Answer: The formula for the surface area of a sphere is given by 4πr^2, and since we have half of a sphere, the surface area of a dome (a half sphere) is 2πr^2.
Plugging in the radius r = 12 meters, we get:
Surface area = 2π(12)^2
Surface area = 2π(144)
Surface area ≈ 904.78
Rounding to the nearest whole number, we get the surface area of the dome as 905 meters squared. Therefore, the closest answer choice is 967 meters squared.
So the answer is: 967 meters squared.
Step-by-step explanation:
I BEG U FOR HELP WILL GIVE BRAINLIEST PLLSSSS
Answer:
3,4,5 is the answer
Step-by-step explanation:
for the explanation using pythagoras theoem
[tex] {3}^{2} + {4}^{2} = {5 \\ }^{2} \\ 3 \times 3 + 4 \times 4 = 5 \times 5 \\ 9 + 16 = 25 \\ 25 = 25[/tex]
may you give me branliest as you promised
Maria works for an online auto trader. She makes a piecewise function to show the cost to place an online
advertisement.
(39
(39+5(x-6)
What is the cusp of the function?
c(x)
whenx ≤6
when x>6
According to the given information, the function has no cusp.
What is a function?
A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.
The given piecewise function is:
c(x) = 39, when x ≤ 6
c(x) = 39 + 5(x - 6), when x > 6
A cusp is a point on the graph where the function changes direction very abruptly, like a sharp turn. This happens when the derivative of the function is not defined at that point.
The derivative of the function is:
c'(x) = 0, when x ≤ 6
c'(x) = 5, when x > 6
Since the derivative is defined and continuous at x = 6, there is no cusp at that point. Therefore, the function has no cusp.
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Use the slip and y-intercept to identify the equation of this line
Answer:
y=2x
Step-by-step explanation:
equation formula is y=mx+b
m is slope
b is y-intercept
you know that slope is 2
y intercept is 0
so plug it into the equation
y=2x+0 or just y=2x
Suppose that the functions fand g are defined as follows.
f(x)=2x-1
g(x)=√3x-5
The composite functions (f/g)(x) and (f-g)(x) are (2x-1)/√(3x-5) and (2x-1) -√(3x-5)
Calculating the composite functions (f/g)(x) and (f-g)(x)To calculate (f/g)(x), we need to divide f(x) by g(x):
(f/g)(x) = f(x)/g(x) = (2x-1)/√(3x-5)
The domain of (f/g)(x) is the set of all x-values for which the denominator √(3x-5) is not equal to zero and non-negative
3x-5 ≥ 0, or x ≥ 5/3
Therefore, the domain of (f/g)(x) is x ≥ 5/3.
To calculate (f-g)(x), we need to subtract g(x) from f(x):
(f-g)(x) = f(x) - g(x) = (2x-1) - √(3x-5)
The domain of (f-g)(x) is the set of all x-values for which the expression inside the square root is non-negative:
3x-5 ≥ 0, or x ≥ 5/3
Therefore, the domain of (f-g)(x) is x ≥ 5/3.
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solve y''+y=t using laplace inverse with y(0)=1 and y'(0)=-2
The solution of the differential equation y'' + y = t with the initial conditions y(0)=1 and y'(0)=-2 is y(t)= 1-2t+te-t.
What is equation?Equation is a mathematical statement that expresses the equality of two expressions. It shows the relationship between two or more variables and can be written using symbols, numbers, and operations. Equations are used to describe physical laws, to make calculations, and to solve problems. Examples of equations include the Pythagorean theorem, Newton's laws of motion, and linear equations.
We solve this differential equation using Laplace inverse, with the initial conditions y(0)=1 and y'(0)=-2. First, we take the Laplace transform of the equation:
L[y''+y]=L[t]
Using the properties of Laplace transform, we can write this as:
s2Y(s)-sy(0)-y'(0)+Y(s)= (1/s)
Substituting the initial conditions and rearranging terms, we have:
Y(s)= (1/s) + (2/s2) + (1/s2)
We can then invert the Laplace transform to get the solution of the original equation:
y(t)= 1-2t+te-t
Therefore, the solution of the differential equation y'' + y = t with the initial conditions y(0)=1 and y'(0)=-2 is y(t)= 1-2t+te-t.
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find the area and perimeter of each figure below.
Answer:
finding the perimeter, you sumthe distance all round that is 7+7.5+17.8+6=38.3
38.3 is the perimeter
I need help solving this thank you
The negation is the fourth option.
6 + 3 ≠ 9 or 6 - 3 ≠ 9
How to write the negation?The negation of an equation is an inequality such that we just change the equal sign, by the "≠" sign.
Here we start with the two equations.
6 + 3 = 9 or 6 - 3 = 9
Just change the equal signs for different signs:
6 + 3 ≠ 9 or 6 - 3 ≠ 9
That is the negation, fourth option.
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help please! state the key features for the graph
Answer:
Axis of symmetry =1
vertex =(1,2)
y intercept =0
min/max= -6,2
domain= 0,1,2
range =y≥1,2
Calculate the volume of a sphere with a diameter of 4.
Answer: 33.51 cubic units.
Step-by-step explanation: The equation for the volume of a circle is:
V = (4/3)πr³
where r is the sweep of the circle.
Since the distance across of the circle is given as 4, we are able discover the span by partitioning the distance across by 2:
r = d/2 = 4/2 = 2
Presently we are able plug within the esteem of the sweep into the equation for the volume:
V = (4/3)π(2³) = (4/3)π(8) = 32/3π
Answer: 33.51
Step-by-step explanation:
The formula is 4/3 pi r^3. The radius is 2. If you do the equation, you get roughly 33.51.
Find an equation of the osculating plane and an equation of the normal
plane of the curve x = sin 2t, y = t, z = cos 2t at the point (0, π, 1).
The equation of the normal plane is 4y = 4π, or equivalently, y = π.
What is osculating plane?The word osculate comes from the Latin osculatus, which is a past participle of the verb osculari, which means "to kiss." Thus, an osculating plane is one that "kisses" a submanifold.
To find the osculating plane and normal plane of the curve x = sin 2t, y = t, z = cos 2t at the point (0, π, 1), we need to follow these steps:
Find the first and second derivatives of the curve with respect to t.Evaluate the derivatives at t = π to get the velocity, acceleration, and curvature vectors at the point (0, π, 1).Use the velocity and acceleration vectors to find the normal vector of the osculating plane.Use the normal vector and the point (0, π, 1) to find the equation of the osculating plane.Use the curvature vector to find the normal vector of the normal plane.Use the normal vector and the point (0, π, 1) to find the equation of the normal plane.Step 1: Find the first and second derivatives of the curve with respect to t.
x' = 2cos2t
y' = 1
z' = -2sin2t
x'' = -4sin2t
y'' = 0
z'' = -4cos2t
Step 2: Evaluate the derivatives at t = π.
x'(π) = 2cos2π = 2
y'(π) = 1
z'(π) = -2sin2π = 0
x''(π) = -4sin2π = 0
y''(π) = 0
z''(π) = -4cos2π = -4
So the velocity vector at the point (0, π, 1) is v = ⟨2, 1, 0⟩, the acceleration vector is a = ⟨0, 0, -4⟩, and the curvature vector is κv = ⟨0, 4, 0⟩.
Step 3: Use the velocity and acceleration vectors to find the normal vector of the osculating plane.
The normal vector of the osculating plane is given by the cross product of the velocity and acceleration vectors:
n = v × a = ⟨2, 1, 0⟩ × ⟨0, 0, -4⟩ = ⟨4, 0, 0⟩
Step 4: Use the normal vector and the point (0, π, 1) to find the equation of the osculating plane.
The equation of the osculating plane is given by:
4(x - 0) + 0(y - π) + 0(z - 1) = 0
Simplifying, we get:
4x - 4 = 0
So the equation of the osculating plane is 4x = 4, or equivalently, x = 1.
Step 5: Use the curvature vector to find the normal vector of the normal plane.
The normal vector of the normal plane is given by the curvature vector:
n' = κv = ⟨0, 4, 0⟩
Step 6: Use the normal vector and the point (0, π, 1) to find the equation of the normal plane.
The equation of the normal plane is given by:
0(x - 0) + 4(y - π) + 0(z - 1) = 0
Simplifying, we get:
4y - 4π = 0
So, the equation of the normal plane is 4y = 4π, or equivalently, y = π.
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m 32 33 There are red tiles and blue tiles in a box. The ratio of red tiles to blue tiles is 3:5. There are 12 more blue tiles than red tiles in the box. How many red tiles are in the box? A 18 B C 20 30 D 48 What is the surface area, in square inches, of the rectangular prism formed by folding the net below? 8 in. 23 in. 8 in. 36 in.
The number of red tiles in the box given the chance ratio of red to blue tiles is 18. The surface area of the rectangular prism is 2600 square inches.
Number of red tiles = x
Number of blue tiles = 12 + x
Total tiles = x + 12 + x
= 12 + 2x
Ratio of red = 3
Ratio of blue = 5
Total ratio = 3 + 5 = 8
Number of red tiles = 3 / 8 × 12+2x
x = 3(12 + 2x) / 8
x = (36 + 6x) / 8
8x = 36 + 6x
8x - 6x = 36
2x = 36
x = 36/2
x = 18 tiles
Therefore, The number of red tiles in the box given the chance ratio of red to blue tiles is 18.
b) To find the surface area of the rectangular prism, we need to find the area of each of its faces and add them together. Looking at the net, we see that there are three pairs of identical rectangles: the top and bottom faces, the front and back faces, and the left and right faces. Each of these rectangles has dimensions of 23 inches by 8 inches.
Therefore, the surface area of the rectangular prism is:
=2 * (23 in. * 8 in.) (top and bottom faces)
=2 * (36 in. * 8 in.) (front and back faces)
=2 * (23 in. * 36 in.) (left and right faces)
= 368 + 576 + 1656
= 2600 square inches
Therefore, the surface area of the rectangular prism is 2600 square inches.
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Suppose that the function h is defined as follows.
if
-2
-1
h(x)= 0
1
2
Graph the function h.
-3.5
if-2.5
if-1.5
if -0.5
if 0.5 ≤x≤1.5
Suppose that the function h is defined as follows. -2 -1 h(x)= if – 2, the graph is given below: (see image)
What is a Graph?A graph is a mathematical structure used to represent relationships between objects or entities. It consists of a set of vertices (also known as nodes) and a set of edges that connect pairs of vertices.
In a graph, the vertices represent the objects or entities being studied, while the edges represent the connections or relationships between them.
For example, in a social network graph, the vertices might represent individual users, and the edges might represent their connections (e.g. friendships) with other users.
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In art class students are mixing blue and red paint to make purple paint. Deondra
mixes 6 cups of blue paint and 7 cups of red paint. Arun mixes 2 cups of blue paint
and 3 cups of red paint. Use Deondra and Arun's percent of red paint to determine
whose purple paint will be redder.
Deondra percent of red paint (to nearest whole number) =
Arun percent of red paint (to nearest whole number) =
O Deondra's purple paint will be redder.
O Arun's purple paint will be redder.
o The two purple paints will be equally red.
Submit Answer
%
%
attempt 1 out of 2
Arun's purple paint will be redder.
Define percentagePercentage is a way of expressing a proportion or a fraction as a number out of 100. It is represented by the symbol "%". For example, if you say that 20% of students in a class scored an A grade in a test, it means that 20 out of every 100 students received an A grade.
Deondra mixed 6 cups of blue paint and 7 cups of red paint, so the percent of red paint in her mixture is:
7 / (6 + 7) × 100% = 53.8%, which rounds to 54%.
Arun mixed 2 cups of blue paint and 3 cups of red paint, so the percent of red paint in his mixture is:
3 / (2 + 3) × 100% = 60%.
Since Arun's mixture has a higher percentage of red paint, his purple paint will be redder than Deondra's.
Therefore, the answer is Arun's purple paint will be redder.
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(a) What is the value of x? Show your work.
(b) What is the measure of angle C? Show your work.
In triangle ABC
a) The value of x = 29⁰
b) The angle c equal to 93⁰
What is a triangle?A triangle is a closed plane figure that is formed by connecting three line segments, also known as sides, at their endpoints. The three endpoints, or vertices, where the sides of the triangle meet are not collinear. Triangles are important in mathematics and geometry because they are the simplest polygon that can exist in two-dimensional space.
According to the given informationIn a triangle, the sum of all interior angles is always 180 degrees. Therefore, we can use this fact to find the value of x and angle c.
We know that:
angle a = 35⁰
angle b = 52⁰
angle c = 3(x+2)⁰
Using the fact that the sum of all interior angles in a triangle is 180 degrees, we can write:
angle a + angle b + angle c = 180
Substituting the values we know, we get:
35 + 52 + 3(x+2) = 180
Simplifying the equation, we get:
87 + 3x + 6 = 180
3x + 93 = 180
3x = 87
x = 29
Therefore, x = 29⁰
To find angle c, we can substitute the value of x into the equation we were given for angle c:
angle c = 3(x+2)
angle c = 3(29+2)
angle c = 3(31)
angle c = 93
Therefore, angle c is equal to 93⁰.
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1. Dorie Sparrow, assistant manager of The Clothes Horse, Inc., must mark all clearance rack dresses back
to their regular selling price. She had marked all of them down 70%. What regular selling price does Dorie
need to sell a dress for that had been marked down to $104.98?
Therefore, Dorie needs to sell the dress for $349.93 in order to mark it back to its regular selling price.
What is selling price?
Selling price refers to the price at which a product or service is sold to customers. It is the amount of money that a buyer pays to the seller in exchange for the product or service. The selling price is usually higher than the cost price, which is the amount that the seller paid to acquire or produce the product or service. The difference between the selling price and the cost price is called the profit margin, and it is the profit that the seller makes on the sale of the product or service.
If a dress had been marked down 70%, this means that it is being sold for only 30% of its original selling price.
Let P be the original selling price of the dress. Then:
0.3P = $104.98
Solving for P, we get:
P = $104.98 / 0.3
P = $349.93
Therefore, Dorie needs to sell the dress for $349.93 in order to mark it back to its regular selling price.
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Regis has a bag with 8 tiles numbered
1 through 8. He randomly draws one tile
from the bag without looking Which of
the following describes a likely outcome?
A. He selects a tile with the number 0.
B. He selects a tile with the number 4.
C. He selects a tile with a number
greater than 7.
D. He selects a tile with a number
less than 6.
The outcome that Regis is likely to get after randomly drawing one tile from the bag would be 0. That is option A.
How to calculate the outcome of that event?To calculate the outcome of the event is to calculate the probability of selecting a tile with a number when one tile is drawn at random.
Probability = possible outcome/sample space.
Possible outcome = 1
sample space = 8
probability = 1/8 = 0.125
The probability is approximately = 0
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if you dilate triangle ABC by a scale factor of 3 and (0,0) is the center, what will be the length of AB?
the new length of AB after a dilation by a scale factor of 3 with (0,0) as the center would be 3 times the original length of AB.
How to solve the question?
To find the new length of AB after a dilation by a scale factor of 3 with (0,0) as the center, we can use the following formula:
AB' = AB x 3
where AB' is the length of AB after the dilation, and AB is the original length of AB.
However, we need to first determine the length of AB in the original right triangle ABC. To do this, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
Let's assume that AB is the hypotenuse of the right triangle ABC, and that AC and BC are the other two sides. Then we have:
AB²= AC²+ BC²
Without more information about the lengths of AC and BC, we cannot determine the value of AB. However, once we have determined the length of AB, we can use the formula above to find the new length of AB after dilation.
Assuming we know the length of AB in the original right triangle ABC, we can now use the formula for dilation to find the new length of AB:
AB' = AB x 3
For example, if AB is 5 units long in the original triangle, then after dilation, AB' would be:
AB' = 5 x 3 = 15 units
Therefore, the new length of AB after a dilation by a scale factor of 3 with (0,0) as the center would be 3 times the original length of AB.
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Determine the circumference and approximate area of the
given circle, using 3.14 for pie.
The circumference and approximate area of the given circle is 69.08 inches & 380.14 square inches.
What is circumference?
Circumference is the distance around the edge of a circular object or a round shape. It is the length of the boundary or perimeter of the circle. The formula is given by C = 2πr, where C is the circumference, r is the radius of the circle, and π is a mathematical constant approximately equal to 3.14.
The circumference of a circle is given by the formula:
C = 2πr
where r is the radius of the circle and π (pi) is a mathematical constant approximately equal to 3.14.
Using this formula and plugging in the given value of radius:
C = 2 x 3.14 x 11
C = 69.08 inches (rounded to two decimal places)
So the circumference of the circle with 11 inches radius is approximately 69.08 inches.
The area of a circle is given by the formula:
A = πr²
Again, using the given value of radius and approximating π to 3.14:
A = 3.14 x 11²
A = 3.14 x 121
A = 380.14 square inches (rounded to two decimal places)
So the approximate area of the circle with 11 inches radius is approximately 380.14 square inches.
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A waiter made $288 in tips after waiting on 12 tables. What was the waiter’s average tip per table?
A$24
B$13
C$15
D$16
Answer:
24
Step-by-step explanation:
Answer:
A. $24
Step-by-step explanation:
Given:
total of $288number of values is 12 tablesSolve for average tip:
Average is the same as the meanTo solve you have add up the total and divide by the total number of values288 / 12 = 24Answer:
Thus, the waiter's average tip per table is $24.
The answer is A.
Will mark brainliest if answer is correct
Answer:
[tex]3( {2}^{2} ) - {2}^{2} + 4 = 12[/tex]
[tex] {2}^{3} + b( {2}^{2} ) + 43(2) - 126 = 4b - 204[/tex]
[tex]4b - 32 = 12[/tex]
[tex]4b = 44[/tex]
[tex]b = 11[/tex]
For this value of b, these graphs will intersect at (2, 12). Please use your graphing calculator to confirm that this is the only point of intersection.
Need help Asap please
Answer:
Summer for 9th Graders: 0.14
Fall for 10th Graders: 0.15
Spring overall total: 0.36
Summer overall total: 0.22
Fall overall total: 0.33
Winter overall total: 0.09
Step-by-step explanation:
Relative frequencies are related to percentages so you can find the answer through that given the total from each grade.
However, adding or subtracting makes the process easier (in my opinion) to find the relative frequency
How could Marc mathematically try to prove that he hit the ball near the top of the tower?While on the golf course last weekend Marc hit into the rough, landing the ball behind a tall tree. To get out of the scenario, his best option was to hit the ball high enough so it goes over the tree and hopefully comes down in the fairway for his next shot. So with a mighty swing, he hit the ball into the air and was surprised to see it hit near the top of a 300 foot tall tower that he had not noticed. The formula for this shot is h(x) = -16xsquared + 120x , where h is the height of the ball and x is the number of seconds the ball is in the air. How could Marc mathematically try to prove that he hit the ball near the top of the tower?While on the golf course last weekend Marc hit into the rough, landing the ball behind a tall tree. To get out of the scenario, his best option was to hit the ball high enough so it goes over the tree and hopefully comes down in the fairway for his next shot. So with a mighty swing, he hit the ball into the air and was surprised to see it hit near the top of a 300 foot tall tower that he had not noticed. The formula for this shot is h(x) = -16xsquared + 120x , where h is the height of the ball and x is the number of seconds the ball is in the air. How could Marc mathematically try to prove that he hit the ball near the top of the tower?
Answer:
To mathematically prove that Marc hit the ball near the top of the tower, he could use the equation h(x) = -16x^2 + 120x, where h is the height of the ball and x is the number of seconds the ball is in the air.
First, Marc would need to determine the maximum height the ball reached during its flight. This can be found by using the vertex formula, which is x = -b/2a. In this case, a = -16 and b = 120, so x = -120/(2*-16) = 3.75 seconds.
Next, Marc can substitute this value back into the original equation to find the maximum height the ball reached. h(3.75) = -16(3.75)^2 + 120(3.75) = 135 feet.
Since the tower is 300 feet tall, Marc could conclude that if the ball hit near the top of the tower, it would have reached a height close to 300 feet. Since the ball reached a maximum height of 135 feet, it is unlikely that it hit the top of the tower.
However, this calculation assumes that the tower is directly in line with Marc's shot and that the ball did not have any horizontal movement. In reality, the tower could have been to the left or right of the shot, and the ball could have had some horizontal movement, which would affect its height at impact. Therefore, this calculation can only provide a rough estimate and cannot definitively prove whether or not the ball hit near the top of the tower.
Find an equation of the plane.
The plane that passes through the line of intersection of the planes
x − z = 3 and y + 3z = 3
and is perpendicular to the plane
x + y − 4z = 6
The equation of the plane that passes through the line of intersection of x - z = 3 and y + 3z = 3 and is perpendicular to x + y - 4z = 6 is x + y - 4z = 3.
What is point normal form?The point-normal form of the equation of a plane is given by:
N · (<x - x0>, <y - y0>, <z - z0>) = 0
Where (x0, y0, z0) is a point on the plane and N = is a normal vector to the plane, we have the point-normal form of the equation of a plane. The dot product of the vector from the supplied location to any point on the plane with the normal vector to the plane yields this form of the equation. The equation states that any vector located in the plane with the normal vector has a zero dot product. The scalar equation of the plane can also be found by expanding the dot product, and it takes the form axe + by + cz = d, where d = N (x0, y0, z0).
Given the equation of the planes is x − z = 3 and y + 3z = 3.
Now, find the direction vector of the line of intersection:
Set z = t:
x = t + 3 and y = 3 - 3t
The direction vector is <1, -3, 1>.
2. Determine the normal vector:
The plane is perpendicular to the plane x + y - 4z = 6, so:
normal vector of x + y - 4z = 6, which is <1, 1, -4>.
3. Using point normal form we have:
(3, 0, 0)
The point satisfies the equation:
x - z = 3 and y + 3z = 3 when z = 0
Thus,
<1, 1, -4> · <x - 3, y, z> = 0
x + y - 4z = 3
Hence, the equation of the plane that passes through the line of intersection of x - z = 3 and y + 3z = 3 and is perpendicular to x + y - 4z = 6 is x + y - 4z = 3.
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Which statement explains the type of function that is represented by the equation y = x^2 + 9?
The function is nonlinear because the variable x is raised to the second power. So, the correct option is D) .
Describe Linear Function?A linear function is a mathematical equation that can be represented by a straight line. It is a function in which the independent variable, say "x," is raised only to the first power, and the dependent variable, say "y," is not multiplied or divided by any variable. Linear functions have a constant rate of change, which means that the slope of the line is the same at all points.
The general form of a linear function is y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point at which the line crosses the y-axis. The slope m represents the rate of change of y with respect to x, and can be calculated as the change in y divided by the change in x between any two points on the line.
A linear function is a function that has a constant rate of change, meaning that as x increases by a certain amount, y also increases by a constant amount. A linear function can be written in the form y = mx + b, where m is the slope and b is the y-intercept.
In the given equation y = x² + 9, the variable x is raised to the second power, which means that the rate of change of y with respect to x is not constant. This is the characteristic of a nonlinear function. Moreover, the graph of the function is a parabola, which is also a characteristic of a nonlinear function.
Therefore, the correct answer is D) The function is nonlinear because the variable x is raised to the second power.
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The complete question is :
Which statement explains the type of function that is represented by the equation y=x² +9?
A The function is linear because it contains more than one term.
B) The function is linear because the variable x is raised to the second power.
C) The function is nonlinear because it contains more than one term.
D) The function is nonlinear because the variable x is raised to the second power.
Which of the numbers 0, 1, 2, 3 or 4 make the equation 8/y2 + 2 true?
None of the given numbers make the equation 8/y² + 2 true.
What is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.
To solve this problem, we can substitute each of the given numbers (0, 1, 2, 3, 4) for y in the equation 8/y² + 2 and see if the equation is true.
Substituting y=0 would make the denominator of the fraction zero, which is undefined, so y=0 is not a valid choice.
Substituting y=1 would give us:
8/1² + 2 = 8 + 2 = 10
So, 1 is not the answer.
Substituting y=2 would give us:
8/2² + 2 = 8/4 + 2 = 2 + 2 = 4
So, 2 is not the answer.
Substituting y=3 would give us:
8/3² + 2 = 8/9 + 2 = 0.888 + 2 = 2.888
So, 3 is not the answer.
Substituting y=4 would give us:
8/4² + 2 = 8/16 + 2 = 0.5 + 2 = 2.5
So, 4 is not the answer.
Therefore, none of the given numbers make the equation 8/y² + 2 true.
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What 2 numbers add up to 13 but multiply to -48??
Answer:
3 and -16
Step-by-step explanation:
To find two numbers that add up to 13 but multiply to -48, we can start by making a list of the factors of -48:
1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 12, -12, 16, -16, 24, -24, 48, -48
We can see that the only two numbers in this list whose sum is 13 are 3 and -16. To verify that these numbers multiply to -48, we can simply multiply them together:
3 x (-16) = -48
Therefore, the two numbers that add up to 13 but multiply to -48 are 3 and -16.
Answer: -3, 16
Step-by-step explanation:
A drawer contains 10 blue pens, 12 black pens, and 3 red pens. Without looking, Mr. Lopez is going to take one pen from the drawer, use it, and then put it back into the drawer. Then he is going to take another pen from the drawer to use. What is the probability of Mr. Lopez taking a red pen first and then taking a blue pen?
Answer: 4.8%
Step-by-step explanation: the total amount of pens in the drawer is (10+12+3) = 25
the amount of red pens in the drawer is 3
the probability of picking out a red pen from the drawer = 3/25
the amount of blue pens in the drawer is 10
the probability of picking out a red pen from the drawer = 10/25
the probability of picking out a red pen then a blue pen afterwards = (10/25 x 3/25) = 4.8%
Evaluate the expression for the given value.
–a – 7 for a = –4
A11
B–11
C3
D–3
Help Please...
You have 67 coins consisting of half-dollars and quarters. The number of quarters is 7 more than three times the number of half-dollars.
How many quarters do you have?
How many half -dollars do you have?
There are 52 quarters and 15 half-dollars
To solve this problem
Let's represent the number of half-dollars as "x" and the number of quarters as "y".
From the problem statement, we know that:
x + y = 67 (because there are a total of 67 coins)
y = 3x + 7 (because the number of quarters is 7 more than three times the number of half-dollars)
We can use substitution to solve for x:
x + (3x + 7) = 67
4x + 7 = 67
4x = 60
x = 15
So there are 15 half-dollars. We can use this to find the number of quarters:
y = 3x + 7
y = 3(15) + 7
y = 52
So there are 52 quarters.
Therefore, there are 52 quarters and 15 half-dollars.
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Write the polynomial function of least degree that has zeros of x=0, x= 2i and x =3
(assume all coefficients must be real)
A. x)=x²-3x³+4x² - 12x
B. x)=x²-3x² + 4x-12
C. x)=x²-3x³+4x² + 12x
D. f(x)=x² + 3x² - 6x + 12
The polynomial function of least degree that has zeros of x=0, x=2i, and x=3, and with all coefficients real is:
f(x) = x² - 3x³ + 4x² - 12xHow to find the polynomialSince the zeros of the polynomial function are given as
x=0, x=2i, and x=3,
we can write the function in factored form as follows:
f(x) = a(x-0)(x-2i)(x-3)
where
a is a constant coefficient and the factors correspond to the given zeros.
Since all coefficients must be real, we know that the complex conjugate of 2i, which is -2i, must also be a zero of the function. Therefore, we can rewrite the function as:
f(x) = a(x-0)(x-2i)(x+2i)(x-3)
Expanding this expression gives:
f(x) = a(x² + 4)(x-3)
Multiplying out the brackets and collecting like terms, we get:
f(x) = ax³ - 3ax² + 4ax - 12a
To find the value of 'a', we can use the fact that the coefficient of the x³ term is 1. Thus, we have:
a = 1/(1*4) = 1/4
Substituting this value of 'a' in the above expression, we get:
f(x) = (1/4)x³ - (3/4)x² + x - 3
Therefore, the polynomial function of least degree that has zeros of x=0, x=2i, and x=3, and with all coefficients real is:
Option A: f(x) = x² - 3x³ + 4x² - 12x
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