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Ordered: 100mg. Available: 0.1g. How many tablets should be given? ________
Answers
Answer:
1 TABLET
Step-by-step explanation:
1 tablet should be given. The aim is to ensure that the amount of medicine you give matches what was prescribed. In order to do that, we must change either the amount we ordered or the amount that is available so that they are both measured in the same unit.
How many tablets should be given?To decide the number of tablets that ought to be given, we have to be change over the accessible sum from grams to milligrams.
Given:
Ordered: 100 mg
Available: 0.1 g
1 g = 1000 mg
Converting the available sum to milligrams:
0.1 g * 1000 mg/g = 100 mg
Since the available amount is equal to the ordered sum, you'd have to be give 1 tablet.
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10.79 less then the product of 26 and x
Answers
Answer:
I believe it's 15.21x
Step-by-step explanation:
10.79 - 26 * x
10.79 - 26x =
15.21x
Y equals X² + 8X + 12show in a graph
Answers
Answer:
Step-by-step explanation:
Harold’s Men’s Clothing sells a suit on clearance. The suit was originally marked down 40% off its retail-selling price, but the suit did not sell. Harold’s Men’s Clothing further marked down the suit 60% below the first discount. What was the original price of the suit before markdowns if the suit finally sold for $125?
Answers
The original price of the suit before markdowns will be $520.83.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
Le's suppose the original price was x dollars.
Now, the first discount of 40%
40% of x = 0.40x
Retail price = x - 0.40x = 0.60x
The second discount is 60% on the first retail price
60% of 0.60x = 0.60×0.60x
⇒ 0.36x
Final retail price = 0.60x - 0.36x
0.24x = 125
x = 520.83
Hence "The original price of the suit before markdowns will be $520.83".
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factor out the greatest common factor (5r-6)(r+3) - (2r-1)(r+3)
Answers
The factor (r + 3) is common. Then the greatest common factor will be (r + 3).
What is the greatest common factor?Simply said, it is the biggest common element. The highest consistent element in the above example is 15, making 15 the greatest common factor amongst 15, 30, and 105. The biggest chunk of the common factors is called the "Greatest Common Factor" (of two or more numbers).
The expression is given below.
⇒ (5r - 6)(r + 3) - (2r - 1)(r + 3)
In both terms, the factor (r + 3) is common. Then the greatest common factor will be (r + 3). Then the expression will be
⇒ (5r - 6)(r + 3) - (2r - 1)(r + 3)
⇒ [(5r - 6) - (2r - 1)](r + 3)
⇒ (3r - 5)(r + 3)
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What is the sum of the polynomials? Need help.
Answers
Answer:
(d) 9x² -12y² -11x
Step-by-step explanation:
The sum of polynomials (8x² -9y² -4x) and (x² -3y² -7x) is found by combining like terms.
Polynomial additionWhen simplifying the sum of polynomials, the distributive property comes into play. It lets you add and remove parentheses, recognizing that factors outside parentheses multiply each term inside parentheses.
(8x² -9y² -4x) + (x² -3y² -7x)
= 8x² -9y² -4x + x² -3y² -7x . . . . . eliminate parentheses
= (8 +1)x² +(-9 -3)y² +(-4 -7)x
= 9x² -12y² -11x
Hi everyoneeee i just need one thing done
solve this in word form
1,900
Answers
There are two ways to say 1900 in word form.
1900 = nineteen hundred
1900 = one thousand, nine hundred
Both are equally valid.
Answer: one thousand nine hundred
Step-by-step explanation:
Approximately how many fencing is needed to enclose a secular pond with a diameter of 23 feet
Answers
The amount of fencing needed to enclose the secular pond is 72.22 feet
What are perimeters?The perimeter of a shape is the sum of the side lengths of the shape
For all regular quadrilaterals, you add up the side lengths to determine the area
How to determine the amount of fencing needed to enclose the secular pond?The given parameter is
Diameter, d = 23 feet
The radius is calculated as
r = d/2
So, we have
r = 23/2
This gives
r = 11.5 feet
The circumference of the circle is calculated as
C = 2pi r
So, we have
C = 2 * 3.14 * 11.5 feet
Evaluate the product
C = 72.22 feet
Hence, the amount of fencing needed to enclose the secular pond is 72.22 feet
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I had 7 bottles and 3 friends how much will be left
Answers
The number of bottles that would be left is 1
How to determine the number of bottles that would be left?The given parameters are
Number of Bottles = 7
Number of Friends = 3
Assume that the bottles are to be shared among the friends only
The number of bottles that would be left is
Bottles left = Number of Bottles % Number of Friends
This gives
Bottles left = 7%3
Evaluate the modulo operation
Bottles left = 1
Hence, the number of bottles that would be left is 1
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A line passes through the points (-20, 4) and (-15, 8).
Calculate the slope of the line - simplify answer if possible. (If the slope is undefined, enter "DNE")
Then, write the equation of the line.
Answers
Answer:
The slope is 4/5
y = 4/5x + 20
Step-by-step explanation:
Slope:
Change in y over the change in x
(4 - 8) / -20 - -15
-4 / -20 + 15
-4 /-5
4 / 5
Equation of the line:
You could use either point given. I am going to use the point (-20,4) I will use -20 for x and 4 for y. I will use 4/5 as the slope. I will need to solve for the y-intercept
y = mx + b
4 = (4/5)(-20) + b
4 = -16 + b Add 16 to both sides
20 = b
The equation will be
y = 4/5x + 20
i’ll give brainliest and about 15 points (i’m talking about the 2-80 ones)
Answers
Here are the values of the expressions :
a. 3(4) = 12
b. 4 + 11 + (-4) = 11
c. 3.2(2) = 6.4
d. | (-2) + (-2) + (-2) | = 6
e. |2 (-7.5) | = 15
f. 10 1/5(-5) = -51
a. 9(410) = 3690
b. 6(592) = 3552
What are the values of the expressions?Take not of the following rules:
When a term is in bracket, it means that the values should be multiplied : 2 (3) = 2 x 3 = 6
When numbers are between this sings | |, it means that the answer should be an absolute value. e.g. | - 5 - 5 | = 10
When a negative sign is multiplied by a positive sign, the result would be a negative sign. -1 x + 1 = -1
a. 3(4) = 3 x 4 = 12
b. 4 + 11 + (-4)
= 4 + 11 - 4 = 11
c. 3.2(2) = 3.2 x 2 = 6.4
d. | (-2) + (-2) + (-2) |
|- 2 - 2 - 2| = 6
e. |2 (-7.5) |
|2 x -7.5| = 15
f. 10 1/5(-5)
10 1/5 x - 5
51/5 x - 5 = -51
a. 9(410)
= (9 x 400) + (10 x 9)
3600 + 90 = 3690
b. 6(592)
= (6 x 500) + (92 x 6)
3000 + 552
3552
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Find the measure of the smaller angle formed by the hands of a clock at the following time. 4:25
Answers
The minute hand has moved 25 times out of a possible 60 from the top of the clock as of 4:25. 150 degrees is 25 multiplied by 6 degrees. Simply subtracting those degrees from the above calculation, the angle from the minute hand to the hour hand is equal to 360 degrees. 342.5 degrees is 360 minus 17.5.
An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex. Using a protractor, angles are measured in degrees (°).
An angle is a figure in plane geometry that is created by two rays or lines that have a common endpoint. The Latin word "angulus," which means "corner," is the source of the English word "angle." The common endpoint of two rays is known as the vertex, and the two rays are referred to as sides of an angle. When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the word "angle" originates.
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What is the area of the triangle below (in square units)?
Remember, the formula for the area of a triangle is
where represents the length of the base of the triangle and represents its height.
Answers
The Area of the triangle with base 6 and height 4 is 12 square units.
Area of triangle with base "b" , and height "h" can be calculated using the formula
Area = 1/2*b*h .
From the figure
It is given that height of triangle = 4
base of the triangle = 6
By using the formula for Area of the triangle we get ,
Area = 1/2*b*h
Substituting the value of base and height from above we get ,
Area= 1/2*6*4
=(6*4)/2
=24/2
=12
Therefore , the Area of the triangle with base 6 and height 4 is 12 Square units .
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Reduce answers to lowest terms 5/9 + 1/10
Answers
The answer for the given question is 59/90
A fraction is said to be in lowest terms when the greatest common factor (GCF) of the numerator and denominator is 1. Now that this is in mind, let's continue to solve.
Given, 5/9+1/10 and we have to convert or reduce it into the lowest terms.
So, let's proceed to solve this question
First add 5/9 and 1/10 i.e.,
= 5/9+1/10
Taken LCM of 9 and 10 which comes out to be 90.
Then, adding, we get
= 50+9/90
= 59/90
59/90 is already in its lowest form because the numerator and denominator have no common factor other than 1. So it's already at its most basic level.
Therefore, 59/90 is the required answer.
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Factor completely 2x³+4x²+ 6x +12.
O20x²+2x²+3x+6)
O (2x²+6)(x+2)
O(x²+3)(2x + 4)
2[(x²+3)(x+2)] Skry
Answers
Answer: use the 'grouping method' to get your answer (answer choice 'B')
Step-by-step explanation:
Take your first two terms, 2x^3 and 4x^2 and find a GCF. In this case, 2x^2 can go into both terms. Your first side should look like this 2x^2(x+2).
Take your last two terms (6x+12) and find a GCF. In this case, your GCF is 6 because both terms can fit into 6. Your second side should look like this 6(x+2).
We know we did this problem correctly because we can see that both parenthesis state the same thing, which is (x+2).
Your equation after finding a GCF in both sets should look something like this; 2x^2(x+2)+6(x+2).
Now, combine the 2x^2 and 6 together to get (2x^2+6) in one parenthesis set. Your second should include ONLY ONE of the '(x+2)'s.
Your final answer should look like this; (2x^2+6)(x+2). Therefore, your answer choice is 'B'.
Hope this helps, dawg.
Please help me out I will mark you brainliest!
Answers
a. The distance around the park is 180 yards
b. QM = 18 yards
c. It takes 49 minutes to travel the entire distance
How to determine the valuesa. The distance around the yard is given as;
PQ + QR + PQ
Where;
PQ = 50 -10 = 40 yardsQR = 80 - 10 = 70 yardsPR = 80 - 10 = 70 yardsTotal = 40 + 70 + 70 = 180 yards
b. To determine QM, we use the Pythagorean theorem;
PQ² = QM² + 1/2 PR²
40² = QM² + (35. 5)²
1600 = QM² + 1260. 25
Make 'QM' the subject
QM² = 1600 - 1260. 25
QM = √339. 75
QM = 18 yards
c. Average speed = 150 yards/ per minute
Total distance = 180 yards
Time = Average speed/ distance
Time = 150/ 180
Time = 0. 8 3 × 60
Time = 49 minutes
Thus, the distance around the park is 180 yards
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