The expressions that show the distance between P and Q are option (d) |-6| + (-2) and option (e) 6 - 2
From the given number line
The distance between P and Q = 4 units
Now we have to solve each expression
Expression 1
|-6| + |-2| = 6 +2
Add the terms
= 8
Expression 2
|2-(-6)| = | 2 + 6|
= |8|
= 8
Expression 3
|-2| - (-6) = 2 + 6
Add the terms
= 8
Expression 4
|-6| + (-2) = 6 - 2
Subtract the term
= 4
Expression 5
6 - 2 = 4
Hence, the expressions that show the distance between -6 and -2 are option (d) |-6| + (-2) and option (e) 6 - 2
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can anyone help with this???
Answer:
L=66 degrees
KL=3.5
LM=8.7
14x²y – 21xy² + 28x²y²
Answer:
7xy(2x-3y+4xy)
Step-by-step explanation:
14÷7=2
21÷7=3
28÷7=4
they all have 7, x and y so that would be on the outside
William buys 5 small boxes of oat porridge and some large boxes too
in total he buys 6825 grams of porridge
work out the number of large boxes of oat porridge William buys
small boxes = 325 grams each
large boxes = 650 grams each
The number of large boxes of porridge that William bought, using a system of equations, was of:
8.
What is a system of equations?A system of equations is a set of equations involving multiple variables that are related, and then operations are made to solve these equations and identify the numeric value of each variable in the context of the problem.
For this problem, the variables are defined as follows:
Variable x: number of small boxes bought.Variable y: number of large boxes bought.William buys 5 small boxes of oat porridge, hence:
x = 5.
The total weight of his purchase is of 6825 grams, hence, considering the weight of each box, the following equation is built:
325x + 650y = 6825.
It is already stated on the problem that x = 5, hence the value of y can be obtained as follows:
325(5) + 650y = 6825.
y = (6825 - 325(5))/650
y = 8 large boxes.
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show algebraically the sum of two consecutive numbers is always odd
the sum of two odd integers will always be resulted in an odd digit.
What are odd numbers?Odd numbers are entire numbers that can't be isolated precisely into matches. Odd numbers, when separated by 2, leave a rest of 1. , 3, 5, , 9, 11, , 15 are consecutive odd numbers.
These are added together to get n + n+1, or 2n+1. Since +1 make it odd, 2n is even. Any two successive integer sums are hence odd. According to the solution is "2n + (2n + 1) = 4n +1."
Even numbers result from the addition of two fractions, but still only digits result from the addition of one odd number with one even number. In order to only receive an odd number, add one odd as well as one even.
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match to form complementary angle pairs. sin(14) cos(37) sin(49) cos(66) sin(41) cos(24)
cos(76) —>
sin(66)—>
sin(53)—>
cos(49)—>
Answer:
see explanation
Step-by-step explanation:
using the cofunction identities
cos x = sin(90 - x)
sin x = cos(90 - x)
then
cos76° = sin(90 - 76)° = sin14°
sin66° = cos(90 - 66)° = cos24°
sin53° = cos(90 - 53)° = cos37°
cos49° = sin(90 - 49)° = sin41°
The Matched values are
cos(76) —> sin (14)
sin(66)—> cos (24)
sin(53)—> cos (37)
cos(49)—> sin (41)
What is Trigonometry?One area of mathematics known as trigonometry examines the relationship between the sides and angles of a right triangle. The relationship between sides and angles is defined for 6 trigonometric functions.
For complementary angle,
a+ b= 90
So, sin (14)
= cos (90 - 76)
= cos 76
and, cos (37)
=sin (90 - 53)
= sin (53)
and, sin (49)
= cos (90- 41)
= cos 41
and, cos (66)
= sin (90 - 24)
= sin 24
Then, the Matched values are
cos(76) —> sin (14)
sin(66)—> cos (24)
sin(53)—> cos (37)
cos(49)—> sin (41)
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Steven hit the ball 12 times out of 26 at bats in the first half of the season and 6 times out of 14 at bats in the second half of the season. What is his batting average for the whole season, written as a decimal?
Answer:123
Step-by-step explanation:
7328x3424
Steven battling average for the whole season he played was 0.45
How to solve an equation?An equation is an expression showing the relationship between two or more numbers and variables.
Steven hit the ball 12 times out of 26 at bats in the first half of the season and 6 times out of 14 at bats in the second half of the season.
Hence:
Batting average = (total number of time he hit the ball in both season half) / (total number of balls thrown)
Therefore:
Battling average = (12 + 6)/ (26 + 14) = 18 / 40 = 0.45
Steven battling average was 0.45
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a package of 4 erasers costs $0.39. At this rate, how much would 54 erasers cost, in dollars and cents?
Answer:
Step-by-step explanation:
5 dollars and 25 cents
(X^2 + 9) / (x-3)
Synthetic Division
Pls show work
The synthetic division (x²+9) by (x-3) has a quotient of x+3 and the remainder of 18
How to use synthetic division to solve polynomials?
Synthetic division is a way of performing the division of polynomials, with less writing and fewer calculations than the long division method
Given: (x²+9) ÷ (x-3)
The numerator can be written as p(x)= x²+9
The zero of the denominator g(x) is 3 (Note: the sign changed)
The coefficients of p(x) are arranged as follows, with the zero of g(x) on the left:
3 | 1 0 9
|________
The first coefficient after the bar is "dropped" to the last row.
3 | 1 0 9
|___________
| 1
The dropped number is multiplied by the number before the bar, and placed in the next column
3 | 1 0 9
| 3
|___________
| 1
An addition is performed in the next column
3 | 1 0 9
| 3
|___________
| 1 3
The previous two steps are repeated and the following is obtained:
3 | 1 0 9
| 3 9
|___________
| 1 3 18
Here, the last term (18) is the remainder while the rest are the coefficients of the quotient
The terms are written with increasing degree from right to left beginning with degree zero for the remainder and the result
1x + 3 | 18
Where the quotient q(x) = x+3 and the remainder r(x) = 18
Therefore, the quotient is x+3 and the remainder is 18
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help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The fraction of a mile that Evan has to hike and the fraction he has hiked, gives the completed statement as follows;
[tex]\frac{5}{6}[/tex] is closest to 1 and [tex]\frac{2}{5}[/tex] is closest to [tex]\frac{1}{2}[/tex]. So the difference is closest to [tex]\frac{1}{2}[/tex]
What is a fraction in mathematics?A fraction is a representation of the part of a whole of an item or collection of items. The distance Evan's hiking trail of [tex]\frac{5}{6}[/tex] miles is a fraction of a mile.
The length of the trail = [tex]\frac{5}{6}[/tex] mile
The distance Evan has hiked = [tex]\frac{2}{5}[/tex] mile
The distance Evan has left to hike is given by the difference between the length of the trail and the distance Evan has hiked as follows;
Distance remaining = [tex]\frac{5}{6} -\frac{2}{5} = \frac{13}{30}[/tex]
Representing the numbers in decimal form, we have;
[tex]\dfrac{5}{6} = 0.8\overline 3[/tex]
The value of [tex]\frac{5}{6}[/tex] is close to 1
[tex]\dfrac{2}{5} = 0.4[/tex]
The value of [tex]\frac{2}{5}[/tex] is closest to 0.5
[tex]\dfrac{13}{30} = 0.4\overline 3[/tex]
The difference between [tex]\frac{5}{6}[/tex] and [tex]\frac{2}{5}[/tex], which is [tex]\frac{13}{30}[/tex] is therefore closest to [tex]\frac{1}{2}[/tex]
The completed statement is therefore;
[tex]\frac{5}{6}[/tex] is closest to 1 and [tex]\frac{2}{5}[/tex] is closest to [tex]\frac{1}{2}[/tex] so the difference is closest to [tex]\frac{1}{2}[/tex]
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41.153 to the nearest tenth
Answer:
41.2
Step-by-step explanation:
1 is in the tenths place. Because the number the next number is a five, we must round up and 0.20 is the nearest tenth to 0.153.
Matilda walks from a castle's tower to its drawbridge by heading 624 m due
east and then heading due south.
The straight-line distance from the tower to the drawbridge is 927 m.
Work out the bearing of the drawbridge from the tower.
Give your answer to the nearest degree.
Answer:
138° (nearest degree)
Step-by-step explanation:
Bearing: The angle (in degrees) measured clockwise from north.
The given scenario can be modelled as a right triangle (see attachment).
Therefore, the bearing is 90° + θ (shown in green on the attached diagram).
To find angle θ, use the cosine trigonometric ratio:
[tex]\implies \cos{\theta}=\dfrac{A}{H}[/tex]
[tex]\implies \cos{\theta}=\dfrac{624}{927}[/tex]
[tex]\implies \theta=\cos^{-1}\left(\dfrac{624}{927}\right)[/tex]
[tex]\implies \theta=47.69018863...[/tex]
[tex]\implies \theta=48^{\circ}\; \; \sf (nearest\;degree)[/tex]
Therefore, the bearing of the drawbridge from the tower is:
[tex]\begin{aligned}\implies \sf Bearing&=90^{\circ}+\theta\\&=90^{\circ}+48^{\circ}\\&=138^{\circ} \end{aligned}[/tex]
Answer:
The bearing of the drawbridge from the tower is 138° SE-----------------------------
The segments that are formed by Matilda walking from the tower to drawbridge form a right triangleHorizontal leg = 624 m,Hypotenuse = 927 m.Find the angle x between the two segmentscosine = adjacent / hypotenusecos x = 624/927x = arccos (624/927)x = 48° (rounded to the whole degree)Find the bearing of the drawbridge from the towerAdd 90° to the angle measure we just found, since bearing is counted from the north direction:
48° + 90° = 138° SE
Darnel and Tammy deposited $4,890.00 into a savings account which earns interest
compounded continuously. After 10 months, they had $5,067.00 in the account which they
used to go on a trip. What was the interest rate on the account?
Round your answer to the nearest tenth of a percent.
The interest rate on the account would be 0.4.
What is compound interest?
The interest earned on savings that is computed using both the original principal and the interest accrued over time is known as compound interest.
Compound interest
[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]
Where,
A = amount,
P = principal
t = no. of years
r = annual interest rate
n = no of times compounded in a year.
By putting the values in the equations we get,
[tex]5067=4890(1+\frac{r}{10} )^{8.3}\\[/tex]
Solving this, we get
[tex]r = 0.356[/tex]
Rounding off to the nearest tenth of a percent we get
[tex]r=0.4[/tex]
Hence, the interest rate on the account will be [tex]0.4[/tex].
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how many different 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, and 6? repeated digits are allowed.
There will be 216 different 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, and 6 when repeated digits are allowed by fundamental counting principle.
What is fundamental counting principle?A rule used to count the entire number of alternative outcomes in a circumstance is known as the fundamental counting principle. It asserts that if there are n ways to do something and then m ways to do something else, then there are nm methods to do both of these acts. The Fundamental Principle of Counting assists in determining how selection is made based on available options. The Fundamental Principle of Counting simplifies the approach to selection by taking into account all of the possible choices and their combinations in order to calculate the Probability.
Here,
Since there are 6 digit given,
In first place, there are 6 ways to arrange the digits. In second place, there are 6 ways to arrange the digits. In third place, there are 6 ways to arrange the digits.
This way,
6×6×6=216 ways
When repeated digits are allowed by the fundamental counting principle, 216 different 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, and 6.
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What is 12 = -4(-6x - 3)
Answer:
no solution
Step-by-step explanation:
12=-4(-6x-3)
12=24x+12
0=24x
Use the "Insert Line" Tool to construct the line
showing the given distance. If you need to extend
the line outside the shape, use a dotted line.
(100 points for brainliest answer)
The distance from B to AC can be constructed as shown in the figure.
The distance from G to EF can be constructed as shown in the figure.
The distance from Q to SR can be constructed as shown in the figure.
What is the distance of a line from a point?
A point-to-line distance is the shortest distance from a point to any point on an infinite line. This is the perpendicular distance from the point to the line and the length of the line segment connecting the point to the nearest point on the line.
For the figure 1, the distance from B to AC, will be the perpendicular line through point B on side AC, so side BD will be the distance.
For the figure 2, the distance from G to EF, will be the perpendicular line through point G on side EF, so side GH will be the distance.
For the figure 1, the distance from Q to SR, will be the perpendicular line through point Q on side SR, so side QT will be the distance.
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Given that
7
x
−
3
y
=
23
Find
x
when
y
=
−
2
Answer: [tex]\frac{17}{7}[/tex]
Step-by-step explanation:
7x - 3y = 23
3y = -2 × 3 = -6
7x + 6 = 23
7x = 23 - 6
7x = 17
x = [tex]\frac{17}{7}[/tex]
Please Help ASAP!!!!!
Answer:
the forth (7,2).........
you wish to survey people who have brought in their cars for service during the past month. you decide to choose a random sample of gas stations in the city and then survey all customers from those stations who had work done during the past month. this procedure is an example of which type of sampling?
An illustration of "Cluster sampling" is the practice of selecting a random sample of the city's gas stations, and then surveying every station's patrons.
Define the term Cluster sampling?In cluster sampling, a population is divided into clusters, which have been smaller groups. They but choose a sample at random from these clustersOften employed to investigate huge populations, typically those that are substantially geographically distributed, cluster sampling is a probability sampling technique. Often, clusters used by researchers have been groups like cities or schools.As per the given question.
People who brought their autos in for service over the past month should be surveyed. You make the decision to selecting a haphazard sample of the city's petrol stations, after which you interview all of their patrons whom have work done on their vehicles well within previous month.Thus, an implementation of "Cluster sampling" is the practice of randomizing sample of the city's gas stations, and thereafter surveying every station's patrons.
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You are painting a room that is 18 ft long, 14 ft wide and
8 ft high. Find the area of the four walls that you are going to paint.
Answer:
do the answer is 532 ft.
u should be careful not to count the area of the ceiling and the floor of the room!
Answer:
512 ft²-------------------------
Perimeter of the room:
P = 2(18 + 14) = 2(32) = 64 ftArea of the four walls:
A = Ph = 64*8 = 512 ft²what is the quotient of 84/0.729
Answer:
115.226337449
Step-by-step explanation:
84/0.729= 115.226337449
And thank you and your welcome
Answer: the quotient of 84/0.729 is 115.226337
Alexa drive a motorcycle 200 kilometers in 3 hours. If she drove at this constant speed, how fat could she travel in 9 hours?
Answer:600
Step-by-step explanation:
i think
Solve the equation:
3/2=4x
x= ____________
Answer:
x = [tex]\frac{3}{8}[/tex]
Step-by-step explanation:
[tex]\frac{3}{2}[/tex] = 4x ( multiply both sides by 2 to clear the fraction )
3 = 8x ( divide both sides by 8 )
[tex]\frac{3}{8}[/tex] = x
URGENT
We're doing some experiments to work out how fast our agents can accelerate
Using v = u + at, work out the acceleration when v = 40, u = 20 and t = 10
Carmen has taken out a loan for $800 to buy a car. She plans to pay back the loan at a rate of $40 per month. Ramona has borrowed $500 to buy a car, which she plans to pay back at a rate of $20 per month.
How long will it take Ramona to pay back her loan?
a.
25 months
b.
20 months
c.
15 months
d.
10 months
Answer:
Carmen will have her loan paid back in 20 months
Sophia spends a winter day recording the temperature once every three hours for science class. At 9 am, the temperature was -2.1°F. Between 9am and noon, the temperature increased by 10.8°F. Between noon and 3pm, the temperature decreased by 13°F. Between 3pm and 6pm, the temperature dropped 18.4°F. What was the temperature at 6pm? PLEASE
Answer:
Step-by-step explanation:
-22.7
Factor −4x2 + 12x. PLease help
Answer:
-4x(x-3)
Step-by-step explanation:
-4x^2+12x
divide by -4x
-4x(x-3)
Sofia is 38 years old. Write an equation that relates Sofia's age to Tony's age, t. How old is Tony?
(Sofia’s age is 2 times the combined ages of Carlos and Lily - Carlos’s age is 4 more years than Tony’s age - and Lily’s age is one more than 6 times Tony’s age)
Answer:
Let s, c, y and t represent the ages of Sofia, Carlos, Lily and Tony respectively.
c + y = 2s ------ equation (1)
t + 4 = c ------ equation (2)
6t + 1 = y ------ equation (3)
Since Sofia is 38 years old, substitute s = 38 into equation (1):
c + y = 2(38)
= 76 ------ equation (4)
Substitute equations (2) and (3) into equation (4):
t + 4 + 6t + 1 = 76
7t + 5 = 76
7t = 71
∴ t = 10 (to the nearest whole number)
∴Tony is 10 years old (to the nearest whole number).
If you have $200 to invest for 10 years, would you rather invest your money in a bank that pays 7% simple interest or 5% interest compounded annually? Is there anything you could change in the problem that would make you change your answer?
a. I would rather compound annually at 5 % interest
b. I would increase the simple interest rate if i were to change my answer
a. How to determine which option to choose?Since you have $200 to invest for 10 years, would you rather invest your money in a bank that pays 7% simple interest or 5% interest compounded annually, we need to determine the amount of each type of interest after 10 years.
Since you have $200 to invest for 10 years at 7% simple interest, using the simple interest formula for the amount, we have
A = P(1 + rt) where
P = principal amount = $ 200, r = rate = 7% = 0.07 and t = time = 10 yearsSubstituting the values of the variables into the equation, we have
A = P(1 + rt)
A = 200(1 + 0.07 × 10)
A = 200(1 + 0.7)
A = 200(1.7)
A = 340
Also, since you have $200 to invest for 10 years at 5% interest compounded annually, using the compound interest formula for the amount, we have
A' = P(1 + r)ⁿ where
P = principal amount = $ 200, r = rate = 7% = 0.07 and n = time = 10 yearsSubstituting the values of the variables into the equation, we have
A' = P(1 + r)ⁿ
A' = 200(1 + 0.07)¹⁰
A' = 200(1.07)¹⁰
A' = 200(1.9672)
A' = 393.43
Since A' = $393.43 > A = $340, i would rather compound annually at 5 % interest
b. Is there anything you could change in the problem that would make you change your answer?To change my answer, I would increase the simple interest rate if i were to change my answer
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A manager of a fast food chain wants to know how his customers rate their service at the restaurany that day. after randomly picking the 9th customer, he surveys every 5th customer that exits the restaurant. which sampling method? your answer: simple random systematic stratified cluster volunteer
The sampling method used in this scenario is random Systematic random sampling
Systematic random sampling
Systematic sampling is a form of probability sampling technique in which sample members are chosen from a wider population using a defined, periodic interval but a random beginning point. By dividing the population size by the desired sample size, this interval, also known as the sampling interval, is computed.
If the periodic interval is predetermined and the starting point is random, systematic sampling is still regarded as random even though the sample population has been chosen in advance.
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Write
y − 2 = (x + 6) in
standard form.