1. Solve the system below by graphing. Show all work. Be sure to label each line, check the
solution in both equations, and clearly state the solution. [10 pts]
6x-2y=10
10x - y=-2
idk guys help

Length of outer boundary =30m

So area of outer boundary =30×30

= 900m²

Length of inner boundary of path=30-1= 29m

Inner area =29×29 =841m²

So area of path is= outer area - inner area

=900- 841

= 59m²

Answer:

  x = 6 m

Step-by-step explanation:

Given a diagram showing a semicircle atop a rectangle that is 8 m wide, you want to know the height of the rectangle when the overall height of the figure is 10 m.

All points on a circle are the same distance from its center. The center of a semicircle is the midpoint of its straight side. Here, the diameter of the semicircle is shown as 8 m, so the midpoint will be 4 m from either side.

The top point of the semicircle will be 4 m from the center on the top edge of the rectangle.

Since the overall height is 10 m, the rectangle must be 10 -4 = 6 meters high.

The value of x is 6 m.

The value where the histogram balances when supported at that point is called the mode of the distribution.

The mode of distribution is the value that appears most frequently in the data set. It is often used as a measure of central tendency, along with the mean and median. The mode is especially useful when dealing with categorical or discrete data, where the possible values are limited and well-defined.

For example, the mode of a list of test scores might be the score that occurs most frequently, indicating the most common level of performance. In a histogram, the mode is the value where the distribution is highest, or where the histogram balances when supported at that point.

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Answer:

3.5kg

Step-by-step explanation:

Let original weight  of grapes in box be X and weight of grapes in basket be Y.

From the first sentence
X = 2Y  (weight in box = 2 times weight in basket)   --- (1)

If you add 2kg of grapes to basket, the weight of grapes in basket = Y + 2

From the second statement

Y + 2 = X + 0.5

Subtracting Y from the LHS gives 2 = X - Y + 0.5

Subtracting 0.5 from both sides gives 2-0.5 = X - Y or X - Y = 1.5  --- (2)

Substituting for X from the first equation in (2) we get
2Y - Y = 1.5 or Y = 1.5kg

But this is the original weight of the grapes in the basket. Since we have added 2 kg of grapes to the original weight, we get the weight of grapes in basket now as 1.5 + 2.0 = 3.5kg

Answer:

Inverse of a 3 by 3 Matrix

MM-1 = M-1 M = I.

Step 1: The first step while finding the inverse matrix is to check whether the given matrix is invertible. ...

Step 2: Calculate the determinant of 2 × 2 minor matrices.

Step 3: Formulate the cofactor matrix.

Step-by-step explanation:

The inverse matrix formula, A-¹ = (1/|A|) Adj A, is used to determine the inverse of a 3×3 matrix.

The multiplicative identity is obtained by multiplying the provided matrix by the other matrix which serves as the inverse of a matrix. A matrix's inverse is A-1, since the I is the identity matrix, A A-1 = A-1 A = I.

The formula A-1 = (adj A)/(det A), where det A is in the denominator, is used to determine the inverse of a 3x3 matrix A. 

• adj A = The adjoint matrix of A

• det A = determinant of A

dAs a result, det A should not be 0 for A-1 to exist. i.e.,

• A-1 exists when det A ≠ 0 (i.e., when A is nonsingular)

• A-1 does not exist when det A = 0 (i.e., when A is singular).

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{ 0,2,4,6,8} is  the complement of the set.

What is natural number in math?

Is zero a natural number?

u = {0, 1, 2, 3, 4, 5, 6, 7, 8}

Odd number less than 8  = { 1,3,5,7 }

complement =  {0, 1, 2, 3, 4, 5, 6, 7, 8} -  { 1,3,5,7 }

                     = { 0,2,4,6,8}

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Answer:

\(x=49.16^{\circ}\)

Step-by-step explanation:

We need to find the value of x in the given figure.

It is a right angled triangle, in which base is 19, height is 22.

We can use trigonometry to find x.

We know that,

\(\tan\theta=\dfrac{P}{B}\)

Where

P is perpendicular and B is base

So,

\(\tan x=\dfrac{22}{19}\\\\x=\tan^{-1}(1.157)\\\\x=49.16^{\circ}\)

So, the value of x is equal to \(49.16^{\circ}\).

Answer:

A

Step-by-step explanation:

Given that the triangles are congruent then corresponding angles are congruent, thus

∠ S = ∠ Y = 108°

∠ T = ∠ Z = 9n - 4

Given ∠ R = 6n + 1

The sum of the 3 angles in Δ RST = 180°

Sum the 3 angles and equate to 180, that is

6n + 1 + 108 + 9n - 4 = 180 , simplify

15n + 105 = 180 ( subtract 105 from both sides )

15n = 75 ( divide both sides by 15 )

n = 5 → A

The Taylor polynomial T3(x) of degree 3 for the function f(x) near x = 0 is given as: T3(x) = 4 - 3x + x^2 + 4x^3

A Taylor series is a series expansion of a function about a point. A one-dimensional Taylor series is an expansion of a real function f(x) about a point x=a is given by f(x)=f(a)+f^'(a)(x-a)+(f^('')(a))/(2!)(x-a)^2+(f^((3))(a))/(3!)(x-a)^3+...+(f^((n))(a))/(n!)(x-a)^n+.... .

If a=0, the expansion is known as a Maclaurin series.

Taylor's theorem (actually discovered first by Gregory) states that any function satisfying certain conditions can be expressed as a Taylor series.

The Taylor (or more general) series of a function f(x) about a point a up to order n may be found using Series[f,  {x, a, n}]. The nth term of a Taylor series of a function f can be computed in the Wolfram Language using SeriesCoefficient[f,  {x, a, n}] and is given by the inverse Z-transform  To find the values of f(0), f'(0), f''(0), and f'''(0), we need to differentiate T3(x) up to the third order and then evaluate the derivatives at x = 0.
So, let's start by finding the first derivative of T3(x):
T3'(x) = -3 + 2x + 12x^2
Now, we can evaluate T3(x), T3'(x), and T3''(x) at x = 0:
f(0) = T3(0) = 4 - 0 + 0 + 0 = 4
f'(0) = T3'(0) = -3 + 0 + 0 = -3
To find the second derivative, we differentiate T3'(x):
T3''(x) = 2 + 24x
Then, we evaluate T3''(x) at x = 0:
f''(0) = T3''(0) = 2 + 0 = 2
Finally, to find the third derivative, we differentiate T3''(x):
T3'''(x) = 24
And evaluate T3'''(x) at x = 0:
f'''(0) = T3'''(0) = 24
Therefore, the values of f(0), f'(0), f''(0), and f'''(0) for the function f(x) approximated near x = 0 by the 3rd degree Taylor polynomial T3(x) = 4 - 3x + x^2 + 4x^3 are:
f(0) = 4
f'(0) = -3
f''(0) = 2
f'''(0) = 24

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The vector (3,9) as a linear combination of the unit vectors i and j is  3 * i + 9 * j

To write the vector (3, 9) as a linear combination of the unit vectors i and j, we need to find the coefficients that multiply the unit vectors to obtain the components of the given vector.

The unit vectors i and j represent the directions of the x-axis and y-axis, respectively. The vector (3, 9) can be expressed as:

(3, 9) = a * i + b * j

where a and b are the coefficients we need to find.

Since the unit vector i corresponds to the x-axis, the coefficient a represents the component of the vector (3, 9) in the x-direction. Similarly, the coefficient b represents the component of the vector (3, 9) in the y-direction.

To find the coefficients, we can equate the corresponding components:

3 = a

9 = b

Therefore, the vector (3, 9) can be written as:

(3, 9) = 3 * i + 9 * j

In this representation, the coefficient 3 indicates that the vector (3, 9) has a magnitude of 3 in the x-direction (i.e., parallel to the x-axis), and the coefficient 9 indicates that it has a magnitude of 9 in the y-direction (i.e., parallel to the y-axis).

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Answer:

132

Step-by-step explanation:

123+9=132?

Answer:

132 degrees and can I get brainliest

Step-by-step explanation:

Absolute value of -9 is 9 so then 123 plus 9.

Answer:

\(12s-120\)

Step-by-step explanation:

Given the following question:

\(12(s-10)\)

To rewrite the expression using the distributive property we have to remember the rule that applies to all expressions, we have to multiply all the terms inside the paratheses by the terms outside of the paratheses.

\(12(s-10)\)
\(12\timess=12s\)
\(12s-10\times12\)
\(10\times12=120\)
\(12s-120\)

Your answer is "12s - 120."

Hope this helps.

Answer:

about 4

Step-by-step explanation:

just guessed

The number of tablespoons of kernels to use to make 6 cups of popcorn will be 4 tablespoons. Option B is correct.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

Serena makes 2 1/4 cups of popcorn using 1 1/2 tablespoons of kernels.

Convert the mixed fraction into a fraction number. Then we have

2  1/4 = 9/4

1  1/2 = 3/2

The ratio of cups of popcorn and tablespoons of kernels will be constant.

The number of tablespoons of kernels to use to make 6 cups of popcorn will be given as,

K / 6 = (3/2) / (9/4)

K = 4 tablespoons

The number of tablespoons of kernels to use to make 6 cups of popcorn will be 4 tablespoons. Option B is correct.

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Answer:

3 8-4× less than 6 ×-5 and then you solve the equation

Answer:

2.743 x 10 6

Step-by-step explanation:

Answer:

2.743 x 10^6

Step-by-step explanation:

Answer: the answer is 4.08

Step-by-step explanation:

Answer:

4.08

Step-by-step explanation:

2.29+2.59-0.50-0.30 is equal to 4.08

it's just addition and subtraction haha

Answer:

Step-by-step explanation:

Answer:

√104

Step-by-step explanation:

missing side = \(\sqrt{15^2-11^2} = \sqrt{225-121} = \sqrt{104}\)

One possible example is the function \(f(x) = (x+1)(x-2)^{2}(x-3)^{2}\), which has roots at x = -1 and x = 2, but whose derivative \(f'(x) = 2(x-2)(x-3)(3x^2-10x+7)\) has roots at x = 1, \(x = 2 - \sqrt(2)\),\(x = 2 + \sqrt(2)\), x = 5/3, and x = 7/3.

To construct such an example, we need a function whose roots are simple and occur at two distinct points, and whose derivative has multiple roots. One way to do this is to take a function that has multiple roots of high multiplicity, and then perturb it so that some of those roots split into simple roots.

In the example given, we start with the function \(f(x) = (x+1)(x-2)^4(x-3)^4\), which has roots at x = -1, x = 2, and x = 3, each with multiplicity 4. We then perturb the function slightly by replacing one of the factors \((x-2)^4\) with \((x-2)^2\), so that the root at x = 2 splits into two simple roots. This gives us the function \(f(x) = (x+1)(x-2)^2(x-3)^4\), which has roots at x = -1 and x = 2, but whose derivative \(f'(x) = 2(x-2)(x-3)^3(3x-10)\) has five roots, as stated above.

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The number of horizontal asymptotes that a function can have depends on its behavior as x approaches positive or negative infinity.

a) If the function approaches a specific value or constant as x approaches positive or negative infinity, it can have 0 horizontal asymptotes.

b) If the function approaches the same value or constant as x approaches positive or negative infinity, it can have 1 horizontal asymptote.

c) If the function approaches different values or constants as x approaches positive or negative infinity, it can have 2 horizontal asymptotes.

d) It is not possible for a function to have exactly 3 horizontal asymptotes. Asymptotes come in pairs, so the number of horizontal asymptotes can be 0, 1, 2, or 4.

e) It is not possible for a function to have exactly 4 horizontal asymptotes. Asymptotes come in pairs, so the number of horizontal asymptotes can be 0, 1, 2, or 3.

the correct options are:

a) 0

b) 1

c) 2

d) 3

e) 4

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The world record for memorizing and reciting the most digits of pi is held by Rajveer Meena from India. He recited 50,000 decimal places of pi in 2020, which is the current recognized world record.

Pi (π) is a mathematical constant that represents the ratio of a circle's circumference to its diameter. It is an irrational number, which means it cannot be expressed as a finite decimal or a fraction. The decimal representation of pi is non-repeating and goes on indefinitely without a pattern. The value of pi is approximately 3.14159, but it is commonly approximated as 3.14 for simplicity in mathematical calculations. However, the exact value of pi has been calculated to trillions of digits using various computational methods. The quest to calculate more digits of pi continues to this day, and the computation of pi serves as a benchmark for testing the performance of supercomputers and computational algorithms. The current record for calculating the most digits of pi is trillions of digits, achieved through the use of powerful computers and advanced algorithms.

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Answer:

y= mx +c

Step-by-step explanation:

The point- slope form of an equation is

y= mx +c, where m is the gradient and c is the y-intercept.

You can find the value of m by using the gradient formula.

\(gradient = \frac{y1 - y2}{x1 - x2} \)

Then substitute the value of m found into the equation. Next substitute a pair of coordinates the line passes through to find the value of c. Substitute the value of c and you will obtain the point-slope form equation of the line.

Here's an example.

Point-slope form of an equation passing through (1, 2) and (5, 6).

① Finding gradient, m.

\(m = \frac{6 - 2}{5 - 1} \\ m = \frac{4}{4} \\ m = 1\)

② Substitute value of m into equation.

y= 1x +c

y= x +c

③ Substitute a pair of coordinates.

when x=1, y=2,

2= 1 +c

c= 2 -1

c= 1

Thus the equation of the line is y= x +1.

You may already know that "y+MX+b" form called the slope-intercept form of the equation of a line. It is the same equation in a different form. The 'b' value called the y intercept is where the line crosses the y- axis

Step-by-step explanation:

Answer:

What is the question? If you comment the question i may be able to help

Step-by-step explanation:

Answer:

62

Step-by-step explanation:

y+94+137+67= 360

y=62

Answer:

C is the correct answer

While linear regression can be a useful tool for prediction, it is important to consider the quality of the data, assess the linearity assumption, and be cautious when extrapolating beyond the observed data range.

This is an example of using linear regression to predict the weight of a kitten at a specific time (10 weeks in this case) based on the given linear model ŷ = 1.7 + 1.48t.

Using linear regression to make predictions is a common practice and can provide reasonable estimates in many cases. However, whether it is considered a best practice for prediction depends on various factors. Here are a few considerations:

Data quality: The accuracy and reliability of the predictions heavily depend on the quality of the data used to build the linear model. If the data used for training the model is representative and accurately reflects the underlying relationship, the predictions are likely to be more reliable.

Linearity assumption: Linear regression assumes a linear relationship between the predictor variable (in this case, time) and the response variable (kitten weight). If the relationship is not truly linear, the predictions may be less accurate. It is important to assess the linearity assumption and consider alternative models if needed.

Extrapolation: When making predictions outside the range of the observed data (such as predicting the weight at 10 weeks when the data only goes up to 8 weeks), caution should be exercised. Extrapolating beyond the observed range can introduce more uncertainty and may lead to less accurate predictions.

In summary, while linear regression can be a useful tool for prediction, it is important to consider the quality of the data, assess the linearity assumption, and be cautious when extrapolating beyond the observed data range.

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So, Lana gave away 26.32% of he Pokemon cards  to her little brother.

To find the percentage of cards Lana gave away, we can use the formula:(Quantity given away / Total quantity) * 100.

In this case, Lana gave away 125 cards out of her total collection of 475 cards.Plugging these values into the formula, we have:

(125 / 475) * 100 = 0.2632 * 100 = 26.32%.

Lana gave away 26.32% of her Pokemon cards to her little brother.

Alternatively, we can calculate the percentage by subtracting the remaining cards from the total and finding the ratio:

Percentage given away

= (Cards given away / Total cards) * 100

= (125 / 475) * 100

= 26.32%.

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Answer:

a variable is a numeric value typically represented by a letter

Step-by-step explanation:

Answer:

- 1

Step-by-step explanation:

Substitute a = - 1 into the expression, that is

(- 1)³ - 2(- 1)² + 3(- 1) + 5

= - 1 - 2(1) - 3 + 5

= - 1 - 2 - 3 + 5

= - 6 + 5

= - 1

Answer:

=(-1)³-2(-1)²+3(-1)+5

=-1-2(1)+3(-1)+5

=-1-2+3+5

=-3+8

=5

Answer:

x=5 and y=2

Step-by-step explanation:

Let's solve your system by substitution.

3x+y=17;4x−y=18

Step: Solve 3x+y=17 for y:

3x+y=17

3x+y+−3x=17+−3x(Add -3x to both sides)

y=−3x+17

Step: Substitute−3x+17 for y in 4x−y=18:

4x−y=18

4x−(−3x+17)=18

7x−17=18(Simplify both sides of the equation)

7x−17+17=18+17(Add 17 to both sides)

7x=35

7x

7

=

35

7

(Divide both sides by 7)

x=5

Step: Substitute 5 for x in y=−3x+17:

y=−3x+17

y=(−3)(5)+17

y=2(Simplify both sides of the equation)