Is it equal to the measure if angle C
In an isosceles triangle, the measure of the vertex angle (Angle B in this case) is equal to the measure of the other base angle. This is because in an isosceles triangle, the angles opposite the equal sides are also equal.
Explanation:In an isosceles triangle ABC, Angle B, the angle between the two sides of equal length, is known as the vertex angle. The two base angles of an isosceles triangle are always equal. Therefore the measure of Angle B will be equal to the measure of Angle C. This property comes from the fundamental characteristics of an isosceles triangle, where two sides are of equal length and the angles opposite these equal sides are also equal.
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the equation 5x+2y=20 represents the cost for a family to attend a play where x is the number of adults and y is the number of children. find the intercepts and interpret the meaning of each one
Answer:
x-intercept: 4 This means that only 4 adults can come under the budjet of $20
y-intercept: 10 This means that only 10 children can come under the budjet of $20
Step-by-step explanation:
for y:
5(0) + 2y = 20
2y = 20
2y/2 = 20/2
y = 10
for x:
5x + 2(0) = 20
5x = 20
5x/5 = 20/5
x = 4
Please help and with steps. I suck at these and really don’t understand them
Answer:
see explanation
Step-by-step explanation:
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 10 and d = - 3, hence
[tex]a_{n}[/tex] = 10 - 3(n - 1) = 10 - 3n + 3 = - 3n + 13, so
[tex]a_{n}[/tex] = - 3n + 13 ← n th term formula
can someone help with this
Answer:
∠4 = 50°
Step-by-step explanation:
∠1 + ∠5 = 100°, but ∠1 = ∠5 ( corresponding angles ), hence
∠1 = ∠5 = 50°
∠4 = ∠1 = 50° ( vertical angles )
Hey guys I need help simplifying this radical expression please. ASAP please.
Answer:
go on symbolab type the equation in and it gives u anwsers and work
Step-by-step explanation:
=\frac{4}{\left(x+2\right)\left(x+4\right)}
What is the compliment of 41°
Answer: 49°
Step-by-step explanation:
I'm guessing you meant complement? Complementary angles add up to 90°. 90° - 41° = 49°
PROBLEM 1 An instant lottery game gives you probability 0.10 of winning on
any one play. Plays are independent of each other. You play 4 times. Let X
represent the number of times you win.
o What is the probability that you don't win at all?
Answer:
X=60% Chance
Step-by-step explanation:
This is because if you take 1 whole (100%), imagine it is at the value of 1, 4x.10=.40. 1-.40=.60 which is equal to 60%
4. Graph the equation using the slope and y-intercept.
y = {x - 4
m
=
b
=
Answer:
m = 1
b = -4
Step-by-step explanation:
The "slope-intercept form" of the equation for a line is often written ...
y = mx + b
The x-coefficient, m, is the slope of the line. The constant, b, is the y-intercept.
Comparing the slope-intercept form to your equation, we see that ...
m = 1
b = -4
_____
The slope is the ratio of "rise" to "run" for the graph. Here, that means the line goes through the point (0, -4), the y-intercept, and rises 1 unit for each 1 unit to the right of that point. For example, the point (4, 0) will also be on the line. (It is right 4 units and up 4 units from the y-intercept.)
The equation can be graphed by entering it into a graphing tool, or by plotting two points on the line and drawing a line through them.
Collin surveyed 12 teachers At his school to determine how much each person budgets for lunch. He recorded his results in the table.
(Answers are listed in photo)
Answer:
mean =median, so the data is symmetrical
Step-by-step explanation:
Given
Data set= {10,5,8,10,12,6,8,10,15,6,12,18}
Mean= Sum of data points/number of data points
= (10+5+8+10+12+6+8+10+15+6+12+18)/12
=10
Median= mid value
={5,6,6,8,8,10,10,10,12,12,15,18}
Middle values are 10 and 10
Median = 10+10/2
= 20/2
= 10
Mean= median so there will be no skewness and the distribution is equal !
Over the course of a year, the population of chipmunks in Boston increased from 300000 to 387000. What was the percent increase of the population of chipmunks? Express your answer as a percent.
Answer:
The percent increase of the population of chipmunks was 29%
Step-by-step explanation:
we know that
The population of 300,000 chipmunks represent the 100%
The increase of population is equal to
(387,000-300,000)=87,000 chipmunks
Using proportion find the percent increase
Let
x-----> the percent increase
300,000/100%=87,000/x
x=100*87,000/300,000
x=29%
A manufacturer of shipping boxes has a box shaped like a cube. The side length is (5a + 4b). What is the volume of the box in terms of a and b? Show your work.
Answer:
125a^3 + 300a^2b + 240ab^2 + 64b^3
Step-by-step explanation:
The volume of a cube is the cube of the side length.
V = s^3
Here, the side length of the cube is 5a + 4b, so we cube 5a + 4b.
V = (5a + 4b)^3
V = (5a + 4b)(5a + 4b)(5a + 4b)
V = (25a^2 + 20ab + 20ab + 16b^2)(5a + 4b)
V = (25a^2 + 40ab + 16b^2)(5a + 4b)
V = 125a^3 + 100a^2b + 200a^2b + 160ab^2 + 80ab^2 + 64b^3
V = 125a^3 + 300a^2b + 240ab^2 + 64b^3
Which statement is true about the given information?
BD = 1/2BC
BC = 1/2 BE
OBD CE
BC - BD
- Since lines BC, CD, and DE are all congruent, then we know that every time a line reaches either a point or an orange line, we can consider that to have a value of 1, for instance. BD and CE, in this case, both have a value of 6, and therefore the correct answer is BD=CE.
The option third BD ≅ CE is correct because BD and CE are equal in length, so they are congruent.
What is the congruent geometry?Congruent geometry are those that are exactly the same size and shape. Congruent is represented by the symbol ≅
We have a line segment shown in the figure:
From the figure:
BD = 2BC
BE = 3BC
BC ≅ BD (as the BC and BD are unequal in length, so they cannot be congruent)
BD ≅ CE (as the BD and CE are equal in length, so they are congruent)
Thus, the option third BD ≅ CE is correct because BD and CE are equal in length, so they are congruent.
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Which of the following numbers is located between points Q and R on the number line?
your answer is b) 3.88
Apply the distributive property to simplify the expression.
−9(−2x − 3)
A) 18x + 27
B) 18x − 27
C) −18x + 27
D) −18x − 27
we called it the rainbow method :)
The answer is A.
-9 • -2x = 18x
-9 • -3 = 27
Therefore, it is 18x+27
The value of the expression -
+ x(100 - 15x) when x = 5 is
Answer:
Step-by-step explanation:
Warning:
. You just wrote - and +, adding them both would result in a 0; (positive + negative = 0). If you haven't checked twice before asking, it is your problem. I'm going to solve for:
x(100-15x) when x = 5.
Answer:
Step By Step Explanation:
You'll need to substitute (that word is hard, it means replace though) the x, and get a proper equation (because they already gave you the x).
Look at how ugly and hard this is: x(100-15x) When x = 5.
Now it's better when replacing the x: 5(100-15×5)
Put it in a calculator if you wanted to avoid step by step work, but I'll show you how to do it step by step if you wanted.
5(100-15×5)
(5)×(100)+(5)(-75)
500-375
=125.
So, write this for your answer:
x(100-15x) = 125 Because 5(100-15×5)=125. And x = 5.
12-5x=7x+3 solve for x i need help
12-5x= 7x+3
12-7x-5x= 7x-7x+3
12-12x= 3
12-12-12x= 3-12
-12x= -9
Divide by -12 for -12x and -9
-12x/-12= -9/-12
x= 9/12
Divide by 3 for 9/12
x= 3/4
Answer is x= 3/4
Step-by-step explanation:
12 - 5x = 7x + 3
Add 5x on the both sides so there would only be 12 on the right side.
So...... 12 = 12x + 3
Then minus 3 from both sides
9 = 12x
0.75 = x
:0 ITS MAGIC
:)))
a circle has a circumfrence of 14mm. Find its area. Give an exact answer
Answer:
15.597 mm^2
Step-by-step explanation:
The formula for circumference of a circle 2πr, in which r is the circle's radius.
The formula for area of a circle π[tex]r^{2}[/tex]. This means that we can find the radius from the circle's circumference and use it to find the area.
First we have to equal 14 to 2πr because both are representations of circumference and we need to find r.
14 = 2πr
Solve:
14/2 = 2πr/2
7 = πr
7/π = πr/π
2.23 = r
Plug 2.23 into the formula for area as r and solve:
π(2.23)^2
π4.96
15.597
A pill has the shape of a cylinder with a hemisphere at each end. The height of the cylindrical portion is 12mm and the overall height is 18mm. Find the volume of the pill in cubic millimeters. Round to the nearest cubic millimeter
Answer:
The volume of the pill is [tex]V=452\ mm^{3}[/tex]
Step-by-step explanation:
Find the volume of the pill in cubic millimeters
we know that
The volume of the pill is equal to the volume of the cylinder plus the volume of a sphere (two hemisphere is equal to one sphere)
so
we have
[tex]V=\frac{4}{3}\pi r^{3}+\pi r^{2}h[/tex]
[tex]r= (18-12)/2=3\ mm\\ h=12\ mm[/tex]
assume
[tex]\pi =3.14[/tex]
substitute
[tex]V=\frac{4}{3}(3.14)(3)^{3}+(3.14)(3)^{2}(12)\\V=452\ mm^{3}[/tex]
Volume is a three-dimensional scalar quantity. The volume of the pill is 452.3893mm³.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The height of the cylindrical portion is 12mm and the overall height is 18mm. Therefore, the radius of the hemisphere at any one end will be half the difference between the cylindrical portion and the overall height. Thus,
The radius of the sphere, R = (18mm - 12mm)/2 = 3mm
The volume of the capsule
= Volume of cylinder +2(Volume of the hemisphere)
= (πR²h) + 2[(4/6)πR³]
= (π×3²×12) + 2[(4/6)×π×3³]
= 339.292mm³ + 113.0973mm³
= 452.3893 mm³
Hence, the volume of the pill is 452.3893mm³.
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Lacy draws a diamond from a standard deck of 52 cards. Without replacing the first card, she then proceeds to draw a second card and gets a spade.
Are these events independent?
Input Yes or No:
Determine the probability of drawing a diamond and then a spade without replacement.
Write your answer in decimal form, rounded to four decimal places as needed.
Answer =
Linda draws a diamond from a standard deck of 52 cards. She returns the diamond to the deck, then draws a second card. Her second card is a spade.
Are these events independent?
Input Yes or No:
Determine the probability of drawing a diamond and then a spade with replacement.
Write your answer in decimal form, rounded to four decimal places as needed.
Answer =
Answer:
a) i) No
ii) Probability of drawing a diamond and then spade without replacement is 0.0637.
b) i) Yes
ii) Probability of drawing a diamond and then spade with replacement is 0.0625
Step-by-step explanation:
Part a) Without replacement:
i) Are these events independent?
No, because the both events are dependent. because a card taken out of the deck is not replaced back before taking out the other card so the chances of event occur change.
ii) Determine the probability of drawing a diamond and then a spade without replacement.
Probability of drawing a diamond and then spade = (Probability of drawing a diamond) * (Probability of drawing a spade)
Probability of drawing a diamond :
Total cards in deck = 52
Diamonds = 13
Probability of drawing a diamond = 13/52
Probability of drawing a spade:
Total cards in deck after taking diamond = 52 -1 =51
Spades = 13
Probability of drawing a spade = 13/51
Probability of drawing a diamond and then spade = 13/52 * 13/51
= 169/2652
=0.0637
So, Probability of drawing a diamond and then spade without replacement is 0.0637
Part b) With replacements
i) Are these events independent?
Input Yes or No:
Yes, these events are independent because a card taken out of the deck is replaced back before taking out the other card so the chances of event occur doesn't change.
ii) Determine the probability of drawing a diamond and then a spade with replacement.
Probability of drawing a diamond and then spade = (Probability of drawing a diamond) * (Probability of drawing a spade)
Probability of drawing a diamond :
Total cards in deck = 52
Diamonds = 13
Probability of drawing a diamond = 13/52
Probability of drawing a spade:
Total cards in deck after replacing diamond = 52
Spades = 13
Probability of drawing a spade = 13/52
Probability of drawing a diamond and then spade = 13/52 * 13/52
= 169/2704
=0.0625
So, Probability of drawing a diamond and then spade with replacement is 0.0625
The first two events are not independent, with a probability P = 0.0637
The second pair of events is independent, and the probability is P = 0.0625
How to get the probabilities?
First, all the cards on the deck have the same probability of being randomly drawn, which will be p = 1/52.
A) Now, if Lacy first draws a diamond card, now the number of cards in the deck are less (now there are 51 cards on the deck). So the probability of drawing now a spade is larger than before. Then the first two events are not independent.
The probability of drawing a diamond card at first is:
P = 13/52 (because there are 13 diamonds and a total of 52 cards).
The probability of drawing a spade after is:
Q = (13/51)
The joint probability is the product of the individual probabilities, this will give:p = P*Q = (13/52)*(13/51) = 0.0637
B) Now we replace the first card, then the events are now independent, as the probability of drawing a spade after the first draw is not changed (because the total number of cards will be 52).
The probability of drawing a diamond is:
P = 13/52
Now we replace the diamond card drawn.
The probability of drawing a spade will be:
Q = 13/52
The joint probability is:
p = P*Q = (13/52)^2 = 0.0625
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PLEASE HELP ME I WILL MARK!!
Answer:
3.2
Step-by-step explanation:
Calculate the length using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (A(2,2) and (x₂, y₂ ) = B(5, 1)
d = [tex]\sqrt{(5-2)^2+(1-2)^2}[/tex]
= [tex]\sqrt{3^2+(-1)^2}[/tex]
= [tex]\sqrt{9+1}[/tex] = [tex]\sqrt{10}[/tex] ≈ 3.2 ( nearest tenth )
Answer:
3.2
Step-by-step explanation:
Distance formula = √ (x₂ - x₁ )² + (y₂ - y₁ )²
Distance = [tex]\sqrt{(5-2)}^{2} + (1-2)^{2}[/tex]
Distance = [tex]\sqrt{ {3}^{2} + ( - 1 )^{2}[/tex]
Distance = 3.16227766
How can this be solved?
Answer:
by multiplying all numbers seperatly by each other and adding those
Step-by-step explanation:
Which statement below is incorrect
The mean is not affected by the existence of an outler
(B) The median is not affected by the existence of an outlet
(c) the standard deviation
affected by the existence of an outler
Answer:
The Answer is A
Step-by-step explanation:
The mean or average is highly sensitive to outliers - and is one reason why the median is a more reliable statistic.
what is 1449.09/81 I need help asap
Answer:
if its division then: 17.89
Step-by-step explanation:
The result of the division 1449.09 divided by 81 equals approximately 17.89 .
To find the result of 1449.09 divided by 81, we simply divide the numerator by the denominator.
The division can be calculated as follows :
1449.09 ÷ 81 = 17.892654321.
Rounded to two decimal places , the result is approximately 17.89.
The result of the division 1449.09 divided by 81 equals approximately 17.89. This means that 1449.09 can be divided evenly by 81 a total of 17 times with a remainder of 0.
The quotient, 17.89, represents the value obtained when equally distributing 1449.09 among 81 parts.
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What's the difference between pro and cons
Answer:
ones good ones bad
Step-by-step explanation:
Answer:
Pros means Advantages
Cons means Disadvantages.
Step-by-step explanation:
Pros and Cons are often used where advantages and disadvantages of certain things need to be explained. Pros and Cons are the terms derived from Latin Language which means 'for or against'.
In simple words, when we describe the advantages of certain topic, theory or concept, we are actually defining the pros of that certain thing. Similarly, when we are talking about the disadvantages of something, we are actually defining the cons of that particular thing.
If triangle ABC is an equilateral triangle and BD = 36 inches, find the value of x
Answer:
The value of x is [tex]24\sqrt{3}\ in[/tex]
Step-by-step explanation:
we know that
An equilateral triangle has three equal sides and three equal internal angles (each internal angle measure 60 degrees)
In this problem
see the attached figure to better understand the problem
In the right triangle ABD
[tex]sin(60\°)=BD/AB[/tex]
Solve for AB
[tex]AB=BD/sin(60\°)[/tex]
we have
[tex]BD=36\ in[/tex]
[tex]sin(60\°)=\frac{\sqrt{3}}{2}[/tex]
substitute
[tex]AB=36/(\frac{\sqrt{3}}{2})=24\sqrt{3}\ in[/tex]
Using the sine ratio, the value of x in the equilateral triangle is: 24√3 inches.
What is the Sine Ratio?The sine ratio used to solve a right triangle is given as, sin ∅ = opposite side/hypotenuse.
Given the following:
∅ = 60 degrees; sin 60 = √3/2Opposite length = 36 inchesHypotenuse length = xApply the sine ratio:
sin 60 = 36/x
√3/2 = 36/x
x = 36/√3/2
x = (36 × 2)/√3
x = 72/√3
Rationalize
x = (72)(√3) / (√3)(√3)
x = 72√3 / 3
x = 24√3
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How do I solve this?
Answer:
B. BStep-by-step explanation:
Look at the picture.
The length of a rectangular park is 20 feet longer than the width of the park. If the lenght of the park is 36 feet, what is the width of the park?
Below is a labeled rectangle:
length = w + 20
we know length is 36 so we plug that in:
36 = w + 20
We need to isolate w and to do that we must subtract 20 from both sides:
(36 - 20) = w + (20 - 20)
16 = w + 0
w = 16
width is 16 feet
Hope this helped!
Ashley has already walked 0.5 miles this week, plus she plans to walk 1.5 miles during each trip to school. If she plans to take 3 trips to school for a total of 5 miles, what is the slope of the equation?
0.5 miles
1.5 miles
5 miles
3 trips
Answer:
Step-by-step explanation:
The slope is 1.5 miles / day
Final answer:
The slope of the equation that represents Ashley's walking distance over the number of trips is 1.5, which indicates that she walks 1.5 miles for each trip to school.
Explanation:
Ashley has already walked 0.5 miles this week and plans to walk 1.5 miles each trip to school for a total of 3 trips. To find the slope of the equation that represents her walking distance as a function of the number of trips, we use the slope formula, which is rise over run, or in this context, the change in distance over the number of trips.
Let's calculate her total planned distance. Since she plans on walking 1.5 miles for each trip and takes 3 trips, that's 1.5 miles/trip × 3 trips = 4.5 miles. Including the 0.5 miles she has already walked, her total distance for the week would be 0.5 miles + 4.5 miles = 5 miles, which matches with her goal.
Now, the slope is the distance she covers per trip, which is consistent and equal to 1.5 miles per trip. Therefore, the slope of the line that represents her distance over the week as a function of each trip is 1.5.
Antonia is standing 2.8 miles away from Mt. Drash. She has to tilt her head upwards 68° in order to look straight at the peak of the mountain. She wants to figure out how high the mountain is.
Please Help!
Answer:
5.3 miles
Step-by-step explanation:
tan(62) = x / 2.8 where x = the height of the mountain
tan(62) * 2.8 = x = 5.3 miles
Using the law of tangents.
Tan(angle) = Opposite Leg / adjacent leg
Tan(68) = x / 2.8 miles
x = 2.8 x tan(68)
x = 6.93
The mountain is about 6.9 miles high.
Use the quadratic formula to determine the exact solutions to the equation.
222 – 50+1=0
Enter your answers in the boxes.
x=
or x =
Answer:
222- 50+1=0? 225 - 50 = 175 175+1 = 176 176+0 = 176
Find the sum of the first 25 terms of a geometric sequence where the first term is 177,147 and the common ratio is -1/3
Answer:
132860 to nearest whole number.
Step-by-step explanation:
Sum of n terms = a1 .(r^n - 1) / (r - 1).
S25 = 177,147 ((-1/3)^25 - 1) / (-1/3 - 1)
= 177,147 * -1 / -4/3
= 132860.
The given task involves finding the sum of the first 25 terms of a geometric sequence with a specific first term and common ratio. This is done using the sum formula for a finite geometric sequence, with the terms alternating in sign due to a negative common ratio.
Explanation:The subject question deals with the concept of a geometric sequence, specifically finding the sum of the first 25 terms. A key formula to solve this question is the sum of a finite geometric sequence: Sₙ = a₁(1 - rⁿ)/(1 - r), where a1 is the first term, r is the common ratio, and n is the number of terms.
In this case, a₁ is 177,147, r is -1/3 and n is 25. Substituting these values into the formula, the sum, S25 = 177,147 × (1 - (-1/3)25) / (1 - -1/3).
By solving this equation, we get the sum of the first 25 terms of the given geometric sequence. Note that due to the negative common ratio, the terms alternate in sign in this particular geometric sequence.
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