Answer: [tex]2 + \sqrt{3}[/tex]
==============================================
Work Shown:
[tex]\frac{6 + \sqrt{27}}{3}\\\\\frac{6 + \sqrt{9*3}}{3}\\\\\frac{6 + \sqrt{9}*\sqrt{3}}{3}\\\\\frac{6 + 3\sqrt{3}}{3}\\\\\frac{3(2 + \sqrt{3})}{3}\\\\2 + \sqrt{3}\\\\[/tex]
The idea with simplifying the square root (steps 2 through 4) has us factoring 27 so that one factor is a perfect square. We want the largest perfect square factor possible.
That way when we use the rule sqrt(x*y) = sqrt(x)*sqrt(y), we pull out that perfect square to then use the rule sqrt(x^2) = x where x is nonnegative.
After simplifying the square root, we factor out the GCF and then cancel out the 3's.
Which equation represents the data shown in the table below? x y 2 9 3 12 4 15 5 18 A. y = 2x + 9 B. y = 3x + 3 C. y = 3x + 12 D. y = 4x + 1
Answer:
Step-by-step explanation:
The answer is B. Because 3 multiplied by x and add it by 3 equates to y. example: (x=2) 3x2+3= y. y=9 .
The data best fit the line y = 3x+3, the correct option is B.
What is an Equation?The equation is a statement that equates two algebraic expressions with an equal sign.
The data is given
x y
2 9
3 12
4 15
5 18
The equation that represents the data can be found by substituting the data and checking if they satisfy the equation.
The first equation is
y = 2x +9
Substitute ( 2,9)
9 = 2 *2 +9
9 ≠ 13
The second equation is
y = 3x +3
Substitute ( 2,9)
y = 3 *2 +3
9 = 9
Substitute ( 3,12)
12 = 3 *3 +3
12 = 12
Therefore, the data best fit the line y = 3x+3, the correct option is B.
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y2-8+7
2x - y >4
Yes
No
When using 3 letters to make an angle the middle letter is
Need helppppppp!!!!Solve the absolute value equation: |3x - 6| = 12
Answer:
3x-6=12
3x-6=-12
x=6
x= -2
1st x = -2
2nd x = 6
Step-by-step explanation:
The intersection of two lines can be a line segment
Answer:
A plane and a line can intersect in a point—- false
Emma was given a system of equations to solve by graphing. Which statement correctly identifies Emma’s error?
Answer:
line one should have a y-intercept at (0,2).
Step-by-step explanation:
Answer: A
Step-by-step explanation: line one should have a y-intercept at (0,2).
What is 33/8 in a mixed number
Answer: 4 1/8
Step-by-step explanation: To change an improper fraction to a mixed number, you need to first divide the numerator by the denominator as the fraction sign is essentially just a division sign. In this case, you do 33 divided by 8, which would get you 4 with a remainder of 1. 33/8 is just equal to 4 and 1/8.
33/8 is equal to 4 [tex]\frac{1}{8}[/tex] in terms of mixed fraction.
What are Fractions?Fractions are numbers of the form [tex]\frac{p}{q}[/tex] where both p and q are real numbers. It can also be defined as a portion of a whole.
p is called the numerator and q is called the denominator.
There are different types of factors such as unit fractions, like fractions, unlike fractions, improper fractions, proper fractions, mixed fractions and so on.
Mixed fractions are fractions of the form q [tex]\frac{r}{d}[/tex] where q is the quotient, r is the remainder and d is the divisor upon dividing the numerator with the denominator of an improper fraction.
33/8 can be expressed in the mixed form by dividing 33 with 8.
We get quotient is 4 and remainder is 1.
So 33/8 = 4 [tex]\frac{1}{8}[/tex]
Hence 33/8 can be written as 4 [tex]\frac{1}{8}[/tex] in terms of mixed fraction.
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Expanded form of 7050024
Expanded Notation Form:
7,000,000
+ 0
+ 50,000
+ 0
+ 0
+ 20
+ 4
Expanded Factors Form:
7 × 1,000,000
+ 0 × 100,000
+ 5 × 10,000
+ 0 × 1,000
+ 0 × 100
+ 2 × 10
+ 4 × 1
Expanded Exponential Form:
7 × 106
+ 0 × 105
+ 5 × 104
+ 0 × 103
+ 0 × 102
+ 2 × 101
+ 4 × 100
Hope this helps? :))
Answer:7,00,000 50,000 20 4n
Step-by-step explanation:
A piece of land is shaped like a right triangle. Two people start at the right angle at the same time, and walk at the same speed along different legs of the triangle while spraying the land. If the area covered is changing at
5 m2/s, how fast are the people moving when they are 5 m from the right angle? (Round approximations to two decimal places.)
Answer:
1 m/s
Step-by-step explanation:
the area of the triangle = A = ¹/₂ab
where a is the distance covered by the first person and b is the distance covered by the second person. since they walk at the same speed, then a = b, so our formula can be changed to A = ¹/₂x²
now we find the derivative of both sides:
dA/dt = ¹/₂ ⋅ dx²/dt
dA/dt = ¹/₂ ⋅ 2x ⋅ dx/dt
dA/dt = x ⋅ dx/dt = x ⋅ velocity
we are told that x = 5 m, and dA/dt = 5 m²/s
velocity = dA/dt / x
velocity = 5 m²/s / 5 m = 1 m/s
what is the difference between 9 - 4 1/5
Hey there!☺
[tex]Answer:\boxed{4\frac{4}{5}}[/tex]
[tex]Explanation:[/tex]
[tex]9-4\frac{1}{5}[/tex]
Subtract the whole number by the fraction.
[tex]\frac{24}{5}[/tex]
24/5 needs to be simplified so we will rewrite it like this:
[tex]4\frac{4}{5}[/tex]
Hope this helps!
The center of circle P is at (-3, 8) and the radius is 12
units. Find its equation.
Answer:
The answer is
x² + y² + 6x - 16y - 71 =0Step-by-step explanation:
The equation of a circle is given by
( x - a)² + ( y - b)² = r²where ( a , b) is the center of the circle and
r is the radius
From the question the center is
P (-3, 8) and radius = 12
Substitute the values into the above formula and solve
That's
( x + 3)² + ( y - 8) = 12²
Expand the terms
That's
x² + 6x + 9 + y² - 16y + 64 = 144
Arrange the terms
x² + y² + 6x - 16y + 9 + 64 - 144 = 0
We have the final answer as
x² + y² + 6x - 16y - 71 =0Hope this helps you
Answer the question in the file
Answer:
30
Step-by-step explanation:
50-2×(3^2+1)
50-2×(9+1)
50-2×(10)
50-20
30
Hey there!
ANSWER: [tex]30[/tex]EXPLANATION:[tex]50-2*(3^2+1)=?[/tex]
You will need to use the order of operations to solve. We will need to start with parenthesis. The parenthesis includes exponents which comes after.
[tex](3^2+1)=10[/tex]
Now go to multiplication.
[tex]2*10=20[/tex]
Now move to subtraction since that's what we have left.
[tex]50-20=30\\30(ANSWER)[/tex]
Hope this helps!
[tex]\text {-TestedHyperr}[/tex]
The sum of three numbers is 82 The second number is 3 times the third. The third number is 8 more than the first. What are the numbers?
Answer:
22 46 15
Step-by-step explanation:
i looked it up because i was even confused. but i think this is right. hope this helps.
One sample has a mean of M=7.2 and a second sample has a mean of M=12.8. The two sample are combined into a single set of scores. a. What is the mean for the combined set if both the samples have n=5? b. What is the mean for the combined set if the first sample has n=5 and the second sample had n=35?
Answer:
a. M = 50
b. M = 242
Step-by-step explanation:
mean = [tex]\frac{sum of scores}{number of samples}[/tex]
⇒ sum of scores = mean x number of samples
Let the mean be represented by M, and the number of samples be represented by n,
sum of scores = M x n
a. When n = 5 for both samples,
The first sample's sum of scores = M x n
= 7.2 x 5
= 36
The second sample's sum of scores = M x n
= 12.8 x 5
= 64
The mean for the sum of scores of the combined set = [tex]\frac{36 + 64}{2}[/tex]
= 50
When both samples have n = 5, the mean of the combined set is 50.
b. When the first sample has n = 5, the sum of scores = 36.
If n = 35 for the second sample, the sum of scores = M x n
= 12.8 x 35
= 448
The mean for the sum of scores of the combined set = [tex]\frac{36 + 448}{2}[/tex]
= 242
The school shop ordered 20 boxes of snacks and there were 89 snacks in each box. If 15 snacks were sold from each box, how many were left?
Answer:
1,480
Step-by-step explanation:
89x20=1,780 total snacks
20x15=300 snacks sold
1,780-300=1,480 snacks left
Which unit should be used to measure mass of pencil?
Answer:
Grams
Step-by-step explanation:
Pencils are pretty light, so they should be measured in grams.
Answer:
grams :)
Step-by-step explanation:
I looked it up
Which shows only a vertical translation from the shaded figure onto the unshaded figure?
On a coordinate plane, a triangle is shifted up.
On a coordinate plane, a triangle is shifted to the left.
On a coordinate plane, a triangle is enlarged to form another triangle.
On a coordinate plane, a triangle is shifted up and to the left.
Answer:A
Step-by-step explanation:
Answer: Answer is A
Step-by-step explanation: i got it right on edge 2023 <33
I need help please
Answer:
Equal 15
Step-by-step explanation:
2+588(357)
4-136
Solve for t.
-3t + 3 – 7t = -90 – 7
Answer:
t = 10Step-by-step explanation:
-3t + 3 - 7t = -90 - 7
Simplify both sides of the equation
That's
- 10t + 3 = - 97
Using the subtraction property subtract 3 from both sides of the equation
We have
- 10t + 3 - 3 = -97 - 3
- 10t = - 100
Divide both sides by - 10
[tex] \frac{ - 10t}{ - 10} = \frac{ - 100}{ - 10} [/tex]
We have the final answer as
t = 10Hope this helps you
Answer:
Step-by-step explanation:
-3t + 3 - 7t = -90 - 7
-10t + 3 = -97
-10t = -100
t = 10
The sum of two numbers is seventy-two. Twice one of them equals ten times the other. What are the numbers? Please Help MEE It would be Amazing
Let's create a system of equations to solve this.
x + y = 72
2x = 10y
Let's solve this equation for x
2x = 10y
Divide both sides by 2
x = 5y
Plug 5y into our first equation to solve for y
5y + y = 72
Combine like terms
6y = 72
Divide by 6
y = 12
x = 5y = 5(12) = 60
What does ¼ x (5.6) equal to
Answer:
The answer is 1.4 because you have to simplify it. Hope this helps :)
Step-by-step explanation:
Find the area of the figure.
9 yd
6,4 yd
Answer:
144 should be your answer
Step-by-step explanation:
Write in standard form 5×100+4×19+6×1+2×1/10+8×1/1000
Answer:
Step-by-step explanation:
i think this is the answer
576.628
Answer:
[tex]\frac{72776}{125}[/tex]
Step-by-step explanation:
500+76+6+1/5+1/125
500*125/125 +76*125/125 + 6*125/125 +25/125 +1/125
62500+9500+750+25+1/125
[tex]\frac{72776}{125}[/tex]
or 582.208
or
[tex]582 \frac{26}{125}[/tex]
Mateo scored in the 55th percentile of his class on the latest math exam. What does this mean in relation to the data set, and what did he score on the exam?
Answer:
d. Mateo scored as well as or better than 55% of his classmates, with a score of 82.Step-by-step explanation:
Mateo scored in the 55th percentile of his class on the latest math exam. What does this mean in relation to the data set and what did he score on the exam?{35, 42, 55, 68, 69, 72, 72, 77, 78, 78, 82, 85, 87, 88, 90, 93, 94, 96, 96, 99)
a. Mateo scored a 55% on his exam. b. Mateo scored as well as or better than 55% of his classmates, with a score of 78. c. Mateo scored worse than 55% of his classmates, with a score of 78. d. Mateo scored as well as or better than 55% of his classmates, with a score of 82. e. Mateo scored worse than 55% of his classmates, with a score of 82. SolutionThere are scores of 20 students. Each score is equivalent of 100%/20 = 5%
The easy way to understand Mateo' s place is to compare scores against 5% slots.
See attached.
We can also get the average score
Sum
∑ {35, 42, 55, 68, 69, 72, 72, 77, 78, 78, 82, 85, 87, 88, 90, 93, 94, 96, 96, 99) = 1556Average or mean score:
1556/20 = 77.8This is matching the 50% score.
As we see Mateo scored 82 which is matching 55%.
Correct option is d.
Colin Davis machine company maintains a general ledger
Step-by-step explanation:
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Help...plzz giving 25 points
Answer: the integers are closed under addition, multiplication, and subtraction, but NOT division.
Step-by-step explanation:
I need help. Three different polygons in this shape and explain how I know? Help please thanks!
Answer:
why it say least
Step-by-step explanation:
as the first word
Well, it's a square, a rhombus and a rectangle.
In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or 100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length.
A rhombus is a quadrilateral whose four sides all have the same length.
Hope I helped :)
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Find the percent change. State whether it is an increase or decrease. Round to the nearest tenth of a percent. From 50 to 42
Answer:
16% decrease
Step-by-step explanation:
I need two tickets to the movies. Each ticket costs $12. How much do I need to purchase 2 tickets to the movies?
Show Work!
Answer: 24$
multiply $12x$2 and get 24$
Step-by-step explanation: I need two tickets to the movies. Each ticket costs $12. How much do I need to purchase 2 tickets to the movies?