What is the y intercept of the line 3y+8x-18=0?​

The slopes of opposite sides are equal and product of slopes of adjacent sides is -1. All the sides are of equal length. So the given parallelogram is a square.

First we have to calculate the slopes of each sides.

Equation for slope, m= (y₂-y₁)/(x₂-x₁)

Slope of JK, m₁ = (3-2)/(0-⁻4) = 1/4

Slope of KL, m₂ = (-1-3)/(1-0) = -4

Slope of LM, m₃ = (-2-⁻1)/(-3-1) = 1/4

Slope of MJ, m₄ = (-2-2)/(-3--4)= -4

m₁= m₃ and m₂= m₄. That means the slope of opposite sides are equal. So they are parallel. Now we have to check whether the slopes are perpendicular.

If two lines are perpendicular, then product of slope will be -1

Multiplying two adjacent slopes,

m₁ ×m₂= 1/4 × -4 = -1

m₂ × m₃ = -4 × 1/4 = -1

m₃ m₄ = -4 × 1/4 = -1

So opposite sides are parallel and corresponding sides are perpendicular. So it may be a square or a rectangle.

Now we have to find the length of each sides,

Distance formula = \(\sqrt{{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}\)

JK = \(\sqrt{(0--4)^{2}+ (3-2)^{2} }\) = √16+1 = √17

KL = √(1-0)²+(-1-3)² = √(1+16) = √17

LM = √(-3-1)²+(-2--1)² =√(16+1) =√17

MJ = √(-3--4)²+(-2-2)² =√1+16) =√17

Length of all sides are equal.

So the given parallelogram is a square.

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Answer:

4

Step-by-step explanation:

What you will need to do is add 4

the 2 to the other 2 which will get you 4

Answer:

4

Step-by-step explanation:

1+1 equal 2

2+2 equal 4

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Answer:

The length if the pool is 12

Step-by-step explanation:

Formula: A=lw or lw=A

> (x+4)(x-2)=72

> (x²-2x+4x-8)=72

> x²+2x-8=72

> x²+2x-8-72=0

> x²+2x-80=0

Factor

> x²+10x-8x-80

> x(x+10)-8(x+10)

>(x+10)(x-8)

Check:

(x-4); (x-2); x=8

(8+4)=12 Length

(8-2)=6 Width

The constant of proportionality in the equation is 5/4

The constant connecting two given numbers in what is known in a proportional relationship is the constant of proportionality.

The constant of proportionality may also be referred to as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.

In the problem, y = 5/4x

The constant term 5/4 as used in the equation is used t multiply the input x values to get the out put y values

The term helps in relating x to y

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Answer:

In a rectangle ABCD of 3 mx 4 m, starting from A and D, along the sides AB and DC after every 30 cm, a square shape of 10 cm is taken out as shown below. What will be the perimeter (in cm)

Step-by-step explanation:

12 CM And 300 CM is the answer

Answer: 3 11/15  please mark brainliest If I helped you.

the question is kayar and 12 by 5 miles on Monday and 21 by three miles on Tuesday what is the total distance in miles kayuren during those two days first phone on Monday how much run that was 12 by 5 miles on Tuesday Shirin to 1 by 3 minus now this whole part and fractional part are written separately so this can be converted into a mixed fraction like when a number is of the form of p by see that is one whole number and fraction then it is written as a + b by c so we can write Monday that was 12 by 5 miles that is

12 by 1 + 2 by 5 that will be 5 will be LCM of 5 + 2 will be 7 by 5 MI and Tuesday it will be 21 by 3 that is 2 + 1 by 3 3 will be the LCM of 3 and 22 will be 6 plus one that is 7 by 3 minus in question is asked that what was the total distance kayar and thus during today's so Monday plus Tuesday will be the total total 27 by 5 + 7 by 3 that will be equal to LCM will be 15 this will be X 307 into 3 + 7 and 25 that

is 21 + 45 upon 15 that will be equal to 56 upon 15 Now since we have to give answer in mixed fraction in whole number and fraction this a bi bi can be divided into a whole number and fraction part when divided by be the remainder is remainder is written here b is written here and question is written here so 56 by 15 can be written as 15 and 23 is 45 three years question remainder will be 11:00 that is 56 - 45 and below will be the denominator will be 15 so this is our answer and the correct

The expression that is equivalent to  ∛ 5 * \(\sqrt[5]{4}\) is \(5^{1/3}*4^{2/5}\)

A radical in mathematics is the opposite of an exponent, which is symbolized by the sign "n√" also known as root.

The number before the symbol or radical is regarded as an index number or degree, and it can either be a square root or a cube root and so on.

This equation represents exponents in fraction form and the basics for the calculation is from

x^(b/n)

\(\sqrt[n]{x}^{b}\)

Rewriting the expression is done as below

∛ 5

= \(5^{1/3}\)

and

\(\sqrt[5]{4}\)

\(= 4^{2/5}\)

combining both gives

∛ 5 * \(\sqrt[5]{4}\)

\(5^{1/3}*4^{2/5}\)

\(5^{1/3}*4^{2/5}\) is the equivalent expression

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The dividends per share for preferred stock for each year are: Year 1 - $1.25, Year 2 - $2.25, Year 3 - $3.25. The dividends per share for common stock for each year are all $0.

To determine the dividends per share for preferred and common stock for each year, we need to divide the total dividends by the number of shares for each type of stock.

Preferred Stock:

Dividends per share of preferred stock = Total dividends for preferred stock / Number of preferred shares

Year 1:

Dividends per share of preferred stock for Year 1 = $50,000 / 40,000 shares = $1.25

Year 2:

Dividends per share of preferred stock for Year 2 = $90,000 / 40,000 shares = $2.25

Year 3:

Dividends per share of preferred stock for Year 3 = $130,000 / 40,000 shares = $3.25

Common Stock:

Dividends per share of common stock = Total dividends for common stock / Number of common shares

Year 1:

Dividends per share of common stock for Year 1 = ($50,000 - Total dividends for preferred stock) / 100,000 shares = ($50,000 - $50,000) / 100,000 shares = $0

Year 2:

Dividends per share of common stock for Year 2 = ($90,000 - Total dividends for preferred stock) / 100,000 shares = ($90,000 - $90,000) / 100,000 shares = $0

Year 3:

Dividends per share of common stock for Year 3 = ($130,000 - Total dividends for preferred stock) / 100,000 shares = ($130,000 - $130,000) / 100,000 shares = $0

The dividends per share for preferred stock for each year are: Year 1 - $1.25, Year 2 - $2.25, Year 3 - $3.25. The dividends per share for common stock for each year are all $0.

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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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Answer:

B.  -414,720 x⁷y⁶

Step-by-step explanation:

To find the 4th term of the expansion of (2x - 3y²)¹⁰, we can use the binomial theorem.

The binomial theorem states that for an expression of the form (a + b)ⁿ:

\(\displaystyle (a+b)^n=\binom{n}{0}a^{n-0}b^0+\binom{n}{1}a^{n-1}b^1+...+\binom{n}{r}a^{n-r}b^r+...+\binom{n}{n}a^{n-n}b^n\\\\\\\textsf{where }\displaystyle \rm \binom{n}{r} \: = \:^{n}C_{r} = \frac{n!}{r!(n-r)!}\)

For the expression (2x - 3y²)¹⁰:

Therefore, each term in the expression can be calculated using:

\(\displaystyle \boxed{\binom{n}{r}(2x)^{10-r}(-3y^2)^r}\quad \textsf{where $r = 0$ is the first term.}\)

The 4th term is when r = 3. Therefore:

\(\begin{aligned}\displaystyle &\;\;\;\;\:\binom{10}{3}(2x)^{10-3}(-3y^2)^3\\\\&=\frac{10!}{3!(10-3)!}(2x)^7(-3y^2)^3\\\\&=\frac{10!}{3!\:7!}\cdot2^7x^7(-3)^3y^6\\\\&=120\cdot 128x^7 \cdot (-27)y^6\\\\&=-414720\:x^7y^6\\\\ \end{aligned}\)

So the 4th term of the given expansion is:

\(\boxed{-414720\:x^7y^6}\)

This question is Incomplete because it lacks the appropriate options

Complete Question

Which number is the best estimate of 866,214,000,000 using powers of 10

a) 9 × 10¹¹

b) 8 × 10¹¹

c) 10 × 11¹⁰

d) 8 × 10-¹¹

Answer:

a) 9 × 10¹¹

Step-by-step explanation:

When we want to estimate a number using the power of 10, we are trying to write the number in a standard form.

We are to estimate :866,214,000,000 using powers of 10

Hence,

8.66214000000 × 10¹¹

We round up to the nearest whole number

= 9 × 10¹¹

Therefore, the best estimate for 866,214,000,000 using powers of 10

= 9 × 10¹¹

Answer:

y = 5x+4

​

Step-by-step explanation:

The slope-intercept form of an equation is like this:

M stands for the slope and b for the y-intercept.

First, we need to find the slope:

Now we know: y= 5x+b

Now, to find b we have to choose one of your points. Let's use the first given point: (1, 9)

With the slope-intercept form equation I showed before, substitute x and y with the values of one point.

Substitute the b in the equation, and that's your answer:

Answer:

x^4 • x^-2 = x^6

Step-by-step explanation:

The probability of drawing blue, red, and white balls consecutively is 120/3375 with replacement and 120/2730 without replacement.

To calculate the probability of drawing three balls from a box containing six white balls, five red balls, and four blue balls, we need to consider two scenarios: with replacement and without replacement.

(i) With replacement:

When each ball is replaced after it is drawn, the total number of balls remains the same for each draw. Therefore, the probability of drawing a specific color on each draw remains constant.

The probability of drawing a blue ball on each draw is 4/15, the probability of drawing a red ball is 5/15, and the probability of drawing a white ball is 6/15 (assuming all colors are equally likely to be drawn).

To find the probability of drawing a blue, red, and white ball consecutively, we multiply the probabilities together since the events are independent:

P(Blue, Red, White) = (4/15) * (5/15) * (6/15) = 120/3375

(ii) Without replacement:

When the balls are not replaced after being drawn, the total number of balls decreases for each subsequent draw. This affects the probability of each color being drawn on subsequent draws.

For the first draw, the probability of drawing a blue ball is 4/15, a red ball is 5/15, and a white ball is 6/15.

For the second draw, the probability of drawing a blue ball is 3/14, a red ball is 5/14 (as one blue ball is already drawn), and a white ball is 6/14.

For the third draw, the probability of drawing a blue ball is 2/13, a red ball is 4/13 (as two blue balls and one red ball are already drawn), and a white ball is 6/13.

To find the probability of drawing a blue, red, and white ball consecutively without replacement, we multiply the probabilities together:

P(Blue, Red, White) = (4/15) * (5/14) * (6/13) = 120/2730

Therefore, the probability of drawing blue, red, and white balls consecutively is 120/3375 with replacement and 120/2730 without replacement.

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The height is 8.4.

Calculated with H = V / πr^2, with H for height, V for volume, and r for radius (the diameter divided by 2).

Observe that the x coords of the roots of a polynomial are,

\(x_{1,2,3,4}=\{-3,0,1,4\}\)

Which can be put into form,

\(y=a(x-x_1)(x-x_2)(x-x_3)(x-x_4)\)

with data

\(y=a(x-(-3))(x-0)(x-1)(x-4)=ax(x+3)(x-1)(x-4)\)

Now if I take any root point and insert it into the equation I won't be able to solve for y because they will always multiply to zero (ie. when I pick \(x=-3\) the right hand side will multiply to zero,

\(y=-3a(-3+3)(-3-1)(-3-4)=0\)

and a will be "lost" in the process.

If we observed a non-root point that we could substitute with x and y and result in a non-loss process then you could find a. But since there is no such point (I don't think you can read it of the graph) there is no other viable way to find a.

Hope this helps :)

Answer:

1

Step-by-step explanation:

The degree of a polynomial is the highest power of the variable in the polynomial. In this case, the highest power of the variable is 1, so the degree of the polynomial 5x+7 is 1.

For example, the polynomial 2x^2 + 3x + 4 has a degree of 2 because the highest power of the variable x is 2. The polynomial x^3 + x + 1 has a degree of 3 because the highest power of x is 3

Answer:

it is 1

Step-by-step explanation:

because it is only one x there

The probability that (50) dies within 10 years and dies after (40) is at least 0.02 but less than 0.04. So the answer is B. At least .02 but less than .04.

To calculate the probability that (50) dies within 10 years and dies after (40), we need to find the joint probability of the two events happening together.

Let X and Y be the future lifetimes of (40) and (50), respectively. We want to find P(Y≤10 and X<Y). Using the Law of Total Probability, we can write:

P(Y≤10 and X<Y) = ∫P(Y≤10 and X<Y|X=t) fX(t)dt

where fX(t) is the probability density function of X.

Since the force of mortality for (40) is constant, the probability density function for X is given by:

f X (t)=ue −ut

where u=0.05.

For (50), we have the survival function S(y) = 1 - y/10. So, the probability density function for Y is:

fY(y) = S'(y) = 1/10

Now, we can substitute these expressions into the integral and simplify:

P(Y≤10 and X<Y) = ∫P(Y≤10 and X<Y|X=t) fX(t)dt

= ∫∫P(Y≤10 and X<Y|X=t) fY(y)fX(t)dydt

= ∫∫P(Y≤10 and t<Y) (1/10)(0.05)e^(-0.05t)dydt

= (1/10)∫e^(-0.05t) ∫1≤y≤10 e^(0.1y) dydt

= (1/10)∫e^(-0.05t) (e - e^(-t/10)) dt

Evaluating this integral, we get:

P(Y≤10 and X<Y) ≈ 0.0286

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Answer:

Step-by-step explanation:

x- intercept, vertex (v) and axis of symmetry, parabola form:x²+bx+c

vertex(h,k)

f(x)=x²-9  a=1,b=0 ,c=-9

h=-b/2a=0

k=f(0)=-9

vertex(0,-9) , x intercept is when f(x)=0

(x-3)(x+3)=0 either x-3=0⇒ x=3 or x+3=0 then x=-3

x=3, x=-3 (-3,0) and (3,0)

the x of symmetry is the h of the vertex=0

g(x)=x²-2x-3 a=1, b=-2,c=-3

h=-b/2a⇒-(-2)/2(1)⇒h=1

k=f(1)=1²-2(1)-3⇒k=-4

v(1,-4)

x of symmetry=h=1

(x+1)(x-3)=0

x+1=0⇒x=-1 (-1,0)

x-3=0 ⇒x=3  (3,0)

x intercept :-1,3

vertex(-3,9)

x intercept:(0,0) and (-6,0)

axis of symmetry =-3

vertex(3,-8)

axis of symmetry=3

x intercept : (5,0), (1,0)

vertex(-1/2,1)

x of symmetry=-1/2

x intercept : (0,0)(-1,0)

vertex(3,0)

x intercept (3,0)

axis of symmetry = 3

Step-by-step explanation:

\(15 = - 5x + 10 \\ - 5x = 15 - 10 \\ - 5x = 5 \\ x = \frac{5}{ - 5} \\ x = - 1 \\ thank \: you\)

Answer:

The correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.

Step-by-step explanation:

What is probability?

Probability is the branch of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely it is that a claim is true.

To find which 2 books describe a pair of dependent events:

A pair of two dependent events are simply those in which the selection of the second item is contingent on the selection of the first item, causing the probability to change.

Because the sample size is lowered when the initial item is taken without replacement, choosing the exact same item reduces the chance.

Now, in regard to the question, this means that for two of the occurrences to be independent, they must be on the same shelf and of the same type of book, so that the second book cannot be selected until the first one is.

Option D, where both books are on the same shelf and are of the same type, is the only option that fulfills this requirement.

Therefore, the correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.

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Answer:

the terms in the expression are p squared, negative 3,3p, negative 8,p,p cubed

Step-by-step explanation:

hope that helps

The position of the image is 42.25 cm in front of the lens. and its height is 5.64 cm and inverted.

We can use the thin lens equation to find the position of the image:

\(1/f = 1/d_o + 1/d_i\)

where f is the focal length of the lens, \(d_o\) is the object distance (distance between object and lens), and \(d_i\) is the image distance (distance between image and lens). We can solve for \(d_i\):

\(1/d_i = 1/f - 1/d_o\)

f = R/2 for a plano-convex lens with radius of curvature R, so in this case

\(f = 13 cm/2 = 6.5 cm\).

Plugging in \(d_o\) = 15 cm and f = 6.5 cm, we get:

\(1/d_i = 1/6.5 - 1/15\\1/d_i = 0.1538\\d_i = 6.5/0.1538\\d_i = 42.25 cm\)

So the position of the image is 42.25 cm in front of the lens.

To find the height of the image, we can use the magnification equation:

\(m = -d_i/d_o\)

where m is the magnification (negative for a virtual image), \(d_i\) is the image distance (which we just found), and \(d_o\) is the object distance (given as 15 cm).

\(m = -42.25/15\\m = -2.82\)

This means that the image is 2.82 times smaller than the object. Since the object is 2.0 cm tall, the height of the image is:

\(h_i = mh_o\\h_i = -2.822.0 cm\\h_i = -5.64 cm\)

The negative sign indicates that the image is inverted (upside down). So the position of the image is 42.25 cm in front of the lens, and its height is 5.64 cm and inverted.

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Answer:

47.647% Increase

Step-by-step explanation:

You need to find the amount it increased by first, so

251-170=81

Then you need to find what percent of 170 that is, so

81/170=0.47647

Finally multiply that by 100 to get the percent:

0.47647×100=47.647%

The answer of the given question based on the expression is , the value of the summation when m = 3 is 137.

In mathematics, an expression is a combination of numbers, variables, and operators that represents a value or a set of values. It can be a simple combination of numbers and variables or a more complex combination involving mathematical operations like addition, subtraction, multiplication, division, exponents, and roots. Expressions can be used to represent a wide range of mathematical concepts, from simple arithmetic to complex functions and equations.

To evaluate the summation 1(1!) + 2(2!) + 3(3!) + 4(4!) + m(m!), where m = 3, we substitute m = 3 and simplify:

1(1!)+2(2!) +3(3!) +4(4!) +3(3!)

= 1(1) + 2(2) + 3(6) + 4(24) + 3(6) (since n! = n(n-1)! for all positive integers n)

= 1 + 4 + 18 + 96 + 18

= 137

Therefore, the value of the summation when m = 3 is 137.

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The perimeter of the square is 16√5 mm, and the area of the square is 80 mm².

To calculate the perimeter and area of the square, we can use the formulas:

Perimeter = 4 * side length

Area = side length * side length

Substituting the given side length of 4√5mm into the formulas, we have:

Perimeter = 4 * 4√5mm = 16√5mm

Area = (4√5mm) * (4√5mm) = 16 * 5mm = 80mm²

Therefore, the perimeter of the square is 16√5mm, and the area of the square is 80mm².

Please note that the values are based on the provided side length of 4√5mm. If there are any changes to the side length, the perimeter and area will differ accordingly.

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The perimeter of the square is 16√5 mm, and the area of the square is 80 mm².

I took the test on plato.

Answer:

Width of rectangle = 4 meter

Length of rectangle = 18 meter

Step-by-step explanation:

Given:

Perimeter of rectangle = 44 m

Assume;

Width of rectangle = a

Length of rectangle = 2a + 10

Find:

Length and width

Computation:

Perimeter of rectangle = 2[l + b]

2[a + 2a + 10] = 44

3a + 10 = 22

3a = 12

a = 4

So,

Width of rectangle = a = 4 meter

Length of rectangle = 2a + 10 = 18 meter