Answers
Equation 2(m + 3) + m - 2 matches with the expression 3m + 4
How to Match EquationsFirst, we can simplify the equations:
2(m + 3) + m - 2 = 3m + 45(m + 1) - 1 = 5m + 4m + m + m + 1 + 3 = 3m + 4Now we can match each equation with the corresponding expression:
3m + 4 matches with 2(m + 3) + m - 2
5m + 4 matches with 5(m + 1) - 1
3m + 4 matches with m + m + m + 1 + 4
Therefore, the equations match with the expressions as follows:
Equation 1: 2(m + 3) + m - 2 matches with 3m + 4
Equation 2: 5(m + 1) - 1 matches with 5m + 4
Equation 3: m + m + m + 1 + 3 matches with 3m + 4
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Related Questions
When a diver descends a depth of 9 feet below the surface, the pressure is 18.7 pounds per square inch. At a depth of 14 feet, the pressure is 20.9 pounds.The pressure increases linearly at a constant rate as the diver descends.
Which function models the amount of pressure, y, in pounds per square inch at a depth of x feet?
To the nearest tenth, determine the pressure per square inch at a depth of 25 feet.
Answers
The pressure per square inch at a depth of 25 feet is approximately 10.9 pounds per square inch.
We have,
We can use the point-slope form of a linear equation to model the pressure as a function of depth.
Let (x1, y1) = (9, 18.7) be a point on the line, and let (x2, y2) = (14, 20.9) be another point on the line.
Then the slope of the line is:
slope = (y2 - y1) / (x2 - x1)
= (20.9 - 18.7) / (14 - 9)
= 0.44
Using the point-slope form with the point (x1, y1):
y - y1 = m(x - x1)
y - 18.7 = 0.44(x - 9)
y = 0.44x - 0.08
So the function that models the amount of pressure as a function of depth is:
y = 0.44x - 0.08
To find the pressure at a depth of 25 feet,
we substitute x = 25 into the equation:
y = 0.44(25) - 0.08
= 10.92
Therefore,
The pressure per square inch at a depth of 25 feet is approximately 10.9 pounds per square inch.
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Amanda is building a soft triangular kennel for her dog. She has four wooden planks of lengths 1 foot, 3 feet, 5 feet, and 6 feet. Determine which planks Amanda should use to build the triangular-shaped kennel. Enter the lengths from least to greatest.
Answers
Answer:
3 feet5 feet6 feetStep-by-step explanation:
Given lengths (in feet) of 1, 3, 5, 6, you want to know which three of them will form a triangle.
Triangle inequalityThe differences between adjacent lengths are 3-1 = 2, 5-3 = 2, 6-5 = 1. The shortest side must be longer than the difference in lengths between the other two sides. Hence the 1 foot plank cannot be used. (It is not longer than either 1 or 2 feet.)
The remaining three planks satisfy the triangle inequality:
3 + 5 > 6
3 + 6 > 5
5 + 6 > 3
Amanda should use the planks that are 3 feet, 5 feet, and 6 feet long.
a local citizen science group is monitoring the water quality of a nearby lake. they gather water samples once a week on wednesday between the hours of 7 a.m. and 9 a.m. from the same location. one day in august they were unable to sample within that time frame and collected the sample at 3 p.m.how might this modification to the sampling procedure affect the results?responseswater sampled later in the day may be warmer and therefore have
Answers
The modification to the system of sampling procedure will affect amount of dissolved oxygen in the water, leading to many consequences and finally resulting in rejection of collected data .
In short, the time of day when a sample is collected is regarded as crucial phase which can adversely affect the results of a water quality test. The temperature of the water plays a important role which can change throughout the day, and also put lots of stress on the amount of dissolved oxygen in the water.
Dissolved oxygen is an imperative measure for checking the water quality because it is a survival need for aquatic life. The total amount of sunlight that penetrates the water seriously affects the amount of dissolved oxygen in the water. In the event if a sample is acquired at a different time than usual, it may not be accurate to other samples that were taken at different times.
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The complete question is
A local citizen science group is monitoring the water quality of a nearby lake. They gather water samples once a week on Wednesday between the hours of 7 A.M. and 9 A.M. from the same location. One day in August they were unable to sample within that time frame and collected the sample at 3 P.M. How might this modification to the sampling procedure affect the results?
a) Write the value of sin for the right-angled triangle below as a fraction.
b) Using your answer to part a), work out the size of angle 0.
Give your answer in degrees to 1 d.p.
Answers
Answer:
Step-by-step explanation:
67
brainliest and 100 points! i really appreciate the help, and please let me know if you need help on anything, thanks!!
Answers
Answer:
SSS, SAS, ASA, AAS, and HL are valid and sufficient criteria to prove that two triangles are congruent.
It is a letter or symbol which represents a number
Answers
This is called a variable or a symbol. In mathematics, letters or symbols are often used to represent numbers or other mathematical objects.
The letter or symbol that represents a number is called a "variable". Variables are often used in algebra and mathematics to represent an unknown or uncertain quantity.
In computer programming, a variable is a symbol or name used to represent a variable value or quantity. In programming, variables are used to store and manipulate data.
For example, in the equation "y = 2x + 3", "y" and "x" are variables.
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The correct question is :
What is it called if It is a letter or symbol which represents a number?
3. The graph of f(x) = |x| is shown below. Write the equation for the stretched graph, g(x).
Graphs f of x and g of x depict V-shape parabolas on a coordinate plane. f of x parabola vertex is at (0, 0). g of x parabola vertex is at (0, 0) with right slope passes through plotted closed circle (2, 6) in quadrant 1.
Step 1: Start with the equation g(x) = k • f(x). Substitute the known point and solve for k. Show your work. (2 points)
Step 2: Use the value of k that you found in Step 1 to write an equation for g(x). (1 point)
Answers
The graph of the equation is g ( x ) = 3 | x |
Given data ,
Step 1:
Let the equation be g(x) = kf(x)
Substitute the known point (2, 6) and solve for k
Given that the vertex of g(x) is at (0, 0) and it passes through the point (2, 6) in quadrant 1, we can substitute these values into the equation g(x) = k • f(x).
Plugging in the point (2, 6)
6 = k|2|
Since the absolute value of 2 is 2, we can rewrite the equation as:
6 = 2k
Now, solving for k by dividing both sides by 2:
k = 6/2
k = 3
So, the value of k is 3
Step 2: Use the value of k that you found in Step 1 to write an equation for g(x)
Using the value of k = 3, we can write the equation for g(x) as:
g(x) = 3f(x)
Since f(x) is given as f(x) = |x|, we can substitute it into the equation for g(x):
g(x) = 3|x|
Hence , the equation for the stretched graph g(x) is g(x) = 3 |x|
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A travel agent offers to convert any US dollars left over
after a holiday at one of two exchange rates, as shown
below.
Customers must choose which exchange rate they want
to convert any leftover money with before going on
holiday.
a) Roger chose to use the premium rate. He returned
from his holiday with $130. How many pounds did he
receive?
b) How much less, in pounds, would Roger have received
if he had chosen the standard exchange rate?
c) Work out how many dollars Roger would have had to
return with to receive the same amount, in pounds,
regardless of which exchange rate he chose.
Standard rate
$1.00 £0.71
Premium rate
$1.00 £0.75
£3.20 charge, deducted
from amount received
Answers
Roger received £97.50. after converting $130 at the premium rate. If Roger had chosen the standard rate, he would have received £5.20 less than what he received with the premium rate. To receive the same amount in pounds regardless of the exchange rate, Roger would need to return with $173.33.
Using the premium rate, Roger would receive $130 x £0.75 = £97.50.
If Roger had chosen the standard rate, he would have received $130 x £0.71 = £92.30. Therefore, he would have received £97.50 - £92.30 = £5.20 less if he had chosen the standard rate.
Let x be the number of dollars Roger would need to return to receive the same amount in pounds, regardless of the exchange rate he chose.
Using the premium rate, he received £97.50 - £3.20 (charge) = £94.30.
Using the standard rate, he would have received x x £0.71 - £3.20 (charge) = £94.30.
Simplifying the equation, we get
x x £0.71 = £97.50
x = £97.50 / £0.71
x ≈ $137.32
Therefore, Roger would need to return $137.32 to receive the same amount, in pounds, regardless of which exchange rate he chose.
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Find the first four terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1
an = 2(2)n
Answers
The first four terms of the sequence are 4, 8, 16, and 32.
Step-by-step explanation:
The given sequence is defined by the formula:
an = 2(2)n
We can find the first four terms of the sequence by substituting the values of n = 1, 2, 3, and 4:
a1 = 2(2)^1 = 4
a2 = 2(2)^2 = 8
a3 = 2(2)^3 = 16
a4 = 2(2)^4 = 32
Therefore, the first four terms of the sequence are 4, 8, 16, and 32.
the annual salaries of employees in a large company are normally distributed with a mean of $50,000 and a standard deviation of $20,000. what percent, or what is the probability, of people earning between $45,000 and $65,000?
Answers
The probability of people earning between $45,000 and $65,000 in this large company is approximately 29.46%.
We need to use the standard normal distribution formula, where we standardize the original distribution with mean and standard deviation to a standard normal distribution with mean 0 and standard deviation 1. We can then use a Z-table to find the probability.
First, we calculate the Z-scores for the lower and upper limits of the range of interest:
Z1 = (45,000 - 50,000) / 20,000 = -0.25
Z2 = (65,000 - 50,000) / 20,000 = 0.75
We can then look up the probabilities associated with these Z-scores in a standard normal distribution table. From the table, we find that the probability of a Z-score between -0.25 and 0.75 is 0.2946. To convert this back to the original units, we need to multiply the probability by 100 to get a percentage:0.2946 x 100 = 29.46%.
The normal distribution is a continuous probability distribution, so the probability of exact values is zero. We are calculating the probability of a range of values.
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At the end of a baseball game, the players were given the choice of having a bottle of
water or a box of juice. Of all of the players, 12 chose a bottle of water, which was
3
q of the total number of players. Write and solve an equation to determine p.
the total number of players at the baseball game.
Show your work.
Help me please
Answers
Answer:
Rather than doing the easy way do it the common way
Fred got his first job in 2020. In that year, Social Security tax was 8.25% of income up to $157,700. Medicare tax was 1.5%. If Fred earned $125,000 in 2020, how much did he pay for Social Security and Medicare taxes?
Answers
Answer:
Step-by-step explanation:
To calculate the amount Fred paid for Social Security and Medicare taxes in 2020, we first need to calculate the amount of income subject to Social Security tax.
Since Fred earned $125,000, which is less than $157,700, all of his income is subject to Social Security tax.
Therefore, the amount of Social Security tax Fred paid in 2020 is:
$125,000 x 8.25% = $10,312.50
To calculate the amount of Medicare tax Fred paid in 2020, we simply multiply his income by the Medicare tax rate:
$125,000 x 1.5% = $1,875
Therefore, Fred paid a total of $10,312.50 + $1,875 = $12,187.50 for Social Security and Medicare taxes in 2020.
Please help (See file)
Answers
Red: 0.225 or 22.5%
Green: 0.5 = 50%
Blue: 11/40 = 0.275 = 27.5%
100% - 50% - 27.5% = 22.5%
The probability of grabbing a red ball is 22.5%
Hope this helps!
the number of students at a local university increased from 1,200 students to 5,200 students in 10 years. based on a geometric mean, the university grew at an average percentage rate of
Answers
The university grew at an average percentage rate of approximately 15.36% per year.
1. In order to find the average percentage growth rate, we will use the formula for geometric mean growth rate:
Growth Rate = ((Ending Value / Starting Value)^(1 / Number of Years)) - 1
2. In this case, the starting value is 1,200 students, the ending value is 5,200 students, and the number of years is 10.
Growth Rate = ((5,200 / 1,200)^(1 / 10)) - 1
3. Calculate the values:
Growth Rate = (4.3333^(1 / 10)) - 1
Growth Rate = 1.1536 - 1
Growth Rate = 0.1536
4. Convert the decimal to a percentage:
Growth Rate = 0.1536 * 100 = 15.36%
Hence, Based on the geometric mean, the local university grew at an average percentage rate of approximately 15.36% per year over the 10-year period.
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Consider a sequence whose first five terms are -2, 1, 6, 13, and 22.
Select the function with domain n = {1,2,3,4,5} that defines this sequence.
Answers
The solution is: a) 1,2,6,24,120 are the first five terms of the sequence in which the nth term is a_n=(n+1)!/n+1.
Here, we have,
The formula for the nth term of the sequence is expressed as
n=(n+1)!/n+1
For the first term, n = 1.
Therefore,
(1+1)!/(1+1)
= 2!/2
= (2×1)/2
= 1
For the second tern, n = 2.
Therefore,
(2+1)!/2+1
= 3! /3
= (3×2×1)/3
= 6/3
= 2
For the third term, n = 3,
therefore
(3+1)!/3+1
= 4!/4
=(4×3×2×1)/4
= 6
For the fourth term, n = 4.
Therefore
(4+1)!/4+1
= 5!/5
= (5×4×3×2×1)/5
= 24
For the fifth term, n = 5.
Therefore
(5+1)!/5+1
= 6!/6
= 6× 5×4×3×2×1)/6
= 120
Hence, The solution is: a) 1,2,6,24,120 are the first five terms of the sequence in which the nth term is a_n=(n+1)!/n+1.
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complete question:
Write the first five terms of the sequence in which the nth term is a_n=(n+1)!/n+1.
a) 1,2,6,24,120
b) 1,2,3,4,5
c) 1,1,3,12,60
d) 1,1,1,1,1
what is the probability of not rolling a 3 on a six sided die
Answers
Answer:
Step-by-step explanation:
5/6
Answer:
5/6 or approximately 0.8333 (83.33%)
Step-by-step explanation:
This is because there are five possible outcomes that are not a 3 (1, 2, 4, 5, 6) out of a total of six possible outcomes.
Find the roots of the polynomial shown. What is the value of the largest root?
f(x)=x^3+2x^2-11x-12
Answers
The required roots of the equation f(x)=x³+2x²-11x-12 are -1, -4, and 3 and the value of the largest root is 3.
The given polynomial is f(x)=x³+2x²-11x-12
We have to find the roots of the given polynomial f(x), we can use a method called "factoring by grouping"
The equation can be written as x³+2x²-11x-12
x(x²+2x-11)-12=0
x(x²+2x+1-1-11)-12=0
x((x+1)²-12)-12=0
x(x+1)² - 12x - 12 =0
(x+1)(x²+x-12)=0
(x+1)(x+4)(x-3)=0
x+1 = 0 ---->x=-1
x+4 = 0---->x=-4
x-3=0---->x=3
Hence, the required roots of the equation f(x)=x³+2x²-11x-12 are -1, -4, and 3 and the value of the largest root is 3.
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Simplificar la fracción 9/27
Answers
Answer:
1/3
Step-by-step explanation:
100 points Due Tomorrow 1. How much will a principal of $2000 become after 5 years in an account with an 8% interest rate compounded quarterly?
Answers
Answer:
Step-by-step explanation:
this and the notation , help!:__)
Answers
After comparing the image and the figure, we found that the direction and angle of rotation are 180° counterclockwise rotation.
A transformation known as a rotation involves turning the figure either clockwise or counterclockwise. The centre of rotation is the fixed location where the rotation occurs. The term "angle of rotation" refers to the amount of rotation. A figure can be rotated 90 degrees, or a quarter turn, in either a clockwise or counterclockwise direction.
You have rotated the figure 180 degrees when you have spun it exactly halfway. The figurine may be rotated 360° by turning it all the way around. A counterclockwise turn has a positive magnitude because a clockwise rotation indicates a negative magnitude. Rotational symmetry exists in every regular polygon. When an object is rotated around its centre, it retains its original appearance. The object is then referred regarded as having rotational symmetry.
Let's write the coordinates of the original figure,
A = (1, -5)
B = (6, -2)
C = (6, -5)
D = (1, -8)
Now, if we rotate it 90 degrees counterclockwise, the coordinates are:
A' = ( 5, 1)
B' = (2, 6)
C' = (5, 6)
D' = (8, 1)
Now if we rotate it again 90 degrees counterclockwise, the coordinates are:
A'' = ( -1, 5)
B'' = (-6, 2)
C'' = (-6, 5)
D'' = (-1, 8)
Now from the figure, let's write the coordinates.
A' = ( -1, 5)
B' = (-6, 2)
C' = (-6, 5)
D' = (-1, 8)
This is the same as the coordinates of the second 90 degrees counterclockwise rotation.
Since we did two 90 degrees rotations, we can say we did a total of 180° counterclockwise rotation.
Therefore after comparing the image and the figure, we found that the direction and angle of rotation are 180° counterclockwise rotation.
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Please help me with this homework
Answers
Answer: x=92
Step-by-step explanation: the total degrees in a triangle is 180 so add the two angles you already have and subtract that number from 180
A circular frame that is 2 inches wide surrounds the mirror. what is the combined area, in sqaure inches, of the circular mirror and the frame
Answers
The combined area of the mirror and the frame is equal to π(r+2)² square inches.
Width of circular frame surrounds the mirror = 2 inches
Let us denote the radius of the circular mirror by r.
Then, the radius of the circular frame that surrounds the mirror is 'r + 2'.
The combined area of the mirror and the frame is the sum of the areas of the mirror and the frame.
The area of the mirror is πr²,
And the area of the frame
= Area of the larger circle with radius r+2 - Area of the smaller circle with radius r
⇒ Area of frame = π(r+2)² - πr²
Simplifying this expression, we get,
⇒ Area of frame = π(r² + 4r + 4) - πr²
⇒ Area of frame = πr² + 4πr + 4π - πr²
⇒ Area of frame = 4πr + 4π
The combined area of the mirror and the frame is,
πr² + 4πr + 4π
There is no specific value for r.
So we cannot calculate the exact area.
Simplify the expression by factoring out π,
=πr² + 4πr + 4π
= π(r² + 4r + 4)
= π(r+2)² square inches.
Therefore, the combined area of the mirror and the frame is π times the square of the sum of the radii of the mirror and the frame, which is (r+2)².
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Edward is making his special punch for the Starry Night homecoming dance.
There is a proportional relationship between the number of cans of peach juice concentrate in a punch bowl, x, and the corresponding number of bottles of lemon-lime soda, y.
x (cans of peach juice concentrate) y (bottles of lemon-lime soda)
2 6
3 9
4 12
5 15
Write an equation for the relationship between x and y. Simplify any fractions.
y=
Answers
Answer: y = 3x
Step-by-step explanation:
In order to solve this particular question, we're first just going to look at the differences between the x and y values.
2 x 3 = 6
3 x 3 = 9
4 x 3 = 12
5 x 3 = 15
Therefore y = 3x
Find the surface area and volume of a sphere with a diameter of 22 mm. Make sure you use 3. 14 for π
, round your answer to the nearest hundredth if necessary
Answers
The surface area of the sphere is 1519.76 mm² and the volume is 5575.87 mm³.
Given that the diameter of the sphere is 22 mm, we can find the radius (r) by dividing the diameter by 2:
Radius (r) = 22 mm / 2 = 11 mm
The surface area (A) and volume (V) of a sphere can be calculated using the formulas:
Surface area (A) = 4πr²
Volume (V) = (4/3)πr³
Now we can substitute the value of the radius into the formulas to calculate the surface area and volume:
Surface area (A) = 4 x 3.14 x (11 mm)²
Volume (V) = (4/3) x 3.14 x (11 mm)³
Calculating the values:
Surface area (A) = 4 x 3.14 x (11 mm)²
= 4 x 3.14 x 121 mm²
= 1519.76 mm²
Volume (V) = (4/3) x 3.14 x (11 mm)³
= (4/3) x 3.14 x 1331 mm³
= 5575.87 mm³
Therefore, the surface area of the sphere is 1519.76 mm² and the volume is 5575.87 mm³.
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please answer: A city held an election for mayor. This table shows the number of votes that were cast by people in different age groups.
How many more votes were cast by people in the 56 and up age group than by people in the 18 to 35 and 36 to 55 age groups combined?
Answers
3,638 more votes were cast by people in the 56 and up age group than by people in the 18 to 35 and 36 to 55 age groups combined.
How to obtain the amounts?From the table, the amount of votes for each age range is given as follows:
18 to 35 years: 10,673 votes.36 to 55 years: 21,372 votes.56 and up: 35,683 votes.The combined amount of votes of people in the 18 to 35 and 36 to 55 age groups is given as follows:
10673 + 21372 = 32,045 votes.
Then the difference in the number of votes of people in the 56 and up age range is given as follows:
35683 - 32045 = 3,638.
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Answer:
3,638 votes more than 18 to 35 and 36 to 55.
Step-by-step explanation:
you subtract and you add
HELP ME PLEASEEEE!! BRAINLIEST!!!!
Question
What is the mean of the values in the stem-and-leaf plot?
Enter your answer in the box.
Key: 2|5 means 25
A stem-and-leaf plot with a stem value of 1 with a leaf value of 2, 3, 5, a stem value of 2 with a leaf value of 8 and 8, a stem value of 3 with a leaf value of 0, and a stem value of 4 with a leaf value of 2. (image may help)
Answers
Rational exponents write final answer is radical form
Answers
In radical form, the rational exponent can be written as [tex]m ^\frac{32}{3}[/tex]
Given rational exponent function is [tex]3^\frac{5}{4}[/tex]
Rational exponents are fractional exponents with power as the numerator and a root as the denominator.
We can write the Rational exponent function into radical form as follow
To write a rational exponent in radical form, keep in mind that it represents a power that can be written as a fraction, with the numerator being the power to which the base is raised and the denominator being the root to which the base is taken.
[tex]3^\frac{5}{4}[/tex] = [tex]3^{5\times\frac{1}{4}[/tex]
= [tex](3^5)^\frac{1}{4}[/tex]
= [tex]\sqrt[4]{3^5}[/tex]
Therefore, in radical form, the rational exponent can be written as [tex]\sqrt[4]{3^5}[/tex]
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Given question is incomplete, the complete question is given below
Rational exponents write the final answer in radical form
[tex]3^\frac{5}{4}[/tex]
could anyone help me with this question?
Answers
Step-by-step explanation:
Angle 6 is equal to angle 2
angle 2 and angle 3 form a straight line = 180 degrees
so angle 2 = 60 degrees
angle 6 = 60 degrees
Since sum of interior angles is equal to 180°, we get
<3 + <6 = 180°
120° + <6 = 180° since <3 = 120°
<6 = 180° - 120°
<6 = 60°
You can also prove this by measuring the angle with a protector:)
Griffin is riding his bike down the street in Churchville, N.Y. at a constant speed, when a nail gets caught in one of his tires. The height of the nail above the ground, in inches, can be represented by the trigonometric function f(t)=-13cos(0.8pi(t))+13, where t represents the time (in seconds) since the nail first became caught in the tire. A) Determine the period of f(t). B) Interpret what the period represents in this context. C) On the grid below, graph at least one cycle of f(t) that includes the y-intercept of the function.
Answers
A) The value of period of f (t) is, 2.5 seconds
B) The period of the function represents the time it takes for the height of the nail above the ground to complete one full cycle.
C) The graph is shown in figure.
Now,
A) To find the period of the function f(t), we need to identify the coefficient of the variable "t" inside the cosine function.
Hence, In this case, the coefficient is 0.8pi.
So, The period of the function is given by the formula;
T = 2π / |0.8π|,
T = 2.5 seconds.
B) The period of the function represents the time it takes for the height of the nail above the ground to complete one full cycle.
This means that every 2.5 seconds, the nail will reach its maximum height of 13 inches, before descending to its minimum height of 0 inches, and then rising again to its maximum height.
C) Here is a graph of one cycle of the function f(t), including the y-intercept:
Hence, From the graph, the function starts at a height of 0 inches, reaches its maximum height of 13 inches at t = 1.25 seconds, descends back to a height of 0 inches at t = 2.5 seconds, and then rises again to its maximum height at t = 3.75 seconds.
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help me plssssssssssssssssssssssssssssssss
Answers
Answer:
If a tangent segment and a secant segment intersect outside a circle, then the square of the measure of the tangent segment equals the product of the measures of the secant segment and its external portion.
6^2 = (x + 4)(4)
36 = 4x + 16
4x = 20, so x = 5
