The value of x in the triangle will be 30°
How to calculate the value?Let the base angles be x. The vertex angle will be:
= 2(x + x) = 4x
Since the sum of the angles in a triangle is 180°, therefore, 4x + x + x = 180°
6x = 180°
x = 180°/6
x = 30°
Therefore, the angles are 30°, 30°, and 120°. This makes up 180°.
Complete question:
In an isosceles triangle, the vertex angle is twice the sum of the base angles. Fund the angles of the triangle.
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A standard number cube was rolled multiple times, and the results were recorded in the table above. What can be said
about the experimental probability of rolling a two versus the theoretical probability of rolling a two?
Answer:
Experimental Probability = 1/3
Theoretical Probability = 1/6
========================================================
Explanation:
Count how many times the number "2" shows up in the "Result" column. There are 4 instances of this value. This is out of 12 trials total.
Divide the two numbers to get 4/12 = 1/3 as the experimental probability
-------------
In contrast, the theoretical probability is 1/6 because there's 1 side labeled "2" out of 6 sides total.
The decimal form of each fraction is:
1/3 = 0.333 approximately
1/6 = 0.167 approximately
A regular hexagon is truncated to form a regular dodecagon (12-gon) by removing identical isosceles triangles from its six corners. What percent of the area of the original hexagon was removed
7.2 percent of the area of the original hexagon was removed
The area of hexagon is the region that lies within the sides of the hexagon. A hexagon is a two-dimensional shape that has 6 sides, 6 angles, and, 9 diagonals, and the sum of its interior angles is 720°
Area of the hexagon = (3√3 s2)/2, where 's' is the length of the side of the hexagon.
Her, We have
[tex]\(1-2s=s\sqrt3, 1=2s+s\sqrt3, 1=s(2+\sqrt3), s=\frac{1}{2+\sqrt3}\)[/tex]
Rationalize the denominator to get [tex]\(s=2-\sqrt3\)[/tex]
The area of the hexagon is [tex]\(\frac{3\sqrt3}{2}\)[/tex] and the dodecagon is [tex]\(\frac{3s^2\sqrt3}{2}\).[/tex]
The deleted area is [tex]\(s^2=0.072=7.2%\)[/tex] percent
Formula used:
Area = (3√3 s2)/2
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one day, duncan and his friends had lunch while sitting at tables of 6. another day, they had lunch at tables of 5. what is the smallest number of people that could be in the group?
Answer:
the smallest number of people that could be in his group with the possibility of it being less than five people, will be three people.
Does anyone know what the answer to this
Answer:
60 degrees
Step-by-step explanation:
Since all three sides are the same length, all three angles must be the same size. This means the triangle is an equilateral triangle
The angles are 60 degrees
Answer:
Hello! The answer is 60°.
Step-by-step explanation:
As marked by the dashes on each side, the sides are congruent. If the sides are congruent, this means that the angle measures are equal.
Having three equal sides is an equilateral triangle, and the total angle measure sum is 180.
To find the measure of angle y, you will have to divide the total angle measure by the number of angles:
180 ÷ 3 = 60
The measure of angle y = 60°
asap! find the length of the arc
Answer:
8π ft
Step-by-step explanation:
Arc length = 2πr ( θ / 360 )
Here,
θ = 90
r = 90 ft
Arc length = 2πr ( θ / 360 )
Arc length = ( 2π * 16 ) ( 90 / 360 )
= ( 2π * 16 ) ( 1 / 4 )
= ( 2π * 16 )/4
= 2π * 4
Arc length = 8π ft
Answer:
B
Step-by-step explanation:
the arc length is calculated as
arc = circumference of circle × fraction of circle
= 2πr × [tex]\frac{90}{360}[/tex]
= 2π × 16 × [tex]\frac{1}{4}[/tex]
= 2π × 16 × [tex]\frac{1}{4}[/tex]
= 32π × [tex]\frac{1}{4}[/tex]
= 8π ft
The number of students who attend a school could be divided among 10, 12, or 16 buses, such that each bus transports an equal number of students. What is the minimum number of students that could attend the school
Answer:
240 students
Step-by-step explanation:
Least common multiple:To find the minimum number of students, we have to find the LCM of 10, 12, 16
10 = 2 * 5
12 = 2 * 2 * 3
16 = 2 * 2 * 2 * 2
LCM = 2 * 2 * 2 * 2 * 3 * 5
= 240
which box is in the wrong spot?
The first function isn't decreasing over the largest interval, so the box in the wrong spot is the first one.
Which box is in the wrong spot?
Here we have 3 cubic functions.
A function is decreasing when reading from left to right, the curve goes downwards.
Now, if you look at the graph, you can see that the interval where the function decreases is really small (the graph is small so I can't see the exact interval).
While if you look at g(x), you can see that, at least in the interval [-2, 2] the function is decreasing.
So the box in the wrong spot is the first box.
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Alyssa's favorite bowling team has 10 players on them. She has taken a picture with every single athlete individually and wants to post some of the pictures on her wall. But she only wants to post 4 pictures on her wall. How many different sets of pictures can she post on her wall
There are 84 sets of pictures she can post on her wall.
Since Alyssa has taken a picture with every single athlete individually. It means she has taken 9 pictures.
Now she wants to post 3 pictures on her wall.
We need to use Combination for arranging pictures. A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, we can select the items in any order.
Therefore, The number of different sets of pictures = Selecting 3 pictures from a set of 9 pictures
9C3 = (9!)/((9-3)!*3!)
(9*8*7)(3*2*1)= 84 ways
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Suppose babies born in a large hospital have a mean weight of 3685 grams, and a variance of 330,625. If 113 babies are sampled at random from the hospital, what is the probability that the mean weight of the sample babies would be less than 3631 grams
The probability that the mean weight of the sample babies would be less than 3631 grams is 0.1591 or 15.91%.
The mean weight of the babies (μ) = 3685 grams.
The variance (σ²) = 330625.
Therefore, the standard deviation (σ) = √330625 = 575.
The sample size (n) = 113.
The sample mean = μ - 3685 grams.
The sample standard deviation (s) = σ/√n = 575/√113 = 54.09145.
We are asked to find the probability that the mean weight of the sample babies is less than 3631 grams, that is,
P(X < 3631) = P(Z < {(3631 - 3685)/54.09145})
Using the formula: Z = (x - μ)/s,
or, P(Z < -0.9983) = 0.1591 or 15.91%.
From the table of area under the z-score.
P(X < 3631) can also be calculated using calculator function:
Normalcdf(-100000000,3631,3685,54.0195), which gives the value 0.1591 or 15.91%.
Thus, the probability that the mean weight of the sample babies would be less than 3631 grams is 0.1591 or 15.91%.
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Which answer describes the type of sequence?
3, 4, 7, 11,
• geometric
•
arithmetic
neither arithmetic nor geometric
Hello and Good Morning/Afternoon!
To determine whether a sequence is arithmetic or geometric:
⇒ must consider their definitions
Arithmetic Sequence: sequences that go up by adding or subtracting a numberGeometric Sequences: sequences that go up by multiplying or dividing a numberLet's test out this sequence to see what kind of sequence it is:
Testing for arithemetic sequence3 ⇒ 4, 3 + 1
4 ⇒ 7, 4 + 3
7 ⇒ 11, 7 + 4
NOT AN ARITHMETIC SEQUENCE
Testing for geometric sequence3 ⇒ 4, 3 * (4/3)
4 ⇒ 7, 4 * (7/4)
7 ⇒ 11, 7 * (11/7)
NOT AN GEOMETRIC SEQUENCE
Answer: Neither arithetic nor geometric
Hopefully that helps!
A scuba diver is 30 ft below sea level. Which of the following best describes this situation?
1. |30|
2. |-30|
3. -30
4. ±30
Answer:
-30
Step-by-step explanation:
The scuba driver is below the sea and ground level which is 0 ft, and he dives down 30 ft so it should be negative.
Hope it helps!
Show you work for full credit Use the SUBSITUTION method or ELIMINATION method to solve this system of equations. y = 4x and 8x + y = 18
Answer:
A. (3/2, 6)
Step-by-step explanation:
Use the substitution method:
8x + y = 18 and y = 4x
8x +4x = 18
12x = 18
x = 18/12 = 3/2
y = 4x
= 4(3/2)
= 12/2
= 6
On a coordinate plane, polygons A B C D and A prime B prime C prime D prime are shown. The points of A B C D are (2, negative 2), (4, negative 2), (3, negative 4), and (1, negative 4). The points of A prime B prime C prime D prime are (3, negative 3), (6, negative 3), (4.5, negative 6), (1.5, negative 6).
Given the pre-image ABCD and the image after a dilation, A'B'C'D', what is true about the polygons? Check all that apply.
The length AB is 2.
The length A'B' is 3.
The image is smaller than the pre-image.
The scale factor is Three-halves.
The scale factor is Two-thirds.
Polygon ABCD was dilated by a scale factor of 3/2 to form polygon A'B'C'D'. The scale factor used was 3/2. The length AB is 2 and the length A'B' is 3.
What is a transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.
Dilation is the increase or decrease in the size of a figure.
[tex]AB=\sqrt{(4-2)^2+(-2-(-2))^2}=2\ units[/tex]
Polygon ABCD was dilated by a scale factor of 3/2 to form polygon A'B'C'D'. The scale factor used was 3/2. The length AB is 2 and the length A'B' is 3.
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Answer:
A, B, and D
Step-by-step explanation:
yw enjoy summer
15. Robin ordered pizza and opted for delivery.
She prepaid $48.95 over the phone using
her credit card and plans to give an 18%
cash tip upon delivery. If she has $7, will this
be enough to cover the tip?
Answer: No she'll need atlease 9 dollars
Step-by-step explanation:
48.95 x 18% is 8.811 which is greater than
Researchers hypothesize that the first self-replicating molecule may have been ____. This is known as the ______world hypothesis.
Researchers hypothesize that the first self-replicating molecule may have been RNA. This is known as the RNA world hypothesis.
Life likely evolved between 3.53.53, point 5 and 3.93.93, point 9 billion years ago, when the Earth formed around 4.54.54, point 5 billion years ago.
According to the Oparin-Haldane hypothesis, "building blocks" like amino acids initially formed and then came together to form complex polymers as life gradually evolved from inorganic molecules.
The first proof that organic molecules required for life might be created from inorganic elements was supplied by the Miller-Urey experiment.
The RNA world hypothesis, which contends that RNA was the primordial form of life, is backed by certain scientists. Others support the concept that metabolic networks come before DNA or RNA.
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What is 3+(−5 2/3)? Write the answer as a mixed number in simplest form.
Answer:
-2 2/3
Step-by-step explanation:
3+(-5 and 2/3)=3-5 2/3= -5 2/3+3=-2 2/3
The sum of two numbers is [tex]-2\frac{2}{3}[/tex] .
What is addition of two fractions?To add fractions there are three simple steps:
Step 1: Make sure the bottom numbers (the denominators) are the same. Step 2: Add the top numbers (the numerators), put that answer over the denominator.
Step 3: Simplify the fraction (if possible)
Given that, 3+([tex]-5\frac{2}{3}[/tex])
= 3-17/3
= (9-17)/3
= -8/3
= [tex]-2\frac{2}{3}[/tex]
Therefore, the sum of two numbers is [tex]-2\frac{2}{3}[/tex] .
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What is DF? Help me please :)
The value of DF = 20.
What is similarity?Two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other.
Given:
Using theorem
If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.
ΔSDF/Δ RTY = (SD/RT)= (DF/TY)= (FS/ YR)
ar ΔSDF² / ar ΔRTY² = 16/81
SD/ RT = 4/9
SD = 4x, RT= 9x
SD= 8
4x = 8
x = 2
So,
RT= 9*2 = 18
SF = RT -2
SF = 16
(SD/RT)= (FS/ YR)
8 / 18 = 16/ YR
YR= 36
TY= 9 +RY = 45
(DF/TY)= (FS/ YR)
DF / 45= 16/ 36
DF=20
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A diver is standing on a spring board 24 feet above the pool. She jumps from the platform with an initial upward velocity of 8feet / (sec(or)) . Use the formula d(t)=-16(2t; -3)(t+1) , where d is the height of the diver above the water and t is the time in seconds. How long will it take for her to hit the water?
It would take 1.5 seconds for the diver standing on a spring board 24 feet above the pool to hit the water.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that d represent the height of the diver above the water and t is the time in seconds.
d(t) = -16(2t - 3)(t + 1)
The diver hit the water at d(t) = 0, hence:
0 = -16(2t - 3)(t + 1)
2t - 3 = 0; or t + 1 = 0
t = 1.5 seconds
It would take 1.5 seconds for the diver standing on a spring board 24 feet above the pool to hit the water.
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Suppose you are given a triangle with hypotenuse of length 2 and legs of length x+1 and x-1 . Find the numerical length of both sides.
Answer:
Step-by-step explanation:
[tex](2)^2=(x+1)^2+(x-1)^2\\[/tex]
By solving this equation we can get:
[tex]x=1 \\x=-1 (Impossible)[/tex]
∴
The value of the x will be equal to 1.
What is the Pythagorean theorem?The section of the zoo is a right triangle. The new path is in front of the right angle, therefore it is the hypotenuse. To find the length of the hypotenuse we use the Pythagorean theorem:
H² = P² + B²
Given that the hypotenuse is of length 2 and legs of length x+1 and x-1. The value of x will be calculated as:-
H² = P² + B²
2² = ( x + 1 )² + ( x - 1 )²
4 = ( x² + 2x + 1 ) + ( x² - 2x + 1 )
4 = 2x² + 0 + 2
4 - 2 = 2x²
x = √1 = ±1
x = 1 and x = -1 ignore negative value.
Therefore, the value of the x will be equal to 1.
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A sports company conducted a road test of a new model of a geared bike. the test rider cycled (3x − 2) miles on a flat road, (x2 − 5) miles uphill, and (2x 7) miles downhill. which simplified expression is equivalent to the total distance, in miles, for which the bike was tested? x2 − x x2 5x x2 − x 14 x2 5x 14
The simplified equation equivalent to the total distance in miles is given as,
[tex]x^{2} +5x[/tex]
What is the equation representing the total distance?
It is given that in a road test of a geared bike,
The distance covered on a flat road = (3x - 2)
The distance covered uphill = (x² - 5)
The distance covered downhill = (2x + 7)
Total distance covered in miles as equation,
(3x - 2) + (x² - 5) + (2x + 7)
= 3x - 2 + x² -5 + 2x + 7
= 5x - 7 + x² + 7
= x² + 5x
Thus, the final equation representing the total distance covered in miles by the bike is (x² + 5x)
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Your friend writes an equation of the line shown. Is your friend correct? Student work is shown. A line is graphed on a coordinate plane. The line passes through the points at ordered pair (0,-2) and ordered pair (4,0). An equation reads y= 1/2x + 4. Is this an equation of the line shown. Is your friend correct?
No, the friend is not correct.
What is equation of line?The equation of a line is a single b of numerous points on the line. The general form of the equation of a line is of the form ax + by + c = 0 and any point on the line satisfies this equation.
slope= 2/4= 1/2
Now,
y-(-2)= 1/2(x-0)
y+2= 1/2x
y= 1/2x - 2
Hence, the equation is incorrect.
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An encryption machine uses a formula to encrypt words, by taking each letter and changing it to the letter that is just before it in the alphabet. If the letter is ‘a’, it changes it to ‘z’. If you put the word STAR into the machine, what would the output be?
A) TARS
B) RSZQ
C) TUBS
D) RSTA
The output of the word STAR is RSZQ
How to determine the output?The encryption rule is given as:
Change a letter to the previous letter
This means that:
S -> R
T -> S
A -> Z
R -> Q
So, we have:
STAR -> RSZQ
Hence, the output of the word STAR is RSZQ
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A 3x2 flag is divided into six squares. Each square is to be coloured green or blue, so that every square shares at least one edge with another square of the same colour. In how many ways can this be done?
The computation shows that the number of ways that this can be done is 64.
How to illustrate the information?From the information given, it's was stated that a 3x2 flag is divided into six squares and that each square is to be coloured green or blue.
In this case, the number of ways that this can be illustrated will be:
= 2^n
= 2^6
= 64
Therefore, there are 64 ways.
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Consider the following system of equations given in slope-intercept form.
y = −1
3
x + 17,
y = 5x - 23
Use the graphing calculator to determine the best window range to find the point of intersection.
–10 Less-than-or-equal-to x Less-than-or-equal-to 10, –10 Less-than-or-equal-to y Less-than-or-equal-to 10
–20 Less-than-or-equal-to x Less-than-or-equal-to 0, –20 Less-than-or-equal-to y Less-than-or-equal-to 0
0 Less-than-or-equal-to x Less-than-or-equal-to 20, 0 Less-than-or-equal-to y Less-than-or-equal-to 20
20 Less-than-or-equal-to x Less-than-or-equal-to 40, 20 Less-than-or-equal-to y Less-than-or-equal-to 40
answer: c.0 Less-than-or-equal-to x Less-than-or-equal-to 20, 0 Less-than-or-equal-to y Less-than-or-equal-to 20
Option c. The range of window for the data is given as 0 Less-than-or-equal-to x Less-than-or-equal-to 20, 0 Less-than-or-equal-to y Less-than-or-equal-to 20
How to solve for the range of the dataWe have the equation to be
y = −3x + 17,
and y = 5x - 23
We have to make the two equations to be equal
This would then give us
−3x + 17 = 5x - 23
The next step is to take the like terms
3x - 5x = -23-17
-2x = -40
From you we have to divide by -2
x = 20
The range would be written as
0 ≤ x ≤ 20, 0 ≤ y ≤ 20
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You enter a room. 2 dogs, 4 horses, 1 giraffe and a duck lie on the bed. 3 hens fly over a chair. How many legs are there on the floor?.
Answer:
28 legs are on the floor once again
There are no legs on the floor.
Hence answer is zero.
According to the question,
For 2 dogs: Each dog has 4 legs.
Therefore, 2 dogs have a total of 8 legs.
For 4 horses: Each horse has 4 legs.
Therefore, 4 horses have a total of 16 legs.
For 1 giraffe: A giraffe has 4 legs.
For 1 duck: A duck has 2 legs.
For 3 hens: Each hen has 2 legs.
Therefore, 3 hens have a total of 6 legs.
To get the total number of legs on the bed,
we simply add up all the legs of the animals on the bed,
⇒ 8 legs + 16 legs + 4 legs + 2 legs + 6 legs = 36 legs.
Now, to get the number of legs on the floor,
We need to subtract the number of legs on the bed from the total number of legs of all the animals,
For 2 dogs with a total of 8 legs.
For 4 horses with a total of 16 legs.
For 1 giraffe with 4 legs.
For 1 duck with 2 legs.
For 3 hens with a total of 6 legs.
So, the total number of legs of all the animals is,
⇒ 8 legs + 16 legs + 4 legs + 2 legs + 6 legs = 36 legs.
Since all the animals are on the bed,
There are no legs on the floor.
Therefore, the answer is 0 legs on the floor.
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The word fable derives from the Latin word fabula, which originally meant about the same as the Greek mythos. Like mythos, it came to mean a fictitious or untrue story. Myths, in contrast, are not presented as fictitious or untrue. Fables, like some myths, feature personified animals or natural objects as characters.
The information given about fables and myths is correct. Therefore, the correct option is true.
What is a fable?It should be noted that a fable simply illustrates a story that's considered false or fictional.
In this case, fable derives from the Latin word fabula, which originally meant about the same as the Greek mythos.
Myths are typically not presented as fictitious or untrue. Therefore, the correct option is true.
Complete question:
The word fable derives from the Latin word fabula, which originally meant about the same as the Greek mythos. Like mythos, it came to mean a fictitious or untrue story. Myths, in contrast, are not presented as fictitious or untrue. Fables, like some myths, feature personified animals or natural objects as characters. True or false.
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Please help with this geometry question.
The exercise below is one that requires the proof that of certain dimensions using the rules of congruence. of triangles.
What does it mean for two angles to be congruent?
It simply means that both angles are similar in measure.
What is the required proof of the given problem?It is given that ∠BAD=∠EAC
∠BAD+∠DAC=∠EAC+∠DAC [add ∠DAC on both sides]
Therefore ∠BAC=∠DAE
In △BAC and △DAE
AB=AD (Given)
∠BAC=∠DAE (Proved above)
AC=AE (Given)
Therefore △BAC≅△DAE (By SAS congruence rule)
Therefore BC=DE because Corresponding Parts of Congruent Triangles CPCT are congruent.
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Which sequence of transformations produced the image?
a counter-clockwise rotation 90° about the origin followed by a translation 2 units to the right and 1 unit up
a translation 2 units to the right and 1 unit up followed by a counter-clockwise rotation 90° about the origin
a clockwise rotation 90° about the origin followed by a reflection across the y-axis
a reflection across the y-axis followed by a clockwise rotation 90° about the origin
The sequence of transformation is; B. A translation 2 units to the right and 1 unit up followed by a counter-clockwise rotation 90° about the origin.
What is the sequence of Transformation?From the given image in the transformation, we can see that the pre image which is the original image is on the right hand side while the image after transformation is on the left hand side.
Now it will be noticed that in the pre image, all the x and y coordinates are positive while the image after transformation has all the x-coordinates as negative with the y-coordinates as positive.
This transformation when critically examined is seen to be a translation 2 units to the right and 1 unit up followed by a counter-clockwise rotation 90° about the origin.
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Answer: its B
Step-by-step explanation:
I Need Help Quickly Please And Thank You
Answer:
Step 2: it should be P - 2x, not P + 2x.
Step-by-step explanation:
[tex]\sqrt(1-2)+\sqrt(1+2)\\[/tex]