What kind of transformation does the graph show?
A) flip
B) reflection
C) rotation
D) slide

Answer:

l = (S - πr²) / π

Step-by-step explanation:

The problem gives us the formula for the surface area of a cone S, we will solve the formula for l.

The formula is

S = πl + πr²

If we take the πr² to the other side, we get:

S - πr² = πl

Now we divide by π, and we get:

(S - πr²) / π = l

Therefore solving for l, we get that

l = (S - πr²) / π.

Answer:

x = 9 and y = 5

Step-by-step explanation:

From the given figure :

In ΔLNM ,

LN = NM = LM

This shows that all the sides of the triangle are given to be equal.

And the triangle whose all sides are equal is called equilateral triangle and in an equilateral triangle the measure of its each angle is 60°

⇒ ∠L = ∠N = ∠M = 60°

Now, ∠N = 60°

⇒ 7x - 3 = 60

⇒ 7x = 63

⇒ x = 9

Also, ∠M = 60°

⇒ 11y + 5 = 60

⇒ 11y = 55

⇒ y = 5

Answer: x=9

Step-by-step explanation:

i did the test and got it right lol

Answer:

y = 3+6x

Step-by-step explanation:

Let us substitute x = 0, then we get

y = 3

This is not the case as the graph clearly shows that when x = 3, then y = 2

y = 2+6x

when x = 0 then y = 2 which valid from the graph

Now put x values from the table into the equation

y = 2+6×-1

⇒y = -4

x = 0 already solved

x = 2

y = 2+6×2

⇒y = 14

All the values fit in the equation. So, the bottom two options are valid.

Hence, the first equation is not valid.

The distance walked together, is the sum of their distances.

Molly walked 1.37 miles farther  than her brother and sister

The given parameters are:

[tex]\mathbf{Molly = 3.45\ miles}[/tex]

[tex]\mathbf{Sister = 1.23\ miles}[/tex]

[tex]\mathbf{Brother = 0.85\ miles}[/tex]

The combined distance walked by her brother and her sister is:

[tex]\mathbf{Both = Sister + Brother}[/tex]

Substitute known values

[tex]\mathbf{Both =1.23\ miles + 0.85\ miles}[/tex]

Evaluate like terms

[tex]\mathbf{Both =2.08\ miles}[/tex]

The distance Molly walked farther is calculated as follows:

[tex]\mathbf{Farther = Molly - Both}[/tex]

Substitute known values

[tex]\mathbf{Farther = 3.45\ miles - 2.08\ miles}[/tex]

Evaluate like terms

[tex]\mathbf{Farther = 1.37\ miles}[/tex]

Hence, Molly walked 1.37 miles farther  than her brother and sister combined

Read more about distance at:

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Answer:

12.08 units.    

Step-by-step explanation:

We have been given that line segments JK and JL in the xy-coordinate plane both have a common endpoint J (-4,11) and midpoints at [tex]M_1 (2,16)[/tex] and [tex]M_2 (-3,5)[/tex].

To find the distance between [tex]M_1[/tex] and [tex]M_2[/tex] we will use distance formula.

[tex]\text{Distance}=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}[/tex]

[tex]x_2[/tex] and [tex]x_1[/tex] are x-coordinates of two points.

[tex]y_2[/tex] and [tex]y_1[/tex] are corresponding y-coordinates of two points.    

Let [tex]M_2[/tex] our first point, then  [tex]x_1=-3[/tex] and  [tex]y_1=5[/tex].

Let [tex]M_1[/tex] will be our second point, then [tex]x_2=2[/tex] and [tex]y_2=16[/tex]  

Upon substituting coordinates of point [tex]M_1[/tex] and [tex]M_2[/tex] in distance formula we will get,    

[tex]\text{Distance}=\sqrt{(2--3)^{2}+(16-5)^{2}}[/tex]

[tex]\text{Distance}=\sqrt{(2+3)^{2}+(11)^{2}}[/tex]

[tex]\text{Distance}=\sqrt{(5)^{2}+(11)^{2}}[/tex]  

[tex]\text{Distance}=\sqrt{25+121}[/tex]

[tex]\text{Distance}=\sqrt{146}[/tex]

[tex]\text{Distance}=12.0830459735945721\approx 12.08[/tex]  

Therefore, distance between [tex]M_1[/tex] and [tex]M_2[/tex] is 12.08 units.

Answer: 32.13

Step-by-step explanation:

Answer:

The answer is:  $32.13

multiply $9 by 80%

80% = 0.80

9 * 0.8 = 7.20

 subtract that from original price

9 - 7.20 = 1.80

 Sale price is $1.80

The change in internal energy (δe) of the system, calculated using the first law of thermodynamics, and considering that the heat and work quantities are converted to the same unit, is 1629 J.

The query you've presented seems to be about the first law of thermodynamics, which states that the change in internal energy (ΔE or in your notation, δe) of a system is equal to the heat (q) added to the system minus the work (w) done by the system. Both heat and work quantities need to be in the same units for this calculation, whereas your values are given in different units: kJ for heat and J for work. To facilitate this calculation, let's first convert the heat quantity from kJ to J (1 kJ equals 1000 J).

So, q = 0.769 kJ = 0.769 * 1000 J = 769 J.

Given, w = -860 J.

Now, according to the first law of thermodynamics, δe = q - w.

Substituting the given values, we get δe = 769 J - (-860 J) = 769 J + 860 J = 1629 J.

Therefore, the change in internal energy, δe, is 1629 J.

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Answer:

Step-by-step explanation:

Given triangle ABC and a translated triangle A'B'C'.

Coordinates of triangle ABC are

A(-1,-1)

B(-3,-3) and

C(2,-2).

Coordinates of triangle A'B'C' are

A'(3,3)

B'(1,1)

C'(6,2).

Let us check the translation is being applied there.

A(-1,-1)  ---> A'(3,3)

We can see that A(-1,-1)  ----> A'(-1+4, -1+4) to get (3,3).

Therefore, (x,y) ---> (x+4,y+4) rule is being applied there to get the translated triangle A'B'C'.

So, the correct option is first option:

Answer:  [tex]10\ m^2\ n^7[/tex]

Step-by-step explanation:

The given monomials : [tex]-50m^4n^7\text{ and }40 m^2 n^{10}[/tex]

The prime factorization of coefficients :-

[tex]50=5\times5\times2\\\\40=5\times2\times2[/tex]

GCF(50, 40)=[tex]2\times5=10[/tex]

The greatest common degree of m is 2

The greatest common degree of n is 7

So , the GCF of the given monomilas will be :-

[tex]10\ m^2\ n^7[/tex]

The correct scientific notation for the number 0.00050210 is 5.0210 x 10^(-4).

The correct scientific notation for the number 0.00050210 is 5.0210 x 10-4. In scientific notation, the decimal point is moved to the right, and the number is multiplied by a power of 10. The exponent indicates how many places the decimal point was moved.

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No, it does not.

x and x + 6 are both prime and cannot be factored.

There are no common factors to divide out.

x over x + 6 is already simplified.

If you substitute in a value for x, the fraction will not be equal to 1/6.

The expression x/(x+6) does not simplify to 1/6 because there are no common factors in the numerator and denominator that can be canceled out.

The expression x/(x+6) does not simplify to 1/6. To understand this, we need to recognize that simplification involves reducing a fraction to its simplest form by factoring or canceling common factors in the numerator and the denominator.

If x were a factor in both the numerator and the denominator, then we could simplify by canceling out the x's.

However, in the expression x/(x+6), the term x+6 in the denominator cannot be simplified with x in the numerator because they are not factors of each other. They are connected by the addition of 6, which means that there are no common factors to cancel out.

The only way x/(x+6) would simplify to 1/6 is if 'x' were to be somehow removed from the denominator, leaving only the constant 6. But since this is not the case, the fraction cannot be simplified to 1/6. Therefore, the original expression is already at its simplest form unless a specific value is given for x, which may then allow further simplification.

The measure of the angle in question is 18 degrees, as found by setting up an equation based on the relationship between an angle and its complement, and solving for the angle.

To find the measure of an angle that is 18 degrees less than one-half of the measure of its complement, first let's define the angle as x. Since the angle and its complement add up to 90 degrees, the complement is 90 - x. The given information tells us that x is 18 degrees less than half of its complement. Therefore, we can set up the equation:

x = (1/2)(90 - x) - 18

Doubling both sides gives:

2x = 90 - x - 36

Adding x to both sides and adding 36 to both sides gives:

3x = 54

Dividing by 3, we find that:

x = 18 degrees.

Therefore, the measure of the angle is 18 degrees.

Answer:

-7, 1

Step-by-step explanation:

Given quadratic equation,

[tex]2x^2+12x-14=0[/tex]

By middle term splitting,

[tex]2x^2+(14-2)x-14=0[/tex]

[tex]2x^2+14x-2x-14=0[/tex]

[tex]2x(x+7)-2(x+7)=0[/tex]

[tex](2x-2)(x+7)=0[/tex]

By the zero product property,

[tex]2x-2=0\text{ or }x+7=0[/tex]

[tex]\implies x=1\text{ or }x=-7[/tex]

Hence, the roots of the given equation are -7 and 1.

Second option is correct.