Plssss helpppp!!!!!!!

x = 0°, 180°

cos²(x) + 2cos(x) = 5cos(x) + 4

let cos x = y

y² + 2y = 5y + 4

collect like terms:

y² + 2y - 5y - 4 = 0

y² - 3y - 4 = 0

Using factorisation method to solve the above equation:

The factors of -4 that we can sum up to get -3 are: -4 and +1

y² - 4y + y - 4 = 0

y(y +4) + 1(y - 4) = 0

(y + 1) (y - 4) = 0

y + 1 = 0 or y - 4 = 0

y = -1 or y = 4

Recall cosx = y

This means:

cos x = -1 or cos x = 4

We were given an interval of [0, 2π). This means the interval is from 0° ≤ x < 360°

Greater than 0° but less than 360°

cosx = -1

x = arc cos (-1)

x = 180 degrees

cos x = 4

x = arc cos (4)

x = 0 degrees

x = 0°, 180°

Answer:

Write down the problem. For this example, you will be dividing x3 + 2x2 - 4x + 8 by x + 2. Write the first polynomial equation, the dividend, in the numerator and write the second equation, the divisor, in the denominator.

Reverse the sign of the constant in the divisor. The constant in the divisor, x + 2, is positive 2, so reversing the sign of the constant would give you -2.

Since the opposite of the constant term is -2, we put the -2 inside a box. A common mistake is to put a 2 inside the box, watch out here.

Write all of the coefficients of the dividend inside the division symbol. [2] Write the terms from left to right, just as they appear. It should look like this: -2| 1 2 -4 8.

Bring down the first coefficient. Bring down the first coefficient, 1, below itself. It should look like this:

-2| 1  2  -4  8

   ↓

   1

Multiply the first coefficient by the divisor and place it under the second coefficient.[3] Simply multiply 1 by -2 to get -2 and write this product under the second term, 2. Here's how it would look:

-2| 1  2  -4  8

       -2

   1

Add the second coefficient and the product and write the answer below the product. Now take the second coefficient, 2, and add it to -2. The result is 0. Write this result below the two numbers, just as you would in long division. Here's how it would look:

-2| 1  2  -4  8

       -2

   1   0

Multiply this sum by the divisor and place the result under the third coefficient. Now take the sum, 0, and multiply it by the divisor, -2. The result is 0. Place this number below 4, the third coefficient. It should look like this:

-2| 1  2  -4  8

       -2  0  

   1  

Add the product and the third coefficient and write the result under the product. Add 0 and -4 to get -4 and write this answer below the 0. Here's how it would look:

-2| 1  2  -4  8

       -2   0  

   1   0   -4

Multiply this number by the divisor, write it under the last coefficient, and add it to the coefficient. Now, multiply -4 by -2 to get 8, write this answer under the fourth coefficient, 8, and add this answer to the fourth coefficient. 8 + 8 = 16, so this is your remainder. Write this number below the product. Here's how it would look:

-2| 1  2  -4  8

       -2   0   8

   1   0   -4   |16

Place each of the new coefficients next to a variable of one less power than their original corresponding variables. In this case, the first sum, 1, is placed next to an x to the second power (one less than three). The second sum, 0, is placed next to an x, but the result is zero, so you can remove this term. And the third coefficient, -4, becomes a constant, a number without a variable, since the original variable was x. You can write an R next to the 16, because that is the remainder. Here's how it would look:

-2| 1  2  -4  8

       -2   0   8

   1   0   -4   |16

   x2   + 0x    - 4    R 16

x2 - 4 R16

Write the final answer. The final answer is the new polynomial, x2 - 4, plus the remainder, 16, over the original divisor, x + 2. Here's how it would look: x2 - 4 +16/(x +2).

Step-by-step explanation:

That was quite long, but those are the steps to synthetically divide polynomials.

Answer:

-18

Step-by-step explanation:

because you take 40 + -58 and you can make the positive and negative sign a negative so now it would be 40-58

if you reverse it to make it 58-40 you would get 18 and then reverse it back to negative because you reversed it once so now its -18

Answer:

30 18+12=30

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

That Frankie has 11 quarters (x) and 16 dimes (x + 5).

Let x be the number of quarters, then x + 5 is the number of dimes.

The sum of the value of dimes and quarters is $4.35.

This information can be used to create an equation that can be solved for the number of dimes and quarters.

Let's solve for this.

Frankie has x quarters, which have a value of 0.25x, and x + 5 dimes, which have a value of 0.10(x + 5).

Since the sum of the value of dimes and quarters is $4.35, we can create the following equation:

0.25x + 0.10(x + 5) = 4.35

Simplify by distributing the 0.10 term:

0.25x + 0.10x + 0.50 = 4.35

Combine like terms:

0.35x + 0.50 = 4.35

Subtract 0.50 from both sides:

0.35x = 3.85

Divide both sides by 0.35:

x = 11

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Two pyramids are similar, so ratio of the corresponding sides are equal.

Determine the height of large pyramid.

The formula for the volume of pyramid is,

Here, A is base area of pyramid.

Determine the volume of pyramid.

So answer is V = 8533.3 inches cube.

A key problem faced by poorer inner-city neighborhoods in America due to their geographical position is a lack of quality food options.

One of the significant challenges faced by poorer inner-city neighborhoods in America is the limited availability of quality food options, commonly referred to as "food deserts." Food deserts are areas where residents have limited access to fresh, nutritious, and affordable food. These neighborhoods often lack grocery stores, farmers markets, and other sources of healthy food, leaving residents with few choices but to rely on convenience stores and fast food outlets that predominantly offer processed and unhealthy food options.

The geographical positioning of these neighborhoods plays a crucial role in this interest. Many low-income inner-city neighborhoods are located in areas that are underserved by grocery stores and supermarkets.

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Answer:

B

Step-by-step explanation:

For example, if i gave u 28

The digit two stands for 20, and the digit 8 stands for 8, therefore u call it 28

Each spot has it own name

For example if i gave u the number 12345

5 is in the first spot, therefore 5 x 1 =5

4 is in the tenth spot, therefor 4 x 10 = 40

3 is in the hundred spot, therefore 3 x 100 =300

2 is in the thousand spot, therefore 2 x 1000=2000

1 is in the ten thousand spot, therefore 1 x 10000

=100000

So if u add all these numbers together u will get

12345

OK, so for your question, the 6 in 558672, is in the hundred spot, so 6 x 100 =600

The 3 in 74139 is in the ten spot, so 3 x 10=30

So the product is to multiply them together

600 x 30 =18000

In the problem given:

W + 15x - 9y + 2z

The term are single mathematical expressions that separate values.

In the expression, there is a + and -; these concludes 2 terms.

There are 3 coefficients next to each variable.

The coefficients are 15x, -9y, and 2z.

That means there are 3 coefficients.

Cheers

- ROR

\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)

____________________________________

\( \large \tt Solution \: : \)

Term refers to each variable or constant separated by a mathematical operator.

Coefficient refers to the numberic part of variable or a constant number present in an expression.

\(\qquad \tt \rightarrow \: 12a - 10b + 6\)

\( \large\textsf{Terms :} \)

\( \texttt{coefficient = 1} \)

\( \texttt{coefficient = 15} \)

\( \texttt{coefficient = -9} \)

\( \texttt{coefficient= 2} \)

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:  C) as x → -∞, y → 3

                    as x→ ∞ , y → ∞

Step-by-step explanation:

see graph

Notice that as x approaches negative infinity (goes to the left), the y value approaches the asymptote of y = 3.

And as x approaches positive infinity (goes to the right), the y-value increases without bound so goes to infinity.

As x decreases without bound f(x) approaches but never reaches 3. As x increases without bound f(x) increases without bound. the option C is correct.

When the expression of function is such that it involves the input to be present as an exponent (power) of some constant, then such function is called exponential function.

Their usual form is specified below. They are written in several such equivalent forms.

From the graph, we can see that as x approaches negative infinity (goes to the left), the y value approaches the asymptote of y = 3.

As x approaches more negative the function will approach the horizontal asymptote,

so lim(f(x)) = 3 as x → -∞.

As x approaches more positive, so does the function,

so lim(f(x)) → +∞ as x → +∞.

As x decreases without bound f(x) approaches but never reaches 3. As x increases without bound f(x) increases without bound.

Hence, the option C is correct.

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Answer:

= 24.

Step-by-step explanation:

-(-5+(-8))-(-9-2)

= -(-5-8)-(-9-2)

= 5 + 8 + 9 + 2

= 13 + 11

= 24

The value of b is 2.

To find the value of b, we need to equate the equations of the semi-circle and the parabola.

The equation of the semi-circle is given as fx = √(9 - x²).

The equation of the parabola is given as gx = b - (1/4)x².

Since both graphs represent the same function, we can equate them and solve for the value of x:

√(9 - x²) = b - (1/4)x²

To simplify the equation, let's square both sides:

9 - x² = (b - (1/4)x²)²

Expanding the right side of the equation:

9 - x² = b² - 2b(1/4)x² + (1/16)x⁴

Combining like terms:

9 - x² = b² - (1/2)bx² + (1/16)x⁴

Since the two sides of the equation are equal for all values of x, the coefficients of each power of x must be equal. Comparing the coefficients, we have:

-1 = -b/2          (coefficient of x² term)

0 = 1/16          (coefficient of x⁴ term)

From the coefficient of the x² term, we can solve for b:

-b/2 = -1

b/2 = 1

b = 2

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Answer:

in simplify this is- 9a2i+42ab+49b2

Step-by-step explanation:

Answer: Rewrite in vertex form and use this form to find the vertex

(

h

,

k

)

.

(

1

,

−

1

)

Rewrite in vertex form and use this form to find the vertex

(

h

,

k

)

.

(

1

,

−

1

)

Step-by-step explanation:

The answer is (d) all of the above. Alice must prefer the gamble ($450 w.p. 0.5 $0 w.p. 0.5) to (a), (b) and (c) since it offers her a higher expected value and complies with the independence axiom.

Alice prefers $450 for sure to the gamble ($1000 w.p. 0.5 $0 w.p. 0.5). The expected value of the gamble is $500, while the expected value of $450 is clearly lower. This complies with the independence axiom, as she is preferring a certain $450 to an uncertain $500.

Therefore, Alice must prefer the gamble ($450 w.p. 0.5 $0 w.p. 0.5) to (a) ($1000 w.p. 25% 0 w.p. 75%), (b) $225, and (c) $200, since it offers her a higher expected value and complies with the independence axiom. Thus, the answer is (d) all of the above.

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Answer:

$1.35

Step-by-step explanation:

8n = 10.80

Divide both sides by 8 to get n alone.

n = 10.80/8 = $1.35

Answer:

ons are in the crayon box.If there are 4 rows of 19 crayons,

Step-by-step explanation:

i. Probability that a note is real but the system identifies it as fake: Let R be the event that a note is real, then the probability of a note being real is\(P(R) = 1 – P(F) = 0.99\)

Then the probability that a note is real but the system identifies it as fake is\(P(T' and R) = P(R) x P(T|R') = 0.01 x 0.05 = 0.0005\)Therefore, the probability that a note is real, but the system identifies it as fake is 0.0005.

ii. Probability that a note is fake, and the system identifies it as fake:

The probability that a note is fake, and the system identifies it as fake can be calculated as:

\(P(F and T) = P(F) x P(T|F) = 0.01 x 0.95 = 0.0095\)  Therefore, the probability that a note is fake, and the system identifies it as fake is 0.0095.

iii. Probability that the system identifies a note as fake.

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Answer:

18v+4 it's just addition with barriers. imagine that aren't there and it'll be easier.

Answer:

Circumference: 15.7 meters

Area: 19.625 meters

Step-by-step explanation:

Formula for Circumference:

\(2\pi r\)

(Tip: To find the radius of a circle from its diameter, you just have to divide the diameter by 2)

pi = 3.14

\(2\pi2.5\)

Which equals 15.7 meters

-----------------------

Formula for Area:

\(\pi {r}^{2} \)

\(\pi {2.5}^{2} \)

Which equals 19.625 meters

Answer:

The equation of a line in the form of y = mx + b, where m is the slope, x is the variable and b is the y-intercept.

Given a point and the slope, we can find the equation of the line that passes through that point. We know that the slope of the line is 0, so we can write the equation of the line as:

y = 0x + b

We also know that the line passes through the point (-3,-8), so we can substitute these values into the equation and solve for b, the y-intercept:

-8 = 0(-3) + b

-8 = 0 + b

b = -8

So the equation of the line that passes through the point (-3,-8) and has a slope of 0 is:

y = 0x - 8

This line is a horizontal line with y-intercept -8, which means that the line passes through the point (0,-8)

The given series can be rewritten as 1+3+5+...+(2n-1).Guess the formula for 1+3+...+(2n-1) by evaluating the sum for n=1,2,3,4:To find the sum, let us look at the first few terms of the sequence:1, 4, 9, 16...

We can see that the nth term of this sequence is given by n², and therefore the sum of the first n terms is given by: 1 + 4 + 9 + ... + n²This is a famous formula that was first discovered by the mathematician Carl Friedrich Gauss when he was just a child. The formula is:n(n + 1)(2n + 1)/6Using this formula, we can evaluate the sum for n = 1, 2, 3, 4 as follows:n = 1: 1n = 2: 1 + 3 = 4n = 3: 1 + 3 + 5 = 9n = 4: 1 + 3 + 5 + 7 = 16The formula for the sum of the first n odd integers is: n².Prove your formula using mathematical induction:To prove this formula using mathematical induction, we need to show that the formula is true for n = 1, and then assume that it is true for some integer k, and use this assumption to prove that it is true for k + 1.For n = 1, we have 1 = 1², which is true.Now assume that the formula is true for some integer k, that is:1 + 3 + 5 + ... + (2k - 1) = k²We need to prove that the formula is true for k + 1, that is:1 + 3 + 5 + ... + (2(k + 1) - 1) = (k + 1)²To do this, we add (2(k + 1) - 1) to both sides of the equation:1 + 3 + 5 + ... + (2k - 1) + (2(k + 1) - 1) = k² + (2(k + 1) - 1)Now we can simplify the right-hand side using algebra:k² + (2(k + 1) - 1) = k² + 2k + 1 = (k + 1)²So we have:1 + 3 + 5 + ... + (2(k + 1) - 1) = (k + 1)²This shows that the formula is true for k + 1, assuming that it is true for k.

Since the formula is true for n = 1, and assuming that it is true for some integer k implies that it is true for k + 1, we can conclude that the formula is true for all positive integers.

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The given series is: \(1 + 3 + 5 + ... + (2n - 1)\)Let the number of terms in the series be n For n = 1, the sum is 1 For n = 2, the sum is \(1 + 3 = 4\)

For n = 3, the sum is \(1 + 3 + 5 = 9\)

For n = 4, the sum is \(1 + 3 + 5 + 7 = 16\) From the above calculation, it is evident that the sum of the given series can be calculated using the formula: Sum = n²

Proof by Mathematical Induction: Let the sum of the first n terms of the given series be \(S(n)\) For \(n = 1\), \(S(1) = 1 = 1^2\) which is true Assume that the formula is true for n = k, i.e.,\(S(k) = k^2 ... (1)\)

Now we need to prove that the formula is true for n = k + 1, i.e., we need to show that:

\(S(k + 1) = (k + 1)^2 ... (2)\\Using (1), we\ can\ write:\\S(k + 1) \\= S(k) + (2(k + 1) - 1)S(k + 1) \\= k^2 + (2k + 1)S(k + 1) \\= k^2 + 2k + 1S(k + 1) \\= (k + 1)^2\)

Hence, the formula is true for n = k + 1 Since we have proven the formula for n = 1, and have shown that it is true for n = k + 1 when it is true for n = k, the formula must be true for all positive integers n by mathematical induction.

The formula for the given series \(1 + 3 + 5 + ... + (2n - 1)\) is \(Sum = n^2.\)

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A) First derivative for y = 3x² + 5x + 10 is dy/dx = 6x + 5; B) First derivative of for, y = 100200x + 7x is dy/dx = 100207 ; C) First derivative for y = In (9x4) is dy/dx = 4 / (3x).

A. y = 3x² + 5x + 10:

First derivative of the given equation, y = 3x² + 5x + 10 is as follows:

dy/dx = d/dx (3x²) + d/dx (5x) + d/dx (10)dy/dx

= 6x + 5

Since there are no exponents in 5x, the derivative of 5x is simply 5.

Similarly, since 10 is a constant, the derivative of 10 is zero.

B. y = 100200x + 7x:

First derivative of the given equation, y = 100200x + 7x is as follows:

dy/dx = d/dx (100200x) + d/dx (7x)dy/dx

= 100200 + 7

= 100207

C. y = In (9x4):

The given equation is, y = In (9x4).

The first derivative of this function can be obtained as follows:

dy/dx = 1 / (9x4) * d/dx (9x4)dy/dx

= 1 / (9x4) * 36x3dy/dx

= 4x3 / (3x4)dy/dx

= 4 / (3x)

Therefore, the first derivative of the given function y = In (9x4) is 4 / (3x).

A) First derivative forgiven equation, y = 3x² + 5x + 10 is dy/dx = 6x + 5; B) First derivative for given equation, y = 100200x + 7x is dy/dx = 100207 ; C) First derivative for given equation, y = In (9x4) is dy/dx = 4 / (3x).

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Answer:

14a^2(2a^6+1)

Step-by-step explanation:

Answer:

14a^{2} (2a^{6}+1)

Step-by-step explanation:

The best estimate for the weight of a cantaloupe is 2 kilograms (B).

A decigram is 1/10th of a gram, which would be too small of weight for a cantaloupe. 2 grams (C) is also too small for a cantaloupe as it would only be the weight of a few small seeds. 2 milligrams (D) is an extremely small weight, only suitable for a single grain of salt or a tiny insect.

Therefore, 2 kilograms (B) is the most reasonable estimate for the weight of a cantaloupe as it falls within the typical range of cantaloupe weights.

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Complete Question:

Choose the best estimate for the weight of a cantaloupe. Responses

A 2 decigrams

B 2 kilograms

C 2 grams

D 2 milligrams

Each side is equal so you divide 100 by 4.

Answer is: 25 m