Answer:
a) x^2 + y^2
b) 9-xy
Step-by-step explanation:
Here, we want to write the algebraic statements as expressions;
a) The sum of the squares of x and y
The square of x is x^2
The square of y is y^2
The sum of the squares is x^2 + y^2
ii) Product of x and y subtracted from 9
The product of x and y is x * y = xy
Subtracting these from 9, we have;
9-xy
Hello! Verify the identity. Please show your work! Use trigonometric identities to verify each expression is equal.
Yes this is from edge.
Answer:
See Below.
Step-by-step explanation:
We want to verify the identity:
[tex]\displaystyle \csc^2 x -2\csc x \cot x +\cot ^2 x = \tan^2\left(\frac{x}{2}\right)[/tex]
Note that the left-hand side is a perfect square trinomial pattern. Namely:
[tex]a^2-2ab+b^2=(a-b)^2[/tex]
If we let a = csc(x) and b = cot(x), we can factor it as such:
[tex]\displaystyle (\csc x - \cot x)^2 = \tan^2\left(\frac{x}{2}\right)[/tex]
Let csc(x) = 1 / sin(x) and cot(x) = cos(x) / sin(x):
[tex]\displaystyle \left(\frac{1}{\sin x}-\frac{\cos x }{\sin x}\right)^2=\tan^2\left(\frac{x}{2}\right)[/tex]
Combine fractions:
[tex]\displaystyle \left(\frac{1-\cos x}{\sin x}\right)^2=\tan^2\left(\frac{x}{2}\right)[/tex]
Square (but do not simplify yet):
[tex]\displaystyle \frac{(1-\cos x)^2}{\sin ^2x}=\tan^2\left(\frac{x}{2}\right)[/tex]
Now, we can make a substitution. Let u = x / 2. So, x = 2u. Substitute:
[tex]\displaystyle \frac{(1-\cos 2u)^2}{\sin ^22u}=\tan^2u[/tex]
Recall that cos(2u) = 1 - sin²(u). Hence:
[tex]\displaystyle \frac{(1-(1-2\sin^2u))^2}{\sin ^2 2u}=\tan^2u[/tex]
Simplify:
[tex]\displaystyle \frac{4\sin^4 u}{\sin ^2 2u}=\tan^2 u[/tex]
Recall that sin(2u) = 2sin(u)cos(u). Hence:
[tex]\displaystyle \frac{4\sin^4 u}{(2\sin u\cos u)^2}=\tan^2 u[/tex]
Square:
[tex]\displaystyle \frac{4\sin^4 u}{4\sin^2 u\cos ^2u}=\tan^2 u[/tex]
Cancel:
[tex]\displaystyle \frac{\sin ^2 u}{\cos ^2 u}=\tan ^2 u[/tex]
Since sin(u) / cos(u) = tan(u):
[tex]\displaystyle \left(\frac{\sin u}{\cos u}\right)^2=\tan^2u=\tan^2u[/tex]
We can substitute u back for x / 2:
[tex]\displaystyle \tan^2\left(\frac{x}{2}\right)= \tan^2\left(\frac{x}{2}\right)[/tex]
Hence proven.
Compare the graph h(x)=1/4x^2 to the graph of f(x) = x2.
Answer:
h(x) is the image after f(x) is horizontally stretched by a scale factor of 4
Step-by-step explanation:
Given
[tex]h(x) = \frac{1}{4}x^2[/tex]
[tex]f(x) = x^2[/tex]
Required
Compare h(x) to f(x)
We have:
[tex]h(x) = \frac{1}{4}x^2[/tex]
Substitute [tex]f(x) = x^2[/tex]
[tex]h(x) = \frac{1}{4}f(x)[/tex]
This means that f(x) is stretched horizontally by a scale factor of 4 to get h(x)
The owner of a produce stand is selling baskets of peaches, priced by the kilogram. She rounded each measurements to the nearest 2 1 start fraction, 1, divided by, 2, end fraction of a kilogram.How much heavier is the heaviest basket than the second heaviest basket?
Answer:
[tex]1\frac{1}{2}kg[/tex]
Step-by-step explanation:
Given
[tex]a = 6\frac{1}{2}[/tex] --- heaviest
[tex]b = 5[/tex] --- second heaviest
Required
The difference (d)
This is calculated as:
[tex]d = 6\frac{1}{2} - 5[/tex]
[tex]d = 1\frac{1}{2}[/tex]
CAN SOMEONE PLEASE HELP?!
Answer:
70in.
Step-by-step explanation:
Since the given formula for perimeter is [tex]2l + 2w[/tex], all that's needed is to fill in the blanks with the numbers they give us.
[tex]2l + 2w[/tex] (Fill in for given length and width)
[tex]2(20)+2(15)[/tex] (Multiply)
[tex]40 + 30[/tex] (Add)
[tex]70[/tex]
It tells us that length ([tex]l[/tex]) is 20 and that width ([tex]w[/tex]) is 15. So all that we have to do is use the equation it gave us to solve the equation.
I hope this helped :)
Step-by-step explanation:
Hey there!
Here;
Length (l) = 20 in
Width (w) = 15 in
Perimeter(p) = ?
We have;
Perimeter of rectangle (p) = 2l + 2w
= 2(l+w)
= 2(20+15)
= 2*35
= 70 inches
Therefore, perimeter of rectangular picture is 70 inches.
Hope it helps!
Line A (y=4x+2) is transformed into Line B (y=x+5). Which best describes the new slope and y-intercept?
Answer:
The new slope is 1 and the line is shifted flatter.
Step-by-step explanation:
Line A slope is 4.
Line B slope is 1.
The y-intercept rose up 3
As far as slope, it became flatter because the line only rises 1 'square' for every 1 'square' it travels to the right. It was rising 4 'squares' for every 1 to the right.
convert 25meter square into centimeter square
Answer:
250,000 cm squared
Step-by-step explanation:
20% of a number is 30. What is 60% of the number?
Answer:
90
Step-by-step explanation:
30 / 0.2 = 150
150 x 0.60 = 90
Step-by-step explanation:
Well, if 20% = 30, then 40% = 60, and 60% = 90
Solve the following:
4x-3=2x+7
Thanks :)
Answer:
6x+10 i think is right(sorry if its not)
Answer:
5
Step-by-step explanation:
4x-3=2x+7
-2x -2x
2x-3=7
+3 +3
2x=10
2x/2x = x
10/2=5
x=5
Choose the correct simplification of the expression (x?y)?
Ох^4у^3
Ox^6y^6
Ох^4у^2
Oxy^4
Which ordered pair is a solution to the following linear system?
y= x + 1
y = -2x + 1
A) (-1,-2)
B) (2,1)
C) (0,1)
D) (0,0)
Answer:
C. (0,1)
Step-by-step explanation:
x + 1 = -2x + 1
3x = 0
x = 0
y = (0) + 1
y = 1
Please help I’ll give brainliest
Answer:
B
Step-by-step explanation: 6 21 9 45
49 × 17 + 49 × 3
49 × (17 + 3)
49 × 20
Find the image of NPQ under the translation of (x, y) + (x + 8, y + 1).
АВС
DEF
KLM
GHJ
Answer:
Triangle KLM
Step-by-step explanation:
Firstly, we need to write the coordinates of triangle NPQ
We have this as;
(-7,-6) for N
(-4,-3) for P
(-4,-6) for Q
Now, we are going to use the given translation formula;
(x + 8, y + 1)
N’ will be (-7+ 8, -6 + 1) = (1,-5)
P’ will be (-4+ 8, -3+1) = (4,-2)
Q’ will be (-4+ 8, -6+1) = (4,-5)
Now, we need to find the triangle with the exact given transformation coordinates calculated above;
We have the triangle as;
KLM
With K as (1,-5) ; L as (4,-2) and ; M as (4,-5)
I need help please!!!
Answer:
answer is line m........
What is the slope of the function?
Answer:
Write function:
y = 3x+4
The slope is what we time x by, 3!
help please, try to explain it in steps for me if u can't that's fine, ty!
Answer:
B
Step-by-step explanation:
We are given that Expression One is:
[tex]2\cdot 10^x[/tex]
And Expression Two is:
[tex]4\cdot 10^{x+y}[/tex]
We are given that the value of Expression Two is 20,000 times greater than the value of Expression One. And we want to find the value of y. In other words:
[tex]4\cdot 10^{x+y}=20000(2\cdot 10^x)[/tex]
We can divide both sides by four:
[tex]10^{x+y}=10000\cdot 10^x[/tex]
Recall that:
[tex]x^a\cdot x^b=x^{a+b}[/tex]
Therefore:
[tex]10^x\cdot 10^y=10000\cdot 10^x[/tex]
Divide both sides by 10ˣ:
[tex]10^y=10000[/tex]
Solve for y:
[tex]\displaystyle y = \log_{10}10000 = 4[/tex]
Our answer is B.
The function h(t) = –16t2 + 96t + 6 represents an object projected into the air from a cannon. The maximum height reached by the object is 150 feet.
After how many seconds does the object reach its maximum height?
2 seconds
3 seconds
6 seconds
9 seconds
Answer:
Step-by-step explanation:
This answer can be found in the h value for the vertex of a parabola, (h, k). The k value is the max height and we were already given that information. We need to solve for h. There's an easy way and a really complicated way...I'll show you the easy way because it's actually quite useful to know, especially when doing a lot of work with quadratics!
The formula to find h is
[tex]h=\frac{-b}{2a}[/tex] and in our quadratic, a = -16, b = 96 and c = 6. Filling in what we need:
[tex]h=\frac{-96}{2(-16)}[/tex] so
h = 3
At 3 seconds the max height of 150 feet is reached.
¿Cuál de los siguientes productos algebraicos es un Binomio Suma por Binomio Diferencia?
Seleccione una:
a. (a + b) (a - b)
b. (a - b) (a - b)
c. (a + b) (a + b)
d. (a + b) (c + d)
Can someone help me understand this? Given that triangle ABC =~ triangle DEF, which of the following must be true?
Answer:
since these triangles are the same these angle must be the same
A=D
B=E
C=F
so the answer is C
Hope This Helps!!!
2+4 = 8 and ½ + ½ = 1 is an example of which type of statement?
Answer:
it is an example of conditional statement.
hope it helps
What’s the answer to this ?
Answer:
a
Step-by-step explanation:
Answer:
I am pretty sure its B
Step-by-step explanation: not sure though
What is the reflection image of P(0, 0) after two reflections, first across x = −3 and then across y = 4?
Answer:
(-6, 8)
Draw the point, draw the lines of reflection, reflect, find coordinates.
A car was traveling at a rate of x miles per
hour for 3 hours. How far did the car travel?
in one day a store sells 254 gallons of milk for a profit of -$0.17 each they also sell 51 half gallons of orange juice for a profit of 0.34 each what was the store's net profit for the day for these two items total
Answer:
-$25.84
Step-by-step explanation:
254* -0.17 = -$43.18 profit from milk
51 * .34 = $17.34 profit from OJ
-43.18 + 17.34 = -$25.84 profit total
A school held a tennis tournament.After each round,one-forth of the players were eliminated.If there were 64 players at the start of the tournament,which equation models the number of players left after 6 rounds?
Answer:
Option B
Step-by-step explanation:
After each round of the tournament one-fourth players are eliminated.
That means the process of elimination will represent the exponential decay.
Equation of exponential decay is given by the expression,
[tex]y=a(1-r)^n[/tex]
Here, a = Initial number of players
r = Fraction of reduction in the number of players
y = Final number of players
n = Number of rounds
In the given question,
Initial number of the players (a) = 64
Fraction of reduction in the number of players (r) = [tex]\frac{1}{4}[/tex]
= 0.25
Number of rounds (n) = 6
By substituting these values in the expression,
[tex]y=64(1-0.25)^6[/tex]
Therefore, Option B is the answer.
Help please thanks! :)
Answer:
Option A = 1/15 cubic meters
Step-by-step explanation:
Formule to find volume of rectangular prism:
Volume = width × height × length
V = w×h×l
V = 1/3 × 1/4 × 4/5
V = 1/15 cubic meters
Draw the graph of y = 3x – 2 for –3 ≤ x ≤ 3
Answer:
In this case, we have a linear equation:
y = 3*x - 2
And we want to graph this in the interval –3 ≤ x ≤ 3
Because this is a linear equation, to graph it we can just evaluate the equation in both extremes of the interval to find the two extremes of the graph.
Then we just need to connect these points with a segment, and that will be the graph of our equation.
Because the symbols used are: ≤
We need to graph the extremes with a black dot, which means that the point is included in the graph (would be different if we had -3 < x < 3)
The first extreme is when we have x = -3
y = 3*(-3) - 2 = -9 - 2 = -11
Then we have one extreme at (-3, -11)
The other is when x = 3
y = 3*3 - 2 = 9 - 2 = 7
Then the other extreme is at (3, 7)
Now we just need to draw these two points and connect them, an example of this can be seen in the image below:
Please help me I really need help
Answer:
-2 + 6i
Parallelogram
Step-by-step explanation:
( 5 - 2i ) + ( - 7 + 8i )
remove parenthesis
5 - 2i + ( -7 ) + 8i
combine like terms
5 + (-7) = -2
-2i + 8i = 6i
-2 + 6i
The arrows on the opposite sides indicate that the sides are parallel
A shape with two sets of parallel sides is known as a parallelogram
Which of these is the algebraic expression for "4 times the sum of 2 and y?"
4 ⋅ 2 + y
4(2 + y)
2 + 4 ⋅ y
2(4 + y)
Answer:
[tex]4(2 + y)[/tex]
Step-by-step explanation:
"4 times the sum of 2 and y".
Hope it is helpful...Answer:
The answer is 4(2+y)
Explanation: No 1 is 4 times two and add 1
No 3 is 2 plus 4 and multiply y
No 4 is 2 times 4 and adds 2 y
The sum of a number and 3:
Answer:
x+3?
Step-by-step explanation:
honestly, there is not alot of information present here. so when a hear "a number" i think variable.... which would be set up as x+3
y=−x+4
y=x−2
What is the solution for the system of equations?
Step-by-step explanation:
y=-x+4
y=x-2
adding both the equations we get
2y=2
:. y=1
and putting the value of y in equation first we get
x=3