Please work these out, If possible can someone just work out 1 providing solutions. Thanks
Answers
Answer:
See below for solution steps for parts (a) and (c)
Step-by-step explanation:
The trick here is to get all the roots to have the same radical. Each of the lowest radical is the square root pf a prime so cannot be reduced further
For example, in a, the lowest is [tex]\sqrt{3}[/tex]
So get all the others to this level a[tex]\sqrt{3}[/tex] and then you can just add up the non-radicals and use the radical as the common expression
I will solve a couple and that will give you a general idea of solving the rest
Let's do a.
[tex]5\sqrt{3} , \sqrt{3}[/tex] are already at the lowest radical level of [tex]\sqrt{3}[/tex] so let's reduce 108 to have [tex]\sqrt{108}[/tex] to have [tex]\sqrt{3}[/tex] as one of its components
We can factor 108 as follows;
108/3 = 36
So 108 = 36 x 3
√108 = √36 × √3 = 6√3
Therefore the original expression becomes
[tex]5\sqrt{3} - 6\sqrt{3} + \sqrt{3} = (5 - 6 + 1)\sqrt{3} = 0 \sqrt{3} = 0[/tex]
[tex]-------------------------------[/tex]
c.
[tex]2\sqrt{20} - 7\sqrt{5} + \sqrt{45}[/tex]
Lowest radical is [tex]\sqrt{5}[/tex] whose coefficient is 7
Factor 20 = 4 x 5
[tex]2\sqrt{20} = 2\sqrt{4 \times 5} = 2\sqrt{4} \times \sqrt{5} = 2\times 2 \times \sqrt{5}\\= \bold{4\sqrt{5}}[/tex]
Factor 45:
45 = 9 x 5
[tex]\sqrt{45} = \sqrt{9} \times \sqrt{5} = \bold{3\sqrt{5}}[/tex]
Original expression becomes:
[tex]4\sqrt{5} - 7\sqrt{5} + 3\sqrt{5}\\\\=(4 - 7 + 3)\sqrt{5}\\\\= 0 \sqrt{5}\\\\= 0\\----------------------------[/tex]
I am sure you can do the rest. If not post them as another question. Maybe someone else will answer a few of the ones I did not.
All the best
Related Questions
A right rectangular prism has a square base with sides 1/2 in. Long. The volume of the prism is 3/8 in to the third power. What is the prism?
Answers
Answer:
If the base of the right rectangular prism is a square with sides that are 1/2 inch long, then the area of the base is (1/2)^2 = 1/4 square inches.
Since the volume of the prism is given as 3/8 cubic inches, we can use the formula for volume of a right rectangular prism (V = Bh) to solve for the height of the prism:
V = Bh
3/8 = (1/4)h
Multiplying both sides by 4, we get:
3 = h
So the height of the prism is 3 inches.
Therefore, the right rectangular prism has a square base with sides 1/2 inch long and a height of 3 inches, making it a 1/2 x 1/2 x 3 inch rectangular prism.
Rick was given 2 new gaming consoles for his birthday, one from each set of grandparents. He wants to return one of the consoles and use the store credit to buy new video games. He will receive $299 in store credit, and each video game costs $60. You can use a function to describe the amount of store credit he will have left after purchasing x video games. Write an equation for the function. If it is linear, write it in the form f(x)=mx+b. If it is exponential, write it in the form f(x)=a(b)x. f(x)=
don't spam ;-;
Answers
The linear function for the amount of store credit he will have left after purchasing x video games is given as follows:
f(x) = 299 - 60x.
How to obtain alinear function?
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.The parameters for this problem are given as follows:
b = 299, which is the initial credit that he has.m = -60, as for each videogame purchased, the amount of credit decays by $60.Hence the function is given as follows:
f(x) = 299 - 60x.
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The time between arrivals of customers at a bank during the noon-to-1 p.m. hour has a uniform distribution between 0 to 120 seconds. What is the probability that the time between the arrival of two customers will be
a. less than 20 seconds?
b. between 10 and 30 seconds?
c. more than 35 seconds?
d. What are the mean and standard deviation of the time between arrivals?
Answers
Answer:
Step-by-step explanation:
Here's a step-by-step solution to finding the probabilities of the time between customer arrivals:
a. less than 20 seconds:
To find the probability that the time between arrivals is less than 20 seconds, we need to find the cumulative distribution function (CDF) of the time between arrivals and evaluate it at 20 seconds. The CDF for a uniform distribution is given by:
F(x) = x/b - a/b, where a is the lower bound and b is the upper bound of the distribution
For this problem, the lower bound a is 0 and the upper bound b is 120, so the CDF of the time between arrivals is:
F(x) = x/120
Now, we can evaluate the CDF at 20 seconds to find the probability that the time between arrivals is less than 20 seconds:
F(20) = 20/120 = 1/6
So, the probability that the time between arrivals is less than 20 seconds is 1/6.
b. between 10 and 30 seconds:
To find the probability that the time between arrivals is between 10 and 30 seconds, we need to find the difference between the CDFs at 30 seconds and 10 seconds:
F(30) - F(10) = 30/120 - 10/120 = 3/12 - 1/12 = 2/12 = 1/6
So, the probability that the time between arrivals is between 10 and 30 seconds is 1/6.
c. more than 35 seconds:
To find the probability that the time between arrivals is more than 35 seconds, we need to subtract the CDF at 35 seconds from 1:
1 - F(35) = 1 - 35/120 = 85/120 = 7/12
So, the probability that the time between arrivals is more than 35 seconds is 7/12.
d. Mean and standard deviation:
The mean of the time between arrivals is given by the average of the lower and upper bounds of the distribution:
mean = (a + b)/2 = (0 + 120)/2 = 60
The standard deviation of the time between arrivals for a uniform distribution is given by:
standard deviation = (b - a)/(2 * sqrt(3))
For this problem, the standard deviation is:
standard deviation = (120 - 0)/(2 * sqrt(3)) = 60/sqrt(3) ≈ 34.64101615
So, the mean time between arrivals is 60 seconds and the standard deviation is approximately 34.64 seconds.
a. The less than 20 seconds 0.1667.
b. The between 10 and 30 seconds 0.1667.
c. The more than 35 seconds 0.7083.
d. The mean and standard deviation of the time between arrivals 34.64 seconds.
To solve the probability questions, to find the probability density function (PDF) of the uniform distribution for the time between customer arrivals. In a uniform distribution, the probability density is constant within the given range.
Given:
Time between arrivals follows a uniform distribution between 0 to 120 seconds.
a. Probability of time between arrivals being less than 20 seconds:
Since the probability density is constant within the given range, we can calculate the probability by dividing the time range of interest (20 seconds) by the total time range (120 seconds).
Probability = (Time of interest) / (Total time range) = 20 / 120 = 1/6 ≈ 0.1667
b. Probability of time between arrivals being between 10 and 30 seconds:
Similar to part (a), the probability for this interval can be found by dividing the time range of interest (30 - 10 = 20 seconds) by the total time range (120 seconds).
Probability = (Time of interest) / (Total time range) = 20 / 120 = 1/6 ≈ 0.1667
c. Probability of time between arrivals being more than 35 seconds:
In this case, we need to calculate the probability of the time between arrivals being in the range from 35 to 120 seconds (as it is more than 35 seconds).
Probability = (Time of interest) / (Total time range) = (120 - 35) / 120 = 85 / 120 ≈ 0.7083
d. Mean and standard deviation of the time between arrivals:
In a uniform distribution, the mean (μ) can be calculated as the average of the minimum and maximum values in the range.
Mean (μ) = (Minimum value + Maximum value) / 2 = (0 + 120) / 2 = 60 seconds
The standard deviation (σ) for a uniform distribution can be calculated using the formula:
Standard deviation (σ) = (Maximum value - Minimum value) / √12
Standard deviation (σ) = (120 - 0) / √12 ≈ 34.64 seconds
So, the mean time between arrivals is 60 seconds, and the standard deviation is approximately 34.64 seconds.
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Raul tried to evaluate an expression step by step. \qquad\begin{aligned} &3 -(-5) - 7\\\\ \\ =&3+5-7&\green{\text{Step } 1}\\\\ \\ =&3+2&\blue{\text{Step } 2}\\\\ \\ =&5&\purple{\text{Step } 3} \\\\ \end{aligned} = = = 3−(−5)−7 3+5−7 3+2 5 Step 1 Step 2 Step 3
Answers
Raul made a mistake in evaluating the expression 3 - (-5) - 7 in B) Step 2 by not following PEMDAS.
What is PEMDAS?PEMDAS means Parentheses, Exponents, Multiplication and Division, Addition and Subtraction from left to right.
PEMDAS refers to the correct order for evaluating mathematical expressions.
The expression 3 - (-5) - 7 should be evaluated as follows:
3 - (-5) - 7
= 3 + 5 - 7
= 8 - 7
= 1
Thus, if Raul did not make a mistake in Step 2, he would have valued the expression as 1.
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Complete Question:Raul tried to evaluate an expression step by step.
3 - (-5) - 7
Step 1: 3 + 5 - 7
Step 2: 3 + 2
Step 3: 5
Find Raul's mistake.
Answer Options:A) Step 1
B) Step 2
C) Step 3
D) Raul did not make a mistake.
Aaron launches a toy rocket from a platform. The graph below shows the height of the
rocket h in feet after t seconds. Find the interval for which the rocket's height is
increasing.
Height (in feet)
240
220
200
1800
160
140
120
100
80
60
40
20
(0, 180)
(1, 196)
(4.5, 0)
Answers
The interval for which the rocket's height is increasing is 0 to 1 second.
What does the graph show?The graph shows the way a toy rocket changes its height once it is launched. In general, it can be seen the height increases for some seconds and then the height decreases.
How to calculate the interval?To calculate the interval let's find out the second or minute at which the rocket loses height.
0 - 1 second (from this moment the rocket loses height)
Based on this, it can be concluded the interval is 0-1 seconds.
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The figure shows a pair of eyeglasses. The lengths RS and TU of the lenses are equal.
Answers
From transitive property of equality, RT = SU.
Given:
RS = TU
What is Segment addition postulate ?
The segment addition postulate states that if we are given two points on a line segment, A and C, a third point B lies on the line segment AC if and only if the distances between the points meet the requirements of the equation AB + BC = AC
Since , from Segment addition postulate
ST = ST
What is addition property of equality ?
The addition property of equality tells us that adding the same number to each side of an equation gives us an equivalent equation. if a-b=c,then a−b+b=c+b, or a=c+b. The same goes with the subtraction property of equality.
Now , by addition property of equality
SU = ST + TU
Similarly,
RT = RS + ST
Now , Using transitive property of equality,
RT = SU
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The circle graph describes the distribution of preferred music from a sample of 400 randomly selected middle school students.
a circle graph titled preferred music, with five sections labeled rock 13 percent, hip hop 25 percent, pop 35 percent, classical 13 percent, and jazz 14 percent
Which of the following conclusions can we draw from the circle graph?
Hip Hop is the preferred music for 25 students.
Together, Pop and Jazz are the preferred music for over half the students.
Classical is the preferred music for 52 students.
Together, Rock and Hip Hop are the preferred music for 172 students.
Answers
The correct conclusion from the given percentage of students of different categories is option(c): Classical is the preferred music for 52 students.
What is meant by percentage?
A figure or ratio stated as a fraction of 100 is called a percentage. It is frequently indicated by the percent sign, "%."
Given,
Total number of middle school students = 400
Percent of students who prefer rock = 13%
Percent of students who prefer hip hop = 25%
Percent of students who prefer pop = 35%
Percent of students who prefer classical = 13%
Percent of students who prefer jazz = 14%
Now we can find the number of students for each category.
Number of students who prefer rock = 13/100 * 400 = 52
Number of students who prefer hip hop = 0.25 * 400 = 100
Number of students who prefer pop = 0.35 * 400 = 140
Number of students who prefer classical = 0.13 * 400 = 52
Number of students who prefer jazz = 0.14 * 400 = 56
We can now look at different options.
a) This is false as hip-hop is preferred by 100 students.
b) Together Pop and jazz are preferred by 140+56 = 196, which is not more than half (200) of students. So this is false.
c) This is true as classical is preferred by 52 students.
d) Together rock and hip hop are preferred by 52+100 = 152, which is not equal to 172. So this is false.
Therefore the correct conclusion from the given percentage of students of different categories is option(c).
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Answer: c
Step-by-step explanation:
I did the test and it’s right
A bag of garden soil weighs 40 pounds and holds 5 cubic feet. Find the weight of 15 bags in kilograms and the volume of 15 bags in cubic yards.
Answers
75
Step-by-step explanation:
I think this is the answer I'm not sure I hope this helps
Solve the quadratic equation by the square root method and write the solutions in radical form. Simplify the solutions.
(3x+20)2=125
Answers
Answer:
Step-by-step explanation:
To solve the equation (3x + 20)^2 = 125 using the square root method, we start by taking the square root of both sides:
√[(3x + 20)^2] = √125
3x + 20 = ± 5
Next, we subtract 20 from both sides:
3x = -20 ± 5
Finally, we divide both sides by 3:
x = -8 or x = 3/3
So, the two solutions to the equation (3x + 20)^2 = 125 are x = -8 and x = 1. These solutions are in radical form and are already simplified.
Help me with this question…..
Answers
Answer:
In order from least to greatest, the numbers would be organized as such: [tex]\frac{2}{3}[/tex] , [tex]\sqrt{5}[/tex] , [tex]\frac{5}{2}[/tex] , [tex]\pi[/tex]. So C is the correct answer.
Step-by-step explanation:
At first glance, these numbers are not the simple whole and decimal numbers one might be used to. However, we can find their approximate values and order them correspondingly. [tex]\frac{2}{3}[/tex] is a fraction that is less than one, so on a number line it would be between 0 and 1, making it the smallest number out of the four. [tex]\sqrt{5}[/tex] and [tex]\frac{5}{2}[/tex] are both between 2 and 3, but [tex]\sqrt{5}[/tex] is approximately equal to 2.24, while [tex]\frac{5}{2}[/tex] is equal to 2.5. Therefore, we can conclude that [tex]\frac{5}{2}[/tex] is greater than [tex]\sqrt{5}[/tex]. Lastly, [tex]\pi[/tex] is a constant number that is the ratio of a circle's circumference to its diameter that equals approximately 3.14, so we can conclude that [tex]\pi[/tex] is the greatest number out of the four.
Now that we have the four numbers in an easier and visually more clear way to find their exact values, we know that the order of these numbers from least to greatest would be choice C: [tex]\frac{2}{3}[/tex] , [tex]\sqrt{5}[/tex] , [tex]\frac{5}{2}[/tex] , [tex]\pi[/tex] .
Have a great day! Feel free to let me know if you have any more questions :)
2
The absolute value function, f(x) = x + 21, is shown.
4
3-
Mark this and return
~
--5-4-3-2-11- 1 2 3 4 5
77774
6
-2+
-3
10
If the graph is reflected over the x-axis, what is the
domain of the function?
TIME REMAINING
37:46
O all real numbers
O all real numbers greater than or equal to 0
Oall real numbers greater than or equal to -2
O all real numbers less than or equal to -2
Save and Exit
Next
Submit
Answers
The correct option regarding the domain of the reflected absolute value function is given as follows:
All real numbers.
How to obtain the domain of a function?The domain of a function is the set that contains all possible input values for the function.
The absolute value function is defined for all real numbers, and the reflection does not change the domain, hence the domain is all real numbers.
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Arturo earns n dollars per hour. Next month he will receive a 2% raise in pay per hour. The expression n + 0.02n is one way to represent Arturo's pay per hour after the raise. Write an equivalent simplified expression that will represent his pay per hour after the raise.
Answers
Answer:
1.02n or 51/50n
Step-by-step explanation:
n + 2% raise = 1.02n and 50/51n
5. Annette bought 8 dozen eggs from Mr. Joseph's Farm Store for $2,800.00. What was the price per dozen?
Answers
In a casee whereby Annette bought 8 dozen eggs from Mr. Joseph's Farm Store for $2,800.00 the price per dozen is $350 per dozen
How can the price per dozen be calculated?The concept that will be use here is division. Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.
The total dozen = 8 dozen eggs
The total price of the 8 dozen eggs $2,800.00
The price per dozen = $2,800.00/ 8 dozen
=$350 per dozen
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Johnny has 3 spring jackets, 2 winter jackets, and 7 running jackets, what is the total number of jackets that Johnny owns?
Answers
Answer:
12
Step-by-step explanation:
3+2+7=12
Hope this helps! Please give brainliest!
Construction each spatial figures
Blue pyramid
Black cown
Yellow cube
Green rectangular prism
Red silendar
Violet sphere
Answers
A pyramid is a three-dimensional geometric shape that has a polygonal base and triangular faces that meet at a common point. The height of a pyramid is the perpendicular distance from the base to the apex.
How to explain the shapesA cube is a three-dimensional shape that has six square faces of equal size. All angles of a cube are right angles, and all edges have the same length. The volume of a cube is given by the formula V = s³ where s is the length of one edge.
A rectangular prism is a three-dimensional shape that has six rectangular faces. The opposite faces are congruent and parallel, and all angles are right angles. The volume of a rectangular prism is given by the formula V = lwh, where l, w, and h are the lengths of the three perpendicular edges.
A sphere is a three-dimensional shape that is perfectly round and has no edges or corners. It is defined as the set of all points in three-dimensional space that are equidistant from a given point called the center. The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere.
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answers please just need help Thank you
Answers
Answer:
162π - 324 (exact) or 184.938
Step-by-step explanation:
You probably don't even need help on this one anymore, its just the same as the previous one I helped you with.
Diameter = a^2 + b^2 = c^2 = 18^2 + 18^2 = c^2
√648 = c (this is exact) so radius is √648/2
Area of square = lw = 324
Area of circle = (√648/2)^2π = (648/4)π = 162π
Area of shaded region = 162π - 324 (exact) or 184.938
BRAINLIEST
QUICKLY HELPP
Answers
Answer:
BEF
What is an angle?An angle is a measure of a turn, measured in degrees or °. Angles are made up of two rays, making the sides of the angle.
What types of angles are there?There are right angles (exactly 90 degrees), acute angles (less than 90 degrees), obtuse angles (more than 90 degrees), and reflex angles (more than 180 degrees).
Looking at the following answers provided, we can see that BEF is a proper angle, because it is made up of two rays in the proper order.
KGH on the other hand, is not. KGH would be a proper angle if it was in the correct order (GHK or KHG), but because it is not in the right order, it is not a proper angle. LEA is not a proper angle either. We know that an angle is made up of two rays, but LEA isn't, and it's the same with ADE.
Answer:
BEF and ADE
Step-by-step explanation:
These points when connected make and angle. The others do not as they sinply dont make sense or have the points in a way that makes the whole statement false.
look at the image below
It's due in 1 hour help Asap
I am giving away 18 points and Will mark brainiest to the correct answer
Answers
Answer:
For -- (1.) 38 / 1 ( apples and baskets)
It is 304 apples distributed evenly among 8 baskets.
For -- (3.) 42 / 1 (apples and baskets)
It is 294 apples distributed evenly among 7 baskets.
Step-by-step explanation:
For the 2nd one, I don't see an answer relating to it. Are there more options when you scroll down?
I hope the other 2 answers helped.
A
B
C
D
Pick a letter
Answers
Answer: D
Step-by-step explanation:
1 in.=1488 milesx5=7440 miles.
Area= pi x r^2
=pi x (7440)^2 or option D.
Hope this helps :)
While on a camping trip with his friends, Finn made a pot of stew over the campfire. He
divided it equally among their 6 bowls. Each bowl had more than 2.5 cups of stew.
Let x represent how much stew Finn made. Which inequality describes the problem?
≥2.5
>2.5
Solve the inequality. Then, complete the sentence to describe the solution.
Finn made more than
cups of stew.
Submit
Answers
The inequality which describes the problem about the pot of stew Finn made is x/6 > 2.5
Which inequality describes the problem?Number of bowls= 6
Quantity of stew in each bowl > 2.5
Quantity of stew Finn made = x
The inequality
Quantity of stew Finn made / Number of bowls > Quantity of stew in each bowl
x/6 > 2.5
Therefore, x divided by 6 greater than 2.5 is the inequality which describes the situation.
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PLEASE HELP!!
i think it wants it in the form of
m = y2-y1
——————
x2-x1
but i could be wrong please please please help if you can it’s greatly appreciated
Answers
a) Two different ways.
x = ln(32)/ln(2)
2^x = 2^5
b) Only the natural logarithm way can be used.
c) x = 3.58
How to solve the equation?We want to solve:
2^x = 32
in two ways.
The first way is trivial, apply the natural logarithm to both sides:
ln(2^x) = ln(32)
x = ln(32)/ln(2)
The second way is the next one:
2^x = 32
The right number can be written as:
4*8 = 32
Now we can factorize the left side:
4*8 = (2*2)*(2*2*2) = 2^5
Replacing that we get:
2^x = 2^5
So we know that x = 5.
b) The second way can't be used to solve:
2^x = 12
Because 12 has a factor different than 2.
c) Using the natural logarithm way:
x = ln(12)/ln(2) = 3.58
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Please help me ASAP THANKS
Answers
Answer:
i think its 1 or 3 or 5 if not what i moslty think it is is (((( 4 )))
Step-by-step explanation:
i hope this helps may luck be with YOU! :)
A researcher establishes that a patient reaction time R in minutes to a dose of particular drug is R(d)=d3+3d2-8where d is the amount of drug in milliliters that absorbed in the patients blood. find the patients reaction time when d=3
Answers
On solving the provided question, we can say that quadratic equation is 46.
What is quadratic equation?A quadratic equation is x ax² +bx +c = 0, which is a quadratic polynοmial in a single variable. a 0. The Fundamental Theοrem of Algebra ensures that it has at least οne solution since this polynomial is of second οrder. Solutions may be simple or cοmplicated.
An equation that is quadratic is a quadratic equatiοn. This indicates that it has at least οne word that has to be squared. The fοrmula "ax² + bx + c = 0" is one of the often used solutions for quadratic equatiοns. where are numerical cοefficients or constants a, b, and c. where the variable "X" is unidentified.
Quadratic equatiοn is
R(d) = d³ +3d² -8
R(3) = (3)³ +3(3)² - 8
R(3) = 27 + 27 - 8
R(3) = 46
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nellie is analyzing a quadratic function f(x) and a linear function g(x). will they intersect?
Yes, at positive x-coordinates
Yes, at negative x-coordinates
Yes, at negative and positive x-coordinates
No, they will not intersect
Answers
Yes, It intersect at positive x-coordinates.
What is Equation of line?The equation of line in point-slope form which passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, Slope (m) = (y₂ - y₁) / (x₂ - x₁)
Given that;
The function f (x) is defined in graph.
Now, The function g (x) is defined as,
⇒ y - 5 = (10 - 5) / (2 - 1) (x - 1)
⇒ y - 5 = 5 (x - 1)
⇒ y - 5 = 5x - 5
⇒ y = 5x
Clearly, By the graph of functions f (x) and g (x), both intersect at positive x - coordinate.
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What’s the correct answer answer asap for brainlist
Answers
The explanation 3 is the path that tells us that the interlopers would have to come between the men in the story.
What is the summary of the passage?The summary here is that the men are faced with a face off. That is they were to fight themselves till they killed themselves.
But while they were to fight they are met with the interloper which is a more ferocious danger that they are facing.
This tells us that they both have more on their plate at the moment.
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what mistake did he make help!!
Answers
Answer: the correct choice is b
Step-by-step explanation:
Figure ABCD is a kite.
Find the value of x.
A
X =
= [?]
14x - 22
H
B
C
Answers
The value of x is equal to 8, in the equation 14x -22.
What is equation?An equation is a mathematical statement consisting of two expressions joined by an equal sign.
Solution:
The diagonals of the dragon intersect at right angles. This gives a solvable relationship for x.
setting the displayed dimensions correspond to 90° angular dimensions.
14x -22 = 90
You can solve this two-level linear equation in the usual way.
14x = 112. . . . . . Step 1, add the reciprocal of the constant to get just x
x = 112/14 = 8 . . . Step 2, divide by the factor of x
Hence, the value of x is 8.
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Graph the following equation -3y+6x+=6
Answers
Answer:
Step-by-step explanation: Here's a step-by-step guide on how to graph the equation -3y + 6x = 6:
Isolate y: To isolate y, first subtract 6x from both sides of the equation: -3y + 6x = 6 => -3y = -6x + 6.
Divide both sides of the equation by -3: Dividing both sides of the equation by -3, we get: -3y / -3 = (-6x + 6) / -3.
Simplify the equation: On simplifying the equation, we get: y = 2x - 2.
Plot the y-intercept: The y-intercept of the equation is when x = 0. So, when x = 0, y = 2 * 0 - 2 = -2. This point is (0, -2). Plot this point on the graph.
Plot a second point: Pick a value of x and plug it into the equation to find the corresponding y value. For example, let's take x = 1. Plugging x = 1 into the equation, we get y = 2 * 1 - 2 = 0. This point is (1, 0). Plot this point on the graph.
Draw the line: Connect the two points plotted on the graph. This line represents the solution set of the equation.
That's it! You have successfully graphed the equation -3y + 6x = 6.
Answer:
Step-by-step explanation:
Evaluate the limit limx approches 0 x square+ x over x
Answers
Step-by-step explanation:
If we use direct substitution, we will get
[tex] \frac{0}{0} [/tex]
Which is intermediate from so we must use.algebraic manipulation
Let's divide everything by x
We would get
[tex] \frac{x + 1}{1} [/tex]
So the limit as x approaches 0 is
[tex]1[/tex]
Proof using a graph:
As x gets close and closer to 0, f(x) approaches 1. Limits does not care about discontinuity, only what the function gets closer to.
Describe the transformation given to the parent function f(x)=sin(x) given the graph of the equation g(x)=sin(3x)-4
A:The graph is vertically stretched by a factor of 1/3 and shifts up 4 units.
B:The graph is vertically stretched by a factor of 1/3 and shifts down 4 units.
C:The graph is horizontally compressed by a factor of 1/3 and shifts up 4 units.
D:The graph is horizontally compressed by a factor of 1/3 and shifts down 4 units.
Answers
The transformation given to the parent function f(x)=sin(x) given the graph of the equation g(x)=sin(3x)-4 will be C. The graph is horizontally compressed by a factor of 1/3 and shifts up 4 units.
How to explain the transformationThe parent function f(x) = sin(x) has been transformed by replacing x with 3x in the argument of the sine function.
This results in a horizontal compression of the graph by a factor of 1/3. In addition, the graph of g(x) = sin(3x) is shifted upward 4 units, as indicated by the subtraction of 4 from the value of the sine function.
The correct option is C.
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