The final answer of the solution is x∈ (-13,1) ∪ [1, 15 ] or, x∈(-13, 15] and x∈ (-∞ , 1) ∪ [1, ∞) or, x∈ (-∞, ∞) or x∈ R.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
For |x - 1 | + 1 < 15 , we should first break the modulus function .
Two cases are possible for this inequality ,
case 1 - when x ≥ 1
x - 1 + 1 < 15 ⇒ x < 15
putting the number line both x ≥ 1 and x≤ 15
Then, x∈ [1, 15)
case 2 - when x < 1
-x + 1 + 1 < 15
⇒ -x + 2 < 15
⇒ -x < 13 ⇒ x > -13
putting the number line both x > -13 and x < 1
then, x∈ (-13, 1)
now, answer is x∈ (-13,1) ∪ [1, 15 ] or, x∈(-13, 15]
Again, for |x - 1| + 1 > 15
Similarly z there are two cases possible for this
case 1 :- when x ≥ 1
x - 1 + 1 > 15 ⇒ x > 15
Putting the number line both x ≥ 1 and x > 15
then, x ∈ [1, ∞)
case 2 - when x < 1
-x + 1 + 1 > 15 ⇒ x < -13
putting the number line both x < 1 and x < -13
Then, x∈ (-∞, 1)
hence, final answer is x∈ (-∞ , 1) ∪ [1, ∞) or, x∈ (-∞, ∞) or x∈ R
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Find the solution to the equation below.
Answer:
Answer is G 1.5
Step-by-step explanation:
1. Distribute the 5 to x and 2 by multiplying. and the 7 to the 4 and -x by multiplying
2. carry over the 7x by adding it to 5x. to get x to one side.
3. subtract 10 from both side
4. Divide both side by 12
5. simplify and convert to decimal
One company makes inflatable swimming pools that come in four sizes of rectangular prisms.
The length of each pool is twice the width and twice the depth.
The depth of each pool is a whole number from 3 to 6 feet.
If the pools are filled all the way to the top, what is the volume of each pool?
Answer:
Pool 1: 2(3)*3*3= 54 ft^3
pool 2: 2(4)*4*4= 128 ft^3
Pool 3: 2(5)*5*5= 250 ft^3
pool 4: 2(6)*6*6= 432 ft^3
Step-by-step explanation:
length can be modeled by twice the width or twice the depth which means that deapth=width,
both the width and the depth are equal, hence
L= 2x
W=X
x=3,4,5,6 (which are values for depth as well as width)
susbtitute values:
Pool 1: 2(3)*3*3= 54 ft^3
pool 2: 2(4)*4*4= 128 ft^3
Pool 3: 2(5)*5*5= 250 ft^3
pool 4: 2(6)*6*6= 432 ft^3
What is the product of the binomials (4a – 1) and (2b 3)? 18ab – 3 8a2b2 10ab – 3 6ab 7a – 2b – 3 8ab 12a – 2b – 3
Binomials are polynomials with two terms.The product of the binomial (4a-1) and (2b+3) is 8ab+12a-2b-3.
What are polynomial?Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.
The product of the binomial can be done as,
[tex](4a-1) \times (2b+3)\\\\= (4a \times 2b)+(4a \times 3)+(-1 \times 2b)+(-1\times 3) \\\\= 8ab+12a-2b-3[/tex]
Thus, the product of the binomial (4a-1) and (2b+3) is 8ab+12a-2b-3.
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Answer:
Answer is D
Step-by-step explanation:
Slope intercept form of x intercept=3 y intercept=-5
Answer:
[tex]y = \frac{5}{3} x - 5[/tex]
Step-by-step explanation:
To write an equation in the slope-intercept form, we need the slope (which can also be calculated) and at least a coordinate.
What is slope-intercept form?
y= mx +c, where m is the slope and c is the y-interceptWhen the coefficient of y is 1, and all the other terms are on the right-hand side of the equationx- intercept occurs at y= 0 while y-intercept occurs at x= 0. With this information, let's write out the two coordinates given.
(3, 0) and (0, -5)With two coordinates, we can calculate the slope using the equation below.
[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]
[tex]slope = \frac{ - 5 - 0}{0 - 3} [/tex]
[tex]slope = \frac{ - 5}{ - 3} [/tex]
[tex]slope = \frac{5}{3} [/tex]
Substitute the value of the slope into m in the equation.
[tex]y = \frac{5}{3} x + c[/tex]
Given that the y-intercept is -5, c= -5.
[tex]y = \frac{5}{3} x - 5[/tex]
Consider two unique parallel lines. What aspects of these
two lines are the same? What aspects of these two lines
would have to be different? Explain your reasoning.
Answer:
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Step-by-step explanation:
Lauren made a scale drawing of a city park. The scale she used was 1 centimeter : 8 meters. If the soccer field is 14 centimeters long in the drawing, how long is the actual field?
Answer:
112
Step-by-step explanation:
1:8
14:x
8x14=112
X=112
Answer:
112 m
Step-by-step explanation:
1 cm : 8 m
14 cm : ?
= 14 x 8
= 112 m
hope someone answer it
Answer:
9) A. ∠1 and ∠3
10) B. Angle 2
11) B. 110°
12) B. 70°
Step-by-step explanation:
Vertical angles: a pair of opposite angles formed by two lines intersecting. Vertical angles are congruent.
The vertical angles in the given diagram are ∠1 and ∠3 AND ∠2 and ∠4
These pairs of angles are equal, so: ∠1 =∠3 AND ∠2 =∠4
Therefore:
If ∠1 = 110° then ∠3 = 110°
If ∠2 = 70° then ∠4 = 70°
Describe two ways to determine the maximum or minimum of the quadratic function f(x)= -3x²+27x-42. Find the maximum or minimum using each method
Answer:
Find by using 1st derivative test (tests slope) or 2nd derivative test (test concavity). Maximum is 18.75.
Step-by-step explanation:
The maximum of the equation is found when the slope is 0; therefore, take the derivative of the equation, find the critical point and find whether the function is increasing or decreasing around the critical point. To do this use test values within the interval of (-∞, 4.5) and (4.5, ∞). You then find that (-∞, 4.5) is increasing meaning there is a maximum. Plug in 4.5 into f(x) to find the y value.
Second method is using the 2nd derivative test. Find the second derivative and use the same method of testing intervals but instead plugging in test values to the 2nd derivative. You then find that f''(x) is < 0 meaning the function is concave down, thus having a maximum. Plug in 4.5 to find the y value.
Shaunta is developing a recursive formula to represent an arithmetic sequence in which 5 is added to each term to determine each successive term. which formula could represent her sequence? f(n 1) = f(n) 5 f(n 1) = f(n 5) f(n 1) = 5f(n) f(n 1) = f(5n)
Answer:
f(n+1) = f(n)+5
Step-by-step explanation:
So lets say
f(1)=5
f(2)=10
1+1=2 so
f(2)=f(1+1)
therefor
f(n+1)=f(n)+5 since the difference of the functions is 5
the answer is A f(n+1)=f(n)+5
we know that
An arithmetic sequence is a sequence of numbers which increases or decreases by a constant amount each term
In this problem
the sequence of numbers increase by a constant amount equal to
5
each term
so
f(2)=f(1)+5
f(3)=f(2)+5
f(4)=f(3)+5
.
.
f(n+1) = f (n) + 5
therefore
the answer is the option
f(n + 1) = f(n) + 5
Answer:
A
Step-by-step explanation:
4. A liter is equal to 1000 cm3. How many liters of water are needed to fill a cylindrical tank that is 1.1 m long and a radius of 0.3 m? A. 150.72 L B. 200.27 L C. 300.72 L D. 310.86 L hold nn ml water How much
Answer:
D. 310.86 L
Step-by-step explanation:
[tex]\textsf{Volume of a cylinder}=\pi r^2h[/tex]
where:
[tex]r[/tex] is the radius[tex]h[/tex] is the heightGiven:
r = 0.3 mh = 1.1 m[tex]\pi[/tex] = 3.14[tex]\implies \sf \textsf{Volume of the tank}=(3.14)(0.3)^2(1.1)=0.31086\:m^3[/tex]
[tex]\sf 1\:liter = 1000\:cm^3[/tex]
To convert cubic cm to cubic meters, divide by 1,000,000:
[tex]\implies \sf 1\:liter =\dfrac{1000}{1,000,000} = 0.001\:m^3[/tex]
[tex]\implies \sf \textsf{Volume of the tank}=\dfrac{0.31086}{0.001}=310.86\:L[/tex]
At a neighbor's garage sale, Rodrigo purchased a big bag of assorted bolts, nuts, screws, and washers. He picks a piece out of the bag, records its type, puts it back in the bag, and mixes them up. He does this 18 times and counts 3 bolts, 6 nuts, 5 screws, and 4 washers.
Based on the data, what is the probability of choosing a washer?
Write your answer as a fraction or whole number.
How do I do this? :(
Answer:
2762 in²
Step-by-step explanation:
The total surface area of a figure is the sum of the areas of its faces.
Area of rectangle= length ×breadth
Assuming that this is a closed box, the total surface area is the total area of its 6 rectangular faces.
Two rectangles have dimensions of 7 in. ×19 in., another two rectangles have dimensions of 48 in. ×7 in., and the last two rectangles have dimensions of 48 in. ×19 in.
Surface area of the figure
= 2(7)(19) +2(48)(7) +2(48)(19)
= 266 +672 +1824
= 2762 in²
What is the solution for the equation startfraction 5 over 3 b cubed minus 2 b squared minus 5 endfraction = startfraction 2 over b cubed minus 2 endfraction? b = –4 and b = 0 b = –4 b = 0 and b = 4 b = 4
An equation is formed of two equal expressions. The solution of the equation is 4.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The solution of the equation can be written as,
[tex]\dfrac{5}{3b^3-2b^2-5} = \dfrac{2}{b^3-2}\\\\5(b^3-2) = 2(3b^3-2b^2-5)\\\\5b^3-10=6b^3-4b^2-10\\\\5b^3-10-6b^3+4b^2+10=0\\\\-b^3+4b^2=0\\\\b^2(-b+4)=0\\\\-b+4=0\\\\-b=-4\\\\b=4[/tex]
Thus, the solution of the equation is 4.
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Answer:
c
Step-by-step explanation:
Determine the monthly payment of a loan for $3,000 at 7.5% interest compounded monthly for 36 months. a. $93.32 b. $95.40 c. $211.33 d. $253.60 please select the best answer from the choices provided a b c d
The monthly payment of a loan for $3,000 at 7.5% interest compounded monthly for 36 months is $93.32.
loan amount P = $3000
Rate of interest = 7.5% per annum
So, monthly rate of interest r= 7.5/12 %
Tenure n = 36 months
What is the formula to calculate monthly payments?The formula to calculate monthly payments is given
[tex]EMI=\frac{Pr}{1-(r+1)^{-n} }[/tex]...........(1)
Where P =loan amount
r = monthly rate of interest
n=tenure
So by substituting the given values in (1) the monthly payment = $93.32
Hence, the monthly payment of a loan for $3,000 at 7.5% interest compounded monthly for 36 months is $93.32.
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PLEASE HELP ME ANSWER THIS QUESTION
Answer:
Scale faction is 4
Step-by-step explanation:
You want to step this up as new/old this is because the shape is increasing in size. 18 times 4 is 72.
y=65x+50
what is this equation equal
What is the factored form of the function? what are the zeros of the quadratic function?
Answer:
The factored form of the equation is f(x) = (x - 2)(x + 10), which makes the zeros of the function x = -10 and x = 2.
In order to factor a quadratic like this, you must find factors of the constant (in this case -20). The pairs of factors are listed below.
1 and -20
-1 and 20
2 and -10
-2 and 10
4 and -5
-4 and 5
Now we must pick out the pair that add to the coefficient of x.
1 and -20
-1 and 20
2 and -10
-2 and 10
4 and -5
-4 and 5
Once you've picked out those numbers, you can place each in a parenthesis with x.
f(x) = (x - 2)(x + 10)
Then to find the zeros to the equation, set each parenthesis equal to 0 and solve.
x - 2 = 0
x = 2
x + 10 = 0
x = -10
Step-by-step explanation:
hope this helps:)
If f (x) = startroot one-half x minus 10 endroot 3, which inequality can be used to find the domain of f(x)? startroot one-half x endroot greater-than-or-equal-to 0 one-half x greater-than-or-equal-to 0 one-half x minus 10 greater-than-or-equal-to 0 startroot one-half x minus 10 endroot 3 greater-than-or-equal-to 0
A function assigns values. The inequality one-half x minus 10 greater-than-or-equal-to 0 should be satisfied.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The domain of a function is a set of values for which the equation is satisfied. Since the function has under root values, the value which is under the root should be non-negative so that it does not give a complex number, therefore,
The inequality [tex]\sqrt{\dfrac12x^2-10}\geq 0[/tex]satisfied to find the domain of the function f(x).
Also, we can write that 0.5x²-10≥0 for the value to be positive.
Hence, the inequality one-half x minus 10 greater-than-or-equal-to 0 should be satisfied.
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HELP PLEASE ASAP
Which situation can be represented by the equation y = 25x
Question 1 options:
David earned y amount of money at a rate of $25 per x hours.
David earned $25 for one day, which x amount is earned for y number of days.
David earned x amount of money at a rate of $25 per y hours.
David earned $25 for one day, which y amount is earned for x number of days.
The situation that best represents the equation y = 25x is David earned y amount of money at a rate of $25 per x hours.
Using equations to represent expressionsRate of payment is the amount of money a worker receives after each hour, day or week.
David receives the amount of y as his payment every hour.
He is paid at the rate of $25 every X hours.
Therefore the amount he will receive which is represented as y would be $25 * X hours.
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HELP PLEASE ASAP!!!
Carol asked a random sample of 10 seventh grade student athletes and 10 seventh grade students who are not athletes how much time, in minutes, they spend studying each weeknight. She recorded her results in the table
Student Athletes: 103, 62, 21, 100, 140, 65, 124, 45, 86, 114
Not Student Athletes: 101, 135, 122, 43, 110, 62, 31, 80, 67, 126
A) Calculate the mean and median data values for the student athletes sample
B) Calculate the mean and median data values for the not student athletes sample.
C) When comparing the two samples, what conclusions can you draw about which group spends more time studying each weeknight?
Answer:i dont know sorry but i think its c
Step-by-step explanation:
Find x and y... Thanks!
i just need the answer to it and then ill do the labels
Answer:
x = 23
Step-by-step explanation:
2x -3 + 47 = 90
2x = 46
x = 23
PLS HELP ASAP Cassandra earns $12. 98 an hour working at Key Food. How much money will she earn this month, if she works 36. 7 hours? Round the amount of time to the nearest hundredth.
1.) The ratio of the number of men to the number of women in a concert is 3 : 5. If there are 4800 people at the concert, how many are men? How many are women?
2.) Alice can type 65 words in 1 min. How many minutes would it take her to type an essay 2275 words long?
3.) Mrs. Ong divided her property worth P 3, 480, 000 between her two children in the ratio of 3 : 5. How much was the bigger share?
4.) In 2 minutes , Mario can run 1800 m. How far can he run in 6 min?
5.) Cielo gets 2 hits out of every 3 times at bat. If she got 16 hits, how many times was it at bat?
6.) Three friends shared in the capital of putting up a computer business in the ratio of 4 : 5 : 6. If the total amount of capital is P450 000, how much was the smallest share?
Answer:
1.) men: 1800, women: 3000
2.)2275/65 = 35 mins
3.)P 2,175,000
4.) 5400 in 6 mins
5.) Probably 5?
6.) P 120 000
Step-by-step explanation:
The area of a rectangle is 46.56 mm2.
If the width is 9.7 mm, find the length.
Answer:
The length is 4.8 mm
Step-by-step explanation:
The area of a rectangle is calculated by multiplying the length times the width. So:
46.56 = l * w
46.56 = l * 9.7
To find the length, we must get "l" alone. To do this, we must divide both sides by 9.7.
46.56/9.7 = 4.8
4.8 = l
The length is 4.8
Two numbers have a least common multiple of 48 and a greatest common factor of 4?
Answer:
The numbers are 12 and 4
Step-by-step explanation:
12÷4=3
4÷4=1
12×4=48
What's the equation of the line that passes through the points (–8,4) and (0,22)?
Answer:
c
Step-by-step explanation:
Sharon has at most $25 to spend on her sister's birthday gift. She already bought a knitting machine for her, which cost $14.99. She would also like to get her sister some skeins of yarn to go with it. Each skein costs $2.75. Write an inequality to represent this problem. Use y to represent the number of skeins of yarn. What is the most number of skeins Sharon can afford to buy? Justify your answer in two or more complete sentences.
Answer:
$25 >= 14.99+2.75x
Step-by-step explanation:
find the value of x.
Answer: 7.2
Step-by-step explanation:
Fred is training for a cross-country race. At practice last week, he ran 6. 25 miles in 1
1
4
hours. At that speed, how long would it take Fred to run 8. 5 miles?
Answer:
1.36
Step-by-step explanation:
Answer:
1.7 hours
Step-by-step explanation:
IXL is pain.