If a line passes through the points (1,2) and (−0.5,1), what is the distance between the x and y intercepts of that line? (A) √13/6 (B) √13/2 (C) 2√13/3 (D) 3√13/2 (E) None of these

Step-by-step explanation:

21

Answer:

c landing on 1 is the answer

hope it helps u mark me BRAINLIST

Answer:

Year 1 Depreciation:$2,000

Depreciation Percentage:20.00%

Total Depreciation:$10,000

Final Year Depreciation:$2,000

Step-by-step explanation:

P.S by teacher told me the answer

The answer is g(-2) = 15.

To find g(-2) using synthetic division, we need to follow these steps:

Write down the coefficients of the polynomial in descending order. The coefficients are 11, 29, 19, 22, and 39.

Write down the value of the divisor in the leftmost column. In this case, the divisor is -2.

Bring down the first coefficient (11) to the bottom row.

Multiply the bottom row value (11) by the divisor (-2) and write the result (-22) in the next column.

Add the coefficient in that column (29) to the result (-22) and write the sum (7) in the bottom row.

Repeat steps 4 and 5 until you reach the last column. The final result in the bottom row is the remainder.

The synthetic division should look like this:

-2 | 11  29  19  22  39
   | -22 -14 -10 -24
   -------------------
     11   7   9  12  15

Therefore, g(-2) = 15.

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The fourth proportion to 15/7,23/14, and 33/5 is 19.25.

To discover the fourth proportion, we require to set up a probability between the 3 presented figures and the fourth unknown variety, which we can name x.

23/1433/5 x

First, we need to transfigure all the mixed figures to unsuitable fragments

= (7/7 * 1)5/7 = 7/75/7 = 12/7

= (14/14 * 2)3/14 = 28/143/14 = 31/14

= (5/5 * 3)3/5 = 15/53/5 = 18/5

Now we're suitable to preference those values into the share

31/1418/5 x

To break for x, we're suitable to cross-multiply

12/7) * x = (31/14) *(18/5)

Simplifying

12x/ 7 = 279/14

Multiplying each aspects via7/12

x = (279/14) *(7/12)

x = 19.25

Thus, the fourth proportion to 15/7,23/14, and 33/5 is 19.25.

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The area of the following circle is A ≈ 153.86 square units.

A circle is a two-dimensional geometric shape that consists of all the points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius, and the distance across the circle passing through the center is called the diameter.

The circumference of a circle is the distance around the edge of the circle, and it is calculated using the formula C = 2πr, where r is the radius and π (pi) is a mathematical constant approximately equal to 3.14159. The area of a circle is the region enclosed by the circle, and it is calculated using the formula A = πr².

The diameter of the circle is 14, so the radius is half of that, which is 7.

The area of the circle is given by the formula A = πr², where r is the radius. Substituting in the values we get:

A = π(7)²

A = 49π

Therefore, the area of the circle is 49π square units. If you want to use an approximation, you can use 3.14 as an estimate for π and get:

A ≈ 153.86 square units.

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The complete question is -

Therefore, [tex]h = \sqrt{(12.25 - x^2)} = 3.73[/tex] feet represents the distance between the two staircases on the tree. Thus, option c is correct.

The Pythagorean theorem states that the square length of the hypotenuse, or the side that faces the right angle, of a right triangle is equal to the sum of the square lengths of the other two sides. The following can be expressed mathematically: [tex]a^2 + b^2 = c^2[/tex] where "c" represents the length of the hypotenuse and "a" and "b" represent the measurements of the two sides of the right triangle.

given

Assume the tree is h feet tall, the higher ladder is 3 feet long, and the lower ladder is x feet long.

Using the Pythagorean formula, we can create two equations:

With regard to the narrower staircase,  x² + h² = (3.5)

Use the formula for the higher ladder. (3x)²+ h²= (7.5)².

The formulas are as follows, simplified: 12.25 x² + 9.25 x² + 56.25

To remove h2, we can solve for x in the first equation and y in the second equation: 8x² = 44.

Finding the value of x is as follows:   [tex]x = \sqrt{(5.5) } = 2.34[/tex]

Therefore, [tex]h = \sqrt{(12.25 - x^2)} = 3.73[/tex]  feet represents the distance between the two staircases on the tree.

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Complete question:

Two ladders are placed at different locations on a coconut palm tree so that lights can be installed, as pictured below. The length of the taller ladder is three times the length of the shorter ladder. The shorter ladder is placed 3.5 feet from the base of the tree while the taller ladder is placed 7.5 feet from the base of the tree. What is the distance on the tree between the two ladders?

O 4.59 feet

O 9.78 feet

O 3.73 feet

O 8.96 feet

Answer: 50%

Step-by-step explanation: There are 5 out of 10 employees at the water slide. 10 in this situation is going to be 100%

since there is only 5 out of 10 employees that are temporary

it would be 50%

Answer: 50%

Step-by-step explanation:

An expression that looks like Sarah's expression but is not equivalent is:

10(5j + j + 3).

A sentence qualifies as a mathematical expression if it comprises one or more mathematical operations, at least two numbers, or variables. Let's examine the writing style of expressions. A number is 6 times larger than the other number, x, by a factor of 2. This statement is represented mathematically by the expression x/2 + 6. Using mathematical expressions, complex puzzles can be solved.

now in the question,

We can write a look alike expression which is not equivalent is:

10(5j + j + 3).

Now translating the new expression into verbal:

Sarah gets paid $10 for every shark tooth she finds. After finding 3, she asked Jhon for help. When Jhon finds a tooth, by that time Sarah finds 5 of them.

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Note that the pair of numbers that solves the system of equations:

y=11x+40; and

y= -7x+9

are,  x = -31/18  ; and y = 379/18.

To solve the system of equations, we need to find the values of x and y that satisfy both equations simultaneously. One way to do this is to set the expressions for y equal to each other, since both expressions represent the same value of y.

So we have:

11x + 40 = -7x + 9

Simplifying and solving for x, we get:

18x = -31

x = -31/18

Now that we have found the value of x, we can substitute it into either equation to find the corresponding value of y. Let's use the first equation:

y = 11(-31/18) + 40

y = -341/18 + 720/18

y = 379/18

Therefore, the pair of numbers that solves the system of equations is (-31/18, 379/18).

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The vectors are linearly independent.

The vectors u = (2,1,0), v = (-4,3,1), and w=(0,-2,-5) are linearly dependent if there exists scalars c1, c2, and c3 such that c1u + c2v + c3w = 0. To determine if this is the case, we can form a matrix with the vectors as columns and find its determinant. If the determinant is 0, then the vectors are linearly dependent. If the determinant is not 0, then the vectors are linearly independent.

The matrix formed by the vectors is:
```
| 2 -4 0 |
| 1  3 -2|
| 0  1 -5|
```

The determinant of this matrix is:
```
2(3(-5) - (-2)(1)) - (-4)(1(-5) - (0)(-2)) + 0(1(1) - (0)(3))
= 2(-15 + 2) + 4(5) + 0
= 2(-13) + 20 + 0
= -26 + 20
= -6
```

Since the determinant is not 0, the vectors are linearly independent.

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Answer:

Area of a triangle =L*W

A= 45*15

A=270cm²

The coordinates of A' and B' after a dilation with a scale factor of 2 with a center point of dilation at the origin is: OA (-8, 2) and B (-2, 6)

To find the coordinates of A' and B' after a dilation with a scale factor of 2 with a center point of dilation at the origin, we can use the following formula:

A' = k * (A - O) + O

B' = k * (B - O) + O

where k is the scale factor, O is the center point of dilation, and A and B are the original points.

In this case, k = 2 and O = (0, 0). So we have:

A' = 2 * (-4, 1 - (0, 0)) + (0, 0) = (-8, 2)

B' = 2 * (-1, 3 - (0, 0)) + (0, 0) = (-2, 6)

Therefore, the coordinates of A' and B' after the dilation are (-8, 2) and (-2, 6), respectively.

So, the answer is option (A) OA (-8, 2) and B (-2, 6).

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Answer:

Step-by-step explanation:

2(2x+2) + 2(x+4) = 36

4x+4 +2x+8 =36

6x+12= 36

6x = 36-12

6x =24

x = 4

longer side = 10

The conditional expectation of Y given that X is less than or equal to 1/2 is calculated by taking the weighted average of the possible values of Y, with the weights being the probabilities of X being less than or equal to 1/2 for each value of Y.
The formula for E(Y | X<=1/2) is:
E(Y | X<=1/2) = ∑y P(Y=y | X<=1/2) * y
To find P(Y=y | X<=1/2), we can use the formula:
P(Y=y | X<=1/2) = P(X<=1/2 | Y=y) * P(Y=y) / P(X<=1/2)
We can then plug in the values for each possible value of Y and calculate the conditional expectation.

For example, if Y can take on the values 0, 1, and 2, and the probabilities of X being less than or equal to 1/2 for each value of Y are 0.2, 0.5, and 0.3, respectively, and the probabilities of Y being 0, 1, and 2 are 0.4, 0.3, and 0.3, respectively, then:
E(Y | X<=1/2) = (0.2 * 0.4 / 0.5) * 0 + (0.5 * 0.3 / 0.5) * 1 + (0.3 * 0.3 / 0.5) * 2
E(Y | X<=1/2) = 0 + 0.3 + 0.36
E(Y | X<=1/2) = 0.66

Therefore, the conditional expectation of Y given that X is less than or equal to 1/2 is 0.66.

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We are only interested in the critical numbers on the interval [1,3], so we can disregard x = 0. Therefore, the critical numbers of the function f(x) on the interval [1,3] are x = 3.

The critical numbers of a function are the points where the derivative of the function is either zero or undefined. To find the critical numbers of the given function f(x) = x^2/(3-x), we need to first find its derivative:

f'(x) = (2x(3-x) - (-1)x^2)/ (3-x)^2 = (6x - x^2 - x^2)/ (3-x)^2 = (6x - 2x^2)/ (3-x)^2

Now, we need to find the values of x for which f'(x) = 0 or f'(x) is undefined. f'(x) is undefined when the denominator (3-x)^2 is equal to 0, which occurs when x = 3. f'(x) is equal to 0 when the numerator 6x - 2x^2 is equal to 0:

6x - 2x^2 = 0
2x(3 - x) = 0
x = 0 or x = 3

However, we are only interested in the critical numbers on the interval [1,3], so we can disregard x = 0. Therefore, the critical numbers of the function f(x) on the interval [1,3] are x = 3.

Answer: 3

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Using the Gaussian elimination method, the general solution is:               [tex]\[ x = -31t + 6 \][/tex], [tex]\[ y = 5 \][/tex], [tex]\[ z = 31t \][/tex].

To solve this system of equations, we can use the Gaussian elimination method. This method involves creating a matrix with the coefficients of the equations and using row operations to reduce the matrix to a form that can be easily solved.

First, we create a matrix with the coefficients of the equations:

[tex]\[ \left( \begin{array}{ccc|c} 1 & 1 & 1 & -1 \\ 2 & 3 & 2 & 3 \\ 2 & 1 & 2 & -7 \\ 1 & -3 & 2 & 10 \\ -1 & 3 & -1 & -6 \\ -1 & 3 & 2 & 6 \\ 6 & -2 & 2 & 4 \\ 3 & -1 & 2 & 2 \\ -12 & 4 & -8 & 8 \end{array} \right) \][/tex]

Next, we use row operations to reduce the matrix to a form that can be easily solved:

[tex]\[ \left( \begin{array}{ccc|c} 1 & 1 & 1 & -1 \\ 0 & 1 & 0 & 5 \\ 0 & -1 & 0 & -5 \\ 0 & -4 & 1 & 11 \\ 0 & 4 & 0 & -5 \\ 0 & 4 & 1 & 7 \\ 0 & -8 & -4 & 10 \\ 0 & -4 & -1 & 5 \\ 0 & 8 & 4 & -4 \end{array} \right) \][/tex]

[tex]\[ \left( \begin{array}{ccc|c} 1 & 1 & 1 & -1 \\ 0 & 1 & 0 & 5 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 31 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 27 \\ 0 & 0 & -4 & 50 \\ 0 & 0 & -1 & 25 \\ 0 & 0 & 4 & -44 \end{array} \right) \][/tex]

[tex]\[ \left( \begin{array}{ccc|c} 1 & 0 & 1 & -6 \\ 0 & 1 & 0 & 5 \\ 0 & 0 & 1 & 31 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & -4 \\ 0 & 0 & 0 & 174 \\ 0 & 0 & 0 & 56 \\ 0 & 0 & 0 & -168 \end{array} \right) \][/tex]

From this reduced matrix, we can see that there are infinitely many solutions to this system of equations. The general solution can be written as:
[tex]\[ x = -31t + 6 \][/tex]
[tex]\[ y = 5 \][/tex]
[tex]\[ z = 31t \][/tex]
Where t is any real number.

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To find f(x)-g(x), we need to subtract the two given functions.

f(x) = x^(2)-6x-40

g(x) = x+4

f(x)-g(x) = (x^(2)-6x-40) - (x+4)

Next, we need to distribute the negative sign to the terms inside the parentheses:

f(x)-g(x) = x^(2)-6x-40 - x - 4

Then, we can combine like terms: f(x)-g(x) = x^(2)-7x-44

Therefore, the result of f(x)-g(x) is a polynomial in simplest form: x^(2)-7x-44.

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The value of the expression (1×1,000)+(3×100)+(5×10)+(9×1/10)+(8 x 1/100) is 1,350.98.

To find the value of the expression (1×1,000)+(3×100)+(5×10)+(9×1/10)+(8 x 1/100), we need to simplify and perform the arithmetic operations.

Multiplying each term in the expression, we get:

1 × 1,000 = 1,000

3 × 100 = 300

5 × 10 = 50

9 × 1/10 = 0.9

8 × 1/100 = 0.08

Adding up all the terms, we get:

1,000 + 300 + 50 + 0.9 + 0.08 = 1,350.98

In summary, to find the value of the expression, we multiply each term by its respective coefficient, then add up all the terms. In this case, the result is 1,350.98.

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Complete question is:

Find the value of the expression (1×1,000)+(3×100)+(5×10)+(9×1/10)+(8 x 1/100)?

The area of the dark region is 164.15 square feet because it is equal to the sum of the areas of the circles and rectangles.

In geometry, a circle is a closed object made up of all the points in a plane that are equally spaced from the circle's centre. The radius and diameter of a circle are measured from the centre to any spot on the circle, respectively. The circumference, which is equivalent to pi times the diameter, is the distance around the circle.

given

[tex]area of circle = π * r * r[/tex]

= 22/7 * 2 * 2 = 88/7 ft2

area of rectangle = length * breadth

= 9.4 * 18.8

= 176.72 ft2

area of shaded region

176.72 - 12.57

= 164.15 ft 2

The area of the dark region is 164.15 square feet because it is equal to the sum of the areas of the circles and rectangles.

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The location of the corner of the rabbit pen that reflects (2.5, 2.5) across the y-axis is (-2.5, 2.5).

The coordinate plane, also called the Cartesian plane, is a two-dimensional grid used to locate points in space. It consists of two perpendicular number lines, one horizontal and one vertical, that intersect at their zero points, called the origin.

Points on the coordinate plane are identified by their coordinates, which are written as ordered pairs of numbers (x, y), where x is the horizontal coordinate and y is the vertical coordinate.

To solve this problem, we need to reflect the point (2.5, 2.5) across the y-axis. When we reflect a point across the y-axis, we keep the y-coordinate the same but change the sign of the x-coordinate.

So, the reflected point will have the same y-coordinate of 2.5, but the x-coordinate will be -2.5. Therefore, the location of the corner of the rabbit pen that reflects (2.5, 2.5) across the y-axis is (-2.5, 2.5).

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The annual interest rate on Susan's savings account is 4%.

Annual interest rate, also known as annual percentage rate is the yearly interest generated by a sum that's charged to borrowers or paid to investors We can use the simple interest formula to calculate the annual interest rate which is Simple Interest = (Principal x Rate x Time)

By plugging our values, we get.

$54 = ($900 x Rate x 1.5)

Simplifying the equation:

Rate = $54 / ($900 x 1.5)

Rate = 0.04

Rate = 4%.

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5. 20% of students said that they enjoy Cookie Cake.

6. 25 students answered a survey regarding their favorite cake.

The percentage is defined as a ratio expressed as a fraction of 100.

The % formula is used to calculate a percentage of a whole in terms of 100.

Percentage = (Value/Total Value) × 100

Percentage of students said they like Cookie Cake:

5/(5 + 6 + 8 + 6) × 100%

5/25 × 100%

20%

The total number of students who answered this survey about their favorite Cake:

5 + 6 + 8 + 6

25

Thus, 25 students answered a survey regarding their favorite cake.

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The equation that describes the plant's height is y = 3 + 0.5x .

The equation that describes the plant's height is a linear equation. A linear equation is an equation that has a single variable that is raised to the power of one.

The general form of a linear equation is:

y = mx + c

Where:

m = slope

c = intercept

Plant's height = starting height + (rate of growth x number of weeks)

y = 3 + (0.5 x x)

y = 3 + 0.5x

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Table that represent input & output value  would be:

Input Output

44            45

45            46

46            47

To determine which table represents inputs and outputs that follow the same rule as 44+1, 44+2, and 44+3, we can simply evaluate each of the expressions and look for a pattern.

44 + 1 = 45

44 + 2 = 46

44 + 3 = 47

Therefore, the rule appears to be adding 1 to each subsequent number. We can check this by evaluating additional terms:

44 + 4 = 48

44 + 5 = 49

Based on this pattern, the correct table would be:

Input Output

44            45

45            46

46            47

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The spinner  probability that the next spin will land either red or green or purple is found 0.70 as a decimal to the nearest hundredth.

Spinner Results

Color Frequency

Red 20

Blue 9

Green 19

Yellow 14

Purple 14

Total outcomes: 20 + 9 + 19 + 14 + 14

Total outcomes: 76

spinner probability = favorable outcome / total outcome

favorable outcome (red or green or purple) = 20 + 19 + 14 = 53

spinner probability = 53 / 76 = 0.69

spinner probability = 0.70

Thus, the probability that the next spin will land either red or green or purple is found 0.70 as a decimal to the nearest hundredth.

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The value of c is 10.

The value of c is 10. To find this, use the limit definition of continuity. This states that for the function to be continuous at x = 4, we must have f(4) = lim f(x) x -> 4. Thus, we can equate f(4) and lim f(x) x -> 4 to get 1/4*4 + c = -4 + 6, giving c = 10.

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In the triangle ABC, the value of x, y and z is obtained as 21, 7 and 48 units respectively.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

A triangle ABC is given.

The measure of AB is given as 16 + z units.

The measure of AD is given as 16 units.

The measure of DB is given as z - 16 units.

The measure of BE is given as 21 units.

The measure of BC is given as x units.

The measure of AC is given as 14 units.

According to the midpoint theorem, the length of DE is -

DE = 1/2 (AC)

y = 1/2 (14)

y = 7 units

Therefore, the value of y is obtained as 7 units.

Now according to indirect measurement -

AB / AC = BD / DE

Substitute the values in the equation -

16 + z / 14 = z - 16 / 7

7(16 + z) = 14(z - 16)

112 + 7z = 14z - 224

7z - 14z = -224 - 112

-7z = -336

z = 48

Therefore, the value of z is obtained as 48 units.

Now according to indirect measurement -

BC / AC = BE / DE

Substitute the values in the equation -

21 + x / 14 = 21 / 7

7(21 + x) = 14 × 21

147 + 7x = 294

7x = 294 - 147

7x = 147

x = 21

Therefore, the value of x is obtained as 21 units.

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Answer:

x = 21

y = 7

z = 32

Step-by-step explanation:

DE = 1/2 (AC)

y = 1/2 (14)

y = 7

AB / AC = BD / DE

Substitute values

16 + z / 14 = z - 16 / 7

7(16 + z) = 14(z - 16)

112 + 7z = 14z - 224

7z - 14z = -224 - 112

-7z = -336

z = 32

BC / AC = BE / DE

Substitute values

21 + x / 14 = 21 / 7

7(21 + x) = 14 × 21

147 + 7x = 294

7x = 294 - 147

7x = 147

x = 21

Answer:

Step-by-step eEIKxplanation: