Graph y = -x^2 – 2. Identify the vertex of the graph. Tell whether it is a minimum or maximum.

Answer:

1) 20.

2) 30.

3) 47.

4) 86.

5) 27.

Step-by-step explanation:

The order of operations consist in, first, evaluate the parenthesis, then the exponents, the multiplication, the division, and as last the addition and subtraction. Having this in mind:

1) (28 ÷ 4) + 3 + (10 - 8) × 5

7 + 3 + 2 × 5

7 + 3 + 10

20

2) 12 - 5 + 6 × 3 + 20 ÷ 4

12 - 5 + 18 + 5

30

3) 36 ÷ 9 + 48 - 10 ÷ 2

4 + 48 - 5

47

4) 10 + 8 × 90 ÷ 9 - 4

10 + 80 - 4

86

5) 8 × 3 + 70 ÷ 7 – 7

24 + 10 - 7

27

Answer:

A reflection over the y-axis.

Step-by-step explanation:

Use ToA method (tan = opposite / adjacent)

For this question we have to use pythagoras' Theorem to find the adjacent side.

take a as the length of the adjacent side.

given b = 12

c = 13

By pythagoras' Theorem,

[tex] {c}^{2} = {a}^{2} + {b}^{2} \\ {a}^{2} = {c}^{2} - {b}^{2} \\ {a}^{2} = {13}^{2} - {12}^{2} \\ {a}^{2} = 169 - 144 \\ {a}^{2} = 25 \\ a = \sqrt{25} \\ = 5[/tex]

Now we can find tan(x)

tan(x) = Opposite / adjacent

[tex] = \frac{12}{5} [/tex]

Answer:

Answer:

To determine to measure of the unknown angle, be sure to use the total sum of 180°. If two angles are given, add them together and then subtract from 180°. If two angles are the same and unknown, subtract the known angle from 180° and then divide by 2.

Answer:

EF = 8

Step-by-step explanation:

BC is half of AB, which means that DE will be half of EF. So if DE is 4, which is half of EF, then EF must be 8.

hope this helped! :)

Answer:

x +12

Step-by-step explanation:

Answer:

x + 12

Step-by-step explanation:

[tex](x + 3) + 9[/tex]

[tex]x + 3 + 9[/tex]

[tex] = x + 12[/tex]

Answer:

answer A shows a rotation

A because B is a mirror, c is a translation

Answer:

5.63cm

Step-by-step explanation:

to find length of side AB

12[tex]cos[/tex][62°]

=5.63cm

Answer:

B

Step-by-step explanation:

total area minus white area give you shaded area

1/2 + 1/5 = 5/10 + 2/10 = 7/10

Answer:

7/10

Step-by-step explanation:

1x5/2x5 + 1x2/5x2

=5/10+2/10

=7/10

Answer:

It would be 8% .

Good luck ^^

The series solution up to and including x⁴ is given by y(x) = 1 + 6x + (1/2)x² + (5/6)x³ + (1/4)x⁴ + ...

1.(a) A sequence is said to converge if its terms approach a specific value as the index of the terms increases without bound. In other words, as you go further along in the sequence, the terms get arbitrarily close to a particular limit value.

A sequence is said to diverge if its terms do not approach a specific value or if they move away from any possible limit as the index increases without bound. In other words, there is no single value that the terms of the sequence tend to as you go further along.

(b) Is there a sequence 01, 02, a3... with lan) <0.0001 for all n = 1,2,3,... that diverges No, there is no such sequence. If a sequence has a limit, then for any positive epsilon (ε), there exists a positive integer N such that for all n > N, |an - L| < ε, where L is the limit. In this case, if the limit exists, all terms beyond a certain index will be arbitrarily close to the limit, and it would violate the condition lan) < 0.0001 for all n = 1,2,3,... Therefore, if the condition holds, the sequence must converge.

(c) Is there a sequence 1000 01, 02, 03... with an < for all n = 1,2,3,... n 45 135 405 that diverges No, there is no such sequence. The sequence you provided starts with 1000, and each subsequent term increments by 1. Since the terms are increasing, the sequence does not approach any limit and therefore diverges.

2. (a)The nth term in the sequence an, assuming the sequence starts at a₀ we can observe that each term is obtained by multiplying the previous term by 4. So the expression for the nth term in the sequence can be given as

Aₙ = a₀ × 4ⁿ⁻¹

Given that a₀ = 15, the expression for the nth term in the sequence is:

aₙ = 15 × 4ⁿ⁻¹

(b) Does the series obtained by adding the terms of the sequence, Σan, converge or diverge

The series obtained by adding the terms of the sequence converges or diverges, we need to calculate the sum of the terms. Let's denote the sum of the series as S.

S = a₀ + a₁ + a₂ + ... + aₙ

Substituting the expression for an derived in part (a), we have:

S = 15 + 15 × 4⁰ + 15 × 4¹ + 15 × 4² + ... + 15 × 4ⁿ⁻¹

Using the formula for the sum of a geometric series, we can simplify this expression:

S = 15 × (1 + 4⁰ + 4¹ + 4² + ... + 4ⁿ⁻¹)

The sum of a geometric series with a common ratio greater than 1 is given by:

S = a × (1 - rⁿ) / (1 - r)

In this case, a = 15 and r = 4. Letting n approach infinity, we have:

S = 15 × (1 - 4ⁿ) / (1 - 4)

As n approaches infinity, the term 4ⁿ grows larger and larger. Since the common ratio (4) is greater than 1, the term 4ⁿ approaches infinity. Therefore, the sum of the series also approaches infinity.

Hence, the series obtained by adding the terms of the sequence diverges.

3) A series solution up to and including x⁴ for the initial value problem (IVP) y" - xy' + y² = 1 with the initial conditions y(0) = 1 and y'(0) = 6, we can use the power series method.

Let's assume that the solution y(x) can be expressed as a power series:

y(x) = a₀ + a₁x + a₂x² + a₃x³ + a₄x⁴ + ...

Differentiating y(x) with respect to x, we get:

y'(x) = a₁ + 2a₂x + 3a₃x² + 4a₄x³ + ...

Similarly, differentiating y'(x) with respect to x, we obtain:

y''(x) = 2a₂ + 6a₃x + 12a₄x² + ...

Now, let's substitute these expressions into the given differential equation:

y''(x) - xy'(x) + y(x)² = 1

(2a₂ + 6a₃x + 12a₄x² + ...) - x(a₁ + 2a₂x + 3a₃x² + 4a₄x³ + ...) + (a₀ + a₁x + a₂x² + a₃x³ + a₄x⁴ + ...)² = 1

Expanding and collecting the terms with the same power of x, we get:

(2a₂ - a₀) + (6a₃ - a₁ - 2a₂) x + (12a₄ - 2a₁ + 3a₃) x² + ...

To satisfy the equation, each coefficient of x must be equal to zero. Setting the coefficients to zero, we have:

2a₂ - a₀ = 0 (Coefficient of x⁰)

6a₃ - a₁ - 2a₂ = 0 (Coefficient of x¹)

12a₄ - 2a₁ + 3a₃ = 0 (Coefficient of x²)

Using the initial conditions y(0) = 1 and y'(0) = 6, we have:

a₀ = 1 (Initial condition)

a₁ = 6 (Initial condition)

Solving the equations above, we find

a₂ = a₀/2 = 1/2

a₃ = (a₁ + 2a₂)/6 = (6 + 2/2)/6 = 5/6

a₄ = (2a₁ - 3a₃)/12 = (2(6) - 3(5/6))/12 = 1/4

Therefore, the series solution up to and including x⁴ is given by:

y(x) = 1 + 6x + (1/2)x² + (5/6)x³ + (1/4)x⁴ + ...

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Answer:

1/12

Step-by-step explanation:

bc ik

Answer:

the right answer is 1/12

Step-by-step explanation:

78/0000

67

777

7654

Answer:

5 ³⁄₁₀ or ⁵³⁄₁₀

Step by step explanation:

Answer:

[tex]5 \frac{3}{10}[/tex]

Answer: 2.54(x)

Step-by-step explanation:

Since an inch is equal to about 2.54 centimeters, the expression which estimates the number of centimeters in X inches will be gotten by multiplying 2.54 by X. This will be:

= 2.54 × X

= 2.54(x)

For example, if there are 4 inches, the number of centimeters in it will be:

= 2.54(x)

= 2.54 × 4

= 10.16 inches

The slope (m) of the regression line can be estimated as approximately 0.6, while the y-intercept (b) can be estimated as around 2.5.

Upon analyzing the graph, we can make a rough estimate for the slope (m) and y-intercept (b) of the regression line. The slope represents the rate of change between the independent variable (x) and the dependent variable (y), while the y-intercept indicates the value of y when x is zero.

From the graph, we observe that the regression line appears to have a positive slope, suggesting a positive correlation between the variables. By estimating the change in y divided by the change in x for two points on the line, we can approximate the slope. In this case, considering the rise and run between two points, the slope (m) is approximately 0.6.

The y-intercept (b) can be determined by identifying the point where the regression line intersects the y-axis. In this graph, the intersection seems to occur around the y-value of 2.5, providing us with an estimated y-intercept.

To gain a more precise understanding of the regression line's characteristics and verify these estimates, it is recommended to utilize statistical techniques such as linear regression analysis. These techniques can provide accurate slope and intercept values, along with additional statistical measures like the coefficient of determination (R-squared) to assess the line's goodness of fit.

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Answer:

D

Step-by-step explanation:

Given the 2 equations

y = 3x - 5 → (1)

6x - 2y = 10 → (2)

Substitute y = 3x - 5 into (2)

6x - 2(3x - 5) = 10

6x - 6x + 10 = 10 ( subtract 10 from both sides )

6x - 6x = 0 , that is

0 = 0 ← True

This indicates the system has infinitely many solutions → D

Answer:

75%

Step-by-step explanation:

54/72 = 0.75

The inverse Laplace transformation of the given Laplace transform `-2s² + 2L^-1 F(s)` is `(t³ - t)u(t)`.

Explanation:

Laplace Transform: We are given the Laplace transform as:

`-2s² + 2L^-1 F(s)`

We can write the Laplace transform as a polynomial:

`-2s² + 2 / (s - 2)`

Inverse Laplace Transform:

Using partial fraction method, we can write:

`-2s² + 2 / (s - 2) = A / (s - 2) + Bs + C`

Multiplying by `s - 2`, we get:

`-2s² + 2 = A + Bs(s - 2) + C(s - 2)`

Substituting `s = 2`, we get:`

-6A = 2` or `A = -1/3`

Comparing coefficients of `s`, we get:

`B - 2C = 0` or `B = 2C`

Comparing constants, we get:`-2C - 2A = 0` or `C = 1/3`

Therefore, the partial fractions decomposition is:

`-2s² + 2 / (s - 2) = (-1/3) / (s - 2) + (2/3) s + (1/3)`

Taking inverse Laplace transform on both sides, we get:

`L^-1 {-2s² + 2 / (s - 2)} = L^-1 {(-1/3) / (s - 2) + (2/3) s + (1/3)}`

Using the linearity of inverse Laplace transform, we get:

`-2L^-1 {s²} + 2L^-1 {1 / (s - 2)} = (-1/3)L^-1 {1 / (s - 2)} + (2/3)L^-1 {s} + (1/3)L^-1 {1}`

We know that `L^-1 {1} = δ(t)` and `L^-1 {1 / (s - a)} = e^at u(t)`

where `a` is a constant. Substituting the values, we get:

`-2L^-1 {s²} + 2L^-1 {1 / (s - 2)} = (-1/3)e^{2t}u(t) + (2/3)L^-1 {s} + (1/3)δ(t)`

We know that `L^-1 {s^n} = t^n / n!`Therefore, `L^-1 {s} = 1`.

Substituting the values, we get:

`-2L^-1 {s²} + 2L^-1 {1 / (s - 2)} = (-1/3)e^{2t}u(t) + (2/3)t + (1/3)δ(t)`

Taking inverse Laplace transform of

`-2s² + 2L^-1 F(s)`, we get:

`L^-1 {-2s² + 2L^-1

F(s)} = L^-1 {(-1/3) / (s - 2) + (2/3) s + (1/3)}

= (t³ - t)u(t)`

Therefore, the option `(a) t³ - t` is the inverse Laplace transformation of `-2s² + 2L^-1 F(s)`.

Hence, the correct option is `(a) t³ - t`.

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Answer:

39°

Step-by-step explanation:

The sum of AXE, AXC and CXF will be 180 because they together span a straight line (EF).

So: y + 90 + y - 12 = 180, which is an equation you can solve by simplifying it:

y + 90 + y - 12 = 180

2y + 78 = 180

y + 39 = 90

y = 90 - 39 = 51

So AXE = 51

AXC = 90

CXF = 51-12 = 39 (the answer)

Check: 51+90+39 = 180

Answer:

$240

Step-by-step explanation:

60% = 0.6

400 divided by 0.6 = 240

Answer:

x = 107

Step-by-step explanation:

44+29+107=180

a triangle equals 180 with all the degrees added together :)

For the given values of SSb, SSW, dfb, and dfw, the value for the mean squares between (MSb) is 7.

To find the mean squares between (MSb), you need to divide the sum of squares between (SSb) by the corresponding degrees of freedom (dfb).

MSb = SSb / dfb

Using the values provided:

SSb = 21

dfb = 3

MSb = 21 / 3

MSb = 7

Therefore, the value for the mean squares between (MSb) is 7.

Mean squares, also known as the mean squared error (MSE), is a statistical measure used to assess the average squared difference between the predicted and actual values in a dataset.

It is commonly used in various fields, including statistics, machine learning, and data analysis, to evaluate the performance of a prediction model or to quantify the dispersion or variability of a set of values.

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Answer:

F(3) = -4.5

Step-by-step explanation:

Replacing x with 3 in F(x) = 0.5x - 6 results in F(3) = 0.5(3) - 6, or -4.5

F(3) = -4.5

Answer:

30

Step-by-step explanation: Because each batch has 18 total m&ms and there are 8 in each batch minus and then multiply.

The number of packages of plain M&M's on the shelf could be any multiples of 5.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

The ratio of a and b is denoted as a : b.

Given that,

Ratio of the number of packages of peanut M&M's to the total number of packages on the shelf = 8 : 18

That is, if there are total of 18 packages, 8 are peanut M&M's.

Number of plain M&M's out of 18 total packages = 18 - 8 = 10.

So,

Ratio of peanut M&M's to plain M&M's = 8 : 10

                                                                = 4 : 5

This indicates that, for a constant x,

Number of peanut M&M's = 4x

Number of plain M&M's = 5x

So the number of packages of plain M&M's on the shelf could only be the multiples of 5.

So it could be 5, 10, 15, 20, 25, 30, .......

Hence the number of plain M&M's on the shelf could be 5, 10, 15, 20, 25, 30, ......

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Answer:

x = 30

since 3x = 90 degrees, then x = 90/3 = 30

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

8.4 ÷ 6 = 1.4

4.2 ÷ 1.4 = 3