Answer:
see explanation
Step-by-step explanation:
Using the cosine addition formula
cos(A ± B ) = cosAcosB ∓ sinAsinB
Then considering the left side
cos²(45 + A) + cos²(45 - A)
= [ cos45cosA - sin45sinA ]² + [cos45cosA + sin45sinA]]²
= [ [tex]\frac{1}{\sqrt{2} }[/tex] cosA - [tex]\frac{1}{\sqrt{2} }[/tex] sinA ]² + [ [tex]\frac{1}{\sqrt{2} }[/tex] cosA + [tex]\frac{1}{\sqrt{2} }[/tex] sinA ]²
= [tex]\frac{1}{2}[/tex]cos²A - sinAcosA + [tex]\frac{1}{2}[/tex] sin²A + [tex]\frac{1}{2}[/tex] cos²A + sinAcosA + [tex]\frac{1}{2}[/tex] sin²A
= cos²A + sin²A
= 1
= right side , then proven
Answer:
Step-by-step explanation:
cos 2x=cos²x-sin²x=cos²x-(1-cos²x)=cos²x-1+cos²x=2cos²x-1
2cos²x=1+cos2x
[tex]cos^2x=\frac{1}{2}(1+cos2x)[/tex]
cos²(45+A)+cos²(45-A)
[tex]=\frac{1}{2}(1+cos(90+2A))+\frac{1}{2}(1+cos(90-2A))\\=\frac{1}{2} (1-sin2A)+\frac{1}{2} (1+sin 2A)\\=\frac{1}{2} (1-sin2A+1+sin 2A)\\=\frac{1}{2} \times2\\=1[/tex]
cos (90-x)=sin x
cos (90+x)=-sin x
Help me please, Domain & Range problem
Answer:
Domain: all reals
Range: 4 ≤y <∞
Step-by-step explanation:
The domain is the possible input values(x)
From the arrows at the left and right ends on the graph, the inputs can be all reals
The range is the possible output values (y)
Y goes from 4 to infinity
4 ≤y <∞
What is the difference of these fractions? use the number line and equivalent fractions to help find the answer -1 1/4+1/2
Answer:
1 3/4 or 7/4
Step-by-step explanation:
- 1 1/4 = -5/4
1/2 = 2/4
difference = 5/4+2/4 =7/4
Answer:
first step find LCM method
An account manager for a local software firm believes there is a relationship between the number of contacts and the amount of the sales. To verify this belief, the following data was collected: Salesperson Number of Contacts Sales (in millions) 1 14 24 2 12 14 3 20 28 What is the dependent variable
Answer:
Amount of sales
Step-by-step explanation:
The dependent variable also called the measured or predicted variable is simply the variable obtained due to inputs in of the independent variable. It is the variable which is being measured in an experiment. Here, the test is that the number of sales depends on the number of contact. Here, the number of contacts will has an influence or determines the amount of sales, hence, the number of contacts is the independent variable while the amount of sales is the dependent variable.
Use the substitution method to solve the system of equations. Choose the
correct ordered pair.
y = 12x-8
y = 8x
A. (4, 12)
B. (5, 11)
C. (2,16)
O D. (3, 15)
Answer:
C. (2,16)
Step-by-step explanation:
[tex]y=12x-8\\y=8x\\\\\\8x=12x-8\\-4x=-8\\x=2\\\\y=8(2)=16[/tex]
Answer:
It might be B
Step-by-step explanation:
12(5)-8
8(11)
52
88
Every year, a town surveys the size of its wetland ecosystems. This equation estimates the total wetland area, in acres, over time, t, in years.
F(t)= 740(0.95)^t
Which statements are supported by the function?
When t=10, the town is predicted to have around 443 acres of wetlands.
At one time, the town had 740 acres of wetlands.
The wetland area in the town decreases by 5% per year.
When t=10, the town is predicted to have around 492 acres of wetlands.
The wetland area in the town increases by 95% per year.
Answer:
When t=10, the town is predicted to have around 443 acres of wetlands.
At one time, the town had 740 acres of wetlands.
The wetland area in the town decreases by 5% per year.
Step-by-step explanation:
Given
[tex]f(t) = 740 * (0.95)^t[/tex]
Required
The true statements
[tex](a)\ f(10) = 443[/tex]
We have:
[tex]f(t) = 740 * (0.95)^t[/tex]
Substitute 10 for t
[tex]f(10) = 740 * (0.95)^{10[/tex]
[tex]f(10) = 443[/tex]
Hence, (a) is true
[tex](b)\ f(t) = 740[/tex]
We have:
[tex]f(t) = 740 * (0.95)^t[/tex]
Substitute 740 for f(t)
[tex]740 = 740 * (0.95)^t[/tex]
Divide through by 740
[tex]1 = 0.95^t[/tex]
Express 1 as 0.95^0
[tex]0.95^0 = 0.95^t[/tex]
Cancel out the bases
[tex]0 = t[/tex]
[tex]t = 0[/tex]
Hence, the area had 740 acres initially;
(b) is true
[tex](c)\ r = 5\%[/tex]
We have:
[tex]f(t) = 740 * (0.95)^t[/tex]
Using the general formula
[tex]f(t) = a * b^t[/tex]
By comparison:
[tex]b = 0.95[/tex]
0.95 < 1 means that:
[tex]b = 1 - r[/tex] --- where r = rates
[tex]0.95 = 1 - r[/tex]
Collect like terms
[tex]r = 1 - 0.95[/tex]
[tex]r = 0.05[/tex]
Express as percentage
[tex]r = 5\%[/tex]
Hence, (c) is true
[tex](d)\ f(10) = 492[/tex]
In (a)
[tex]f(10) = 443[/tex]
Hence, (d) is false
[tex](e)\ r = 95\%[/tex]
In (c)
[tex]r = 5\%[/tex] ---- decrement
Hence, (e) is incorrect
Answer: When the town is predicted to have around 443 acres of wetlands.
At one time, the town had 740 acres of wetlands.
The wetland area in the town decreases by 5% per year.
Step-by-step explanation:
Your friend offers to place a bet with you. He will pay you $1 if your favorite sports team wins the game on Tuesday night. But you will pay him $3 if his team wins. Your team has an 80% chance of winning, whereas his only has a 20% chance. This bet is in your favor. True or False.
False because $1 =$1 not $3
True. The expected value of the bet is positive ($0.2),
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
Let's calculate the expected value of the bet for both outcomes:
If your team wins: You get paid $1, so the expected value is 0.8 × $1 = $0.8
If your friend's team wins: You pay $3, so the expected value is 0.2 × -$3 = -$0.6
The overall expected value of the bet is the sum of these two outcomes: $0.8 + (-$0.6) = $0.2
Since the expected value of the bet is positive ($0.2), this means that on average, you can expect to win money if you take this bet. Therefore, the bet is in your favor.
Learn more about probability here:
brainly.com/question/11234923
#SPJ2
The length of the base of a triangle is twice it’s height. If the area of the triangle is 441 square kilometers, find the height
Answer:
21 kilometers
Step-by-step explanation:
Let the height be [tex]x[/tex]. Then, the length of the base is [tex]2x[/tex]. The formula for the area is of the triangle is given by base*height/2. Therefore, the area of the triangle is equal to [tex]\frac{x \cdot 2x}{2} = x^2[/tex], which is in turn equal to 441. Since [tex]x[/tex] must be positive, then [tex]21^2=441[/tex], meaning that the height is [tex]21[/tex] kilometers.
What is the area of the shaded part of the figure?
Answer:
14cm²
Step-by-step explanation:
3x2=6,
3x2=6,
2x1=2,
6+6+2=14 cm^2
Question 13 plz show ALL STEPS so I can learn thnx
9514 1404 393
Answer:
a) (x³ -x² +x +2) +2/(x+1)
b) (x² +2x -5) +6/(x+3)
Step-by-step explanation:
Polynomial long division is virtually identical to numerical long division, except that the quotient term does not require any guessing. It is simply the ratio of the leading terms of the dividend and divisor. As with numerical long division, the product of the quotient term and the divisor is subtracted from the dividend to form the new dividend for the next step.
The process stops when the dividend is of lower degree than the divisor.
In part (a), you need to make sure the dividend expression has all of the powers of x present. This means terms 0x³ and 0x² must be added as placeholders in the given dividend. They will become important as the work progresses.
During the construction of a road a mountain of 250 metres in height, through it will be the construction of a tunnel. The top of the mountain is seen at an angle of 48°30' from a point P at one end of the mountain, and at an angle of 38° from the other end. How long will this tunnel be?
Answer:
542.74 m
Step-by-step explanation:
Tan(48.3) = 250/a Multiply by a
a*tan(48.3) = 250 Divide by tan(48.3)
a = 250/Tan(48.3)
a =222.74
By a similar method b = 250/tan(38)
b = 319.99'
The total length =542.73 meters
Internet providers: In a survey of 780 homeowners with high-speed Internet, the average monthly cost of a high-speed Internet plan was $64.22 with standard deviation S10.75. Assume the plan costs to be approximately bell-shaped. Estimate the number of plans that cost between $42.72 and $85.72. pprosimately bell-shaped. The number of plans that cost between $42.72 and $85.72 is:_________
Answer:
Hence the number of plans that cost between $42.72 and $ 85.72 is
95.44 %.
Step-by-step explanation:
Now the given are
μ = $64.22.
σ = $10.75.
Here,
[tex]P\left ( 42.72 < x< 85.72 \right )=P\left ( \frac{42..72-64.22}{10.75}< \frac{x-\mu }{\sigma } < \frac{85.72-64.22}{10.75}\right )\\P\left ( 42.72 < x< 85.72 \right )= P\left ( -2.00< Z <2.00 \right )\\P\left ( 42.72 < x< 85.72 \right )= P\left (Z<2.00\right )-P\left ( Z<-2.00 \right )\\P\left ( 42.72 < x< 85.72 \right )= P\left (0.9772\right )-P\left (0.0228\right )\\Probability = 0.9544[/tex]
Probability = 95.44%.
25[tex]25^x=125^x^+^3[/tex] = 125x + 3
Answer:
x = -9
Step-by-step explanation:
25^x = 125 ^(x+3)
Rewriting
5^2^x = 5^3^(x+3)
We know a^b^c = a^(b*c)
5^(2x) = 5^(3(x+3))
5^(2x) = 5^(3x+9)
The bases are the same so the exponents are the same
2x = 3x+9
Subtract 3x from each side
2x-3x = 3x+9-3x
-x =9
x = -9
Answer:
x is -9
Step-by-step explanation:
Write an expression 9 multiplied by t
Answer:
9t
Step-by-step explanation:
That's 9 multiplied by t
The sum of two integers is -360. One of them is 60, then the other integer is
X^2 + bx + 49 is a perfect squad trinomial what is one possible value of b? & I need help with the others also due soon!
20. (2) 14
A perfect square trinomial will factor into two expressions that are the same, for example: x^2 + 6x + 9 = (x + 3)(x + 3). Since this problem has a C value of 49, it will factor into (x + 7)(x + 7). 7 doubled is 14, therefore one possible value of B is 7.
21. (4) 2, -12
x^2 + 10x + 25 = 24 + 25
(x + 5)^2 = 49
x + 5 = +/- 7
x = 2, -12
22. (3) 3 + sqrt(17)
x^2 - 6x = 8
Complete the Square
x^2 - 6x + 9 = 8 + 9
(x - 3)^2 = 17
x - 3 = +/- sqrt(17)
x = 3 + sqrt(17), 3 - sqrt(17)
23. (1) 1, -5
x^2 + 4x - 5 = 0
x^2 + 4x = 5
x^2 + 4x + 4 = 5 + 4
(x + 2)^2 = 9
x + 2 = +/- 3
x = 1, -5
Hope this helps!
Solve by elimination.
8x + 4y = 20
-10x – 5y = –25
A. (14, -1)
B.(-4,4)
c. (0,3)
D. infinite number of solutions
Hi there!
»»————- ★ ————-««
I believe your answer is:
D. infinite number of solutions
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Calculating the Answer...}}\\\\\left \{ {{8x + 4y = 20} \atop {-10x - 5y = -25}} \right.\\-----------\\5(8x + 4y = 20)\\4(-10x - 5y = -25)\\\\40x+ 20y = 100\\\-40x-20y=-100\\\\\boxed{0 = 0}[/tex]
⸻⸻⸻⸻
There are an infinite number of solutions.
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
find the solution to this system of equations x+y=1
2x-y+z=1
x+2y+z=8/3
9514 1404 393
Answer:
(x, y, z) = (1/3, 2/3, 1)
Step-by-step explanation:
We can use the first equation to write an expression for x that can be substituted into the other equations.
x = 1 -y
2(1 -y) -y +z = 1 ⇒ -3y +z = -1
(1 -y) +2y +z = 8/3 ⇒ y +z = 5/3
Subtracting the first of these equations from the second gives ...
(y +z) -(-3y +z) = (5/3) -(-1)
4y = 8/3
y = 2/3
z = 5/3 -y = 1
x = 1 -y = 1/3
The solution is (x, y, z) = (1/3, 2/3, 1).
Which of the following choices shows the complete factorization of 50?
52 • 5
2 • 25
52 • 2
None of these choices are correct.
Hello can anyone answer this question please I need help
9514 1404 393
Answer:
maximum: 40(8/3, 8/3)Step-by-step explanation:
The graph shows the relevant vertex of the feasible region is ...
(x, y) = (8/3, 8/3).
The value of z there is ...
z = 11(8/3) +4(8/3) = (88 +32)/3
z = 40
An investor puts $800 into an account that pays 7.5% interest compounded annually. The total amount A in the account after t years is given by which function below?
A = 800(1.75) ^t
A = 800(1.075) t
A = 800(1.075)^ t
A = 800 + (1.075)^ t
Answer:
A = 800( 1.075)^(t)
Step-by-step explanation:
The equation for interest is
A = p (1+r/n) ^ nt where p is the principle, r is the interest rate, n is the number of times per year and t is the years
A = 800( 1+ .075/1)^(1*t)
A = 800( 1.075)^(t)
Let's see
[tex]\\ \tt\leadsto A=P(1+r/n)^{nt}[/tex]
n is 1[tex]\\ \tt\leadsto A=P(1+r)^t[/tex]
[tex]\\ \tt\leadsto A=800(1+0.075)^t[/tex]
[tex]\\ \tt\leadsto A=800(1.075)^t[/tex]
Option C
What is the different of (5-3x) and (5x-10)
a. 8x-5
b. 15-8x
c. 8x + 15
d. none of the above
Answer:
15 - 8x
Step-by-step explanation:
Remark
This all depends on how you read the question. In other words, which comes first 5 - 3x or 5x - 10. It's not clear.
If you do the first one first, you get
5 - 3x - (5x - 10) Remove the brackets.
5 - 3x - 5x + 10 Collect like terms
15 - 8x So that makes the middle one correct.
Now do it the other way.
5x - 10 - (5 - 3x)
5x - 10 - 5 + 3x
8x - 15
That answer isn't available here. So ..
The answer is 15 - 8x
give me examples of equivalent expressions of square root 54 with a radican of 3
Mr. G wants to cut boards that are 1 1/2 foot long. If he has an 18 foot long board, how man pieces can he cut?
Answer:
18 ft* (1 piece/ 1 1/3 ft)= 13.5 pieces.
Step-by-step explanation:
Which expression is equivalent to 7√x^2/5√y^3? Assume y≠0
Answer:
Step-by-step explanation:
If the √y³ term is in the denominator, then the expression needs to be written with parentheses: 7√x²/(5√y³)
A tennis player plays with an equal opponent. What is more likely for him: to win one game out of two or two out of four?
Answer:
two out of four
Step-by-step explanation:
there are 4 different outcomes for the one out of two and 2 of them involve him winning one out of two but for the two out of 4 there are more possibilities and there are 10 possibilities
in a class, 64 offers mathematics while 94 offers chemistry , How many will offer the both course?
Answer:
30
Step-by-step explanation:
94-64=30 will offer the same course because the chemistry offers ocerride the mathematics offers
Chứng minh hệ thức De Morgan sau:
~(P ^ Q) = ~P v ~Q
Use a truth table:
p … q … p ∧ q … ¬(p ∧ q) … ¬p … ¬q … ¬p ∨ ¬q
T … T … T … F … F … F … F
T … F … F … T … F … T … T
F … T … F … T … T … F … T
F … F … F … T … T … T … T
There is a rectangular terrain with dimensions "x" and "y". If it is known that its area of is 22m ^ 2 and that x ^ 2 + y ^ 2 = 100, what is the perimeter of said terrain?
9514 1404 393
Answer:
24 m
Step-by-step explanation:
The area formula tells us ...
22 = xy . . . . . square meters
Adding twice this to the quadratic constraint gives ...
(x^2 +y^2) +2(xy) = (100) +2(22)
(x +y)^2 = 144
x +y = √144 = 12
The perimeter is double this amount, so is ...
P = 2(x +y) = 2(12) = 24 . . . . meters
HELP THIS IS DUE BY THURSDAY PLZZ HELP ME (05.03)Bev has to cut her grandma's grass this weekend and wants to know exactly how much area she will be cutting. Calculate the area of the polygon. Be sure to show all your work and explain your answer
Answer: 220.5 ft^2
That's the answer.
Evaluate the given expression for x = 4 and y= 3. 7x2 + 6xy + 6y?
The answer is: _____
Answer:
104
Step-by-step explanation:
x=4 ; y=3
7×2 +6xy+6y
7×2+6(4)(3)+6(3)
14+72+18
104
