what is the initial value of the equation shown? y=-4x+3

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.

To learn more about the radius of the circle, refer

https://brainly.com/question/11699

#SPJ2

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.

https://brainly.com/question/33159023

#SPJ11

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:

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

Learn about PEDMAS at: https://brainly.com/question/345677
#SPJ6

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]

[tex]\bf (\stackrel{x_1}{6}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{3}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{3-4}{-5-6}\implies \cfrac{-1}{-11}\implies \cfrac{1}{11}[/tex]

Answer:

1/11

Step-by-step explanation:

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:

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]

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.

To learn more about transformed function

https://brainly.com/question/15810158

#SPJ2

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.

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:

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:

[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]

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:

[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:

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:

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:

Answer:$0.08 per pen

Step-by-step explanation:

$1.60/20=0.08

Hope this helps :)

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:

Yes there is GCF > 1 ⇒ (GCF = 4)

The completely factored form is 4(x - 2)(x² + 2x + 4)

Step-by-step explanation:

* Lets find the greatest common factor of the two terms

- The binomial is 4x³ - 32

- The terms of the binomial are 4x³ and 32

- The greatest common factor of 4 and 32 is 4 because both of them

  can divided by 4

∵ 4x³ ÷ 4 = x³

∵ 32 ÷ 4 = 8

∴ The greatest common factor GCF is 4

∴ 4x³ - 32 = 4(x³ - 8)

* Yes there is GCF > 1

# x³ - 8 is the difference of two cubs, it can factorize it into two

  brackets

- The first bracket has cube root of x³ and cube root of 8

- The second bracket comes from the first bracket it has three terms

# The 1st term is square the 1st term in the first bracket

# The 2nd term is the product of the 1st term and the 2nd term of the

  1st bracket with opposite sign of the 2nd term in the 1st bracket

# The 3rd term is the square of the 2nd term in the 1st bracket

* Lets do these steps with x³ - 8

∵ The first bracket = (∛x³ - ∛8)

∵ ∛x³ = x and ∛8 = 2

∴ The first bracket = (∛x³ - ∛8) = (x - 2)

- Lets make the 2nd bracket from the 1st bracket

∴ The second bracket = (x² + (x)(2) + 2²)

∴ The second bracket = (x² + 2x + 4)

∴ The factorization of x³ - 8 = (x - 2)(x² + 2x + 4)

* The completely factored form is 4(x - 2)(x² + 2x + 4)

Answer:

....Yes it is 4                                                                                                                       ....4(x-2)

Step-by-step explanation:

the screenshot shows proof :))

Answer:

I believe it's C.

Step-by-step explanation:

Hope my answer has helped you!

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:

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

Answer:

2.5

Step-by-step explanation:

because half of 5 is 2.5

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.

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

Answer: OPTION A.

Step-by-step explanation:

Find the length scale factor by dividing the known length of the larger triangle by the known length of the smaller triangle:

[tex]lenght\ scale\ factor=\frac{35}{25}=\frac{7}{5}[/tex]

Then, the  area scale factor is:

[tex]area\ scale\ factor=(\frac{7}{5})^2=\frac{49}{25}[/tex]

To find the area of the the larger triangle, multiply the area of the smaller triangle by the area scale factor. Then:

[tex]A_{(larger)}=(270ft^2)(\frac{49}{25})=529.2ft^2[/tex]

So, the option that shows an approximation of the area of the larger triangle is the option A:

[tex]A_{(larger)}[/tex]≈[tex]530ft^2[/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

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.