Help me please!!
A watering can dispenses water at the rate of 0.3 gallon per minute. The original volume of water in the can was 7 gallons. Which set of ordered pairs shows the volume of water in the can in gallons (y), as a function of time in minutes (x), from the first minute after the can starts dispensing water?

{(1, 6.7), (2, 6.4), (3, 6.1)}
{(1, 7.0), (2, 6.7), (3, 6.4)}
{(6.7, 1), (6.4, 2), (6.1, 3)}
{(7.0, 1), (6.7, 2), (6.4, 3)}

Explicit formula [tex]a_{n} =8n+15[/tex]

Recursive formula [tex]\left \{ {{a_{1} =23} \atop {a_{n}=a_{n-1}+8 }} \right.[/tex]

To solve this problem we have to use an arithmetic sequence. The cost of renting a kayak for 1 hour is $23, each additional hour is $8 more. So, the first element of the secuence will be 23 for one hour, then each addittional hour will be 23 + 8, making the secuence:

{23, 31, 39, 47, 55,.....,n}

Writing a recursive formula of the form [tex]a_{n} =a_{n-1} +d[/tex] where [tex]a_{n}[/tex] is the nth term, n the number of terms, and d the common difference in the secuence.

The common difference of the secuence {23, 31, 39, 47, 55,.....,n}. So, the first term is [tex]a_{1} =23[/tex], and the common diffenece is d = 8 which is the difference between each term.

[tex]\left \{ {{a_{1} =23} \atop {a_{n} =a_{n-1}+8 }} \right.[/tex]

Writing a explicit formula of the form [tex]a_{n} =a_{1} +d(n-1)[/tex] where where [tex]a_{n}[/tex] is the nth term, n the number of terms, [tex]a_{1}[/tex] the first term of the secuence, and d the common difference in the secuence.

With [tex]a_{1}=23[/tex], and d = 8:

[tex]a_{n} =23+8(n-1)[/tex]

[tex]a_{n} =23+8n-8[/tex]

[tex]a_{n} =8n+15[/tex]

Answer:

Step-by-step explanation:

The standard form of an equation of a circle:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

where

[tex](h, k)[/tex] - center

[tex]r[/tex] - radius

We have:

[tex](x-7)^2+(y-10)^2=4[/tex]

Therefore

[tex]h=7,\ k=10,\ r^2=4\to r=\sqrt4\to r=2[/tex]

The standard form of the equation of a circle is

(x - h)2 + (y - k)2 = r2

Where (h, k) is the center,

r is the radius

(x - 7)2 + (y - 10)2 = 4 [Given]

This is rewritten as (x - 7)2 + (y - 10)2 = 22

Comparing it with the standard form

(h, k) = (7, 10)

The radius of the circle r = 2 units

The radius of a circle is  Option A. 2 units

The diameter is a straight line that passes through the center of the circle. The radius is half of the diameter. It starts from a point on the circle, and ends at the center of the circle.

A straight line extending from the center of a circle or sphere to the circumference or surface: The radius of a circle is half the diameter. the length of such a line.

The radius of a circle is the distance from the center of the circle to any point on its circumference. It is usually denoted by 'R' or 'r'. This quantity has importance in almost all circle-related formulas. The area and circumference of a circle are also measured in terms of radius.

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Solution:

A

Step-by-step explanation:

It's y =-2x³

Hope it helps you..☺

The graph of y = x³ is transformed as y = -6x³.

It's a unique type of connection with a predetermined domain and range, and every value in the domain exists associated with precisely one value in the range, according to the function.

The given equation exists, y = x³

The graph of y = x³ describes the transformed function.

Therefore, the correct answer is option B. y = -6x³.

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Answer:

[tex]18g + 7 - 12g - 3 = 6g + 4[/tex]

Step-by-step explanation:

[tex]18g+7-12g-3\\=18g-12g+7-3\\=6g+7-3\\=6g+4[/tex]

Answer:

7

Step-by-step explanation:

Replace a with 5 and b with 3.

5+3-1=7

Answer:

7.

Step-by-step explanation:

Substitute for a and b in the given identity:

5 * 3 = 5 + 3 - 1

= 8 - 1

= 7.

Answer:

[tex]x=3\\y=-1\\\\(3,-1)[/tex]

Step-by-step explanation:

We have the following system of equations

[tex]4x-3y=15\\2x+2y=4[/tex]

To solve the system of equations multiply the second equation by -2 and add it to the first equation

[tex]-2*(2x+2y)=-2*4[/tex]

[tex]-4x - 4y=-8\\4x-3y=15[/tex]

-------------------

[tex]-7y = 7\\y=-1[/tex]

Now substitute the value of y in any of the two equations and solve for the variable x

[tex]4x-3(-1)=15[/tex]

[tex]4x+3=15[/tex]

[tex]4x=15-3[/tex]

[tex]4x=12[/tex]

[tex]x=\frac{12}{4}[/tex]

[tex]x=3[/tex]

Finally the solution is:

(3, -1)

Answer:$0.08 per pen

Step-by-step explanation:

$1.60/20=0.08

Hope this helps :)

Answer:

So, the inverse of function

[tex]f(x) = \frac{-1}{2} \sqrt{x+3}[/tex] is [tex]f^{-1}(x)= 4x^2-3[/tex]

Step-by-step explanation:

We need to find the inverse of the given function

[tex]f(x) = \frac{-1}{2} \sqrt{x+3}[/tex]

To find the inverse we replace f(x) with y

[tex]y = \frac{-1}{2} \sqrt{x+3}[/tex]

Now, replacing x with y and y with x

[tex]x = \frac{-1}{2} \sqrt{y+3}[/tex]

Now, we will find the value of y in the above equation

Multiplying both sides by -2

[tex]-2x = \sqrt{y+3}[/tex]

Taking square on both sides

[tex](-2x)^2 = (\sqrt{y+3})^2[/tex]

[tex]4x^2 = y+3[/tex]  

Finding value of y

[tex]y = 4x^2-3[/tex]

Replacing y with f⁻¹(x)

[tex]f⁻¹(x)= 4x^2-3[/tex]

So, the inverse of function

[tex]f(x) = \frac{-1}{2} \sqrt{x+3}[/tex] is [tex]f^{-1}(x)= 4x^2-3[/tex]

ANSWER

[tex]f^{ - 1} (x) =4 {x}^{2}- 3[/tex]

EXPLANATION

A function will have an inverse if and only if it is a one-to-one function.

The given function is

[tex]f(x) = - \frac{1}{2} \sqrt{x + 3} \: \: where \: \: x \geqslant - 3 [/tex]

To find the inverse of this function, we let

[tex]y=- \frac{1}{2} \sqrt{x + 3}[/tex]

Next, we interchange x and y to get,

[tex]x=- \frac{1}{2} \sqrt{y+ 3}[/tex]

We now solve for y.

We must clear the fraction by multiplying through with -2 to get;

[tex] - 2x = \sqrt{y + 3} [/tex]

Square both sides of the equation to get:

[tex](- 2x)^{2} = (\sqrt{y+ 3}) ^{2} [/tex]

[tex]4x^{2} = y + 3[/tex]

Add -3 to both sides

[tex]4 {x}^{2} - 3 = y[/tex]

Or

[tex]y = 4 {x}^{2}- 3[/tex]

This implies that,

[tex]f^{ - 1} (x) =4 {x}^{2}- 3[/tex]

This is valid if and only if

[tex]x \geqslant - 3[/tex]

For this case we must find an expression equivalent to:

[tex]\frac {10x ^ 6y ^ {12}} {- 5x ^ {- 2} y^ {- 6}}[/tex]

We have to:

[tex]\frac {10} {- 5} = - 2[/tex]

Now, by definition of division of powers of equal base, we put the same base and subtract the exponents. Rewriting the expression we have:

[tex]-2x ^ {6 - (- 2)} y^ {12 - (- 6)} =\\-2x ^ {6 + 2} y ^ {12 + 6} =\\-2x ^ 8y ^ {18}[/tex]

Answer:

Option B

Note that perimeter of rectangle [tex]P=2l+2w[/tex]

So we have to solve for width or w.

[tex]P=2l+2w[/tex]

[tex]30=2\times10+2w[/tex]

[tex]w=5[/tex]

Width of a rectangle is 5 units.

Hope this helps.

r3t40

Final answer:

To solve the equation 9x + 4 = 11 for x using the change of base formula log base b of y equals log y over log b, isolate x on one side of the equation, subtract 4 from both sides, then divide both sides by 9.

Explanation:

To solve the equation 9x + 4 = 11 for x using the change of base formula log base b of y equals log y over log b, we need to isolate x on one side of the equation. Here's how to do it:

Therefore, the solution to the equation is x = 7/9.

Answer:

2.5

Step-by-step explanation:

because half of 5 is 2.5

Range is all the y values in this case that would be...

{-1, 4, 11, 13}

Keep in mind that there are different ways to show range. The one I showed it just one of them

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

[tex]\large\boxed{(g\circ f)(2)=1296}[/tex]

Step-by-step explanation:

[tex]f(x)=-x+8,\ g(x)=x^4\\\\(g\circ f)(x)=g\bigg(f(x)\bigg)\\\\(g\circ f)(x)=\bigg(-x+8\bigg)^4\\\\(g\circ f)(2)\to\text{put x - 0 to the equation of the function:}\\\\(g\circ f)(2)=(-2+8)^4=(6)^4=1296[/tex]

Answer:

I believe it's C.

Step-by-step explanation:

Hope my answer has helped you!

Answer:

Mykel you should have 2 rows of -5

Step-by-step explanation:

so the first row should have 5 red blocks and the second row should also have 5 red blocks. The reason it should be red is because red stands for negative.

Answer:

The mistake is he said"The equation has infinitely many solutions."

But based on what he was solving for, this equation does not have any solutions, so that's his mistake.

The other answer is correct, but the answer is D if you just want the answer.

Answer:

280 mL

Step-by-step explanation:

If x is the amount of 35% solution and y is the amount of pure water, then:

0.15 = (0.35x + 0y) / (x + y)

0.15 = (0.35x) / (x + y)

Given that x = 210 mL:

0.15 = (0.35×210) / (210 + y)

210 + y = 490

y = 280

Answer:

x=-1 or (-1,0)

Step-by-step explanation:

(-4 +- sqrt(4^2-4(5)(-1)))/2*5

(-4 +- sqrt(16+20))/10

(-4 +- sqrt(36))/10

(-4 +- 6)/10

x= (-4+6)/10 = 2/10 = 1/5 = 0.2

x= (-4-6)/10 = -10/10 = -1

x-intercepts: (0.2,0), (-1,0)

Answer:

AB or x =6sqrt(3) (which is what the pic ask for)

but you ask for AC which is 9

Step-by-step explanation:

The hypotenuse is twice the length of the short leg.

The short leg is 3sqrt(3) (because I see it is opposite the smallest angle which is 30 in this case).

So the hypotenuse is twice 3sqrt(3) which is 6sqrt(3)

You are also asking for AC though... That is the short leg times sqrt(3) so that measurement is 3sqrt(3)*sqrt(3)=3(sqrt(3*3))=3(3)=9

Answer:

8,000,000

Step-by-step explanation:

all you have to do is multiply the 4*2 then add the missing 0's for example so its 8 then add the six zeros behind the 8

The value of the multiplication is 8, 000 , 000

First, we need to know that multiplication is an arithmetic operation.

Also, PEDMAS is the mathematical acronym used to represent the different arithmetic operations.

They are given as;

From the information given, we have that;

2,000 times 4,000

This is represented as;

2000 ×4000

Multiply the values

8, 000 , 000

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Step one: 3x+4y=20; 10=40-3y

Step two: 3y=40-10, so y=(40-10)/3=10

Step three: 3x+4*10=20

Step four: 3x=20-40=-20, so x=-20/3=-6.66666...~ -6.67

Answer:

Step-by-step explanation:

[tex]\text{The formula of a perimeter of a rectangle:}\\\\P=2(l+w)\\\\l-length\\w-width\\\\\text{We have}\ l=(w+24)\ in,\ P=128\ in\\\\\text{Substitute:}\\\\128=2(w+24+w)\qquad\text{divide both sides by 2}\\\\64=2w+24\qquad\text{subtract 24 from both sides}\\\\40=2w\qquad\text{divide both sides by 2}\\\\20=w\to w=20\ in\\\\l=20+24=44\ in[/tex]

Answer:

0.3.

Step-by-step explanation:

The residual of a data point is equal to the observed value minus the predicted value. (Stat Trek)

What's the predicted y-value of a point with [tex]x = 5[/tex] based on this best-fit regression line?

[tex]y = -0.2\times 5 + 1.7 = 0.7[/tex].

The observed value here is [tex]y = 1[/tex]. As a result, the residual for this point is [tex]1 - 0.7 = 0.3[/tex].

Answer: 0.2

Step-by-step explanation:

Step-by-step explanation:

Let's do the volume first. Volume of any prism is the area of the base times the height.

V = Ah

The base is a large square with a smaller rectangle cut from the corner, so its area is:

A = (14)(14) - (7)(10)

A = 126

So the volume is:

V = (126)(6)

V = 756 m^3

Now the surface area of a prism is the area of the bases plus the base perimeter times the height:

S = 2A + Ph

We already found the area of the base. Now we just have to add the perimeter times height.

S = 2(126) + (14 + 14 +7 + 10 + 7)(6)

S = 480 m^2

Answer:

[tex]\large\boxed{\log_2\dfrac{x^3}{\left(\dfrac{3}{x+4}\right)}}[/tex]

Step-by-step explanation:

[tex]\text{Use}\\\\\log_ab^n=n\log_ab\\\\\log_a\left(\dfrac{c}{d}\right)=\log_ac-\log_ad\\\\==============================[/tex]

[tex]\text{We have:}\\\\3\log_2x-(\log_23-\log_2(x+4))\\\\=\log_2x^3-\log_2\dfrac{3}{x+4}\\\\=\log_2\dfrac{x^3}{\frac{3}{x+4}}[/tex]

The expression 3log(2)3 - log(2)(x+4) can be simplified by using the logarithmic laws, resulting in the final single logarithm of log2(39 / (x+4)).

The original expression, 3log(2)3 - log(2)(x+4), can be simplified using a few laws of logarithms. Firstly, using the rule that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number, we can simplify. We find that the expression becomes log(2)33 - log(2)(x+4). Secondly, by applying the rule that the logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers, we can further simplify. The final expression is now log2(39 / (x+4)). This is the expression written as a single logarithm.

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Answer:

The quotient is 2x^2 - x + 1.

Step-by-step explanation:

If x + 1 is the divisor in long division, then -1 is the divisor in synthetic division:

-1   /   2    1    0    1

              -2    1    -1

    ----------------------

       2      -1     1    0

The quotient is 2x^2 - x + 1.  The coefficients were obtained through synthetic division.

Answer:

A. 40 mph

Step-by-step explanation:

A bird flies 2/3 miles per minute. You are trying to solve miles per hour.

Note that there are 60 minutes in an hour. Multiply 2/3 with 60:

2/3 x 60 = (2 * 60)/3 = (120)/3 = 40

A. 40 mph is your answer.

~

Answer:

D

Step-by-step explanation:

From the graph we can see:

Given the information extract, we can rule out A, B, and C immediately. Answer choice D is right.

Answer:

B

Step-by-step explanation:

x is the number of years of experience.

In the graph, the point (y) is not shown for 5 years of experience but we can easly figure this out by plugging in 5 into x of the equation of best fit given.

Hence

[tex]y= 1.3x +5.5\\y= 1.3(5) +5.5\\y=12[/tex]

So, the best estimate is $12 per hour, the correct answer is B

Answer:

its b

hope its right