is 3-6x=y proportional

[tex]\bf \begin{array}{|cc|ll} \cline{1-2} n&a_n\\ \cline{1-2} 1&4\\ &\\ 2&\stackrel{4(-3)}{-12}\\ &\\ 3&\stackrel{-12(-3)}{36}\\ \cline{1-2} \end{array}\qquad \impliedby \textit{common ratio of "r" is -3} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\[-0.5em] \hrulefill\\ r=-3\\ a_1=4\\ n=15 \end{cases} \\\\\\ S_{15}\implies \displaystyle\sum\limits_{i=4}^{15}~4(-3)^{i-1}[/tex]

Answer:

[tex]\sum_{n=4}^{15}4(-3)^{n-1}[/tex]

Step-by-step explanation:

The given sequence is 4, -12, 36

We can see there is a common ratio

[tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-12}{4}=(-3)[/tex]

[tex]\frac{a_{2} }{a_{3} }[/tex] = [tex]\frac{36}{-12}=(-3)[/tex]

Therefore, the given sequence is a geometric sequence.

Now we have to determine the sigma notation of the sum for term 4 through term 15.

Since explicit formula of the sigma can be represented as

[tex]T_{n}=a(r)^{n-1}[/tex]

where [tex]T_{n}[/tex] = nth term

a = first term

n = number of term term

r = common ratio

and sum is denoted by [tex]\sum_{n=1}^{n}a(r)^{n-1}[/tex]

Now for the given sequence sigma notation will be

[tex]\sum_{n=4}^{15}4(-3)^{n-1}[/tex]

Here,

[tex]1.578 \times {10}^{ - 5} miles = 1 \: inches \\ 1 \: miles = \frac{1}{1.578 \times {10}^{ - 5} } \: inches\\ 1425 \: miles = \frac{1}{1.578 \times {10}^{ - 5} } \times 1425 inches\\ = 9.03 \times {10}^{7} inches[/tex]

I hope it helps you

The smallest angle is a which is 35 and from 7 to 35 it X5 so times 18 and 11 by 5 as well which comes to the ratio 35:90:55 , you can tell this is right because angles in a triangle add up to 180 , 35+90+55 =180

What are you solving for?

For this case we must find the quotient of[tex]6x ^ 2 + 23x + 20[/tex] between [tex]5 + 2x.[/tex]

As you can see in the figure, we must build a quotient in such a way that when multiplied by the divisor, we eliminate the terms of the dividend until we reach the remainder.

Answer:

[tex]3x + 4[/tex]

See attached image

4.02, 5, 7.3, 19, 23, 23, 34, 35, 41, 42

(Numbers are organized in ascending order from smallest to largest)

0.55

Hope this helps :)

Answer: 0.55

This is the answer... hope this will help y'all. If I'm wrong, please tell me. Thanks ☺️

ANSWER

B. 1

EXPLANATION

The given function is

[tex]f(x) =\left \{ {{x^{2} +3 (if) -5 \leq x< 1} \atop {x (if) 1 \leq x \leq 5 }} \right.[/tex]

This is a piece-wise defined function.

We want to find f(1)

We substitute x=1 into f(x)=x because, 1 belongs to the interval,

1≤x≤5

f(1)=1

The correct answer is B.

Answer:

5.625π m³

Step-by-step explanation:

The formula for the volume of a cylinder of radius R and length L is:

V = π·R²·L.

Here, V = π·(1.5 m)²(2.5 m) = 5.625π m³

Answer:

Step-by-step explanation:

Givens

r = 1.5 meters.

h = 2.5 meters.

Formula

V = pi * r^2 * h

Solution

V = pi * 1.5^2 * 2.5

V = pi * 2.25 * 2.5

V = 5.625 pi

Answer:

It’s B

6x log (4)

The statements about the functions that are true include:

A. f(x) and g(x) intersect at exactly two points.

B. The x-intercepts of f(x) are common to g(x).

In Mathematics and Geometry, the x-intercept of any function is the point at which the graph of a function crosses or touches the x-axis and the y-value or value of "y" is equal to zero (0).

By critically observing the table of values and graph shown in the image attached above, we can reasonably and logically deduce the following x-intercepts for both f(x) and g(x):

x-intercepts of f(x) = (-1, 0) and (1, 0).

x-intercepts of g(x) = (-1, 0) and (1, 0).

Therefore, the x-intercepts of f(x) are common to g(x), which means they intersect at exactly two points.

For the minimum value of f(x) and g(x), we have;

Minimum value of f(x) = -1

Minimum value of g(x) = -3

Therefore, the minimum value of f(x) is greater than the minimum value of g(x).

For the y-intercept of f(x) and g(x), we have;

y-intercept of f(x) = (0, -1).

x-intercepts of g(x) = (0, 1).

In conclusion, we can logically deduce that f(x) and g(x) have different y-intercept.

Answer:

b)0, yes

Step-by-step explanation:

Given:

Vectors (4,8) . (6,-3)

Finding inner product of vectors:

= 4x6 + 8x-3

=24-24

=0

Now to check the angle between them using formula a.b=|a|.|b|cosθ

|a|= [tex]\sqrt{4^{2} +8^{2} } \\\sqrt{16+64}[/tex]

   =8.9

|b|=[tex]\sqrt{6^{2} +(-3)^{2} } \\\sqrt{36+9}[/tex]

   =6.7

Putting values of a.b=0 and |a|=8.9, |b|=6.7 in a.b=|a|.|b|cosθ we get,

0= 8.9(6.7)cosθ

cosθ =0

θ=90 degrees

Hence the two vectors are perpendicular !

ANSWER

{},{1},{3},{5},{7},{1,3},{1,5},{1,7},{3,5},{3,7},{5,7},{1,3,5},{1,3,7},{3,5,7},{1,5,7},{1,3,5,7}

EXPLANATION

The given set is {1,3,5,7}.

This set has

[tex] {2}^{n} = {2}^{4} = 16[/tex]

subsets.

Where n=4 is the number of elements in the set.

Recall that the null set is a subset of every set and every set is a subset of itself.

The subsets are:

{}

{1},{3},{5},{7}

{1,3},{1,5},{1,7},{3,5},{3,7},{5,7}

{1,3,5},{1,3,7},{3,5,7},{1,5,7}

{1,3,5,7}

Answer:

Point I

Step-by-step explanation:

Point I is the farthest away from the line of best fit

Answer:

Whoa that's easyyyy

Step-by-step explanation:

Point I because it's not close to the others and it's not anywhere near becing connected to another letter

Answer:

45pairs

Step-by-step explanation:

15x3=45

Answer:

D) The relationship between y-intercepts cannot be determined.

Step-by-step explanation:

We have been given two different functions f(x) and g(x). Now we need to find about what can be determined about their y-intercepts. Then match with the correct choice from the given choices:

A) The function f(x) has a higher y-intercept.

B) The function g(x) has a higher y-intercept.

C) They both have the same y-intercept.

D) The relationship between y-intercepts cannot be determined.

We know that y-intercept is the y of function value when x=0.

In the table of g(x), we don't see any point that has x=0

So we can't find the y-intercept for g(x)

Hence correct choice is :

D) The relationship between y-intercepts cannot be determined.

The answer is:

C) They both have the same y-intercept.

In order to find the correct option, we need to find the equation of the function g(x), and then, compare its y-intercept with the y-intercept of the f(x) function.

So,

- Finding the equation of the g(x):

Calculating the slope of the function, using the first two points (-1,8) and (1,0), we have:

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{0-8}{1-(-1)}=\frac{-8}{2}=-4[/tex]

Now, calculating the value of "b" using the first point (-1,8)  and the slope of the function, we have:

[tex]y=mx+b[/tex]

[tex]y=-x+b[/tex]

[tex]8=-4(-1)+b[/tex]

[tex]b=4[/tex]

So, the equation of g(x) is:

[tex]y=-4x+4[/tex]

- Comparing the y-intercepts of f(x) and g(x):

Finding the y-intercept of f(x),  by making "x" equal to 0, we have:

[tex]y=x+4\\\\y=4[/tex]

We have that the function f(x) has its y-intercept at "y" equal to 4.

Finding the y-intercept of g(x), by making "x" equal to 0, we have:

[tex]y=-4x+4[/tex]

[tex]y=-4*(0)+4[/tex]

[tex]y=4[/tex]

We have that the function g(x) has its y-intercept at "y" equal to 4.

Hence, we have that both functions have their y-intercepts at the same point, so, the correct option is:

C) They both have the same y-intercept.

Have a nice day!

can the answer not being an integer?

The angle of elevation is at angle D

So the answer would be 13.8

Answer:

A  Open circle at 6, line going to the right

Step-by-step explanation:

The area of a rectangle is given by

A = l*w

We know the area is greater than 24

24 < l*w

One dimension is 4

24 < 4*w

Divide each side by 4

24/4 < 4w/4

6 < w

The other dimension must be greater than 6

Open circle at 6, line going to the right

Answer:

5.50 + 75g <= 15

5.50 - 5.50 + 75g <= 15 - 5.50

75g <= 9.5

75g / 75 <= 75 / 15

g = 5

Step-by-step explanation:

I'm going to assume that you meant y = mx + b not y = my + b

To do this move 7x to the right side by subtracting it to both sides

(7x - 7x) - y = 8 - 7x

0 - y = 8 -7x

-y = 8 - 7x

Y still isn't full isolated! There is still the negative sign that you have to get rid of. To do this divide -1 to both sides

-y/-1 = (8 - 7x)/ -1

y = -8 + 7x

y = 7x - 8

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

One of the many reasons of this is because the diet soda is less dense than the normal soda, therefor, it will float even though there's the same amount of liquid in each can, and the cans weigh the same amount

I hope this helps

Step-by-step explanation:

Answer:

The options in the question are missing, but the answer is "The can of diet soda will float due to the Archimedes principle.

Step-by-step explanation:

Now, Archimedes Principle can be defined as,

when a body is partially or completely immersed in a fluid, the body losses its weight in the fluid equal to the amount of fluid displaced by this body.

Notice that the phenomena of floating and sinking is based on Archimedes principle. If, the weight of body is higher than the amount of liquid it displaced, body will sink and if the weight of body is lower than the amount of liquid it displaced, then it will float. Now, in comparison of regular can with diet can, one needs to notice that diet can is slightly lighter due to absence of sugar in the liquid it contained. But the volume of both regular and diet can are same. When immersed, both displace same amount of water, but the weight of diet can is slightly lesser than the amount of water it displaced, so it floats, while on the other hand, the weight of normal can is slightly higher than the amount of water it displaced, so it sinks.

Answer:

Its the first one

Step-by-step explanation:

Final answer:

The rational expression[tex](r^2 - 4r + 5)/(r - 4)[/tex] is already in its simplest form, as the numerator cannot be factored to cancel out any terms with the denominator.

Explanation:

The question asks for the simplified rational expression for the quadratic equation [tex]r2 - 4r + 5[/tex] divided by the linear expression r - 4. Simplifying rational expressions often involves factoring the numerator and the denominator and then canceling out common factors. However, in this case, the numerator cannot be factored in a way that will cancel out terms with the denominator. Simplifying further requires either polynomial division or realization that the expression is already in its simplest form because there are no common factors. Therefore, the rational expression[tex]r2 - 4r + 5[/tex] over r - 4 is already simplified as no further reduction is possible.

Answer: f(x^-1) = x/5 - 3/5

Step-by-step explanation:

1. Replace f(x) with y

2. Swap the positions of x and y to make x = 5y + 3

3. Solve for y by subtracting 3 from both sides and dividing each side by 5

The inverse of the function is f(x) = (x-3)/5 if the function f(x) is 5x +3 by taking the subject as x in the parent function.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have a function:

f(x) = 5x+3

To find the inverse of the function, take the subject x and the value of x.

f(x) - 3 = 5x

x = (f(x) - 3)/5

Replace the f(x) →x and x →f(x)

f(x) = (x-3)/5

Thus, the inverse of the function is f(x) = (x-3)/5 if the function f(x) is 5x +3 by taking the subject as x in the parent function.

Learn more about the fraction here:

brainly.com/question/1301963

#SPJ2

Answer:

(1,2)

Step-by-step explanation:

we know that

The rule of the transformation is equal to

(x, y)  ------> (x + 3, y + 1)

Pre-image -----> Image

(x, y)  ------> (4, 3)

so

x+3=4 ----> x=4-3=1

y+1=3 ---> y=3-1=2

therefore

The pre-image is the point (1,2)

Answer:

I believe it is surface area

Answer:

Step-by-step explanation:

c

For this case we have a quadratic equation of the form:

[tex]ax ^ 2 + bx + c = 0[/tex]

Rewriting the equation we have:

[tex]3k ^ 2-4k-7 = 0[/tex]

So we have to:

[tex]a = 3\\b = -4\\c = -7[/tex]

The solutions will come from:

[tex]k = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]

Thus, the value of "b" is -4

Answer:

[tex]b = -4[/tex]

Answer:

The numbers are -9 and -7 or 13 and 15

Step-by-step explanation:

Let

x and x+2 ----> two consecutive odd integers

we know that

[tex]x(x+2)=3[x+x+2]+111[/tex]  

Solve for x

[tex]x(x+2)=3[x+x+2]+111\\ \\x^{2}+2x=6x+6+111\\ \\x^{2}-4x-117=0[/tex]

Solve the quadratic equation by graphing

The solution is x=-9, x=13

see the attached figure

First solution

x=-9

x+2=-9+2=-7

The numbers are -9 and -7

Second solution

x=13

x+2=13+2=15

The numbers are 13 and 15

I know the first 3 are c. I'm pretty sure the last one is a or d

Answer: 7. 2n + 162 = 424

              8. 3 hours

              9. K ≥ 18

7. The number of Delicious apples sold is represented by n. Because they  sold 162 more Empire apples than Delicious apples, the number of Empire apples sold can be represented by (n + 162). The total number of apples sold was 424, so the equation is Delicious apples + Empire apples = 424.

[tex]n + (n + 162) = 424\\\\n + n + 162 = 424\\\\2n + 162 = 424[/tex]

8. The equation is given for this problem. Simply solve for h in the equation.

[tex]55h + 275 = 440\\\\55h = 165\\\\h = 3[/tex]

9. The term "at least" generally means greater than or equal to. Thus, since Suzy scored at least 18 points, she scored 18 or more points.

[tex]K \geq 18[/tex]

Answer:

x<2

Step-by-step explanation:

-x+8>6

-x>6-8

-x>-2 (flip the sign)

x<2

Answer:

x < 2

Step-by-step explanation:

-x+8>6

Subtract 8 from each side

-x+8-8>6-8

-x > -2

Divide each side by -1.  Remember to flip the inequality

-x/-1 < -2/-1

x < 2

Answer:

$2.04

Step-by-step explanation:

Note that: 1 yard = 3 feet.

First, change the amount of yard (6) to feet:

6 x 3 = 18

6 yard = 18 feet.

Note: 18 feet = $36.72

Find the cost per foot (1 feet). Note the equal sign, what you do to one side, you do to the other. Divide 18 from both sides.

(18 ft)/18 = ($36.72)/18

1 ft = 36.72/18

1 ft = 2.04/1

1 ft = $2.04

~

Answer:

$2.04

Step-by-step explanation:

36.72/6

So that would make the answer $2.04