Which is the equation of the line with a slope of 9 that goes through the point (1, 10.6)?

Answer:

True

Step-by-step explanation:

64x³ + 125

64x³ = (4x)³ ← a perfect cube

125 = 5³ ← a perfect cube

Thus 64x³ + 125 ← is a sum of cubes

It is true that the expression which is given below is a sum of cubes.

The given expression is:

                          [tex]64x^{3} +125[/tex]

As we can see that there are two terms in it:

one is [tex]64x^{3}[/tex] and the second one is [tex]125[/tex].

So, at first, we will see [tex]64x^{3}[/tex]        

[tex]64x^{3}=4^{3} *x^{3}[/tex]

from the above, we can state that [tex]64x^{3}[/tex] is a cube of [tex]4x[/tex].

Now, we will look at [tex]125[/tex].

So, [tex]125=5^{3}[/tex]

Therefore, we can also state that [tex]125[/tex] is a cube of [tex]5[/tex].

Hence, the given statement is true.

The sum of cubes (a3 + b3) formula is expressed as a3 + b3 = (a + b) (a2 - ab + b2).

Sum of cubes:The sum of a cubed of two binomial is equal to the cube of the first term, plus three times the square of the first term by the second term, plus three times the first term by the square of the second term, plus the cube of the second term.

The formula to find the sum of cubes of n natural numbers is S = [n2 (n + 1)2]/4, where n is the count of natural numbers that we take.

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Answer: 11

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

the prime numbers (1-15 is the furthes i will go for this) are 2,3,5,7,11,13

as you can see the smallest two didget prime number is 11------------

Answer:

[tex]y=-\frac{1}{16}x^2[/tex]

Step-by-step explanation:

The focus of the parabola is (0,-4)

and the directrix is y=4.

The equation of this parabola is given by:

[tex]x^2=-4py[/tex]

The vertex of this parabola is at the origin.

The value of p is the distance from the vertex to the focus.

p=0--4=4

The equation of the parabola is

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

[tex]x^2=-16y[/tex]

Or

[tex]y=-\frac{1}{16}x^2[/tex]

Answer: [tex]x=7[/tex]

Step-by-step explanation:

By the Intersecting Secants Theorem, we know that:

[tex](5)(x+5)=(6)(6+4)[/tex]

Having this, we can find the value of "x" by solving for "x":

Applying Distributive property:

[tex](5)(x+5)=(6)(24)\\5x+25=60[/tex]

Subtract 25 from both sides of the equation:

[tex]5x+25-25=60-25\\5x=35[/tex]

And finally dviding both sides of the equation by 5, we get:

[tex]\frac{5x}{5}=\frac{35}{5}\\x=7[/tex]

Answer:

35/5 it would be 35 over 5

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

(x+2)(x^2+1)

=(x+2)(x+1)(x+1)

Answer:

( x + i)(x -i) ( x +2).

Step-by-step explanation:

Given  : x³ + 2x² +x +2.

To find :  complete factorization of the polynomial below.

Solution : We have given x³ + 2x² +x +2.

On taking common x² from first two terms and 1 from last two terms .

x² ( x +2) +1 (x +2).

On grouping

(x²  +1) ( x +2).

Now factor of (x²  +1) become ( x + i)(x -i) in complex form .

Factors are  ( x + i)(x -i) ( x +2).

Therefore,  ( x + i)(x -i) ( x +2).

Answer:

[tex]\boxed{\text{\$2313.40}}[/tex]

Step-by-step explanation:

The tax rate is $3.78/$100 assessed

[tex]\text{Tax} = \text{\$61 200 assessed} \times \dfrac{\text{\$3.78}}{\text{\$100 assessed}}[/tex]

Cancel the $100 assessed.

612 × $3.78 = $2313.40

Angela's real estate tax will be [tex]\boxed{ \textbf{\$2313.40}}[/tex]

Answer:

Option D. 8

Step-by-step explanation:

we have

[tex]f(x)=\frac{x^{2}-16 }{x-4}[/tex]

Remember that

[tex]x^{2}-16 =(x+4)(x-4)[/tex]

substitute

[tex]f(x)=\frac{(x+4)(x-4)}{x-4}[/tex]

Remove the discontinuity at x=4

Simplify

[tex]f(x)=(x+4)[/tex]

so

Find the value of f(4)

For x=4

[tex]f(4)=(4+4)=8[/tex]

Answer:

8

Step-by-step explanation:

I have the plato platform

First of all, you have to send the measurements; otherwise, there would not be an answer

Answer:   A) [tex](x,y)\to(4x,4y)[/tex]

Step-by-step explanation:

The rule of dilating a shape by scale factor k centered at the origin is given by :-

[tex](x,y)\rightarrow (kx,ky)[/tex]  [We multiply k to the coordinates of pre-image ]

It means Option C) and D) is incorrect.

From the given graph , it can be observe that quadrilateral R'S'T'U' (image) is larger than the RSTU (pre-image) .

It means the scale factor should be greater than 1. [∵ Scale factor for enlargement is k>1]

Then, Option B is also incorrect.

Hence, the rule yields the dilation of the figure RSTU centered at the origin is given by option A)

i.e. [tex](x,y)\to(4x,4y)[/tex]

Answer:

3/7

Step-by-step explanation:

its 3/7 because there are 3 weekend days and there are 7 days in total in one week, so out of the week there is 3 weekend days.

i hope this helps :)

The probability will be "[tex]\frac{1}{7}[/tex]". A further solution is below.

According to the question,

Number of days in a week,

Number of weekend,

Now,

The probability of you picking weekend day from the days of the week will be:

= [tex]\frac{Number \ of \ weekend}{Number \ of \ days \ in \ week}[/tex]

By substituting the values, we get

= [tex]\frac{1}{7}[/tex]

Thus the response above is appropriate.

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Answer:

about 32.9

Step-by-step explanation:

By looking at the triangle, you can see that there is both an angle and a side provided. This allows you to use trigonometry (sin, cos, tan). You have to use tan to find the answer since it is used when you have either the opposite side or adjacent side and are solving for one of them. You take the tangent of the angle and set it equal to the opposite over the adjacent (see image attached).

I hope this helps.

Also sorry that the image is the wrong way, but it wouldn't let me attach it the right way.

QUESTION 1

Given a right triangle, the unknown side is opposite to the 35° angle.

The side adjacent to this angle is 47 units.

We use the tangent ratio to get:

[tex] \tan(35 \degree) = \frac{opposite}{adjacent} [/tex]

[tex] \tan(35 \degree) = \frac{x}{47} [/tex]

[tex] x = 47\tan(35 \degree)[/tex]

[tex]x = 32.9units[/tex]

to the nearest tenth.

QUESTION 2

The given angle is 47°

The opposite side is x units.

The adjacent side is 40 units.

We again use the tangent ratio to obtain:

[tex] \tan(47 \degree) = \frac{x}{40} [/tex]

[tex]x = 40\tan(47\degree) [/tex]

[tex]x = 42.9units \: to \: the \: nearest \: tenth[/tex]

Answer:

see explanation

Step-by-step explanation:

Given

[tex]\frac{x^2-9}{x^2-3x}[/tex]

Factorise the numerator/denominator

x² - 9 = (x - 3)(x + 3) ← difference of squares

x² - 3x = x(x - 3) ← common factor of x

The fraction simplifies to

[tex]\frac{(x-3)(x+3)}{x(x-3)}[/tex] ← cancel (x - 3) on numerator/denominator

= [tex]\frac{x+3}{x}[/tex]

5/25 = x/20

To solve a proportion cross multiply:

(5 * 20) = (25 * x)

Simplify:

100 = 25x

Divide both sides by 25:

x = 100/25

x = 4

Answer:

A

Step-by-step explanation:

The triangle is being scaled down by a factor of 1/4.  So Q'R'S is smaller than QRS because the scale factor is less than 1.  Answer A.

Answer:\

The answer is A :) I took the assignment

Answer:

2^ .3^.5  

Step-by-step explanation:

We need to obtain factors of 180 which are prime numbers

2^=4

3^=9

4.9.5 = 180

I believe it’s B of joy them A

Answer:

A

Step-by-step explanation:

Got a 100

the concept is to find the value of h

Answer:

it is an algebraic expression (answer is h = -2 )

Simplify the expression

−4h−6 + 15 = 17

(Combine Like Terms)

(−4h)+(−6+15)=17

−4h + 9 = 17

Step 2: Subtract 9 from both sides.

−4h + 9 − 9 = 17 − 9

−4h=8

Step 3: Divide both sides by -4.

[tex]\frac{-4h}{-4}[/tex] = [tex]\frac{8}{-4}[/tex]

h = -2

Step-by-step explanation:

Question 1:

Substitution.

x+y=2

y=-x+2

2x+(-x+2)=4

x=2

(2)+y=2

y=0

Solution: (2,0)

There is one solution

Question 7 is too confusing, just find where the points intersect at (-5,2).

Question 9:

Elimination.

(-1)y=2x+6

y=2x+2

New: -y=-2x-6

0=-4

No Solution

Question 11:

Just look at explanations.

It's (5,17) both lines etc..

Final answer:

The set of equations for Line A and Line B has one solution. The graph correctly represents the solution (-5, 2) if the lines intersect 5 units to the left and 2 units up. Equations C and D have no solution since the lines are parallel, and the solution to Lines C and D is (5, 17), with both lines passing through this point.

Explanation:

Question 1: To determine the relationship between Line A: x + y = 2 and Line B: 2x + y = 4, we can solve for y in both equations.

For Line A, y = 2 - x.

For Line B, y = 4 - 2x.

Since the coefficients of x are different in the two equations, and the y-intercepts are also different, the lines are not parallel nor identical. Therefore, they intersect at exactly one point, which means there is one solution to the set of equations.

Question 7: The coordinates of the solution is given as (-5, 2). Among the options, the one showing the lines intersecting at the point 5 units to the left and 2 units up represents the correct set of lines, so the graph that corresponds to this description contains the solution.

Question 9: Comparing the two equations: Equation C: y = 2x + 6 and Equation D: y = 2x + 2, we see that both have the same slope but different y-intercepts. Because they have the same slope but different y-intercepts, these lines are parallel and never intersect. Hence, there is no solution to this set of equations.

Question 11: To find the intersection point, we set the equations of Line C: y = x + 12 and Line D: y = 3x + 2 equal to each other and solve for x:

x + 12 = 3x + 2

Subtract x from both sides: 12 = 2x + 2

Subtract 2 from both sides: 10 = 2x

Divide by 2: x = 5

We then substitute x = 5 into one of the equations to find y:

For Line C: y = 5 + 12 = 17.

Hence, the solution to the set of equations is (5, 17), and both lines pass through this point, which lies between the two axes, but that is irrelevant to why it is the solution.

5x^5•y^2 + 15x^2•y^3 + x^3•y^5

GCF = (x^2)(y^2)

The greatest common factor of the given polynomial is x²y².

The GCF (Greatest Common Factor) of two or more numbers is the greatest number among all the common factors of the given numbers. The GCF of two natural numbers x and y is the largest possible number that divides both x and y without leaving any remainder.

The given expression is 5x⁵y²+15x²y³+x³y⁵.

In the given expression, there are three terms 5x⁵y², 15x²y³ and x³y⁵

5x⁵y²=5×x×x×x×x×x×y×y

15x²y³=3×5×x×x×y×y×y

x³y⁵ =x×x×x×y×y×y×y×y

So, the common factor = x×x×y×y

= x²y²

Therefore, the greatest common factor is x²y².

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Answer:

[tex]\large\boxed{\dfrac{3s^2+19s-4}{(s-1)^2(s+5)}=\dfrac{3s^2+19s-4}{s^3+3s^2-9s+5}}[/tex]

Step-by-step explanation:

[tex]s^2-2s+1=s^2-s-s+1=s(s-1)-1(s-1)=(s-1)(s-1)=(s-1)^2\\\\s^2+4s-5=s^2+5s-s-5=s(s+5)-1(s+5)=(s+5)(s-1)\\\\\text{Therefore}\ LCD\ \text{is}\ (s-1)^2(s+5).[/tex]

[tex]\dfrac{3s}{s^2-2s+1}+\dfrac{4}{s^2+4s-5}=\dfrac{3s(s+5)}{(s-1)^2(s+5)}+\dfrac{4(s-1)}{(s-1)^2(s+5)}\\\\\text{use the distributive property}\\\\=\dfrac{(3s)(s)+(3s)(5)+(4)(s)+(4)(-1)}{(s-1)^2+(s+5)}=\dfrac{3s^2+15s+4s-4}{(s-1)^2(s+5)}\\\\=\dfrac{3s^2+19s-4}{(s-1)^2(s+5)}[/tex]

Divide the number of black marbles by 10, the total number of marbles. If there is one black marble, the chances of choosing a black marble is 1/10.

Answer:

1 3 5set/dhzhhhhhhhhhhhhhhhhhhh

The expression [tex]\(4^5/3\)[/tex] is indeed equivalent to[tex]\(\sqrt[3]{4^5}\)[/tex].

The correct option is (a).

To demonstrate that the expression[tex]\(4^5/3\) is equivalent to \(\sqrt[3]{4^5}\)[/tex], we can apply the following properties:

1. Radical to Exponent Property:

  - The expression [tex]\(\sqrt[3]{4^5}\) can be rewritten as \(4^{5/3}\)[/tex].

  - This property allows us to convert a radical expression to an exponent expression by raising the base to the reciprocal of the index of the radical.

2. Exponent to Radical Change Property:

  - The fraction exponent [tex]\(5/3\)[/tex] can be expressed as a radical: [tex]\(\sqrt[3]{4^5}\)[/tex].

down step-by-step:

1. Start with the given expression: [tex]\(4^5/3\)[/tex].

2. Apply the **Radical to Exponent Property: [tex]\[4^5/3 = 4^{5/3}\][/tex]

3. Now, express the fraction exponent as a radical:

[tex]\[4^{5/3} = \sqrt[3]{4^5}\][/tex]

Therefore, the expression [tex]\(4^5/3\)[/tex] is indeed equivalent to[tex]\(\sqrt[3]{4^5}\)[/tex].

Answer:

7. 5/6 8. 3/12

Step-by-step explanation:

Answer:

Well we only have one star in our solar system so the Sun?

The sun is the biggest star. The sun is at the center of our solar system and is the nearest star to Earth. The sun is a huge ball of very hot, burning gas. The sun sends out heat and light into space.

Answer:

x=-9

Step-by-step explanation:

5x+8-3x=-10

2x+8=-10

2x=-18

Divide both sides by 2 to get

Answer is -9

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-1}{ h},\stackrel{1}{ k})\qquad \qquad radius=\stackrel{3}{ r}\\[2em] [x-(-1)]^2+[y-1]^2=3^2\implies (x+1)^2+(y-1)^2=9[/tex]

The equation of the circle will be ( x + 1 )² + ( y - 1 )² = 9.

All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

The equation of the circle can be written as,

( x - h)² + ( y - k )² = r².

Given that the circle below is centered at (-1, 1) and has a radius of 3. The equation of the circle will be written as,

( x - h)² + ( y - k )² = r².

( x + 1 )² + ( y - 1 )² = 9.

Hence, the equation can be written as ( x + 1 )² + ( y - 1 )² = 9.

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i need a life fast plz

Answer:

[tex]m=0.002kg[/tex]

Step-by-step explanation:

The given formula is:

[tex]E=mc^2[/tex]

Divide both sides by [tex]c^2[/tex].

[tex]\implies \frac{E}{c^2}=\frac{mc^2}{c^2}[/tex]

Cancel out the common factors to get;

[tex]\implies \frac{E}{c^2}=m[/tex]

[tex]m=\frac{E}{c^2}[/tex]

When [tex]E=1.8\times10^{14}J[/tex] and [tex]c=300,000,000ms^{-1}[/tex], then

[tex]m=\frac{1.8\times10^{14}}{300,000,000^2}[/tex]

This simplifies to

[tex]m=0.002kg[/tex]

Answer:

[tex]h=V/(\pi r^{2})[/tex]

Step-by-step explanation:

we know that

The formula for the volume of a cylinder is equal to

[tex]V=\pi r^{2} h[/tex]

where

r is the radius

h is the height of the cylinder

Solve for h

That means -----> isolate the variable h

Divide by πr² both sides

[tex]V/(\pi r^{2})=h[/tex]

Rewrite

[tex]h=V/(\pi r^{2})[/tex]

Answer:

The formula for the Volume of a cylinder [note: area of circle times height]:

     V = Πr2h

 Solve for r in terms of h

     r2 = V / (Πh)

For this cylinder, V=539.

     r2 = 539 / (Πh)

     r = √(539/(Πh))

This is also:

     r = 23.1 / √(Πh)

     r = 13.1 / √h

[tex]

7x-4=5x+15 \\

2x=11

x=\boxed{\frac{11}{2}}

[/tex]

Hope this helps.

r3t40