Solve the the equation by substitution
5x=-2y+48
x=-3y+20​

Answer:

The solutions are x = -6 or x = +2

Step-by-step explanation:

In this question, we are asked to get the series of the equation given. we can find this by equating what we have to zero

Mathematically, we proceed as follows;

(x +2)^2 -16 = 0

This can be rewritten as;

(x + 2)^2 - 4^2 = 0

we can then proceed to use the difference of two squares to finish this off

Thus, we have

(x + 2 + 4)(x + 2 - 4) = 0

(x + 6)(x-2) = 0

X + 6 = 0 or x-2 = 0

x = -6 or x = +2

Answer:

0-(-655)

Step-by-step explanation:

I's hopw this helps you.

Answer:

0-(-655)

Step-by-step explanation:

Answer:

i dont know

Step-by-step explanation:

hi

Answer:

The exact value of tan A in simplest form is \(tan (A) = \dfrac{9}{40}\)

Step-by-step explanation:

The parameters of the given right triangle are;

The length of the hypotenuse side = 41

The length of the vertical leg of the right triangle = 9

The  length of the opposite leg of the right triangle = 40

By trigonometric rule, we have;

\(tan (A) = \dfrac{Opposite \ leg \ length \ to \ angle \ A}{Adjacent \ leg \ length \ to \ angle \ A }\)

Therefore, we have;

\(tan (A) = \dfrac{9}{40} = 0.225\)

Answer:

100

Step-by-step explanation:

x-value is width and y-value is height. Therefore if you multiply the height x width you get the constant.

The value of the constant in the equation is 100.

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

Given that, Height=Constant/Width

1) (4, 25)

Here, Height = 25 and Width = 4

25 = Constant/4

Constant = 100

2) (5, 20)

Here, Height = 20 and Width = 5

20 = Constant/5

Constant = 100

3) (10, 10)

Here, Height = 10 and Width = 10

10 = Constant/10

Constant = 100

4) (20, 5)

Here, Height = 20 and Width = 5

20 = Constant/5

Constant = 100

Therefore, the value of the constant in the equation is 100.

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Answer:

35x+15y is less than or equal to 100.

Step-by-step explanation:

35 per Jean + 15 per shirt is less than or equal to 100

Answer:

{-4,-2,4}

Step-by-step explanation:

range are y values so we just look at the y values of the coordinates plotted on the graph

Hopes this helps

The range of the relation that is graphed above is: {-4, -2, 4}.

All values of x that are plotted on a graph of a relation is the domain, while the corresponding y-values on the graph is the range of the relation.

Given the graph of the relation above, the x-values of each of the points make up the domain of the relation, while the corresponding y-values of each point make up the range of the relation.

The y-values of each of the points are: -4, -2, and 4

Therefore, the range is: {-4, -2, 4}.

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A continuous variable does allow fractional amounts. a discrete variable  does not allow fractional amounts.

Which variables require boundaries, also known as real limits, in their measurement scales?

A researcher must utilize genuine limits, which are boundaries that are exactly halfway between adjacent categories, to specify the units for a continuous variable.

What distinguishes a ratio scale from an ordinal scale?

For continuous data, what kind of data would you use?

Line graphs, skews, and other data analysis techniques are used to measure continuous data. One of the most popular kinds of continuous data analysis is regression analysis.

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Answer:

I will use "complete-the-square" approach if thats ok

first 0.5(x - 2)² - 2

second -2(x - 4)² + 8

The solution to the integral equation x(t) = \(e^t\) + 2∫[0,t] \(e^{t- \theta}\) x(θ) dθ is x(t) = 0.

To solve the integral equation using the Laplace transform, we will apply the transform to both sides of the equation. Let X(s) represent the Laplace transform of x(t).

Applying the Laplace transform to the integral term using the property of the Laplace transform for integrals, we have:

L{∫[0,t] \(e^{t- \theta}\) x(θ) dθ} = X(s) * (1/(s+1)).

Using the Laplace transform of \(e^{t- \theta}\) = 1/(s+1), we obtain:

sX(s) - x(0) = X(s) * (1/(s+1)) + 1/(s-1).

Rearranging the equation, we have:

sX(s) - X(s)/(s+1) = 1/(s-1) + x(0).

Combining the terms with X(s), we get:

X(s) * (s² + s) - X(s) = 1/(s-1) + x(0).

Simplifying further, we have:

X(s) * (s² + s - 1) = 1/(s-1) + x(0).

Now, solving for X(s), we get:

X(s) = (1/(s-1) + x(0))/(s² + s - 1).

The expression for X(s) using partial fraction decomposition. Let's decompose it as follows:

X(s) = (1/(s-1) + x(0))/(s² + s - 1)

= A/(s-1) + B/(s² + s - 1),

where A and B are constants to be determined.

To find the values of A and B, we can multiply both sides by the denominators and equate the numerators:

1 = A(s² + s - 1) + B(s-1).

Expanding and collecting like terms:

1 = (A + B) s² + (A + B - A) s + (-A - B + A).

Matching coefficients, we have the following system of equations:

A + B = 0,

A - B + A = 1,

-A - B + A = 0.

Simplifying the equations, we get:

A + B = 0,

2A - B = 1,

-2B = 0.

From the third equation, we find B = 0. Substituting this into the first equation, we get A = 0. Therefore, A = 0 and B = 0.

Now, the expression for X(s) becomes:

X(s) = 0/(s-1) + 0/(s² + s - 1)

= 0 + 0

= 0.

Taking the inverse Laplace transform of X(s), we find:

x(t) = L⁻¹{X(s)}

= L⁻¹{0}

= 0.

Therefore, the solution to the given integral equation is x(t) = 0.

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Answer: can buy (2x³ - 3x² + 4x - 6) reams

\(6x^{4} -17x^{3}+24x^{2} -34x+24\\\\\\=6x^{4}-8x^{3} -9x^{3} +12x^{2} +12x^{2} -16x-18x+24\\\\=2x^{3}(3x-4) -3x^{2} (3x-4)+4x(3x-4)-6(3x-4)\\\\\\=(2x^{3}-3x^{2} +4x-6)(3x-4)\)

Step-by-step explanation:

The number of reams of bondpaper that can be bought from \(6x^4-17x^3+24x^2-34x+24\) pesos are \(2x^3-3x^2+4x-6\).

Cost of a ream of bondpaper is \((3x-4)\) pesos.

The number of reams that can be bought from \(6x^4-17x^3+24x^2-34x+24\) pesos is calculated by following the long division method as-

\(\dfrac{6x^4-17x^3+24x^2-34x+24}{3x-4}=2x^3-3x^2+4x-6\)

So,

The number of reams that can be bought from \(6x^4-17x^3+24x^2-34x+24\) pesos are \(2x^3-3x^2+4x-6\).

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Answer:

the inequality is x  <  − 11 /2

Answer:

1,072

Step-by-step explanation:

The power series representation for f(x) is  x²(1 - 2x)² = x² × Σ[n = 0 to ∞] \(C(2, n) (-2x)^{n}\) and the radius of convergence, r, is equal to 1/2.

To find a power series representation for the function f(x) = x²(1 - 2x)², we will first find a power series for the function (1 - 2x)² and then multiply it by x².
The power series representation for (1 - 2x)² can be found using the binomial series formula:
\((1 - 2x)^{k}\) = Σ[n = 0 to ∞] \((C(k, n)\) × \((-2x)^{n})\), where C(k, n) represents the binomial coefficient.
For k = 2, the series becomes:
(1 - 2x)² = Σ[n = 0 to ∞] \((C(2, n)\) × \((-2x)^{n})\)
Now, we will multiply this series by x² to get the power series representation for f(x):
f(x) = x²(1 - 2x)² = x² × Σ[n = 0 to ∞] \((C(2, n)\) × \((-2x)^{n})\)
Now, we will determine the radius of convergence, r, using the Ratio Test:
\(\lim_{n \to \infty} |(a_{n+1}/(a_{n})| = |((-2)^{n+1} x^{n+1})/(2^n x^n)| = |(-2x)|\)
For convergence, the limit must be less than 1:
|-2x| < 1
Divide both sides by 2:
|-x| < 1/2
The radius of convergence, r, is equal to 1/2.

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Using the Combination formula,

Total number of ways there to paint 10 hotel rooms in a hotel with five colours is 527 ways .

We have given that,

total number of rooms available for paint = 10

number of colour avaliabile for painting = 5

Atmost three rooms can be painted green i.e

the number of ways for atmost three rooms are painted green = ¹⁰C₃ + ¹⁰C₂ + ¹⁰C₁ = 120 + 45 + 10 = 175

similarly, the number of ways for atmost three rooms are painted red = 175

the number of ways for atmost three rooms are painted blue = 175

Now, one room is remained for painting and two colours are available for it

the number of painting the remained room with aany of two available colours i.e black and white

= 2 ways

thus , total ways to paint the 10 hotel rooms with five different paints are (175×3 +2) = 527

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The required probability of the randomly selected steel rod with the average length greater than 206.1cm whose mean is 205.8cm and standard deviation is 0.5cm is equal to 0.0024012.

As given in the question,

Mean of the normally distributed steel rod ' μ '= 205.8cm

Standard deviation of the normally distributed steed rod 'σ ' = 0.5cm

Number of steel rod bundled together 'n' = 22

Randomly selected steel rods bundle the average length is greater than

'\(\bar {X}\)' = 206.1cm

Required probability is given by :

P( \(\bar {X}\) > 206.1 )

= P [(\(\bar {X}\) - μ )/ (σ/√n) > ( 206.1 - 205.8)/ (0.5/√22) ]

= P ( Z > (0.3/ 0.1064))

= P ( Z > 2.8195)

= P ( Z > 2.820)

= 0.0024012

Therefore, the probability of the randomly selected steel rod with the average length greater than 206.1cm is equal to 0.0024012.

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Hello,

In prime decomposition:

180=2²*3²*5

140=2²*5*7

lcm(180,140)=2²*3²*5*7=1260

Proof: 1260/180=7 and 1260/140=9

Part A: An open circle on a number line represents an excluded value, indicating that the endpoint is not included in the solution set of the inequality. It is used when the inequality includes the symbols < (less than) or > (greater than), which denote strict inequality.

Part B: A closed circle on a number line represents an included value, indicating that the endpoint is part of the solution set of the inequality. It is used when the inequality includes the symbols ≤ (less than or equal to) or ≥ (greater than or equal to), which denote inclusive inequality.

Part C: The shading on the number line represents the range of values that satisfy the given inequality. It indicates which values make the inequality true. Typically, the shading is done to the right or left of the circle(s) depending on whether the inequality is greater than or less than.

Part A:

For example, if we have the inequality x > 2, we would represent it with an open circle at 2 on the number line. This means that 2 itself is not a valid solution, but any value greater than 2 is included.

Part B:

For example, if we have the inequality x ≥ -3, we would represent it with a closed circle at -3 on the number line. This means that -3 itself is a valid solution, as well as any value greater than or equal to -3.

Part C:

For example, if we have the inequality x > 2, we would shade the portion of the number line to the right of the open circle at 2. The shaded region represents all the values greater than 2 that satisfy the inequality. The shading visually illustrates the solution set and helps identify the range of valid values for the variable in the given inequality.

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Here's a Scheme function that checks whether a matrix is symmetric or not:

```scheme

(define (is-symmetric-matrix matrix)

 (define (get-element matrix i j)

   (if (null? matrix)

       #f

       (if (= i 0)

           (if (null? (car matrix))

               #f

               (if (= j 0)

                   (car (car matrix))

                   (get-element (cdr matrix) i (- j 1))))

           (get-element (cdr matrix) (- i 1) j))))

 (define (is-matrix-symmetric-helper matrix i j)

   (if (null? matrix)

       #t

       (if (equal? (get-element matrix i j)

                   (get-element matrix j i))

           (is-matrix-symmetric-helper matrix i (+ j 1))

           #f)))

 (if (null? matrix)

     #t

     (is-matrix-symmetric-helper matrix 0 0)))

```

The function `is-symmetric-matrix` takes a matrix as an input, which is represented as a list of lists. It uses a helper function called `is-matrix-symmetric-helper` to compare each element of the matrix with its corresponding element in the transposed position. The `get-element` function is used to retrieve the element at position `(i, j)` in the matrix.

The `is-matrix-symmetric-helper` function recursively iterates over the matrix, comparing each element with its transposed element. If any pair of corresponding elements is found to be different, it immediately returns `#f` (False), indicating that the matrix is not symmetric. If it reaches the end of the matrix without finding any differences, it returns `#t` (True), indicating that the matrix is symmetric.

Finally, the main `is-symmetric-matrix` function first checks if the matrix is empty. If it is, it immediately returns `#t` since an empty matrix is considered symmetric. Otherwise, it calls the helper function with the initial indices `(0, 0)` and returns its result.

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Note that based on probabilities,

The expected number of Democrats on the committee is 5.

The expected number of states represented on the committee is 26.

The expected number of states such that both of the state's senators are on the committee is 9.09.

a)  The probability that a randomly chosen senator is a Democrat is 50/100 = 1/2.

So, the expected number of Democrats on a committee of size 10 is

1/2 * 10 = 5.

b) The minimum number of   states that can be represented on a committee of size 10 is 2, and the maximum numberis 50.

The expected number of states representedon the committee is the average of these two values, which is (2 + 50)/  2 = 26.

c)  There are 50 states, and each state has 2 senators. So, there are a total of 100 pairs of senators.

The probability that a randomly chosen pair of senators both belong to the same state is 50/100 * 49/99

= 1/11.

The expected number of states such that both of the state's senators are on the committee is 100 * 1/11 = 9.09.

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Answer:

5/6

Step-by-step explanation:

If you minus 1 1/2 from 2 1/3 you get 5/6 left.

Please mark brainliest.

5/6 cups of more chocolate chips should be added to the batter.

Given that, the recipe calls for \(2\frac{1}{3}\) cups of semi-sweet chocolate chips. Selena has already put in \(1\frac{1}{2}\) cups into the batter.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Number of more cups of chocolate chips should be added to the batter = \(2\frac{1}{3}-1\frac{1}{2}\)

= 7/3 - 3/2

= 14/6 - 9/6

= (14-9)/6

= 5/6

Therefore, 5/6 cups of more chocolate chips should be added to the batter.

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Answer:

Option C: One solution

Step-by-step explanation:

5x + 6 = 2 + 3x

Subtract 3x from both sides;

2x + 6 = 2

Subtract 6 from both sides;

2x = -4

Divide both sides by 2;

x = -2

Answer:

20

Step-by-step explanation:

Triangle inequality says that the third side can only be 18-3...15, that is bigger than 15.

And 18+3... 21, that is smaller than 21.

If the third side is 21, the 18 and the 3 will just lay right on top of the 21 and not make a triangle. So it has to be 20 in order to be a whole number.

Answer:

Part-A: refer to the attachment

Part-B: (10,11)

Part-C: yes

step-by-step explanation:

Part-A:

refer to the attachment

(I used a online graphing calculator to graph the equations which made the work easy)

Part-B:

When two lines share exactly one common point, they are called the intersecting lines and the point is called the point of interception

Looking at the graph,we can understand that the two lines share a common point at (10,11),

hence,

The lines intercept at the point (10,11)

Part C :

well, to find the answer of this part, we can consider doing equality check by substituting the value of the point we got.

The point (10,11) means that the left and right hand side of both of the equations i.e \(\text{y=x+1 and y=-x+21}\) are equal when x and y equal to 10 and 11 respectively.

So let's justify the points:

equation-1:

substitute the value of x and y respectively:

simplify addition:

equation-2:

substitute the value of x and y respectively:

simplify addition:

so,

Yes,the coordinates of the point of intersection satisfy both equations simultaneously

Answer:

h

Step-by-step explanation:

If Elon earns $45 per hour, spend $75 on dry cleaning everyday and wants to make at least $260 a day then the inequality that shows the situation is 45x-75≥260 and he atleast work for 7 and half hour each day.

Given that Elon earns $45 per hour, spend $75 on dry cleaning everyday and wants to make at least $260 a day.

We are required to write the inequality that represent the situation of Elon.

Inequality is just like an equation that shows the relationship between two variables but in greater than, less than,greater than or equal to,less than or equal to signs.

Suppose the number of hours that Elon works be x hours each day.

The earning of Elon will be 45x.

Since the expenditure is $75,the saving will be 45x-75 and if he wants to make $260 a day, the inequality will be 45x-75≥260.

45x≥260+75

45x≥335

x≥335/45

x≥7.55

Hence if Elon earns $45 per hour, spend $75 on dry cleaning everyday and wants to make at least $260 a day then the inequality that shows the situation is 45x-75≥260 and he atleast work for 7 and half hour each day.

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Answer:

J plus 47 = 55

If you need to find J

The value of J is

J=55-47

J=8

Step-by-step explanation

ZW is 37 units long. By subtracting the length of WY, which is found to be -1, from ZW, we found that ZY is 38 units long. However, the lengths of TX and WY are negative, suggesting a potential error in the given information.

In the given figure, we are provided with the lengths of various line segments. Using this information, we can determine the length of ZW. Given that XY = 15 and ZX = 52, we can subtract the length of XY from ZX to find the length of ZW. Therefore, ZW = ZX - XY = 52 - 15 = 37.

Now let's provide a detailed explanation of each length:

ZY = 37

To find the length of ZY, we need to subtract the length of WY from ZW. From the previous calculation, we know that ZW = 37. However, the length of WY is not given directly. To find it, we can use the fact that WX = 22 and WT = 23. Since WY is a part of WX and WT, we can subtract WT from WX to get WY. Therefore, WY = WX - WT = 22 - 23 = -1.

Now, we can substitute the value of WY into the equation for ZY: ZY = ZW - WY = 37 - (-1) = 38. Thus, ZY is equal to 38.

TX = 15

To find the length of TX, we need to subtract the length of WT from XY. We know that XY = 15 and WT = 23. Therefore, TX = XY - WT = 15 - 23 = -8. However, it is important to note that lengths cannot be negative, so TX cannot be -8. This indicates that there might be an error in the given information or measurements.

WY = -1

As calculated earlier, the length of WY is -1. However, it is important to note that lengths cannot be negative in a geometrical context. Therefore, we can conclude that there might be an error in the given information or measurements. It is advisable to double-check the given lengths or clarify any inconsistencies before proceeding with further calculations.

In summary, using the given information, we determined that ZW is 37 units long. By subtracting the length of WY, which is found to be -1, from ZW, we found that ZY is 38 units long. However, the lengths of TX and WY are negative, suggesting a potential error in the given information. It is recommended to verify the measurements to ensure accurate results.

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Answer:

c= e/d-ab/d

Step-by-step explanation:

The equation ab + cd = e is solved for the variable 'c' will be c = (e + ab) / d.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The equation is given below.

ab + cd = e

Simplify the equation for c, then we have

ab + cd = e

cd = e + ab

c = (e + ab) / d

The equation ab + cd = e is solved for the variable 'c' will be c = (e + ab) / d.

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