prove that: cos^2 (45+A)+cos^2 (45-A)=1​

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).

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.  

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

9514 1404 393

Answer:

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

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

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)

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 <∞

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:

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.

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

Answer:

9t

Step-by-step explanation:

That's 9 multiplied by t

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

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.

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

Answer:

30

Step-by-step explanation:

94-64=30 will offer the same course because the chemistry offers ocerride the mathematics offers

Answer: 220.5 ft^2

That's the answer.

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

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%.

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

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:

False because $1 =$1 not $3

True. The expected value of the bet is positive ($0.2),

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

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]

[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

Answer:

14cm²

Step-by-step explanation:

3x2=6,

3x2=6,

2x1=2,

6+6+2=14 cm^2

Answer:

18 ft* (1 piece/ 1 1/3 ft)= 13.5 pieces.

Step-by-step explanation:

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!

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 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