Solve this equation and show your work! (1 point for the correct answer and 1 point for showing how to solve the equation) x³ = -2,197
Here we are given with a equation:
[tex] {x}^{3} = - 2197[/tex]
And we have to solve it with appropriate steps.
So, let's start solving.
Add 2197 to both sides of the equation,
[tex] {x}^{3} + 2197 = - 2197 + 2197[/tex]
[tex] {x}^{ 3} + 2197 = 0[/tex]
Now, using the identity:
a³ + b³ = (a + b)(a² - ab + b²)Let's proceed further.
x³ is the cube of x and 2197 is the cube of 13
[tex](x) {}^{3} + (13) {}^{3} = 0[/tex]
[tex](x + 13)( {x}^{2} - x \times 13 + {13}^{2} ) = 0[/tex]
[tex](x + 13)( {x}^{2} - 13x + 13) = 0[/tex]
Now,
x + 13 = 0x² - 13x + 13 = 0So, x = -13
And, for the second let's use the discriminate formula,
➝ D = b² - 4ac
➝ D = (-13)² - 4(1)(13)
➝ D = 169 - 52
➝ D = 117
Now, using the D. formula,
[tex]x = \dfrac{ - b \pm \sqrt{ D} }{2a} [/tex]
[tex]x = \dfrac{13 \pm \sqrt{117} }{2} [/tex]
[tex]x = \dfrac{13 \pm 3 \sqrt{13} }{2} [/tex]
So the roots of the equation are:
[tex]{ \boxed{ \bf{x = - 1 ,\: \frac{13 + 3 \sqrt{13} }{2} and \: \frac{13 - 3 \sqrt{13} }{2} }}}[/tex]
And we are done !!
#CarryOnLearning
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Which of the following sets of numbers does square root of 49?
Answer:
7
Step-by-step explanation:
Natural numbers , Real numbers ,Whole numbers ,Integers , Rational numbers
sqrt(49) = 7
So this number is in the set of...
Natural numbersWhole numbersIntegersRational numbersReal numbersThe set of natural numbers is {1,2,3,...} and the set of whole numbers is {0,1,2,3,...}. Basically we just added in 0. Integers will be similar but we now have negative values too {..., -3, -2, -1, 0, 1, 2, 3, ...}
Rational numbers are anything of the form a/b with a,b being integers. In other words, if we can write the number as a fraction of two integers, then we have a rational number. In the case of 7, we have 7 = 7/1, so it is rational.
The set of real numbers includes every number type you have learned of so far (natural, whole, integer, etc). If you haven't learned about imaginary or complex numbers yet, then every number your teacher will go over is a real number.
Please help quick !!!!!! Simplify 6(x + 4).
Answer:
6(x + 4)
opening brackets
=6x+24 is the answer
Step-by-step explanation:
Which table corresponds to the graph of the function below?
Answer:
I belive its the second 1
Step-by-step explanation:
kakalkjslkajslkjslkjalk
Answer: A is the answer
Step-by-step explanation:
Please help me out!!
[tex] {32}^{ \frac{1}{5} } = \sqrt[5]{32} = 2[/tex]
Answer:2
Answer:
Step-by-step explanation:
Prime factorize 32
32 - 2*2*2*2*2 = 2⁵
[tex]32^{\frac{1}{5}}=(2^{5}})^{\frac{1}{5}}=2^{5*{\frac{1}{5}}}\\\\\\=2[/tex]
In June 2012, Twitter was reporting 400 million tweets per day. Each tweet can consist of up to 140 characters (letter, numbers, etc.). Create a comparison to help understand the amount of tweets in a year by imagining each character was a drop of water and comparing to filling something up
Please help!!! I would like an explanation along with your answer. Thanks
Answer:
(-4, 7)
Step-by-step explanation:
The x and y coordinates of the midpoint are the average of the x and y coordinates of the endpoints.
-1 = (2 + x) / 2
-2 = 2 + x
x = -4
5 = (3 + y) / 2
10 = 3 + y
y = 7
The coordinates of point S are therefore (-4, 7).
9. When you get to the island, you decide to take a kayak tour to a nearby reef. A kayak is a small boat you row with a paddle. Find the speed for the kayak. Use one of these facts to help. The steamboat's speed is 4 less than 8 times the speed of the kayak. The tall ship's speed is 1 more than 3 times the speed of the kayak. The yacht's speed is 5 less than 15 times the speed of the kayak. Write and solve an equation for the speed of the kayak. Show your work. (5 points: 2 points for writing a correct equation, 3 points for the solution) 10. The length of your trip to the island is 40 nautical miles less than 20 times the distance to the reef. It's 2:00 p.m. now, and your boat leaves the island at 7:30 p.m. Will you be able to kayak to the reef and back by then? If so, how long will you have to spend at the reef? If not, how late will you be for the return trip? Explain how you plan to solve this problem. Then solve the problem, showing all work. (5 points: 2 points for the explanation of the plan, 1 point for deciding if you will make it back to the island on time, and 2 points for determining either how long you can spend at the reef or how late you'll be)
Answer:
heres what i did on the 2.1.4 practice problem on apex
Step-by-step explanation:
1. Circle the two boats you picked for your trip.
the yacht and the tall ship (aka the pirate ship)
2. Make sense of the problem.
what do you know?
The tall ship makes the trip in 10 hours. The yacht makes the trip in 2.5 hours. The tall ship is 30 knots slower than the yacht.
what do you want to find out?
How fast is each boat traveling in knots (nautical miles per hour)?
what kind of answer do you expect?
probably just some numbers like 10 miles per hour or 40 miles per hour
Writing some expressions
3. Write an expression for the distance going to the island. Let x be the speed of the boat you are taking to the island. Distance is equal to speed times time. (2 points)
the expression would be D = 10(x-30), d is the distance. it could also be simplified to 10x - 300
4. Write an expression for the speed of the boat coming back from the island in terms of the other boat's speed. Let x be the speed of the boat you are taking to the island. (2 points)
so the yacht's speed would be S = x knots, s is for speed.
5. Write an expression for the distance returning from the island. Use the expression for speed you found in question 4. Remember that distance is equal to speed times time. (2 points)
the distance returning from the island would be D = 2.5x.
6. Each ship travels the same distance. Set the distances equal to each other to get the equation for the speed of the ship you are taking to the island. (1 point)
10x - 300 = 2.5x
7. Solve the equation from question 6 for x. What does this tell you? (5 points: 1 point for showing your work, 3 points for solving for x, 1 point for explaining the answer)
10x - 300 = 2.5x
10x - 300 + 300 = 2.5x + 300
10x -2.5x = 300
7.5x = 300
x = 40
x is the speed of the yacht. (40 nautical miles per hour)
8. How fast does the second boat travel? Show your work. (2 points: 1 point for showing your work, 1 point for the answer)
the yacht travels at 40 nautical miles per hour and the tall ship travels at 100 (10x - 300) nautical miles per hour.
9. When you get to the island, you decide to take a kayak tour to a nearby reef. A kayak is a small boat you row with a paddle.
Find the speed for the kayak. Use one of these facts to help.
The steamboat's speed is 4 less than 8 times the speed of the kayak.
The tall ship's speed is 1 more than 3 times the speed of the kayak.
The yacht's speed is 5 less than 15 times the speed of the kayak.
Write and solve an equation for the speed of the kayak. Show your work. (5 points: 2 points for writing a correct equation, 3 points for the solution)
the equation for the speed of the kayak is 40 = 15x - 5, which in this case, x is the speed of the kayak
40 = 15x - 5
40 + 5 = 15x -5 + 5
45 = 15x
x = 3
therefore, the speed of the kayak is 3 nautical miles per hour.
10. The length of your trip to the island is 40 nautical miles less than 20 times the distance to the reef.
It's 2:00 p.m. now, and your boat leaves the island at 7:30 p.m. Will you be able to kayak to the reef and back by then?
If so, how long will you have to spend at the reef?
If not, how late will you be for the return trip?
Explain how you plan to solve this problem. Then solve the problem, showing all work. (5 points: 2 points for the explanation of the plan, 1 point for deciding if you will make it back to the island on time, and 2 points for determining either how long you can spend at the reef or how late you'll be)
the distance to the island is 100 nautical miles, so the expression would be 100 = 20x -40, with x being the distance to the reef.
we can solve for x by doing:
100 = 20x -40
100 + 40 = 20x - 40 + 40
140 = 20x
140 / 20 = x
x = 7
so the distance from my starting point to the reef will be 7 nautical miles, and the distance from the island to the reef would be 93 nautical miles.in that case, I would be like a day and a half late, but if you are trying to say that the ship is waiting for me at the starting point of my "adventure", then I would not be late if I kayak from my starting point to the reef, in fact, I could stay at the reef for like 50 min, because:
7 / 3 = 2 1/3 hours.
2 1/3 x 2 = 4 2/3 hours or 280 min. (to the reef and back)
7:30 p.m. - 2:00 p.m. = 5 1/2 hours or 330 min. (how much time I have till the ship leaves)
330 - 280 = 50 min. (how many min I can spend at the reef)
There are nine water bottles in devins refrigerator.
my boy wants to stay hydrated and we all know that he's that one kid who screams YESSSIRR at 3;00am because he got one kill on a free game ( fortnite) a dead game btw . but he love the boys he kisses them on the cheek and tuck them in every night and he makes sure they got 9 bottles of water in there refrigerator too. he that one kid at school that gets every new iphone but asks YOU for a PENCIL he that one kid that brags about how his mom bought him the new fortnite skin he the one to call you a bot when he the one who died. but he love the boys tho there bond do be unbreakable.
to the boy devin the 9 water bottle drinker, he drink from so many water bottles his head starting to look like a water bottle
What is the decimal form of 92/125 !???
Answer:
0.736
Step-by-step explanation:
Answer:
0.736
Step-by-step explanation:
decimal form of 92/125
25 pts
Question 5
25 points
Jack and Jill went to the grocery store. They purchased 2 packages of
hamburger buns for $1.10 per package, one pound of hamburger meat for
$3.79, and 3 bottles of soda for $0.95 per soda. If Jack and Jill split the bill
evenly, then how much money did each person pay?
Answer:
$4.42!
Step-by-step explanation:
Just add all the prices together then divide by 2!
$1.10 * 2 + $3.79 + $0.95 * 3 = $8. 84
$8.84 ÷ 2 = $4.42!
Rosalyn paid $55.00 for 4 pizza. Each pizza cost the same amount. What was the cost of each pizza in dollars and cents?
Answer:
$13.75 is ur answer
Answer:
13.75
Step-by-step explanation:55 divided by 4
simply: -2 1/3 - (-10 1/6)
Answer: 7.83
Step-by-step explanation:
Answer:
−8/3≈−2.666666667
Step-by-step explanation:
-2 1/3 - (-10 1/6)
Multiply −2 times 2/1=0.5.
−1−10×( 1/6 )≈−2.666666667
Multiply 10 and 1/6≈0.166666667 to get 10/6≈1.666666667
−1− 10/6 ≈−2.666666667
Reduce the fraction 10/6 ≈1.666666667 to lowest terms by extracting and canceling out 2.
−1−5/3 ≈−2.666666667
Convert −1 to fraction −3/3 =−1.
− 3/3−5/3≈−2.666666667
Since −3/3 =−1 and 5/3 ≈1.666666667 have the same denominator, subtract them by subtracting their numerators.
−3−5/3 ≈−2.666666667
Subtract 5 from −3 to get −8.
-8/3=−2.666666667
On Thursday, a local hamburger shop sold a combined total of 580 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Thursday?
Answer:
Hey there!
Let h be the number of hamburgers sold.
Let c be the number of cheeseburgers sold.
h+c=580
c=3h
4h=580
h=145
145 hamburgers were sold.
Let me know if this helps :)
Josiah bought 22 chicken wings for $26.40. How much would it cost for 9 wings?
Answer:
it would cost $10.8 for 9 chicken wings.
Step-by-step explanation:
Cost of 22 chicken wings = $26.40
we have to find first, cost of 1 chicken wings
For that we divide both side by 22
cost of 22/22 chicken wings = $26.40/22 = 1.2
Thus, cost of 1 chicken wings = $1.2
to fins cost of 9 chicken wings
we multiply both sides by 9
cost of 1*9 chicken wings = $1.2*9
cost of 9 chicken wings = $10.8
Thus, it would cost $10.8 for 9 chicken wings.
the answer to your question is 10.8
Use the given conditions to write an equation in point-slope form. Keep parenthesis in point-slope form. slope = 7, passing through (1,-3)
Answer:
Step-by-step explanation:
y + 3 = 7(x - 1)
y + 3 = 7x - 7
y = 7x - 10
Mrs. Quill wrote a check for $66 for 22 school lunches. What is the cost per lunch?
is this division?
Answer:
Yes it is division
Step-by-step explanation:
It should be 3
Answer: yes division
66÷22=$3 per lunch
Step-by-step explanation:
What is the value of the expression |5x+12| when x=5
Answer:
|5x+12| when x=5
I5*5=12I
I37I
37
Step-by-step explanation:
Answer:
37
Step-by-step explanation:
X=5
5x=(5×5)=25
25+12=37
If elephant grass grows 2 3/4 inches a day, how many inches will it grow in 6 days?
The pizza dough recipe recipe shown makes one batch of dough charlie wants to make a half batch she has 1 cup of flour how much more flour does she need
Solve
5k+6=7 for x
please I need it quick and fast
A bookstore had 60 copies of a magazine. Yesterday, it sold 1/3 of them. Today, it sold 3/5 of what remained. How many copies does the bookstore have left?
Answer: 8 copies
Step-by-step explanation:
1/3 of 60 is 20. 1/5 of 40 is 8. 8x3=24, 40-24=16
Question 7
2 pts
If you bought something in Wyoming for $54, you would be charged $3.56 in state sales tax. What is the
state sales tax rate in Wyoming?
Insert your answer as a percentage to the tenth WITHOUT the % symbol.
Question 8
2 pts
Answer:
6.6
Step-by-step explanation:
The way to do this is to find the tax as a decimal. Worry about the 100 later.
54 * x = 3.56
Divide by 54
x = 3.56/54
x = .06593
Now use the 100
0.06592 * 100 = 6.593
But you want it rounded to the 1/10
So you should get 6.6 %
Which one of these is ordered from greatest to least?
A: -6.5, -4/5, 1/2, 4.25
B: -6.5, 4.25, -4/5, 1/2
C: 4.25, 1/2, -4/5, -6.5
D: 4.25, -4/5, 1/2, -6.5
HELLPPP! ASAPP
Answer:
the answer would be C :)
simplify the following expression 2x cubed y cubed over 4y squared
3xcubed y to the fifth over 2
Compare the number of stars to the number of circles. If the ratio remains the same, how many stars will there be when there are 15 circles?
There is 4 stars 3 circles
Answer:
the answer is 20 because if you want to keep the ratio the same, you have to multiply 3 by 5 to get 15 right? and so 4 times 5 is 20. see if it works
Step-by-step explanation:
34=9r-11
help plzzzzzzzzzzzzz hurry
Answer:
5
Step-by-step explanation:
Swap sides so that all variable terms are on the left hand side.
9r−11=34
Add 11 to both sides.
9r=34+11
Add 34 and 11 to get 45.
9r=45
Divide both sides by 9.
r= 45/9
Divide 45 by 9 to get 5.
r=5
Determine whether the following graph represents a function.
A.function
B. Not function
b i think...
lmk if it's wrong, if it is i'm sooooo sorry!!
:)
Have some points, i have to put in a question anyway to be "Part of The Community"
Answer:
yay!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
Answer:
:)
Step-by-step explanation:
thanks! have a nice day!
ruger has a dartboard with an area of 1600 cm^2. The dartborad has a circular bullseye centered at (0 cm, 0 cm). The point ( square root 3cm, square root 7cm) is on the circumference of the bullseye.
A percentage is given by dividing a given value by a total and multiplying the result by 100
The percentage of the dartboard occupied by the bullseye is approximately 1.963 %
Reason:
The given parameters are;
The area of the dartboard, A = 1,600 cm²
The location of the center of the bullseye = (0 cm, 0 cm)
The coordinates of a point on the circumference = (√3 cm, √7 cm)
Question: Possible question with regards to the given parameter; The percentage of the dartboard covered by the bullseye
Solution;
The radius of the bullseye, r = [tex]\sqrt{(\sqrt{3})^2 + (\sqrt{9})^2} = \sqrt{10}[/tex]
The area of the bullseye, [tex]A_b[/tex] = π· r² = π × [tex](\sqrt{10})^2[/tex] = 10·π
∴ The area of the bullseye, [tex]A_b[/tex] = 10·π cm²
The percentage area is given as follows;
[tex]Percentage \ area = \dfrac{A_b}{A} \times 100[/tex]
Therefore;
[tex]Percentage \ area \ occupies \ by \ bulleseye = \dfrac{10 \cdot \pi}{1,600} \times 100 \approx 1.963 \%[/tex]
The percentage of the dartboard occupied by the bullseye ≈ 1.963 %
Learn more about percentage area here:
https://brainly.com/question/11642822
Answer:
2%
Step-by-step explanation:
Should be Choice B