Find the variation constant and an equation of variation where y varies directly as x and y=16 when x=2

Replace x with x+3:

f(x+3) = (x+3)²

which is x² translated 3 units left

Answer:

(- 5, 0 ), (7, 0 )

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (1, - 108 ), thus

y = a(x - 1)² - 108

To find a substitute (0, - 105 ) into the equation

- 105 = a(- 1)² - 108 ( add 108 to both sides )

3 = a

y = 3(x - 1)² - 108 ← equation in vertex form

To find the x- intercepts, let y = 0, that is

3(x - 1)² - 108 = 0 ( add 108 to both sides )

3(x - 1)² = 108 ( divide both sides by 3 )

(x - 1)² = 36 ( take the square root of both sides )

x - 1 = ± [tex]\sqrt{36}[/tex] = ± 6  ( add 1 to both sides )

x = 1 ± 6, so

x = 1 - 6 = - 5

x = 1 + 6 = 7

x- intercepts are (- 5, 0), (7, 0)

Answer:

[tex]\boxed{1}[/tex]

Step-by-step explanation:

[tex]\left[\begin{array}{ccc}1 \times 1&2 \times 1\\3 \times 5&4 \times 5 \end{array}\right][/tex]

Steps to solve:

6/3x = 3

~Multiply 3/6 to both sides

x = 3/2

Best of Luck!

Answer:

x = 3/2

Step-by-step explanation:

Hey there!

To solve this equation, let's rewrite it for cohesive purposes. This would result in (6/3)(x) = 3.

Now, we can simplify the fraction because it reduces to a whole number. Three will go into six two times, so 6/3 is equivalent to 2.

This leaves us with 2x = 3.

Now, we need to isolate the x. Because there is a coefficient leading the variable, we can divide the entire term (2x) by 2 as well as dividing the 3 on the righthand side of the equation by 2.

Remember the mathematical rule of thumb: what you do to one side of the equation, you must perform to the other side. Therefore, if we divide by 2 on the left side of the equation, we must also divide the righthand side of the equation by 2.

By performing this step, it leaves us with x = 1.5.

[tex]{\frac{2x}{2}=\frac{3}{2}}\\\\\bold{x = \frac{3}{2}}[/tex]

We can reduce [tex]\frac{3}{2}[/tex] to a decimal, which transfers to 1.5. However, it's best to leave the answer in fractional form. This leaves our final answer as [tex]\bold{x=\frac{3}{2}}[/tex].

Answer:

(20, 800) and (27, 1080)

Step-by-step explanation:

The chart shows that it costs 40 per person, so you need to identify which bills costs 40 times the number of people.

12x40=460 No

20x40=800 Yes

24x40=1020 No

27x40=1080 Yes

28x40=1110 No

Answer:

220=48+h or 220=48h

Step-by-step explanation:

the word more can refer to a greater degree or extent.  possibly referring

to addition or multiplication.

Answer:

220=48+h

Step-by-step explanation:

We know that 220 is the sum of 48 and h so you just represent it in an equation/equality statement.

Answer:

the number [tex]6\,\,\,10^{-2}[/tex] is three million times larger than [tex]2\,\,\,10^{-8}[/tex]

Step-by-step explanation:

To answer this, just do the quotient of the first one over the second one, and use the rules for quotient of exponential expressions of the same base:

[tex]\frac{6\,\,\,10^{-2}}{2\,\,\,10^{-8}} =\frac{6}{2} \,\frac{10^{-2}}{10^{-8}} =3\,\,\,10^{-2+8}=3\,\,\,10^6=3000000[/tex]

So the answer is: the number [tex]6\,\,\,10^{-2}[/tex] is three million times larger than [tex]2\,\,\,10^{-8}[/tex]

Answer:

y = 60x

(0, 0)

(5, 300)

(10, 600)

Step-by-step explanation:

since x is the number of hours, 60 will represent m.

y = 60x.

Plug in x values.

Plug in 0 and get a y of 0.  (0,0)

Plug in 5 and get a y of 300. (5, 300)

Plug in 10 and get a y of 600. (10, 600)

Answer:

144 units

Step-by-step explanation:

3x + 8 + 4x + 10 = 8x

7x + 18 = 8x

8x - 7x = 18

x = 18

8x is length of BC

8 × 18 is length of BC

144 units

Answer:

What is the length of segment BC?

144 units

explanation:

<3

Answer:The set of possible values for the independent variable is called the domain. Similarly, there are constraints on the values for any dependent variable. ... Graphs of functions are traditionally drawn with the independent variable on the horizontal axis and the dependent variable on the vertical axis.

Step-by-step explanation:

Answer:

is 1

step by step explanation:

Answer:

For 13, there are 25 possible words, and for 14, depending on what the meaning of leaves is in this, the answer is 590.

Answer:

The first one is 25 and the second is 1080.

Step-by-step explanation:

To find how many 5-letter words you can make out of the letters, H, Q, L, R, and S, find the answer to 5². 5² = 25, so we can make 25 5-letter words. To find the number of "leaves" on the tree, just multiply the number of choices for color, monitor size, hard-drive size, and battery type together. So, 5×9×12×2 = 1080, so there are 1080 "leaves" on the tree.

Hope this helps! Plz give me brainliest like you said, it will help me achieve my next rank.

Answer:

graph c is 2x> 50 and graph b is x+6<32

Step-by-step explanation:

For 2x>50 you first divide 50 by2 leaving you with x>25 therefore x is all numbers greater than 25.

For x+6<32 you first subtract 6 from 32 leaving you with x<26 therefore x is  all numbers less than 26.

Hope this helps, please mark brainliest if it does!!! Thank you!!

Answer:

graph c is 2x> 50 and graph b is x+6<32

Step-by-step explanation:

For 2x>50 you first divide 50 by2 leaving you with x>25 therefore x is all numbers greater than 25.

For x+6<32 you first subtract 6 from 32 leaving you with x<26 therefore x is  all numbers less than 26.

Hope this helps, please mark brainliest if it does!!! Thank you!!

Answer:

exponential decay

Step-by-step explanation:

The function  f(x)=0.85ˣ is a exponential decay.

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

The given function is f(x)=0.85ˣ.

The function f of x is equal to zero point eight five to the power of x.

Exponential decay refers to a process in which a quantity decreases over time, with the rate of decrease becoming proportionally smaller as the quantity gets smaller.

The function  f(x)=0.85ˣ is a exponential decay.

Hence, the function  f(x)=0.85ˣ is a exponential decay.

To learn more on Functions click:

https://brainly.com/question/21145944

#SPJ2

Answer: x=12

Step-by-step explanation:

OQ is equal to NL since both contain 90 degree angles and are intersected by a radius. Since OS is 3x-2 and NL is 32, then we need to find OQ and set it equal to NL. OS is half of OQ, so multiplying OS by 2 will get you OQ. 6x-4=32

That yields x=12.

Answer:

X=12

Step-by-step explanation:

Answer:

I think the closest to the correct answer is choice B:

[tex]f^{-1} (x)=\frac{1}{x-1}[/tex]

Step-by-step explanation:

the accurate answer is: [tex]f^{-1} (x)=-\frac{1}{1-x}[/tex]

Answer:

Step-by-step explanation:

The function represented by the yellow graph has exactly one y-intercept and one x-intercept.  The y-intercept is (0, 4) and the x-intercept is (2, 0).

Answer:

Its the one shown

Step-by-step explanation:

Answer:

blank 1: 2xy(4x-5y)+3(4x-5y)

blank 2: (2xy+3)(4x-5y)

Step-by-step explanation:

Using factoring group to factor the polynomial 8x²y−10xy²+12x−15y

Step 1: Group the polynomial function

(8x²y−10xy²)+(12x−15y)

Step 2: Factor the common value and variables from the functions in parentheses.

= (2xy*4x - 2xy(5y)) + (3(4x) - 3(5y))

= 2xy(4x-5y)+3(4x-5y)

Step 3: Rearrange the expression by selecting one of the function in parentheses and combine those not in parenthesis.

(2xy+3)(4x-5y)

The final expression gives the factor form of the polynomial.

Hence the statement for each blank that correctly completes Lana's work are;

blank 1: 2xy(4x-5y)+3(4x-5y)

blank 2: (2xy+3)(4x-5y)

The probability of not drawing a red marble is   7/10

The probability of drawing a red marble is  3/10

=======================================================

Explanation:

We have 3 red marbles out of 5+2+3 = 10 total. Therefore, the probability of selecting a red marble is 3/10.

The probability of not selecting a red marble is 7/10 because 3/10+7/10 = 1. Put another way, we have 7 marbles that aren't red (the 5 blue and 2 black ones) out of 10 total.

*see attachment below for the dot plots that completes the question.

Answer:

B. Centers: The sea turtles have a greater median age than the koi.

D. Spreads: The ages of the koi are more spread out.

Step-by-step explanation:

The measure of center that can be used for comparison is the median, while the spread can simply be visualised by mere looking at how spread out the dots on the number line are. The spread of both can also be compared using their range. The greater the range, the more spread a data is.

=>Median Differences:

The median age for turtle = the middle value = 55

The median age for koi = 30

Therefore, sea turtles have a greater median age than the koi.

=>Spread Differences:

Range for turtle = the highest age - the least age represented on the dot plot = 65 - 45 = 20

Range for koi =  55 - 10 = 45

Koi has a greater range value than koi. Therefore, the ages of the koi are more spread out.

Answer:

Linear

Step-by-step explanation:

y = 2x + 4 is linear -- any equation involving only first powers of x and y (and constants) is linear. You'll usually see linear equations in the forms y = mx + b, ax + by = c, or y - y1 = m(x - x1).

If you take any two points, find the slope of the line between them, and then plug in one point to solve for the constant term (like you did), you will get a linear equation through those points.

Answer:

it is linear pair of the variable

Every y coordinate on the horizontal line is the same, so each point has a y coordinate of y = 8. This is to be able to pass through (-5,8)

Every x coordinate on the vertical line is the same, so each point has an x coordinate of x = 4. This is to be able to pass through (4,-1)

Put this together to get the answer (x,y) = (4,8)

Answer:

The two lines intersect at (4,8).

Answer:range is -2

Step-by-step explanation:

Answer: [tex]\dfrac{x^2}{81}+\dfrac{y^2}{56}=1[/tex]

Step-by-step explanation:

General equation of ellipse : [tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}[/tex]

Given: Vertices of ellipse : (± 9,0)

Since the vertices are of the form (± a, 0).

i.e. a=9

Thus, the major axis is along x-axis.

Also, foci of the ellipse = (±5,0)

Since, foci is of the form (± c,0), i.e. c=5

Since

[tex]c^2=a^2-b^2\\\\\Rightarrow\ 5^2= 9^2-b^2\\\\\Rightarrow\ b^2=81-25\\\\\Rightarrow\ b^2=56[/tex]

Equation of ellipse :

[tex]\dfrac{x^2}{9^2}+\dfrac{y^2}{56}=1\\\\\Rightarrow\ \dfrac{x^2}{81}+\dfrac{y^2}{56}=1[/tex]

Hence, the required equation : [tex]\dfrac{x^2}{81}+\dfrac{y^2}{56}=1[/tex]

Answer:

  BC/BE = FG/FI

Step-by-step explanation:

Corresponding segments are proportional:

  BC/BE = FG/FI

Answer:

n=16 kg

c=44 kg

Step-by-step explanation:

Let

n=nuts at $2.50 per kg

c=cereal at $1 per kg

n+c=60 (1)

2.5n + c=1.40(60) (2)

From (1)

n=60-c

Substitute n=60-c into (2)

2.5n + c=1.40(60)

2.5(60-c) +c=84

150-2.5c+c=84

-1.5c=84-150

-1.5c= -66

Divide both sides by -1.5

c=44 kg

Substitute c=44 into (1)

n+c=60

n+44=60

n=60-44

=16

n=16 kg

The amount of nuts is 16 kg and cereal mixture is 44 kg to obtain 60 kg of a mix that will sell for $1.40 per kg.

Answer: [tex]f(x)=2(0.5)^x[/tex]

Step-by-step explanation:

Given, the exponential function [tex]y = ab^x[/tex] for a graph that includes (–3, 16) and (–1, 4).

On putting these points, we will have

[tex]f(-3)=16=ab^{-3}\\\\ f(-1)=4=ab^{-1}[/tex]

Now,

[tex]\dfrac{f(-3)}{f(-1)}=\dfrac{16}{4}=\dfrac{ab^{-3}}{ab^{-1}}\\\\\Rightarrow\ \dfrac{4}{1}=\dfrac{b^{-3}}{b^{-1}}\\\\\Rightarrow\ \dfrac{4}{1}=\dfrac{b}{b^3}=\dfrac{1}{b^2}\\\\\Rightarrow\ b^2=\dfrac{1}{4}\\\\\Rightarrow\ b=\pm\dfrac{1}{2}=\pm0.5[/tex]

since the multiplicative factor cannot be negative, so b= 0.5.

At b= 0.5

[tex]4=a(0.5)^{-1}\\\\\Rightarrow\ 4=a(\dfrac{1}{2})^{-1}\\\\\Rightarrow\ 4=a(2)\\\\\Rightarrow \ a=2[/tex]

So, the required function is [tex]f(x)=2(0.5)^x[/tex].

Answer:

[tex]\boxed{3.464}[/tex]

Step-by-step explanation:

Calculate the square root.

[tex]\sqrt{12} = 3.46410161514[/tex]

Approximate the value.

[tex]\sqrt{12} \approx 3.464[/tex]

Answer:

d

Step-by-step explanation:

to find the square root of a # see how many times a # can go into the root, find the # with the greatest value