The equivalent expression of the different of two square is -1
Given the following expressions
a cot α = 1
a = 1/cot α = sinα/cosα
b = 1/cos α
We are to find the expression a² - b²
According to difference of two squares;
a² - b² = (a + b) (a - b)
Substitute the given expressions into the formula as shown:
[tex]a^2 - b^2 = (\frac{sin \alpha}{cos \alpha} )^2 - (\frac{1}{cos \alpha} )^2\\a^2 - b^2=\frac{sin^2 \alpha}{cos^2 \alpha} -\frac{1}{cos ^2 \alpha}\\a^2 - b^2=\frac{sin^2 \alpha-1}{cos^2\alpha}\\a^2 - b^2=\frac{-(1-sin^2\alpha)}{cos^2\alpha} \\a^2 - b^2=\frac{-os^2 \alpha}{cos^2 \alpha}\\a^2 - b^2 = -1[/tex]
This shows that the equivalent expression of the difference of two squares is -1
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Suppose f(x) = 5x - 4. Describe how the graph of g compares with the graph of f.
g(x)=f(x) + 12
IDEE
Select the correct choice below, and fill in the answer box to complete your choice.
O A. g(x) has a scale factor of compared to f(x). Because it scales the horizontal direction, the graph is stretched horizontally.
OB. The graph of g(x) is translated unit(s) to the left compared to the graph of f(x).
OC. The graph of g(x) is translated unit(s) down compared to graph of f(x).
OD. g(x) has a scale factor of compared to f(x). Because it scales the vertical direction, the graph is stretched vertically.
O E. g(x) has a scale factor of compared to f(x). Because it scales the horizontal direction, the graph is compressed horizontally.
O F. g(x) has a scale factor of compared to f(x). Because it scales the vertical direction, the graph is compressed vertically.
O G. The graph of g(x) is translated unit(s) to the right compared to the graph of f(x).
O H. The graph of g(x) is translated unit(s) up compared to graph of f(x).
The graph of g(x) and f(x) are related by the given equation g(x) = f(x) + 12,
therefore, the ordered pair of the graph of g(x) is (f(x) + 12, x).
The choice that correctly describes how the graph of g(x) compares with f(x)
is the option; H. The graph of g(x) is translated unit(s) up compared to graph
of f(x).
Reasons:
The given function is f(x) = 5·x - 4
The function g(x) = f(x) + 12
Required:
To select the correct choice from the given options
Solution:
The difference between f(x) and the required function, g(x), is the addition
of a constant positive value of 12 to the function f(x).
Therefore, each f(x) output value is further increased by 12 to obtain the
graph of g(x), which gives;
The graph of g(x) is translated 12 units up compared to the graph of f(x),
which corresponds with the option H.
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Foundation Geometry
midpoint of AC
A. 18
B. 6
C.27
D.54
Answer:
D
Step-by-step explanation:
Since B is the midpoint of AC , then
AB = BC , substitute values
4x + 3 = 3x + 9 ( subtract 3x from both sides )
x + 3 = 9 ( subtract 3 from both sides )
x = 6
Then
AC = AB + BC
= 4x + 3 + 3x + 9
= 7x + 12
= 7(6) + 12
= 42 + 12
= 54 → D
Consider the line y=-1/2x+9
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
Answer:
Parallel line: - 1/2
Perpendicular line: 2
Step-by-step explanation:
Hayami was riding her bike on a loop that is 15/16 mile long. she rode for 3/4 mile and then stopped to rest she rode another 1/8 mile and then has a flat tire. how far does Hayami have to walk her bike to complete the loop?
A.1/16 mile
b.1/32
c. 3/16
d. 1/8
1/16 mile
3/4 = 12/16
1/8 = 2/16
12/16 + 2/16 = 14/16
1/16 Mile left to walk
Hayami has to walk her bike Option A) 1/16 mile to complete the loop.
Hayami rode a total of 3/4 + 1/8 = 7/8 mile before getting a flat tire. To complete the loop, she needs to cover the remaining distance of the loop, which is
= 15/16 - 7/8
= 15/16 - 14/16
= 1/16 mile.
Thus, Hayami has to walk her bike 1/16 mile to complete the loop. Therefore, the correct answer is 1/16 mile.
To find out how far Hayami has to walk her bike to complete the loop, we need to calculate the remaining distance after she rode her bike before stopping for a rest and getting a flat tire.
1. First, we calculate the distance Hayami rode before stopping for a rest:
She rode 3/4 mile.
2. Then, we calculate the distance she rode after stopping for a rest but before getting a flat tire:
She rode 1/8 mile.
3. Now, let's find out the total distance she rode:
= 3/4 + 1/8
= 6/8 + 1/8
= 7/8 mile.
4. The length of the loop is \(15/16\) mile.
5. To find the remaining distance to complete the loop, subtract the distance she rode from the total loop length:
= 15/16 - 7/8
= 15/16 - 14/16
= 1/16 mile.
6. Therefore, Hayami has to walk her bike 1/16 mile to complete the loop.
In conclusion, the correct answer is 1/16 mile (Option A).
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Complete Question
Choose the correct answer from the given options:
Hayami was riding her bike on a loop that is 15/16 mile long. she rode for 3/4 mile and then stopped to rest she rode another 1/8 mile and then has a flat tire. how far does Hayami have to walk her bike to complete the loop?
A.1/16 mile
b.1/32 mile
c. 3/16 mile
d. 1/8 mile
4x(3x - 1) - 2(3x + 1) - (x + 3)
Answer:
[tex]12x^{2} -11x-5[/tex]
Step-by-step explanation:
1) Distribute
[tex]4x(3x-1)-2(3x+1)-(x+3)\\12x^{2} -4x-2(3x+1)-(x+3)[/tex]
2) Distribute
[tex]12x^{2} -4x-2(3x+1)-(x+3)\\12x^{2} -4x-6x-2-(x+3)[/tex]
3) Distribute
[tex]12x^{2} -4x-6x-2(x+3)\\12x^{2} -4x-6x-2-x-3[/tex]
4) Subtract the numbers
[tex]12x^{2} -4x-6x-2-x-3\\12x^{2} -4x-6x-5-x[/tex]
5) Combine like terms
[tex]12x^{2} -4x-6x-5-x\\12x^{2} -11x-5[/tex]
One fifth of the difference of a number and 1?
If you are asking for that to be in expression form, that would be:
1/5(x-1)
Let x be the number.
Answer: The expression that models this situation is given by:
x-1/5
---------------------------
The number is unknown, so it is called x.
The difference between 3 and 2 is 3 - 2 = 1, between 10 and 5 is 10 - 5 = 5, and so on. Thus, the difference between a number and 1 is x - 1.
One fifth of a number is the number divided by 5. Thus, in this context, the expression that represents one fifth of the difference of a number and 1 is given by:
x-1/5
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NEED help asap please find the percentage
Hope this helps, have a nice day!!
Find the missing angles
Step-by-step explanation:
<3 = 47°, alternate angle.
<2 = 52° , alternate angle.
<5=180-47-52=81°, linear pair.
<1= 180-52=128°, alternate angle, linear pair.
<4= 180-47= 133°, alternate angle, linear pair.
hope this helps you.
What is 4t - t + 2=This is in combinding terms into equvilent equations
Answer:
=3t+2
Step-by-step explanation:
if you ONLY solve the equations the answer is (3t+2) but if you evaluate the equation and the answer together it's (9t+8). So which ever answer you were looking for there's two different choices for two different ways.
(you're welcome, and hope this helps) :)
The price of a baseball card began at $5.00. A collector marked the price up 500% and is reselling the card online. What is the new sales price of the baseball card?
Answer:
25.00
Step-by-step explanation:
5.00 x 500% = 25
Simplify by collecting like terms
r^+5r+3r^-2r
By the way
^= square
Ill also attach a photo, thankssss!
Answer:
Step-by-step explanation:
Like terms have same variable with same power.
r² + 5r + 3r² - 2r = r² + 3r² + 5r - 2r
= 4r² + 3r
Date 3) Paula baked two batches of chocolate chip cookies. She used 3 cups of flour for the first batch of cookies and 2 cups for the second batch. What fraction of flour was used to make the first batch of cookies?
Answer:
3/2
Step-by-step explanation: I took the test
can someone answer this?
Answer:
324 ft²
Step-by-step explanation:
Given 2 similar figures with ratio of sides a : b , then
ratio of areas = a² : b²
Here ratio of sides = 3 : 18 = 1 : 6
ratio of areas = 1² : 6² = 1 : 36
That is the area of the larger parallelogram is 36 times the smaller
area of larger parallelogram = 36 × 9 = 324 ft²
In January, 1950, the minimum wage was $.75. What should the minimum
wage be in July, 2009?
Answer:
On July 24, 2009, the federal minimum wage will increase to $7.25 per hour. This is the final step of a three-step increase passed in 2007 when the minimum wage was only $5.15. In this last step, about 4.5 million workers will receive a raise, providing an additional $1.6 billion annually in increased wages. However, when adjusted for inflation, the new federal minimum is still less than the minimum wage through most of the period from 1961 to 1981.
Step-by-step explanation:
Find the distance between parallel lines whose equations are y = x - 6 and y = x + 8.
Answer:
14
Step-by-step explanation:
Distance between y2 = x + 8 and y1 = x - 6
y2 - y1 = (x + 8) - (x - 6) = 14
Kira is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.
Company A charges an initial fee of $35 and an additional 60 cents for every mile driven.
Company B charges an initial fee of $42 and an additional 50 cents for every mile driven.
For what mileages will Company A charge less than Company B?
Write your answer as an inequality, using m for the number of miles driven.
Answer:
m < 0.7
Miles less than 0.7
Step-by-step explanation:
Company A: 60m + 35
Company B: 50m + 42
60m + 35 < 50m + 42
60m - 50m < 42 - 35
10m < 7
m < 7/10 (0.7)
Write an equation that represents a discount of 18% on a retail price of $55. Let p represent the new price.
Enter the correct answer in the box.
[tex]\boxed{\tt{55(55-0.18)=pA}}[/tex]
What is the value of r?
Answer:
its 40
Step-by-step explanation:
180-100=80
80/2= 40
You spent a total of $63. How much will pay in 6% tax?
Answer:
You will pay $3.78 in tax. And you would pay a total of $66.78
Step-by-step explanation:
Answer: $3.78 or $66.78 if you are looking for the total amount including tax.
Step-by-step explanation:
6% can be represented by 0.06 so multiply that by 63
63*0.06=3.78
You will pay $3.78 in taxes
The total is 66.78 but I think you are asking for the tax.
Pretty please help me with answering with the right answer? 100 points will be given and brainliest! NO LINKS
Answer:
last and second answer
Step-by-step explanation:
HELPPPP PLEASEEEE will give brainliest
Answer:
I think it's the 3rd or fourth one. I'm not positive tho
What were two impacts of the first great depression?
help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
1: unemployment (more homeless people)
2: House prices rose down drastically by 70%.
(My sources: TheBalance.com)
the difference between 4x and 2x is 70. Find the 2x
Answer:
2x = 70
Step-by-step explanation:
4x - 2x = 70
2x = 70
x = 70/2
x = 35
Rachel earns $42,000 per year. Find how much she would make if she was paid weekly, semimonthly, and monthly.
Answer:
in a monthly shy much $3500
in a weekly she much $807.69
Step-by-step explanation:
Answer:
Below! : )
Step-by-step explanation:
$3,500 monthly
$807.69 per week
$1,615.38 biweekly
Hope this helps! : )
Help me please Asap
Answer:
it is the last one {-4, -1, 0, 1, 2}
Step-by-step explanation:
PLEASE HELP NOW
Rewrite the equation in Ax+By=C form.
Use integers for A, B, and C.
y+6=5(x-3)
2
Answer:
answer is 21= 5x- y
Step-by-step explanation:
y+6=5(x-3)
y+6=5x-15
y = 5x-15-6
y = 5x-21
rearrange this equation as formAx+By=C
5X - y = 21
Which criterion, if any, could prove the triangles are congruent?
Answer:
ASA stands for "angle, side, angle" and means that we have two triangles where we know two angles and the included side are equal.
So A
Explanation: If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent
Which of the following relations is a function?
O {(9,0), (10,3), (11, 6), (11, 9)}
O {(1, 1), (1, 2), (1, 3), (1,4)}
O {(1, 3), (2, 10), (6, 24), (24, 6)}
O {(0,6), (-1, 10), (-1, 14), (-3, 18)}
Answer:
O {(1, 3), (2, 10), (6, 24), (24, 6
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Mr. Fullerton sold half of his “Captain Underpants” comic books and then bought sixteen more. He now has 36 “Captain Underpants” all together. How many comic books did he begin with?
Answer:
40 comic books
Step-by-step explanation:
36-16=20
20×2=40