Answer:
[tex]x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}[/tex]
Step-by-step explanation:
1) Move all terms to one side.
[tex]2x^{3} -x^{2} -3x-210=0[/tex]
2) Factor [tex]2{x}^{3}-{x}^{2}-3x-210[/tex] using Polynomial Division.
1 - Factor the following.
[tex]2x^{3} -x^{2} -3x-210[/tex]
2 - First, find all factors of the constant term 210.
[tex]1,2,3,4,5,6,7,10,14,15,21,30,35,42,70,105,210[/tex]
3) Try each factor above using the Remainder Theorem.
Substitute 1 into x. Since the result is not 0, x-1 is not a factor..
[tex]2*1^{3} -1^{2} -3*1-210=-212[/tex]
Substitute -1 into x. Since the result is not 0, x+1 is not a factor..
[tex]2(-1)^{3} -(-1)^{2} -3*-1-210=-210[/tex]
Substitute 2 into x. Since the result is not 0, x-2 is not a factor..
[tex]2*2^{3} -2^{2} -3*2-210=-204[/tex]
Substitute -2 into x. Since the result is not 0, x+2 is not a factor..
[tex]2{(-2)}^{3}-{(-2)}^{2}-3\times -2-210 = -224[/tex]
Substitute 3 into x. Since the result is not 0, x-3 is not a factor..
[tex]2\times {3}^{3}-{3}^{2}-3\times 3-210 = -174[/tex]
Substitute -3 into x. Since the result is not 0, x+3 is not a factor..
[tex]2{(-3)}^{3}-{(-3)}^{2}-3\times -3-210 = -264[/tex]
Substitute 5 into x. Since the result is 0, x-5 is a factor..
[tex]2\times {5}^{3}-{5}^{2}-3\times 5-210 =0[/tex]
------------------------------------------------------------------------------------------
⇒ [tex]x-5[/tex]
4) Polynomial Division: Divide [tex]2{x}^{3}-{x}^{2}-3x-210[/tex] by [tex]x-5[/tex].
[tex]2x^{2}[/tex] [tex]9x[/tex] [tex]42[/tex]
-------------------------------------------------------------------------
[tex]x-5[/tex] | [tex]2x^{3}[/tex] [tex]-x^{2}[/tex] [tex]-3x[/tex] [tex]-210[/tex]
[tex]2x^{3}[/tex] [tex]-10x^{2}[/tex]
-----------------------------------------------------------------------
[tex]9x^{2}[/tex] [tex]-3x[/tex] [tex]-210[/tex]
--------------------------------------------------------------------------
[tex]42x[/tex] [tex]-210[/tex]
[tex]42x[/tex] [tex]-210[/tex]
-------------------------------------------------------------------------
5) Rewrite the expression using the above.
[tex]2x^2+9x+42[/tex]
[tex](2x^2+9x+42)(x-5)=0[/tex]
3) Solve for [tex]x.[/tex]
[tex]x=5[/tex]
4) Use the Quadratic Formula.
1 - In general, given [tex]a{x}^{2}+bx+c=0[/tex] , there exists two solutions where:
[tex]x=\frac{-b+\sqrt{b^{2} -4ac} }{2a} ,\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]
2 - In this case, [tex]a=2,b=9[/tex] and [tex]c = 42.[/tex]
[tex]x=\frac{-9+\sqrt{9^2*-4*2*42} }{2*2} ,\frac{-9-\sqrt{9^2-4*2*42} }{2*2}[/tex]
3 - Simplify.
[tex]x=\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}[/tex]
5) Collect all solutions from the previous steps.
[tex]x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}[/tex]
Jillian guessed at random for each question on a true-false quiz of ten questions. what is the probability that she got exactly seven questions correct?
Answer:
11/64
Step-by-step explanation:
Each question can be answered in 2 ways
∴ Total ways in which 10 questions can be answered
=2¹⁰
No. of ways of guessing at least 7 questions
out of 10
=7 questions correct +8 questions correct
+9 questions correct +10 questions correct
= ¹⁰C7(1)⁷+ ¹⁰C8(1)⁸+ ¹⁰C9(1)⁹+ ¹⁰C10(1)¹⁰
= 120 + 45 + 10 +1
=176
..Required Probability =176/2¹⁰
.. =11×16/2¹⁰
=11/64
A box is shaped like a rectangular prism. the base area of the box is 630 square centimetres, and the height is 20 centimetres. determine the volume of the box.
Answer:
12600 cm³
Step-by-step explanation:
The volume of a prism is the product of its base area and height:
V = Bh
__
For your prism, this product is ...
V = (630 cm²)(20 cm) = 12600 cm³
The volume of the box is 12600 cm³.
A teacher assigns 10 questions for homework and wants to randomly pick 3 questions to be graded. Which of the following procedures would produce a simple random sample? 1.Assign the homework questions the numbers 1-10. Use a random number table to select the first three numbers between 1 and 10. These represent the questions that will be graded. 2.Assign the homework questions the numbers 0 to 9. Use a random number table to select the first three numbers between 0 and 9. These represent the questions that will be graded. 3.Assign the homework questions the numbers 01–10. Use a random number table to select the first three 2-digit numbers between 01 and 10. These represent the questions that will be graded.
3. Assign the homework questions the numbers 0–9. Use a random number table to select the first three unique numbers between 0 and 9. These represent the questions that will be graded.
The answer will be option D which is to Assign the homework questions the numbers 0–9. Use a random number table to select the first three unique numbers between 0 and 9.
What is randomization?
Randomization allows a sample or small groups with similar characteristics to determine a probability or to hypothesize an event, that is why this type of sample is important in an experiment, that is, to carry it out in a random way.
Given that:-
A teacher assigns 10 questions for homework and wants to randomly pick 3 questions to be graded.
Assign the homework questions the numbers 0–9. Use a random number table to select the first three unique numbers between 0 and 9. These represent the questions that will be graded.
Hence the answer will be option D which is to Assign the homework questions to the numbers 0–9. Use a random number table to select the first three unique numbers between 0 and 9.
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I need help me with math homework please .?
[tex]x = 5 \\ y = 4 \\ m = \frac{1}{5} [/tex]
y= mx+b
[tex]4 = ( \frac{1}{5} \times( 5) )+ b \\ 4 = 1 + b \\ 4 - 1 = b \\ 3 = b \\ y = \frac{1}{5} x + 3[/tex]
Answer:
y = 1/5x + 3
Step-by-step explanation:
In which number does the digit 2 have a value that is ten times as great as the value of the digit 2 in the number 135,284? A 29,831
B 42,938
C 298,893
D 326,894
Answer:
it's option B 42,938
Step-by-step explanation:
in the question the value of 2 in 135,284 is 200
200× 10 =2000
therefore the number with 2 in thousands place is option B 42,938
You score an 84 on the first of two exams. Write and solve an equation to find the score x that you need on the second exam to have a mean score of 92. I got the answer -76 I need to know if that's correct.
Answer: 100
Step-by-step explanation:
▪︎ To find the mean we take the sum of the values and divide it by the number of values.
▪︎ Let x be your score on the second exam.
(84 + x) / 2 = 92
84 + x = 92*2
84 + x = 184
x = 100
can someone help me
Answer:
S=49
Step-by-step explanation:
Any triangle has an interior angle of 180.
So just add them up and set the sum equal to 180 degrees.
2s+s+33=180
3s=180-33
3s=147 . Divide both sides by 3 to isolate variable s
s=49
(3x-5y)+(x+2y)? Someone help me. Will give brainliest
Answer: 4x - 3y (choice B)
===========================================================
Explanation:
The letter x is a variable, and a placeholder for a number. Which number? We don't know. It's basically a box where a number goes inside.
x represents having 1 box
2x is two boxes, and so on
If we add 3x and 1x, then we'll have four boxes and 3x+1x = 4x
We can only add the x terms together, which we consider to be called "like terms".
The y terms -5y and 2y are the other pair of like terms, which combine to -3y
If you want, you can draw a vertical number line. Start at -5 which is five units below zero. Then move up two spaces to arrive at -3. This is a visual way to demonstrate that -5+2 = -3, and by extension, -5y+2y = -3y
How to find area of 1 ???
Answer: 1 What???
Step-by-step explanation:
Find the value of x if the perimeter is 20
Answer:
x = 3Step-by-step explanation:
Find the value of x if the perimeter is 20
20 = X + 4X - 6 + X + 8
20 + 6 - 8 = 6X
18 = 6X
x = 18 : 6
x = 3
-----------------
check
20 = 3 + 3 * 4 - 6 + 3 + 8
20 = 20
the answer is good
Answer:
Value of x is 3
Step-by-step explanation:
Given perimeter of figure = 20
x + (x+8) + (4x-6) = 20
x + x + 8 + 4x - 6 = 20
6x + 2 = 20
6x = 20 - 2
6x = 18
x = 18 / 6
x = 3
What does this graph show
inverse
direct
neither
Answer:
i think the given graph is inverse
3
x + 2
3
3
12
32
12
Solve for x.
Answer:
6
explanation
[tex]since \: they \: are \: similar \\ \frac{x + 2}{32} = \frac{3}{12} \\ crossmultiplying \\ 32 \times 3 = 12(x + 2) \\ 96= 12x + 24 \\ 12x = 96 - 24 \\ 12x = 72 \\ dividing \: bothsides \: y \: 12 \\ x = \frac{72}{12} \\ x = 6[/tex]
Question 3 of 10
The minimum monthly payment for Janet's credit card is 2% of her balance or
$10, whichever is higher. If Janet's balance at the end of her last billing cycle
was $760, what is her minimum monthly payment?
A. $10.00
O B. $5.20
C. $25.20
OD. $15.20
Triangles are stacked beside each other to form a prism. which statements are true regarding the prism? check all that apply. the prism has no vertices. the prism has 9 edges. the bases of the prism are triangles. the bases of the prism are rectangles. the prism has 5 faces.
The true statements based on the information are the bases of the prism are rectangles and the prism has 5 faces.
What is a pyramid?A pyramid is defines as a polyhedron formed by connecting a base to a point known as a vertex.
The pyramid formed from stacking triangles besides each other will have vertices, even number of edges and faces
The true statements based on the information are the bases of the prism are rectangles and the prism has 5 faces.
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Answer:
B C E , edge22
Step-by-step explanation
drink some water today and remember to take a break for yourself have a wonderful dayday
Is a megabyte bigger than a gigabyte.
Answer:
NO!!! Megabytes AREN'T bigger than Gigabytes!
Step-by-step explanation:
Here's the table!
1 Kilobyte = 1,024 Bytes
1 Megabyte = 1,024 Kilobytes
1 Gigabyte = 1,024 Megabytes
1 Terabyte = 1,024 Gigabytes
From this we can see that Megabyte ISN'T bigger than Gigabyte
What is more than 11 but less than 12?
Answer:
136
Step-by-step explanation:
Answer:
There are infinite numbers that fit this range, but one is 11.5
25
24.
What is the value of x?
(4x + 1)
F 9.5
G 18
(2x - 19)
H 33
J 81
Answer:
33 degrees
Step-by-step explanation:
(4x+1) and (2x-19) add up to 180 degrees
[tex](4x+1)+(2x-19)=180\\6x-18=180\\6x=198\\x=33[/tex]
Can someone please answer this, ill give you brainliest Would be very appreciated.
Answer:
See below ~
Step-by-step explanation:
More revenue would be generated at $5 than $17 because on the graph, when the price is at $5, there is about $3750 in revenue compared to when the price is $17, the revenue is $2500.The company should sell their product at $10. At this price, the revenue they will make is $5,000.The domain is the possible intervals in which x lies. Therefore, the domain is : 0 ≤ p ≤ 20.Find the area of the kite or rhombus.
Answer:
126 cm^2 (please mark me brainliest)
Step-by-step explanation:
(14x16)/2+(2*14)/2=
112+14=126
help me
?
10
450
15
675
20
900
Answer:
Y=45x
Step-by-step explanation:
Y = f(x)
If you plot a chart, you can find that relation is just a linear relation. So y = mx + c
By putting any one case into the equation, you can find c = 0 and m = 45
Retest the equation for other cases to ensure u are correct
Only 4 students have won the track races this year gina has won 4 times Hal has won 3 times Isabel has won 3 times and Jamal has won 4 times
In American football, a touchdown scores 7 points, a field goal scores 3 points, and a safety scores 2 points. If a team scored a total of 24 points, how many combinations of plays is possible
The number of combinations of plays that is possible will be 2.
How to calculate the combination?Let the number of combinations be represented by x.
From the information given, we are informed that the touchdown scores 7 points, a field goal scores 3 points, and a safety scores 2 points.
Therefore, this will be:
7x + 3x + 2x = 24
12x = 24
x = 24/12
x = 2
Therefore, there are 2 combinations.
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A block of sugar maple wood has a mass of 82.8 g and density of 0.69 g/cm3. the block is a rectangular prism with a length of 5 cm and a width of 4 cm. what is the height of the block of sugar maple? enter your answer in the box.
The density of an object is the ratio of the mass of the object to its volume. The height of the block of sugar maple is 6cm
Density of an objectThe density of an object is the ratio of the mass of the object to its volume. Mathematically;
Density = mass/volume
Given the following
Mass of block = 82.8grams
Density = 0.69g/cm^3
volume = lwh
Volume = 20h
Substitute
0.69 = 82.8/20h
20h = 82.8/0.69
20h = 120
h = 6cm
Hence the height of the block of sugar maple is 6cm
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6cm
Step-by-step explanation i can confirm that the answer is 6 ;}
Given h(x) = −3 |x + 1| evaluate h (-3)
Need help this is for final’s study’s
Answer:
-6
Step-by-step explanation:
h(x) = −3 |x + 1| evaluate h (-3)
h (-3) means x = -3
Plug in:
h(x) = −3 |(-3) + 1| → h(x) = −3 |-3 + 1|
h(x) = −3 |-2| since -2 is an absolute value it becomes 2
h(x) = −3(2)
h(x) = -6
Let me know if you have anymore questions,
Good Luck studying :) YOU GOT THIS !!!
A push-cart vendor is selling sodas at the beach. partway into the day, he raises his
price per bottle by one quarter. after this price increase, the total dollar amount
collected for the day after selling n bottles at the new price is given by the following
equation:
t = 12 + 1.75n
according to this equation, how many bottles did the vendor sell today before raising the
price?
o a
8
ob.
12
c. 18
d. 21
Answer:
[tex]8[/tex].
Step-by-step explanation:
Notice that in equation for the total dollar amount collected ([tex]12+ 1.75\, n[/tex]), every additional bottle sold at the new price brings in [tex]1.75[/tex] dollars:
[tex]\begin{aligned}& 12 + 1.75\, n && \text{$n$ bottles at new price} \\ -\; & 12 + 1.75\, (n+1) && \text{$(n+1)$ bottles at new price} \\ =\; & 1.75\end{aligned}[/tex].
Therefore, the per-bottle price after the [tex]\$0.25[/tex] price increase would be [tex]\$1.75[/tex]. The per-bottle price before the price increase would be [tex]\$1.75 - \$0.25 = \$1.50[/tex].
Also notice that when [tex]n = 0[/tex], the total amount collected was [tex]t = 12 + 1.75\, n = 12[/tex]. In other words, the total amount collected was [tex]\$12[/tex] before any bottle was sold at the new price.
Thus, the vendor had collected [tex]\$12\![/tex] by selling at the initial price of [tex]\$1.50[/tex] per bottle. The number of bottles sold at that price would be:
[tex]\begin{aligned}\frac{12}{1.50} = 8\end{aligned}[/tex].
Which of the three following graphs display the same data? i. a bar graph titled county voter turnout (thousands) has year on the x-axis and number on the y-axis. 1992, 99; 1996, 107; 2000, 103; 2004, 97; 2008, 98. ii. a line graph titled county voter turnout (thousands) has year on the x-axis and number on the y-axis. 1992, 99; 1996, 107; 2000, 103; 2004, 97; 2008, 98. iii. a circle graph titled county voter turnout (thousands). cuyahoga county, 99; maricopa county, 107; fort bend county, 103; susquehanna county, 97; clark county, 98. a. i and ii b. i and iii c. ii and iii d. i, ii, and iii
The graphs that display the same data are a. I and II
What is Data Representation?This refers to the different ways in which a set of data are displayed in a certain place such as a bar graph, frequency table, line graph, etc.
Hence, we can see that from the evaluation of the data, there is the use of the same data in I and II as the bar and line graphs contain the same country voter turnout.
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Answer:
a
Step-by-step explanation:
Employees of the sports department at a television station want to measure the number of viewers for a particular exercise program. They call the homes of all the members of a nearby health club. Why might this be a biased sample?
A.The station does not include everyone in the viewing area.
B.The station does not include people all across the country.
C.People who belong to a health club may have many television sets in their homes.
D.People who belong to a health club may be more likely to watch an exercise program.
Answer:
d
Step-by-step explanation:
elijah run 68 yards in a 100 yd how many more yards does she have to run what is the answer
Answer:
32
100-68=32
Step-by-step explanation:
help asap please!! <3
Answer:
y = -2x + 4 or y = -2(x - 2)
Step-by-step explanation:
Equation of Line AB
y = mx + cm = slopec = y-interceptFinding slope (m)
m = -2 - 6 / 3 + 1m = -8/4m = -2Finding c using point slope equation
c - 6 = -2(0 + 1)c - 6 = -2c = 4Equation
Line AB : y = -2x + 4 or y = -2(x - 2)Answer:
The easiest way to do this is to put the line into slope intercept form. This is equal to y = mx + b, where m is the slope and y is the intercept. I'm assuming the point at which the line intercepts the y axis is at (0, 4) The graph isn't numbered, so its hard to tell.
Assuming b = 4, we need to find m
Slope = rise / run
Or
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\[/tex]
Substitute -2 for y2, 6 for y1, 3 for x2 and -1 for x1
[tex]m = \frac{-2 - 6}{3 - -1}\\ m = \frac{-8}{4}\\m = -2[/tex]
Plug these values in and
[tex]y = -2x + 4[/tex]
When you graph this on desmos, the two points (-1, 6) and (3, -2) are on the graph. Therefore, I'm assuming the y intercept was in fact 4 :)
Cooper asked his classmates, "How many days do you floss your teeth in a
typical week?" The table shows Cooper's data.
Days of Flossing per Week
4
5
4 2
3
3
1
0
3
3
6
7
2
6
0
5
3
2
7
0
4
4
4
3 3
0
1
2
2
3
5 3
7
1
3
How many observations did he record?
OA. 40
OB. 35
OC. 30
D. 7
сл
Considering the given table, it is found that he recorded 35 observations, hence option B is correct.
How do we find the number of observations on the table?We have to look at the number of rows and columns the table. The table has 7 rows, each with 5 columns, hence the number of observations is given by:
N = 7 x 5 = 35.
Hence option B is correct.
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