What is the greatest common factor of 8xy^5−16x^2y^3+20x^4y^4 ?
A. 8xy^5
B. 2xy^3
C. 4xy^3
D. 4x^4y^5
The answer is C 4xy^3
What is the median of this data set?
Answer:
7
Step-by-step explanation:
Median is middle, the middle is 7. So the median is 7.
Match each as a Compound (C) or Element (E)
Cu
HCI
CCI4
Co
HI
CH4
Draw the translation of LM along the vector (4, -5)
Which postulate or theorem can be used to prove that △PQR is similar to △PST?
Answer: SAS similarity theorem.
Step-by-step explanation:
In the given picture , we have two triangles △PQR and △PST with common vertex P and common angle ∠P.
Also, the ratio of sides that include the common angle ∠P of ΔPQR and ΔPST is given by :-
[tex]\frac{PS}{PQ}=\frac{45}{20}=\frac{9}{4}\\\\\frac{PT}{PR}=\frac{36}{16}=\frac{9}{4}[/tex]
Therefore, SAS similarity postulate ΔPQR is similar to ΔPST.
SAS similarity postulate says that if an angle of one triangle is equal to the corresponding angle of another triangle and the sides that include this angle are proportional, then the two triangles are similar.
A point P (x, y) is shown on the unit circle U corresponding to a real number t. Find the values of the trigonometric functions at t.
Point P is on the unit circle U. The values of trigonometric functions at t are [tex]sin\theta=\dfrac{8}{17},\;cos\theta=-\dfrac{15}{17}[/tex][tex],tan\theta=-\dfrac{8}{15},\;cot \theta=-\dfrac{15}{8},\;cosec\theta=\dfrac{17}{8},\;sec\theta=-\dfrac{17}{15}[/tex].
Given:
From the given figure, the coordinate of point P is [tex](-\dfrac{15}{17}, \dfrac{8}{17})[/tex].
The point P is present on a unit circle U. So, in general, the coordinates of a point on the circle will be [tex](x,y)\equiv (cos\theta, sin\theta)[/tex].
By comparing the given coordinate with the general expression, the value sine and cosine function will be,
[tex]sin\theta=\dfrac{8}{17}\\cos\theta=-\dfrac{15}{17}[/tex]
Now, the other trigonometric functions will be,
[tex]tan\theta=\dfrac{sin\theta}{cos\theta}\\tan\theta=-\dfrac{8}{15}\\cot \theta=-\dfrac{15}{8}\\cosec\theta=1/sin\theta=\dfrac{17}{8}\\sec\theta=1/cos\theta=-\dfrac{17}{15}[/tex]
Therefore, the values of trigonometric functions at t are [tex]sin\theta=\dfrac{8}{17},\;cos\theta=-\dfrac{15}{17}[/tex][tex],tan\theta=-\dfrac{8}{15},\;cot \theta=-\dfrac{15}{8},\;cosec\theta=\dfrac{17}{8},\;sec\theta=-\dfrac{17}{15}[/tex].
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In the diagram below, m = 96 and m = 114. What is the measure of
JPM?
Answer:
C.Apex(105)
Step-by-step explanation:
Part 1.] Indicate the general rule for the arithmetic sequence with [tex] a_{3}=-4[/tex] and [tex] a_{8}=-29[/tex]
A.] [tex] a_{n}=-6+(n-1)(-5)[/tex]
B.] [tex] a_{n}=-6+(n-1)(5)[/tex]
C.] [tex] a_{n}=6+(n-1)(-5)[/tex]
D.] [tex] a_{n}=6+(n-1)(5)[/tex]
Part 2.] Which of the following is the general term for the sequence m, -m, m, -m, . . .?
A.] [tex]m(-1)^{n-1}[/tex]
B.] [tex](-m)^{n}[/tex]
C.] [tex](-1)m^{n+1}[/tex]
D.] [tex](-1)m^{n-1}[/tex]
Part 3.] Indicate a general rule for the [tex] n^{th}[/tex] term of the sequence when [tex] a_{1}=5[/tex] and [tex]r= \sqrt{3}[/tex]
A.] [tex] a_{n}=( \sqrt{3})(5)^{n+1}[/tex]
B.] [tex] a_{n}=( \sqrt{3})(5)^{n-1}[/tex]
C.] [tex] a_{n}=(5)( \sqrt{3})^{n-1}[/tex]
D.] [tex] a_{n}=(5)( \sqrt{3})^{n+1}[/tex]
Which answer describes the function f(x) = x^6−x^4 ?
neither
even
odd
to determine if it is even replace x with -x and see if the answer is identical.
In this case, this function is even
Answer:
The function [tex]f(x)=x^6-x^4[/tex] is:
Even
Step-by-step explanation:
A function f(x) is even if:
f(-x)= f(x)
A function f(x) is odd if:
f(-x)= -f(x)
Here, we are given a function f(x) as:
[tex]f(x)=x^6-x^4[/tex]
[tex]f(-x)=(-x)^6-(-x)^4\\\\ =x^6-x^4\\\\=f(x)[/tex]
f(-x)=f(x)
Hence, the function [tex]f(x)=x^6-x^4[/tex] is:
Even
If the circle x2 - 4x + y2 + 2y = 4 is translated 3 units to the right and 1 unit down, what is the center of the circle?
Answer:
(5,-2).
Step-by-step explanation:
First, let's find the original center of the circle, we have
[tex]x^2 - 4x + y^2 + 2y = 4[/tex]
we are going to complete square adding and subtracting 4 for the x terms and 1 for the y terms
[tex]x^2 - 4x+4-4 + y^2 + 2y+1-1 = 4[/tex]
[tex](x-2)^2 - 4 + (y+1)^2 - 1 = 4[/tex]
[tex](x-2)^2+ (y+1)^2 - 5 = 4[/tex]
[tex](x-2)^2+ (y+1)^2 = 4+5[/tex]
[tex](x-2)^2+ (y+1)^2 = 9.[/tex]
The canonical formula of a circumference is [tex](x-h)^2+(y-k)^2=r^2[/tex]
Then, we have a circle with [tex]r^2 =9[/tex] and center (h,k)=(2,-1).
Now, if we translate the circle 3 units to right and 1 unit down, then all the points in the circle will be translated including the center. Especifically, the x values will be added 3 units and the y-vaues will be subtracted 1 unit, then the new center will be
(2+3,-1-1) = (5,-2).
which of the binomials below is a factor of this trinomial
5x^2+14x-3
a. x-3
b. x+3
c. 5x+3
d. 5x-3
Answer: Option 'B' is correct.
Step-by-step explanation:
Since we have given that
[tex]5x^2+14x-3[/tex]
As we know "Split the middle term":
[tex]5x^2+15x-x-3\\\\=5x(x+3)-1(x+3)\\\\=(5x-1)(x+3)[/tex]
Since it is quadratic equation so, it has 2 roots.
So, the roots are (x+3) and (5x-1).
Hence, Option 'B' is correct.
You buy a new laptop for
$299.99
$299.99
.
The sales tax is
6%
6%
.
What is the total cost for the laptop including the sales tax?
helppppppppppppppppppppppppppppppp
Consider the net of a triangular prism where each unit on the coordinate plane represents five feet. If a can of spray paint covers 25 square feet, how many cans of spray paint are needed to paint the outside of the prism blue?
PLEASE HELP AND SHOW ALL WORK
7.04
Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false.
(4 points each.)
1. 4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) = quantity four times quantity four n plus one times quantity eight n plus seven divided all divided by six
2. 12 + 42 + 72 + ... + (3n - 2)2 = quantity n times quantity six n squared minus three n minus one all divided by two
For the given statement Pn, write the statements P1, Pk, and Pk+1.
(2 points)
2 + 4 + 6 + . . . + 2n = n(n+1)
Answer
answer C
Step-by-step explanation:
Lines p and q are perpendicular. If the slope of line p is 2, what is the slope of line q?
A. 1/2
B. -1/2
C. -2
D. 2
Answer:
- 1/2
Step-by-step explanation:
I just did it
Corey spent 20% of his savings on a printer at Louie's ElectronisHow much did Corey have in his savings account before he bought the printer?
Answer:
5
Step-by-step explanation:
prove that root 7 is irrational by the method of contradiction
Let assume that [tex]\sqrt7[/tex] is a rational number. Therefore it can be expressed as a fraction [tex]\dfrac{a}{b}[/tex] where[tex]a,b\in\mathbb{Z}[/tex] and [tex]\text{gcd}(a,b)=1[/tex].
[tex]\sqrt7=\dfrac{a}{b}\\\\7=\dfrac{a^2}{b^2}\\\\a^2=7b^2[/tex]
This means that [tex]a^2[/tex] is divisible by 7, and therefore also [tex]a[/tex] is divisible by 7.
So, [tex]a=7k[/tex] where [tex]k\in\mathbb{Z}[/tex]
[tex](7k)^2=7b^2\\\\49k^2=7b^2\\\\7k^2=b^2[/tex]
Analogically to [tex]a^2=7b^2[/tex] ------- [tex]b^2[/tex] is divisible by 7 and therefore so is [tex]b[/tex].
But if both numbers [tex]a[/tex] and [tex]b[/tex] are divisible by 7, then [tex]\text{gcd}(a,b)=7[/tex] which contradicts our earlier assumption that [tex]\text{gcd}(a,b)=1[/tex].
Therefore [tex]\sqrt7[/tex] is an irrational number.
Final answer:
To prove that √7 is irrational, we assume the opposite and show that it leads to a contradiction. We start by assuming that √7 is rational and can be expressed as a fraction. By squaring both sides of the equation and simplifying, we get an equation that leads to p and q being divisible by 7, which contradicts our initial assumption. Therefore, √7 must be irrational.
Explanation:
To prove that √7 is irrational using the method of contradiction, we assume the opposite, which is that √7 is rational. This means that it can be expressed as a fraction p/q, where p and q are integers with no common factors other than 1. We can then square both sides of the equation (√7)² = (p/q)² and simplify to get the equation 7 = p²/q². Rearranging, we have p²= 7q².
From this equation, we can deduce that p² is divisible by 7, which means p must also be divisible by 7. Let's represent p as 7r, where r is another integer. Substituting back into the equation, we get (7r)² = 7q², which simplifies to 49r² = 7q². Dividing both sides by 7, we have 7r² = q². This implies that q² is also divisible by 7, so q must also be divisible by 7.
However, if both p and q are divisible by 7, this contradicts our initial assumption that p/q has no common factors other than 1. Therefore, our assumption that √7 is rational must be false, and hence √7 is irrational.
The graph of [tex]y= \sqrt[3]{x} [/tex] was shifted 5 units down and 4 units to the left. What is the equation of the resulting graph?
Please answer quickly!
Using translation concepts, it is found that the equation of the resulting graph is given by:
[tex]y = \sqrt[3]{x + 4} - 5[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the changes are given as follows:
Shift down of 5 units, hence y -> y - 5.Shift left of 4 units, hence x -> x + 4.Hence the equation of the resulting graph is given by:
[tex]y = \sqrt[3]{x + 4} - 5[/tex]
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The equation of the graph \\sqrt[3]{x} shifted down by 5 units and to the left by 4 units is \\sqrt[3]{x + 4} - 5.
Explanation:The transformation of the graph of y = \\sqrt[3]{x} down by 5 units and to the left by 4 units is represented by the function y = \\sqrt[3]{x + 4} - 5. When a graph is shifted to the left by 'a' units, we replace 'x' in the equation with (x + a). Similarly, when a graph is shifted down by 'b' units, we subtract 'b' from the function, resulting in f(x) - b. Therefore, incorporating both transformations into the original function, we get y = \\sqrt[3]{x + 4} - 5.
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Jade is painting a rectangular wall. The wall is 4 1/4 yards long and 2 2/3 yards high. The formula for the area of a rectangle is A=bh. What is the area of the wall?
Answer:
11 1/3
Step-by-step explanation:
If carpet cost$5 per square yard, what would it cost to carpet a room that is 5 yards wide and 22 yards long?
Jesse took out a 30-year loan for $85,000 at 7.2% interest, compounded monthly. If his monthly payment on the loan is $576.97, how much of his first payment went toward note reduction(reducing principal)? Show your work.
Answer:
$66.97 is his first payment went toward reduction.
Step-by-step explanation:
Given : Jesse took out a 30-year loan for $85,000 at 7.2% interest, compounded monthly. If his monthly payment on the loan is $576.97.
To find : How much of his first payment went toward note reduction(reducing principal)?
Solution :
First we find the interest of 1 month on a loan of $85,000 at 7.2% interest.
[tex]I=85000\times \frac{7.2}{12\times 100}[/tex]
[tex]I=85000\times 0.006[/tex]
[tex]I=510[/tex]
Interest of 1 month is $510.
Monthly payment = $576.97
Now, first payment or reducing principal is given by
F= monthly payment - interest of 1 month
F=$576.97- $510
F=$66.97
Therefore, $66.97 is his first payment went toward reduction.
Carrie has 32 ounces of ice cream to divide equally among 10 people how much ice cream will each person get? SHOW WORK
I need help fast. Identify the apothem (a), the radius (r), and the perimeter (p) of the regular figure.
The apothem (a), radius (r), and perimeter (p) of a regular figure are defined as follows: the apothem is the perpendicular distance from the center of the figure to one of its sides, the radius is the distance from the center of the figure to any point on its circumference, and the perimeter is the total length of all its sides.
Explanation:The apothem (a) of a regular figure is the perpendicular distance from the center of the figure to one of its sides.
The radius (r) of a regular figure is the distance from the center of the figure to any point on its circumference.
The perimeter (p) of a regular figure is the total length of all its sides.
[7.07] Choose the correct product of (6x + 2)2.
36x2 − 4
36x2 + 4
36x2 − 24x + 4
36x2 + 24x + 4
Alana bought 2 5/8 pounds of mixed nuts for the school picnic. Her classmates ate 3/4 of the mixed nuts. How much of the mixed nuts did her classmates eat
Final answer:
Alana's classmates ate 1 31/32 pounds of the mixed nuts.
Explanation:
To determine how much of the mixed nuts Alana's classmates ate, you need to multiply the total amount of nuts by the fraction that was eaten.
Alana bought 2 5/8 pounds of mixed nuts and her classmates ate 3/4 of them. To find out how much was eaten, you multiply 2 5/8 by 3/4.
First, convert 2 5/8 to an improper fraction:
(2 * 8) + 5 = 21/8.
Now, multiply this improper fraction by 3/4:
(21/8) * (3/4) = 63/32 pounds.
This is an improper fraction, which you can convert to a mixed number.
63 divided by 32 is 1 with a remainder of 31, so the mixed number is 1 31/32 pounds.
Therefore, Alana's classmates ate 1 31/32 pounds of the mixed nuts.
What is the volume of a sphere with a surface area of 64π cm²? 16π cm³ 2113π cm³ 48π cm³ 8513π cm³
Answer:
Literally just finished the test its 83 1/3
Step-by-step explanation:
The number of gallons of water,y, in a swimming pool is modeled by the equation y=7.5x+500,where x represents the time in minutes after the pump is turned on. How many gallons of water are in the pool if the pump is on for 200 minutes.