The area of a triangle △ABC with side lengths a, b, c and height h is shown to be equal to 1/2 ab sin C using the triangle area formula, definition of sine in right triangles, multiplication property of equality and commutative property of multiplication.
Explanation:In the triangle △ABC with side lengths a, b, and c, and height h, we can start with the triangle area formula, which is Area = 1/2 bh. Here, h denotes the height of the triangle, which when drawn from the angle C would be adjacent to the angle while b represents the side that is opposite to the angle C. By the definition of sine in right-angled triangles, sin C = h/a. Now, we can use the Multiplication Property of Equality to write asinC=h. Mixing the given formula of the area with this equality, we get Area=1/2 ba sin C. As the multiplication is commutative, we can re-write this as Area = 1/2 ab sin C.
Learn more about Triangle Area here:https://brainly.com/question/27683633
#SPJ12
To prove the area of a triangle, use the formula 1/2 base × height and substitute sin C with h/a.
Explanation:To prove that the area of △ABC is equal to 1/2 ab sin C, we can use the formula for the area of a triangle: Area = 1/2 base × height. In this case, the base is b and the height is h, so the area is 1/2 bh. We also know that sin C = h/a, so we can substitute h/a for sin C in the area formula to get Area = 1/2 ab sin C.
Learn more about Triangle area formula here:https://brainly.com/question/29133099
#SPJ12
How many times can 7 go into 336?
Answer: 48
Step-by-step explanation:
336/7=48
Answer:
48
Step-by-step explanation:
Well, 336/7 is 48
E=mc square m=3 c=6 solve for E
Answer:
E = 3(62)
E = 3(36)
E = 108
if 8 is 100% of 100 what is 2 of 100%?
Answer:25%
Step-by-step explanation:
Because 2 is only a quarter of 8 and 25%=quarter from 100%
Answer:
25%
Step-by-step explanation:
PLEASE HELP ME ASAPP!!!!
Answer:
y = x + 3
y = 3x²
y = [tex]3^{x}[/tex]
Step-by-step explanation:
Relationship1
y = x + 3
y = (0) + 3 = 3
y = (1) + 3 = 4
y = (2) + 3 = 5
Relationship 2
y = 3x²
y = 3(0)² = 0
y = 3(1)² = 3
y = 3(2)² = 3(4) = 12
Relationship 3
y = [tex]3^{x}[/tex]
y = [tex]3^{0}=1[/tex]
y = [tex]3^{1}=3[/tex]
y = [tex]3^{2}=9[/tex]
Calculate the equivalent decimals for the following fractions.
a. 1⁄4
b. 2⁄5
c. 2⁄3
d. 3⁄4
Answer:
a. 0.25
b. 0.4
c. 0.66 repeating
d. 0.75
Step-by-step explanation:
a. 1/4 is equal to one quarter which is 0.25
b. 2/5 is equal to 4/10 which equals 0.40 or 0.4
c. 2/3 is 0.6666666 and goes on forever so we would call that a repeating decimal
d. 3/4 is equal to three quarters which would be 0.75
i hope this helps :)
1/4=0.25 2/5=0.4 2/3=0.666666666666667 3/4=0.75
Can someone PLZZZZ HELP!!!!
Answer:
The solution is:
Part A. [tex]\sqrt{5}^{\frac{7k}{3}})[/tex] which is sqrt(5)^7k/3[/tex]
Part B. k = 18/7
Step-by-step explanation:
Part A.
To solve this part, we're going two use THREE important properties of exponents:
1. [tex](x^{n})^{m} = x^{nm}[/tex]
2. [tex]\frac{x^{n}}{x^{m}} = x^{n-m}[/tex]
3. [tex]\sqrt[n]{x^{m}} = x^{\frac{m}{n} }[/tex]
Let's work the numerator using the properties 1, 2 and 3:
[tex](\sqrt{5}^{3} )^{\frac{k}{9} } } = (\sqrt{5}^{3\frac{k}{9}}) = (\sqrt{5}^{\frac{k}{3}})[/tex]
Let's work the denominator using the properties 1, 2 and 3:
[tex](\sqrt{5}^{6} )^{-\frac{k}{3} } } = (\sqrt{5}^{6\frac{k}{3}}) = (\sqrt{5}^(2k))[/tex]
Now dividing the numerator by the denominator:
[tex]\sqrt{5}^{\frac{k}{3}-(-2k)})=\sqrt{5}^{\frac{7k}{3}})[/tex]
Part B
if [tex]5^{\frac{3}{2} } 5^{\frac{3}{2}} = \sqrt{5}^{\frac{7k}{3}})[/tex]
Then:
[tex]5^{3} = 5^{\frac{7k}{6}})[/tex]
So [tex]\frac{7k}{6}} = 3[/tex]
Solving for k, we have:
k = 18/7
How fast is a train going that makes a 330 mile trip in 4 hours?
ANSWER
The car moves at 32 mi/hr
EXPLANATION
This question is asking us to determine how fast is a train that makes 330 mile trip in 4 hours.
This is the same as calculating the speed of the train:
Speed = distance covered/time taken
The distance covered is 330 mile
The time taken is 4 hours.
Speed =330/4 =82.5 mi/hr
how do u simplify 3/30
[tex]\bf \cfrac{3}{30}\implies \cfrac{3\cdot 1}{3\cdot 10}\implies \cfrac{3}{3}\cdot \cfrac{1}{10}\implies 1\cdot \cfrac{1}{10}\implies \cfrac{1}{10}[/tex]
solve the inequality
Answer:
[tex]\large\boxed{q\geq-8}[/tex]
Step-by-step explanation:
[tex]7q-5\leq10q+19\qquad\text{add 5 to both sides}\\\\7q\leq10q+24\qquad\text{subtract 10q from both sides}\\\\-3q\leq24\qquad\text{change the signs}\\\\3q\geq-24\qquad\text{divide both sides by 3}\\\\q\geq-8[/tex]
Inferences about Data Distributions
choices
mean is higher than the median
median is higher than the mean
same mean, different standard deviation
same standard deviation, different mean
Answer:
1. same standard deviation, different means
2. same mean, different standard deviation
3. median is higher than the mean
4. mean is higher than the median
Step-by-step explanation:
What is the sum of the infinite geometric series?
Answer: This series would have no last term. The general form of the infinite geometric series is a1+a1r+a1r2+a1r3+... , where a1 is the first term and r is the common ratio.
Step-by-step explanation:
Answer:
[tex]S_{\infty}=\frac{80}{3}[/tex]
Step-by-step explanation:
The sum of an infinite geometric series is given by:
[tex]S_{\infty}=\frac{a}{1-r}[/tex],
The given geometric series is
[tex]\sum_{n=1}^{\infty}32(-\frac{1}{5})^{n-1}[/tex]
The constant ratio for this series is
[tex]r=-\frac{1}{5}[/tex]
The first term of the series is [tex]a=32(-\frac{1}{5})^{1-1}=32[/tex]
The sum to infinity is [tex]S_{\infty}=\frac{32}{1--\frac{1}{5}}[/tex]
[tex]\implies S_{\infty}=\frac{32}{\frac{6}{5}}=\frac{80}{3}[/tex]
In a triangle if two angles measure 65 degrees and 25 degrees, what is the measure of the third angle and what is the type of triangle?
Answer
90 degrees , it's a right angled triangle
Step-by-step explanation:
180 - 65 - 25 = 90
The sum of all the interior angles of a triangle equals 180 degrees
a right angled triangle has one 90 degree angle and two different angles
Answer:
The measurement of the third angle is 90 degrees
Step-by-step explanation:
There are 180 degrees in a triangle.
180 - 65 = 115 - 25 = 90
It is a right angled triangle
a large bottle of water holds 2 liters. for numbers 10a-10e choose yes or no to tell whether the container will hold all of the water.
10a.kitchen sink/ yes or no
10b.water glass/ yes or no
10c.ice cube tray/yes or no
10d.large soup pot/yes or no
10e.lunchbox thermos/yes or no
Answer:
See below
Step-by-step explanation:
This question is about estimation of volumes. Think of a 2 L bottle of pop or a 2 L carton of milk. Could its contents fit inside
a. a kitchen sink? Yes. Even a small kitchen sink can hold a volume of 2 L. b. a water glass? No. A typical water glass has a volume of about 0.2 L. c. an ice cube tray? No. A typical ice cube tray may hold more than a water glass, say, about 0.5 L. d. a large soup pot? Yes. A large soup pot can hold up to 20 L of liquid. e. a lunch box thermos? No. A typical lunch box thermos may have a volume of 0.4 L .which function has a vertex at (2, -9)
Answer:
Where are the answer choices?
Step-by-step explanation:
Answer:
C: f(x) = (x - 5)(x + 1)
Step-by-step explanation:
What is the approximate volume of the cylinder?
Use 3.14 to approximate .
height is 5 ft and radius is 15 ft
A.
236 ft3
B.
471 ft3
C.
3533 ft3
D.
11,092 ft3
Answer:
C
Step-by-step explanation:
Use the formula for the volume of a cylinder.
[tex]V=\pi r^2h[/tex]
Plug in the height, the radius, and 3.14 for [tex]\pi[/tex].
[tex]V=3.14(15^2)(5) \\ \\ V=3.14(225)(5) \\ \\ V=3.14*1125 \\ \\ V=3532.5[/tex]
If you round that number you'll get [tex]V=3533[/tex].
So the answer is answer choice C.
17. Which of the following measures can be calculated for qualitative data? a. Mean b. Median c. Mode d. All of these
Answer: C. Mode
Step-by-step explanation:
Qualitative data applies to observable data such as reoccurring patterns (mode)
Quantitative data applies to numbers and numerical calculations (Mean, Median)
Mode is the best way to analyze qualitative data as it makes the analysis easier.
What is the definition of Mode?Mode is the most frequently occurring value in the data.
What is qualitative data?
Qualitative data is the descriptive and conceptual findings collected through questionnaires, interviews, or observation. Analyzing qualitative data allows us to explore ideas.
For example
Each child’s gender
His or her favorite color
Whether he or she owns at least one pet
How he or she gets to and from school
In order to analyze the above data, Mode is the best method because the mode is the most frequently occurring value in data and one can easily analyze the data.
Therefore, Mode is the best way to analyze qualitative data.
To get more about mode refer:
https://brainly.com/question/14532771
Use the figure below to find the short leg HELP PLZZ
Answer:
The short leg is 7 because half of 14 is 7 and the hypotenuse is always twice as long as the shortest one.
The required short leg is 7inches.
Given that,
Hypotenuse = 14 inches,
In triangle 30-60-90
We have to determine,
By using figure find the short leg.
According to the question,
A 30-60-90 triangle is a special right triangle whose angles are 30º, 60º, and 90º.
The triangle is special because its side lengths are always in the ratio of 1: √3:2.
The 30-60-90 triangle rule is for finding the the lengths of two sides when one side is given.
The shorter side is opposite the 30 degree angle, the longer side is opposite the 60 degree angle, and the hypotenuse is opposite the 90 degree angle.
Therefore,
The hypotenuse is always twice as long as the shortest one.
Where, Hypotenuse = 14inches
Then,
[tex]Hypotenuse = 2 \times short \ leg \\\\14 = 2 \times short \ leg\\\\short\ leg = \dfrac{14}{2}\\\\short \ leg = 7[/tex]
Hence, The required short leg is 7inches.
To know more about Pythagoras theorem click the link given below.
https://brainly.com/question/22698523
Let f(x)=x^2+1. Let g(x)=(x+2)^2+1. Which statement described the graph of g(x) with respect to the graph of f(x)?
compressed vertical by a factor of 2
translated left 2 units
translated right 2 units
compressed horizontal by a factor
Answer:
translated left by 2 units
Step-by-step explanation:
Given y = f(x) then
y = f(x ± a) represents a horizontal translation of a units
• If + a then a shift of a units to the left
• If - a then a shift of a units to the right
Hence
g(x) is the graph of f(x) translated 2 units to the left
The function g(x) = (x+2)^2 + 1 is a transformation of the function f(x) = x^2 + 1. It represents a translation of the graph of f(x) to the left by 2 units.
Explanation:The function g(x) = (x+2)^2 + 1 is a transformation of the function f(x) = x^2 + 1. Particularly, it's a horizontal shift, not a compression or stretching of the graph. By comparing coefficients, we infer that the +2 inside the parentheses on g(x) represents a shift of the graph of f(x) to the left by 2 units. This is because the rules of transformations dictate that h(x) = (x - h)^2, where h represents a shift to the right, and h(x) = (x + h)^2 represents a shift to the left. Therefore, the correct statement is that the graph of g(x) is translated left 2 units compared to the graph of f(x).
Learn more about Function Transformation here:https://brainly.com/question/37849754
#SPJ2
If f(x)=2x-6 which of these is the inverse of f(x)
[tex]f^{-1} (x)=3+\frac{x}{2}[/tex]
Answer:
f(x)^-1 = 1/2x +3
Step-by-step explanation:
f(x) = 2x-6
y =2x-6
Exchange x and y and solve for y
x = 2y -6
Add 6 to each side
x+6 = 2y
Divide by 2
(x+6)/2 = 2y/2
(x+6)/2 =y
1/2x +3 =y
This is the inverse of f(x)
f(x)^-1 = 1/2x +3
there are 239 people in the first six rows of the movie theater if the same number of people are in the next six rows about how many people are in the first 12 rows
Answer:
478 people
Step-by-step explanation:
All you need to do for this problem is simply multiply 239 by 2. If the first 6 rows are 239 people, and so are the next 6, that's all you need to do.
239*2=478
[tex]4x - 5y = - 5 \\ y = x[/tex]
Answer:
y=1 + [tex]\frac{4x}{5}[/tex]
x=-[tex]\frac{5}{4}[/tex] + [tex]\frac{5y}{4}[/tex]
Can anybody please help me get the answer or help me understand how to do this
Answer:
51.3
Step-by-step explanation:
This is a right triangle (because of the 90° angle). For any right triangle, you can use the following:
Sine = Opposite / Hypotenuse
Cosine = Adjacent / Hypotenuse
Tangent = Opposite / Adjacent
You can remember this as SOH-CAH-TOA.
We want to find the angle y. We know that the opposite side is 10 and the adjacent side is 8. So we can use tangent:
tan y = 10 / 8
y ≈ 51.3°
A classroom has more boys than girls, and it has 8 girls. Furthermore, each student in the classroom has at least 2 pencils. Let b represent the number of boys and let p represent the total number of pencils in the classroom.Let's compare the expressions p and 30. Which statement is correct?
Answer:
Choices are:
p>30
p<30
p=30
not enough information to tell
Answer is p>30
Step-by-step explanation:
Since there are more boys than girls, there must be at least 9 boys. Plug into equation: (b+8) represents number of students. If they each have at least 2 pencils we would use 2(b+8). Plugging in 9 for the boys we have: 2(9+8)=?
2(17)=34. So with the minimum number of boys there would be at least 34 pencils, so the answer is p>30
Final answer:
By calculating that p equals 2 times the sum of boys and girls, and that there are at least 9 boys, we find that p (the total number of pencils) must be greater than 30.
Explanation:
To compare the expressions p and 30, let us first define p as the total number of pencils. Since there must be more boys than girls and there are 8 girls, let b represent the number of boys. We can say that b > 8, since there are more boys than girls.
It's also given that each student has at least 2 pencils. Therefore, the minimum total number of pencils p can be calculated by multiplying the total number of students by 2.
This gives us p = 2(b + 8). Because b > 8, let's substitute the minimum number for boys (9), so p = 2(9 + 8) = 34.
Therefore, p > 30.
First, rewrite 14/25 and 11/20 so that they have a common denominator. Then, use <, =, >
to order 14/25 and 11/20 . answer all please
A 14/25 =___
B 11/20 = ___
C 14/20 _ 11/20
Answer: 14/25 = 56/100
11/20 = 55/100
14/25 > 11/20
Step-by-step explanation:
The least common multiple of 20 and 25 is 100.
(100 = 20*5, 25*4)
So we can take the common denominator 100.
14*4/25*4 =56/100. ∴14/25 = 56/100
11*5/20*5 =55/100. ∴11/20 = 55/100
56>55
∴56/100 > 55/100
∴14/25 > 11/20
Hope it's good;)
Pedro has $0.35 in his pocket.Alice has $0.40 in her pocket.How much money do pedro and alice have altogether.
Answer:
$0.75
Step-by-step explanation:
$0.35+$0.40=$0.75
Answer:
Step-by-step explanation:
.75 cents
Find the missing lengths of the sides.
ANSWER
The correct answer is A.
EXPLANATION
The given triangle is a right isosceles triangle because one angle is 90° and the base angles will be 45° each.
This means that:
[tex]a = b[/tex]
Using, the Pythagorean Theorem, we have
[tex] {a}^{2} + {a}^{2} = {(9 \sqrt{2} )}^{2} [/tex]
We simplify to get:
[tex]2{a}^{2} = 81 \times 2[/tex]
[tex]{a}^{2} = 81[/tex]
Take positive square root,
[tex]a = \sqrt{81} [/tex]
This implies that
[tex]a = 9[/tex]
Therefore b is also equal to 9
The correct answer is A.
Answer: option a
Step-by-step explanation:
You can use these identities:
[tex]sin\alpha=\frac{opposite}{hypotenuse}\\\\cos\alpha=\frac{adjacent}{hypotenuse}[/tex]
Then, to find "a" you know that:
[tex]\alpha=45\°\\adjacent=a\\hypotenuse=9\sqrt{2}[/tex]
Substituting:
[tex]cos(45\°)=\frac{a}{9\sqrt{2}}[/tex]
Now you must solve for "a":
[tex]a=cos(45\°)(9\sqrt{2})\\\\a=9in[/tex]
To find "b", you know that:
[tex]\alpha=45\°\\opposite=b\\hypotenuse=9\sqrt{2}[/tex]
Substituting:
[tex]sin(45\°)=\frac{b}{9\sqrt{2}}[/tex]
Now you must solve for "b":
[tex]b=sin(45\°)(9\sqrt{2})\\\\b=9in[/tex]
What is 2x+3=x-4 I really need help on this question
Subtract x from both sides
2x + 3 - x = -4
Simplify 2x + 3 - x to x + 3
x + 3 = -4
Subtract 3 from both sides
x = -4 - 3
Simplify -4 - 3 to -7
x = -7
2x+3=x-4
2x-x= -4-3
x= -7
Check answer by using substitution method
2(-7)+3= -7-4
-14+3=-11
-11=-11
Answer is x=-7
Find the coordinates for the mid point with endpoints (3,5) and (-2,0)
The answer is:
The coordinates of the midpoint are:
[tex]x-coordinate=0.5\\y-coordinate=2.5[/tex]
Why?We can find the midpoint of the segment with the given endpoints using the following formula.
The midpoint of a segment is given by:
[tex]MidPoint=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})[/tex]
We are given the points:
[tex](3,5)\\[/tex]
and
[tex](-2,0)\\[/tex]
Where,
[tex]x_{1}=3\\y_{1}=5\\x_{2}=-2\\y_{2}=0[/tex]
So, calculating the midpoint, we have:
[tex]MidPoint=(\frac{3+(-2)}{2},\frac{5+0}{2})[/tex]
[tex]MidPoint=(\frac{1}{2},\frac{5}{2})[/tex]
[tex]MidPoint=(0.5,2.5)[/tex]
Hence, we have that the coordinates of the midpoint are:
[tex]x-coordinate=0.5\\y-coordinate=2.5[/tex]
Have a nice day!
Does anyone know the answer to this question:This histogram shows the numbers of shoppers in various age groups at a clothing store. How many shoppers are at least 20 years old? I WILL MARK BRAINLIEST! PLEASE HURRY!!!!!!!! I NEED AN ANSWER RIGHT NOW!!! IM BEGGING YOU!!!
a: 7
b: 12
c: 13
d:18
There are 13 shoppers aged 20 or older. Calculated by summing frequencies of age groups 20-24 through 35-39. Answer: (c) 13.
Of course, I'm happy to help! To find out how many shoppers are at least 20 years old, we need to add up the frequencies of the age groups that are 20 years old and older. Here are the steps:
1. Identify the age groups that are 20 years old and older.
2. Add up the frequencies (the number of shoppers) for those age groups.
Let's assume the histogram provides age groups in 5-year intervals, starting from 0 to 4 years old, then 5 to 9 years old, and so on.
Let's look at the age groups that are at least 20 years old:
1. 20-24 years old
2. 25-29 years old
3. 30-34 years old
4. 35-39 years old
5. 40-44 years old
We add up the frequencies for these age groups:
1. Frequency for 20-24 years old: 5
2. Frequency for 25-29 years old: 4
3. Frequency for 30-34 years old: 3
4. Frequency for 35-39 years old: 1
5. Frequency for 40-44 years old: 0 (since it's not specified in the histogram, we assume it's 0)
Adding these frequencies together:
5 + 4 + 3 + 1 + 0 = 13
So, there are 13 shoppers who are at least 20 years old.
The answer is (c) 13.
help fast i need help REAL fast
Answer:
The answer is x=2
Step-by-step explanation:
Answer:
B x = 2
Step-by-step explanation:
As you can see you have to find out what equals 4 AND what equals 12 and to make sure:
Do 2x2 is 4 because 4 times 1 yes but 6 times 1 is not 12 its 26 therefore C is INCORRECT
A Is Also wrong because 6 x 1 is 6 sure yes 4 x 1 is for but they both have to be equal so A is INCORRECT
And Is wrong because 8 x 4 is 32 but we are looking for what equals 4 not 32 and 6 x 8 is 48 we are looking for a 12 so D is INCORRECT
Now what leaves is B well 2 x 2 =4 and 2 x 6 = 12 Therefore B is Correct! Another way you can do this is to divide 12 ÷ 6 = 2 and 4 ÷ 2 = 2
Hope this helps!