What are the coordinates of the point on the directed line segment from (-10, 4) to (-5, -6) that partitions the segment into a ratio of 1 to 4?

Answer:

72.25

Step-by-step explanation:

17% of 425

=17\100 ×425

=7225/100

=72.25

Answer:

72.25

Step-by-step explanation:

Lets say you are trying to find p percent (p%) of a number n. To do this, you would divide the percent (p) by 100 and multiply it by the number (n). In other words:

\(n*\frac{p}{100}\)

We can use this to find 17 percent of 425. 17 would be our percent and 425 would be our number.

\(425*\frac{17}{100}=425*0.17=72.25\)

So 17 percent of 425 would be 72.25.

I hope you find my answer and explanation to be helpful. Happy studying. :)

Answer:

Top is A bottom is B. ........

Answer:

Area of Parallelogram Using Diagonals ; Using Base and Height, A = b × h ; Using Trigonometry, A = ab sin (x) ; Using Diagonals, A = ½ × d1 × d2 .....

Using Diagonals: A = ½ × d1 × d2 sin (y)

Using Base and Height: A = b × h

Using Trigonometry: A = ab sin (x)

y = 1/4x + 1 is parallel to line a

-4x + y = -8 is neither parallel nor perpendicular to line a

4x + y = -3 is perpendicular to line a

From the question, we are to determine how the given equations compare to line a.

From the given information,

Line a is -x + 4y = 32

First, we will determine the slope of line a

To do this, we will compare the equation to the slope-intercept form of a line

The slope-intercept form of a line is

y = mx + b
Where m is the slope

and b is the y-intercept

Writing -x + 4y = 32 in the slope-intercept form

-x + 4y = 32

4y = x + 32

Divide through by

y = 1/4 x + 8

By comparison, the slope of line a is 1/4

NOTE: If two lines are parallel, their slopes will be equal

and

If two lines are perpendicular, their slopes will be the negative reciprocal of each other

Now, we will determine the slopes of each of the lines

For y = 1/4x + 1

By comparing with the slope-intercept form of a line, y = mx + b

The slope of the line is 1/4

Thus, the line is parallel to line a

For -4x+y=-8

Rewrite in the slope-intercept form of a line

-4x + y = -8

y = 4x - 8

By comparing with the slope-intercept form of a line, y = mx + b

The slope of the line is 4

4 is not equal to 1/4 and 4 is not the negative reciprocal of 1/4.

Thus, the line is neither parallel nor perpendicular to line a.

For 4x+y=-3

Rewrite in the slope-intercept form of a line

4x + y = -3

y = -4x - 3

By comparing with the slope-intercept of a line, y = mx + b

The slope of the line is -4

-4 is the negative reciprocal of 1/4.

Thus, the line is perpendicular to line a.

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The probability expressed as P(1 ≤ x ≤3) using probability distribution is; 0.90

We are given that;

Sections in which spinner is divided = 4 sections

Number of times spinner is spun = 100 times

From the probability distribution, we see that;

P(1) = 0.33

P(2) = 0.15

P(3) = 0.42

P(4) = 0.10

Thus;

P(1 ≤ x ≤3) = P(1) + P(2) + P(3)

= 0.33 + 0.15 + 0.42

= 0.9

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Answer:

slope (m) = 2/3

Step-by-step explanation:

slope = change in x /change in y

Also, slope is y2 - y1 / x2 -x1. That is what I apply for this activity, hence:

slope = 3 - (-1) / 0 - (-6)

         = 3 + 1 / 0 + 6

         = 4 / 6

         = 2/3

∴ slope(m) = 2/3

the left side of this equation equal the right side through the process of completing the square that establishes the equality between the left side and the right side of the Gaussian integral equation.

using  completing the square method:

Starting with the left side of the equation:

∫\(e^(^-^x^2)\) dx

\(e^(^-^x^2) = (e^(^-x^2/2))^2\)

∫\((e^(^-^x^2/2))^2 dx\)

let  u = √(x²/2) =  x = √(2u²).

dx = √2u du.

∫ \((e^(^x^2/2))^2 dx\)

= ∫ \((e^(^-2u^2)\)) (√2u du)

The integral of \(e^(-2u^2)\)= √(π/2).

∫ \((e^(-x^2/2))^2\) dx

= ∫  (√2u du) \((e^(-2u^2))\\\)

= √(π/2) ∫ (√2u du)

We substitute back  u = √(x²/2), we obtain:

∫ \((e^(-x^2/2))^2\)dx

= √(π/2) (√(x²/2))²

= √(π/2) (x²/2)

= (√π/2) x²

A comparison  with the right side of the equation  shows that they are are equal.

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Answer:

2

Step-by-step explanation:

Five added to the sum of -7 and 4, the phrase "sum of -7 and 4" indicates that we need to add 4 to -7. Do as so :

-7 + 4 = -3

Now we have the portion of "Five added to the [sum]", which shows to add five to the result. :

-3 + 5

= 2

Answer:

the answer is

Step-by-step explanation:

5+4

9-7

2

Hope you like answer

Answer:

-3 < x ≤ 6

Step-by-step explanation:

Left side is exclusive, right side is inclusive, hence the < and ≤, respectively.

Part A: The total area of the brick paver border is \(960\) square feet.

Part B: The total cost of the brick pavers needed for this project is $\(7,680\).

Part A: To find the total area of the brick paver border, we need to subtract the area of the pool from the area of the larger rectangle. The area of the pool is \(32\) feet multiplied by 12 feet, which is equal to \(384\)square feet.

The area of the larger rectangle is \(48\) feet multiplied by \(28\) feet, which is equal to \(1,344\) square feet. Therefore, the area of the brick paver border is \(1,344\) square feet minus \(384\) square feet, which equals \(960\) square feet.

Part B: If brick pavers cost $\(8\)per square foot, we can calculate the total cost by multiplying the cost per square foot by the total area of the brick paver border. The total area of the brick paver border is \(960\) square feet, and the cost per square foot is $\(8\).

Therefore, the total cost of the brick pavers needed for this project is $\(8\)multiplied by \(960\) square feet, which equals $\(7,680\).

Note: The calculations provided assume that the border consists of a single layer of brick pavers.

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Answer:

a) MA conditional with C can be interpreted as A which is known and C which is unknown match

b) 10/11

c) 2/11

Step-by-step explanation:

A={A is the guilty party}

\(M_A\) = {A blood type matches that of the guilty party}

C = {B is the guilty party}

\(M_C\) = {B blood type matches that of the guilty party}

a) The chance is 10% because MA conditional with C can be interpreted as A which is known and C which is unknown match

b) the probability that A is the guilty party is given by \(P(A/M_A)\). Using bayes theorem:

\(P(A/M_A)=\frac{P(M_A/A)P(A)}{P(M_A/A)P(A)+P(M_C/C)P(C)} =\frac{1*1/2}{(1*1/2)+(1/10*1/2)} =\frac{10}{11}\)

c) the probability that B’s blood type matches that of the guilty party is given as \(P(M_C/M_A)\). Using LOTS Therefore:

\(P(M_C/M_A)=P(M_C/M_A,A)P(A/M_A)+P(M_C/M_A,A)P(C/M_A)=\frac{1}{10}*\frac{10}{11} +1*\frac{1}{11} =\frac{2}{11}\)

Answer:

Cost of adult ticket = $12.5

Cost of child ticket = $7.5

Step-by-step explanation:

Given:

Cost of 6 adult ticket and 5 child ticket = $112.5

Cost of 8 adult ticket and 4 child ticket = $130

Find:

Equation and solution

Computation:

Assume;

Cost of adult ticket = a

Cost of child ticket = b

So,

6a + 5b = 112.5....eq1

8a + 4b = 130 ......eq2

Eq2 x 1.25

10a + 5b = 162.5 .....eq3

eq3 - eq1

4a  = 50

Cost of adult ticket = $12.5

8a + 4b = 130

8(12.5) + 4b = 130

Cost of child ticket = $7.5

The inequality expression that corresponds to the solution of the inequality graph is x² + 3x - 3 < 0.

option B.

The inequality expression that corresponds to the solution of the inequality graph is determined by simplifying the equations as follows;

The solution of the graph,

x > -4 and x < 1

The first equation with "≥" is ruled out because the graph doesn't have a thick dot.

Let's simplify the second expression;

x² + 3x - 3 < 0

solve using quadratic formula;

x > -3.79 or x < 0.79

The third expression is ruled out since its solution will be complex.

For the last expression;

x² + 3x - 3 > 0

x < -3.79 or x > 0.79

Thus, the correct inequality expression is x² + 3x - 3 < 0.

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In brains, we want a balance between excitatory and inhibitory signals to maintain proper neural functioning.

Since, We know that;

In brains, we want a balance between excitatory and inhibitory signals to maintain proper neural functioning.

This balance is important because too much excitatory signaling can cause overstimulation and potential harm, while too much inhibitory signaling can lead to neural suppression and lack of responsiveness.

Hence, The proper balance between the two types of signals is necessary for healthy neuronal activity, and maintaining that balance is a key aspect of neural health.

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The three consecutive multiples of 3 are 15, 18 and 21

First, let's determine three successive multiples of 3:

The subsequent two would be "x+3" and "x+6" if we call the initial number "x".

Since we are aware that the third number (x+6) is one more than the first two numbers (x + x+3), we can write the following equation:

2/3(x + x+3) = (x+6) + 1

Simplifying this equation, we get:

2/3(2x+3) = x+7

Multiplying both sides by 3, we get:

2(2x+3) = 3(x+7)

Expanding and simplifying, we get:

4x + 6 = 3x + 21

Subtracting 3x and 6 from both sides, we get:

x = 15

Therefore, the three consecutive multiples of 3 are 15, 18 and 21

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Answer:

Most likely answers are either 6 or 8.

Step-by-step explanation:

The sequence could be of all even numbers, so 2, 4, 6, 8, etc.

Or of all powers of 2, starting at 2, so 2, 4, 8, 16, etc.

Since there are an infinite number of sequences that fit the pattern, you just have to choose the most likely.

Answer:

The sum of the series b 2 b 4 b 6 b 8 b {10} is \($\dfrac{180}{3}$\) since it is a geometric series with a common ratio of \($\dfrac{7}{4}$\).

Since the given series \($b 1 b 2 b 3 \cdots b {10}$\) has a sum of 180, it can be deduced that the series is a geometric series with a common ratio of\($\dfrac{7}{4}$\). This means that the ratio of any two consecutive terms in the series is a constant, \($\dfrac{7}{4}$\). Therefore, the sum of the series b 2 b 4 b 6 b 8 b {10} can be calculated as follows:

\($S = b2 + b4 + b6 + b8 + b_{10}$\)

\($= b2\left(\dfrac{7}{4}\right)^0 + b2\left(\dfrac{7}{4}\right)^2 + b2\left(\dfrac{7}{4}\right)^4 + b2\left(\dfrac{7}{4}\right)^6 + b2\left(\dfrac{7}{4}\right)^8$\)

\($= b2 \left[1 + \left(\dfrac{7}{4}\right)^2 + \left(\dfrac{7}{4}\right)^4 + \left(\dfrac{7}{4}\right)^6 + \left(\dfrac{7}{4}\right)^8\right]$\)

\($= b2 \left[\dfrac{1-\left(\dfrac{7}{4}\right)^{10}}{1-\left(\dfrac{7}{4}\right)^2}\right]$\)

\($= b2 \left[\dfrac{1-\left(\dfrac{7}{4}\right)^{10}}{\dfrac{3}{4}}\right]$\)

\($= \dfrac{4b2}{3} \left[1-\left(\dfrac{7}{4}\right)^{10}\right]$\)

Since the sum of the series\($b 1 b 2 b 3 \cdots b {10}$\) is 180, we can substitute $b2$ with \($\dfrac{180}{3}$\)nd calculate the sum of the series $b 2 b 4 b 6 b 8 b {10}$:

\($S = \dfrac{4\left(\dfrac{180}{3}\right)}{3} \left[1-\left(\dfrac{7}{4}\right)^{10}\right]$\)

\($= \dfrac{180}{3} \left[1-\left(\dfrac{7}{4}\right)^{10}\right]$\)

Therefore, the sum of the series \($b 2 b 4 b 6 b 8 b {10}$ is $\dfrac{180}{3}$\).

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Answer:

alternate interior angles are congruent

According to the question an example of C = 3 and D = 2 supports the answer that Equation A gives a bigger value than Equation B.

Two equations are considered to be comparable when their roots and solutions line up. To create an equivalent equation, the identical quantity, symbol, or expression has to be added to or removed from both of the equation's two sides. We can also create a similar equation by dividing or multiplying each component of an equation with a nonzero value.

given,

To determine which equation would give a bigger value, we can compare the expressions obtained by expanding Equation A and simplifying Equation B.

Expanding Equation A, we get:

A = (C + D) x (C + D) = C² + 2CD + D²

Simplifying Equation B, we get:

B = 2 x (C + D) = 2C + 2D

To compare the values of A and B, let's choose some values for C and D that are greater than zero. Let's choose C = 3 and D = 2.

Plugging these values into Equation A, we get:

A = 3² + 2(3)(2) + 2² = 9 + 12 + 4 = 25

Plugging these values into Equation B, we get:

B = 2(3 + 2) = 2(5) = 10

Since A is greater than B for the values of C = 3 and D = 2, we can conclude that Equation A gives a bigger value than Equation B for positive values of C and D.

Therefore, an example of C = 3 and D = 2 supports the answer that Equation A gives a bigger value than Equation B.

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The values into the slope-intercept form, we have y = -5x - 6

The slope-intercept form of a linear equation is given by:

y = mx + b

where 'm' represents the slope of the line, and 'b' represents the y-intercept.

In this case, the y-intercept is (0, -6), which means that the line crosses the y-axis at the point (0, -6).

The slope is given as -5.

Therefore, substituting the values into the slope-intercept form, we have:

y = -5x - 6

This equation represents the line with a y-intercept of (0, -6) and a slope of -5.

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Answer:

Step-by-step explanation:

Given function is

\(f(x) = \dfrac{\left(x^2-9\right)}{\left(x^2-x-6\right)}\)

Part 1

Graph attached

y-intercepts can be found by finding f(0) ie the value of f(x) at x = 0

\(f(0) = \dfrac{\left(0^2-9\right)}{\left(0^2-0-6\right)} = \dfrac{-9}{-6} = \dfrac{3}{2}\)

Roots of a function can be found by setting f(x) = 0 and solving for x

Setting f(x) = 0

==> \(\dfrac{x^2-9}{x^2-x-6} = 0\\\\\)

We can factor the numerator  as follows:
x² - 9 = (x + 3) (x -3)     since (a + b)(a-b) = a² - b²

Denominator can be factored as follows
x² - x - 6 = (x-3)(x+2)

So
\(f(x) = \dfrac{(x + 3)(x-3)}{(x-3)(x+2)}\\\\\)

The (x-3) term cancels leaving
\(f(x) = \dfrac{x+3}{x+2}\)

Setting this equal to 0 gives
\(\dfrac{x+3}{x+2} = 0\)

This is 0 when x + 3 = 0 or x = -3

So there is only one root and that is x = -3

Asymptotes

The vertical asymptote occurs when at a value of x when the denominator becomes 0

The given function has been factored as
\(f(x) = \dfrac{x + 3}{x + 2}\)

The denominator becomes 0 at x = -2
Vertical asymptote is x = - 2

To find the horizontal asymptote use the fact that when the degrees of the numerator and denominator are equal, the horizontal asymptote is given by
\(y=\dfrac{\mathrm{numerator's\:leading\:coefficient}}{\mathrm{denominator's\:leading\:coefficient}}\)

The degree of the numerator x + 3 is 1 and the degree of the denominator x + 2 is also 1

So the horizontal asymptote is y = 1/1 = 1

y = 1 is the horizontal asymptote

End behavior is the behavior of the function as x → ±∞  

This is determined by examining the leading term of the function and determining what its behavior is as x → ±∞

In the function
\(f(x) = \dfrac{x + 3}{x + 2}\)
which is the factored form of the originally given function
the domain of x = all real numbers with the exception of -2 since at x = -2, the function is undefined

The end behavior can be determined by finding the limit of f(x) as x tends to infinity

\(\lim _{x\to \infty \:}\left(\dfrac{x+3}{x+2}\right)\\\\\dfrac{x+3}{x+2} \text{ can be transformed by dividing by x both numerator and denomiator :}\\\\\\=\dfrac{\dfrac{x}{x}+\dfrac{3}{x}}{\dfrac{x}{x}+\dfrac{2}{x}}\\\\\\=\dfrac{1+\frac{3}{x}}{1+\dfrac{2}{x}}\)

\(\lim _{x\to \infty \:}\left(\dfrac{x+3}{x+2}\right) \\\\\\\\=\lim _{x\to \infty \:}\left(\dfrac{1+\dfrac{3}{x}}{1+\dfrac{2}{x}}\right)\\\\\\\\=\dfrac{\lim _{x\to \infty \:}\left(1+\dfrac{3}{x}\right)}{\lim _{x\to \infty \:}\left(1+\dfrac{2}{x}\right)}\)

\(\lim _{x\to \infty \:}\left(1+\dfrac{3}{x}\right) = 1\\\\\lim _{x\to \infty \:}\left(1+\dfrac{2}{x}\right) = 1\)

\(\lim _{x\to \:-\infty \:}\left(\dfrac{x+3}{x+2}\right) = 1\)

End behavior
\(\mathrm{as}\:x\to \:+\infty \:,\:y\to \:1,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:y\to \:1\)

Table:
x                y

-4            1/2

- 3            0

-1               2

0               3/2

1                4/3

2                5/4

3               6/5

Note that the function is undefined at x = -2

we have the expression

40+25x

Remember that

40=(2)(2)(2)(5)

25=(5)(5)

so

GCF=5

therefore

40+25x=5(8+5x)

the answer is

Answer:

A=33.33

Step-by-step explanation:

Answer: Part A) 25%

Part B) 75%

Step-by-step explanation: Hope this helps.

Answer:

B. 46.

Step-by-step explanation:

First we set up the equation A(n)=-172 and substitute the given equation for A(n), giving us -172=8+(n-1)(-4). Simplifying, we get -180=(-4n+12), or -4n=-192, or n=48. However, n represents the number of terms in the sequence, and since the sequence starts with n=1, we need to subtract 1 from our answer to get the term number corresponding to A(n)=-172. Therefore, the answer is B) 46.

Answer:

270 if not simplified and

1/1 if simlifies

Step-by-step explanation:

Answer:

4x+6

Step-by-step explanation:

(x-2) + (3x + 8)

combine like terms

4x + 6

Hope this helps!!!

Answer:

4x+6

Step-by-step explanation:

Answer:

440

Step-by-step explanation:

I learned with parenthesis if its like this 4(7)

It usually means to multiply

soo

88 times 5

=440

soo

88