Answer: The area of a triangle is the region enclosed between the sides of the triangle. Area of ΔABC = 1/2 × Base × Height
Step-by-step explanation:
Area of ΔABC= 1/2 × Base × Height = 1/2 × h × BC
If ABC is an equilateral triangle, Area of ΔABC = (√3/4)a2 where a is the length of a side of the equilateral triangle.
Thus, we have seen the formula and definition of the area of triangle ABC.
n of the following are factors of x² - 7x - 30 ?
a
(x-3) (x - 10)
B
(x-3) (x + 10)
C
(x - 15) (x + 2)
D
(x - 10) (x + 3)
Answer:
D
Step-by-step explanation:
1. Solve the equation using square roots.
x² +10=9
Answer:
x=±√−1 (NO REAL SOLUTION)Step-by-step explanation:
x² + 1 = 0
1× x²+1=0
x=±√(−1×1)
x=±√−1 (NO REAL SOLUTION)
An account has $26,000 after 15 years. The account received 2.3 percent interest compounded continuously. How much was deposited initially. Show all work.
The intital amount deposited was $18485.82.
How to find the compound interest?If n is the number of times the interested is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:
[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]
An account has $26,000 after 15 years. The account received 2.3 percent interest compounded continuously.
A = 26000
R = 0.02.3
[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]
[tex]26000 = p(1 + \dfrac{2.3}{100})^{15}\\\\26000 = p \times 1.4064\\\\\P= 18485.82[/tex]
Therefore, the intital amount deposited was $18485.82.
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Q4. The diagram shows a triangle inside a rectangle.
2x
All measurements are given in centimetres.
Show that the total area, in cm², of the shaded regions is 18x - 30
3x-5
Diagram NOT
accurately drawn
The prove to show that the area of the shaded portion is 18x - 30 is as follows: 3x² + 13x - 30 - 3x² + 5x = 18x - 30
How to find the area of the shaded region?The area of the shaded region can be represented as follows:
area of the shaded region = area of rectangle - area of triangle
Therefore,
area of the rectangle = (x + 6)(3x - 5)
area of the rectangle = 3x² - 5x + 18x - 30
area of the rectangle = 3x² + 13x - 30
area of triangle = 1 / 2 × 2x × 3x - 5
area of triangle = 3x² - 5x
Therefore,
area of the shaded portion = 3x² + 13x - 30 - 3x² + 5x
area of the shaded portion = 18x - 30
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PLEASE HELP I NEED HELP BADDD PLS CORRECT ANSWERS ONLY
Answer:
Hi,
Step-by-step explanation:
Answer B : 51
1+4+7+10+13+16=51
20(6x4) Can you pls help me
Answer:
480
Step-by-step explanation:
We will use the order of PEMDAS. First, everything in parenthesis must be completed. Since 6x4 is in parenthesis, we multiply it and get 24.
Since we now have 20(24). We can multiply them by each other.
A trick to do this manually is to notice that 20 is 10 x 2, meaning that in reality this equation is 10 x 2 x 24. Multiply 2 x 24 = 48, and 48 x 10 = 480.
determine the period of each function
Answer: hmmm, all i could say it is 2,2 function, you have to calculete the other parts yourself.
Step-by-step explanation:
someone please help me to learn new things i am a 5th grade student and im hoping to learn new things in math
Answer:
Here you go!
Step-by-step explanation:
Do tell if it still seems difficult.
:)
1/2x-20-x = 3(2x - 1) - (2x - 1)
Answer:
x = -4
Step-by-step explanation:
1/2x - 20 - x = 6x -3 -2x +1
-1/2x -20 = 4x -2
-1/2x -4x = -2 +20
-9/2x = 18
9/2x = -18
9x = -36
x = -4
Give brainliest please!
hope this helps :)
Evaluate. Write your answer as a whole number or as a simplified fraction.
12-².4³ =
Submit
[tex]12^{-2} \times 4^3\\\\=(4 \times 3)^{-2} \times 4^3\\\\=4^{-2} \times 4^3 \times 3^{-2}\\\\=4^{-2+3} \times 3^{-2}\\\\=4^1 \times \dfrac1{3^2}\\\\=\dfrac 49[/tex]
Solve system of equation using elimination by addition.
Will give brainliest!!
Answer:
x = 2
y = -1
Step-by-step explanation:
You can add together the equations so the x term cancels out:
-3x + 5y = -11
+ (3x + 7y = -1)
The -3x and 3x cancel out, 5y and 7y add to 12y, and -11 and -1 add to -12:
12y = -12
Divide by 12 on both sides to get
y = -1
We can substitute this value into one of the equations to solve for x:
3x + 7y = -1
3x +7(-1) = -1
3x - 7 = -1
3x = 6
x = 2
The coordinates (1, 1), (1, 3), (3, 3), and (x, y) form a square when graphed on a coordinate plane. Which ordered pair would be the fourth vertex of the square? A (3, 1) B (1,3) C (3,5) D (3, 0
)
Answer:
3,1
....................................
What is the volume of the three-dimensional object formed by continuously rotating the right triangle around line segment AC
The volume of the three-dimensional object (cone) formed is equal to 32π cubic units.
How to determine the volume of the three-dimensional object?In this scenario, the effect of rotating the right triangle around line segment AB would form a three-dimensional object known as a cone, with the following dimensions:
Radius, r = 4 units.Height, h = 6 units.How to calculate the volume of a cone?Mathematically, the volume of a cone can be calculated by using this formula:
V = 1/3 × πr²h
Substituting the given parameters into the formula, we have;
V = 1/3 × π × 4² × 6
V = π × 16 × 2
V = 32π cubic units.
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Complete Question:
In the diagram below, right triangle ABC has legs whose lengths are 4 and 6. What is the volume of the three-dimensional object formed by continuously rotating the right triangle around line segment AB?
(1) 32π
(2) 48π
(3) 96π
(4) 144π
A circle has a area of 49 pie cm2 work out its radius
Area of a circle: pi x r^2
49 pi = pi x r^2
49 = r^2
r = +/- 7
---In this case, the radius is a measurement, so the answer must be positive.
r = 7
Hope this helps!
How many times longer is the wavelength of a sound wave with a frequency of 20 waves per second than the wavelength of a sound wave with a frequency of 16,000 waves per second?
The sound wave with a frequency of 20 waves/sec is 800 longer than the wavelength of a sound wave with a frequency of 16,000 waves/sec
Calculating wavelengthFrom the question, we are to determine how many times longer is the first sound wave compared to the second sound water
Using the formula,
v = fλ
∴ λ = v/f
Where v is the velocity
f is the frequency
and λ is the wavelength
For the first wave
f = 20 waves/sec
Then,
λ₁ = v/20
For the second wave
f = 16,000 waves/sec
λ₂ = v/16000
Then,
The factor by which the first sound wave is longer than the second sound wave is
λ₁/ λ₂ = (v/20) ÷( v/16000)
= (v/20) × 16000/v)
= 16000/20
= 800
Hence, the sound wave with a frequency of 20 waves/sec is 800 longer than the wavelength of a sound wave with a frequency of 16,000 waves/sec
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last week, 4/5 of the students in Mr. Zanker's class went on a field trip. 9/10 of the students in Mr. Haynes's went. What is the average fraction of students in the two classes who went on the field trip?
The average fraction of the students in the two classes is 17/20.
What is a fraction?A fraction is a ratio of two integers called the numerator and denominator.
Analysis:
sum of the fraction of both students in the two classes = 4/5 + 9/10 =
LCM of the denominators which are 5 and 10 is 10
so the sum of both fractions = 8/10 + 9/10 = 17/10
The average = 17/10 /2 = 17/10 x 2 = 17/20
In conclusion, the average of the fraction of students on both classes is 17/20.
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6. What is an equation of the line that passes through the point (6,8)
and is perpendicular to a line with equation y = 3
2x + 5?
(1) y − 8 = 2(x − 6)
(3) y + 8 =
2(x + 6)
(2) y - 8 = -(x − 6)
-
(4) y + 8 =
− ½(x + 6)
Answer:
x = 6
Step-by-step explanation:
y = 3 is a horizontal line parallel to the x- axis and passing through all points with a y- coordinate of 3
A line perpendicular to this will be a vertical line parallel to the y- axis with equation
x = c ( c is the value of the x- coordinates the line passes through )
the line passes through (6, 8 ) with x- coordinate 6 , then
x = 6 ← equation of perpendicular line
Hi please answer fast worth 98 points
Answer:
congruent.
Step-by-step explanation:
each side and each angle in one polygon is paired with a side or angle in the second polygon .
hope this helps
Set A= 1, 3, 4, 5, 9, 10, 11
Set B= 2, 4, 6, 7, 11, 12
What is the union of sets A and B?
Answer:
1 ,2,3,4,5,6,7,9,10,11,12 is the union
Answer:
A U B = {1,2,3,4,5,6,7,9,10,11,12}
Step-by-step explanation:
Union of sets is a set containing all elements that are in A or B.
A = {1,3,4,5,9,10,11}
B= {2,4,6,7,11,12}
A U B = {1,2,3,4,5,6,7,9,10,11,12}
PLEASE ASAPPP 50 POINTS
Answer:
A,B,C,J,K,M
A=B,L is parallel to K
C=J
What are some examples of a linear system
Answer:
Describe the middle class of Central America. Mention jobs, homes, and education.ury
Step-by-step explanation:
I need to get this done quick and I'm tired so plx help me
Answer:
6 cups
Step-by-step explanation:
hope this helps!
The tables show the battery lives (in hours) of two brands of laptops. Which brand's battery lives are more spread out? Explain
a student is asked to solve the equation below and to justify her steps identify what if anything is incorrect in her math or justification j-6=-10
Answer:
B
Step-by-step explanation:
New Zealand consists of hundreds of islands. Most of the population lives on the North Island, which has an area of 1.14x105 square kilometers, and the South Island, which has an area of 151,000 square kilometers.
· Which island has a greater area? How many square kilometers greater is it? Express your answer in scientific notation.
· The population of the North Island and South Island combined is about 4.8 x 106. Find the approximate population density in people per square kilometer, rounded to the nearest unit. Explain your steps
Answer:
151,000
Step-by-step explanation:
1.14×105=119.7
151,000
Evaluate:
[tex]\bf{\sum^6_{n=0\:}(3)^n}[/tex]
Need help A.S.A.P., thank you! :)
Answer:
1093
Explanation:
Given expression:
[tex]\sf \huge{ \sum _{n=0}^6\left(3\right)^n}[/tex]Summation:
[tex]\sf a_0+\sum _{n=1}^63^n[/tex]Formula:
[tex]\sf \sum\limits_{i=1}^n x_i = x_1 + x_2 + \dots + x_n[/tex]Compute:
[tex]\rightarrow \sf 3^0 + 3^1 + 3^2 + 3^3 + 3^4 + 3^5 + 3^6[/tex]
[tex]\rightarrow \sf 1 + 3 + 9 + 27 + 81 + 243 + 729[/tex]
[tex]\rightarrow \sf 1093[/tex]
Answer:
[tex] \boxed{\rm \: SUM = 1093 }[/tex]
Step-by-step explanation:
Given:
[tex] \huge\rm {{ \sum}^6_{n=0\:} (3)^n}[/tex]
To Find:
Sum of the given finite series
Solution:
We'll use this formula:
[tex] \boxed{\rm SUM = a \cdot\bigg( \cfrac{1 - r {}^{n} }{1 - r} \bigg)}[/tex]
where,
a = first termr = ratio in between termsLet's find out the ratio R by using this formulae:
[tex] \rm \: r = \cfrac{a_{n + 1} }{a_n}[/tex]
According to the question,
[tex]\rm a_n = 3^n[/tex][tex]\rm a_{n+1}= 3^{n+1}[/tex]Substitute:
[tex] \rm \: r = \cfrac{3 {}^{n + 1} }{3 {}^{n} } [/tex]
Apply law of exponents:[a^m/a^n] = a^m-n
[tex] \rm \: r = {3}^{n + 1 - n} [/tex]
Rearrange it as:
[tex] \rm \: r = 3 {}^{n - n + 1} [/tex]
[tex] \rm \: r = 3 {}^{1} = 3[/tex]
So,the ratio R is 3.
Now let's find out the First term A.
To find, substitute the value of n in 3^n:
[It is given that n = 0][tex] \rm \: a = 3 {}^{0} [/tex]
[x^0 = 1][tex] \rm \: a = 1[/tex]
Hence, first term A is 1.
NOW Substitute the value of the first term A and ratio R onto the formulae of sum:
[tex] \rm \: a \cdot\bigg( \cfrac{1 - r {}^{n} }{1 - r} \bigg)[/tex]
a = 1r = 3n = 7Simplify.
[tex] \rm SUM = \rm \: 1 \times \cfrac{1 - 3 {}^{7} }{ 1 - 1 \times 3} [/tex]
[tex] \rm \: SUM = \cfrac{ - 2186}{1 - 3} [/tex]
[tex] \rm \: SUM = \cfrac{ \cancel{ - 2186} \: \: {}^{1093} }{ \cancel{ - 2} \: \: ^{1} } [/tex]
[tex] \rm \: SUM = 1093[/tex]
We're done!
Hence, the sum of the given Finite series is 1093.
[tex] \rule{225pt}{2pt}[/tex]
Evaluate each function.
14) g(x)= 3x² - 1; Find g(-3)
Answer:
g(-3)= 26
Step-by-step explanation:
g(x)= 3x² - 1
g(-3) means use -3 for x in the given equation.
g(-3)= 3(-3)² - 1
g(-3)= 3(9) - 1
g(-3)= 27 - 1
g(-3)= 26
Can someone please help me witht his question (i will give brainliest)
Answer:
n = 3
Step-by-step explanation:
there are 80 people in choir
half are women , that is 40
quarter of number of women are men , that is 10
number of children = 80 - 40 - 10 = 80 - 50 = 30
number of children : number of men = 30 : 10 ( divide both parts by 10 )
children : men = 30 : 10 = 3 : 1 ← in simplest form
with n = 3
Answer:
30
Step-by-step explanation:
=> number of people in the choir = 80
=> number of women in the choir = half the total people = 80/2 = 40
=> number of men in the choir = one quarter of the number of women =
(1/4)*40 = 40/4 = 10
=> for the number of children,
we subtract the sum of number of men and women from the total
people = 80 - (40+10) = 80 - 50 = 30
number of children = 30
hope this helps :)
Show and explain how replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions as the one shown.
8x + 7y = 39
4x – 14y = –68
Answer:
Sample Response: Using the linear combination method, you can multiply the first equation by 2 and add the equations to get 20x = 10. Dividing both sides by 20, x = 1/2. To solve for y, substitute 1/2 for x in the equation 8x + 7y = 39 to get 4 + 7y = 39. Solving this equation, y = 5. Checking this in the other equation, 4(1/2) – 14(5) = –68 results in 2 – 70 = –68 or –68 = –68. The solution of the system shown is (1/2, 5). The system 8x + 7y = 39 and 20x = 10 is formed by replacing 4x –14y = –68 by a sum of it and a multiple of 8x + 7y = 39. Since 20(1/2) = 10, the system 8x + 7y = 39 and 20x = 10 also has a solution of (1/2, 5).
Hope this was helpful..
A triangle has side lengths 12 centimeters and b. The hypotenuse is 15 centimeters.
What is the unknown leg length?
Pythagorean theorem:a2+b2=c2
122+b2 = 152
144 + b2 = 225
b2 = 81
Answer:
b = 9
Step-by-step explanation:
All the steps are correct. This final step in finding the value of "b" is to take the square root of both sides. This gets rid of the power that "b" is raised to. Once you do this, you are just left with the variable and the answer of 9.
b² = 81
√b² =√81
b = 9