Answer:
The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, the length of one side of a triangle must always be shorter than the sum of the lengths of the other two sides. This theorem is often used in geometry to determine whether or not a given set of lines can form a triangle.
When it comes to angles, the Triangle Inequality Theorem can be used to determine whether or not a triangle can be formed given the measures of its angles. For example, if the measures of two angles in a triangle are 45 degrees and 60 degrees, the measure of the third angle must be less than 180 degrees - 45 degrees - 60 degrees, or 75 degrees. If the measure of the third angle is greater than 75 degrees, it is not possible for the three angles to form a triangle.
Overall, the Triangle Inequality Theorem is a useful tool for understanding the relationships between the sides and angles of a triangle, and for determining whether or not a given set of lines or angles can form a triangle.
Step-by-step explanation:
The regular price is $150 but there is a 20% off coupon. What is the sale price?
Answer:
30
Step-by-step explanation:
30
Which ordered
pair is on the line
y = -5x + 2?
Answer:
(0,2)
(1,-3)
(2,-8)
How many numbers are on a fair dice?
Answer:
When you roll a fair die you have an equal chance of getting each of the six numbers 1 to 6. The expected value of your die roll, however, is 3.5.
Step-by-step explanation:
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What do you call 2 4 6 8 10?
The general rule that describe 2 4 6 8 10 the sequence.
What exactly are sequence and example?
An ordered list of numbers is a sequence. To go forward in the defined pattern, three dots are shown. A phrase is used to describe each number in the series.
One is the first word, three is the second, five is the third, and so on, in the series 1, 3, 5, 7, 9,...
Which four forms of sequence are there?
Arithmetic sequences, geometric sequences, quadratic sequences, and special sequences are the four primary categories of distinct sequences you need to be familiar with.
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State whether each figure has a line of symmetry (yes or no.) If so, draw all possible lines of symmetry. (Some may have more than one.)
Answer:
Step-by-step explanation:
How do you write a preimage?
Answer: The image T(V) is defined as the set {k | k=T(v) for some v in V}. So x=T(y) where y is an element of T^-1(S). The preimage of S is the set {m | T(m) is in S}. Thus T(y) is in S, so since x=T(y), we have that x is in S.
Given a function f:A→B, and D⊆B, the preimage D of under f is defined as f−1(D)={x∈A∣f(x)∈D}. Hence, f−1(D) is the set of elements in the domain whose images are in C. The symbol f−1(D) is also pronounced as “f inverse of D.”
In geometry, figures in a plane can be transformed in a variety of ways, including shifts and scaling, to produce new shapes. The new (transformed) shapes are called images and the original, unaltered shapes are called preimages.
In geometry, figures in a plane can be transformed in a variety of ways, including shifts and scaling, to produce new shapes. The new (transformed) shapes are called images and the original, unaltered shapes are called preimages.
Step-by-step explanation:
What is special about rigid motion transformations?
A rigid body motion, also known as a rigid transformation, happens when a point or object travels while maintaining its size and shape.
What are the characteristics of a rigid motion transformations?While the image's size and shape are unaffected by rigid body motion, its location and orientation are. The three fundamental movements of a rigid body are translation, reflection, and rotation. Prior to movement, archetypes depict points or forms.
A rigid body motion, also known as a rigid transformation, happens when a point or object travels while maintaining its size and shape. Stretching and other non-rigid motions, which alter an object's size, are not comparable to this.
Area of triangle = 1/2 X b X h
b= 10
h=5
A = 1/2 X 10X 5
A = 25 unit sq.
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How do you describe the graph of x is equal to 2?
The graph of x = 2 is a vertical line parallel to y-axis. Also, the slope of x = 2 is undefined and there is no y-intercept.
In this question we need to describe the graph of x is equal to 2.
To draw the graph of x = 2, firstwe find some coordinates of the points.
Consider the points (2, 1), (2, 0), (2, -1)
[As the x coordinate is fixed, we can take any value of y coordinate]
The graph of x = 2 is as shown below.
The graph of x = 2 is a straight vertical line, which is parallel to y-axis.
There is no y-intercept to the graph of x = 2.
Also the slope of line x = 2 is undefined.
Therefore, the graph of x = 2 is a straight line with Slope = Undefined
and no y-intercept.
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Please help me with this question
many thanks
The surface area of the cuboid is 148 cm².
What is surface area of a cuboid?The surface area of a cuboid is the total space occupied by it. A cuboid is a six-faced three-dimensional shape in which each face is in the shape of a rectangle.
Given that, a cuboid has volume of 120 cm³ and the area of the base of the cuboid is 30 cm².
We know that, the volume of cuboid is l×b×h.
Here, l×b=30
Now, 30×h=120
h=4 cm
We know that, surface area of the cuboid is 2(lb+bh+hl)
= 2(30+h(b+l))
= 2(30+4(b+l))
We have, l×b=30
Pair of factors of 30 are
2×15=30
3×10=30
5×6=30
So, the possible surface area is
2(30+4(2+17))
= 2×106
= 212 cm²
2(30+4(3+10))
= 2×82
= 164 cm²
2(30+4(5+6))
= 2×74
= 148 cm²
Therefore, the surface area of the cuboid is 148 cm².
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If the truth values of both and are , then which of the following is a valid statement?
The truth value of p → q is F.
The truth value of p → q is T.
The truth value of p → q cannot be determined without knowing what p and q represent.
The truth value of p → q could be either T or F.
The valid statement regarding the truth value is B. The truth value of p → q is T.
What is a truth value?A truth value, also known as a logical value, is a measure of how true a proposition is in logic and mathematics. In classical logic, there are only two possible truth values.
A proposition's attribute indicating whether it is true or false is the definition of a truth value. A statement or proposition's truth or falsehood determines its truth value. Every statement has one of the two truth values, true or false, according to our theory.
Since the truth values of p and q are both false, the truth value of p → q is T according to the truth table.The correct option is B.
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Complete question
If the truth values of both p and q are false, then which of the following is a valid statement?
The truth value of p → q is F.
The truth value of p → q is T.
The truth value of p → q cannot be determined without knowing what p and q represent.
The truth value of p → q could be either T or F.
prove the identity
sin2theta = 2 tan theta over 1 + tan squared theta
help!
Step-by-step explanation:
kya tablet side apply the side of the wall has 22 M and 20 m
find the area and perimeter of an equilateral triangle whose equal side is 6cm
Answer:
Area = 9√3 cm²
Perimeter = 18 cm
Step-by-step explanation:
Area of equilateral triangle ABC =
(√3/4) × 6²
= (√3/4) × 36
= 9√3 inches2
ABC is an equilateral triangle with side = 6 cm
Perimeter of an equilateral triangle = AB+BC+CA
Perimeter of an equilateral triangle = 6+6+6
Perimeter of an equilateral triangle = 18 cm
What is the formula for height?
The height of the triangle is determined by the formula, 2 × Area / Base
Given,
Triangle;-
A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.
We have to find the formula for height of triangle;
According to theorem;
The area of the triangle = 1/2 × base × height
Then,
Height of the triangle = 2 × Area / Base
That is,
The formula for the height of the triangle is 2 × Area / Base
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Complete question is here;
What is the formula to find the height of a triangle?
What is pyramid equation?
The equation of the pyramid is as follow,
Volume is equal to one by third of the Area of the base into Height.
V=(1/3) X A X H, where A is area and H is height.
The sum of a pyramid's side faces makes up the lateral surface area.
LSA of the pyramid multiplied by the base's area gives the total surface area.
A pyramid is a 3D shape that has a base made of a polygon and faces that are all triangular and linked. The conventional form of a pyramid is created by joining each vertex of the base to a single common tip or apex. In this part, let's study more about pyramids.
Volume of a PyramidThe area encompassed between a pyramid's faces is referred to as the pyramid's volume. The formula for each pyramid varies based on the pyramid's foundation. The formula used to determine a pyramid's volume, which is expressed in cubic units, is as follows V=(1/3) X A X H.
Surface Area of a PyramidDifferent forms of pyramids have varying amounts of surface area. The following formula is used to determine a pyramid's surface area:
Surface Area = Base Area + (½ × Perimeter of the base × Slant height)
Surface Area = Base Area + Lateral Area.
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there are six balls in a box if we select three balls what is the probability of having one white ball
The probability of having one white ball is 1/20 or approximately 0.05.
To find the probability of selecting one white ball out of three balls, you need to know the number of white balls in the box and the total number of balls in the box. You also need to know whether the balls are being selected randomly or not.
Assuming that there is only one white ball in the box and the rest are some other color, and that the balls are being selected randomly.
The probability of selecting one white ball out of three would be:
Probability = (number of ways to select one white ball out of three) / (total number of ways to select three balls)
Since there is only one white ball, there is only one way to select one white ball out of three. The total number of ways to select three balls out of six is 6 choose 3, which is equal to 20.
Therefore, the probability of selecting one white ball out of three would be
Probability = (number of ways to select one white ball out of three) / (total number of ways to select three balls)
Probability = 1/20
Probability = approximately 0.05.
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In ΔSTU, s = 3.4 cm, ∠T=165° and ∠U=13°. Find the length of t, to the nearest 10th of a centimeter.
Answer:
25.2 cm
Step-by-step explanation:
[tex]\angle S=180^{\circ}-165^{\circ}-13^{\circ}=2^{\circ} \\ \\ \frac{t}{\sin T}=\frac{s}{\sin S} \\ \\ \frac{t}{\sin 165^{\circ}}=\frac{3.4}{\sin 2^{\circ}} \\ \\ t=\frac{3.4\sin 165^{\circ}}{\sin 2^{\circ}} \\ \\ t \approx 25.2[/tex]
Bonnie makes $12.40/hr and works as a server. on tuesday she worked for 6 hours and twenty minutes and made $110 in tips. how much did she make in total and what is her hourly wage?
Answer: 188.53$ in total.
$31.42 as hourly wage .
Step-by-step explanation:
Wage1 for 6hours = $12.4 * 6
Wage2 for 20minutes = $12.4 / 3
Since an Hour has three 20 minutes in it , so hourly wage $12.4 is divided by 3 to get the wage for a 20minute work.
Wage3 as Tips = $110
Total Wages for Tuesday = Wage1 + Wage2 + Wage3
= $188.53
New hourly Wage = $188.53 / 6 = $31.42
A clerk counted 13 small baseball caps, 36 medium baseball caps, and 27 large baseball caps on the store shelves. She also counted 10 small baseball caps and 15 medium baseball caps in the stockroom.
Organize the data in a matrix. Name the matrix B. Label the rows and columns.
Each baseball cap sells for $19. Create the matrix that shows the total value of each cap size in each location. Show your work.
The matrix B that organizes the data is given as follows:
B = [13, 36, 27,
10, 15, 0,
23, 51, 27].
The matrix that shows the total value of each cap size in each location is given as follows:
C = [247, 684, 513,
190, 285, 0,
437, 969, 513].
How to define the matrix B?The matrix B is defined considering that it will have three rows and three columns, as follows:
Row 1: Number of each type of cap on the store shelves.Row 2: Number of each type of cap on the stockroom.Row 3: Total number of each type of car -> Row 1 + Row 2.Column 1: Small caps.Column 2: Medium caps.Column 3: Large caps.Then the matrix B is defined as follows:
B = [13, 36, 27,
10, 15, 0,
23, 51, 27].
The cost of each baseball cap is of $19, thus the cost matrix is obtained multiplying the matrix B by the constant of 19.
When a matrix is multiplied by a constant, all the elements of the matrix are multiplied by the constant, hence the cost matrix is given as follows:
C = [247, 684, 513,
190, 285, 0,
437, 969, 513].
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HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer: Adult: $20 Child: $9
Step-by-step explanation:
20 + 20 + 20 = 60
9 + 9 + 9 + 9 = 36
60 + 36 =96
How do I solve for x?
Step-by-step explanation:
I just answered this question. how often did you post it ?
in short again :
360 = 8x + 20 + 104 + arc angle KJP
arc angle KJP = 2× opposite angle of K and P =
= 2×(5x + 1)
so, together
360 = 8x + 124 + 2×(5x + 1) = 8x + 124 + 10x + 2 =
= 18x + 126
234 = 18x
x = 13
p varies directly with T and p = 400. When T = 500. Find the value of p when T = 600
Answer:
Step-by-step explanation:
When the temperature T is 500, the pressure p is 400. If we let "k" represent the constant of proportionality that relates p and T, then we can write the relationship between p and T as:
p = k * T
Substituting the known values of p and T into this equation, we get:
400 = k * 500
Solving for the constant of proportionality k, we find that:
k = 400/500 = 0.8
Now that we know the value of the constant of proportionality k, we can use it to find the value of p when T = 600. Substituting this value of T into the equation above and solving for p, we get:
p = 0.8 * 600 = 480
Therefore, when T = 600, the pressure p is 480.
Answer the questions about the work below:
3x − 8 ≤5x + 6
3x ≤5x −2
−2x ≤−2
Are there any errors in the above work so far? Response area
The correct final answer is:
Answer:
Yes, there is an error in the third step of the solution. The correct result of the third step should be -2x ≤ 8, not -2x ≤ -2. The error occurred because the incorrect value was subtracted from both sides of the inequality
Step-by-step explanation:
The final answer for the inequality 3x − 8 ≤5x + 6 is x ≥ -7, and the third step is wrong, the right answer is -14 ≤ 2x.
What is inequality?An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. It is most frequently used to compare the sizes of two numbers on the number line.
Given:
3x − 8 ≤ 5x + 6
Add 8 on both sides of the inequality as shown below,
3x − 8 + 8 ≤ 5x + 6 + 8
3x ≤ 5x + 14
Subtract -3x from both sides as shown below,
3x - 3x ≤ 5x + 14 - 3x
0 ≤ 2x + 14
Subtract 14 from both sides as shown below,
0 - 14 ≤ 2x + 14 - 14
-14 ≤ 2x
Divide both sides by 2 as shown below,
-14 / 2 ≤ 2x / 2
-7 ≤ x
or x ≥ -7
Thus, the final answer is x ≥ -7.
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The ratio of reeta and neha income is 8:6. If reeta income is 2800. Find the income of neha
Answer: I don't believe the explanation above provides the correct answer. You would need to use the concept of proportions to solve this problem. The Answer I got is 2100.
Step-by-step explanation:
It is very simple all you have to do is setup a proportion with Reena's on top and Neha's on the bottom.
8/6 = 2800/x
Now cross multiply,
2800 * 6 = 8x
x=16800/8
x=2100
Now we can double-check by dividing the original ratio with the ratio we found.
8/6 = 1.3333333...
2800/2100 = 1.333333...
Thus, the answer is correct.
A mountain in jackson county is eroding and losing elevation at a rate of 5% every millennium. If the current elevation is 1,300 meters, how tall will the mountain be in 8 millennia?.
So the mountain will be approximately 798.02 meters tall after 8 millennia.
The mountain loses 5% of its elevation every millennium, which is the same as losing 0.05 * its current elevation. Therefore, after 1 millennium, the mountain's elevation will be 1 - 0.05 = 0.95 times its current elevation. After 2 millennia, it will be 0.95 * 0.95 = 0.9025 times its current elevation, and so on.
After 8 millennia, the mountain's elevation will be 0.95^8 times its current elevation. We can calculate this as follows:
Elevation after 8 millennia = 1,300 meters * 0.95^8
= 1,300 meters * 0.6134
= approximately 798.02 meters
So the mountain will be approximately 798.02 meters tall after 8 millennia.
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After 8 millennia, the mountain's elevation will be 0.95^8 times its current elevation. We can calculate this as follows:
Elevation after 8 millennia = 1,300 meters * 0.95^8
= 1,300 meters * 0.6134
= approximately 798.02 meters
So the mountain will be approximately 798.02 meters tall after 8 millennia.
the proportion of people in each sample who experience side effects is recorded. are the sample sizes large enough to assume that the sampling distribution of the difference in sample proportions is approximately normal?
As the sample size is large enough to assume so the sample proportion mentioned in the above question is approximately normally distributed.
What is approximately normal distribution?It is a statistical expression used to determine an approximate value of some random variables.
How to calculate if a sample proportion is approximately normal?we measure the approximately normal proportion by the outcome of the product of the size of population, n and the proportion of population, p
p =X/n, where X is the sample size and n denote the size of population
If n×p ≥ 10 then the sampling distribution is approximately normal.
hence, as we have large proportion of sample, so it is approximately normal.
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2x + 5x = 3x + 16
Someone help. Can you help me figure out what x is and simplify this equation?
Answer:
Step-by-step explanation:
Rena Roosh, fun name :P so, just use your algebra skillz
2x + 5x = 3x + 16
I'm wondering if there is an extra "x" on the right hand side,
anyway
7x -3x = 16
4x = 16
x = 4
see??
Answer:
Step-by-step explanation: Perform any simplification of like terms if possible
7x=3x+16
Collect x terms on one side. Can use the left side for x terms. That means 3x must dissapear. To do this we need to take 3x from both sides.
7x-3x=3x-3x+16
4x=16
To solve for x we need to divide by 4 on both sides
4x/4=16/4
x=4
What are the 4 functions of a roots?
Four main functions of the roots of the plant is given by:
1. Anchorage
2. Absorption of water and minerals
4. Prevention of the soil erosion.
5. Transportation of food from the soil.
Four function of the roots of any terrestrial plants:
Anchorage of the plant :Due to anchorage of the plant root fix in the soil and help in growing the aerial shoot system part of the any tree or plant.
Absorption of water and minerals: It helps to absorb water and minerals from the soil to the roots of the plants .
Prevention of the Soil Erosion : Due to root of the plant soil gets binds to the roots of the plants and does not or in very less quantity get eroded by water or wind.
Transport : Roots of the plants helps to transport food , salt , mineral , and water which given or present in the soil to the shoot or leaves and flowers , fruit of the plant.
Therefore, the four functions of the roots are:
1.Anchorage of the plant
2. Absorption of water and minerals
3. Prevention of the soil erosion
5. Transportation of food.
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if ABC = PQR, then AC =
Answer:
PR
Step-by-step explanation:
Because both triangles are equal to each other, so their sides will equal each other too!
You are about to take a major assessment, and each question is one two types. Multiple-choice questions are worth 2 points each, and short-response questions are worth 4 points each. The assessment is worth 100 total points. Let x represent the number of multiple-choice questions, and let y represent the number of short-response questions.
2X + 4Y = 100 is the equation.
What is the equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Let's assume that X is the quantity of multiple-choice questions and Y is the quantity of short-answer questions.
Given that the short-answer questions are worth four points and the multiple-choice questions are for two, the equation is 2X + 4Y = 100.
Thus the equation for 2 points each, and short-response questions are worth 4 points each. The assessment is worth 100 total points where x represent the number of multiple-choice questions, and let y represent the number of short-response questions.
2X + 4Y = 100.
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5
6
A curve has equation y = x³ + ax + b.
The stationary points of the curve have coordinates (2, k) and (-2, 10-k).
Work out the value of a, the value of b and the value of k.
The value of 'a' is equal to -12, the value of 'b' is equal to 5 and the value of 'k' is equal to -11.
The stationary points of a curve are those points at which the first derivative of the function f(x) becomes zero. At the stationary points, the nature of the function is neither increasing nor decreasing.
→ The stationary points of a curve can either be a local minima or a local maxima of the function.
→ If we plot the graph of the curve, then stationary points can be said to be those points at which the tangent to the curve becomes horizontal which means the tangent becomes parallel to the x-axis.
→ Therefore for a point (a,b) to be the stationary point of a function f(x): f'(a) must be equal to zero.
→ For the given question:
f(x) = y = x³ + ax + b
f'(x) = 3x² + a
(2, k) is a stationary point:
f'(2) = 0
f'(2) = 3(2)² + a = 0
a = -12
The value of 'a' comes out to be equal to -12.
→ Hence the equation of the curve is: y = x³ - 12x + b
→ The stationary points (2, k) and (-2, 10-k) must be lying on the curve, hence they must satisfy the equation of the curve:
→ Putting (2, k) in the equation of the curve:
k = (2)³ - 12(2) + b
(k - b) = -16 - Equation (i)
→ Putting (-2, 10 - k) in the equation of the curve:
(10 - k) = (-2)³ -12(-2) + b
(10 - k) = -8 + 24 + b
b = -6 - k - Equation (ii)
→ Putting the value of 'b' from the equation (ii) in equation (i):
k - (-6 - k) = -16
k + 6 + k = -16
2k = -22
k = -11
∴ The value of 'k' comes out to be equal to -11.
→ Putting the value of 'k' in equation (i):
k - b = -16
-11 - b = -16
b = 5
∴ The value of 'b' comes out to be equal to 5.
Therefore, the value of 'a' is equal to -12, the value of 'b' is equal to 5 and the value of 'k' is equal to -11.
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