The equation representing the sum of three consecutive integers as 42 are x [tex]+[/tex] (x [tex]+[/tex] 1) [tex]+[/tex] (x + 2) [tex]=[/tex] 42 and (x - 1) [tex]+[/tex] x + (x [tex]+[/tex] 1) [tex]=[/tex] 42 , the correct option are (a) and (c) .
In the question ,
it is given that ,
the sum of the three consecutive integers = 42
the equations that shows the relationship is only option (a) and option(c) , because
option (a)
x [tex]+[/tex] (x [tex]+[/tex] 1) [tex]+[/tex] (x + 2) [tex]=[/tex] 42
3x + 3 = 42
3x = 39
x = 13
yes , the terms are consecutive and are 13 , 14 , 15 .
option(c)
(x - 1) [tex]+[/tex] x [tex]+[/tex] (x [tex]+[/tex] 1) [tex]=[/tex] 42
3x = 42
x = 14
putting in equation we get 14-1 = 13 , 14 , 14+1 = 15
yes , the terms are consecutive and are 13 , 14 , 15 .
Therefore , The equation representing the sum of three consecutive integers as 42 are x + (x + 1) + (x + 2) = 42 and (x - 1) + x + (x + 1) = 42 .
The given question is incomplete , the complete question is
The sum of three consecutive integers is 42. Which of the equations could represent this relationship? Select the two correct answers.
(a) x + (x + 1) + (x + 2) = 42
(b) x + (x + 2) + (x + 4) = 42
(c) (x - 1) + x + (x + 1) = 42
(d) (x - 2) + x + (x + 2) = 42
(e) x + 2 x + 3 x = 42
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I don’t understand how to do it
According to the information, it can be established that both divers will be at 181.5 feet then after 9,075 minutes.
After how long are the divers at the same depth?To find the time it took for both divers to be at the same depth, we must take into account the information provided by the question.
Distance traveled by diver A: 20 feet per minute.Distance traveled by diver B: 60 feet per minute.Diver Astart point: 0 feet.Diver B start point: 726 feet.To solve this problem we must use the following mathematical operations. We must first find the time it takes for diver A to be at 181.5 ft.
20 * 9.075 = 181.5ft
Second, we must find the time it takes for diver B to be at the same depth.
60 * 9,075 = 544.5726 - 544.5 = 181.5ftAs shown above, both divers are at 181.5 feet after 9,075 minutes.
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Donnie has a pool and recently discovered a leak. He continues to patch the leak until someone can come out to repair it. After all the water has completely drained out of the pool due to the patch coming off, it takes him two days to fill the pool back up. It takes three days for the pool to drain completely. How long would it take to fill the pool if the patch is off while Donnie is refilling it?
The time it will take to fill the pool if the patch is off while Donnie is filling it, found using the combined filling rate is 6 days.
What is a flow rate?A flow rate is the fluid volume that passes a specified area within a unit of time.
The number days it takes to fill the pool = 2 days
The number of days it takes for the pool to drain = 3 days
The rate at which the pool fills = [tex]\dfrac{1}{2}[/tex] per day
The rate at which the pool drains = [tex]\dfrac{1}{3}[/tex] per day
The number of days it will take the pool to fill while the patch is off is found from the combined filling rate as follows;
The combined filling rate is [tex]\dfrac{1}{2} -\dfrac{1}{3} = \dfrac{3-2}{6} = \dfrac{1}{6}[/tex]
The combined filling rate can be taken as a combined flow rate.
The combined filling rate for filling the pool while the patch is off is [tex]\dfrac{1}{6}[/tex], which is a 6th of the pool is filled per day, therefore, it takes 6 days to fill the pool while the patch is off.
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A 2-column table with 6 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2, 3. The second column is labeled f of x with entries negative 8, negative 3, negative 3, 4, 1, 3. What ordered pair is closest to a local minimum of the function, f(x)?.
The ordered pair which is closest to a local minimum of the function f(x) is (2,0)
Given that,
A 6-row, 2-column table. The items in the first column, x, are negative 2, negative 1, 0, 1, and 3. The second column, f of x, contains the values -8, -3, -4, 1, 3 in the entries.
The system shows a table with values of x and its correspondent in a function f(x):
x f(x)
2 -8
-1 -3
0 -3
1 4
2 1
3 3
f(x) is a local minimum of the function at x =2 and y=0 and the value of the function f(x) is -8. So, the ordered pair that lies closest to the function f(x)'s minimum is (2,0)
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Greatest Common Factor (96,144)
The greatest common factor of 96 and 144 is 48
How to determine the greatest common factor of 96 and 144Information given in the question
144
96
Greatest common factor can be found by listing the factors of the numbers required and choosing the common factors, the biggest number among them is the greatest common factor
listing the factors
144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.
96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96
the common factors = 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48,
the greatest among the factors is 48
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Which table represents a direct variation function?
Input x 3 4 5
Output y 6 10 14
Input x 1 2 3
Output y 2 4 8
Input x 4 6 8
Output y 6 9 12
Input x 1 2 3
Output y 3 9 15
Option 3. The table that represents a direct variation function is Input x 4 6 8 Output y 6 9 12
What is a direct variation?Y = kx, where k is the constant proportionality, is the form of the direct variation equation. It is a two-variable linear equation. The direct variation graph is a straight line in a coordinate plane. The ratio of two directly varying quantities is a constant.
Y = kx is the given formula.
at that location,
y = 6
x = 4 as its value
It would provide us with
6 = 4k
4 divided
6 / 4 = 1.5
1.5 x 6 = 9
1.5 x 8 = 12
Thus, the third selection.
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Can anyone teach me how to do this? Kinda stuck
Answer:
to me it look like a reflection
Step-by-step explanation:
note in photo
Which is true of the southern states during the early 1800’s?
A) Slave labor was needed for the economy.
B) Slavery was banned in the southern states.
C) Slave labor was not allowed in the newer states.
D) Slaves were allowed to vote.
Answer:
a) Slave labor was needed for the economy.
Step-by-step explanation:
Slave labor was needed for the economy of the southern states during the early 1800’s. Hence, the option (a) is correct.
Find measure angle ACB
i need it step by step
please help :/
Alex leaves home, travels 5 miles east, and arrives at the library. He leaves the library and travels 3 miles north to a friend's house. This trip can be plotted on the coordinate plane, where home is the point (0,0). Alex wants to find out how far his house is from his friend's house and uses the distance formula. Which other formula can he use?.
Alex uses the Pythagorean distance method to calculate the distance between his home and his friend's home.
5² (a) + 3² (β). Can use any other formulas
Given
After leaving his house, Alex drives five miles to the east to reach the library. He leaves the library and drives three miles to a friend's home in the north.
Home would be, followed by the library and the homes of your friends.
By the Pythagoras theorem, we now have points a, b, and c.
House a2 plus library b2 equals friend's house c2.
He must utilize this formula to resolve the issue. √5² + 3².
√5² + 3².
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Find '?' in the following series:
1, 4, 10, ?, 46, 94
answers: (a) 20 (b) 16 (c) 15 (d) 22 (e) 94
please put the correct one if you are going to answer
Answer:
(d) 22
Step-by-step explanation:
1 to 4 difference is 3
4 to 10 difference is 6
10 to 22 difference is 12
22 to 46 difference is 24
46 to 94 difference is 48
so, you can see that the difference multiplies by 2 (3x2 = 6, 6x2 = 12, etc.)
thus the answer is d. 22
2. Write a quadratic equation with 3 and 6 as its roots. Write the equation in the
form ax2+bx+c = 0, where a, b, and c are integers.
Answer:
x^2 - 9x + 18 = 0
Step-by-step explanation:
(x-3)(x-6) = 0
x^2 -6x - 3x + 18 = 0
x^2 - 9x + 18 = 0
Answer:
x² - 9x + 18 = 0
Step-by-step explanation:
given a quadratic with roots x = a and x = b then the factors are
(x - a) and (x - b) and the equation is the product of the factors
here roots are x = 3 and x = 6 then the factors are (x - 3) and (x - 6), then
(x - 3)(x - 6) = 0 ← expand factors using FOIL
x² - 9x + 18 = 0
what is the number that goes in the blank
30/36 = ?/12
I NEED HELP ASAP WITH THESE
Answer:
10/12
Step-by-step explanation:
36 divided by 3 is 12 so you would have to divide 30 by 3 to make it equivalent and you would get 10/12.
Hope this helped!
The mean difference of the successive squares of the first six prime numbers is
A 24
D 33.6
B 24.2
C 33
The answer is;
62.83
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Now,
The first 6 prime numbers are 2, 3, 5, 7, 11 ,13
The square of 6 prime number
4, 9 ,25, 49 , 121 , 169
The mean difference of these number is
⇒ (4 + 9 + 25 + 49 + 121 + 169) / 6
⇒ 62.83
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Complete the equation of this circle:
A
(x - [?])²+(y -[_])²=[ ]
Enter
[tex]{ \sf{the \: equation \: of \: circle}}[/tex]
[tex]{ \red{ \sf{ {(x - h)}^{2} + {(y - k)}^{2} = {a}^{2}}}} [/tex]
How do i find range?________________________________________________________________.How do i find median?______________________________________________________________________________________.How do i find Mean?____________________________________________________________________________________________________________________. Measures of center
The range of a list or set is the difference between the smallest and largest numbers. To find the range, arrange all of the numbers in ascending order. Subtract (deduct) the lowest number from the highest. The answer provides the list's range.
What is the median?The median is discovered by sorting all data points and selecting the one in the middle (or if there are two middle numbers, taking the mean of those two numbers)
In two simple steps, you can calculate the mean or average of a data set: Add up all of the values to find the sum. Subtract the sum from the total number of values in the data set.
The mode, median, and mean are the three main measures of central tendency. Each of these measures describes a different indication of the distribution's typical or central value.
The mean (average) and the median are the two most commonly used measures of the data's "center."
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Jacob bought 5. 5 pounds of jelly beans for $14. 74. How much would 7. 25 pounds of jelly beans cost, to the nearest cent?.
Answer:
$19.43
Step-by-step explanation:
when 5.5 pounds cost $14.74 then 1 pound costs $2.68
because 14.74 divided by 5.5 equals 2.68
To calculate the price of 7.25 you multiply the price for 1 pund by 7.25
7.25 * 2.68 = 19.43
You took out a loan for $5000, with a 7.5% interest rate, over a period of 2 years. What is the accumulated interest?
Answers should be in $1,000.00 form (include $, comma, and period when necessary)
The accumulated interest on the loan given, equals to $778.125.
What is an accumulated interest?Also known as compound interest, means the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
Amount payable equals to:
= P(1+i/100)*n
= $5,000*(1 + 7.5%)^2
= $5,000 * 1.155625
= $5,778.125
The computation of the accumulated Interest goes as:
= Amount payable on loan - Loan Amount
= $5,778.125 - $5,000
= $778.125
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Write an equation in slope-intercept form of the line that passes through (6, 11). and
(2, 25/3).
y=2/3x+7 is equation in slope-intercept form of the line that passes through (6, 11). and (2, 25/3).
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The given two points are (6, 11) and (2, 25/3).
m=25/3-11/2-6
=-8/3/-4
=8/12=2/3
Now we have to find y intercept by considering (6,11)
y=2/3x+c
11=2/3(6)+c
11=4+c
11-4=c
7=c
The slope intercept form of line is y=2/3x+7
Hence y=2/3x+7 is equation in slope-intercept form of the line that passes through (6, 11). and (2, 25/3).
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A regular polygon has an interior angle of 157.5°. Calculate the number of sides of the polygon.
Answer:
16
Step-by-step explanation:
(n-2)*180=total of the interior angles
(n-2)*180=157.5n
180n-360=157.5n
22.5n-360=0
22.5n=360
n=16
HELP ASAP Question 2: Luna is riding her skateboard. She went a distance of 10 miles at a rate of 5 miles per hour. Using the distance formula, d = rt, solve for Luna's time in minutes. (1 hour = 60 minutes)
120 minutes
30 minutes
2 minutes
5 minutes
By using the distance formula, we can see that Luna's time in minutes is 120 minutes.
How to find the time in minutes?We know that she went a distance of 10 miles at a rate of 5 miles per hour.
Remember the linear relation:
distance = rate*time
Then if we define t as the time:
10 mi = (5mi/h)*t
(10 mi)/(5mi/h) = t
2 h = t
And we want the time in minutes, remember that:
1 hour = 60 min
Then:
2 hours = 2*(60 min) = 120 min
The correct option is the first one.
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The Sugar Sweet Company is going to transport its sugar to market. It will cost $6500 to rent trucks, and it will cost an additional $175 for each ton of sugar transported.
let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported. Write an equation relating C to S. Then use this equation to find the total cost to transport 16 tons of sugar.
The equation is C = 6500 + 175S
The total cost to transport 16 tons of sugar is $9300
From the question, we have
C = total cost
S represent the amount of sugar (in tons) transported.
C = 6500 + 175S
total cost to transport 16 tons of sugar = 6500 + 175(16)
= 6500 + 2800
= $9300
The total cost to transport 16 tons of sugar is $9300.
Addition:
The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three. Additionally, the number of times the plus symbol (+) is used is up to you. For example, 3 + 3 + 3 + 3. Mathematical addition is a crucial component of the learning curriculum for kids. In primary school, students learn simple addition sums such as one-digit facts, Math addition sums, and double-digit Math addition sums. One of the most fundamental and interesting Math concepts for elementary school children is addition sums. Math is a fascinating subject, and children first learn basic mathematical concepts like adding numbers in their early years.
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A nutrition company is marketing a low calorie snack brownie. A serving size of the snack is 3 brownies and has a total of 50 calories.
If c represents the number of calories and b represents the number of brownies write a proportional relationship involving c and b and solve it for c.
The relationship between the variables c and b is c = [tex]\frac{50}{3}b[/tex]
What is Variation?A variation is a relation between a set of values of one variable and a set of values of other variables. Direct variation. In the equation y = mx + b, if m is a nonzero constant and b = 0, then you have the function y = mx (often written y = kx), which is called a direct variation.
if c ∝ b
Then,
c = kb where k is a constant
When c = 50, b = 3
substituting into the equation above,
50 = 3k
k = 50/3
substitute k into the equation
c = [tex]\frac{50}{3}b[/tex]
In conclusion c is related to b by the equation c = [tex]\frac{50}{3}b[/tex]
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On a certain hot summer's day, 586 people used the public swimming pool. The daily prices are for children$1.75 and $2.00 for adults. The receipts for admission totaled $1,078.75 How many children and how many adults swam at the public pool that day?
Answer: 373 children and 213 adults
Step-by-step explanation:
Children can be represented by x and adults can be represented by y.
x+y=586
1.75x+2y= $1078.75
x=586-y <-- substitute into 1.75x+2y=1078.75.
1.75(586-y) +2y=1078.75
1025.5 - 1.75y+2y =1078.75
0.25y = 53.25
y=213 adults
x + 213 = 586
x= 373 children
Check:
1.75(373) +2(213)=1078.75
1078.75=1078.75
The table shows the amount of money in your bank account over a period of 5 weeks. You plan to keep saving at the same rate until you have $800 in the account. Which equation could you use to find the number of weeks, n, it would take to reach your goal?.
The equation which is useful to find "n" number of weeks to reach our goal is 35n + 100 = 800.
How to form an equation?
Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
As per the given table,
Amount of money in 0 weeks = $100
Amount of money in 1st week = $135
In 2nd week = $170, in 3rd week = $205
So there is a $35 increment each week.
Let's say it takes "n" number of weeks to reach the goal.
So, 35n + 100 = 800
Hence the answer is The equation which is useful to find "n" number of weeks to reach our goal is 35n + 100 = 800".
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An unstretched hanging-spring is 50 cm long. Suspending a 100-N block from it increases its length to 60 cm. Adding another 100-N block makes the spring's new length
70 cm
The new length of the unstretched hanging-spring is 70 cm.
Define the term Hooke's law?Hooke's law states that the spring's length change as a result of a compressive or tensile load is directly proportionate to the size of the force placed on the spring. Mathematically,
F = kx
Where;
K is the spring constant, while x represents the spring's length change.
As per the question-
L is the spring's uncompressed length: L = 0.5 m
Weight F1 linked to the spring: F1 = 100 N
First weight's effect on elongation x1: 60 - 50 = 10 = .01 m.
As per the Hooke's law;
F1 = Kx1
K = F1/X1
K = 100 / 0.1
K = 1000 N/m
Spring constant = 1000 N/m.
For the added 100-N block.
F = Kx2
x2 = F/K
x2 = 100 + 100 / 1000
x2 = 0.2m
x2 = 20 cm
L = 50 + 20 = 70 cm.
Thus, new length of the unstretched hanging-spring is 70 cm.
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A brown bear can weigh 220 to 1,500 pounds. Suppose a bear traveled 65.1 miles at top speed in 3 hours. How far could the bear travel in one hour?
Answer:
21.7 mi/hr
Step-by-step explanation:
Weight of the bear is irrelevant
Unit rate = 65.1 mi / 3 hr = 21.7 mi /hr
Find the value of x, please show your work
Answer:
x = 80
Step-by-step explanation:
This shape is a pentagon, and all of the angles in a pentagon always add up to 540. So, using this, we can create an equation, 3x + 300 = 540. we can then use the reverse order of operations to solve this, first subtracting 300 from both sides. this gets us the equation 3x = 240. We then divide 3 from both sides to get x alone and get x = 80.
Answer:
x = 80°
Step-by-step explanation:
You want the value of x given a pentagon with two angles marked with expressions in x.
Sum of anglesThe sum of interior angles in an n-gon is 180° × (n -2). For the 5-sided figure shown, the sum of angles is 180° × 3 = 540°.
Using this value, we have ...
(x +40°) +125° +(x +5°) +(x +50°) +80° = 540°
3x +300° = 540° . . . . . . simplify
x +100° = 180° . . . . . . . divide by 3
x = 80° . . . . . . . . . . . . subtract 100°
The value of x is 80°.
In order to recive a B in your english class, you must earn more than 350 points of reading credits. Last week you earned 120 points. How many more points must you earn to recive a B
In order to get a B in my class, I will need at least 230 points
Ratio and ProportionsA ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.
But there's a direct way of doing that which is simply subtracting what we have from the total to get what is left.
Total points required to pass > 350Points gotten = 120 Points needed = ?The points needed = Total points required - points gotten.
Points needed = 350 - 120
Points needed = 230
I will need 230 points
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In a game, players roll a number cube. the faces of the cube are numbered from 1 to 6. for the player to win a prize, the number cube must land with the top face showing the number 3. what is the probability of the complement of this event occurring?
The probability of the complement of this event occurring is 5/6.
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
The likelihood that a population parameter will be less than a given value when the null hypothesis is true is expressed as the p-value, also known as a probability value or a measure of significance, for a particular statistical model.
Sample space: {1,2,3,4,5,6}
Total number of outcomes=6
Complement of an Event: All outcomes that are NOT the event
In this case:
So, possible outcomes in the complement event:{1,2,4,5,6}
Number of possible outcomes=5
Formula:
Probability = (Number of possible outcomes)/(Total number of outcomes)
= 5/6
So, the probability of the complement of this event occurring is 5/6.
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todd prefers to drink mug root beer which contains 160 calories per 12 ounces. if he drinks a 44 ounce mug root beer, how many calories will he consume? round to the nearest whole number
Answer:
Step-by-step explanation:
