what is the equation for the line that passes through the points (4,2) and (0,6)?

Answer:

Step-by-step explanation:

this the gemetric  sequence  because : -12/6 =24/-12=-48/24=-2 (common rat)

the sum is : S=  u1 ×(d^n - 1)(d-1)

d = -2     u1  = 6     S= -2046

6((-2)^n -1) /(-2 -1) = -2046

(-2)^n -1  =1023

(-2)^n = 1024      but 1024 = 2^10 = (-2)^10

so : (-2)^n = (-2)^10

n=10  conclusion : 10 terms

The number of terms of the sequence is 10.

A geometric sequence exists a sequence of numbers where each term after the first term exists found by multiplying the earlier one by a fixed non-zero number, named the common ratio.

The terms of the sequence 6, -12, 24, -48, ...

Sum = -2046

Geometric sequence:

-12/6 = 24/-12 = -48/24 = -2

Sum of terms:

[tex]$S = u_{1} *(d^n - 1)(d-1)[/tex]

Let, d = -2, [tex]u_{1} = 6[/tex] and S = -2046

[tex]6((-2)^n -1) /(-2 -1) = -2046[/tex]

[tex](-2)^n -1 =1023[/tex]

[tex](-2)^n = 1024[/tex]

But the number of terms = 10

[tex]1024 = 2^{10} = (-2)^{10}[/tex]

so,[tex](-2)^{n} = (-2)^{10}[/tex]

Therefore, the correct answer is 10.

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Answer: 4/8 or 1/2

Step-by-step explanation:

See attached photo. - my answer got deleted lol

Answer:

4/8 or 1/2

Step-by-step explanation:

got it right on preworks

Answer:

you would first have a straight, increasing line with a small slope. (walking slowly and consistently)

then you have a flat, straight line (not moving as you pet the kitten)

then you have a big, increasing slope (running fast)

then it's straight line again(distance doesnt change at friend's house)

and then a decreasing line with pretty big slope all the way to the x axis(running home)

Answer:

Step-by-step explanation:

[tex]f(x)=3x^2-2x+7\\\\f(-2)\to\text{put x = -2 to the equation of a function:}\\\\f(-2)=3(-2)^2-2(-2)+7=3(4)+4+7=12+4+7=23[/tex]

Answer:

The correct option is 4. The value of f(-2) is 23.

Step-by-step explanation:

The given function is

[tex]f(x)=3x^2-2x+7[/tex]

We have to find the value of f(-2). It means we need to find the value of function f(x) at x=-2.

Substitute x=-2 in the given function to find the value of f(-2).

[tex]f(-2)=3(-2)^2-2(-2)+7[/tex]

On simplification we get

[tex]f(-2)=3(4)-(-4)+7[/tex]

[tex]f(-2)=12+4+7[/tex]

[tex]f(-2)=23[/tex]

The value of f(-2) is 23. Therefore the correct option is 4.

Answer:

Option B 3,-3,-6 is correct.

Step-by-step explanation:

We need to find real zeroes of [tex]x^3+6x^2-9x-54[/tex]

Solving

[tex]x^3+6x^2-9x-54\\=(x^3+6x^2)+(-9x-54)[/tex]

Taking x^2 common from first 2 terms and -9 from last two terms we get

[tex]=(x^3+6x^2)+(-9x-54)\\=x^2(x+6)-9(x+6)\\[/tex]

Taking (x+6) common

[tex](x+6)(x^2-9)\\[/tex]

x^2-9 can be solved using formula a^2-b^2 = (a+b)(a-b)

[tex]=(x+6)((x)^2-(3)^2)\\=(x+6)(x+3)(x-3)[/tex]

Putting it equal to zero,

[tex](x+6)(x+3)(x-3) =0\\x+6 =0, x+3=0\,\, and\,\, x-3=0\\x=-6, x=-3\,\, and\,\,  x=3[/tex]

So, Option B 3,-3,-6 is correct.

Answer:

B. 3,-3,-6

Step-by-step explanation:

Cost of items = $0.25 × 100

= $25.00

Final answer:

The volume of the tilted solid is 1200 cubic feet.

Explanation:

The volume of the cube in the image is given as 1000 cubic feet. Let's call the height of the cube 'h'. The length and width of the cube are also 'h', so the volume of the cube is h x h x h = h³ = 1000. Solving for 'h', we find that h = 10 feet.

The tilted solid has the same base and height as the cube, but the length of each of its slanted sides is 2 units longer than the height. So the length of each slanted side is h + 2 = 10 + 2 = 12 feet.

To find the volume of the tilted solid, we can use the formula for the volume of a rectangular prism: volume = base area x height. The base area is h x h = h², and the height is 12 feet. Therefore, the volume of the tilted solid is h² x 12 = 10² x 12 = 1200 cubic feet.

Answer:

5p-6 is your answer.

Step-by-step explanation:

p^2 + p - 6

-p^2 - 4p

leaves you with

p--4p-6, which equals p+4p-6,

so simplifying: 5p+6 is your answer.

Hope this helps!

Answer:

Treat the lesser than sign as an equal sign. What you do to one side, you do to the other. Isolate the variable x. Do the opposite of PEMDAS.

PEMDAS = Parenthesis, Exponents ( & roots), Multiplication, Division, Addition, Subtraction.

Solve -6x + 14 < -28

First, subtract 14 from both sides:

-6x + 14 (-14) < -28 (-14)

-6x < -42

Next, divide -6 from both sides to isolate the variable x. Note that when you divide (or multiply) by a negative number, you must flip the greater than or less than sign.

(-6x)/-6 < (-42)/-6

x > (-42)/(-6)

x > 7

x > 7 is your answer.

Solve 3x + 28 < 25

First, subtract 28 from both sides.

3x + 28 (-28) < 25 (-28)

3x < -3

Isolate the variable x. Divide 3 from both sides. Note that because you aren't dividing by a negative number (rather a positive 3), you do not flip the sign.

(3x)/3 < (-3)/3

x < (-3)/(3)

x < -1

x < -1 is your answer.

~

To solve the given inequalities, we found that x > 7 and x < -1. Since no number satisfies both conditions simultaneously, there is no solution to this system of inequalities.

We are given two inequalities to solve for x:

-6x + 14 < -28

3x + 28 < 25

Solving the first inequality:

Solving the second inequality:

Combining the two inequalities, we find:

x > 7 AND x < -1

Since there is no number that satisfies both conditions simultaneously, there is no solution to this system of inequalities.

Answer:

y > 2x + 2 and y < 2x-1 .

Step-by-step explanation:

The line which the blue shaded area represent has y intercept 2 and slope [tex]\frac{2}{1} =2[/tex]

Hence equation of the line is y=2x+2.

To check the inequality for the shaded region we take any  point (-3,0) in the shaded region .Plugging the values in the given equation :

0 > 2(-3)+2  or 0 >-4.

The inequality equation represented by the blue shaded part is y > 2x+2.

The line for the red shaded region has y intercept -1 and slope 2.

Hence equation of the line is y= 2x-1 .

Taking a point (2,0) in the shaded part and substituting the values in the equation of line we have :

0< 2(2)-1 or 0< 3 .

Hence the inequality representing the red shaded region is y<2x-1 .

y > 2x + 2 and y < 2x - 1

In this problem, we will compose the system of linear inequalities is represented by the graph. Firstly, let us state each line on the graph in terms of the equation of the line.

A shortcut to form a linear equation through the intercepts of the axes at (0, a) and (b, 0) is [tex]\boxed{\boxed{ \ ax + by = ab \ }}[/tex].

Part-1: a dashed line that intersects the axes at points (0, 2) and (-1, 0).

Step-1: make a linear function  

[tex]\boxed{ \ ax + by = ab \ } \rightarrow \boxed{ \ 2x + (-1)y = 2 \times (-1) \ }[/tex]

2x - y = -2

Add by 2 and y on both sides.

Hence, the equation of line is [tex]\boxed{y = 2x + 2 \ }[/tex]  

Step-2: make a linear inequality  

Since the test point (0, 0) is not in the blue shaded area, which means the test results must be false (or 0 > 2), then linear inequality is arranged as follows:

[tex]\boxed{\boxed{ \ y > 2x + 2 \ }}[/tex]

Part-2: a dashed line that intersects the axes at points (¹/₂, 0) and (0, -1)..

Step-1: make a linear function  

[tex]\boxed{ \ ax + by = ab \ } \rightarrow \boxed{ \ (-1)x + \frac{1}{2}y = -1 \times \frac{1}{2} \ }[/tex]

[tex]\boxed{ \ -x + \frac{1}{2}y = -\frac{1}{2} \ }[/tex]

Multiply by 2 on both sides.

-2x + y = -1

Add by 2x on both sides.

Hence, the equation of line is [tex]\boxed{y = 2x - 1 \ }[/tex]  

Step-2: make a linear inequality  

Since the test point (0, 0) is not in the red shaded area, which means the test results must be false (or 0 < -1), then linear inequality is arranged as follows:

[tex]\boxed{\boxed{ \ y < 2x - 1 \ }}[/tex]

Thus the system of linear inequalities is represented by the  graph is y > 2x + 2 and y < 2x - 1.

Answer:

3,4

6,6

9,8

Step-by-step explanation:

Answer:

The answer is C.250%

Step-by-step explanation:

Got it right on the quiz

The formula for slope is [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

In this case:

[tex]y_{2} = 1\\ y_{1} }= -3\\x_{2} = -4\\x_{1} = 0[/tex]

so...

[tex]\frac{1 - (-3)}{-4 - 0}[/tex]

[tex]\frac{4}{-4}[/tex]

-1 <<<The slope

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

m = -1

Step-by-step explanation:

The slope is also called the gradient, m.

m=(y2-y1)/(x2-x1)

x1 = 0

y1 = 3

x2 = -4

y2 = 1

we therefore substitute for the values in the formula

m = (1-⁻3)/(⁻4-0)

m = -1

The answer would be 5, - 8

Answer:5,-8

Step-by-step explanation:

For this case we must indicate an expression equivalent to:

[tex]\sqrt {\frac {2x ^ 5} {18}}[/tex]

We rewrite 18 as 2 * 9:

[tex]\sqrt {\frac {2x ^ 5} {2 * 9}} =[/tex]

We simplify common factors:

[tex]\sqrt {\frac {x ^ 5} {9}} =[/tex]

We rewrite:

[tex]x ^ 5 = x ^ 4 * x = (x ^ 2) ^ 2 * x\\9 = 3 ^ 2[/tex]

So, we have:

[tex]\sqrt {\frac {(x ^ 2) ^ 2 * x} {3 ^ 2}} =\\\sqrt {(\frac {x ^ 2} {3}) ^ 2 * x} =[/tex]

We get the terms of the radical "

[tex]\frac {x ^ 2} {3} \sqrt {x}[/tex]

Answer:

[tex]\frac {x ^ 2} {3} \sqrt {x}[/tex]

Answer:

The answer is A

Step-by-step explanation:

The other guy is correct I'm just making it easier to get the answer quickly.

Answer:8 ,-8

Step-by-step explanation:the absolute value of a number is how far it is from 0 so 8 and -8 are both 8 spots from 0. Hope this helps!

let's notice the y-coordinate is the same for both points, thus is a horizontal line.

Check the picture below.

nothing can further be done with this?

The solution to the system of equations given by the ordered pairs (7x+3y,2x+3y) and (24, 0) is x= -4.8 and y=3.2.

To solve for x and y, you need to equate each component of the ordered pairs and solve the resulting equations. In this case, you have:

Solving the second equation for x: x = -1.5y

Substitute x into the first equation: 7(-1.5y) + 3y = 24, which becomes -10.5y + 3y = 24, then -7.5y = 24

Solving for y, you get: y = -24 / -7.5 which equals y = 3.2.

Substituting y into the second equation 2x + 3(3.2) = 0, we get 2x = -9.6, so x = -9.6 / 2, so x = -4.8.

So, the values of x and y are -4.8 and 3.2 respectively.

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Answer:

[tex]\displaystyle 24x^{2} - 41x + 12 = 24\left(x - \frac{3}{8}\right) \cdot \left(x - \frac{4}{3}\right) = (8x-3)\cdot (3x - 4)[/tex].

Step-by-step explanation:

Apply the quadratic formula to find all factors. For a quadratic equation in the form

[tex]a\cdot x^{2} + b\cdot x + c = 0[/tex],

where [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are constants, the two roots will be

[tex]\displaystyle x_1 = \frac{-b + \sqrt{b^{2} - 4\cdot a \cdot c}}{2a}[/tex], and

[tex]\displaystyle x_2 = \frac{-b - \sqrt{b^{2} - 4\cdot a \cdot c}}{2a}[/tex].

For this quadratic polynomial,

Apply the quadratic formula to find any [tex]x[/tex] value or values that will set this polynomial to zero:

[tex]\displaystyle x_1 = \frac{-(-41) + \sqrt{(-41)^{2} - 4\times 24 \times 12}}{2\times 24} = \frac{3}{8}[/tex].

[tex]\displaystyle x_2 = \frac{-(-41) - \sqrt{(-41)^{2} - 4\times 24 \times 12}}{2\times 24} = \frac{4}{3}[/tex].

Apply the factor theorem to find the two factors of this polynomial:

Keep in mind that simply multiplying the two factors will not reproduce the original polynomial. Doing so assumes that the leading coefficient of [tex]x[/tex] in the original polynomial is one, which isn't the case for this question.

Multiply the product of the two factors by the leading coefficient of [tex]x[/tex] in the original polynomial.

[tex]\displaystyle 24\left(x - \frac{3}{8}\right) \cdot \left(x - \frac{4}{3}\right) = (8x-3)\cdot (3x - 4)[/tex].

Expand to make sure that the factored form is equivalent to the original polynomial:

[tex](8x-3)\cdot (3x - 4)\\ = (8\times 3)x^{2} + ((-3)\times 3 + (-4)\times 8)\cdot x + ((-3)\times (-4))\\ = 24x^{2} - 41x + 12[/tex].

d = rt ( d = distance, r = rate (speed) and t = time)

14  = 7t

Divide both sides by 7:

t = 14/7

t = 2 hours

1 hour = 60 minutes.

2 hours x 60 = 120 minutes total.

Based on the distance Andrew went and the rate at which he went, Andrew's time in minutes was 120 minutes.

The distance formula is:

Distance = Rate x Time

Andrew's time is therefore:

14 = 7 x Time

Time = 14 / 7

= 2 hours

In minutes this is:

= 2 x 60 minutes per hour

= 120 minutes

In conclusion, Andrew covered that distance in 120 minutes.

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Step-by-step explanation:

Volume of a cone is [tex]\pi r^{2} .height[/tex]/3 so [tex](3x)^{3}[/tex] is equal to

[tex]\pi r^{2} .x[/tex]/3 .  Also  [tex](3x)^{3}[/tex] = [tex]27x^{3}[/tex]

[tex]27x^{3}[/tex] = [tex]\pi r^{2} .x[/tex]/3. Pi equals to 3 so pi and the 3 in the denominator will simplfy each other. lets simplfy the "x" so [tex]r^{2}  = 27x^{2}[/tex] so the radius is 9x.

The expression that represents the radius of the cone's base is →

{r} = 3/√π.

Volume is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write Volume as -

V = ∫∫∫ F(x, y, z) dx dy dz

Given is that the volume of a cone is {3x} cubic units and its height is {x} units.

The volume of a cone is -

V = 1/3 πr²h

We can write the volume as -

3x = 1/3 πr²x

3 = 1/3 πr²

πr² = 9

r² = 9/π

r = 3/√π

Therefore, the expression that represents the radius of the cone's base is → {r} = 3/√π.

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Answer: [tex]24\sqrt{3}[/tex]

Step-by-step explanation:

You need to remember that [tex]\sqrt[n]{a}[/tex] can be written in the following for:

[tex]a^{\frac{1}{n}}[/tex]

Knowing this and given the expression [tex](2*6)^{\frac{3}{2}}[/tex], you need to  multiply the numbers inside the parentheses:

 [tex](12)^{\frac{3}{2}}[/tex]

Rewrite it in this form:

[tex]=\sqrt{12^3}==\sqrt{1,728}[/tex]

Descompose 1,728 into its prime factors:

[tex]1,728=2*2*2*2*2*2*3*3*3=2^6*3^3[/tex]

Applying the Product of power property, which states that:

[tex](a^m)(a^n)=a^{(m+n)}[/tex]

You can say that:

 [tex]=\sqrt{1,728}=\sqrt{2^6*3^2*3}[/tex]

Simplifying, you get:

[tex]=2^3*3\sqrt{3}=24\sqrt{3}[/tex]

Answer:

Second option: One solution. Independent.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

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

Where "m" is the slope and "b" is the y-intercept.

Since the equations of the system have this form, we know that they are lines.

We can identify that the y-intercept of the first equation [tex]y=-5x+1[/tex] is:

[tex]b=1[/tex]

Now we need to find the x-intercept. Substitute [tex]y=0[/tex] and solve for "x":

[tex]0=-5x+1\\\\5x=1\\\\x=\frac{1}{5}=0.2[/tex]

Then, we can graph the first line which passess through the points (0,1) and (0.2,0). Observe the graph attached.

The y-intercept of the second equation [tex]y=-2x-2[/tex] is:

[tex]b=-2[/tex]

Now we need to find the x-intercept. Substitute [tex]y=0[/tex] and solve for "x":

[tex]0=-2x-2\\\\2x=-2\\\\x=\frac{-2}{2}=-1[/tex]

Then, we can graph the second line, which passess through the points (0,-2) and (-1,0).

You can observe in the graph that the lines intersect at the point (1,-4). Therefore, that point is the solution of the system of equations.

Since the lines intersect, then there is one solution that is true for both equations. It is independent

Answer:

You cant find this type of stuff on the internet without some shady questions.If your doing linear functions which im guessing basic algebra where ur from gof to google and look up linear funcion calc. The one by symbolab and try that . If it doesent work or dosent look right try some other calcs.

The equivalent exponential form of the equation log2n=4 is 2⁴ = n, which simplifies to n = 16.

The equation log2n=4 can be rewritten using the definition of a logarithm. To convert from logarithmic to exponential form, we use the fact that a logarithm answers 'to power must the base be raised to produce the given number'. So, log2n = 4 is equivalent to 24 = n, because 2 is the base in this logarithm, and 4 is the power to which this base must be raised. Therefore, n is equal to 16, as 2 raised to the fourth power is 16 (24 = 16).

Answer:

Step-by-step explanation:

The graph of g(x) is the same as that of f(x), EXCEPT that the graph of f(x) has been translated upward by 2 units.

The function is added and with a positive number so the function will shift towards the left , Option D is the correct answer.

A function can be defined as an algebraic expression which states relation between an independent and a dependent variable.

A function always comes with a defined range and domain.

It is given in the question that

There are two functions

g(x), f(x)

and they are related as

g(x)=f(x)+2.

and it has been asked that which statement given in the option describes it the best.

A. The graph of g(x) is the graph of f(x) shifted 2 units to the right.

B.The graph of g(x) is the graph of f(x) shifted 2 units down.

C.The graph of g(x) is the graph of f(x) shifted 2 units up.

D. The graph of g(x) is the graph of f(x) shifted 2 units to the left.

When a function is added , subtracted or multiplied it shifts or translates, and the new function is called the translated function

As the function is added and with a positive number so the function will shift towards the left.

Therefore , D is the answer the graph of G (x) is the graph of f(x) shifted 2 units to the left.

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Answer: 30+18x C is correct

Step-by-step explanation: You distribute the 6 to both of the values in the parenthesis.

Answer:

C 30 + 18x

Step-by-step explanation:

6(5 + 3x)

Distribute the 6 to both terms inside the parentheses

6*5 +6*3x

30 +18x

Step-by-step explanation:

from the graph above, the intersect of both lines would give the answer...

C. 5 quarts, 25 gallons

You can substitute the values in both equations to verify the answer

Answer:

The z-score for this kernel is -2.3

Step-by-step explanation:

* Lets revise how to find the z-score

- The rule the z-score is z = (x - μ)/σ , where

# x is the score

# μ is the mean

# σ is the standard deviation

* Lets solve the problem

- The popping-times of the kernels in a certain brand of microwave

  popcorn are  normally distributed

- The mean is 150 seconds

- The standard deviation is 10 seconds

- The first kernel pops is 127 seconds

- We want to find the z-score for this kernel

∵ z-score = (x - μ)/σ

∵ x = 127

∵ μ = 150

∵ σ = 10

∴ z-score = (127 - 150)/10 = -23/10 = -2.3

* The z-score for this kernel is -2.3

Answer:

-2.3

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Hihi. So, this is a nice application of interest rates as well as properties of exponentials/logarithms. As you know, the basic equation for interest rates is A= Pe^(rt) where A is your final amount, P is your initial, r is your rate of interest, and t is the time the money was accumulating interest. After cleaning up, you get in a situation due to you having e still lying around. Luckily, if you take the natural log of e, all you have left behind is the previous exponent. Thus, you can take the natural log of both sides, divide by 4, and then simplify to see that your final interest rate is ~6%

Answer:

A. 6%

Step-by-step explanation:

Since, the given amount formula is,

[tex]A=Pe^{rt}[/tex]

Where, P is the initial amount,

r is the periodic rate of interest,

t is the number of periods,

Here, P = $ 2000,

t = 4 years,

A = $ 2543,

By substituting the values,

[tex]2543=2000e^{4r}[/tex]

[tex]1.2715=e^{4r}[/tex]

Taking ln on both sides,

[tex]ln(1.2715)=4r[/tex]

[tex]\implies r = 0.06004932647\approx 0.06 = 6\%[/tex]

Hence, the rate of interest is 6 %.

Option 'A' is correct.