The real roots of the equation x^(2/3) + x^(1/3) - 2 = 0 are 1 and -8.
The equation x^(2/3) + x^(1/3) - 2 = 0 does not have any real roots. Since the exponents are not integers, x^(2/3) and x^(1/3) are not defined for negative values of x, and so the equation has no solutions for real values of x.
But,
Let y = x^(1/3)
The equation x^(2/3) + x^(1/3) - 2 = 0 will become y² + y - 2 = 0.
Solving for the roots of this equation,
y² + y - 2 = 0
(y + 2)(y - 1) = 0
y = -2 ; y = 1
Substitute the value of y and solve for x.
y = x^(1/3)
-2 = x^(1/3) ; 1 = x^(1/3)
x = -8 ; x = 1
Therefore, the real roots of the equation is 1 and -8.
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John gains 5% by selling a book for 273. Find the cost price of the book
Answer:
$260
Step-by-step explanation:
$273 - 5% = $260
5% commission = $13
Answer:
260
Step-by-step explanation:
273-5%=260
7. The rectangle below is dilated by a scale factor of
3.6
to create a new rectangle. Which of the following
could be the dimensions of the new rectangle?
The new dimension of the rectangle is 14.4 cm ×5.4 cm option (A) is correct if the rectangle is dilated by a scale factor of 3.6.
What is dilation?The transformation dilation is used to resize an item. Dilation is a technique for making items appear larger or smaller. The image created by this transformation is identical to the original shape.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have a rectangle shown in the picture.
The width of the rectangle = 1 1/2 = 3/2 = 1.5 cm
The length of the rectangle = 4 cm
The rectangle is dilated by a scale factor of 3.6:
The new width of the rectangle = 1.5×3.6 = 5.4 cm
The new length of the rectangle = 4×3.6 = 14.4 cm
The dimension of the new rectangle = 14.4 cm ×5.4 cm
Thus, the new dimension of the rectangle is 14.4 cm ×5.4 cm option (A) is correct if the rectangle is dilated by a scale factor of 3.6.
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A bag contains 2 snicker bars, 8 trix bars , and 5 crunch bars. A candy is chosen, replaced, then another is chosen, what is the probability of choosing a trix bar then a crunch bar?
The probability of choosing a trix bar then a crunch bar exists 8/45.
What is Probability?Mathematics' field of probability deals with numerical assessments of how likely an event is to occur.
Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.
The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities.
Probability = Number of favorable outcome / Number of total outcome
Given,
Number of snicker bars = 2
Number of trix bars = 8
Number of crunch bars = 5
Total number of candy bars = 2 + 8 + 5 = 15
8 trix, so picking a trix would be 8/15
5 crunch bars, picking a crunch would be 5/15, which reduces to 1/3
Probability of both: 8/15 x 1/3 = 8/45
Therefore, the probability of choosing a trix bar then a crunch bar exists 8/45.
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The probability of choosing a trix bar then a crunch bar exists 8/45.
What is Probability?Probability theory deals with numerical evaluations of the likelihood that an event will occur.
Probabilities are mathematical explanations of the likelihood that an event will occur or that a proposition is true. The likelihood of an event is represented by a number between 0 and 1, with 0 typically signifying impossibility and 1 typically signifying certainty.
A probability represents the likelihood or chance that a particular occurrence will take place. Probabilities can be expressed as ratios between 0 and 1, or as percentages between 0% and 100%.
Probability = Number of favorable outcome / Number of total outcome
Given,
Number of snicker bars = 2
Number of trix bars = 8
Number of crunch bars = 5
Total number of candy bars = 2 + 8 + 5 = 15
8 trix, so picking a trix would be 8/15
5 crunch bars, picking a crunch would be 5/15, which reduces to 1/3
Probability of both: 8/15 x 1/3 = 8/45
Therefore, the probability of choosing a trix bar then a crunch bar exists 8/45.
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How do you find the missing side of an obtuse triangle?
Answer:
Using the cosines law
Step-by-step explanation:
So, we need to find the length of the other side, we will use the version of the Cosine Rule where a2 is the subject of the formula, which is given by, a2=b2+c2−2bccosA, Side a is the one we are trying to find. Sides band care the other two sides, and angle Ais the angle opposite side a. c2=a2+b2−2abcosC
1) Alice decides to take a trip from the East Coast of the United States to the West Coast. While planning, she chooses to drive, fly, and ride a train. Her first leg of the trip is traveling by car, from Sacramento, California to Denver, Colorado. Along the way, she fills up her tank using regular unleaded gas, costing $4.65 per gallon, and premium gas, $4.95 per gallon. After driving for many hours, Alice finally makes it to Denver, Colorado spending $874.80 in gas.
a) Let r represent gallons of regular unleaded gas and let p represent gallons of premium gas. Create an equation that models the situation.
b) If Alice purchases 87 gallons for regular unleaded gas, how many gallons of premium gas did she purchase? Show all work to receive full credit.
2) After spending a week in Denver, Alice decides to leave her car at a friend’s house in order fly from Denver, Colorado to Chicago, Illinois. Her plane ticket cost $475 and $35 per checked bag.
a) Write a function that models the number of checked bags, b, as it relates to the total cost, c(b).
b) Compete the table
Number of Bags (b) Total Cost c(b)
0
1
2
3
4
6
8
3) After spending time in Chicago, Alice decides to finish her trip by riding a train 700 miles to Washington D.C. The train travels at an average speed of 80mph. Answer the following questions using the graph.
a) Describe the y-intercept in this scenario.
b) Describe the x-intercept in this scenario
c) Finish the ordered pairs (2.5, ____ ) and (____,300).
d) What are the domain and range?
Domain: {h I ___ < h < ____}
Range: {f(h) I ___ < f(h) < ____}
We see Alice chose a journey to travel from the East coast United States to the West Coast. She had a starting place and ending place in mind and did not aimlessly find her way from Sacramento, California to Washington D.C. But rather, she made decisions along the way to accomplish her goal. One could also say your life is like a journey or race in which you are running. 1 Corinthians 9:24-25 (NIV version) says, “Do you not know that in a race all the runners run, but only one gets the prize? Run in such a way as to get the prize. Everyone who competes in the games goes into strict training. They do it to get a crown that will not last, but we do it to get a crown that will last forever.” How do you interpret this passage in the bible and what does it look like in your life?
All Answers:
1a) The equation that models the situation is: 4.65r + 4.95p = 874.80
1b) Using the equation from part 1a, we know that 4.65r + 4.95p = 874.80. If we know that Alice purchased 87 gallons of regular unleaded gas, we can substitute that value into the equation: 4.65(87) + 4.95p = 874.80. Solving for p, we get: 4.65(87) + 4.95p = 874.80
4.0995 + 4.95p = 874.80
4.95p = 869.805
p = 175.6 gallons
2a) The function that models the number of checked bags, b, as it relates to the total cost, c(b), is: c(b) = 35b + 475.
2b) Number of Bags (b) Total Cost c(b)
0 475
1 510
2 545
3 580
4 615
6 675
8 835
3a) The y-intercept in this scenario represents the total distance travelled when the time spent on the trip is zero. As the distance traveled is 700 miles when time is zero, the y-intercept is (0,700)
3b) The x-intercept in this scenario represents the total time spent on the trip when the distance travelled is zero. As time is zero when the distance traveled is zero, the x-intercept is (0,0)
3c) (2.5, 200) (10, 300)
3d) The domain and range are based on the permissible values of time and distance travelled. Based on the information provided, the domain would be {h | 0 < h < 10} and the range would be {f(h) | 0 < f(h) < 700}
About the last part of the question, it is referring to the fact that life is like a journey, and we should strive to be like runners who run to win the prize, not just to participate. This passage encourages us to put in the hard work and dedication necessary to achieve our goals in life, and to not be satisfied with simply going through the motions. It also reminds us that our ultimate goal should be eternal reward, not temporary ones. In your life, it might mean setting a goal, making a plan, and putting in the effort to achieve it, but also keeping a perspective of what is important in the long run, not just in the short run.
Help me please I would really appreciate it
Step-by-step explanation:
The coordinates of the points are P1(2, 2) and P2(10, 2). The distance d between these two points are given by
[tex]d = \sqrt{ {(x\frac{}{2} - x\frac{}{1} ) }^{2} + ({y\frac{}{2} - y\frac{}{1}) }^{2} } \\ = \sqrt{ ({10 - 2})^{2} +( {2 - 2)}^{2}} \\ = 8[/tex]
Make a tree diagram to show sample space. Then select the total number of outcomes.
rolling a number cube, tossing a coin and choosing a card from cards marked A and B
a. 24
C.
18
b. 12
d. 6
HELP PLEASE
Answer:
a. 24
Step-by-step explanation:
Rolling a number cube: 6 outcomes
tossing a coin: 2 outcomes
At this point, we have 6 x 2 = 12 outcomes, because each of the 6 numbers on the cube can each have a heads or tails outcome
Choosing card A or card B gives us 2 more outcomes for each of the 12 outcomes we have so far.
12 x 2 = 24
The median is __________________ a value in a data set
A) never
B) always
C) sometimes
AG= 2y-3= feet
BG= 6x-2.5= feet
is this a question or a answer
Find the volume of the prism.
Answer:
1120
Step-by-step explanation:
Is 2 by 7 recccuring decimal or terminating decimal
Given:
The number is 2 by 7.
To find:
Whether 2 by 7 recurring decimal or terminating decimal.
Solution:
If all the prime factors of denominator value of a fraction is either 2 or 5 or both, then the fraction is terminating decimal.
If the prime factors of denominator value of a fraction is other than 2 or 5 , then the fraction is recurring decimal.
The given number is:
[tex]\dfrac{2}{7}[/tex].
The denominator value is 7 and prime factor of 7 is 7, which is different from 2 and 5.
Therefore, the number 2 by 7 is recurring decimal.
How many one-cup servings of milk are in a two-liter bottle? Round your answer to the nearest tenth.
____________one-cup servings
The number of cups of serving that is possible in a two-liter bottle is 8.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
We know 1 liter is equal to 4 cups.
Therefore, The number of cups serves possible in a two-liter bottle is,
= (2×4) cups.
= 8 cups.
So, 8 cups of servings are possible from a two-liter bottle.
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Martina walked 34 of a mile in 35 of an hour. At this rate, how far can Martina walk in one hour?
Answer:
34 = 35
Step-by-step explanation:
34x35
Answer:
Martina can walk 1 1/4 miles in one hour.
Step-by-step explanation:
Find the reciprocal of 3/5 (by flipping the fraction)
5/3
Multiply 5/3 by 3/4
3/4(5/3)= 15/12= 1 1/4
Help ill give u brainliest when I can
Answer:
A)82
b)16807
c)10
d)625
Step-by-step explanation:
a: 3^4 or 81
b 7^5. 16807
c 10^2 or 100
d 5^7 78125
Please help, will give brainliest, 5 star, and thanks!
Answer:
[tex]y\geq -2[/tex]
Step-by-step explanation:
Credit: Desmos
Can you please help with this question
In a word game, 1 letter is worth 1 point. This dot plot shows the scores for 20 common words. What is the first quartile (Q1)?
Answer:
5
Step-by-step explanation:
Write a rule to describe each reflection.
Rule:r() (x,y)=()
Who ever answers this question will get 25 points.
Answer: ok so if it is ok im sorry but like how is it like is there supposed to be a number? im sorryyy i thught i had it before i saw the picture
Step-by-step explanation:
y=-3x+15 create a word problem
Answer:
John starts with $12 dollars in his bank account, each day he spends $3.
Step-by-step explanation:
please help no links please??
Answer:
5(3)² - 4
5x9-4
the answer is 41
Answer:
41
Step-by-step explanation:
5(9) - 4
45-4
41
........... I donr know what I'm doing-
Intercept = 1
Equation - y = -(2/5)x + 1
If 5 inches is added to both the length and the width of a rectangle, then the
perimeter is increased by -
Answer
the perimeter is increased by 5
Step-by-step explanation:
If 5 inches is added to both sides of the rectangle. Then the perimeter of the rectangle is increased by 20.
What is the perimeter of the rectangle?Let W be the rectangle's width and L its length.
The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be
Perimeter of the rectangle = 2(L + W) units
If 5 inches is added to both the length and the width of a rectangle.
Then the new perimeter of the rectangle is given as,
P = 2[(L + 5) + (W + 5)]
P = 2[L + W + 10]
P = 2(L + W) + 20
If 5 inches is added to both sides of the rectangle. Then the perimeter of the rectangle is increased by 20.
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A truck uses 2.5 litres of fuel to travel 8 kilometres.
a How far will the truck travel on 1 litre of fuel?
b How far will the truck travel on 120 litres of fuel?
Answer:
a：20 km
b：384
Step-by-step explanation:
a：
[tex] \frac{2.5}{ 8} = \frac{1}{x} [/tex]
[tex]x = 20[/tex]
b：
[tex] \frac{2.5}{8} = \frac{120}{y} [/tex]
[tex]y = 384[/tex]
10.)The charge for electricity consumption, E,
is partly constant and partly varies as the
number N of units used. The charge for 163
units is N453.80 while the charge for 42 units
is #139.20.
a Calculate the charge per unit of
electricity.
b Obtain a formula for E in terms of N.
On solving the provided question, we can say that - the charge for 42 units = is $139.20; so, charge per unit is 139.20/42 = $3.3142857143
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
here,
the charge for 42 units = is $139.20.
so, charge per unit is 139.20/42 = $3.3142857143
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in is 26 miles into a 62-mile backpacking trip in the wilderness. Jin ca
ike 6 miles per day. How many more days does Jin need to finish?
Jin needs how many
more days.
Answer:6 days
Step-by-step explanation:
62-26=36
36/6=
6
I need help I don’t get it
Answer:
its 2:3 if im not wrong
Step-by-step explanation:
Consider a species that occupies a large, but fixed, number of islands. The distribution of the species across all islands is maintained by a balance between local extinctions and local colonization events. Devise a model for the relationship between the fraction of islands occupied by the species and time. Be clear to outline the assumptions you make and be sure to describe your key predictions
The most probable prediction( according to biogeography theory of islands) for this situation would be continued colonization of large species population( due to balance between immigration and extinction of species) through time on the island.
What is species?A species is a unit of biodiversity as well as the fundamental classification and taxonomic rank of an organism in biology.
Given:
Consider a species that occupies a large, but fixed, number of islands.
The distribution of the species across all islands is maintained by a balance between local extinctions and local colonization events.
According to island biogeography theory the population of an island is maintained constant through time when the immigration rate of new species to the island and extinction rate of species in the island is constant.
In a model for the relationship between the fraction of islands occupied by species and time, if the number of new species immigrating to the island will be equal to the number of species that become extinct in the island species population and will thrive continuously through time( will never become extinct) as the island species population will be maintained due to the existence of a dynamic equilibrium of species in the island.
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PLEASE HELP IM LOST ILL GIVE BRAINLIEST
Answer:
c. The Median is 46, not 45
Find the vertices and foci of the hyperbola with equation quantity x plus 4 squared divided by 9 minus the quantity of y plus 3 squared divided by 16
Vertices are at (-7, 5) and (-1, 5) and foci are at (-9, 5) and (1, 5) of the hyperbola with equation quantity x plus 4 squared divided by 9 minus the quantity of y plus 3 squared divided by 16.
As per the given data the given equation is:
[tex]\\$$\frac{ (x+4)^2}{9} - \frac{(y-5)^2 }{16}=1$$[/tex]
The standard form for the equation of a hyperbola with center (h, k) is [tex]\frac{(x-h)^{2} }{a^{2} } - \frac{(y-k)^2}{b^{2} } =1[/tex]
Your hyperbola opens left/right, because it is of form x - y.
Comparing terms, we find that
h = -4, k = 5, a = 3, y = 4
In the general equation, the coordinates of the vertices are at [tex]$(h \pm a, k)$[/tex].
Thus, the vertices of your hyperbola are at (-7,5) and (-1,5).
The foci are at a distance c from the center, with coordinates [tex]$(\mathrm{h} \pm \mathrm{c}, \mathrm{k})$[/tex], where [tex]$c^2=a^2+b^2$[/tex]
[tex]c^2=9+16=25$[/tex], so c = 5.
The coordinates of the foci are (-9, 5) and (-1, 5).
The Figure below shows the graph of the hyperbola with its vertices and foci.(attached at the end of solution)
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Triangle A and triangle B are drawn on the grid. Describe fully the single transformation which maps triangle A onto triangle B.
Answer:
Step-by-step explanation:
Triangle A, transforms into a smaler size, and goes into full shape. Triangle B, goes into the negative numbers.