Solution
[tex]x^3+3x^2-6x-18[/tex]We can do the following:
[tex]x^2(x+3)-6(x+3)=(x+3)(x^2-6)[/tex]Then the correct answer would be:
[tex]B\mathrm{}(x^2-6)(x+3)[/tex]For the second case we have the following:
[tex]9x^2-64y^2[/tex]We can do this:
[tex](3x-8y)(3x+8y)[/tex]Zoo AttendanceZoo D 234,679Zoo E 872,544Zoo F 350,952For each zoo in the table, round the attendance to the nearest hundred thousand.4 grade student
Explanation
We can round to the nearest hundreds of thousands below.
Answer:
Zoo D: 200,000
Zoo E: 900,000
Zoo F: 400,000
6 The length of a city block running north to south in New York City is about 5 X 10-2 miles The distance from New York City to Mumbai, India, is about 7.5 X 103 miles. The distance from New York City to Mumbai is about how many times the length of a New York City north-south block? Show your work.
What is 5x2 (This is a joke)
Answer:
10 (duh)
Step-by-step explanation:
Write the slope-intercept form of the equation of each line.3) 10 = -2y-x
Recall that the slope-intercept form of the line equation is of the form y=mx+b, where m is the slope and b is the y-intercept.
To transform the equation 10=-2y-x into the slope-intercept form we should apply algebraic operations so we isolate the y on one side of the equation.
Let's add x on both sides, we get
[tex]-2y=10+x[/tex]Now, lets divide by -2 on both sides, we get
[tex]y=\frac{10}{-2}+\frac{x}{-2}=-\frac{1}{2}\cdot x-5[/tex]we see that this now has the slope-intercept form, where the slope is m=(-1/2) and b=-5
Can someone help me out with this because i looked at all the videos that my teacher gave us and none of them explained it.
The meaning of;
[tex]\frac{x}{4}[/tex]In algebra, when there is an unknown number it is generally represented by a letter (such as x,y,z etc.)
The letters x in x/4 represents an unkown number.
So, x/4 represent the unknown number x divided by 4.
For example; if x=20, then;
[tex]\frac{x}{4}=\frac{20}{4}=5[/tex]It is multiple choice and you will have two boxes checked
The correct options are : x = 1.5, side length is 1.6, and side length is 3.9.
We are given a triangle. The vertices of the triangle are P, Q, and R. The lengths of the sides PQ, QR, and RP are "x + 0.1", "x + 2.4", and "3x - 0.6". The triangle is an isosceles triangle. The lengths of the sides RP and QR are equal to each other. So, we can form an equation and find the value of the variable "x".
RP = QR
3x - 0.6 = x + 2.4
2x = 3
x = 1.5
The length of the side PQ is x + 0.1 = 1.5 + 0.1 = 1.6. The length of the side QR is x + 2.4 = 1.5 + 2.4 = 3.9. The length of the side RP is 3x - 0.6 = 3(1.5) - 0.6 = 3.9.
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What is 64 feet in 8 inches
Given
[tex]The\text{ actual house is 64ft long.}[/tex]To draw 64ft long house using a 8 inch scale.
Explanation:
Since the unit of inch is smaller than the unit of feet.
Then, by using the 8inches long scale.
Consider, 1 inch is equal to 8ft.
That implies,
[tex]\begin{gathered} 1inch=8ft \\ 8inch=8\times8ft \\ =64ft \end{gathered}[/tex]Hence,
what are the solutions to this equations ? 2y = 4x + 12y = 2x - 6
Solve the following system of equations;
[tex]\begin{gathered} 2y=4x+12---(1) \\ y=2x-6---(2) \\ \text{From equation (2) substitute for y=2x-6 into equation (1) } \\ 2(2x-6)=4x+12 \\ 4x-12=4x+12 \\ \text{Collect all like terms} \\ 4x-4x=12+12 \\ 0=24 \end{gathered}[/tex]The answer is 0 = 24, which is not possible.
Hence, the system of equations has NO SOLUTION
Just need one answer.Is it reflectional symmetry, Rotational symmetry, or is it both
This is a simple question to solve.
First, let's focus on the reflection symmetry, What is it?
Having a reflection symmetry means if we split the image in half the left side is identical to the right side. To illustrate better, we have the following picture:
As we can see above, the left side of our shape is identical to the right side, it is like a reflection, so: yes, the image has reflectional symmetry.
Now let's focus on rotational symmetry. A
The perimeters of the square and equilateral triangle shown below are equal. Which of the following is NOT a true statement about the figures. Remember: perimeter of a square = 4(one side), and perimeter of an equilateral triangle = 3(one side)
ANSWER
The incorrect option is Each side length of the square is 6 units
EXPLANATION
We are given that the perimeter of the square and the equilateral triangle are equal.
The length of the side of the square is 2x.
The perimeter of a square is given as:
P = 4 * L
=> P = 4 * 2x
P(square) = 8x
The length of side of the triangle is given as 3x - 1.5.
The perimeter of an equilateral triangle is given as:
P = 3 * L
=> P = 3 * (3x - 1.5)
P(triangle) = 9x - 4.5
Therefore, since both perimeters are equal:
8x = 9x - 4.5
Collect like terms:
9x - 8x = 4.5
x = 4.5
Now, for the options:
- The value of x is 4.5
- The perimeter of the square is 8 * 4.5 i.e. 36 units.
- Each side length of the square is 2 * 4.5 = 9 units
- Each side length of the triangle is :
3 * 4.5 - 1.5 = 13.5 - 1.5 = 12 units
So, the incorrect option is Each side length of the square is 6 units
1AcellusFind the area of the shaded region.Help Resources80°5 cmA = [?] cm2Enter a decimal rounded to the nearest tenth.Enter
The formula for finding the area of the unshaded segment is given as
[tex]A=(\frac{\pi\theta}{360}-\frac{\sin \theta}{2})r^2[/tex]Given the following parameters,
π = 3.14
θ = 80°
r = 5 cm
Substituting,
[tex]\begin{gathered} A=(\frac{3.14\times80}{360}-\frac{\sin \text{ 80}}{2})\times5^2 \\ =(\frac{251.2}{360}-\frac{0.9848}{2})\times25 \\ =(0.6978-0.4924)\times25 \\ =0.2054\times25 \\ =5.135\approx5.1\operatorname{cm}^2 \end{gathered}[/tex]To find the area of the shaded portion, we would subtract the area of the unshaded segment from the area of the circle.
Area of circle = πr²
[tex]3.14\times5^2=78.5\operatorname{cm}^2[/tex]Therefore,
The area of the shaded region = 78.5 - 5.1 = 73.4 cm²
Find thr value of x for which 1 II m.
The value of x is 50 for which line l is parallel to line m and the angles are equal by the properties of parallel lines that is vertically opposite angles are equal.
What is parallel lines?Two lines (in the same plane) are said to be parallel if they never collide, regardless matter how far they are extended on either side. Parallel lines travel parallel to each other, like train tracks. Parallel lines in geometry are two lines in the same plane that are at equal distance from each other but never intersect. They can be both horizontal and vertical in orientation. Parallel lines can be found in everyday life, such as zebra crossings, notepad lines, and railway tracks.
Here,
Since l ⇵ m,
Vertically opposite angles are equal by the properties of parallel lines.
2x-5=95
2x=100
x=50
The value of x is 50, which means that line l is parallel to line m and the angles are equal according to the property of parallel lines, which states that vertically opposing angles are equal.
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What happens to the graph of y=2x^3+x^2−7x−6 as x heads toward ∞ and −∞?A. as x→∞, y→∞ as x→−∞, y→−∞B. as x→∞, y→∞ as x→−∞, y→∞C. as x→∞, y→−∞ as x→−∞, y→−∞D. as x→∞, y→−∞ as x→−∞, y→∞
Answer:
A. as x→∞, y→∞ as x→−∞, y→−∞
Explanation:
Given the function:
[tex]y=2x^3+x^2−7x−6[/tex]In order to determine the end behavior of f(x), we use the leading coefficient test.
When using the Leading coefficient test, the following rule applies:
• When the ,degree is odd and the leading coefficient is positive,, the graph falls to the left and rises to the right.
,• When the ,degree is odd and the leading coefficient is negative,, the graph rises to the left and falls to the right.
,• When the ,degree is even and the leading coefficient is positive,, the graph rises to the left and right.
,• When the ,degree is even and the leading coefficient is negative,, the graph falls to the left and right.
From the function, f(x):
• The degree of the polynomial = 3 (Odd)
,• The leading coefficient is 2 (Positive)
Thus, using the 1st rule of the 4 given above, we have that as x→∞, y→∞ as x→−∞, y→−∞.
The correct option is A.
The water temperature of the Pacific Ocean vanes inversely as the water's depth. At a depth of 1000 meters, the water temperature is 4.4 degrees Celsius. What is the water temperature at a depth of 5000 meters?
Mr. Bernard paid $4,794 in social security tax on earnings of $68,000 one year. What was the social security tax rate for that year to the nearest hundredth of a percent)?6.85%7.05%7.15%7.65%None of these choices are correct.
Answer:
7.05%
Explanation:
Mr Bernard taxable income = $68,000
Amount paid as social security tax on earnings = $4,794
Let the social security tax rate = x
This gives:
[tex]\frac{x}{100}\times68,000=4,794[/tex]Next, solve for x:
[tex]\begin{gathered} 680x=4794 \\ x=\frac{4794}{680} \\ x=7.05 \end{gathered}[/tex]The social security tax rate for that year (to the nearest hundredth of a percent) is 7.05%.
Given the function k(n) = -3n + 2, and its domain is described by the set {6,-8, 4, 2}, what is therange?
The domain of a function is the set of values where the function is defined (values of x where y is defined).
The range of a function are the values of the function where is defined (values of y).
For the given function:
[tex]k(n)=-3n+2[/tex]Domain: values of n {6,-8, 4, 2}
Range: values of k(n)
n= 6
[tex]\begin{gathered} k(6)=-3(6)+2 \\ =-18+2 \\ =-16 \end{gathered}[/tex]n=-8
[tex]\begin{gathered} k(-8)=-3(-8)+2 \\ =24+2 \\ =26 \end{gathered}[/tex]n=4
[tex]\begin{gathered} k(4)=-3(4)+2 \\ =-12+2 \\ =-10 \end{gathered}[/tex]n=2
[tex]\begin{gathered} k(2)=-3(2)+2 \\ =-6+2 \\ =-4 \end{gathered}[/tex]Then, the range is: {-16, 26, -10, -4}
Entrance to a state park costs $5 per vehicle, plus $2 per person in the vehicle. How much would it cost for a car with 4 people in the vehicle to enter the park?
From the information given, the entrance to a state park costs $5 per vehicle, plus $2 per person in the vehicle. Given that 4 people entered the one vehicle, the amount that would be paid for the vehicle is $5. Sinec it is $2 per person, the amount for 4 persons would be 2 * 4 = 8
Thus, the total cost would be
5 + 8 = $13
The length of a rectangular garden is 9 feet longer than its width. If the garden's perimeter is 202 feet, what is the area of the garden in square feet?
We have the following rectangular garden
The perimeter is 202 feet, we can do the following equality
[tex]2(x+9)+2x=202[/tex]Now we solve "x"
[tex]\begin{gathered} 2x+18+2x=202 \\ 4x=202-18 \\ x=\frac{184}{4} \\ x=46 \end{gathered}[/tex]Now, we know the longer (l = 55) and the width (w = 46)
To find the area we use the following equation
[tex]\begin{gathered} A_R=l\cdot w \\ A_R=55\cdot46 \\ A_R=2530 \end{gathered}[/tex]In conclusion, the area of the garden is 2530 square feet
Is this the correct solution for this question? I need help please
Given equation:
[tex]9x^2\text{ - 12x + 4 = 0}[/tex]Let's solve the question to identify the type of solution.
Using factorization method:
[tex]\begin{gathered} 9x^2\text{ - 12x + 4 =0} \\ 9x^2-6x\text{ -6x + 4 = 0} \\ 3x(3x-2)\text{ -2(3x-2)= 0} \\ (3x-2)(3x-2)\text{ =0} \end{gathered}[/tex]The solution is thus
[tex]\begin{gathered} 3x\text{ -2 = 0} \\ 3x\text{ = 2} \\ x\text{ = }\frac{2}{3} \end{gathered}[/tex]Hence, there is one solution and it is real.
Answer: 1 real (Option B)
8. * The functions f(x) and g(x) are both linear. f(2) = 4 and f(3) = -1, while g(2) = 6 and g(-3) = 7. Are these lines parallel, perpendicular, or neither? Show your work algebraically. 9. ** f(x) = 5x – 2 and g(x) = 2x + 4. Are f(x) and g(x) parallel, perpendicular or neither parallel nor perpendicular to each other. Justify.
Simplify the expression.
(x)2(2xy3)5
2x3y15
32x7y8
32x7y15
10x3y8
Answer:
[tex]32x^7y^{15}[/tex]
Step-by-step explanation:
[tex]x^2 (2xy^3)^5 \\ \\ =x^2(2^5)(x^5)(y^{(3)(5)}) \\ \\ =x^2(32)(x^5)(y^{15}) \\ \\ =32x^7y^{15}[/tex]
The sum of 4 consecutive integers is 254. What is the value of the greatest integer?
The sum of 4 consecutive integers is 254. What is the value of the greatest integer?
Let
x -----> the first integeer
x+1 ----> second integer
x+2----> third integer
x+3 ----> fourth integer
we have that
x+(x+1)+(x+2)+(x+3)=254
solve for x
4x+6=254
4x=254-6
4x=248
x=62
therefore
the greatest integer is x+3
so
62+3=65
answer is 65I have a question regarding a math topic on my review
The set of real numbers strictly contains the set of integers.
Every integer is a real number.
But pi is a real number and is not an integer
Hence choice A is correct
Find an equation for the perpendicular bisector of the line segment whose endpointsare (-3, 2) and (7,6).
First, we need to find the midpoint. We can find it using the following equations:
[tex]\begin{gathered} Mp=(xm,ym) \\ xm=\frac{x1+x2}{2} \\ ym=\frac{y1+y2}{2} \end{gathered}[/tex]Where:
[tex]\begin{gathered} (x1,y1)=(-3,2) \\ (x2,y2)=(7,6) \end{gathered}[/tex]So:
[tex]\begin{gathered} xm=\frac{-3+7}{2}=\frac{4}{2}=2 \\ ym=\frac{6+2}{2}=\frac{8}{2}=4 \end{gathered}[/tex]Now, we need to find the slope of the line segment:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{6-2}{7-(-3)}=\frac{4}{10}=\frac{2}{5}[/tex]Since it is the line of the perpendicular bisector:
[tex]\begin{gathered} m\cdot mb=-1 \\ \frac{2}{5}mb=-1 \\ mb=-\frac{5}{2} \end{gathered}[/tex]Using the point-slope equation:
[tex]\begin{gathered} y-ym=mb(x-xm_) \\ y-4=-\frac{5}{2}(x-2) \\ y-4=-\frac{5}{2}x+5 \\ y=-\frac{5}{2}x+9 \end{gathered}[/tex]Answer:
[tex]y=-\frac{5}{2}x+9[/tex]6. Find all the solutions of the recurrence relation an = 2an-1 + an-2 + 2n + 1 with initial conditions a1 =7 and a2 = 19
aₙ = 1/2(5/2-4√2)(1-√2)ⁿ+1/2(5/2+4√2)(1+√2)ⁿ-n-5/2 is the solution of aₙ -2aₙ₋₁ + aₙ₋₂ = 2n + 1
What is Recurrence relation?Recurrence relation is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms
aₙ -2aₙ₋₁ + aₙ₋₂ = 2n + 1
Homogenous case,
aₙ -2aₙ₋₁ + aₙ₋₂ with characteristic t²-2t-1=0
t=1
aₙ=C₁.(1-√2)ⁿ+C₂.(1+√2)ⁿ
Special case, Since non homogenous part is 2n+1
Let aₙ=pn+q, then
aₙ -aₙ₋₁ + aₙ₋₂=2n+1
pn+q-2(p(n-1)+q)-p(n-2)-q=2n+1
-2pn+qp-2q=2n+1
p=-1 and q=4p-1/2=-5/2
Combine both cases, aₙ = C₁(1-√2)ⁿ+C₂((1+√2)ⁿ-n-5/2
Substitute a₁=7 and a₂=19
a₁ = C₁(1-√2)+C₂((1+√2)-1-5/2
a₁ = C₁(1-√2)+C₂((1+√2)-7/2=7
(C₁+C₂)+(C₂-C₁)√2)=21/2..(1)
a₂ = C₁(1-√2)²+C₂((1+√2)²-2-5/2
= C₁(1-√2)²+C₂((1+√2)²-9/2=19
3(C₁+C₂)+2(C₂-C₁)√2)=97/2..(2)
By solving 1 and 2 we get
C₁=1/2(5/2-4√2)
C2=1/2(5/2+4√2)
aₙ = 1/2(5/2-4√2)(1-√2)ⁿ+1/2(5/2+4√2)(1+√2)ⁿ-n-5/2
Hence, aₙ = 1/2(5/2-4√2)(1-√2)ⁿ+1/2(5/2+4√2)(1+√2)ⁿ-n-5/2 is the solution of aₙ -2aₙ₋₁ + aₙ₋₂ = 2n + 1
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A function is translated from f(x)=9⋅3x−2 to g(x)=9⋅3x+4−2. What is the effect on f(x)?
Given the functions:
[tex]\begin{gathered} f(x)=9*3x-2 \\ \\ g(x)=9*3x+4-2 \end{gathered}[/tex]Let's determine the transformation that occurred from f(x) to g(x).
Apply the transformation rules for functions.
After a shift d units to theupwards, we have:
[tex]g(x)=f(x)+d[/tex]Thus, from the given translation, we can see that the function f(x) is translated 4 units to get the function g(x).
[tex][/tex]Sketch the graphs for each of the following equations. 7 a. y = 5-X+7 b.y=9 c. y= 3x + 6
a)
Given:
The equation is,
[tex]y=-\frac{7}{5}x+7[/tex]The objective is to sketch the graph of the equation.
Since, the highest degree of the equation is 1, it could be a straight line. The general equation of straight line is,
[tex]y=mx+c[/tex]Here, m represents the slope of the equation and c represents the y intercept. Then comparing the both equations,
[tex]\begin{gathered} \text{slope, m=-}\frac{\text{7}}{5} \\ y\text{ intercept, c=7} \end{gathered}[/tex]Substitute, y = 0 in the given equation.
[tex]\begin{gathered} 0=-\frac{7}{5}x+7 \\ \frac{7}{5}x=7 \\ x=7\cdot\frac{5}{7} \\ x=5 \end{gathered}[/tex]Thus, at y = 0, the value of x = 5.
Using the coordinates (5,0) and y intercept c = 7, the graph will be,
Hence, the required graph is obtained,
3x squared negative 4x squared plus 7x 4x squared negative 4x
ANSWER
[tex]12x^5-28x^4+44x^3-28x^2[/tex]EXPLANATION
First we have to find the partial products by multiplying each term of the first polynomial by each term of the second polynomial:
Now the second term of the second polynomial:
And now we just have to add these partial products:
Identify the mistake
There is no mistake in Chase solving steps.
What is an equation? What is a coefficient?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. In a equation say : ax + b, [a] is called coefficient of [x] and [b] is independent of [x] and hence is called constant.
We have a equation :
(1/3)(g - 3) = 3
We can write -
(1/3)(g - 3) = 3
We can write -
g - 3 = 3 x 3
g - 3 = 9
g = 12
Therefore, there is no mistake in Chase solving steps.
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5. Find the perimeter for the figure. Show the set-up and allwork.
The perimeter of a polygon is given by the sum of the length of its sides. For the polygon in the picture we have the following side lengths:
[tex]7,9x,10,3x,12,4x,15,2x[/tex]Then their sum is:
[tex]7+9x+10+3x+12+4x+15+2x[/tex]We can group like terms. Like terms are terms multiplied by the same power of x. In this case we have two groups of like terms: constants and terms multiplied by x. Then we group them:
[tex](7+10+12+15)+(9x+3x+4x+2x)[/tex]We can use the distributive property in the terms with x. For example:
[tex]ax+bx+cx=(a+b+c)x[/tex]We use this and we also add the constants so we get:
[tex]\begin{gathered} (7+10+12+15)+(9x+3x+4x+2x)=44+(9+3+4+2)x \\ 44+(9+3+4+2)x=44+18x \end{gathered}[/tex]AnswerThen the answer is that the perimeter of the figure is 18x+44.