The solution of the equation is x=±i or x=±i√2.
Given that the equation is x⁴+3x²+2=0 and use u substitution method to solve.
We can rewrite our given equation as:
(x²)²+3x²+2=0
Let's assume that the (x²)=u.
The given equation is rewritten as u²+3u+2=0.
Factorize the quadratic equation by adding or subtracting two number that gives the sum of 3u and product 2u² as
u²+2u+u+2=0
u(u+2)+1(u+2)=0
Taking out (u+2) as common and get
(u+2)(u+1)=0
Compare each equation with 0 and get
u+2=0 or u+1=0
u=-2 or u=-1
Performing back substitution by substituting the values of u in x²
when u=-1 then x is
x²=-1
x=±√(-1)
As we know that √(-1)=i.
So, we get
x=±i
And when u=-2 then x is
x²=-2
x=±√(-2)
As we know that √(-1)=i.
So, substituting this, we get
x=±i√2
Hence, the solutions of the x⁴+3x²+2=0 is x=±i and x=±i√2.
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77 = 88 because they both equal 1. Peter takes one part away from each. Will the results be equal? Use the drop-down menus to complete an explanation.
Yes, the results will be equal as it follows from the task content that both numbers were equal initially.
What will he the equality verdict on both results?As evident in the task content, it follows that the numbers 77 and 88 although, not equal in the real sense, are equal according to the task content.
Hence, it follows that when equal parts are taken away from the two numbers, they would still be equal as both numbers were equal initially.
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In the figure above, AP and CQ are tangents to the circle.
If ∠ABC = 60° and ∠BAP = 40°, find ∠BCQ.
Answer:
30
Step-by-step explanation:
You take a protractor and put at c then you measure
A point is chosen at random on the number line between $0$ and $1$, and the point is colored green. Then, another point is chosen at random on the number line between $0$ and $1$, and this point is colored purple. What is the probability that the number of the purple point is greater than the number of the green point, but less than twice the number of the green point
The probability that the number of the purple point is greater than the number of the green point, but less than twice the number of the green point is 1/4
How to find the Probability?Let the "green" value be an x value lying on segment AC.
Now, the segment AC has the equation y = x. Then, let the "purple" value that is twice a selected x value lie on the segment AE and as such, the equation of this line is y = 2x.
It must be noted that at point E, x = 0.5 and y = 1. This means at every x value on AC greater than 0.5, the value of y on EC associated with this x value is is less than twice that x value.
Then, between segments AE and AC, every value of y will be greater than, but less than twice, its associated x value.
Since triangle ACD has an area of 1/2 and triangle BEA has an area of 1/4, then we can say that;
Triangle AEC area = 1 - (1/2) - (1/4) = 1/4.
Thus, the probability that the number of the purple point is greater than the number of the green point, but less than twice the number of the green point is 1/4
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Container measures 24ft by 8ft by 10ft, if 1 bushel is approximately 2220 cubic inches, approximately how many bushels of grain can the container hold ( 1ft=12in) Show Your work
Answer:
see below
Step-by-step explanation:
24 ft * 12 in/ft * 8ft * 12 in/ft * 10 ft * 12 in/ft = 3317760 in^3
3 317 760 in^3 / 2220 in^3/bushel = 1494.49 bushels
HELP HALP
x =x=x, equals
^\circ
∘
Answer:
Step-by-step explanation:
x=25 degrees.
A vertical angle is two angles formed by intersecting lines, just like the two that form 25 degrees and x degrees. The angles formed by vertical angles are congruent (meaning they are equivalent). So, x=25 degrees.
can someone help me please
answer:
oops, I accidentally messed this one up, so sorry
Answer:
"We can't use any of the patterns"
Step-by-step explanation:
You can't use [tex](U+V)^2[/tex] because that would result in some stuff in the middle. In general if you have something like that it would expand to [tex]U^2+2UV + V^2[/tex]. and same thing for the (U-V)^2 except the middle would be a negative number. You also can't use [tex](U+V)(U-V)[/tex] because it specifies "constant integers" and the "integer" part is what's really important, because you can technically rewrite the sum of squares as (U + V)(U - V) but you would need to use imaginary numbers. Because the difference of squares is defined as [tex]a^2-b^2 = (a-b)(a+b)[/tex]. But you can also think of it like this [tex]a-b = (\sqrt{a} - \sqrt{b})(\sqrt{a}+\sqrt{b})[/tex] because that's essentially what the original identity is saying. Using this definition you can write the sum of squares as [tex]a+b = a - (-b) = (\sqrt{a} + \sqrt{-b})(\sqrt{a} - \sqrt{-b}) = (\sqrt{a} + i\sqrt{b})(\sqrt{a} - i\sqrt{b})[/tex]. So with the restriction of constant integers "We can't use any of the patterns" is the correct answer
samanth drew this pictogram
Answer:
la verdad noce no me acuerdo
Answer:
4
Step-by-step explanation:
There are 6 grey diamonds in the row labelled "cat".
Each diamond means two hours.
6 × 2 = 12
Samanth's table shows that cats sleep 12 hours.
Tony is going to use a circle that means 3 hours.
12 ÷ 3 = 4
Tony needs 4 circles to show 12 hours.
4 × 3 = 12
Tony will use 4 circles.
What is the recursive formula for this geometric sequence? -3. -21, -147, -1029, …
Answer:
[tex]a_{n}[/tex] = 7[tex]a_{n-1}[/tex]
Step-by-step explanation:
A recursive formula allows a rem in the sequence to be found by multiplying the previous term by the common ratio r
For this sequence
r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-21}{-3}[/tex] = 7 , then recursive formula is
[tex]a_{n}[/tex] = 7[tex]a_{n-1}[/tex]
I'm lazy and dont feel like doing math myself. So pls help me!
I'm asking this again cuz no one answer it the first time T-T
Answer:
55
Step-by-step explanation:
Well you just plug in 10 as n.. and you get the equation:
[tex]\frac{10(10+1)}{2} \\\frac{10(11)}{2}\\\\\frac{110}{2}\\\\55[/tex]
Are these two equal ?
Can we make -x/x+1 to x/-(x+1) and becomes x/-x-1
Answer:
Yes, they are equivalent.
One way you can check this is by substituting any number into x.
For example, x = 2:
• First equation : [tex]\frac{-x}{x + 1}[/tex]
⇒ [tex]\frac{-2}{2 + 1}[/tex]
⇒ [tex]\frac{-2}{3}[/tex]
• Second equation: [tex]\frac{x}{-x-1}[/tex]
⇒ [tex]\frac{2}{-2-1}[/tex]
⇒ [tex]\frac{-2}{3}[/tex]
As both forms of the equation give the same result after substitution, they are equivalent.
What is the degree form for 4π/5 radians?
Answer: 144 degrees
Step-by-step explanation:
Formulas:Radian ⇒ Degree = 180/π
Degree ⇒ Radian = π/180
[tex]\frac{4\pi }{5} *\frac{180}{\pi } =\frac{4}{5} *\frac{180}{1} =\frac{720}{5} =144[/tex]
Therefore your answer is 144 degrees
Hello !
π rad <=> 180°
4π/5 rad <=> ?°
The calculation ils attached.
We found 144°.
Have a nice day ;)
38. For the following exercises, sketch a line with the given features.
38. An x-intercept of (-4,0) and y-intercept of (0,-2)
Answer:
see image
Step-by-step explanation:
The x-intercept is the point where the line crosses the x-axis (horizontal, left and right line with numbers, arrows at both ends, usually marked x at the right end)
The y-intercept is where your line crosses the y-axis (vertical, up-and-down line with numbers, arrows at the ends, usually marked y at the top)
Two points determine a line.
Draw a line through the two points given. See image.
Which of the following systems of inequalities has point C as a solution? Two linear functions f of x equals 3 times x plus 4 and g of x equals negative one half times x minus 5 intersecting at one point, forming an X on the page. A point above the intersection is labeled A. A point to the left of the intersection is labeled B. A point below the intersection is labeled C. A point to the right of the intersections is labeled D. f(x) ≤ 3x + 4 g of x is less than or equal to negative one half times x minus 5 f(x) ≥ 3x + 4 g of x is less than or equal to negative one half times x minus 5 f(x) ≤ 3x + 4 g of x is greater than or equal to negative one half times x minus 5 f(x) ≥ 3x + 4 g of x is greater than or equal to negative one half times x minus 5
The inequalities that will have point C as a solution are;
f(x) ≥ 3x + 4
g of x is greater than or equal to negative one half times x minus 5
What is the solution of the Inequality?We can see the inequality graph in the attached file.
Now, the two lines in the graph represent the equations;
f(x) = 3x + 4
g(x) = -¹/₂x - 5
Now, we see the point C and from inspection of the graph, we can see that it is to the right of f(x) and to the bottom of g(x) an as such the inequalities that will have point C as a solution is;
f(x) ≥ 3x + 4
g of x is greater than or equal to negative one half times x minus 5
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Mr. Frankel bought 8 tickets to a puppet show and spent $49. He bought a combination of child tickets for $5 and adult tickets for $8
each. Write a system of equations to determine the number of adult, a, and the number of child tickets, c, he bought. solve for equations
Answer: adult = 3 child = 5
Step-by-step explanation:
49 = 8a+5c
8 = a+c
use those equations to solve^^
Which number line represents the solution for the
inequality |2x - 5] ≥ 3?
The attached graph represents the number line of the inequality |2x - 5] ≥ 3
How to determine the number line?The inequality is given as:
|2x - 5] ≥ 3
Remove the absolute value sign
2x - 5 ≥ 3 or 2x - 5 ≥ -3
Add 5 to both sides
2x ≥ 5 + 3 or 2x ≥ 5-3
Evaluate
2x ≥ 8 or 2x ≥ 2
Divide through by 2
x ≥ 4 or x ≥ 1
Combine both inequalities
x ≤ 1 and x ≥ 4
See attachment for the number line
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Find the volume in cm^3 of a right circular cylinder with a radius of 10 cm and height of 14 cm
4398.22 cm³ the volume of cylinder.
What is volume of cylinder?
'Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface. The unit of volume is in cubic units such as m3, cm3, in3 etc.Given,
Height of cylinder = 14 cm
radius of cylinder = 10 cm
Now using formula volume of the cylinder = π r² h
put value in formula,
3.14 × 10× 10 × 14 = 4398.22 cm³
Therefore, 4398.22 cm³ the volume of cylinder.
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What is the equivalent 6/10 1. 3/5 2. 9/12 3. 20/50 4. 40/50
Answer:
1.) 3/5
Step-by-step explanation:
When know that 3/5 is equivalent to 6/10 because both the numerator and the denominator are scaled up/down by the same amount. To be precise, we can get the answer of 3/5 by dividing the numerator and denominator by 2.
6 / 2 = 3
10 / 2 = 5
Can someone help me out on this geometry postulate questions? It’s urgent
20) [tex]\overline{AC} \cong \overline{AC}[/tex] by the reflexive property, so SSS
21) [tex]\overline{CD} \cong \overline{CD}[/tex] by the reflexive property, so ASA
22) [tex]\overline{CE} \cong \overline{CB}, \overline{AC} \cong \overline{CD}[/tex] by the definition of a midpoint and [tex]\angle 1 \cong \angle 2[/tex], so SAS
23) [tex]\overline{AC} \cong \overline{AC}[/tex] by the reflexive property, so ASA
Find the total surface area of this triangular prism.
18 cm
30 cm
24 cm
7 cm
Answer:
936 cm^2
Step-by-step explanation:
Solution
Back (This is a rectangle)
Area = w * h
w = 7
h = 18
Area = 7 * 18 = 126 cm^2
Front and Back
Area = 1/2 * B * H (This is a triangle -- There are 2 of them)
Givens
B = 24
h = 18
Area = 1/2 * 24 * 18
Area = 216
But there are two such triangles = 2*216 = 432 cm ^2
Ramp
Formula Area = L*w (This is a rectangle)
L = 30
W = 7
Area = 30 * 7 = 210 cm^2
Base
This is also a rectangle
L = 24
W = 7
Area = L*W
Area = 24 *7 = 168 cm^2
Total
168 cm^2
210 cm^2
432 cm^2
126 cm^2
936 cm^2
PROBLABILITY!!!
(I added the picture needed)
1.Create a sample space and find the product of each combination. What is the probability that a person wins the game? Express your answer as a fraction in lowest terms and as a percent rounded to the nearest tenth.
(answer to this one is 9/28 and 32.1%)
2. You realize a short time into the carnival that you don’t have enough prizes to last the entire event. You call your teacher, and she suggests that you change the winning number so that a participant will win only 25% of the time. What number will that be? Support your answer.
3. Participants achieving a winning score of 36 or higher in four consecutive attempts will receive a large prize! What is the probability of this occurring?
4. After changing the game rules, participants and the crowd are disappointed when the first five games yield scores of 12, 18, 30, 28, and 24. What statement can you recommend the teacher posts to reassure everyone that the game is fair?
Based on the rules of the game, the probability that a person wins the game is 3/8 or 37.5%.
If participants can only win 25% of the time, the number that they need to get would be 32 or higher.
The probability of a winning score of 36 or higher in four consecutive attempts is 1/1,296.
To show that the game is fair, the teacher can post that every number apart from 24 and 30 has an equal chance of appearing.
What is a good sample space to represent the data?There are 6 sides to dice and 4 cards. The sample space is:
Dice Card Product Frequency of Product
1 5 5 1
1 6 6 1
1 7 7 1
1 8 8 1
2 5 10 1
2 6 12 1
2 7 14 1
2 8 16 1
3 5 15 1
3 6 18 1
3 7 21 1
3 8 24 2
4 5 20 1
4 6 24 1
4 7 28 1
4 8 32 1
5 5 25 1
5 6 30 2
5 7 35 1
5 8 40 1
6 5 30
6 6 36 1
6 7 42 1
6 8 48 1
Total 24
24 and 30 have frequencies of 2 as they appear twice.
From the table, in order to win, a player needs to get 28 or higher.
There are only 8 numbers that are 28 or higher but including the chance that 30 has a relative frequency of 2, we have 9 chances to win the game. The probability is:
= 9 / 24
= 3 / 8
How can a player win 25% of the time?If people are to win only 25% of the time, this means that the number of products that can be picked is:
= 25% x 24
= 6
To find the winning number, count down from the highest product 6 times to get 32.
A person therefore needs to get 32 or above to win 25% of the time.
What is the probability of winning the large price?The probability of getting 36 or higher is:
= Chance of 36 + chance of 40 + chance of 42 + chance of 48
= 1 / 24 + 1/24 + 1/24 + 1/24
= 1 / 6
The probability of repeating this 4 times is:
= 1 / 6 x 1 / 6 x 1/ 6 x 1 / 6
= 1 / 1,296
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Find the slant height x of the pyramid shown, to the nearest tenth.
6mm
7mm
7mm
Options:
A: 4.35
B: 9.2
C: 6.9
D: 3.9
Answer: C
Step-by-step explanation:
Construct the segment connecting the point where the height meets to the base to where the slant height meets the base.
This forms a right triangle with legs of length 3.5 and 6.
So, by the Pythagorean theorem, [tex]x=\sqrt{3.5^2 + 6^2} \approx 6.9[/tex]
Factor the expression. q²r+ blank s^2t)(blankq^4r^2-6q^2rs^2t+blanks^4t^2
The equivalent expression of (q² − r²s) (q⁴ + q²r²s + r⁴s²) is q⁶ - r⁶s³
How to factor the expression?The expression is given as:
(q² − r²s) (q⁴ + q²r²s + r⁴s²)
Expand the expression
(q² − r²s) (q⁴ + q²r²s + r⁴s²) = q²(q⁴ + q²r²s + r⁴s²) − r²s(q⁴ + q²r²s + r⁴s²)
Open the brackets
(q² − r²s) (q⁴ + q²r²s + r⁴s²) = q⁶ + q⁴r²s + q²r⁴s² -q⁴r²s - q²r⁴s² - r⁶s³
Evaluate the like terms
(q² − r²s) (q⁴ + q²r²s + r⁴s²) = q⁶ - r⁶s³
Hence, the equivalent expression of (q² − r²s) (q⁴ + q²r²s + r⁴s²) is q⁶ - r⁶s³
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Complete questionFactor the expression. (q² − r²s) (q⁴ + q²r²s + r⁴s²)
The triangles are congruent by the SSS congruence theorem.
Triangles A B C and F E D are shown. Triangle A B C is reflected across A C and then is shifted down and to the left to form triangle F E D.
Which rigid transformation(s) can map TriangleABC onto TriangleFED?
reflection, then dilation
reflection, then translation
rotation, then translation
rotation, then reflection
The rigid transformations that maps ΔABC onto ΔFED by reflection then translation.
The correct option is (B).
What is Translation?Translation is also another form of transformation whereby all the points of a figure are shifted at exactly the same distance and in the same direction without being resized, reflected nor rotated.
given:
ΔABC ≅ ΔFED are congruent by the SSS Congruence Theorem.
Hence, the rigid transformations that maps ΔABC onto ΔFED by reflection then translation.
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Answer:
B
Step-by-step explanation:
Can someone explain 03.05 Polynomial Identities and Proofs for me?
The polynomial Identities and an example of a proof of an identity have been explained below.
What are polynomial Identities and Proofs?Polynomial identities are defined as equations that are always true, regardless of the variable values. These polynomial identities are used while factorizing the polynomial or expanding the polynomial. These polynomial identities are;
(a + b)² = a² + b² + 2ab
(a - b)² = a² + b² - 2ab
(a + b)(a - b) = a² - b²
(x + a)(x + b) = x² + x(a + b)+ ab
Let us prove the polynomial identity (a + b)² = a² + b² + 2ab.
Now, (a + b)² is simply the product of (a + b) and (a + b).
That is; (a + b)² = (a + b) × (a + b)
This can simply be imagined to be a square whose side are (a + b) with its' area equal to (a + b)²
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Which is equivalent to start root 10 EndRoot Superscript three-fourths x ?
Answer:
d&#&#;#;'xn x;e;÷hr&÷h÷ebb ehehhbbsssshhheu73334914218899110
Find m, given that the three angles of a triangle are (m+18), (2m+28) and (3m+47).
Step-by-step explanation:
As all angles in a triangle add up to 180°
we can write:
(m+18)+(2m+28)+(3m+47) = 180
6m + 93 = 180
6m = 180 - 93
6m = 87
m = 87 / 6
m = 14.5
i need the answer for this question, look at the image below for help
Answer:
x axis is -2.
y axis is +1.
(-1, 3)
What is Meant By Graphing Functions?Graphing functions is drawing the curve that represents the function on the coordinate plane. If a curve (graph) represents a function, then every point on the curve satisfies the function equation.
According to the question,
The following graph represents the linear function f(x) = x -2
Take any point on this line, say, (-1, 3).
Let us substitute (-1, 3) = (x, y) (i.e., x = -1 and y = 3) in the function f(x) = -x + 2 (note that it can be written as y = x - 2).
Then
3 = -(-1) + 2
3 = 1 + 2
3 = 3, thus, (-1, 3) satisfies the function.
In the same way, you can try taking different points and checking whether they satisfy the function. Each and every point on the line (in general called "curve") satisfies the function.
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HELP!!!!!!!!
Find the direction of vector shown above. A. -68.2 N of E B. -21.8 N of E C. 21.8 N of W D. 68.2 N of W
The direction of the vector is - 21.8 N of E , Option B is the answer.
What is a Vector ?A vector is an object with both magnitude and direction.
A vector is shown in the graph.
To determine the direction , The angle needs to be determined
The slope of the vector will give the direction of the vector
The vector starts from the point (1 , 1)
Another point on the vector (-4 , 3)
slope = -2 /5
It is making angle x with the line y = 1
tan x = -2 /5
x = - 21.8 N of E.
Therefore the direction of the vector is - 21.8 N of E , Option B is the answer.
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John bought a computer scanner and supplies for $215.70, which will
allow him to scan images for $0.34 each. A computer center charges
$0.59 to scan each image. How many images must John scan before
his total cost is less than getting scanned images at the computer
center?
John must scan more than 862 images before his total cost is less than getting scanned images at the computer center.
To determine how many images John must scan before his total cost is less than getting scanned images at the computer center, we can set up an equation.
Let's denote the number of images John needs to scan as "x."
The total cost for John to scan x images is given by:
John's total cost = cost of scanner + cost of supplies + cost per image scanned
John's total cost = $215.70 + ($0.34 * x)
The total cost for scanning x images at the computer center is given by:
Computer center's cost = cost per image scanned * x
Computer center's cost = $0.59 * x
We want to find the point at which John's total cost is less than the computer center's cost. In other words, we want to find the value of x for which John's total cost is less than the computer center's cost:
John's total cost < Computer center's cost
$215.70 + ($0.34 * x) < $0.59 * x
Now, we can solve for x:
$215.70 + ($0.34 * x) < $0.59 * x
$215.70 < $0.59 * x - $0.34 * x
$215.70 < $0.25 * x
Divide both sides of the inequality by $0.25:
$\frac{215.70}{0.25} < \frac{0.25 * x}{0.25}$
862.80 < x
Therefore, John must scan more than 862 images before his total cost is less than getting scanned images at the computer center.
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In a Fischer projection with only one horizontal line crossing through the vertical line, the point at which the two lines cross represents ______________.
The Central Carbon
What is Fischer's projection?It is a method that represents the three-dimensional structures of molecules on a single page. These are a convenient way to represent the molecules and distribute them between the pairs of enantiomers. These are very often used to represent isomers of sugars.
The Fischer Projection consists of horizontal and vertical lines, the horizontal lines represent atoms that are pointed out of the plane and the vertical line represents atoms that are pointed away from the plane. The intersection point of the horizontal line and the vertical line represents the central carbon.
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