Angle-Angle Similarity Postulate states that two polygons are similar if and only if they have two corresponding angles that are congruent.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
Given that two polygons are similar if and only if there is a correspondence among their angles and among their sides so that all corresponding angles are congruent and all corresponding sides are proportional.
The statement above is the Angle-Angle Similarity Postulate, which states that two polygons are similar if and only if they have two corresponding angles that are congruent.
Hence, Angle-Angle Similarity Postulate states that two polygons are similar if and only if they have two corresponding angles that are congruent.
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Answer:
Angle-Angle Similarity Postulate
Step-by-step explanation:
9tailsminato9.
One slice of cheese pizza contains 340 calories. A medium-size orange has one-fifth that number of calories. How many calories are in a medium-size orange
A medium-sized orange contains 68 calories. Which is one-fifth the number of calories in a slice of cheese pizza.
If one slice of cheese pizza contains 340 calories, and a medium-size orange has one-fifth that number of calories, we can find the number of calories in a medium-size orange by dividing 340 by 5. Calories in a medium-sized orange = [tex]\frac{340}{5}[/tex] calories = 68 calories. The division is an arithmetic operation used to find out how many times one number is contained within another number. The result of a division operation is called the quotient.
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AB= Round your answer to the nearest hundredth.
The length of the side AB in triangle ABC is 6.58 units.
What are trigonometric ratios in terms of a right-angle triangle?
We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjacent/hypotenuse and
tan = opposite/adjacent.
From the given figure we can conclude that we have length of the adjacent
with an angle of 20° and we have been asked to find the hypotenuse.
We know cos = adjacent/hypotenuse.
∴ cos20° = adjacent/7.
0.937 = adjacent/7.
adjacent = 7*0.937.
adjacent = 6.58.
Hence , the length of the side AB in triangle ABC is 6.58 units.
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what is the definition for relation in math?
A relation in math is a set of ordered pairs containing two elements, one from each set. The first element is from the domain and the second from the range.
Relations can be expressed as a set of ordered pairs, as a graph, or as a mapping diagram. A function is a special type of relation in which, for every element in the domain, there is one and only one element in the range. This is expressed mathematically by stating that for every x in the domain, there is one and only one y in the range such that y = f(x). To calculate a relation, the domain and range values are paired with each other, and the ordered pairs are written down. For example, if the domain is {2,3,4,5} and the range is {7,8,9,10}, then the relation would be {(2,7),(3,8),(4,9),(5,10)}.
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f(3/4) if f(x) =2x-1/4
The value of f(3/4) is 5/4.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Given is a function.
f(x) = 2x - 1/4
We have to find the value of the function when the input value x = 3/4.
For that, substitute 3/4 in place of x.
f(3/4) = (2 × 3/4) - 1/4
= 6/4 - 1/4
= 5/4
Hence the value of the function is 5/4.
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what is 3/5 into a percent?
3/5 = 0,6, it is 0.6 × 100 = 60%
Therefore, 3/5 is expressed as 60% in terms of percentage.
Percentage:
In mathematics, a percentage is a number or ratio that represents a fraction of 100. This is one way of representing a dimensionless ratio between two numbers. Other methods include ratios, fractions, and decimals. Percentage is often indicated by writing a "%" sign after the number.
According to the Question:
To convert a fraction to a decimal, it's always best to look at the denominator first. If the denominator only has prime factors of 2 and 5, you can easily pick a number multiplied by the denominator and convert it to a denominator that is a power of 10, and the result is the final prime number. If you have prime factors other than 2 and 5, converting to decimal takes longer and can result in infinite but repeating decimals.
In this case, the denominator is 5, so you can easily convert to decimal by multiplying the denominator and numerator by 2.
(3 × 20) / (5 × 20) = 60/100
Now,
To convert a fraction to a percentage, simply multiply by 100 and put a % sign next to the result.
As 3/5 = 0,6, it is 0.6 × 100 = 60%
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If Allie wants to give each of her classmates 3 pencils and the pencils come in packs of 8, and her class has 26 kids and it , how many packs of pencils does she need
Answer:
10 packs
Step-by-step explanation:
Allie wants to give each of her classmates 3 pencils, so she needs a total of 3 pencils * 26 classmates = 78 pencils.
The pencils come in packs of 8, so she needs 78 pencils / 8 pencils per pack = 9.75 packs of pencils.
Since you can't buy a fraction of a pack, Allie needs to buy 10 packs of pencils.
The EPA reports that the exhaust emissions for a certain car model has a normal distribution with a mean of 1.45 grams of nitrous oxide per mile and a standard deviation of 0.4. The car manufacturer claims their new process reduces the mean level of exhaust emitted for this car model. A SRS of 28 cars is taken and the mean level of exhaust emitted for this sample is 1.21 grams. (a) State the null and alternative hypotheses.
H0: mean=1.45
H1: mean< 1.45
=-3.175
The result is significant at p < .01.
Reject Null Hypothesis
the mean level of exhaust emitted for this model reduces emissions
What is the Null hypothesis:?
A)
Null hypothesis:
H0: mean=1.45
Alternative hypothesis:
H1: mean< 1.45
b)
estimate - the value we hypothesize standard error test statıstıc - t-statisticS
[tex]\begin{gathered}\text { test statistic }=\frac{\text { estimate }-\text { value we hypothesize }}{\text { standard error }} \\\text { t-statistic }=\frac{\bar{x}-\mu_o}{s / \sqrt{n}}\end{gathered}[/tex]
t=1.21-1.45/0.4/sqrt(28)
=-3.175
c)
t=-3.175
df=28-1=27
alpha=0.01
The P-Value is .001863.
The result is significant at p < .01.
d)
p=0.001
< alpha of 0.01
Reject Null Hypothesis
e)
there is sufficient evidence
the mean level of exhaust emitted for this model reduces emissions
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the figure below illustrates constructing___________
The figure below illustrates constructing: A. a bisector of a segment.
What is a line segment?In Mathematics, a line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points. Additionally, a line segment typically has a fixed length.
What is an angle bisector?In Mathematics, an angle bisector can be defined as a type of line, ray, or segment, that bisects or divides a line segment exactly into two (2) equal angles.
By critically observing the construction illustrated in the image attached above, we can logically deduce that it represents the bisector of line segment AB.
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How to rewrite 6x-18y=-72 in slope intersept form
Answer:
y=1/3x+4
Step-by-step explanation:
Yep
What is 2.362 divided .002
Answer: 1181
Step-by-step explanation:
A rectangle rug has an area of 500 square inches. The width of the rug is 20 inches. How many inches long is the rug?
Answer:
Step-by-step explanation:
Answer: 25 inches
Step-by-step explanation:
The equation for area of a rectangle is Length x Width, since we have the width which is 20 in., we can multiply it by a variable and set it equal to 500.
20(b)=500
divide both sides by 20
b=25
How do you find the limit of one side?
One must evaluate the function as the independent variable gets closer to the point from the provided side.
So in order to determine the limit of a function at a point from one side, one must evaluate the function as the independent variable gets closer to the point from the provided side. Take the subsequent function, for instance: scss. Copy the code f(x) = (x2 - 4) /. (x - 2)
You can evaluate the function for x values that are getting closer to 2 but always greater than 2 in order to determine the limit of this function as x approaches 2 from the positive side (i.e., as x goes closer and closer to 2 from values greater than 2). The function can be evaluated, for instance, at x = 2.1, x = 2.01, x = 2.001, and so forth. The function values will approach the target value as x approaches 2, which is 2. In order to determine the limit of this function as x approaches 2 from the positive side (i.e., as x goes closer and closer to 2 from values greater than 2). The function can be evaluated, for instance, at x = 2.1, x = 2.01, x = 2.001, and so forth.
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Solve for r r+7≥10 what is the answer
Answer:
0, 1, 2, or 3
Step-by-step explanation:
If we insert 0 into the equation:0 + 7 = ≥ 10
It is true.
If we insert 1 into the equation:1 + 7 = ≥ 10
It is true.
If we insert 2 into the equation:2 + 7 = ≥ 10
It is true.
If we insert 3 into the equation:3 + 7 = ≥ 10
It is true.
But, if we insert 4 into the equation:4 + 7 = ≥ 10
It is false.
Positive Direction:
11
5-722=22
12
29
Determine the values for x by completing the steps
shown.
0 x = 22 orx=-15
○ x=-22 orx = 15
Ox=-29 or x=-15
2
0 x = 29 or x = 15
The values for x by completing the given steps to solve for |x/6 - 7/12| = 11/6 is x=29/2 or x= -15/2.
What is modulus function?A modulus function is a function which gives the absolute value of a number or variable. It produces the magnitude of the number of variables.
Given is a modulus function, |x/6 - 7/12| = 11/6
Solving for x,
Negative Direction;
x/6 - 7/12 = -11/6
x/6 = -22/12 + 7/12 = - 15/12
x = (-15/12)6 = -15/2
x = -15/2
Positive Direction;
x/6 - 7/12 = 11/6
x/6 = 22/12 + 7/12 = 29/12
x = (29/12)6 = 29/2
x = 29/2
Hence, the values for x by completing the given steps to solve for |x/6 - 7/12| = 11/6 is x=29/2 or x= -15/2.
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The question is not complete the similar question is solved.
An equilateral triangle shares a single side with a kite to form a new
quadrilateral, as shown below.
Calculate the size of angle p.
Give your answer in degrees (°).
Answer:
<P = 41
Step-by-step explanation:
we can consider this first figure as a quadrilateral and the trianlgle attached to be is equilateral triangle (as it is already shown in the figure that sides are equal)
we know that each angle of equalateral triangle is 60°
we can see that angle 79° is attached to it and even other angle is also attached
let the other angle be x
we can notice that x and the angle of equi triangle make a linear pair
so 180 - 60
= 120°
the opposite angle to the angle x will be also equal as angles on the same side of qual sides will be equal
now we know that total angle sum of quadrilateral is 360°
so
79 + 120 + 120 + <P = 360
319 + <P = 360
<P = 360 - 319
<P = 41
1. The rectangular prism and rectangular
pyramid below have the same volume.
Determine the value of x, the height of the
pyramid.
6 in
X:
12 in
3 in
XI
12 in
6 in
The value of x is 9. A quadrilateral having four equal, right-angled angles is called a rectangle.
What is meant by rectangular?A rectangle is a closed 2-D shape with four sides, four corners, and four right angles (90°). The opposing sides of a rectangle are equal and parallel. A rectangle is a type of quadrilateral with four 90-degree-distance vertices and parallel sides that are equal to one another.It is also referred to as an equiangular quadrilateral because of this. A rectangle can also be referred to as a parallelogram since its opposing sides are equal and parallel.A rectangle is a quadrilateral with four equal, right-angled angles. In addition to having all equal angles, a square also has all equal sides. So, a specific example of a square is a rectangle.The following formula determines a rectangular prism's volume:
V = l × b × h
To achieve, we substitute the dimensions.
V = 6 × 3 × 12 in^3
The rectangular pyramid's volume is,
V = 1/3 × 6 × 12 × x in^3
Comparing the two volumes results in,
1/3 × 6 × 12 × x = 6 × 3 × 12
We divide through by 6 × 12 to get,
x/3 = 3
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The numerical value of standard deviation can never be______
The standard deviation lies in the range of 0 to 1. The numerical value of standard deviation can never be negative.
The standard deviation is a measure of amount of variation or dispersion of a set of values. When we compare two unequal observations, the result is always greater than zero i.e., always positive.
Standard deviation is the square root of the variance of the observations and the root always gives values either positive or zero, it can never be negative.
Therefore, the numerical value of the standard deviation can be positive. The value of standard deviation is always greater or equal to zero.
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Please answer this. will get alot of points
The horizontal distance between Ryan and the dolphin is 57.87 feet.
The airplane is 10735.96 feet away from the control tower
The angle of depression from the top of the lighthouse to the boat is 0 degrees.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Using trigonometry, we can find the horizontal distance x:
tan(15) = x / 228
x = 228 tan(15)
x = 57.87 feet
Therefore, the horizontal distance between Ryan and the dolphin is 57.87 feet.
2. Using trigonometry, we can find the horizontal distance between the airplane and the control tower:
tan(56) = x / 7450
x = 7450tan(56)
x = 10735.96 feet
Therefore, the airplane is approximately 10735.96 feet away from the control tower
3. We want to find the angle of depression from the top of the lighthouse to the boat. Since the lighthouse is 275 feet above the water, we can use trigonometry to find the height of the lighthouse above the boat:
tan(90) = 275 / x
x = 275 / tan(90)
x = undefined
Therefore, the angle of depression from the top of the lighthouse to the boat is 0 degrees.
Hence, the horizontal distance between Ryan and the dolphin is approximately 57.87 feet.
the airplane is approximately 10735.96 feet away from the control tower
the angle of depression from the top of the lighthouse to the boat is 0 degrees.
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One serving of pasta salad needs a cup of macaroni. How many 1/3 servings can I make with a cup of macaroni? 5/6
Answer: You can make 5/3 * (1/1) = 5 servings with a cup of macaroni.
And, with 5 servings, you can make 5 * (3/1) = 15 1/3 servings of pasta salad.
Step-by-step explanation:
Urgent calculating the time of a trip
The number of minutes that you walk directly from the parking lot to the house will be 12.73 minutes.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
The house is located 1480 ft down a paved path that parallels the beach, which is 740 ft wide. Along the path, you can walk 330 ft/min, but on the beach, you can only walk 130 ft/min.
The distance between the house and the parking is given as,
d² = 740² + 1480²
d² = 547,600 + 2,190,400
d² = 2,738,000
d = 1,654.69 feet
Then the time taken is given as,
T = 1,654.69 / 130
T = 12.73 minutes
The number of minutes that you walk directly from the parking lot to the house will be 12.73 minutes.
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3x-6= 5x - 2
Based on the equation above, what is the value of
2x-4?
A) -8
B) -2
C) 2
D) 6
The value of the expression is -8. Option A
How to determine the value
It is important to note that algebraic expressions are expressions that are made up of variables, terms, coefficients, constant and factors.
From the information given, we have that;
3x-6= 5x - 2
collect like terms
3x - 5x = -2 +6
subtract the like terms
-2x = 4
Make 'x' subject
x = -2
Substitute the value in the equation
2x - 4
2(-2) - 4
expand bracket
-8
Hence, the value is -8
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Carman has a piece of wood that is 8 1/2 inches in length. Licia has a piece of wood that is 1 5/8 longer than Carman piece of wood. How long is lucia piece of wood.
Based on the information provided, it can be concluded that Licia's piece of wood is 10 1/8 long.
How to determine how long is Licia's piece of wood?To determine Licia's piece of wood, let's first consider the information given:
Carman piece of wood = 8 1/2Licia wood is 1 5/8 longer than CarmanBased on this, to find out the length of Licia's let's add the fractions provided, the process is shown as follows:
Licia piece of wood = 8 1/2 + 1 5/8= 17/2 +13/8= 81/8= 10 1/8
Therefore, Licia's piece of wood is 10 1/8
This result is equal to 10,125
1/8 = 0,125
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Use the drawing tool(s) to form the correct answer on the provided graph.
Draw the resulting image after the given triangle is rotated 90° counterclockwise about the origin.
Drawing Tools
Select
Point
Line Segment
Click on a tool to begin drawing
Reset
<+
Delete Undo
10
The triangle is rotated 90° counterclockwise about the origin shown below.
What is Transformation?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
we have to rotate 90° counterclockwise about the origin.
as, the rule for 90° counterclockwise about the origin is (x, y) becomes
(-y, x).
As, the coordinates after rotation are :
(-8, 3)---> (-3, -8)
(-2, 8)---> (-8, -2)
(-5, 7) -----> (-7, -5)
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Convert this rational number to its decimal form and round to the nearest thousandth 4/7
Answer:
4/7 to decimal rounded to nearest thousandth is 0.571
What is 4 2 1 rule ?
The 4-2-1 rule is a guideline used to help determine the amount of water an individual needs to drink each day.
The rule states that an individual should drink 4 liters of water for every 50 pounds of body weight, 2 liters of water for every 50 pounds of body weight if they are exercising, and 1 liter of water for every 50 pounds of body weight if they are in a hot or dry environment.
To calculate how much water you need to drink using the 4-2-1 rule, simply follow these steps:
1. Determine your body weight in pounds.
2. Divide your body weight by 50 to get the number of 50-pound increments in your weight.
3. Multiply the number of 50-pound increments by 4 to get the amount of water you need to drink if you are not exercising or in a hot or dry environment.
4. Multiply the number of 50-pound increments by 2 to get the amount of water you need to drink if you are exercising.
5. Multiply the number of 50-pound increments by 1 to get the amount of water you need to drink if you are in a hot or dry environment.
6. Add the amounts from steps 3, 4, and 5 together to get the total amount of water you need to drink each day.
For example, if you weigh 150 pounds, you would need to drink 4 liters of water for every 50 pounds of body weight (150 / 50 = 3), 2 liters of water for every 50 pounds of body weight if you are exercising (3 x 2 = 6), and 1 liter of water for every 50 pounds of body weight if you are in a hot or dry environment (3 x 1 = 3). Therefore, you would need to drink a total of 13 liters of water each day (4 + 6 + 3 = 13).
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What is the equation of a line that contains the points (8, -3) and (-8, 3)?
Answer:
the answer is y=/0.375x
Step-by-step explanation:
solve foe x. 6x = 72
Answer:
Answer: x=12
6 x 12=72
Answer:
x = 12 .....................
Step-by-step explanation:
.
Jane is choosing between two exercise routines. In Routine # 1, she burns 22 calories walking. She then runs at a rate that burns 5.75 calories per minute. In Routine #2, she does only running, burning 8.5 calories per minute. For what amounts of time spent running will Routine #1 burn at least as many calories as Routine #2? Use t for the number of minutes spent running, and solve your inequality for t.
Answer: 3.8 minutes!
Step-by-step explanation:
The answer is 3.8 minutes. To solve for t, we need to set up an inequality where the calories burned in routine #1 is equal to or greater than the calories burned in routine #2. We can write this as 22 + 5.75t ≥ 8.5t. Then, we can subtract 8.5t from both sides to get 22 ≥ -2.75t. Finally, we can divide both sides by -2.75 to get t ≤ -8/2.75, which simplifies to t ≤ 3.8. Therefore, Jane needs to run for 3.8 minutes in Routine #1 in order to burn at least as many calories as Routine #2.
Answer:
Jane needs to run for 8 minutes or less in Routine #1 for it to burn at least as many calories as Routine #2. If she runs for more than 8 minutes in Routine #1, then Routine #2 will burn more calories.
Step-by-step explanation:
In Routine #1, the total number of calories burned is:
C1(t) = 22 + 5.75t
The first term represents the calories burned while walking, and the second term represents the calories burned while running.
In Routine #2, the total number of calories burned is:
C2(t) = 8.5t
This represents the calories burned while running, as there is no walking in Routine #2.
We want to find the values of t for which C1(t) is greater than or equal to C2(t). So we can set up the following inequality:
C1(t) ≥ C2(t)
Substituting the expressions for C1(t) and C2(t), we get:
22 + 5.75t ≥ 8.5t
Simplifying the inequality, we get:
22 ≥ 2.75t
Dividing both sides by 2.75, we get:
t ≤ 8
So Jane needs to run for 8 minutes or less in Routine #1 for it to burn at least as many calories as Routine #2. If she runs for more than 8 minutes in Routine #1, then Routine #2 will burn more calories.
Please help
When 5 cups of flour are used in a recipe, 2.5 teaspoons of baking soda are required. Anna wants to reduce the recipe to only 3 cups of flour. How many teaspoons of baking soda should she use? Show your work.
The amount of baking soda he used is 1.5 teaspoons.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
Given that
When 5 cups of flour are used in a recipe, 2.5 teaspoons of baking soda are required.
Anna wants to reduce the recipe to only 3 cups of flour.
We have to determine
How much baking powder should he use?
According to the question
Let x be the amount of baking soda he used,
A recipe for waffles calls for 5 cups of flour and 2.5 teaspoons of baking powder.
If Jason uses 3 cups of flour.
Then,
The amount of baking soda he used is
x/3 = 2.5/5
solving we get,
x = 1.5
Hence, The amount of baking soda he used is 1.5 teaspoons.
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In a 120-volt circuit having a resistance of 12 Ω (ohms), the power W in watts when a current I (in amperes) is flowing is given by W = 1201 - 121^2. Determine the maximum power that can be delivered in this circuit.
If you could show work, it would be excellent, thank you!
Answer:
300 w
Step-by-step explanation:
swim this question we have an equation w = 21 25 - 2012 I square which represents the power w where w is the power in watts and 120 volt circuit is there which has a resistance of 12 ohm when current I is flowing through the circuit the voltage resistance and current is what is the maximum power in war that can be delivered in this circuit so we have to find out the maximum value of power that can exist in the circuit with 120 volts AC circuit and 12 homes of resistance ok so to find the maximum value of this in an equation we need to find vi we can the best way is we can find out the Maxima Abhishek creation and how do you
find the maximum to find the maximum we can differentiate this equation with respect to I and when the equator when we will equip the differentiation of this equation 20 the value of I that will obtain that will be obtained after doing this will be the maximum for this equation let me show you how that is differentiate DW by D I can we differentiate this this equation with respect to I we get 120 - 24 I know what we have to do this week with this 20 now 120 - 24 I = 20 with this I = 25 we get the value of equal to 55 is the maximum for this equation which means that if we put the value of I
45 we replace if the Avengers equation replace iPhone 5 will get the maximum value of w which is what you wanted right we wanted the maximum power in watts letters replace I buy 5 this equation the equation is 120 I -12 I square be replaced by 5 we get the answer as 300 w this is our answer