Answers
Representing intervals as we are doing for your question means we will represent all the possible values of x. To do that we will colour in blue all possible values of x but there is a detail we must to consider. The limits of the interval. for that we have two symbols, [ that means "closed on the value" and ( that means "opened on the value". So if there is a [ on a number it means that number makes part of the interval, but if there is a ( it means that number is not in the interval.
Now, for our inequality we have
Once x can be equal or superior to 2 it means 2 is part of the interval because x can be this value, but x is inferior to 8 but it can not be 8 so 8 is not on the interval. Once we know that, know we can represent our interval as follows:
And that is our final answer.
For an interval notation we can write [2,8).
Related Questions
Solve. 4 + x/7 = 2Question 3 options:12-144210
Answers
1) Since we have a Rational Equation let's proceed with that, isolating the x on one side and then we can get rid of that fraction. This way:
[tex]\begin{gathered} 4+\frac{x}{7}=2 \\ 4-4+\frac{x}{7}=2-4 \\ \frac{x}{7}=-2 \end{gathered}[/tex]Notice that now, we're going to get rid of that fraction on the left side, multiplying it by 7 (both sides) :
[tex]\begin{gathered} 7\times\frac{x}{7}=-2\times7 \\ x=-14 \end{gathered}[/tex]Thus, the answer is -14
Identify each of the following statements as true or false in relation to confidence intervals (CIs).
Answers
Let's analyze each sentence to check if it is true or false:
First:
This sentence is true, the confidence interval is an interval where the true mean is likely to be.
Second:
This sentence is true, with a sample size smaller than 30, it is better to use the t-distribution instead of the normal distribution.
Third:
This sentence is true, the confidence interval is not a 100% guarantee that the true mean will be inside it.
Fourth:
Ti s sentence is true, this theorem states that when getting a large enough sample of a distribution with mean and standard deviation, the sample will be approximately normally distributed.
Fifth:
This sentence is false, because the number of degrees of freedom is 1 less than the sample size, so it would be 10.
Therefore the answer is:
True, True, True, True, False.
A forest products company claims that the amount of usable lumber in its harvested trees averages142 cubic feet and has a standard deviation of 9 cubic feet. Assume that these amounts haveapproximately a normal distribution.1. What percent of the trees contain between 133 and 169 cubic feet of lumber? Round to twodecimal places.II. If 18,000 trees are usable, how many trees yield more than 151 cubic feet of lumber?
Answers
1) Considering that the amount of lumber in this Data Set has been normally distributed, then we can start by finding this Percentage (or probability in this interval, writing out the following expressions:
[tex]\begin{gathered} P(133Now we can replace it with the Z score formula, plugging into that the Mean, the Standard Deviation, and the given values:[tex]Z=\frac{X-\mu}{\sigma}[/tex]Then:
[tex]\begin{gathered} P(\frac{133-142}{9}<\frac{X-\mu}{\sigma}<\frac{169-142}{9}) \\ P(-1Checking a Z-score table we can state that the Percentage of the trees between 133 and 169 ft³ is:[tex]P(-12) Now, let's check for the second part, the number of trees. But before that, let's use the same process to get a percentage that fits into that:[tex]\begin{gathered} P(X>151)=\frac{151-142}{9}=1 \\ P(Z>1)=0.1587 \end{gathered}[/tex]Note that 0.1587 is the same as 15.87%. Multiplying that by the total number of trees we have:
[tex]18000\times0.1587=2856.6\approx2857[/tex]Rounding it off to the nearest whole.
3) Thus, The answers are:
i.84%
ii. 2857 trees
Production has indicated that they can produce widgets at a cost of $16.00 each if they lease new equipment at a cost of $40,000. Marketing has estimated the number of units they can sell at a number of prices (shown below). Which price/volume option will allow the firm to avoid losing money on this project?
Answers
The price/volume option that will allow the firm to avoid losing money on this project is C. 2,300 units at $34.00 each.
How is this option determined?To determine the correct option, we use the cost-volume-profit analysis tool.
The cost-volume-profit (CVP) analysis involves determining how the volume of sales drives profitability.
The CVP technique classifies costs into their variable and fixed cost elements for the purpose of this analysis.
Variable cost per unit = $16
Fixed cost = $40,000
Option A Option B Option C Option D Option E
Sales units 3,000 1,900 2,300 2,500 1,700
Unit selling price $29 $36.50 $34 $31.50 $39
Sales revenue $87,000 $69,350 $78,200 $78,750 $66,300
Variable costs 48,000 30,400 36,800 40,000 27,200
Fixed cost 40,000 40,000 40,000 40,000 40,000
Total costs 88,000 70,400 76,800 80,000 67,200
Thus, the price/volume option that meets the firm's goal is Option C because the sales revenue exceeds the total costs.
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Question Completion with Price/Volume Options:A. 3,000 units at $29.00 each.
B. 1,900 units at $36.50 each.
C. 2,300 units at $34.00 each.
D. 2,500 units at $31.50 each.
E. 1,700 units at $39.00 each.
3. You draw one card from a standard deck.(a) What is the probability of selecting a king or a queen? (b) What is the probability of selecting a face card or a 10? (c) What is the probability of selecting a spade or a heart? (d) What is the probability of selecting a red card or a black card?
Answers
Given:
The objective is to find,
a) The probability of selecting a king or a queen.
b) The probability of selecting a face card or a 10.
Explanation:
The total number of cards in a deck is, N = 52 cards.
a)
Out of 52 cards, the number of king cards is,
[tex]n(k)=4[/tex]Similarly, out of 52 cards, the number of queen cards is,
[tex]n(q)=4[/tex]Then, the probability of drawing one out of 4 king cards or one out of 4 queen cards can be calculated as,
[tex]\begin{gathered} P(E)=P(k)+P(q) \\ =\frac{n(k)}{N}+\frac{n(q)}{N} \\ =\frac{4}{52}+\frac{4}{52} \\ =\frac{8}{52} \end{gathered}[/tex]Hence, the probsability of selecting a king or a queen is (8/52).
b)
Out of 52 cards, the number of face cards is 12.
[tex]n(f)=12[/tex]Similarly, out of 52 cards, the number of 10 is,
[tex]n(10)=4[/tex]Then, the probability of drawing one out of 12 face cards or one out of 4 ten cards can be calculated as,
[tex]\begin{gathered} P(E)=P(f)+P(10) \\ =\frac{12}{52}+\frac{4}{52} \\ =\frac{12+4}{52} \\ =\frac{16}{52} \end{gathered}[/tex]Hence, the probability of selecting a face card or a 10 is (16/52).
c)
Out of 52 cards, the number of spade cards is 13.
[tex]n(s)=13[/tex]Similarly, out of 52 cards, the number of heart cards is 13.
[tex]n(h)=13[/tex]Then, the probability of drawing one out of 13 spade cards or one out of 13 heart cards can be calculated as,
[tex]\begin{gathered} P(E)=P(s)+P(h) \\ =\frac{n(s)}{N}+\frac{n(h)}{N} \\ =\frac{13}{52}+\frac{13}{52} \\ =\frac{26}{52} \end{gathered}[/tex]Hence, the probability of selecting a spade or a heart is 26/52.
d)
Out of 52 cards, the number of red cards is,
[tex]n(r)=26[/tex]Out of 52 cards, the number of black cards is,
[tex]n(b)=26[/tex]Then, the probability of drawing one out of 26 red cards or one out of 26 black cards is,
[tex]\begin{gathered} P(E)=P(r)+P(b) \\ =\frac{n(r)}{N}+\frac{n(b)}{N} \\ =\frac{26}{52}+\frac{26}{52} \\ =\frac{52}{52} \\ =1 \end{gathered}[/tex]Hence, the probability of selecting a red card or a black card is 1.
Abdul will rent a car for a day. The rental company offers two pricing options: Option A and Option B. For each pricing option, cost (in dollars) depends on miles driven, as shown below.
Answers
From the graph, we are to determine the following:
(a) We are to find the option that costs less if Abdul drives 300 miles of the rental car and also how much less is it from the other option.
Option A: when x = 300, y = 140
Option B: when x = 300, y = 120
So the difference is:
140 - 120 = 20
So the option that costs less is B
And it costs $20 lesser than option A
(b) For what number of miles does the option costs the same and if Abdul drives less than that amount, what option cost more.
Option A: when x = 100, y = 60
Option B: when x = 100, y = 60
Therefore, the number of miles where the options cost the same is 100 miles.
If Abdul drives less than the amount:
That is x < 100, the B > A,
Which means, if Abdul drives less than 100 miles, Option B, costs more.
Let f(t) = 3 + 2, g(x) = -x^2?, andhe) = (x - 2)/5. Find the indicated value:24. h (g(5))
Answers
The Solution to Question 24:
Given the function below:
[tex]\begin{gathered} g(x)=-x^2 \\ h(x)=\frac{x-2}{5} \end{gathered}[/tex]We are asked to find the value of h(g(5)).
Step 1:
We shall find g(5) by substituting 5 for x in g(x).
[tex]g(5)=-5^2=-25[/tex]So that:
[tex]h(g(5))=h(-25)[/tex]Similarly, we shall find h(-25) by substituting -25 for x in h(x).
[tex]h(-25)=\frac{-25-2}{5}=\frac{-27}{5}[/tex]Therefore, the correct answer is
[tex]\frac{-27}{5}[/tex]4. Solve the polynomial.
7x³ + 21x² - 63x = 0
Answers
After solving the given polynomial (7x³ + 21x² - 63x = 0), the value of x are (x = 0) and {x = [(-3 ± 3√5)/2]}
What is a polynomial?An expression that consists of variables, constants, and exponents and is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable). A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x² 4x + 7 is an illustration of a polynomial with a single indeterminate x.So, 7x³ + 21x² - 63x = 0:
Now, solve for x as follows:
7x³ + 21x² - 63x = 07x(x² + 3x - 9) = 0Zero factor principal, if ab = 0, then a = 0 and b = 0.
x = 0 and x² + 3x - 9 = 0Now, x² + 3x - 9 = 0:
x = [(-3 ± 3√5)/2]x = 0Therefore, after solving the given polynomial (7x³ + 21x² - 63x = 0), the value of x are (x = 0) and {x = [(-3 ± 3√5)/2]}
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#17 - A bin contains 90 batteries (all size C). There are 30 Eveready, 24 Duracell, 20 Sony,10 Panasonic, and 6 Rayovac batteries. What is the probability that the battery selected is aDuracell?0 27.6%0 26.7%24.6%0 29.2%
Answers
According to the basic definition of probability,
[tex]\text{Probability}=\frac{\text{ No. of favorable events}}{\text{ Total no. of events}}[/tex]Given that the bin contains total 90 batteries, out of which 24 are duracell.
So the probability that a randomly selected battery is Duracell, is calculated as,
[tex]\begin{gathered} P(\text{Duracell)}=\frac{\text{ No. of Duracell Batteries}}{\text{ Total no. of batteries}} \\ P(\text{Duracell)}=\frac{24}{90} \\ P(\text{Duracell)}\approx0.267 \\ P(\text{Duracell)}\approx26.7\text{ percent} \end{gathered}[/tex]Thus, the probability that a randomly selected battery is Duracell, is 26.7% approximately.
Given a triangle ABC at points A = ( - 2, 2 ) B = ( 2, 5 ) C = ( 2, 0 ), and a first transformation of right 4 and up 3, and a second transformation of left 2 and down 5, what would be the location of the final point B'' ?
Answers
Answer
a. (4, 3)
Step-by-step explanation
The translation of a point (x, y) a units to the right and b units up transforms the point into (x + a, y + b).
Considering point B(2, 5), translating it 4 units to the right and 3 units up, we get:
B(2, 5) → (2+4, 5+3) → B'(6, 8)
The translation of a point (x, y) c units to the left and d units down transforms the point into (x - c, y - d).
Considering point B'(6, 8), translating it 2 units to the left and 5 units down, we get:
B'(6, 8) → (6 - 2, 8 - 5) → B''(4, 3)
Answer: The answer would be (4,3)
Step-by-step explanation: because if you started with (2,5), which would be (x,y) x goes left and right, and y goes up and down, and the questions says that you have to go 4 to the right and 3 up, then add 4 to 2, which is 6, and 3 to 5, which is 8, so now you have the point (6,8), then the second translation would be 2 to the left, and down 5, this is negative so you subtract this time, so subtract 2 from 6, which is 4, and 5 from 8, which is 3, so your final answer is (4,3).
1) There is a proportional relationship between the number of months a person has had a streaming movie subscription and the total amount of money they have paid for the subscription. The cost for 6 months is $47.94. The point (6,47.94) is shown on the graph below. 180 160 140 120 100 cost (dollars) 80 60 (6, 47.94) 40 20 16 18 8 20 22 2. 4 6 10 12 14 time (months)
Answers
Given:
The point which describes the relationship between the months and total amount is, (6, 47.94).
a) To find the constant proportionality:
6 months =47.94
Then, for 1 month,
[tex]\frac{47.94}{6}=7.99[/tex]Hence, the constant proportionality is $7.99.
b) The constant proportionality tells that, if the month is increased then the cost is also increased by $7.99.
c) To find the three more points and label it:
For the month, m=1, then the cost c=$7.99
For the month, m=2, then the cost c=$15.98
For the month m=3, then the cost c=$23.97
Therefore, the three points are (1, 7.99), (2,15.98) and (3, 23.97).
The graph is,
d) The relationship between the months and the cost is,
C=7.99 m
jessica bought 4 gallons of paint. Jessica needed to use 3/4 of the paint to paint her living room and dining room. How many gallons did she use, write the number of gallons.
Answers
Jessica bought 4 gallons of paint. Of that, she used 3/4 to paint. So the ammount she used was
[tex]4\cdot(\frac{3}{4})=\frac{4\cdot3}{4}=3[/tex]So she used 3 gallons of paint.
Read the problem below and find the solution. Use a model or act the
problem out to help solve it.
A group of 24 students have recess together. They are making teams to play
a game. Each team has to have exactly 5 players, and no one can be on more
than one team. How many teams can they make? (It is possible that not
everyone can be on a team.)
Answers
Answer:
possible
Step-by-step explanation:
The table shows the total cost c for the number of aquarium tickets purchased t. Write an equationthat can be used to find the cost c oft aquarium tickets. Use the equation and complete the table tofind the cost of 7 tickets.7Number of Tickets, tCost, cWrite an equation3$29.2510 12$97.50 $117.00(Use the operation symbols in the math palette as needed. Use integers or decimals for any numbers in the equatioDo not include the $ symbol in your answer.)
Answers
We can model the cost and number of tickets by a linear equation of the form
[tex]c=mt+b[/tex]Where c is the cost, t is the number of tickets.
m is the slope of the equation and b is the y-intercept.
First, let us find the slope which is given by
[tex]m=\frac{c_2-c_1}{t_2-t_1}[/tex]You can take any two pairs of values from the table.
[tex]m=\frac{117-97.50}{12-10}=\frac{19.5}{2}=9.75[/tex]The slope is 9.75 and the equation becomes
[tex]c=9.75t+b[/tex]Now we need to find the y-intercept (b)
Choose any one pair of values from the table and substitute them into the above equation and solve for b.
Let's choose (12, 117)
[tex]\begin{gathered} c=9.75t+b \\ 117=9.75(12)+b \\ 117=117+b \\ b=117-117 \\ b=0 \end{gathered}[/tex]The y-intercept is 0 so the equation is
[tex]c=9.75t[/tex]Now to find the cost of 7 tickets, simply substitute t = 7 into the above equation
[tex]\begin{gathered} c=9.75t \\ c=9.75(7) \\ c=68.25 \end{gathered}[/tex]Therefore, the cost of 7 tickets is $68.25
The safe load, L, of a wooden beam of width w, height h, and length l, supported at both ends, varies directly as the product of the width and the square of the height, and inversely as the length. A wooden beam 5 inches wide, 8 inches high, and 216 inches long can hold a load of 7670 pounds. What load would a beam 3 inches wide, 5 inches high, and 240 inches long of the same material, support? Round your answer to the nearest integer if necessary.
Answers
we know that
L=KW(h^2)/l
we have that
W=5 in
h=8 in
l=216 in
L=7670 pounds
step 1
Find the value of K (constant of proportionality)
substitute the given values in the equation
7670=K(5)(8^2)/216
7670=k(1.4815)
k=5,177.25
step 2
we have the equation
L=(5,177.25)W(h^2)/l
for
W=3 in
h=5 in
l=240 in
substitute in the equation and solve for L
L=(5,177.25)(3)(5^2)/240
L=1,617.89 pounds
Round your answer to the nearest integer
so
L=1,618 pounds
For the function f(x)=3x2−4x−4,a. Calculate the discriminant.b. Determine whether there are 0, 1, or 2 real solutions to f(x)=0.
Answers
Answer:
a) Using the formula for the discriminant we get:
[tex]\begin{gathered} \Delta=(-4)^2-4(3)(-4), \\ \Delta=16+48, \\ \Delta=64. \end{gathered}[/tex]The discriminant is 64.
b) Based on the above result we know that the f(x)=0 has 2 real solutions,
ave read 14 pages in 28 minutes how much pages can she read for 50 minutes
Answers
Answer:
Step-by-step explanation:
14x2=28
50 divided by 2 = 25 pages
14pages=28mins
page=2mins
so
pages =50/2
=25
Please help this is due tomorrow!!
Answers
The expression 2x⁷· y⁴ would be equivalent to the given polynomial expression.
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
The given polynomial expression below is:
⇒ 10x⁵y⁷/5x⁵y · 3x⁴y⁸/3x⁻³y¹⁰
Apply the division operation in the constant terms
⇒ 2x⁵y⁷/x⁵y · x⁴y⁸/x⁻³y¹⁰
Apply the arithmetic operation in the Exponents of the same base variables
⇒ 2y⁶ · x⁷y⁻²
⇒ 2y⁶⁻² · x⁷
⇒ 2y⁴ · x⁷
⇒ 2x⁷· y⁴
Therefore, the expression 2x⁷· y⁴ would be equivalent to the given polynomial expression.
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the Center is (2,0) the circle passes through the point (4.5,0) What is the Radius?
Answers
The radius of the circumference would be
x2 = 4.5
x1 = 2
r = x2 - x1
r = 4.5 - 2.0
r = 2.5
The radius would be 2.5
Number 5 need help I really forgot how to solve this problem
Answers
Line Segments and Rays
A line segment has two endpoints. It contains these endpoints and all the points of the line between them,
A ray is a part of a line that has one endpoint and goes on infinitely in only one direction. You cannot measure the length of a ray.
The figure shows a line that starts in B and goes infinitely to the left side, passing through A, thus the correct choice is B. Ray BA
A window washer drops a tool from their platform 155 ft high. The polynomial -16r2 + 155 tells us the height, in feet, of
the tool / seconds after it was dropped. Find the height, in feet, after t = 1.5 seconds.
Answers
At t = 1.5 sec the tool is at the height of 119 feet.
Given, A window washer drops a tool from their platform 155 ft high.
The polynomial -16r² + 155 tells us the height, in feet, of the tool / seconds after it was dropped.
we are asked to determine the height, in feet, after t = 1.5 seconds.
we know that h(t) = -16r² + 155
hence at t=1.5 sec, height is = ?
⇒ h(1.5) = -16t² + 155
⇒ h(1.5) = -16(1.5)² + 155
⇒ h(1.5) = -16(2.25) + 155
⇒ h(1.5) = -36 + 155
⇒ h(1.5) = 119
at t=1.5 sec the tool is at the height of 119 feet.
Hence we get the height as 119 feet.
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A student entering a doctoral program in educational psychology is required to select two courses from the list provided as part of his or her program (a)List all possible two-course selections (b)Comment on the likelihood that you EPR 625 and EPR 686 will be selected The course list EPR 613, EPR 664, EPR 625, EPR 685, EPR 686(a)select all the possible two-course selections belowA. 613, 686B. 625,686C. 613,613,664D. 664,685E. 625,685F. 625,672G. 613,625H. 685,686I. 664,625J 686,686K. 613,613L. 613,685M. 664, 686N. 613,664
Answers
List of courses that the student entering a doctoral program in educational psychology can take:
EPR 613, EPR 664, EPR 625, EPR 685, EPR 686
Therefore, the possible two-course selections for the student are:
A. Both courses are on the list given: 613, 686
B. Both courses are on the list given: 625, 686
C. It's not possible. This option contains three courses.
D. Both courses are on the list given: 664, 685
E. Both courses are on the list given: 625, 685
F. It's not possible, Course 672 isn't available.
G. Both courses are on the list given: 613, 625
H. Both courses are on the list given: 685, 686
I. Both courses are on the list given: 664, 625
J. It's not possible. Just one course is given.
K. Same case than J. Just one course.
L. Both courses are on the list given: 613, 685
M. Both courses are on the list given: 664, 686
N. Both courses are on the list given: 613, 664
The total fixed costs of producing a product is $55,000 and the variable cost is $190 per item. If the company believes they can sell 2,500 items at $245 each, what is thebreak-even point?800 items900 items960 items 1,000 itemsNone of these choices are correct.
Answers
Let's call FC the fixed cost for production and VC the variable cost per item.
The company believes they can sell 2,500 items at $245 each.
Production costs:
For producing 2,500 items, the company has to spend (total cost, TC):
[tex]\begin{gathered} TC=FC+2,500\cdot VC \\ TC=55,000+2,500\cdot190 \\ TC=530,000 \end{gathered}[/tex]Sells:
Now, company sells eacho of the 2,500 items at $245, so, the company income (I) is:
[tex]I=245\cdot x[/tex]where x is the number of items sold.
Break-even point:
This point is reached when company can recover the money they spend (TC). So, we have the following eaquation to solve:
[tex]\begin{gathered} TC\text{ = I} \\ \to530,000=245\cdot x \\ \to x=\frac{530,000}{245}\text{ =2,163.3 (rounded) } \end{gathered}[/tex]Since company can not sell fractions of items, they have to sell 2,164 items to take back the money they invested.
So, "None of these choices are correct".
A house casts a shadow that is 12 feet tall. A woman who is 5.5 feet tall casts a shadow that is 3 feet tall.
What is the height of the house?
A. 22 ft.
B. 55 ft.
C. 5.5 ft.
D.220 ft.
Answers
To find how many feet of shadow are cast from a one foot shadow, divide 5.5 by 3. This should give you about 1.83 ft of shadow per foot. Now, multiply the 12 foot shadow by 1.83 ft to get about 22 ft.
Question 1. Write the equation of the line that goes through the points (-2,1) and (4,2).
Answers
Slope-intercept equation:
y=mx+b
Where:
m= slope
b=y- intercept
Point 1 = (x1,y1) = (-2,1)
Point 2 = (x2,y2)= (4,2)
First, find the slope by applying the formula:
[tex]m=\text{ }\frac{y2-y1}{x2-x1}=\frac{2-1}{4-(-2)}=\frac{1}{6}[/tex]Now we have:
y=1/6x+b
Replace x,y by a point ( for example point 1 (-2,1)) and solve for b:
1 = 1/6 (-2) +b
1= -1/3 +b
1+1/3 = b
b= 4/3
Final equation:
y= 1/6x+4/3
Drag each tile to the correct box. Not all tiles will be used. Arrange the steps to solve the equation x + 3 − 2 x − 1 = - 2 . Simplify to obtain the final radical term on one side of the equation. Raise both sides of the equation to the power of 2. Apply the Zero Product Rule. Use the quadratic formula to find the values of x. Simplify to get a quadratic equation. Raise both sides of the equation to the power of 2 again.
Answers
The value of x = 16 + 4[tex]\sqrt{15}[/tex]
Given,
To solve the equations :
[tex]\sqrt{x+3} - \sqrt{x -1}[/tex] = -2
Solve by the given steps :
Now, According to the question:
Step 1: Simplify to obtain the radical form on one side of the equation:
[tex]\sqrt{x+3} - \sqrt{x -1}[/tex] = -2
Step 2: Raise both sides of the equation to the power of 2
[tex](\sqrt{x+3} - \sqrt{x -1})^2 = (-2)^2[/tex]
x + 3 + 2x - 1 -2 [tex]\sqrt{(x+3)(2x -1)}[/tex] = 4
3x - 2 = 2 [tex]\sqrt{(x+3)(2x -1)}[/tex]
[tex](3x - 2)^2 = [2\sqrt{(x+3)(2x -1)}]^2[/tex]
9[tex]x^{2}[/tex] - 12x + 4 = 4 (2[tex]x^{2}[/tex] + 5x -3)
Step 3: Apply the zero product rule, Simplify to get a quadratic equation :
[tex]x^{2}[/tex] - 32x +16 = 0
Step 4: Use the quadratic formula to find the values of x :
[tex]x^{2}[/tex] - 32x + 16 =0
x = 16 + 4[tex]\sqrt{15}[/tex] and x = 16 - 4[tex]\sqrt{15}[/tex]
x = 16 - 4[tex]\sqrt{15}[/tex] (It is rejected)
So, the value of x = 16 + 4[tex]\sqrt{15}[/tex]
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Answer: Raise both sides of the equation to the power of 2
simplify to obtain the final radical term on one side of the equation
raise both sides of the equation to the power of 2 again
simplify to get a quadratic equation
use the quadratic formula to find the xvalues
Step-by-step explanation:
solve p(x+q)^4=r for x
Answers
Given the following equation:
[tex]p\mleft(x+q\mright)^4=r[/tex]You can solve for the variable "x" as following:
1. You need to apply the Division property of equality by dividing both sides of the equation by "p":
[tex]\begin{gathered} \frac{p\mleft(x+q\mright)^4}{p}=\frac{r}{p} \\ \\ \mleft(x+q\mright)^4=\frac{r}{p} \end{gathered}[/tex]2. Remember that:
[tex]\sqrt[n]{a^n}=a[/tex]Then:
[tex]\begin{gathered} \sqrt[4]{(x+q)^4}=\sqrt[4]{\frac{r}{p}} \\ \\ x+q=\sqrt[4]{\frac{r}{p}} \end{gathered}[/tex]3. Now you have to apply the Subtraction property of equality by subtracting "q" from both sides of the equation:
[tex]\begin{gathered} x+q-(q)=\sqrt[4]{\frac{r}{p}}-(q) \\ \\ x=\sqrt[4]{\frac{r}{p}}-q \end{gathered}[/tex]The answer is:
[tex]x=\sqrt[4]{\frac{r}{p}}-q[/tex]there are 150 oranges in 10 craftes of each crate has the same amount of oranges how many oranges are in each crate?
Answers
Take the total number of oranges and divide by the number of crates
150 orange
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10 crates
15 oranges per crate
Let set E be defined as follows:
E = {english, math, french, art}
Which of the following are subsets of set
E
Answers
The subsets of E is all the above .
What are subsets of set ?If every component present in Set A is also present in Set B, then Set A is said to be a subset of Set B. To put it another way, Set B contains Set A. As an illustration, if set A has the elements X, Y, and set B contains the elements X, Y, and Z, then set A is the subset of set B.
If every element in a set A is also an element in a set B, then the set A is a subset of the set B. The set A is therefore contained within the set B. AB is used to represent the subset connection. For instance, if the sets A and B are equal, AB but BB, respectively.
Let the event E = {english, math, french, art}
The subsets of E is all the above .
null set is also subset of E
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Question 3 10 pts When solving an absolute value equation, such as |2x + 51 = 13, it is important to create two equations: 2x + 5= [ Select] and 2.1 + 5 = [Select ] [ Select] Resulting in z = vor [Select] Question 4 5 pts
Answers
1) Solving that absolute value equation:
|2x+5|=13 Applying the absolute value eq. property
2x +5 = 13 subtracting 5 from both sides
2x = 13-5
2x= 8 Dividing by 2
x =4
2x +5=-13 subtracting 5 from both sides
2x = -13-5
2x = -18 Dividing by 2
x= -9
Then x=4 or x =-9
2) The equations 2x +5 =13 and 2x +15= -13
Resulting in x=4 or x =-9