How to simplify and expression by combining like terms?
If f(x)=2x^2-x-6 and g(x)=x^2-4, find f(x)/g(x)
2x+3/x-2
2x-3/x+2
2x+3/x+2
2x-3/x-2
To find f(x)/g(x), we factor both f(x) and g(x), and then simplify by canceling common terms. The simplified result is 2x + 3 / x + 2.
To find the quotient of two functions, f(x) and g(x), we divide the first function by the second. In this case, we have f(x) = 2x² - x - 6 and g(x) = x² - 4. The process involves the following steps:
Write the division of the two functions: f(x)/g(x).Simplify the expressions, if possible, by factoring and reducing them.We start by factoring both f(x) and g(x):
f(x) = (2x + 3)(x - 2)
g(x) = (x + 2)(x - 2)
Now we divide f(x) by g(x):
f(x)/g(x) = ((2x + 3)(x - 2)) / ((x + 2)(x - 2))
Notice that the term (x - 2) is common in both the numerator and the denominator, so we can reduce the expression by canceling out the common term, resulting in:
f(x)/g(x) = (2x + 3) / (x + 2)
The correct result is the second option: 2x + 3 / x + 2.
Sara tells Michael she is 160 centimeters tall, while Michael says he is 60 inches tall. If there
are 2.54 centimeters in an inch, who is taller?
A flower vase, in the form of a hexagonal prism, is to be filled with 512 cubic inches of water. Find the height of the water if the wet portion of the flower vase and its volume are numerically equal.
Height of water in hexagonal prism vase = 384 inches, given equal volume of water and wet portion.
Let's denote the height of the water in the vase as [tex]\( h \)[/tex] inches.
The volume of a hexagonal prism can be calculated using the formula:
[tex]\[ V = \frac{3\sqrt{3}}{2}a^2h \][/tex]
where [tex]\( a \)[/tex] is the length of one side of the hexagon (which represents the base of the prism), and [tex]\( h \)[/tex] is the height of the prism.
Since the base of the vase is a hexagon, we need to find the side length of this hexagon.
The area of a regular hexagon can be calculated using the formula:
[tex]\[ A = \frac{3\sqrt{3}}{2}a^2 \][/tex]
Given that the volume of water in the vase is 512 cubic inches, and the wet portion's volume and its height are equal, we have:
[tex]\[ 512 = \frac{3\sqrt{3}}{2}a^2h \][/tex]
We are also given that the wet portion's volume is numerically equal to its height, so:
[tex]\[ h = 512 \][/tex]
Substituting this value of [tex]\( h \)[/tex] into the volume equation, we have:
[tex]\[ 512 = \frac{3\sqrt{3}}{2}a^2(512) \][/tex]
Now, we can solve for [tex]\( a \).[/tex]
[tex]\[ a^2 = \frac{512}{\frac{3\sqrt{3}}{2} \times 512} \]\[ a^2 = \frac{512}{\frac{3\sqrt{3}}{2} \times 512} \]\[ a^2 = \frac{2}{3\sqrt{3}} \]\[ a^2 = \frac{2\sqrt{3}}{9} \]\[ a = \sqrt{\frac{2\sqrt{3}}{9}} \]\[ a = \frac{\sqrt{2\sqrt{3}}}{3} \][/tex]
Now, let's find the height of the water by substituting the value of [tex]\( a \)[/tex]into the volume equation:
[tex]\[ 512 = \frac{3\sqrt{3}}{2}\left(\frac{\sqrt{2\sqrt{3}}}{3}\right)^2h \]\[ 512 = \frac{3\sqrt{3}}{2}\left(\frac{2\sqrt{3}}{9}\right)h \]\[ 512 = \frac{3\sqrt{3}}{2}\left(\frac{2\sqrt{3}}{9}\right)h \]\[ 512 = \frac{4}{3}h \]\[ h = \frac{512 \times 3}{4} \]\[ h = 384 \][/tex]
So, the height of the water in the vase is 384 inches.
Which input value produces the same output value for the two functions on the graph?
x = -3
x = -2
x = -1
x = 3
what is the correct expansion of the binomial (x+y)^5
Answer: The correct expansion is,
[tex]x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5[/tex]
Step-by-step explanation:
Since, by the binomial expansion,
[tex](p+q)^n=\sum_{r=0}^{n} ^nC_r (p)^{n-r}(q)^r[/tex]
Where,
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
Here, p = x and q = y and n = 5,
By substituting values,
[tex](x+y)^5=\sum_{r=0}^{5} ^5C_r (x)^{n-r}(y)^r[/tex]
[tex] =^5C_0(x)^{5-0}(y)^0+^5C_1 (x)^{5-1}(y)^1+^5C_2 (x)^{5-2}(y)^2+^5C_3 (x)^{5-3}(y)^3+^5C_4 (x)^{5-4}(y)^4+^5C_5(x)^{5-5}(y)^{5}[/tex]
[tex]=1(x)^5(y)^0+\frac{5!}{4!(5-4)!}x^4y^1+\frac{5!}{3!(5-3)!}x^3y^2+\frac{5!}{2!(5-2)!}x^2y^3+\frac{5!}{1!(5-1)!}xy^4+\frac{5!}{5!(5-5)!}x^0y^5[/tex]
[tex]=x^5+\frac{5!}{4!1!}x^4y^1+\frac{5!}{3!2!}x^3y^2+\frac{5!}{2!3!}x^2y^3+\frac{5!}{1!4!}x^1y^4+\frac{5!}{5!0!}x^0y^5[/tex]
[tex]=x^5+\frac{5\times 4!}{4!}x^4y^1+\frac{5\times 4\times 3!}{3!2!}x^3y^2+\frac{5\times 4\times 3!}{2!3!}x^2y^3+\frac{5\times 4!}{4!}x^1y^4+\frac{5!}{5!}y^5[/tex]
[tex]=x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5[/tex]
Which is the required expansion.
Word Problem help please
1. The magician said "The average of seven numbers is 49. If 1 is added to the fisr number, 2 is added to the second number, 3 is added to the third number and so on up to seventh number". what is the new average ? ...?
mx+4y=3t, Solve for the value of x
To solve mx+4y=3t for x, subtract 4y from both sides to isolate the x term, giving mx = 3t - 4y. Then, divide both sides by m to solve for x, resulting in x = (3t - 4y) / m.
Explanation:To solve the equation mx+4y=3t for the value of x, follow these steps:
First, isolate the x term by moving the 4y to the other side of the equation. This gives us:mx = 3t - 4yNext, divide both sides of the equation by m to solve for x:x = (3t - 4y) / mYou can now plug in the known values for y, t, and m to find the value of x.
Find the measure of
What is the resulting ordered pair if the value of the independent variable is x=-3?f(x) = –2x-3
Am I able to evaluate sin(cos^1(7/11)) without a calculator? If yes, how? ...?
Yes, you can evaluate sin(cos^-1(7/11)) without a calculator. The result can be simplified to √(72/121).
Explanation:Yes, you can evaluate sin(cos-1(7/11)) without a calculator. Let's break it down step by step:
cos-1(7/11) represents the inverse cosine of 7/11. Inverse cosine is the angle whose cosine is equal to the given value. So, cos-1(7/11) is the angle whose cosine is 7/11.To evaluate sin(cos-1(7/11)), we need to find the sine of the angle we found in the previous step.Since we know that sin2(θ) + cos2(θ) = 1, we can use this relationship to find sin(θ) when we know cos(θ).Let's assume the angle we found in step 1 is θ. We know that cos(θ) = 7/11, so we can substitute this value into the equation sin2(θ) + (7/11)2 = 1 and solve for sin(θ).By solving the equation, we find that sin(θ) = √(1 - (7/11)2).Finally, we can simplify the expression sin(θ) = √(1 - (49/121)) or sin(θ) = √(72/121).Therefore, sin(cos-1(7/11)) can be evaluated as √(72/121).
x + 2 > -8
a. x > -6
b. x > -10
c. x <-10
d. x < -6
-2i over 1+i ... help :(
Rate of Change , you are given the dollar value of a product in 2004 and the rate at which the value of the product is expected to change during the next 5 years. Write a linear equation that gives the dollar value (v) of the product in terms of the year
(Let t=0 represent 2000.)
2004 value= $156 with $4.50 increase per year
...?
Answer:
The linear equation is v = 4.5t +138
The product had value of $138 in 2000.
Step-by-step explanation:
In 2004, dollar value(v) = $156 and rate of change (m) = $4.50
The linear equation is in the form of y = mx + b, where "m" is slope or rate of change, b is the y-intercept.
We can rewrite the equation as v = m(t) + b.
Now let's find the value of b, when t = 4, m = 4.5, v = 156
156 = 4.5(4) + b
b = 156 - 4.5(4)
b = 156 - 18
b = 138
So, the linear equation is v = 4.5t +138
When t=0, the dollar value (v) = 4.5(0) + 138
v = $138
So, the product had value of $138 in 2000
Need help ASAP
Will upvote!
I think it's A but i'm not sure
Lines A and B are represented by the equations given below:
Line A: x + 2y = 3
Line B: x + y = 3
Which statement is true about the solution to the set of equations?
There are infinitely many solutions.
There are two solutions.
There is one solution.
There is no solution.
What are the zeros of the polynomial function: f(x) = x3 + x2 – 6x ? ...?
How many pounds does 64 ounces weigh?
Answer:
4 lbs
Step-by-step explanation:
There are 16 ounces in a pound, so divide 64 by 16 to get the number of pounds. 64 ÷ 16 = 4 lbs
Enter the slope-intercept equation of the line that has slope -6 and y-intercept (0, 2).
The slope-intercept form of equation of the line that has slope -6 and y-intercept (0, 2) is y=-6x+2.
What is the slope intercept form?The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.
The standard form of the slope intercept form is y=mx+c.
Given that, the line that has slope -6 and y-intercept (0, 2).
The y-intercept is the point where a graph crosses the y-axis. In other words, it is the value of y when x=0.
Here, m=-6 and c=2
Substitute m=-6 and c=2 in y=mx+c, we get
y=-6x+2
Therefore, the slope-intercept form of equation of the line that has slope -6 and y-intercept (0, 2) is y=-6x+2.
To learn more about the slope intercept form visit:
brainly.com/question/9682526.
#SPJ2
Determine the coordinates of the vertices of the triangle to compute the area of the triangle using the distance formula (round to the nearest integer).
FIRST GRAPH
A) 20 units^2
B) 30 units^2
C) 40 units^2
D) 50 units^2
Solve the equation.
–2 3/7 + b = 6 1/7
A.
b = 3 5/7
B.
b = 4 2/7
C.
b = 8 2/7
D.
b = 8 4/7
Jeremiah has a batting average of 0.312 this baseball season. Express his average as a fraction in lowest terms.
A quadrilateral has angles that measure 74°, 93°, and 117°.
Ahmed is taking orders for lunch. A slice of pizza cost $2 and a chicken sandwich costs $3. He collects $24 for the group of 10 people.How many people ordered a chicken sandwich?
1.5x+2.5y=21.50
x+y=9
8 people ordered chicken sandwich
Identify the converse of the following conditional:
If a point is in the fourth quadrant, then its coordinates are negative.
A. If a point is in the fourth quadrant, then its coordinates are negative.
B. If the coordinates of a point are not negative, then the point is not in the fourth quadrant.
C. If a point is not in the fourth quadrant, then the coordinates of the point are not negative.
D. If the coordinates of a point are negative, then the point is in the fourth quadrant.
Suppose you deposited $10 into your savings account each month, as indicated in the table. Your account pays 4%, compounded monthly. How much will you have in your account at the end of 15 years? a. $2,908 c. $3,668 b. $2,461 d. $1,800 Please select the best answer from the choices provided
Identify the slope and y-intercept.
y=2x−8
Enter your answers in the boxes in simplest form.
M=
B=
11 less than the product of a number y and -2 is z
You estimate that a baby pig weighs 20 pounds. The actual weight of the baby pig is 16 pounds. Find the percent error.
Answer:
It's mainly 25% as the percent error.
Step-by-step explanation:
Jarek buys jerseys for his team online. He pays a constant shipping price plus a special rate for each jersey. During the spring season, Jarek paid $151 for 24 jerseys. In the summer season, he paid $79 for 12 jerseys. What is the special rate Jarek pays for each jersey and how much does he pay for shipping?
Thanks to anyone who can help!
What is the formula that relates circumference and radius?
A. C = 2r
B. C = 2/r
C. C = 2D
D. C + 2 = r
Answer:
The formula that relates circumference and radius is [tex]C=2\pi r[/tex].
Step-by-step explanation:
The circumference of a circle is calculated by the formula
[tex]C=2\pi r[/tex]
Where,
C is circumference of the circle.
r is radius of the circle.
π is 22/7 or 3.14.
In the given options π is not missing. So, all the given options are incorrect.
Therefore the formula that relates circumference and radius is [tex]C=2\pi r[/tex].