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Please help me with #18, 19, & 20

Answer:

[tex]\displaystyle y=-\frac{3}{8}x+2[/tex]

Step-by-step explanation:

Perpendicular lines have opposite reciprocal slopes. So, we must first determine our slope of the original equation by converting to slope-intercept form:

[tex]-8x+3y=-6\\3y=8x-6\\y=\frac{8}{3}x-2[/tex]

Hence, because the slope of the original line is 8/3, then the slope of the perpendicular line is -3/8. We are not done, however, as we need to account for the point that the perpendicular line passes through by solving for the new y-intercept:

[tex]y=-\frac{3}{8}x+b\\ \\8=-\frac{3}{8}(-16)+b\\\\8=6+b\\\\2=b[/tex]

Thus, the perpendicular line equation is [tex]y=-\frac{3}{8}x+2[/tex]. See below for a graph.

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]-8x+3y=-6\implies 3y=8x-6\implies y=\cfrac{8x-6}{3} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{8}{3}}x-2\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{8}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{8}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{8} }}[/tex]

so we're really looking for the equation of a line whose slope is -3/8 and it passes through (-16 , 8)

[tex](\stackrel{x_1}{-16}~,~\stackrel{y_1}{8})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{3}{8} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{- \cfrac{3}{8}}(x-\stackrel{x_1}{(-16)}) \implies y -8= -\cfrac{3}{8} (x +16) \\\\\\ y-8=-\cfrac{3}{8}x-6\implies {\Large \begin{array}{llll} y=-\cfrac{3}{8}x+2 \end{array}}[/tex]

A line has a slope of –9 and includes the points (–7,u) and (9,9).

The value of u is 153.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Given:

A line has a slope of –9 and includes the points (–7,u) and (9,9).

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

-9 = (9 - u)/(9 + 7)

-9 = (9- u)/16

9 - u = -144

u = 153.

Therefore, the value of u is 153.

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On solving the provided question, we can say that so, the Interest Rate to be paid will be as = 5.08%

Simple interest is calculated by dividing the principal by the interest rate, the passage of time, and other elements. The formula used in marketing is simple return = principal + interest + hours. Using this approach, interest may be calculated most easily. The most common way to calculate interest is as a percentage of the principal balance. If he borrows $100 from a friend and agrees to pay it back with 5% interest, for instance, he will only pay his proportion of the 100% interest. $100 (0.05) = $5. You must pay interest when you borrow money and charge interest when you lend it. The majority of the time, interest is calculated as an annual percentage of the loan balance. This proportion is referred to as the loan's interest rate.

Interest Rate =($ Paid in Interest / $ Amount borrowed) X (360 / borrowed period)

= ($33 / $2600) X (360 /90)

=0.050769231

=5.08%

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Therefore , the solution of the given problem of limit comes out to be it is the definition of the limit f(x,y).

A function's limit is a value that the function takes on as its input approaches or approaches a certain number. Continuity, integrals, & derivative are defined by limits. A function's limit is always interested in how the function behaves at a specific location.

Here,

Given :

If f(x,y) is a function that depends on x and y, then we have this function. Then, assuming that  ϵ>0,∃ δ > 0  positive definite

|f (x,y)C| whenever, this given function does have the limit of C as (x,y) (a,b). 0 < ( x − a ) 2 + ( y − b ) 2 < δ

It's described as. lim (a, b) f (x, y) => ( x , y )

Thus , it is the definition of the limit f(x,y).

Therefore , the solution of the given problem of limit comes out to be it is the definition of the limit f(x,y).

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Answer: 2:5

Step-by-step explanation:

Given,

Number of sunfish = 12

Number of rainbow shiner = 30

To find,

The ratio of sunfish to rainbow shiner.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

Ratio of sunfish to rainbow shiner :

= Number of sunfish : Number of rainbow shiner

= 12 : 30

= 6 : 15

= 2 : 5

(This ratio cannot be for the simplified so we will have to assume this as the final answer of this question.)

Hence, the ratio is 2:5

Answer:

2:5

Find the number both sides can be divided by in this case, it is 6. Diving both sides by a common number gives us 2 from 12 and 5 from 30.

Answer:

the answer is y≤1

Step-by-step explanation:

i hope it is right sorry if wrong

The equation of the line of Kaya’s line in slope-intercept form is y = 15x  + 25.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given this, Kaya babysits to add money to her savings. She draws a graph to show how much she can earn by babysitting.

To calculate the equation of the line we at least need Two points on the line.

Two points on the graph (0, 25) and (5, 100) and also the y-intercept of the given line is 25(where x is 0)

From the general formula of the slope-intercept form of an equation:

y=mx+b,

where m is the slope

b is the y-intercept,

Since. m = (y - y')/ (x -x')

In our case m = (100 - 25)/5-0)

m = 75 /5

m = 15

and b = 25

Thus, the equation of a line:

y = 15x  + 25

Therefore, The equation of the line of Kaya’s line in slope-intercept form is y = 15x  + 25.

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Answer:

8 teams of 4 players or 4 teams of 8 players

Step-by-step explanation:

8 x 4 = 32

The scientific notation is [tex]3.7 \times10 ^8[/tex] in a blood volume of 60 ml. Take note that the power of 10 is evaluated using the product of power property.

The reliability of a value, which is frequently an estimation affected by the item's decimal bit count. Beginning with the first non-zero digit, count the decimal places.

Up to the quel decimal place, all zeros are allowed. For example, the number 0.0079800 has five three-digit digits. When present, any digits to the right of the measurement's final non-zero number are required. equivalently increases an integer by three significant digits and three places.

After three, move upward, and start measuring at the first non-zero digit. The final digit must then be removed. The last two numbers are multiplied by zeros to the right of the decimal point.

given

If there are 6,200,000 red blood cells per cubic millimeter of blood,

then there are

[tex]60 \times 6,200,000=60 \times 6.2 \times 10^ 6=372 \times 10^6[/tex]

= [tex]3.7 \times10 ^8[/tex]

= [tex]3.7 \times10 ^8[/tex] in a blood volume of 60 ml. Take note that the power of 10 is evaluated using the product of power property.

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Answer:

78

Step-by-step explanation:

312 divided by 4 equals 78

The solution is Option D.

The limit of the infinite series diverges and the limit goes off to infinity

If a series is convergent then it has bounded partial sums. Equivalently, if a series fails to have bounded partial sums then it is divergent.

When the series' limits reach its finite range of values, the series is said to be convergent. It is important that, partial sum of series, there should be a limit existed and that is finite in nature then only series converges

An infinite series is one that doesn't converge at any point , had a series of incomplete sums that went on forever and had no end. A series diverges when each sum does not approach zero.

Given data ,

Let the infinite series be represented as A

Now , the value of A is

A = ∑n=1 to ∝ ( 3n⁴ / ( 15n⁴ + 5 )

On simplifying the equation , we get

A = 3 ∑n=1 to ∝ ( n⁴ / ( 15n⁴ + 5 )

In the equation , where the limit goes to infinity, there will finally be no exact solution because the sum of the series will be infinity and the infinite series diverges

Hence , the limit of the equation is infinity

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18x+26.6

18x+133/5

1/5(90x+133)

A straight line defines the intersection of the two planes.

Given is that Points {X} and {Y} lie in both plane P and plane Q.

Two common points can only lie on a straight line. So, a straight line defines the intersection of the two planes.

Therefore, a straight line defines the intersection of the two planes.

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Answer:

18

Step-by-step explanation:

GCF - The highest number that divides into two or more numbers, we are given the number 18 and 36.

Out of all the numbers divisible by 18 and 36, 18 is the greatest number out of all, making it the GCF.

Answer:

6

Step-by-step explanation:

The HCF (highest common factor) is the product of all the primes of both numbers!

1) List the prime factors of 18...

18 = 2 × 3 × 3

2) List the prime factors of 36...

2 × 2 × 3 × 3

3) Now see what numbers are in both!

We can see that the numbers 2 & 3 are in both prime factors so all we need to do is multiply them...

Have a lovely day :)

The probability of rolling an even number is P = 0.5

We know that the possible outcomes of a standard die are {1, 2, 3, 4, 5, 6}

The outcomes that are even are {2, 4, 6}

If all the outcomes have the same probability, then the probability of rolling an even number is equal to the quotient between the nmber of even outcomes (3) and the total number of outcomes (6).

Then the probability is:

P = 3/6 = 1/2

That is the probability of rolling an even number,

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In a case whereby a number has the same digits in its hundreds place and it’s hundredths place the number of times that the value is greater in the hundreds place than the value of the digit in the hundreds place is 10,000 times.

The question can be interpreted that the particular number has the same digit  which is seen in hundreds place  hence  hundredths place.

we can then represent the digit  as '1'.

The value of number's hundreds place can be represented as  100

we can as well represent the number's hundredths place as 0.01

the number of times the value of the hundreds place digit exceeds the value of the hundredths place digit can be expressed as 100/0.01 =(100*100)/1 = 10, 000

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missing options:

A. 100,00

B. 100

C. 1,000

D. 10,000

Answer:

tu x ella = ERROR

Step-by-step explanation:

Answer:

x = - 5/9

Step-by-step explanatiion:

8x-8+3(2x+2) = -4(x+3) is the original equation

Consider each term and simplify

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

-4(x + 3) = -4x - 12

Therefore the original expression becomes:
8x - 8 + 6x + 6 = -4x - 12

Move -4x to the left side; becomes + 4x
4x + 8x - 8 + 6x = -12

Group like terms on left side and simplify
(4x + 8x + 6x) (-8 +6) = -12

18x - 2  = - 12

Move -2 to right side -> becomes +2

18x = 2 - 12 = - 10

x = -10/18 = - 5/9

Answer:

49/3 or 16 1/3

Step-by-step explanation:

Answer:

Jacob uses 5.67 yards of fabric for the cape.

Step-by-step explanation:

Answer:drag 1st 2 3rd box 2nd to 1st box 3rd to 1st box 4th to 4th

Step-by-step explanation:

so easy

Domain of the function is all real numbers

A relation is a function if it has only One y-value for each x-value.

Let us consider a function f(x)= x² + 2x - 3

Now let us find the value of f(x-3)

Plug in the value x as x-3

f(x-3)= (x-3)² + 2(x-3) - 3

= x² +9-6x+ 2x-6 - 3

= x² -4x

The domain of this function is all real numbers. This means that any real value can be plugged into the function and produce a real output.

Hence, domain of this function is all real numbers

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A. 9 students offer all three subjects.

B. The only possible value of m is 8.

A. We can use the Principle of Inclusion-Exclusion (PIE) to find the number of students who offer all three subjects.

Let's call the number of students who offer all three subjects "x".

The total number of students who offer Biology is 35, but we have to subtract the number of students who offer only Biology and Economics (12) and only Biology and Physics (7) to avoid counting them twice.

So, the number of students who offer Biology only is 35 - 12 - 7 + x = 16 + x.

Similarly, the number of students who offer Economics only is 28 - 12 - 5 + x = 11 + x.

And the number of students who offer Physics only is 15 - 7 - 5 + x = 3 + x.

The total number of students who offer at least one of the three subjects is 58, so:

16 + x + 11 + x + 3 + x = 58

30 + 3x = 58

3x = 28

x = 9

So, 9 students offer all three subjects.

B. In a regular polygon with (2m + 1) sides, each interior angle is equal to (2m + 1 - 2) * 180 / (2m + 1) = (2m - 1) * 180 / (2m + 1).

We know that this value is equal to 1440, so:

(2m - 1) * 180 / (2m + 1) = 1440

Expanding the right side:

2m - 1 = 1440 * (2m + 1) / 180

Dividing both sides by (2m + 1) and rearranging:

2m = 1440 * 2 / 180 + 1

2m = 16 + 1

m = 8.5

Since m must be a positive integer, the only possible value of m is 8.

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Answer:

One number is equal to 4228 and the other is equal to 1057

Step-by-step explanation:

1. Let's consider the number that four times the other X, and the other as N

2. We can write X as 4N to make it easier

3. Next, we can form a simple equation X + N = 5285 and substitute the value of X to get 4n + n = 5285

4. We get 5n = 5285

5. To get N we divide 5285 by 5 to get 1057

6. 5285 - 1057 = 4228

Therefore, one number is equal to 4228 and the other is 1057

Answer:

∠ LKH = 25°

Step-by-step explanation:

LK is the midsegment of Δ FGH

LK joins the midpoints of the sides FH and GH and is parallel to the third side FG.

Then

∠ LKH = ∠ FGH = 25° ( corresponding angles )

Answer:

-9

Step-by-step explanation:

First combine like terms.

-8x+5-2x-4+5x       -8x-2x+5x=-5x

-8x+5-2x-4+5x       5-4=1

Now plug in 2 for x

-5x+1

   ↓

-5(2)+1= -10+1=-9

If this is wrong, I'm sorry for the misguidance.

Answer: A: 3/10 of the school has blonde hair. B: there are 120 students

Step-by-step explanation: I might have done this wrong but anyway, I multiplied 2/5 by 1/4 and got 1/10, meaning 1/10 of the boys have blonde hair. I multiplied 3/5 (because 5/5 - 2/5 = 3/5) by 1/3 and got that 2/10 of the girls are blonde. I added these, and got that 3/10 of the school are blondes. That's A. Then, I set up the equation 3/10 = 36/x (x equals the total number of students in the school). When I solved it I got x = 120, meaning there are 120 students in the school.  

Going by current exchange rates, Mitchell has $134.13 dollars remaining.

Unit conversion is a multi-step process that involves multiplication or division by a numerical factor, selection of the correct number of significant digits, and rounding.

The current exchange rate of Canadian dollars to US dollars is:

CAD $ 1.26 : 1 USD

When Mitchell first exchanged the USD to CAD$, it became:

= 150 x 1.26

= CAD$ 189

He then spends CAD$ 20 which leaves him with:

= 189 - 20

= CAD$ 169

He then exchanges this back to US$:

= 169 / 1.26

= US$ 134.13

Mitchell has US$ 134.13 remaining.

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Answer: 4ac

Step-by-step explanation: Combine like terms and follow PEMDAS