16. If y varies directly as x, and x = 9 when y = 15, find y when x = 33?​

Answer:

The rate of change is -4.5 and the relation of the table is a linear function

Step-by-step explanation:

Linear function.

A linear function can be identified because the rate of change is constant at every point of its domain.

The graph of a linear function is a straight line with a constant slope.

Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]

We'll show the relation shown in the table is a linear function. We'll calculate the slope for any random pair of points. For example, using (2,83) and (3,78.5):

[tex]\displaystyle m=\frac{78.5-83}{3-2}=-4.5[/tex]

Now for (7,60.5) and (14,29):

[tex]\displaystyle m=\frac{29-60.5}{14-7}=\frac{-31.5}{7}=-4.5[/tex]

Proceeding in a similar way with any pair of points, the slope will always result in the same value, thus the rate of change is -4.5 and the relation of the table is a linear function.

Answer:

[tex]x = \displaystyle \frac{5 + \sqrt{17}}{2}[/tex].

Step-by-step explanation:

Because [tex]3\, x[/tex] is found in the input to a logarithm function in the original equation, it must be true that [tex]3\, x > 0[/tex]. Therefore, [tex]x > 0[/tex].

Similarly, because [tex](x - 4)[/tex] and [tex](2\, x - 1)[/tex] are two other inputs to the logarithm function in the original equation, they should also be positive. Therefore, [tex]x > 4[/tex].

Let [tex]a[/tex] and [tex]b[/tex] represent two positive numbers (that is: [tex]a > 0[/tex] and [tex]b > 0[/tex].) The following are two properties of logarithm:

[tex]\displaystyle \ln (a) + \ln(b) = \ln\left(a \cdot b\right)[/tex].

[tex]\displaystyle \ln (a) - \ln(b) = \ln\left(\frac{a}{b}\right)[/tex].

Apply these two properties to rewrite the original equation.

Left-hand side of this equation:

[tex]\begin{aligned}&\ln(3\, x) - \ln(x - 4)= \ln\left(\frac{3\, x}{x -4}\right)\end{aligned}[/tex]

Right-hand side of this equation:

[tex]\ln(2\, x- 1) + \ln(3) = \ln\left(3 \left(2\, x - 1\right)\right)[/tex].

Equate these two expressions:

[tex]\begin{aligned}\ln\left(\frac{3\, x}{x -4}\right) = \ln(3(2\, x - 1))\end{aligned}[/tex].

The natural logarithm function [tex]\ln[/tex] is one-to-one for all positive inputs. Therefore, for the equality [tex]\begin{aligned}\ln\left(\frac{3\, x}{x -4}\right) = \ln(3(2\, x - 1))\end{aligned}[/tex] to hold, the two inputs to the logarithm function have to be equal and positive. That is:

[tex]\displaystyle \frac{3\ x}{x - 4} = 3\, (2\, x - 1)[/tex].

Simplify and solve this equation for [tex]x[/tex]:

[tex]x^2 - 5\, x + 2 = 0[/tex].

There are two real (but not rational) solutions to this quadratic equation: [tex]\displaystyle \frac{5 + \sqrt{17}}{2}[/tex] and [tex]\displaystyle \frac{5 - \sqrt{17}}{2}[/tex].

However, the second solution, [tex]\displaystyle \frac{5 - \sqrt{17}}{2}[/tex], is not suitable. The reason is that if [tex]x = \displaystyle \frac{5 - \sqrt{17}}{2}[/tex], then [tex](x - 4)[/tex], one of the inputs to the logarithm function in the original equation, would be smaller than zero. That is not acceptable because the inputs to logarithm functions should be greater than zero.

The only solution that satisfies the requirements would be [tex]\displaystyle \frac{5 + \sqrt{17}}{2}[/tex].

Therefore, [tex]x = \displaystyle \frac{5 + \sqrt{17}}{2}[/tex].

Answer: its four inches

Step-by-step explanation:

one green block is 1 inch and there is 4 green blocks meaning that it is four inches

Answer:

4 inches

Step-by-step explanation:

Answer:

12x + 3y = 15

Step-by-step explanation:

Answer:

c and a

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let J(t) represent Juan's equation and A(t) represent Aubree's equation. If Juan starts this venture on page 5, even if he didn't read any more days at all, when t = 0, he would still have read those 5 pages. Because he reads 14 pages per day, then he reads 14t and t represents the number of days gone by. His equation then is

J(t) = 14t + 5

Likewise, for Aubree, even if she decides not to read any more past the original 25 pages she started with, she would still have read those 25 pages. Her equation then would be

A(t) = 10t + 25

We need to know how many days will go by before they are both on the same page, so set the equations equal to each other and solve for t:

14t + 5 = 10t + 25 and

4t = 20 so

t = 5

After 5 days they will have both read the same number of pages.

Answer:

the percentage of adults have stage 2 high blood pressure is 0.0057

Step-by-step explanation:

The computation of the percentage of adults have stage 2 high blood pressure is shown below;

Given that

mean = 117

Standard deviation = 17

and, the sample is 160

Now based on the above information,

The percentage is

= (Sample - mean) ÷ (standard deviation)

= (160 - 117) ÷ (17)

= 2.529

p(z>2.53) = 0.0057

hence, the percentage of adults have stage 2 high blood pressure is 0.0057

Answer:35 degrees

Step-by-step explanation:

Answer:

angle KLN° + angle NLM° =180° ( l.p)

angle NLM°=180°-145°

angle NLM=35°

Answer:

l = 23 cm and w = 5.7 cm

Step-by-step explanation:

Perimeter = twice the length plus twice the width

let w = width

let l = length

l = 5.9 + 3w

57.4 = 2(5.9 + 3w) + 2w

57.4 = 11.8 + 6w + 2w

57.4 = 11.8 + 8w

45.6 = 8w

w = 5.7

Substitute 5.7 for 'w' to get 'l':

l = 5.9 + 3(5.7)

l = 23

[tex] {x}^{2} + 2x - 15 = 0 \\ (x + 5)(x - 3) = 0 \\ x = - 5 \\ x = 3[/tex]

Therefore the answer is D.

Answer:

x = 7

Step-by-step explanation:

Given

2(2x + 1) = 30

4x + 2 = 30

4x = 30 - 2

4x = 28

x = 28/ 4

x = 7

Hope it helps :)❤

Answer:

x= 7

Step-by-step explanation:

2(2x+1) =30

2×2x+2×1=30

4x+2=30

4x=30-2

4x=28

x=28÷4

x=7

Answer:

A. 1/5

Step-by-step explanation:

First off, ignore the "each one is five tickets" part, that's just there to confuse you. There are ten tickets total sold, of which two are sold to girls. You can express this as 2/10, which simplifies to 1/5.

Answer: 8/3

Step-by-step explanation:

So first what you do is you have to add the whole number to the numerator and you do that by multiplying the whole number by the deniminator which is 6. Now you add the 6 to the numerator which is 8, so you get 8/3.

Sorry this got so complicated. Hope this helped!

Answer:

The first piece has a length of 7 inches, the second has a length of 14 inches and the third has a length of 21 inches.

Step-by-step explanation:

x represents the length of the first​ piece.

Hence, the second piece has a length of 2x and the third piece has a length of 3x.

Hence, x + 2x + 3x = 42 inches.

x + 2x + 3x = 42 inches

6x = 42 inches

x = 7 inches

Hence, the first piece has a length of 7 inches, the second has a length of 14 inches and the third has a length of 21 inches.

Hope this helped!

Answer:

C

Step-by-step explanation:

Oleg is correct because the least common denominator of both is 4, so each must have 4 peices

Answer:

59

Step-by-step explanation:

b^3 is 27

2(27) is 54

54+5 is 59

if u mean (2b)^3 then 2b is 6

6^3 is 216

plus 5 is 221

Answer: It is 59 For part 2 But for part 1 it is 3

Step-by-step explanation:

Answer:

27%

Step-by-step explanation:

3/11 = 0.27272727

so about 27%

Answer:

The remainder is 6 !

Step-by-step explanation:

The remainder of the equation A = 46 / 8 is r = 6

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the remainder of the equation be denoted as = r

Let the dividend number be = 46

Let the divisor number be = 8

Now , the equation is represented as = A

The value of A is given by

A = 46 / 8

Now , the remainder will be

5 x 8 = 40

Substituting the values in the equation , we get

Dividend - 40 = 6

Therefore , the remainder of the equation A is 6

Hence , The remainder of the equation A = 46 / 8 is r = 6

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ2

Answer:

X=2

DG=4

Step-by-step explanation:

Answer:

X=2

DE=4

THE ANSWER IS UPPP

Answer:

It would be $ for 2 other planes of glass because if you take 7 divided by 7 to get 1 pane of glass you have to divide 16.45 by 7 to get how much it costs for 1 pane of glass. So for 1 pane of glass, it is $2.35 then lastly you can either add 2.35 and 2.35 to get $4.70 or take 2.35 times 2 to get your total. So it will cost $4.70 to get 2 panes of glass.

Step-by-step explanation:

1. Area of a circle is pi x R^2

Area = 3.14 x 18^2

Area = 3.14 x 324= 1017.36 sq. In.

The blade covers 122 out of 360 degrees.

1017.36 x 122/360 = 345 square inches.

2.

Like above.

Area =3.14 x 75^2 = 17,662.5 square feet

17662.5 x 80/360 = 3,925 square feet.

Answer:

Happy conversation

Step-by-step explanation:

Be happy. It's good for you.

Answer:

Yes sure want to be friends?

:)

Answer:

111 can i get brailyist for replying so fast.

Answer:

23

Step-by-step explanation:

[tex] \frac{2}{5} \times \frac{x}{59} [/tex]

the number of drops of nectar goes on the bottom, and the number of butterflies goes on the top

then you cross multiply to get 5x= 118

solve for × and you get 23.6

for this situation, 0.6 of a butterfly doesn't make sense, so we need to round down.

we round down because it's okay if there's extra nectar, but there can't be less than enough.

you can be 23 butterflies with 59 drops of nectar

Answer:

d=-40t+2100

Step-by-step explanation:

Let d be the distance between New York to Los Angeles and speed of driving is v miles/hour.

As when they have driven for 10 hours, they are 1700 miles away from Los Angeles, so the distance covered in 10 hours is d-1700 miles.

Similarly, the distance covered in 15 hours is d-1500 miles.

So, the distance covered in 5 hours = (d-1500)-(d-1700) =d-1500-d+1700=200 miles.

As speed = distance/time,

So the speed of driving, v=200/5=40 miles/hour

Let d (in miles) be the remaining distance at any time instant t (in hour) and the linear relation between d and t is

d=at+b ...(i)

where a and b are constants.

When they have driven for 10 hours, they are 1700 miles away from Los Angeles, so putting t=10 and d=1700 in the equation (i), we have

1700=10a+b

b=1700-10a...(ii)

Similarly, when they have driven for 15 hours, they are 1500 miles away from Los Angeles, so

1500=15a+b

1500=15a+1700-10a

1500-1700=5a

-200=5a

a= -200/5

a= -40

From equation (ii), we have

b=1700-10(-40)=1700+400=2100

From equation (i), the required equation is

d=-40t+2100

Hence the required linear function is d=-40t+2100.

Answer:

The scale factor is just the ratio like 3/15

little traingle/big triangle

Step-by-step explanation:

Answer:

(0.9036, 0.9064)

Step-by-step explanation:

Given that:

True mean (m) = 0.9050

Standard deviation (s) = 0.0100

Sample size ( n) = 48

Interval for 90% of the sample mean :

Mean ± Error

Error = Zcritical * (standard deviation /sqrt(n))

Zcritical at 90% confidence interval = 1.64

Hence,

Error = 1.64 * (0.0100/sqrt(48)) = 0.0014433

Lower boundary = m - Error = (0.9050 - 0.0014433) = 0.9035567

Upper boundary = m + Error = (0.9050 + 0.0014433) = 0.9064433

(0.9036, 0.9064)

Answer:

0 dollars

=E(M)

=μ  

M

​  

=−$10,000(0.81)+$40,000(0.18)+$90,000(0.01)

=−8,100+7,200+900

=0

​  

Answer:

0.2, as stated on Khan.

Step-by-step explanation:

Pay attention to the wording. There are two similar problems with wording, but the numbers are altered.