A. The net of a triangular prism is a flattened version of the prism that shows all the faces of the prism.
The prism's base is a right triangle with a base of 3 units and a height of 4 units. The prism is six units tall. The net of the triangular prism would look like a rectangle with a length of 3 units and a width of 4 units. On top of this rectangle, there would be two smaller triangles, each with a base of 3 units and a height of 6 units.
B. To calculate the surface area of the prism, we need to add the area of all the faces.
The base of the prism is a right triangle with an area of (1/2) (3 units) (4 units) = 6 square units.
The two triangular faces have an area of (1/2) (3 units) (6 units) = 9 square units each.
The rectangular face has an area of (3 units) (6 units) = 18 square units.
So, the total surface area of the prism is:
6 square units (base) + 9 square units (triangular face) + 9 square units (triangular face) + 18 square units (rectangular face) = 42 square units.
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f(x) and g(x) below, find the value of (fog)(-8).
f(x) = 3x²-3x - 8
g(x) = -x - 7
Therefore , the solution of the given problem of function comes out to be fog(-8)= 622.
Function: A DefinitionA function is a relationship between a collection of sources or one product for each input. Simply described, a function is a group of equations linked to a single, distinct output. A declaration, rule, or law that specifies the relationship between two variables is known as a function in mathematics (the dependent variable). When a rules of this kind is employed, there is just one output. by photographer Alex Federspiel. This sentence provides a y=x2 example. Any input for x has only one output for y. Since x is indeed the input value, y is, by definition, a function of x.
Here,
Given :
f(x) = 3x²-3x - 8
g(x) = -x - 7
To find : fog)(-8)= ?
Thus,
We find
=> F(g(x)) => 3g(x)² -3g(x) - 8
=> f(-x-7) =3⋅(-x-7)²-3⋅(-x-7)-8
At x =-8
=> 3(-8-7)² - 3(-8-7)-8
=> 3(225)-3(15) -8
=> 675 - 45 -8
=> 622
Therefore , the solution of the given problem of function comes out to be fog(-8)= 622.
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What unit is equal to Avogadro's number ?
Avogadro's number is a unitless object. It represents a number.
What is unit?
The mass of a particular piece of metal or the length of a particular rod are examples of quantities (specific properties) of objects that have historically been used to define measurement units. An object that has no units is known as unitless.
The proportionality factor that connects the number of constituent particles (often molecules, atoms, or ions) in a sample with the amount of material in that sample is called the Avogadro constant, also known as NA or L. It has a precise value of 6.02214076 × 10²³ reciprocal moles and serves as a SI defining constant.
The value of Avogadro's number is 6.02214076 × 10²³.
One mole of the chemical compound consists of 6.02214076 × 10²³ atoms.
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hi everyone help my math pls
show ur solutions
On solving the provided question, we can say that - the area of the provided circle is A = [tex]113.04 cm^2[/tex]
What is circle?Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. At every angle, it is also rotationally symmetric about the center. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.
here,
radius, r = 6 cm
Area of circle = [tex]\pi X r^2 = 3.14 X 6 X 6 \\[/tex]
A = [tex]113.04 cm^2[/tex]
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.A car is traveling on a small highway and is either going 55 miles per hour or 35 miles per hour, depending on the speed limits, until it reaches its destination 200 miles away. Letting x represent the amount of time in hours that the car is going 55 miles per hour, and y being the time in hours that the car is going 35 miles per hour, an equation describing the relationship is: 55x+35y=200
A: If the car spends 2.5 hours going 35 miles per hour on the trip, how long does it spend going 55 miles per hour?
B: If the car spends 3 hours going 55 miles per hour on the trip, how long does it spend going 35 miles per hour?
C: If the car spends no time going 35 miles per hour, how long would the trip take? Explain your reasoning.
Answer:
This equation can be used to determine how long the car was traveling at each speed. You can solve for one of the variables by using algebraic techniques. For example, you could subtract 35y from both sides to get:
55x = 200 - 35y
Then divide both sides by 55 to get:
x = (200 - 35y)/55
This equation shows that the value of x (the time spent traveling at 55 mph) is determined by the value of y (the time spent traveling at 35 mph). If you know the value of y, you can use this equation to calculate the value of x.
To find the values of x and y that satisfy the equation, you will need to use additional information. For example, you could set up a system of equations and solve for x and y using techniques such as substitution or elimination.
Step-by-step explanation:
Yara is 8 years old. Yara's mother is 4n times older than Yara. How old
was Yara's mother 5 years ago in terms of n?
Yara's mother was 32n-5 years old 5 years ago in terms of n.
Yara's mother is 4n times older than Yara, and Yara is 8 years old, so we can set up the equation:
Mother's age = 4n * 8 years
We are also told that Yara's mother is 5 years older than she is now, so we can add 5 to the equation above:
Mother's age 5 years ago = 4n * 8 years - 5 years
Now we can simplify this equation:
Mother's age 5 years ago = 32n - 5 years
Now we can substitute the value of n to find the mother's age in terms of n.
To find the age of Yara's mother 5 years ago in terms of n, we need to know the value of n. But we don't have the value of n so we can't find the exact age but we can find it in terms of n which is 32n-5 years.
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Solve the following system of equations: −2x + 3y = 7 y = 3x + 7 (−5, −1) (−2, 1) (−1, 4) (1, 3)
Answer:
(-2, 1)
Step-by-step explanation:
−2x + 3y = 7
y = 3x + 7
Since the second equation is already solved for y, we can use the substitution method. Substitute y of the first equation with 3x + 7 and solve for x.
-2x + 3y = 7
-2x + 3(3x + 7) = 7
-2x + 9x + 21 = 7
7x = -14
x = -2
Now substitute x in the second equation with -2 and solve for y.
y = 3x + 7
y = 3(-2) + 7
y = 1
Answer: (-2, 1)
find the values of x, z and y
The values of x is 82° , z is 98°and y is 69°. in the given triangle.
Is the sum of all triangle angles always 180 degrees?Because one outside angle of a triangle is equal to the total of the other two angles in the triangle, the angles of a triangle add up to 180 degrees. In other words, the third angle must join with the other two angles in the triangle to generate a 180-degree angle (the two angles that add up to form the outside angle).
we know that the sum of angle of triangle = 180
so,
x+ 60 +38=180
x=180-8
x=82°
and also
x+z = 180
z= 98°
for value of y
13 + 98 +y = 180
y= 69°
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b. How should Kiran change the quantities that he used
so that his smoothie tastes
just like Clare's?
Answer:
Kiran's smoothie would be more chocolatey than Clare's. All ingredients are doubled, but there is an extra teaspoon of chocolate syrup in his smoothie.
Step-by-step explanation:
(aryan)
PLEASE HELP ASAP
Which is the following is not an attribute of a right rectangular prism?
1 apex
12 edges
rectangular faces
square bases
Square bases is not an attribute of a right rectangular prism. Option D
What is a right rectangular prism?A right rectangular prism can be described as a three-dimensional solid shape with 6 faces, 12 edges, and 8 vertices.
It is sometimes called a cuboid.
All the faces of the right rectangular prism are rectangular in shape.
Examples of right rectangular prisms are books, bricks and aquarium.
Some properties of a right rectangular prism include;
There are 12 edges There are 8 verticesAll the faces are rectanglesAll the angles formed at the vertices are of 90 degreesThese prisms have no square base(s)
Hence, the right option is square bases.
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A falcon was recorded travelling 100 metres in 0. 93 seconds.
What was its average speed
a in m/s to 3 significant figures
The average speed of the falcon to 3 significant figures will be 107.526 m/s
Distance travelled by falcon = 100 meters
Time taken by falcon to travel the distance = 0.93 seconds
As we have the formula for finding the average speed:
Average speed is a pace defined as a quantity divided by the time required to obtain that quantity. Meters per second is the SI unit of speed. The formula S = d/t is used to compute average speed, where S is the average speed, d is total distance, and t is total time.
Average speed can be find by simply dividing the total distance covered by falcon by the total time taken by him to cover the distance.
So, the value of the average speed will be = (100 m/0.93 sec) =107.526 m/s
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im 12 and struggling help me please i need my grades up
Answer:
you would multiply 17% by 228,000
Step-by-step explanation:
you would get 177840
A club consisting of 11 men and 12 women needs to choose a committee from among its members so that the number of women on the committee is one more than the number of men on the committee. The committee could have from 1 to 23 members. How many committees can be formed
The total number of such committees that may be created, divided by the prime numbers that divide N, is 81.
What is the prime numbers that divide N?In the scenario presented in this question, a club with 11 men and 12 women must elect a committee from among its members in order for there to be one more woman on the committee than males.
The committee might consist of only 1 person or up to 23 people.
Let N represent the maximum possible number of such committees.
The total number of prime numbers that divide N must be determined.
The number of ladies chosen will be m.
The number of guys who were not chosen would thus be:
11 - (m - 1) = 12 - m
Each pairing of men who were not chosen and women who were chosen represents a committee choice.
Since selecting 12 people from a total of 23 would result in m women and 12 - m males, the committee chose:
making use of a combination formula
N = 23C12
N = 23!/12!(23 - 12)!
N = 1352078
These are the main components of 1352078: 2, 7, 13, 17, 19, and 23.
Consequently, the prime number total would be,
2 + 7 + 13 + 17 + 19 + 23 = 81
The total of the prime numbers is thus 81.
The complete question is:
A club consisting of 11 men and 12 women needs to choose a committee from among its members so that the number of women on the committee is one more than the number of men on the committee. The committee could have as few as 1 member or as many as 23 members. Let N be the number of such committees that can be formed. Find the sum of the prime numbers that divide N.
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What is Polya's 4 step method?
Polya's 4 step method is a process designed to help problem solvers become better at tackling difficult problems.
It was developed by the mathematician George Polya in 1945 and consists of four basic steps:
1. Understand the problem: The first step is to read and understand the problem. This means understanding the problem and identifying what information is given and what is required.
2. Devise a plan: The second step is to identify a strategy or plan of attack. This involves breaking the problem down into smaller parts, identifying the key elements, and using logical reasoning to identify a solution.
3. Carry out the plan: The third step is to execute the plan. This involves following the steps of the plan in order to solve the problem.
4. Look back: The fourth and final step is to take a look back at the solution and evaluate it. This involves checking to make sure the solution is correct and making any necessary adjustments.
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A researcher hypothesizes that the variation in the amount of money spent on business dinners is greater than the amount spent on lunches. The variance of the cost of nine business dinners was and the variance on 12 lunches was . What test value should be used in an F test
upper and lower bounds question
The upper bound and lower bound of a using the equation will result to
upper bound value 136015.499
lower bound value 136014.500
How to find the upper bound and lower bound valuesEvaluating the given expression a = b + 2c
where
b = 15 to 2 significant figures
c = 68 000 to 2 significant figures
solving for a
a = b + 2c
a = 15 + 2(68000)
a = 136015
The bound values
upper bond value is the largest possible vale of a
upper bond value = 136015.499
lower bound value is the lowest possible value of a
lower bound value = 136014.500
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What is a 100 sided shape called?
Answer:
hectogon or hecatontagon or 100-gon
Step-by-step explanation:
It is a hundred - sided polygon ( shape ). The sum of all hectogon's interior angles are 17640 degrees.
Answer:
Regular exercise has been shown to aid in the prevention and management of noncommunicable illnesses such as diabetes, heart disease, stroke, and a number of malignancies. Additionally, it lowers blood pressure, supports healthy body weight, and enhances well-being through enhancing mental health.
Step-by-step explanation:
find the height of the two pillar with same height
Answer:
ED = AB = 25√3
Step-by-step explanation:
Let ED = AB = X
DC = 100 - BC
Tan 60 = [tex]\frac{\sqrt{3} }{1} = \frac{ED}{DC}[/tex] = [tex]\frac{X}{100-BC}[/tex]
[tex]\sqrt{3} (100-BC) = X[/tex]
Tan 30 = [tex]\frac{1}{\sqrt{3} } = \frac{AB}{BC} = \frac{X}{BC}[/tex]
[tex]\frac{BC}{\sqrt{3} } = X[/tex]
[tex]\sqrt{3} (100-BC) = \frac{BC}{\sqrt{3} } \\3(100-BC) = BC\\300 - 3BC = BC\\300 = BC + 3BC\\300 = 4BC \\75 = BC[/tex]
X = [tex]\frac{BC}{\sqrt{3} } = \frac{75}{\sqrt{3} }\\[/tex]
X = 25√3
Find the inverse of y = √x + 8, y ≥ 8
To find the inverse of a function, you can follow these steps:
Swap the variables x and y in the original function. For example, if the original function is y = √x + 8, you would swap the variables to get x = √y + 8.
Solve the equation for y. In this case, you would get:
x = √y + 8
y = x - 8
Replace y with f^-1(x) to denote the inverse function. The inverse function is defined as f^-1(x) = y, so you would get:
f^-1(x) = x - 8
This is the inverse function of y = √x + 8.
Note that the inverse function is only defined for values of x such that y ≥ 8. This is because the original function y = √x + 8 is only defined for y ≥ 8.
Evaluate the gradient of f(x, y, z) = log(x2 + y2 + z2) at (1, 0, 1)
The gradient of f(x, y, z) = log(x2 + y2 + z2) at (1, 0, 1) is (2/1, 0, 2/1)
This gradient is a vector that points in the direction of the greatest rate of increase of the function f(x, y, z) = log(x2 + y2 + z2). To evaluate this gradient, the partial derivatives of the function with respect to x, y, and z must be calculated.
The partial derivative of the function with respect to x is (2x / (x2 + y2 + z2)). When x is 1, this simplifies to 2/1. Similarly, the partial derivative with respect to y is 0, and the partial derivative with respect to z is (2z / (x2 + y2 + z2)), which simplifies to 2/1 when z is 1. Therefore, the gradient of f(x, y, z) = log(x2 + y2 + z2) at (1, 0, 1) is (2/1, 0, 2/1).
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Calculate the size of the angle marked 'x' in the pentagon shown below. Give your answer in degrees (°).
Answer: x= 96 degrees
Step-by-step explanation:
It we figure out the rest of the angles they would be (the outside ans inside angles are straight angles):
123+153+49+119= 444
Since the total of angles in a pentagon = 540 degrees
540-444 96 degrees
The measure of an angle x will be equal to 96°.
What is the Pentagon?A Pentagon is a two-dimensional geometric shape that consists of five straight sides and five angles. It is a type of polygon, which is a closed shape with three or more sides.
The Pentagon is often used to represent the shape of buildings, monuments, and symbols in architecture and design.
If we figure out the rest of the angles they would be (the outside and inside angles are straight angles):
123+153+49+119= 444
Since the total of angles in a pentagon = 540 degrees
540-444= 96°
Therefore, the measure of an angle x will be equal to 96°.
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prove that cos x = sin x cot x.
Answer:
can u give me the brainliest
the answer is in the attached documents
Alberts double number line worked example find mistake
Albert has made mistake in double number line in step 3 and 4.
The best time to utilize a double number line diagram is when the quantities have various units. The existence of several, maybe indefinitely numerous pairs of numbers in the same ratio, including those with rational number elements, can be illustrated using double number line diagrams. Unit rates (R) appear in the pair, just like in tables (R, 1).
Numerous equivalent ratios can be discovered using a double number line diagram. For instance, "Mix 5 cups of cranberry juice with 2 cups of soda water," is how a recipe for fizzy juice is written. Cranberry juice and soda water are combined in a 5:2 ratio. Equivalent ratios are produced by multiplying each constituents by the same number.
Albert has made mistake in step 3 and step 4,
Firstly he has written wrong units for the respective number line,
If ratio of 2 parts of blue and 5 parts of red is used(2:5)
The equivalent ratio will be 10:25
We get the desired output by multiplying (2:5) by 5.
The Correct units will be 5 instead of 20
And the number corresponding to 25 will be 10.
The correct double number line is drawn below.
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The admission fee to the carnival is $4. 50 for children and $7. 25 for adults. If a large group purchased 28 tickets and paid $159 how many adult tickets did they purchase?
The number of adult tickets purchased is 12.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
Let no. of adult = x
No. of children = 28 -x
So, 7. 25 * x + (28 - x) *4. 50 = 159
⇒2.75x +126=159
⇒2.75x =33
⇒x=33/2.75
x=12
Hence, the number of adult tickets purchased is 12.
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Is this a perfect square trinomial X² 6x 9?
x² + 6x + 9, this is a perfect square trinomial, which is expressed as
(x + 3)².
What is trinomial?Trinomials are algebraic formulas that include three dissimilar terms, therefore the name "trinomial."
An algebraic expression called a trinomial contains three terms that are non-zero. Trinomial expression illustrations: The trinomial x + y + z has three variables: x, y, and z.
A trinomial is formed when three monomials are added together or subtracted from one another. A quadratic trinomial has the following form: ax² + bx + c, where a, b, and c are real, non-zero values.
Given that,
x² + 6x + 9
= (x)² + 2(3x) + 9
= (x)² + 2(x)(3) + 3²
This is similar to a² + 2ab + b² = (a + b)²
so, we can write:
= (x + 3)²
= (x +3) (x + 3)
so, this is a perfect square trinomial.
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the graph represents the piecewise function
The piecewise function represented by the graph is:
f(x) = 2x when -3 ≤ x < 0
f(x) = 3 When 1/2 < x < 3/2
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Let f(x) = y = mx + c
From the graph, when -3 ≤ x < 0.
(-3, -6) and (-1, -2)
m = (-2 + 6) / (-1 + 3) = 4 / 2 = 2
(-1, -2) = (x, y)
-2 = 2 x (-1) + c
-2 = -2 + c
c = 0
f(x) = 2x
From the graph, When 1/2 < x < 3/2.
It is a horizontal line of y = 3.
f(x) = 3
Thus,
f(x) = 2x when -3 ≤ x < 0
f(x) = 3 When 1/2 < x < 3/2
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How many 1/3 cubes does it take to fill a box with a width of 2 2/3 inches length 3 1/3 inches and height 2 1/3
It takes 560 of 1/3 inch cubes to fill a box with width 2 2/3 inches, length 3 1/3 inches, and height 2 1/3 inches.
In Math's or in Geometry, a Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.
It is also said to be a regular hexahedron.
We will convert the dimensions of the given box into simple fractions for easy calculations.
The dimensions of the given box:
Length = 3 + 1/3 inches = 10/3 inches
Breadth = 2 + 2/3 inches = 8/3 inches
Height = 2 + 1/3 inches = 7/3 inches
The side of each cube = 1/3 inches
Therefore,
The no. of cubes required to fill the box is,
= (volume of the box) / (volume of each 1/3 inch cube)
= ( 10/3 * 8/3 * 7/3 ) / (1/3)^2
= 10 * 8 * 7
= 560
Thus, it takes 560 of 1/3 inch cubes to fill a box with width 2 2/3 inches, length 3 1/3 inches, and height 2 1/3 inches.
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What kind of triangle has 25 90 65?
25-90-65 is a right-angle triangle because one of the angles is 90°.
A right-angle triangle or orthogonal triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle), and two sides are perpendicular. The relationship between the sides and angles of the right triangle is the basis for trigonometry.
The hypotenuse is the facing side to the right angle. Legs are the adjoining sides to the right angle.
Properties of right angle triangle:
The right angle is the largest angle in a right-angle triangle.The hypotenuse, the opposite of the right angle, is the longest side.There are no obtuse angles in a right-angle triangle.Read more about right-angle triangles:
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What is the value of x if the points A 4 3 and B x 5 are on the circle with Centre O 2 3?
The value of x with points A ( 4, 3 ) and B ( x ,5 ) on the circle and O(2,3) as centre is equal to 2.
As given in the question,
Points A(4,3 ) and B ( x, 5 ) are on the circle.
Centre of the circle is represented by O( 2,3)
OA and OB represents the radius of the circle.
This implies
OA = OB
Using distance formula we get,
√ ( 2 - 4 )² + ( 3 - 3 )² = √ ( 2 - x )² + ( 3 - 5 )²
⇒ √ 4 + 0 = √ 4 - 4x + x² + 4
⇒4 = 4 - 4x + x² + 4
⇒4 - 4x + x² = 0
⇒ ( x - 2 )² = 0
⇒ x - 2 = 0
⇒ x = 2
Therefore, the value of x for the given point of the circle is equal to 2.
The above question is incomplete , the complete question is :
What is the value of x , if the points A(4, 3) & B(x, 5) are on the circles with Centre O(2, 3), find the value of x.
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Why 1 [infinity] is not defined?
1 [infinity] is not defined because infinity is an abstract concept and cannot be used in the same way as numeric values. Infinity is not a number or a numerical value, and therefore it cannot be used in equations or arithmetic operations.
1. Infinity is an abstract concept and cannot be used in the same way as numeric values.
2. Infinity is not a number or a numerical value.
3. Therefore, it cannot be used in equations or arithmetic operations.
4. Therefore, 1 [infinity] is not defined.
1 [infinity] is not defined because infinity is an abstract concept and cannot be used in the same way as numeric values. Infinity is not a number or a numerical value, and therefore it cannot be used in equations or arithmetic operations.
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Marcus is shopping for pants. The available styles are boot cut (B), skinny (S), and relaxed fit (R). Make an organized list to show all possible outcomes if he buts two new pair of pants.
There are 9 possible outcomes to buy two new pair of pants.
What is combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order.
Given:
we have the following Styles
Boot cut (B), Skinny (S), and Relaxed fit (R).
So, if her buys two paints then the possible combination he can take as
Boot cut x Boot cut
Skinny x Skinny
Relaxed fit x Relaxed fit
Boot cut x Skinny
Boot cut x Relaxed fit
Skinny x Relaxed fit
Skinny x Boot cut
Relaxed fit x Boot cut
Relaxed fit x Skinny
Hence, there are 9 possible ways.
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