which of the following describes the correct process for solving the equation 3x+6=21 and arrives at the correct solution?
Answers
To solve the equation 3x + 6 = 21, follow the following steps.
Step 1: Collect like terms
"6" crosses the equality sign to the right and becomes "-6"
3x = 21 - 6
Step 2: Simplify the expression in step 1
Note that 21 - 6 = 15
The equation becomes:
3x = 15
Step 3: Divide both sides 3
The equation becomes
3x / 3 = 15/3
x = 5
Related Questions
Which pile of laundry has more shirts?
Pile 1
Three pants two shirts
Pile 2
Two shirts 4 pants
Answers
Answer:111
Step-by-step explanation:
1111
Simplify the linear expression.
−3x+5(−8x−1)
Enter your answer in the box.
Answers
Answer:
-43x - 5
Step-by-step explanation:
−3x + 5 (−8x −1)
First, distribute 5 into the parenthesis:
= −3x + 5 (−8x −1)
= -3x - 40x -5
Combine like terms:
= -43x - 5
Answer:
-43x - 5
Step-by-step explanation:
I took the K12 test
Find the solution(s) for x in the equation below.
x^2 - 25 = 0
A. x = -5
В. no solutions
C. x = 5
D. x = 5; x = -5
Answers
Answer:
D. x = 5; x = -5
Step-by-step explanation:
x^2 - 25 = 0
Add 25 to each side
x^2 - 25+25 = 0+25
x^2 = 25
Take the square root of each side
sqrt(x^2) = sqrt(25)
x = ±5
Joe is new to cooking. The probability that joe burns dinner is 50%
Answers
Given that the probability that Joe burns dinner is:
\(p=50\text{\%}=\frac{50}{100}=0.5\)You need to use the following Binomial Distribution Formula, in order to solve the exercise:
\(P(X)=\frac{n!}{(n-x)!x!}\cdot p^x(1-p)^{n-x}\)Where "n" is the sample size, "x" is the number of successes desired, and "p" is the probability of getting a success in a trial.
(a) You must find the probability that in the next 7 dinners Joe prepares, 4 of them will burn. Therefore, for this case:
\(\begin{gathered} n=7 \\ x=4 \end{gathered}\)Then, you can substitute values into the formula and evaluate:
\(P(X=4)=\frac{7!}{(7-4)!4!}(0.5)^4(1-0.5)^{7-4}\)\(P(X=4)\approx0.2734\)(b) You must find the probability that in the next 7 dinners Joe prepares, at least 5 of them will burn. Therefore, since "at least" indicates greater than or equal to 5, you need to set up this Sum for:
\(\begin{gathered} x=5 \\ x=6 \\ x=7 \end{gathered}\)Then:
\(P(X\ge5)=\frac{7!}{(7-5)!5!}(0.5)^5(1-0.5)^{7-5}+\frac{7!}{(7-6)!6!}(0.5)^6(1-0.5)^{7-6}+\frac{7!}{(7-7)!7!}(0.5)^7(1-0.5)^{7-7}\)Evaluating, you get:
\(P(X\ge5)\approx0.2266\)(c) You must find the probability that in the next 7 dinners Joe prepares, less than 3 of them will burn. Therefore, you need to set up a Sum for:
\(\begin{gathered} x=0 \\ x=1 \\ x=2 \end{gathered}\)As follows:
\(P(X<3)=\frac{7!}{(7-0)!0!}(0.5)^0(1-0.5)^{7-0}+\frac{7!}{(7-1)!1!}(0.5)^1(1-0.5)^{7-1}+\frac{7!}{(7-2)!2!}(0.5)^2(1-0.5)^{7-2}\)Evaluating, you get:
\(P(X<3)\approx0.2266\)Hence, the answers are:
(a)
\(0.2734\)(b)
\(0.2266\)(c)
\(0.2266\)What is one fifth of twenty more than half
of 80?
(A) 8
(B) 10
(C) 12
(D) 13
Answers
Answer:
(C) 12
Step-by-step explanation:
To solve this problem, we can use the following steps:
Find half of 80: 80/2 = 40
Add 20 to half of 80: 40 + 20 = 60
Find one fifth of the result: 60/5 = 12
Therefore, one fifth of twenty more than half of 80 is equal to 12. The correct answer is (C) 12.
Answer:
(C) 12
Step-by-step explanation:
What is one fifth of twenty more than half of 80
0.5 × 80 = 40
What is one fifth of twenty more than half of 80
40 + 20 = 60
What is one fifth of twenty more than half of 80
1/5 × 60 = 60/5 = 12
Suppose we want to choose 5 objects, without replacement, from 15 distinct objects.
Answers
The number of ways it can be done if order of the choices is taken into consideration is 15,444 ways
Permutation and combinationPermutation has to do with arrangement and combination has to do with selection.
If we are choosing 5 objects, without replacement, from 15 distinct objects, this has to do with permutation if the order of the choices is taken into consideration
15P5 = 15!/(15-5)!5!
15P5 = 15!/10!5!
15P5 = 15*14*13*12*11/5*4*3*2
15P5 = 15,444 ways
Hence the number of ways it can be done if order of the choices is taken into consideration is 15,444 ways
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Complete question
Suppose we want to choose 5 objects, without replacement, from 15 distinct objects. How many ways can this be done, if the order of the choices is taken into consideration?
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
The length KL is 8 units
The value of x is undefined
The length KL is 12 units
Calculating the length KLFrom the question, we have the following parameters that can be used in our computation:
The rhombus
Also, we have
DK = 8
A rhombus is a quadrilateral with all sides equal.
So, we have
KL = 8
Calculating the value of xHere, we have
SKAL = 2x - 8
There is no point S on the rhombus
This means that
x = undefined
Calculating the length KLHere, we have
DM = 5y + 2 and DK = 3y + 6
A rhombus is a quadrilateral with all sides equal.
So, we have
5y + 2 = 3y + 6
Evaluate
2y = 4
Divide
y = 2
So, we have
KL = 5 * 2 + 2
KL = 12
Hence, the length KL is 12 units
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Given that a+b = 10 and a square - b square = 40 find the value of a-b
Answers
Answer:
the value of a - b is 4.
Step-by-step explanation:
We have been given the following two equations:
a + b = 10 ------------(1)
a² - b² = 40 -------(2)
We can factor the left-hand side of equation (2) using the difference of squares identity:
(a + b)(a - b) = 40
Substituting equation (1) into this equation, we get:
10(a - b) = 40
Dividing both sides by 10, we get:
a - b = 4
Therefore, the value of a - b is 4.
Step-by-step explanation:
if I understand this correctly :
a + b = 10
a² - b² = 40
(a² - b²) = (a + b)(a - b) = 40
10(a - b) = 40
(a - b) = 4
On the SAT exam a total of 25 minutes is allotted for students to answer 20 math questions without the use of a calculator. A guidance counselor would like to know if the students in his school are prepared to complete this portion of the exam in the timeframe allotted. To investigate, the counselor selects a random sample of 35 students and administers this portion of the test. The students are instructed to turn in their test as soon as they have completed the questions. The mean amount of time taken by the students is 23.5 minutes with a standard deviation of 4.8 minutes. The counselor would like to know if the data provide convincing evidence that the true mean amount of time needed for all students of this school to complete this portion of the test is less than 25 minutes and therefore tests the hypotheses H0: μ = 25 versus Ha: μ < 25, where μ = the true mean amount of time needed by students at this school to complete this portion of the exam. The conditions for inference are met. What are the appropriate test statistic and P-value?
Answers
The P-value is between 0.025 and 0.05. and t = -1.85
On the SAT exam a total of 25 minutes is allotted for students to answer 20 math questions without the use of a calculator.
Therefore tests the hypotheses:
\(H_0\) : μ = 25 versus Ha: μ < 25,
where μ = the true mean amount of time needed by students at this school to complete this portion of the exam.
The alternative hypothesis is:
\(H_1:\mu < 25\)
The test statistic is given by:
\(t=\frac{x-\mu}{\frac{s}{\sqrt{n} } }\)
The parameters are:
'x' is the sample mean. \(\mu\) is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.the values of the parameters are:
x = 23.5 , \(\mu=25\) , s = 4.8, n = 35
Plug all the values in above formula of t- statistic is:
\(t = \frac{23.5-25}{\frac{4.8}{\sqrt{35} } }\)
t = -1.85
Using a t-distribution , with a left-tailed test, as we are testing if the mean is less than a value and 35 - 1 = 34 df, the p-value is of 0.0365.
t = –1.85; the P-value is between 0.025 and 0.05.
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Which expression represents the
number of reams of paper the company
produced during the second year?
Answers
The expression that represents the number of reams of paper the company produced during the second year is 4.704 × 10¹⁰. The correct option is D. 4.704 × 10¹⁰
Writing an ExpressionFrom the question, we are to determine the expression that represents the number of reams of paper the company produced during the second year
From the given information,
During the first year of operation,
The company produced 8.4 × 10⁹ reams of paper
And
During the second year,
the company produced 5.6 times the number of reams of paper that it produced during the first year.
Thus,
The number of reams of paper the company produced during the second year = 5.6 × 8.4 × 10⁹ reams of paper
The number of reams of paper the company produced during the second year = 47.04 × 10⁹ reams of paper
= 4.704 × 10¹ × 10⁹ reams of paper
= 4.704 × 10¹⁰ reams of paper
Hence, the expression that represents the number of reams of paper the company produced during the second year is 4.704 × 10¹⁰. The correct option is D. 4.704 × 10¹⁰
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6. The fixed costs of producing a Wild Widget are $34,000. The variable costs are $5.00 per widget. What is the average cost per widget of producing 7,000 Wild Widgets? Round to the nearest cent. :))))
Answers
Answer: To calculate the average cost per widget, we need to consider both the fixed costs and the variable costs.
Fixed costs: $34,000
Variable costs per widget: $5.00
Total costs = Fixed costs + (Variable costs per widget × Number of widgets)
Total costs = $34,000 + ($5.00 × 7,000)
Total costs = $34,000 + $35,000
Total costs = $69,000
Average cost per widget = Total costs / Number of widgets
Average cost per widget = $69,000 / 7,000
Average cost per widget ≈ $9.86
Therefore, the average cost per widget of producing 7,000 Wild Widgets is approximately $9.86.
Step-by-step explanation: :)
Hey can someone please help me with this
Answers
x = -2
The graph is the top one on the left.
what is 37,056 round to the nearest thousand
Answers
Answer: 37,000
Step-by-step explanation:
A carpenter is building a rectangular shed with a fixed perimeter of 68 ft. What are the dimensions of the largest shed that can be built? What is its area?
The dimensions of the largest shed are _____ by _____.
The area of the largest shed is _____.
Answers
Answer:
The dimensions of the largest shed are 17 ft by 17 ft.
The area of the largest shed is 289 sq ft.
Step-by-step explanation:
Given that:
Fixed perimeter of the rectangular shed = 68 ft
To find:
The dimensions of the largest shed that can be built = ?
And
Area of the largest shed that can be built = ?
Solution:
First of all, let us have a look at the formula for perimeter of a rectangular shape shed:
Perimeter of a rectangle = 2 \(\times\) (Length + Width)
68 = 2 \(\times\) (Length + Width)
Length + Width = 34
The largest possible values are only in the case when the rectangle is a square.
i.e. Length = Width
Therefore values of length and width are:
Length = Width = \(\frac{34}{2} = 17\ ft\)
Area of a square is given by the formula:
\(A = Side \times Side\)
\(A\) = 17 \(\times\) 17 = 289 sq ft
The answer is:
The dimensions of the largest shed are 17 ft by 17 ft.
The area of the largest shed is 289 sq ft.
The measure of Angle RNY and the measure of Angle GNC = 128. Angle RNY is congruent to Angle GNC. What is true about these two angles?
Answers
Answer:
They have the same angle measure
Step-by-step explanation:
Congruent angles have the same angle measure, theyre the same. That’s the definition of “congruent”. Both of their angle measures are 128 degrees.
Henry's savings account has an APR of 3.65%, calculates interest daily, and
pays interest at the end of the month. If during the month of November, his
balance was $300 for the first 10 days of the month, $1200 for the next 10
days of the month, and $800 for the last 10 days of the month, how much
total interest did Henry earn in November?
Answers
First, we need to calculate the daily interest rate:
Daily interest rate = APR / 365 = 0.0365 / 365 = 0.0001
For the first 10 days, the interest earned on $300 is:
Interest = Principal x Daily interest rate x Time
Time = 10 days
Interest = 300 x 0.0001 x 10 = $0.30
For the next 10 days, the interest earned on $1200 is:
Interest = Principal x Daily interest rate x Time
Time = 10 days
Interest = 1200 x 0.0001 x 10 = $1.20
For the last 10 days, the interest earned on $800 is:
Interest = Principal x Daily interest rate x Time
Time = 10 days
Interest = 800 x 0.0001 x 10 = $0.80
Therefore, the total interest earned by Henry in November is:
Total interest = $0.30 + $1.20 + $0.80 = $2.30
Therefore, Henry earned $2.30 interest in November.
Please help me w the following or else I can’t go to my softball game tomorrow ♀️
Answers
The graph cannot be used to complete the table of values and the missing value of a is 7
How to determine the missing value of y's?The graph represents the given parameter
There are no points plotted on the graph
This means that the table of values cannot be completed
Hence, the graph cannot be used to complete the table of values
How to determine the missing value of a?The table represents the given parameter
On the table, we have the following points
(x, y) = (0, -2), (2, 4), (3, a)
Also, we have that the points fall on a line
This means that the points make a linear equation
By analyzing the x and y values, we can see that
As x increases by 2, y increases by 6
This means that as x increases by 1, y increases by 3
So, when x = 3, the value of y is
y = 4 + 3
Evaluate
y = 7
Rewrite as
a= 7
Hence, the missing value of a is 7
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Hank made payments of $219 per month at the end of each month for 30 years to purchase a piece of property. He promptly sold it for $195,258. What interest rate, compounded monthly, would he need to earn on an ordinary annuity for a comparable rate of return?
Answers
To achieve a comparable rate of return, Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly on his ordinary annuity.
To find the interest rate, compounded monthly, that Hank would need to earn on an ordinary annuity for a comparable rate of return, we can use the present value formula for an ordinary annuity.
First, let's calculate the present value of Hank's payments. He made payments of $219 per month for 30 years, so the total payments amount to $219 * 12 * 30 = $78840.
Now, we need to find the interest rate that would make this present value equal to the selling price of the property, which is $195,258.
Using the formula for the present value of an ordinary annuity, we have:
PV = P * (1 - (1+r)\(^{(-n)})\)/r,
where PV is the present value, P is the payment per period, r is the interest rate per period, and n is the number of periods.
Plugging in the values we have, we get:
$78840 = $219 * (1 - (1+r)\({(-360)}\))/r.
Solving this equation for r, we find that Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly, in order to have a comparable rate of return.
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Find the solution to the system of equations.
3x + 2y - 4z= 3
3
x - 4y + 2z= -11
2x + y - 2z = 2
A. x = 3, y = 2, z = 4
B. x = 1, y = 4, z = 2
O C. x = 6, y=-3, z = -4
O D. x= 1, y = 6, z = 2
Answers
Answer:
B.
\(x = 1 \\ y = 4 \\ z = 2\)
The solution to the system of equations is x-1, y = 4 and z= 2.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
We have the equation
3x + 2y - 4z = 3
x -4y +2z = -11
2x + y + 2z = -11
Solving the above equation we get
3x + 2y - 4z - 3x + 12y + 6z = 3 + 33
14y + 2z = 36
and, 2x - 8y + 4z - 2x - y - 2z = -22 + 11
-9y + 2z = -11
So, y =4 and z = 2
and, x = 1
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Brendan says that when a rectangle with length 6 cm and width 4 cm is dilated by a scale factor of 2, the perimeter and area of the rectangle are doubled. Explain what is incorrect about Brendan’s statement.
Answers
The area of a rectangle does double when dilated by a scale factor of 2, the Perimeter does not double. It increases by a factor of 2.
Brendan's statement that when a rectangle with a length of 6 cm and a width of 4 cm is dilated by a scale factor of 2, the perimeter and area of the rectangle are doubled is incorrect. While the area of the rectangle does indeed increase by a factor of 2 when dilated, the perimeter does not necessarily double.
Brendan's statement and understand the concept of dilation:
1. Perimeter: The perimeter of a rectangle is the sum of all its sides. In this case, the original rectangle has a length of 6 cm and a width of 4 cm, resulting in a perimeter of 2*(6 cm + 4 cm) = 20 cm. If we dilate this rectangle by a scale factor of 2, the new rectangle will have a length of 2 * 6 cm = 12 cm and a width of 2 * 4 cm = 8 cm. The perimeter of the new rectangle is 2*(12 cm + 8 cm) = 40 cm. As we can see, the perimeter has not doubled; it has increased by a factor of 2.
2. Area: The area of a rectangle is calculated by multiplying its length by its width. For the original rectangle with a length of 6 cm and a width of 4 cm, the area is 6 cm * 4 cm = 24 cm². When we dilate the rectangle by a scale factor of 2, the new rectangle will have a length of 2 * 6 cm = 12 cm and a width of 2 * 4 cm = 8 cm. The area of the new rectangle is 12 cm * 8 cm = 96 cm². The area has indeed doubled, as Brendan mentioned.
Therefore, while the area of a rectangle does double when dilated by a scale factor of 2, the perimeter does not double. It increases by a factor of 2. It is crucial to differentiate between the effects of dilation on the area and the perimeter of a shape to have a clear understanding of geometric transformations.
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PLEASE ANSWER! Which expression is equal to the length of the hypotenuse of a right triangle, formed inside the unit circle, with a radius of 1?
A: sin 0/ cos 0
B: sin^2 0 + tan^2 0
C: sin 0 + cos 0
D: sin^2 0 + cos^2 0
Answers
Answer:
b
Step-by-step explanation:
b: sin^2 0 + tan^2 0 this is just a gut feelings its been awhile since i done this kind of think i hope i could help
The expression equal to the length of the hypotenuse of a right triangle formed inside the unit circle with a radius of 1 is Option (D) \(sin^{2}\)θ+\(cos^{2}\)θ
What is Right triangle?A right-angled triangle is a type of triangle that has one of its angles equal to 90 degrees.
What is Hypotenuse?A hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle.
Here,
The length of the hypotenuse of a right triangle, formed inside the unit circle, with a radius of 1 is 1 unit.
We know that,
\(sin^{2}\)θ+\(cos^{2}\)θ=1
Hence, The expression equal to the length of the hypotenuse of a right triangle formed inside the unit circle with a radius of 1 is Option (D) \(sin^{2}\)θ+\(cos^{2}\)θ
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Name the relationship: complementary, supplementary, linear pair, vertical, or adjacent. Some may have more than one name.
Answers
The type of relationship that angle a and angle b have is that they are complementary.
What are Complementary Angles?A right angle equals the measure of 90 degrees. If two angles equals a right angle, then their sum equals 90 degrees. Complementary angles have a sum of 90 degrees, therefore, if two angles form a right angle, then they are a pair of complementary angles.
In the image given, angle a and angle b form a right angle. Thus, the sum of angle a and angle b equals 90 degrees. This means they are complementary angles.
Therefore, the type of relationship that angle a and angle b have is that they are complementary.
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if jermeey has 9 apples, and sabrina has 10, how many apples do they have if erica takes 19 of them?
Answers
Answer:
0 apples
Step-by-step explanation:
Find the exact volume of a waffle ice cream cone with 15-in. Diameter and a height of 23 inches
Answers
Volume of cone: pi(r)^2*h/2
= pi(7.5)^2*23/2
pi(56.25) * 23/2
(3.14)(56.25)(23)/2 = 2,031 inches
HELP ME WHICH ANSWER
Answers
Answer:
D
Step-by-step explanation:
30 : 13 = 30/13
Answer:
The answer is 13:30
Step-by-step explanation:
All you have to do is make sure that you put the ice skating fist because that is the one that the question mentioned first. Hope this helps :)
The number line below shows information
about a variable, m.
Select all of the following values that m
could take:
-2, 4, -3.5, 0, -5, -7
-5 -4 -3 -2 -1 0 1 2 3 4 5
m
Answers
From the given number line, the variable "m" could take the values of -2, -3.5, 0, and -5
To determine which values the variable "m" could take from the given number line, we need to identify the points or intervals on the number line that correspond to the possible values of "m".
Looking at the number line, we can see the following values:
-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5
From this list, the values that "m" could take are:
-2, -3.5, 0, -5
These values are present on the number line, indicating that they are possible values for "m".
Therefore, the variable "m" could take the values -2, -3.5, 0, and -5 from the given number line.
It's important to note that the values -7 and 4 are not present on the number line, so they are not possible values for "m" based on the information provided.
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3 6 9 12 15 18 21 24 27 30 is odd or even numbers?
Answers
Answer: Half of them are even and half of them are odd.
Step-by-step explanation:
The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.
The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.
Therefore, out of the given numbers, half of them are even and half of them are odd.
________________________________________________________
Find the area of the blue-shaded region. Please help I need it asap. The answer is 20.0m squared I cannot figure out the work for it
Answers
The area of the blue-shaded region is 19.95 m²
What is area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
Given that, a rectangle with length 14 m, and diagonal 15.5 m, a parallelogram has been cut out of it, we need to find the area remaining,
Using the Pythagoras theorem,
15.5² = 14²+w² [width]
w² = 240.25-196
w² = 44.25
w = 6.65
Therefore, the width of the rectangle is 6.65 m
That mean, the height of the parallelogram is 6.65 m,
The area of the blue-shaded region, is calculated by subtracting the area of the parallelogram by the area of the rectangle,
Area of the remaining region = 14×6.65-11×6.65
= 6.65(14-11) = 6.65×3
= 19.95 m²
Hence, the area of the blue-shaded region is 19.95 m²
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A runner ran of a 5 kilometer race in 21 minutes. They ran the entire race at a constant speed.
How long did it take to run the entire race?
How many minutes did it take to run 1 kilometer?
Answers
the answer is 6 minutes and 46 seconds
plz explain in a paragraph to get brainliest
Answers
Answer:
500 people took the survey.
Step-by-step explanation:
12 divided by 3 is 4 and 15 divided by 3 is 5. that means 4 of every 5 people prefer restaurants. Multiply that by 100 and you get 400 of every 500 people prefer restaurants. Hope this helps!