The solution of the equation x³ + x² - 6x = 0 are x=0, x=2 and x=-3.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is x³ + x² - 6x = 0
x cube plus x square minus six times of x equal to zero.
Take x as common
x(x² + x - 6) = 0
Now factorize the equation within the parenthesis
x(x² + 3x - 2x - 6) = 0
x[x(x + 3) - 2(x + 3)] = 0
x(x - 2)(x + 3) = 0
Now
x = 0
x - 2 = 0 => x = 2
x + 3 = 0 => x = - 3
Hence, the solution of the equation x³ + x² - 6x = 0 are x=0, x=2 and x=-3.
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Final answer:
The equation [tex]x^3 + x^2 - 6x = 0[/tex]is factored into x(x + 3)(x - 2) = 0 to find the roots, which are x = 0, x = -3, and x = 2.
Explanation:
To solve the equation [tex]x^3 + x^2 - 6x = 0[/tex], we first recognize that the equation is not a quadratic, but a cubic equation. However, we can factor out an x, which simplifies the equation to [tex]x(x^2 + x - 6) = 0.[/tex]The cubic term now has been factored into a linear term and a quadratic term. The quadratic equation [tex]x^2 + x - 6[/tex] can be factored further into (x + 3)(x - 2).
The roots of the equation are the values of x that make the equation equal to zero. By setting each factor equal to zero, x = 0, x + 3 = 0, and x - 2 = 0, we find the solutions to be x = 0, x = -3, and x = 2.
Line AB is parallel to line CD. Which statement is true?
A)
Angle d is congruent to angle b.
B)
Angle d is congruent to angle c.
Angle d is congruent to angle e.
Angle d is congruent to angle f.
Answer:
c
Step-by-step explanation:
Select the equivalent expression
The equivalent expression is: (C) [tex]$\frac{1}{3^9 \cdot 6^{18}}$[/tex].
To simplify the given expression, we can apply the rules of exponents.
First, we raise 3 to the power of 3 and 6 to the power of 6, individually:
3^3 = 27 and 6^6 = 46656.
Next, we multiply these two values together:
27 * 46656 = 1259712.
Now, we raise the result to the power of -3:
1259712^(-3).
To simplify this expression, we can rewrite it as the reciprocal of the base raised to the positive exponent:
(1 / 1259712^3).
This can be further simplified by raising the base to the power of 3:
(1 / (1259712 * 1259712 * 1259712)).
Finally, we can simplify the expression by multiplying the denominators:
1 / (1954890816015872).
CAN SOMEONE PLEASE HELP ME??!!!
PLZ HURRY!!!
Answer:
It's the first one
22 points Please Help!!
Which is enough information to prove that u parallel to v? Lines u and v are cut by transversal t. Clockwise from top left, the angles formed by t and u are 1, 2, 3, 4; formed by v and t are 5, 6, 7, 8.
A) Angle 2 is congruent to angle 4
B) Angle 4 is congruent to angle 8
C) Angle 6 + angle 7 = 180 degrees
D) Angle 3 + angle 4 = 180 degrees
Answer:
B) Angle 4 is congruent to angle 8
Step-by-step explanation:
In ΔSTU, u = 23 inches, ∠T=158° and ∠U=17°. Find the length of t, to the nearest 10th of an inch.
Answer: t = 29.5 inches
Step-by-step explanation:
Given that the ΔSTU, u = 23 inches, ∠T=158° and ∠U=17°.
We can Find the length of t by using sine rule
t/saint = u/sinU
t/sin158 = 23/sin17
t = sin158 × 23/sin17
t = 29.47 inches
t = 29.5 inches
Answer:
29.5
Step-by-step explanation:
HELPPP MEEEE I showed picture up there
Answer:
median
Step-by-step explanation:
Answer:
C is the median
Step-by-step explanation:
The center line in the box is the median of the data. The median is the middle point of the data set.
4. A book club earns $230 for its meetings. They want to divide the money to pay for 7 meetings. When the treasurer types 230 ÷ 7 into a calculator, the number that appears is 32.8571. Where should the treasurer round the answer? Explain. Pls explain
Answer:
to the tenths place, 32.86
Step-by-step explanation: It is because money is always rounded to the tenths place
93, 95 , 102, 91, 104, 93, 95, 98, 97, 92 , 102 , 96, 92, 104 , 100, 98,
Find the MEAN is this data set ?
And the ABSOLUTE DEVIATION ?
The mean of a dataset is the sum of the elements divided by how many elements are present in the data set.
The sum of the elements in this dataset is
[tex]93+95+102+91+104+93+95+98+97+92+102+96+92+104+100+98=1552[/tex]
And there are 16 elements, so the mean is
[tex]\mu = \dfrac{1552}{16}=97[/tex]
The absolute deviation is computed as follows:
For each term in the dataset, we consider its distance from the mean. In formulas, we compute [tex]|x_i-\mu|[/tex] for every element [tex]x_i[/tex] We take the average of all these terms: [tex]\frac{1}{n}\sum|x_i-\mu|[/tex]So, following the first point, the new dataset is
[tex]\{4, 2, 5, 6, 7, 4, 2, 1, 0, 5, 5, 1, 5, 7, 3, 1\}[/tex]
And the average of this dataset is
[tex]\dfrac{4+2+5+6+7+4+2+1+0+5+5+1+5+7+3+1}{16} = \dfrac{58}{16}=3.625[/tex]
How does the photo support the sidebar about how migrant children were treated? Check all that apply.
It shows how people felt about the children.
It shows why children needed medical attention.
It shows the way migrant children dressed.
It shows how migrant children had to work.
It shows feelings of sadness from unfair treatment.
Answer:
It shows the way migrant children dressed.
It shows how migrant children had to work.
It shows feelings of sadness from unfair treatment.
Step-by-step explanation:
those 3 are correct
Answer:
It shows the way migrant children dressed.
It shows how migrant children had to work.
It shows feelings of sadness from unfair treatment.
Step-by-step explanation:
Just took test
On Monday a team of street sweepers cleaned 2 1/2 city blocks Tuesday the team cleaned 1/4 as many blocks as on Monday how many city blocks did the streets sweepers clean on tuesday
On Tuesday, the street sweepers cleaned [tex]\( \frac{5}{8} \)[/tex] city blocks.
On Tuesday, the team of street sweepers cleaned [tex]\( \frac{1}{4} \)[/tex] as many blocks as they did on Monday.
Given that they cleaned [tex]\( 2\frac{1}{2} \)[/tex] city blocks on Monday, we need to find [tex]\( \frac{1}{4} \)[/tex] of this amount to determine how many blocks they cleaned on Tuesday.
To find [tex]\( \frac{1}{4} \)[/tex] of [tex]\( 2\frac{1}{2} \),[/tex] we multiply [tex]\( 2\frac{1}{2} \)[/tex] by [tex]\( \frac{1}{4} \)[/tex]:
[tex]\[ 2\frac{1}{2} \times \frac{1}{4} = \frac{5}{2} \times \frac{1}{4} = \frac{5}{8} \][/tex]
So, the street sweepers cleaned [tex]\( \frac{5}{8} \)[/tex] city blocks on Tuesday.
A cyclist rode at constant speed of 23 mph for 4 hours. Then, she decreased her rate of speed to 16 mph for 5 hours. How far did the cyclist ride in 9 hours?
The cyclist rode a total of 172 miles in 9 hours, covering 92 miles at 23 mph for 4 hours and 80 miles at 16 mph for 5 hours.
Explanation:To find out how far the cyclist rode in 9 hours, we need to calculate the distance covered at each speed and then add those distances together. The cyclist rode at a constant speed of 23 mph for 4 hours and then at a speed of 16 mph for 5 hours.
First, we calculate the distance at 23 mph:
Distance = Speed × Time
Distance at 23 mph = 23 mph × 4 hours = 92 miles
Next, we calculate the distance at 16 mph:
Distance at 16 mph = 16 mph × 5 hours = 80 miles
Now, we add the distances together to get the total distance:
Total Distance = Distance at 23 mph + Distance at 16 mph
Total Distance = 92 miles + 80 miles = 172 miles
Therefore, the cyclist rode a total of 172 miles in 9 hours.
What is the length of side s of the square shown below?
The length of side "s" of the square is 3 units, as it is equal to one of the legs of the 45-45-90 right triangle formed by the diagonal of the square.
To find the length of side "s" of the square shown below, we can use trigonometry, specifically the properties of right triangles and the fact that the diagonal divides the square into two congruent 45-45-90 right triangles.
Given information:
The diagonal of the square measures 6 units.
One of the angles at the top of the square is 45 degrees.
Step 1: Recognize the properties of the 45-45-90 triangle:
Since the diagonal divides the square into two congruent right triangles, and one angle is 45 degrees, we have a 45-45-90 triangle. In such a triangle, the two legs (the sides opposite the 45-degree angles) are congruent, and the hypotenuse (the side opposite the 90-degree angle) is √2 times the length of a leg.
Step 2: Use trigonometric ratios:
Let "x" be the length of one leg of the 45-45-90 triangle, which is also equal to side "s" of the square.
From the properties of the 45-45-90 triangle:
x (leg) = s (side of the square)
Hypotenuse = √2 * leg
Given that the diagonal of the square is 6 units, we can relate the diagonal to the legs:
Diagonal = 2 * leg
6 = 2 * x
Now, solve for x (the length of one leg of the triangle and side "s" of the square):
x = 6 / 2 = 3 units
So, the length of side "s" of the square is 3 units.
Therefore, from the given options the correct one is B.
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In a lab experiment, 1900 bacteria are placed in a petri dish. The conditions are such
that the number of bacteria is able to double every 29 hours. How many bacteria
would there be after 6 hours, to the nearest whole number?
Answer:
393 bacteria
Step-by-step explanation:
First find how much it would increase per hours :
1900 / 29 = 65.5172414
Then take this and multiply it by 6 to get :
393.103448
Round it to the nearest whole number to get:
393 bacteria
Answer:2193
Step-by-step explanation:
y= 1900(2)^6/29
4e^x -2= 14 solve for X
Answer:
x = 1.386
Step-by-step explanation:
4e^x= 16
e^x=4
ln(e^x)=ln4
x=ln4=1.386
please help with this
Answer:
Arc Length: [tex]S=r\theta[/tex]
[tex]S=3\frac{7\pi}{3}\\S=7\pi in[/tex]
Ina city school, 65% of students have green eyes. 25% have red hair, and 15% have green eyes and
red hair. What is the probability (rounded to the nearest whole percent) that a randomly selected
student will have red hair given that the student has green eyes?
Answer:
23% of student will have red hair given that the student has green eyes.
Step-by-step explanation:
We are given the following in the question:
Percentage of students that have green eyes = 65%
[tex]P(G) =0.65[/tex]
Percentage of students that have red hairs = 25%
[tex]P(R) =0.25[/tex]
Percentage of students that have green eyes and red hairs = 15%
[tex]P(G\cap R) =0.15[/tex]
We have to find the conditional probability of randomly selected student that will have red hair given that the student has green eyes.
[tex]P(R|G) = \dfrac{P(R\cap G)}{P(G)}[/tex]
Putting values, we get,
[tex]P(R|G)=\dfrac{0.15}{0.65} = 0.2307\approx 23\%[/tex]
Thus, 23% of student will have red hair given that the student has green eyes.
How to find the mad of the numbers 3,7,4,2
Answer:
the mean absolute deviation would be 1.5.
Step-by-step explanation:
Mean: 3 + 7 + 4 + 2 = 16/4 = 4
4 - 3 = 1
4 - 7 = 3
4 - 4 = 0
4 - 2 = 2
(M.A.D) Mean Absolute Deviation: 1 + 3 + 0 + 2 = 6/4 = 1.5
Which coordinate pair identifies a point in the third quadrant of the coordinate plane?
A) (8, 12)
B) (7, −9)
C) (−10, 6)
D) (−6, −8)
DO NOT GUESS
Answer:
The answer is D) (-6,-8) because in order to have a coordinate in the III quadrant you need two negatives.
Step-by-step explanation:
Answer:
The correct answer is D) (-6,-8)
Step-by-step explanation:
All points in the third quadrant have two negative numbers.
The length of the diagonal of a rectangle is 181 inches.
Which statement describes the length of the diagonal?
Answer:
181 is the thing is what it says it is just find the volum
Step-by-step explanation:
Answer:
13 and 14 inches
Step-by-step explanation:
Question 2
0 Find 2/3 + 1/2
Answer:
1 1/6
Step-by-step explanation:
Answer:
7/6
Step-by-step explanation:
2/3 + 1/2 = (2*2)/(3*2)+ (1*3)/(2*3)=4/6+3/6=(4+3)/6=7/6
Or the mixed numer: 7/6 =1 1/6
On a coordinate plane, line A goes through points (negative 3, 0) and (0, 4), and line B goes through points (0, negative 4) and (2, 0). Which line has the steeper slope? Line has a steeper slope
Answer:
Line B
Step-by-step explanation:
I got it right
Line B has a steeper slope than line A because its slope is greater than the slope of line A.
What is the slope of the line?The slope of a line is defined as the angle of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)
For line A, the two points are (-3, 0) and (0, 4).
Plugging these values into the formula, we get:
slope = (4 - 0) / (0 - (-3)) = 4 / 3
For line B, the two points are (0, -4) and (2, 0).
Plugging these values into the formula, we get:
slope = (0 - (-4)) / (2 - 0) = 4 / 2 = 2
Therefore, line B has a steeper slope than line A, because its slope is greater than the slope of line A. Line A has a slope of 4/3, while line B has a slope of 2.
We can also visualize this by drawing the lines on a coordinate plane. Line B will have a more steeply inclined slope than line A, as it will rise more quickly as it moves from left to right.
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The parks department is installing a new picnic area that measures 20 yards by 48 feet.
They are going to cover the new picnic area with square pieces of sod.
If the sod costs $11 per square yard, how much will the parks department pay to completely cover the picnic area with sod?
Answer:
$3520
Step-by-step explanation:
Conversion
To convert feet to yards, we divide the measurement of feet by 3 hence for dimenaion given as 48 ft, it will be 48÷3=16 yards
The area will be given by the product of length and width and since both measurements are given
A=lw
A=16*20=320 yd²
Cost will be 320*11=$3520
Therefore, the department will have to pay $3520 for the work to be completed
After opening day, theme park attendance has been tracked at a new park in Destin, FL..
Answer:
13.9% marginal
Step-by-step explanation:
The percentage of tickets sold to Seniors can be found as:
[tex]p(s)=\frac{S}{N}\cdot 100[/tex]
where
S is the number of all tickets sold to seniors
N is the total number of tickets sold
By looking at the table, we see that:
S = 32 + 14 + 54 = 100 is the number of tickets sold to seniors
N = 35 + 87 + 62 + 56 + 177 + 205 + 32 + 14 + 54 = 722 is the total number of tickets sold
Therefore, the percentage is:
[tex]p(s)=\frac{100}{722}\cdot 100 =13.9\%[/tex]
The three different types of frequencies are defined as:
- Joint: the frequency of a single category calculated with respect to the total number --> this is not the case
- Marginal: the frequency of an entire row/column over the total --> this is the case
- Conditional: the frequency of a single category over a subset of the total --> this is not the case
So, the correct answer is
13.9% marginal
Is the leading coefficient of the function positive or negative?
Answer:
Negative.
Step-by-step explanation:
To understand the question, you first must understand the slopes of different types of equations.
A linear equation: [tex]y = 2x[/tex] will travel from the third quadrant to the first.
If you plug in 2 for x, y will equal 4. Both values are positive, leading to a positive correlation.
A linear equation: [tex]y = -3x[/tex] will face the other direction, as shown in your attached image. When you plug in a positive number for x, like 5, y will equal -15, making the graph go up and left towards negative values.
3 + x + x = 15
Just need a simple answer and explanation thank you
Answer:
6
Step-by-step explanation:
3+x+x=15
3+2x=15
2x=15-3
2x=12
x=12/2
x=6
Answer:
x=6
Step-by-step explanation:
x=6 because if you simplify this equation you get 3 + 2x = 15. The first step to solving a equation is having the x value on one side of the equation and the number value on one side. to do this we can subtract 3 from both sides of the equation and get the equation 2x=12. which would mean x=6.
Which equation will help you find the measure of
angle x?
Answer:
x + 97 = 180
Step-by-step explanation:
Being that vertical line is straight, that 97 degrees and x must add up to equal 180 degrees. Therefore, x + 97 = 180 would help you solve for x.
James cut out four parallelograms, the dimensions of which are shown below. Parallelogram 1 length: 12 in. width: 15 in. diagonal: 20 in. Parallelogram 2 length: 16 in. width: 30 in. diagonal: 34 in. Parallelogram 3 length: 20 in. width: 21 in. diagonal: 29 in. Parallelogram 4 length: 18 in. width: 20 in. diagonal: 26 in. James put the parallelograms together so one vertex from each paper exists on a point, as shown in the circle. 4 parallelograms are put together so that one vertex from each paper exists on a point. Which statement explains whether or not the parallelgrams can be put together so each occupies one-quarter of the area of the circle without overlapping any other pieces? Check all that apply. The quadrilaterals can be placed such that each occupies one-quarter of the circle. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 1 do not form right angles. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 2 do not form right angles. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 3 do not form right angles. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 4 do not form right angles.
Answer: The correct options are options 1 and 4.
The quadrilaterals cannot be placed such that each occupies one quarter of the circle because the vertices of parallelogram 1 do not form right angles.
The quadrilaterals cannot be placed such that each occupies one quarter of the circle because the vertices of parallelogram 4 do not form right angles.
Step-by-step explanation: When you have the dimensions of a quadrilateral given along with the diagonal (which is also the hypotenuse) you basically have the quadrilateral divided into two triangles. You can determine if the triangles are going to be right angled or not simply by using the Pythagoras theorem as a test.
Note also that if the angles are right angled, then the quadrilaterals can all be conveniently placed, one in each quarter of the circle without overlapping. This is possible because each quarter of a circle measures 90 degrees.
To test if the angles formed are right angled we shall take the following steps;
Pythagoras theorem states that; AC² = AB² + BC²
Where AC is the longest side (hypotenuse), and AB and BC are the other two sides.
(Quad 1) ------> 20² = 12² + 15²
400 = 144 + 225
400 ≠ 369
Both sides pf the equation are not equal, hence the vertices of parallelogram 1 do not form a right angle.
(Quad 2)------> 34² = 16² + 30²
1156 = 256 + 900
1156 = 1156
Both sides of the equation are equal, hence the vertices of parallelogram 2 forms a right angle
(Quad 3)------> 29² = 20² + 21²
841 = 400 + 441
841 = 841
Both sides of the equation are equal, hence the vertices of parallelogram 3 forms a right angle
(Quad 4)------> 26² = 18² + 20²
676 = 324 + 400
676 ≠ 724
Both sides sides of the equation are not equal, hence the vertices of parallelogram 4 do not form a right angle.
From the results shown above, if the four parallelograms are placed in each of the four corners of the circle, they would definitely overlap because two of them do not form right angles at their vertices.
Answer:
B & E
Step-by-step explanation:
The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 1 do not form right angles.
The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 4 do not form right angles.
Use a trigonometric ratio to find the value of x. Round your answer to the nearest
tenth.
Answer:
x=63.256% 63.3-rounded to the nearest tenth.
Step-by-step explanation:
Find the value of x.
Answer:
x = 50
Step-by-step explanation:
The measure of the secant- secant angle is one half the difference of the measures of the intercepted arcs, that is
x = [tex]\frac{1}{2}[/tex] (130 - 30) = 0.5 × 100 = 50
A person is carrying a dog that weighs 50 pounds. The person weighs x pounds. Which equation can be used to find w, the total weight of the person and the dog in pounds?
Answer:
w = x + 50
Step-by-step explanation:
The dog is 50 pounds. The person's weight is x. You are trying to find the total weight of the dog and person. Therefore, you need to combine the two values to get the total, making the equation w = x + 50, or x + 50 = w