Step-by-step explanation:
x, x+1, x+2 are the 3 consecutive positive integers.
(x+1)(x+2) = 2(x+1) + 2×(x+x+1+x+2)
x² + 3x + 2 = 2x + 2 + 2×(3x + 3)
x² + 3x + 2 = 2x + 2 + 6x + 6 = 8x + 8
x² - 5x - 6 = 0
we can solve this by finding the factoring.
that means we find a, b so that
(x - a)(x - b) = x² - 5x - 6 = 0
because then x = a and x = b are the 2 solutions of the quadratic equation.
we have
x² - ax - bx + ab = x² - (a+b)x + ab = x² - 5x - 6
a+b = 5
ab = -6
that means, either a or b must be 6 and the other -1.
so we get
(x - 6)(x + 1) = 0
x = 6
or
x = -1
since we are only looking for positive integers, the x = -1 solution is invalid, and we get only x = 6 as solution.
therefore the 3 consecutive positive integers are
6, 7, 8
3(2x + 5)= 4 (c-3) I know how to solve it but can someone explain it.
Answer:
3x×2c+1
Step-by-step explanation:
6x+15 =4c-12
[tex] \frac{6x + 15}{4c - 12} = \frac{4c - 12}{4c - 12} [/tex]
[tex] \frac{6x + 15}{4c - 12} [/tex]
[tex] \frac{3x + 5}{2c - 4} [/tex]
[tex]3x + 5 \div 2c - 4[/tex]
[tex]3x \times 2c + 5 - 4[/tex]
[tex]3x \times 2c + 1[/tex]
lets write the possible subset of the following sets and list the proper subset separately
An improper subset of set T contains all the elements of set T and a null element. The improper subset of set T is {2,3}
What is a subset?In mathematics, set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be identical;
A) Integers are whole numbers (without fractions) that are either positive or negative. If T={x:X is an integer between 1 and 4}, therefore the elements in set T = {2, 3}
B) Since the elements in set T = {2, 3}, then the number of elements in set T = 2
C) The subsets of set T are {}, {2}, {3} and {2,3}
D) Proper subset of set T are subsets of T that is not equal to T. The proper subsets of T are {2} and {3}
An improper subset of set T contains all the elements of set T and a null element. The improper subset of set T is {2,3}
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A cylinder has a volume of 72 cubic inches. What is the volume of a cone with the same height and radius as the cylinder? Explain.
What is the ratio of the volumes of two similar rectangles, if the ratio of their perimeters is 2:9?
Answer:
Step-the base is equal to length * width.
the formula for the volume of a rectangular prism becomes length * width * height.
the ratio of the volume of a three sided figure is the ratio of their corresponding sides cubed.
so if the ratio of their volumes is 125/64, then the ratio of their corresponding sides id 5/4 because 5^3 = 125 and 4^3 = 64.
since the base area is equal to length * widfth, then the ratio of the areas becomes 5^2 / 4^2 which is equal to 25/16.
the ratio of the base area becomes 25/16.
to confirm, use an example:
original prism has dimensions as shown below:
length = 20
width = 40
height = 60
volume = 20 * 40 * 60 = 48000
base area = 20 * 40 = 800
prims that has sides in a ratio of 5/4 to original prism is shown below:
length = 20 * 5/4 = 25
width = 40 * 5/4 = 50
height = 60 * 5/4 = 75
volume = 25 * 50 * 75 = 93750
base area = 25 * 50 = 1250
ratio of the volumes = 93750 / 48000 = 1.953125
ratio of the base areas = 1250 / 800 = 1.5625
125/64 = 1.953125
25/16 = 1.5625
the formulas work.
the ratio of the volume is 125/64
the ratio of the base area is 25/16by-step explanation:
volume = 20 * 40 * 60 = 48000
base area = 20 * 40 = 800
prims that has sides in a ratio of 5/4 to original prism is shown below:
length = 20 * 5/4 = 25
width = 40 * 5/4 = 50
height = 60 * 5/4 = 75
volume = 25 * 50 * 75 = 93750
base area = 25 * 50 = 1250
5. Find the area of the figure below:
5 cm
4 cm
2cm
5 cm
Answer:
33 cm^2
Step-by-step explanation:
To find the are of the figure as a whole, find the area of each rectangle individually and then add them together.
The area of a rectangle is [tex]A = bh[/tex], so the area of the small rectangle would be [tex]4*2[/tex], or [tex]8cm^2[/tex].
The area of the larger rectangle would be [tex]5*5[/tex], or [tex]25cm^2[/tex].
So, adding those areas together, we get [tex]33cm^2[/tex] as the area of the whole figure.
PLEASE HELP ASAP!! DUE IN 10 MINUTES!! I'LL MARk BRAINLIEST ADN HIGH POINTS!! PLEASE HELP!!
Answer:
*speedrunning intensifies*
A:
Min is 15
LQ is 23
Median is 36
UQ is 38
B:
IQR is 38 minus 23, or 15, I guess that the data is not very consistent and it is spread out?
C:
Min is calculated by looking at the end of the far left line
LQ is the far left of the box
Median is the line inside the box
UQ is the the far right of the box
IQR is UQ subtract LQ
I answered because I wanted you to get brainliest!
Which statements about the design are true? select three options. each sprinkler head is placed more than 3 feet from the walkway. if two additional sprinkler heads are placed on the lawn, every square foot of the yard would be watered. the total area watered by each sprinkler is approximately 63.6 square feet. the total area watered by all the sprinklers is approximately 254 square feet. if the sprinklers were placed in two straight lines on the yard, they would water a greater amount of the lawn.
The true statements are:
A. Each sprinkler head is placed more than 3 feet from the walkway.C. The total area watered by each sprinkler is approximately 63.6 square feet.D. The total area watered by all the sprinklers is approximately 254 square feet.Calculations and Parameters:Given that:
Sprinkler head = More than one grid box awayEach grid= 3 feetSprinkler distance= 1.5 boxesRadius=?Area=?To find the radius, 3 * 1.5= 4.5 feet.
The area of each circle=
[tex]3.15(4.5)^2 \\= 63.585 \\ 63.6 ft^2.[/tex]
Hence, the statements that are true are options A, C, and D.
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Answer:
It is A C D
Step-by-step explanation:
:) good luck
36) A new car dealership celebrated its grand opening by awarding prizes to 10 buyers. Five of
the buyers received a cash prize of $500, and 3 buyers received a cash prize of $1000. Two
buyers received $2500. If one of the buyers receiving a prize is selected at random, what is the
probability that the buyer received $2500?
Answer:
.20
Step-by-step explanation:
Do a web search to find the sunrise and sunset times for the last year in Osnabrück.
Starting with January 1, calculate the number of daylight hours every 30 days. (You should have 13 items of data.) Convert the time from hours and minutes to the nearest tenth of an hour. For example, if the sunrise time is 0708, write the decimal 7.1, by dividing 8 by 60.
Graph this set of data on graph paper. The horizontal axis will represent the day of the year, and the vertical axis will represent the number of daylight hours. Be sure to title your graph and label the axis.
Draw a regression curve, a curve that best represents your set of data. (This is similar to drawing a line of best fit.)
Answer the following questions about your graph in the box below. Number the responses of your answers as you enter them.
Turn in your set of data and graph to your teacher.
Answer the following questions in the essay box below:
Locate the lowest and highest points on your graph. What is the amplitude?
There are 365 days in a year. Explain this value's relationship to the graph.
What is the vertical shift of the graph?
What is the phase shift of the graph?
Write a sinusoidal function that models the number of daylight hours for the year in this city.
Using your equation, estimate the number of daylight hours in this city on the 220th day of the year. Based on your graph, does this answer seem reasonable? Explain any discrepancy that might occur between the two values.
Answer:
Step-by-step explanation:
A vertical shift is when the graph literally moves vertically, up or down. The movement is all based on what happens to the y-value of the graph. The y-axis of a coordinate plane is the vertical axis. When a function shifts vertically, the y-value changes.
y X X
y = 85 when x = 17
Using the information above, write an equation for y in terms of x.
y=
?
Answer:
y= x5
Step-by-step explanation:
y = 5 times the number of x.
The length of a log of wood is 90 in. How many cuts do you need to make to obtain
the greatest number of pieces, where each piece will have a different length and the
length of each piece is a whole number, in inches?
The greatest number of pieces will be 12 where each piece will have a different length and the length of each piece is a whole number, in inches and the remaining piece length will be 12 in(90 - 78).
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
The total length of the wood = 90 in
We have to cut it into the greatest number of pieces, where each piece will have a different length and the length of each piece is a whole number, in inches.
We can cut it like:
1 in, 2 in, 3 in, 4 in, and so on
The above shows the arithmetic sequence,
The sum of the n natural number is given by:
[tex]\rm S_n = \dfrac{n(n+1)}{2}[/tex]
[tex]\rm 90 = \dfrac{n(n+1)}{2}[/tex]
After solving, we will get a quadratic equation:
n² + n -180 = 0
After solving, we will get:
n = 12.92 and n = -13.92(term can not be negative)
n = 12 (taking whole number)
Thus, the greatest number of pieces will be 12 where each piece will have a different length and the length of each piece is a whole number, in inches and the remaining piece length will be 12 in(90 - 78).
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Select the graph of the equation below.
y= 3 over 2 x²+4x-2
if spur gear system has a driver gear with 100 teeth and rotates at a speed of 10 RPM and is meshed with a driven gear of 20 teeth, then the driven gear will rotate at a speed of:
A. 200 RPM
B. 100 RPM
C. 50 RPM
D. 20 RPM
E. none of the above
100 teeth / 20 teeth = 5
5 x 10 rpm = 50 rpm
answer: 50 rpm
if f(x) = 7 x - 3 and g(x) = x^2 - 4x - 8 find (f+g)(x)
Answer:
x² + 3x - 11
Step-by-step explanation:
Adding functions: (f + g)(x) is equivalent to f(x) + g(x)
Here, we are given:
f(x) = 7x - 3g(x) = x² - 4x - 8Simplify:
(7x - 3) + (x² - 4x - 8)
7x - 3 + x² - 4x - 8
x² + 3x - 11
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The circumference of a circle is approximately 43.96 centimeters. What is the radius of the circle? 3.14 for Pie
-7 Centimeters
-11 Centimeters
-14 Centimeters
-22 Centimeters
Answer:
7 Centimeters
Step-by-step explanation:
I WILL GIVE BRAINLIST HURRY PLS
The box plot shows the total amount of time, in minutes, the students of a class spend reading each day:
What information is provided by the box plot? (3 points)
The mean for the data
The median for the data
The number of students who provided information
The number of students who read for more than 21.5 minutes
Answer:
10000000 Thousand second ........°°°°°°
At a local pizza place, the cost of a large cheese pizza is $13.99. Each additional topping is $1.25. The Tigerd family orders a large pizza topped with pepperoni, mushrooms, olives, and sausage. How much did their pizza cost? Show your work.
Answer:
$18.99
Step-by-step explanation:
The total cost is the base cost plus that of the added toppings.
total cost = base cost + (number of toppings) × (topping cost)
total cost = $13.99 + 4 × $1.25 = $18.99
Their pizza costs $18.99.
Brady borrowed $59.99 from his brother
to buy concert tickets. His brother charges
him a weekly simple interest rate of 3.25%.
Brady pays him back in 4 weeks.
Answer:
Pay back $ 67.79 in four weeks
Step-by-step explanation:
He will have to pay INTEREST FO
59.99 x .0325 x 4 = 7.7987
PLUS the 59.99 that he borrowed
= 67.79
Malik randomly selects 60 students at Williams High School about their favorite flavor of milkshake. Of the students selected, 24 identified chocolate as their favorite milkshake. There are 1,990 students at Williams High School. Based on the data, what is the most realistic estimate for the number of students at Williams High School whose favorite ice-cream is Chocolate? A. 60 Students, B. 796 Students, C. 1,194 Students, or D. 1,400 Students?
Answer:
B
Step-by-step explanation:
The answer is B as this is a simple ration question.
All you need to do is convert the question into ration fraction form:
24/60 =x/1990
x is the number of people whose favourite ice-cream is chocolate.
Do cross multiply on both sides and you will get 47760=60x.
x= 796.
Thus, you get your answer.
find the value of x
please help me out here ill do anything
Answer:
let's find the value of x:
4)
10x=6(5)10x=30x=35)
9(x+4)=8(8+10)9x+81=1449x=63x=76)
y^2=2(2+9)y^2=2×11y^2=22y=√(22)y= 4.69 or 4.7A basketball team made $3,094 selling team hats. Each hat sold for $34. How many hats did the team sell?
Answer:
The team sold 91 hats.
Step-by-step explanation:
$3,094 ÷ %34 = 91
Lara has been hired for a new sales position at a local store. The salaries of the seven people who have been working at the store for one year are listed in this table.
Which statistic(s) can Lara use to predict what her salary most likely will be after one year?
Answer:
The Median or The Mode
Step-by-step explanation:
I had the same question on a quiz and got it right
I need the answer for the what if one
so you would ski down the mountain to the nearest foot is 2556.06ft
Which table represents a linear function?
Answer:
B. Is linear
Step-by-step explanation:
if you graph it it’s a straight line going up
Hope this helps! ;-)
Suppose that 30 percent of the bottles produced in a certain plant are defective. If a bottle is defective, the probability is 0.9 that an inspector will notice it and remove it from the filling line. If a bottle is not defective, the probability is 0.2 that the inspector will think that it is defective and remove it from the filling line.
a. If a bottle is removed from the filling line, what is the probability that it is defective?
b. If a customer buys a bottle that has not been removed from the filling line, what is the probability that it is defective?
The probability that a bottle on the line is defective and removed is 0.27 and the probability that a bottle on the line is defective and not removed is 0.03
The probability that a bottle on the line is defective?The given parameters are:
P(Defective) = 30%P(Remove) = 0.9P(Not defective and remove) = 0.2The probability that a bottle on the line is removed if defective is:
P = P(Defective) * P(Remove)
This gives
P = 30% * 0.9
Evaluate
P = 0.27
Hence, the probability that a bottle on the line is defective and removed is 0.27
The probability that a bottle not on the line is defective?This probability is represented as:
Defective and Not removed
It is calculated as:
P = P(Defective) * P(Not Remove)
Using the complement rule, the probability that a defective bottle would not be removed is:
P(Not Remove) = 1- P(Remove)
P(Not Remove) = 1 - 0.9 = 0.1
So, we have:
P = 30% * 0.1
Evaluate
P = 0.03
Hence, the probability that a bottle on the line is defective and not removed is 0.03
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Hey guys! Please read this whole thing!
Ok, so I just went into this coarse and I read the lesson and it can’t answer this anywhere! Should I just like ignore the 4 in there? If not, can you walk me through step by step how I would find the volume in this question? I’m completely stuck. Help!
Answer: Yes, you can ignore the four on this one. Since the shape is irregular, you have the separate them. The bigger box will be 54.
Length(6) × Width(3) × Height(3)
Do the same for the smaller box = 3 × 1 × 2
The volume of this irregular shape will be 60.
2x^2-8x factor
the folowing polynomials
Consider the cone with slant height of 13 m and perpendicular height of 12 m: a) Find the length of the radius, r. b) Find the length of the diameter of the cone's base.
Answer:
Step-by-step explanation:
Which of the following is a rational function?
O A. F(x) =
x² +5x-6
3x
OB. F(x)=x-x+8
O C. F(x)=√2x-1+9
OD. F(x) = -7x+15
Answer:c
Step-by-step explanation:
The function x² +5x-6/3x is a rational function, option A is correct.
What is a function?A relation is a function if it has only One y-value for each x-value.
x² +5x-6/3x is a rational function, as it can be written in the form:
F(x) = (x² + 5x - 6) / (3x)
where the numerator and denominator are polynomials.
F(x)=x-x+8 is not a rational function, as it simplifies to F(x) = 8, which is a constant and not a fraction.
F(x)=√2x-1+9 is not a rational function, as it contains a square root and cannot be expressed as a ratio of two polynomials.
F(x) = -7x+15 is not a rational function, as it is a polynomial and not a fraction.
Therefore, the function x² +5x-6/3x is a rational function, option A is correct.
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Jayne stacked 2 cubes on top of each other as shown. The edge length of the smaller cube is half the edge length of the cube below it. What is the surface area of the new figure?
Considering the surface area of a cube, and that the figure has two cubes, the total surface area is of 1470 m².
What is the surface area of a cube?The surface area of a cube of edge length a is given by:
S(a) = 6a².
In this problem, we have two cubes, one with a = 14 m and the other with a = 7 m. Hence, the total surface area, in m², is given by:
S(a) = 6 x 14² + 6 x 7² = 1470.
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