Answer:
C
Step-by-step explanation:
The surface area (A) of a sphere is calculated as
A = 4πr² ← r is the radius, here r = 12, hence
A = 4π × 12²
= 4π × 144 = 576π units² → C
The surface area of the sphere is 576 square units. The correct option is B.
What is surface area?The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called as the surface area.
The surface area (A) of a sphere is calculated as
A = 4πr² ← r is the radius, here r = 12, hence
A = 4π × 12²
A= 4π × 144
A = 576π units²
Hence, the correct option is B.
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Factor 7x3 - 28x2 + 3x - 12
Answer:Solution
(
−
4
)
(
7
2
+
3
)
Step-by-step explanation:
7
3
−
2
8
2
+
3
−
1
2
7x^{3}-28x^{2}+3x-12
7x3−28x2+3x−12
Grouping
1
Find one factor
Factor by grouping
Factor by grouping
Factor by grouping
(
−
4
)
(
7
2
+
3
)
{\color{#c92786}{({\color{#c92786}{x-4}})({\color{#c92786}{7x^{2}+3}})}}
(x−4)(7x2+3)
Marvin is buying a watch from his brother
for $130. His brother tells him that he
can pay $30 down and the rest in 10
equal installments.
Answer:
$30 down
and 10 installments of $10 each
Step-by-step explanation:
paying $30 down means the left price to divide into installments is : 130-30 = 100
since he will pay the rest in equal installments, we divide by the number of installments to get how much each one will be :
100/10 = $10
Lisa's dog is 11 pounds heavier than Marcia's dog. Let m represent the weight of Marcia's dog. Write a variable expression to represent the weight of Lisa's dog.
Answer:
The required variable expression is [tex]L= M + 11[/tex]
Step-by-step explanation:
Consider the provided information.
Let m represent the weight of Marcia's dog.
Let L represent the weight of Lisa's dog.
Lisa's dog is 11 pounds heavier than Marcia's dog.
That means if we add 11 pounds in Marcia's dog weight, the weight of Marcia's dog will be equal to Lisa's dog.
This can be written as:
[tex]L= M + 11[/tex]
Where m represent the weight of Marcia's dog and L represent the weight of Lisa's dog.
Hence, the required variable expression is [tex]L= M + 11[/tex]
A parallelogram has base 20 cm and height 9 cm. What is its area?
To find the area, you multiply b×h. (Base × height) b=20 and h=9. Multiply it and you will get 180. The answer is 180 cm².
The area of the parallelogram is equal to 180 square meters.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the parallelogram in a two-dimensional plane is called as the area of the parallelogram.
Given that a parallelogram has a base of 20 cm and a height of 9 cm. The area of the parallelogram is calculated by the formula,
Area of the parallelogram = Base x Height
Area of the parallelogram = 20 x 9
Area of the parallelogram = 180 square meters
Therefore, the area of the parallelogram is equal to 180 square meters.
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The Smith family has 80 movies in their collection. The types of movies are shown in the table below. Smith Family Movies Type of Movie Percentage Drama 10% Action 25% Animated/Children’s 50% Comedy 15% How many of the movies in the collection are action movies?
Answer:
20 movies
Step-by-step explanation:
no of movies= 80
action movies percentage=25%
no of action movies=25/100*80(25% of 80)
-3(-x)-6=-3x+10 solve
Answer:
[tex]\large\boxed{x=\dfrac{8}{3}}[/tex]
Step-by-step explanation:
[tex]-3(-x)-6=-3x+10\\\\3x-6=-3x+10\qquad\text{add 6 to both sideS}\\\\3x=-3x+16\qquad\text{add}\ 3x\ \text{to both sides}\\\\6x=16\qquad\text{divide both sides by 6}\\\\x=\dfrac{16}{6}\\\\x=\dfrac{8}{3}[/tex]
Which equations and/or functions represent the graphed line? Select four options. f(x) = 0.2x - 4
f(x) = 0.5x + 2
f(x) = 1/2x + 2
y – 3 = 1/2(x – 2)
y – 1 = 0.5(x + 2)
Answer:
f(x) = 0.2x - 4 (incorrect)
f(x) = 0.5x + 2 (correct)
f(x) = 1/2x + 2 (correct)
y – 3 = 1/2(x – 2) (correct)
y – 1 = 0.5(x + 2)
Step-by-step explanation:
Step 1 : Find two coordinates
(0, 2) (-4, 0)
Step 2 : Find the slope
Slope = m = Y2-Y1/X2-X1
m = 0-2/-4-0
m = -2/-4
m = 1/2 or 0.5
Step 3 : Find the y-intercept
Y-intercept is where the line intersects the y-axis
c = 2
Step 4 : Form the equation y=mx + c
Given Equations and their slope intercept forms:
1) f(x) = 0.2x - 4
This is incorrect because slope is 1/2 or 0.5 and y intercept is 2
2) f(x) = 1/2x + 2
y = 1/2x + 2
This is correct because slope is 1/2 or 0.5 and y intercept is 2
3) f(x) = 0.5x + 2
y= 0.5x + 2 (As m=0.5)
This is correct because slope is 1/2 or 0.5 and y intercept is 2
4) y – 3 = 1/2(x – 2)
Rearranging in slope intercept form:
y-3=1/2x - 1
y = 1/2x-1+3
y = 1/2x + 2
This is correct because slope is 1/2 or 0.5 and y intercept is 2
5) y – 1 = 0.5(x + 2)
y -1 = 0.5x+1
y = 0.5x +1+1
y = 0.5x + 2
This is correct because slope is 1/2 or 0.5 and y intercept is 2
!!
first off, let's notice something on this line, the graph touches the y-axis at 2, namely when x = 0, y = 2, so that's the y-intercept for this line.
now, let's notice something else, as the line moves from x = -4, to the right towards x = 0, the run is 4 units, the rise is 2 units, so its slope is rise/run or 2/4 or 1/2, that said, that gives us an equation of
[tex]\bf y=\cfrac{1}{2}x+2\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\implies y=0.5x+2[/tex]
[tex]\bf y-3 = \cfrac{1}{2}(x-2)\implies y-3=\cfrac{1}{2}x-1\implies y=\cfrac{1}{2}x+2\qquad \textit{\Large\checkmark} \\\\\\ y-1=0.5(x+2)\implies y-1=0.5x+1\implies y=0.5x+2\qquad \textit{\Large\checkmark} \\\\\\ f(x) = 0.2x-4\qquad \bigotimes[/tex]
Factor completely x2 - 8x + 16.
(x + 4)(x + 4)
(X - 4)(x - 4)
(x + 4)(x - 4)
(x-2)(x - 8)
Answer:
(X - 4)(x - 4)
Step-by-step explanation:
x2 - 8x + 16
What two numbers multiply to 16 and add to -8
-4 * -4 = 16
-4 +-4 = -8
(x-4) (x-4)
(x-4)^2
Answer:
B
Step-by-step explanation:
(x - 4)(x - 4)
Factor the expression 18x^2 - 8
Answer:
2(3x-2(3x+2)
Step-by-step explanation:
1) 18x^2-8
2) 2(9x^2-4)
3) 2(3x-2)(3x+2)
Answer:
2(3x-2(3x-2) instead of the + 2
Step-by-step explanation:
Triangle ABC is similar to triangle A’B’C’. Which sequence of similar transformation could map triangle ABC onto triangle A’B’C’?
Answer: dilation and translation
Step-by-step explanation:
A dilation is a transformation that maps a similar image that is the exactly same shape as the original, but with a different size. A translation is a kind of rigid transformation used in geometry that moves a shape a particular distance.Here Δ ABC and ΔA'B'C' are similar triangles (By AAA similarity postulate), so one of the transformation used here is dilation and also the there is some distance between the triangles without any change in its orientation , so the other transformation used here is translation.
Which of the following is the coordinate for the image of point M(3, –7) after a 90° clockwise rotation?
Answer:
(-7,-3)
Step-by-step explanation:
The rule of 90° clockwise rotation is given below:
If a point (x,y) is rotated 90° clockwise, the new point would be (y, -x)
Since the point M is given as (3,-7), the rotated point will be (-7,-3).
Note: you can graph and check also
Answer:
(-7, -3)
Step-by-step explanation:
using the discriminant, how many solutions and what type of solution(s) does 3p-9p^2=6 have?
a. 2; irrational
b. 2; rational
c. 1; rational
d. no real solutions
Answer:
d. no real solutions
Step-by-step explanation:
3p − 9p² = 6
0 = 9p² − 3p + 6
0 = 3p² − p + 2
The discriminant of ax² + bx + c is b² − 4ac.
If the discriminant is negative, there are no real roots.
If the discriminant is zero, there is 1 real root.
If the discriminant is positive, there are 2 real roots.
If the discriminant is a perfect square, the root(s) are rational.
If the discriminant isn't a perfect square, the root(s) are irrational.
Finding the discriminant:
a = 3, b = -1, c = 2
(-1)² − 4(3)(2) = -23
The discriminant is negative, so there are no real roots.
Final answer:
After rewriting the equation 3p-9p²=6 in standard quadratic form and calculating the discriminant, we find that the discriminant is negative, indicating the equation has d. no real solutions.
Explanation:
To determine the number and type of solutions the equation 3p-9p²=6 has using the discriminant, we first need to rewrite the equation in standard quadratic form, which is ax² + bx + c = 0. Moving all terms to one side gives us -9p² + 3p - 6 = 0, where a = -9, b = 3, and c = -6. The discriminant of a quadratic equation is defined as b² - 4ac.
A discriminant greater than zero indicates two real solutions, equal to zero indicates one real solution, and less than zero indicates no real solutions. Calculating the discriminant for our equation: (3)² - 4(-9)(-6)=9-216=-207, which is less than zero. Therefore, the equation -9p²+ 3p - 6 = 0 has d. no real solutions.
Solve for x. 7 – 4x = 31 A. x = 6 B. x = 9.5 C. x = –6 D. x = –9.5
7-4x= 31
Bring over 7 to the other side
Positive 7 changes into negative 7
7-7-4x= 31-7
-4x= 24
Divide by -4 for -4x and 24
-4x/-4= 24/-4
x= -6
Check answer by using substitution method
7-4x= 31
7-4(-6)= 31
7+24= 31
31= 31
Answer : C. x= -6
Answer:
C. x = -6
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
First, subtract 7 from both sides:
7 - 4x = 31
7 (-7) - 4x = 31 (-7)
-4x = 31 - 7
-4x = 24
Divide -4 from both sides to isolate the variable, x:
(-4x)/-4 = (24)/-4
x = 24/-4
x = -6
x = -6, or C. is your answer.
~
Really don’t understand help. With picture
[tex]\bf \textit{Jim's Gym}\\\\ \begin{array}{cccll} initial~fee&visits&cost\\ \cline{1-3} 300&1&300+3(1)\\ &2&300+3(2)\\ &3&300+3(3)\\ &4&300+3(4)\\ &x&300+3(x) \end{array}\implies y = 300+3x \\\\[-0.35em] ~\dotfill\\\\ \textit{Sally's Salon}\\\\ \begin{array}{cccll} initial~fee&visits&cost\\ \cline{1-3} 250&1&250+5(1)\\ &2&250+5(2)\\ &3&250+5(3)\\ &4&250+5(4)\\ &x&250+5(x) \end{array}\implies y = 250+5x[/tex]
when are the plans equal?
[tex]\bf \stackrel{Jim's}{300+3x}~~=~~\stackrel{Sally's}{250+5x}\implies 50+3x=5x \\\\\\ 50=2x\implies \cfrac{50}{2}=x\implies 25=x[/tex]
So, we can start off by just listing the facts.
The Initial fee for Jim's Gym has an initial fee of $300, and Sally's Salon has an initial fee of $250. Every visit to Jim's Gym costs $3, and Sally's Salon costs $5.
The question is using the variable x, in which x represents the number of visits that person has made.
So the equation for Jim's Gym is 300 + 3x (since, like we've established earlier, it costs $3 per visit.
The equation for Sally's Salon is 250 + 5x (since it costs $5 per visit)
Since we're trying to equalize costs, make the entire equation
300 + 3x = 250 + 5x
Subtract both sides by 250
50 + 3x = 5x
Subtract both sides by 3x
50 = 2x
Divide both sides by 2
x = 25
Option D is the answer.
-15
-3
3
15
Pls help idk this
Answer:
-3
Step-by-step explanation:
4^x = (1/8)^(x+5)
(2^2)^x = (2^-3)^(x+5)
2^2x = 2^(-3x - 15)
Since both sides have the same base of 2, then the exponents are equal
So
2x = - 3x - 15
5x = -15
x = -3
Answer:
-3
Step-by-step explanation:
see attached
Classify ABC by its angles if mA=x, mB=2x and mC=3x
Answer:
All 3 angles of any triangle have a sum = 180. Therefore, x + 2x + 3x = 180 6x = 180 x = 180/6 = 30. So It is a 30-60-90 special right triangle!!
Step-by-step explanation:
Which operations involving complex numbers have solutions represented by point A on the graph? PLEASE HELP
Answer:
Option 3 and 4
Step-by-step explanation:
We have to find the solutions represented by point A on graph
The point A is represented by (-6,7i)
Lets check all options one by one
1.
[tex]2(1-2i)-(4+3i)\\= (2-4i)-(4+3i)\\=2-4i-4-3i\\=2-4-4i-3i\\=-2-7i[/tex]
This option is not correct
2.
[tex]2(1+2i)+(-4-3i)\\=(2+4i)-4-3i\\=2+4i-4-3i\\=2-4+4i-3i\\=-2+i[/tex]
This option is also not correct
3.
[tex]2(-1+2i)-(4-3i)\\=(-2+4i)-4+3i\\=-2+4i-4+3i\\=-2-4+4i+3i\\=-6+7i[/tex]
This solution is same as point A so this option is correct
4.
[tex](-2+4i)+(-4+3i)\\=-2+4i-4+3i\\=-2-4+4i+3i\\=-6+7i[/tex]
Solution same as point A so this is correct option.
5.
[tex](-2-4i)+(4-3i)\\=-2-4i+4-3i\\=-2+4-4i-3i\\=2-7i[/tex]
Not correct
The correct options are option no 3 and 4 ..
In the complex plane, complex numbers are represented as points with the real part as the x-coordinate and the imaginary part as the y-coordinate. Therefore, various complex number operations like addition, subtraction, multiplication, or division could result in point A, depending on the specific numbers and operations involved.
Explanation:To understand which operations involving complex numbers would have solutions represented by point A on a graph, we need to firstly understand that in the complex plane, complex numbers are represented as points. The x-axis corresponds to the real part of the number and the y-axis corresponds to the imaginary part. For example, complex number a + bi would correspond to a point at coordinates (a, b) on the graph.
Various operations involving complex numbers could potentially yield the given point A, such as addition, subtraction, multiplication, or division of two complex numbers. However, without the specific coordinates of point A or other pertinent information (such as the specific complex numbers involved in the operation or the nature of the operation), we cannot definitively say which operation would result in point A output.
For instance, addition of two complex numbers can be visually depicted as adding the vectors for the two numbers together. Depending on what the two initial numbers are, their sum could land at point A.
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HELP ASAP I WILL GIE 100 POINTS AND BRANLIEST HELP ASAP
Answer:
m=-1
Step-by-step explanation:
9m+13 =4
Subtract 13 from each side
9m+13-13 =4-13
9m = -9
Divide each side by 9
9m/9 = -9/9
m = -1
Answer:
m=-1
Step-by-step explanation:
About 99.7% of sixth-grade students will have
heights between _____ inches and _____ inches. the mean is 58 inches and standard deviation is 2.3 inches.
Answer: About 99.7% of sixth-grade students will have
heights between 51.1 inches and 64.9 inches.
Step-by-step explanation:
According to the empirical rule, 99.7% of data falls within the three standard deviations from the mean.
Given : Mean: [tex]\mu=58\text{ inches}[/tex]
Standard deviation:= [tex]\sigma=2.3\text{ inches}[/tex]
Then, the 99.7% of sixth-grade students will have heights between
[tex]\mu-3\sigma[/tex] inches and [tex]\mu+3\sigma[/tex] inches
i.e. [tex]58-3(2.3)[/tex] inches and [tex]58+3(2.3)[/tex] inches
i.e. 51.1 inches and 64.9 inches.
Answer:
About 99.7% of sixth-grade students will have
heights between 51.1 inches and 64.9 inches.
Step-by-step explanation:
Got it right :/
Which of the following is an extraneous solution of (45-3x)^1/2=x-9?
A= -12
B= -3
C= 3
D= 12
Answer:
C. x =3
Step-by-step explanation:
Extraneous solution is that root of a transformed equation that doesn't satisfy the equation in it's original form because it was excluded from the domain of the original equation.
Let's solve the equation first
[tex]\sqrt{45-3x} = x-9\\Taking\ square\ on\ both\ sides\\{(\sqrt{45-3x})}^2 = {(x-9)}^2\\45-3x = x^2-18x+81\\0 = x^2-18x+81-45+3x\\x^2-15x+36 = 0\\x^2-12x-3x+36 = 0\\x(x-12)-3(x-12) = 0\\(x-3)(x-12)\\x-3 = 0\\=> x =3\\x-12 = 0\\x = 12\\We\ will\ check\ the\ solutions\ one\ by\ one\\So,\\for\ x=3\\\sqrt{45-3(3)} = 3-9\\\sqrt{45-9} = -6\\\sqrt{36}= -6\\6\neq -6\\For x=12\\\sqrt{45-3(12)} = 12-9\\\sqrt{45-36} = 6\\\sqrt{36}= 6\\6=6[/tex]
Hence, we can conclude that x=3 is an extraneous solution of the equation ..
Answer:
C
Step-by-step explanation:
the vertex of the parabola is (-3,6). which of the following could be it’s equation
Answer:
Step-by-step explanation:
The most general form of this, without seeing any of the options, would be:
[tex]y=(x+3)^2+6[/tex]
Again, there might have been a value outside the parenthesis that may or may not have been negative, but either way, this is the most basic translation of the parabola.
solution to m^2- 36=0
Answer:
m=(-6,6)
Step-by-step explanation:
m^2 -36 = 0
Reorder the terms:
-36 + m^2 = 0
Solving for variable 'm'.
Add '36' to each side of the equation.
-36 + 36 + m^2 = 0 + 36
Combine like terms: -36 + 36 = 0
0 + m^2 = 0 + 36
m^2 = 0 + 36
Combine like terms: 0 + 36 = 36
m^2 = 36
Simplifying
m^2 = 36
Take the square root of each side:
√m^2=+/-√36
m=(+/-)6
m = {-6, 6}
What is the value of -3r+8 when r =4
Answer:
-4
Step-by-step explanation:
To find your answer, plug in 4 for r.
[tex]-3r+8\\-3(4)+8[/tex]
You can start by multiplying -3 by 4.
[tex]-3(4)+8\\-12+8[/tex]
Next, add -12 to 8 and you'll have your answer.
[tex]-12+8\\-4[/tex]
Answer:
-4.
Step-by-step explanation:
Substitute r = 4 into the given expression:
= -3(4) + 8
= -12 + 8
= -4.
Simplify (-2/3)/(-7/4)
Answer:
8/21
Step-by-step explanation:
(-2/3)/(-7/4)
When dividing, reciprocate the dividend then multiply to the divisor.
Reciprocate
-4/7
Multiply
-2/3 * -4/7
8/21
Answer
8/21
To simplify (-2/3)/(-7/4), we first convert the division operation into multiplication by using the reciprocal of the second fraction. This results in (-2/3)×(-4/7). We, then, multiply the numerators together and the denominators together, leading to the final simplified fraction of 8/21.
Explanation:To simplify this expression, (-2/3)/(-7/4), it is useful to first understand that division is the same as multiplying by the reciprocal. The reciprocal of a fraction is obtained by switching the numerator and the denominator. The reciprocal of (-7/4) is thus (-4/7). Therefore, the expression becomes (-2/3)×(-4/7).
The next step is to multiply the numerators together and the denominators together. So (-2 × -4) / (3 × 7) gives 8/21. The negative signs cancel each other out as a negative time a negative equals a positive.
So therefore (-2/3)/(-7/4) simplifies to 8/21.
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Which equation can be used to find the measure of angle BAC?
Answer:
Step-by-step explanation:
let angle [tex]B[/tex] . be [tex]y[/tex] then,
using angle sum property,
x+y+90=180 (angle c is 90 because its given)
hence you have the equation
Answer:
Cos() = AC / AB
So in this case: Cos() = 5 / 13
Solve the following trigonometric equation for 0to2pi
(a) cos(4x) - 9 sin(2x) + 4 = 0
Answer:
x = pi/12, 5pi/12, 13pi/12, 17pi/12.
Step-by-step explanation:
Note that cos (4x) = 1 - 2sin^2 (2x)
Substituting we have:
1 - 2sin^2 (2x) - 9 sin(2x) + 4 = 0
2 sin^2 (2x) + 9 sin(2x) - 5 = 0
(2 sin 2x - 1 )(sin 2x + 5 ) = 0
sin 2x = 1/2 and sin 2x = -5.
sin 2x = 1/2, gives 2x = pi/6, 5pi/6, 13pi/6, 17pi/6.
There are no solutions to sin 2x = -5 because the range of sin x is -1 to +1.
So x = pi/12, 5pi/12, 13pi/12, 17pi/12.
To solve the trigonometric equation cos(4x) - 9 sin(2x) + 4 = 0, we can use trigonometric identities and algebraic manipulation. The steps to solve the equation are writing it as a quadratic equation, substituting with sin(x), solving the quadratic equation, and substituting back to solve for x.
Explanation:To solve the trigonometric equation cos(4x) - 9 sin(2x) + 4 = 0 for 0 to 2pi, we can use trigonometric identities and algebraic manipulation. Here are the steps to solve the equation:
Write the equation as a quadratic equation in terms of sin(x) and cos(x).Use the substitution u = sin(x) to rewrite the equation in terms of u.Solve the quadratic equation for u.Substitute back the value of u to solve for x.The solutions to the equation will be the values of x that make the equation true.
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PLEASE HELP!!!!!
Camilla borrows a book from the library for d days. The library charges a late fee of 0.10 dollars per day that the book is late.
If Camilla returns the book more than 21 days after she borrowed it, the expression 0.10(d-21), represents the total late fee Camilla owes.
What does (d-21) represent in this context?
Choose 1 answer:
(Choice A)
The number of days Camilla borrows the book
(Choice B)
The late fee Camilla owes per day the book is late
(Choice C)
The late fee Camilla owes per day she borrowed the book
(Choice D)
The number of days the book is late
Answer: Choice D
Step-by-step explanation: Why? Because (d-21) is what how many days she was late. The problem is asking what (d-21) presents and Choice D says 'The number of days the book is late'. If the problem did have the 0.10 before (d-21) THEN it would've been Choice C.
In the expression 0.10(d-21), the term (d-21) represents the number of days the book is late, beyond the initial 21-day borrowing period.
Explanation:The expression (d-21) in the context of the late fee calculation represents the number of days the book is late. Since the library charges a late fee only if the book is returned more than 21 days after it was borrowed, subtracting 21 from the total days borrowed, which is represented by 'd,' gives us the number of days Camilla returned the book late. Multiplying this by the per-day late fee of $0.10 gives us the total late fee owed.
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Identifying Slope and y-Intercept of a Line
Identify the slope and y-intercept of each linear function's equation
y = 1 - 3x
slope = 3 y-intercept at -1
y = 3x - 1
slope = -1 y-intercept at 3
X-3 = y
slope = -3; z-intercept at 1
--> + 3 = y
slope = 1:y-intercept at -3
Previous Activity
Step-by-step explanation:
The slope-intercept form of an equation of a line:
y = mx + b
m - slope
b - y-intercept
y = 1 - 3x = -3x + 1
slope = -3
y-intercept at 1
y = 3x - 1
slope = 3
y-intercept at -1
x - 3 = y → y = 1x - 3
slope = 1
y-intercept at -3
x + 3 = y → y = 1x + 3
slope = 1
y-intercept at 3
What is the slope of a line perpendicular to y=-7/4x
Answer:
7/4
Step-by-step explanation:
Answer:
4/7
Step-by-step explanation:
To answer this, take the negative reciprocal of -7/4, obtaining 4/7.
Jennifer sold 57 pieces of art if she sold twice as many paintings as sculptures how many painting did she sell??
so we know she has sculptures and paintings, if she sold twice as many paintings as sculptures, that means that for every 2 paintings, she sold 1 sculpture, so the paintings and sculptures are on a 2:1 ratio.
we know she sold a total of 57, so we'll need to split 57 in a 2:1 ratio, we'll simply divide the whole amount of 57 by (2+1) and distribute accordingly.
[tex]\bf \cfrac{paintings}{sculptures}\qquad 2:1\qquad \cfrac{2}{1}\qquad \qquad \cfrac{2\cdot \frac{57}{2+1}}{1\cdot \frac{57}{2+1}}\implies \cfrac{2\cdot 19}{1\cdot 19}\implies \cfrac{\boxed{38}}{19}[/tex]