An altitude is drawn to the base of equilateral triangle abc. if ac=13, find the length of the altitude.
Answers
The length of the altitude of the equilateral triangle ABC is [tex]\frac{13\sqrt{3} }{2}[/tex].
Equilateral Triangle is defined as the triangle with all the sides equal and all the angles = 60 deg.
Altitude of a Triangle can be defined as the perpendicular drawn from the vertex of a triangle to the opposite side.
According to the question
In the figure given below
In ΔADC
Since ΔADC is a right angle triangle we can apply Pythagoras Theorem.
Let the sides of the equilateral triangle be "a". and "h" be the altitude.
Since the altitude is of equilateral triangle it divides the base i.e. DC=a/2
[tex](AC)^{2} =(AD)^{2}+(DC)^{2}[/tex]
[tex]a^{2} =h^{2}+(\frac{a}{2})^{2}\\ \\ h^{2}=\frac{4a^{2}-a^{2}}{4} \\ \\ h=\sqrt{3} *\frac{1}{2} *a[/tex]
Substituting the value of a=13 we get
Altitude [tex]h=\frac{13\sqrt{3} }{2}[/tex]
Therefore , The length of the altitude of the equilateral ΔABC is [tex]\frac{13\sqrt{3} }{2}[/tex].
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Related Questions
3/1(x+9)-2
steps to figure out problem and answer
Answers
Answer: 3x+25
Step-by-step explanation: Fraction 3/1 is the same as 3. Using PEMDAS we multiply the numbers in the parenthesis 3x+3x9-2, 3x+27-2, Answer=3x+25
What is the nth term of 8-n
Answers
Answer:
-1
Step-by-step explanation:
Tn = a+(n-1)d (general formula)
Tn = 8-n (given formula)
T9 =8-9
T9=-1
A rectangular area is being fenced in along a river that serves as one side of the rectangle.
(a) Write an expression for the total amount of
fencing needed in terms of the width, w, and the
length, 1.
(b) If w=12 feet and 1= 20 feet, how much fencing
is needed? Use proper units
W
river
W
(c) If the amount of fencing we have available is 120 feet and we want to devote 30 feet of it to the length, 1,
then set up an equation to solve for w and find the width.
Answers
a. Total amount of fencing needed = perimeter of the rectangular area excluding one length of the side close to the river = F = l + 2w
b. F = 44 ft
c. The width (w) = 45 ft.
What is the Perimeter of a Rectangle?Perimeter of rectangle = 2(length + width)
a. Total amount of fencing needed = perimeter of the rectangular area excluding one length of the side close to the river = l + 2w
F = l + 2w
b. w = 12 ft
l = 20 ft
Amount of fencing needed, F = l + 2w = 20 + 2(12)
F = 44 ft
c. F = 120 ft
l = 30 ft
Substitute F = 120 and l = 30 into F = l + 2w to solve for w
120 = 30 + 2w
120 - 30 = 2w
90 = 2w
90/2 = w
w = 45
The width (w) = 45 ft.
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a function is decreasing on an interval if the output values decrease as the input values decrease
true or false?
Answers
The statement that a function is decreasing on an interval if the output values decrease as the input values decrease is FALSE.
What is a decreasing function?A decreasing function refers to a function where the value of the output moves in a different direction from the value of the input.
For instance, in a decreasing function, the value of the output would decrease when the value of the input increases.
In conclusion, it is false that a function is decreasing if the output and the input are both decreasing.
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Use the distribution property to rewrite the expression. Then evaluate.
-3(2x-6)
Answers
Answer: -6x+18
Step-by-step explanation:
-3(2x-6)=
-3*2x-(-3*6)= ==> During distribution
-6x-(-18)=-6x+18 ==> After distribution property
please help step by step -8n +3 +n + 11
Answers
Answer: −8n+3+n+11
Add the terms
−7n+3+11
Solution
−7n+14
Step-by-step explanation: hope this helps
Add the terms
-7n+3+11
-7n+14
100 PTS!! Answer for alg 2a (U3 L10) unit test
1. Which set of ordered pairs in the form of (x, y) does not represent a function of x?
{(0, 2), (1, –1), (2, 3), (3, –2)}
{(0, –2), (1, 1), (2, 3), (3, –2)}
{(0, 2), (–1, –1), (2, –3), (3, 2)}
{(0, 2), (1, 2), (1, –2), (3, 2)}
2.What is (are) the x-intercept(s) of the function graphed above?
0 only
–3, 0, and 4
–4, 0, and 3
–12.5 and 21
3. What is f(–5) if f(x) = |2x – 1| + 10?
21
19
–1
–21
4. Which does not describe the same situation?
(A) y = 3x + 5
(B) x –3 1 4
y –4 8 17
(C) graph
(D) y is five more than three times x.
5. What is an equation of the line in slope-intercept form?
m = 2 and the y-intercept is (0, 3)
y = 3x + 3
y = 2x + 3
y = 2x – 3
y = –3x + 2
Answer if you know the answers and the rest of the answers as well. (19 question test)
Answers
Answer:
Step-by-step explanation:
{(0, 2), (1, –1), (2, 3), (3, –2)}
Answer:basically, x never reats with a different y
(x,y)
A is a fn of x since x never repeats
B is a fn of x since x never repeats
C is a fn of x since x never repeats
D is not since we have (1,2) and (1,-2) so this is the answer
Step-by-step explanation:
Pls pls help whoever gets it right gets a crown
Answers
Solve following proportion. 5/ 8 = y/3
Answers
Step-by-step explanation:
5/8 = y/3
(5/8) times 3 = 15/8
y=15/8
or
y = 1 and 7 over 8
or y = 1.875
9 A and B are integers. A = 300,000 to the nearest 100,000 B = 300,000 to the nearest 10,000 a) What is the greatest possible value of A + B? b) What is the smallest possible value of A + B? c) What is the greatest possible value of A - B?
Answers
The greatest possible value of A + B is 600000.
The smallest possible value of A + B is 600000.
The greatest possible value of A - B is 0.
How to illustrate the information?It should be noted that from the information, A and B are integers.
A = 300,000 to the nearest 100,000
B = 300,000 to the nearest 10,000
Therefore, the greatest possible value of A + B will be:
= 300,000 + 300,000
= 600000.
The smallest possible value of A + B is also, 600000.
The greatest possible value of A - B will be:
= 300,000 - 300,000
= 0.
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The ratio of students who made
only 30 students are in
kindergarten. What is the ratio
of grade 1 students to
kindergarten students?
Answers
Based on the lesson, identify the first operation needed to solve the following equation.
x/3 - 3 = 11
multiplication
division
subtraction
addition
Answers
ayuda mañana tengo examen y nesesito saber cuanto es 4 dividido entre 0.93
Answers
[tex]\displaystyle\\Answer: \frac{400}{93}\approx4.3[/tex]
Step-by-step explanation:
[tex]\displaystyle\\4:0.93=\\\\\frac{4}{0.93 }=\\\\\frac{4}{\frac{93}{100} } \\\\\frac{4*100}{93} \\\\\frac{400}{93} \approx\\\\4.3[/tex]
A sled team consists of 11 dogs and the musher. each dog weighs 70 pounds and the musher weighs 160 pounds. what is the average weight of the sled team members?
Answers
Answer:
C. 73.5lbs
Step-by-step explanation:
Sasha purchased a pair of jeans for 40% off of $75. How much did she pay for the jeans
Answers
Answer:
$45
Step-by-step explanation:
100% = $75
100% - 40% = 60% (discounted price)
60% = 0.6
0.6 x 75 = 45
60% = $45 (discounted price)
10% of 75 is 7.5, right because you shifted the decimal point so multiply 7.5 by 6 and you end up with 45
tickets to the zoo cost $4 for children, $5 for teenagers and $6 for adults. in the high season, 1200 people come to the zoo every day. on a certian day, the total revenue at the zoo was $5300. for every 3 teenagers, 8 children went to the zoo. how many teenagers went to the zoo? a. 100 teenagers c. 300 teenagers b. 200 teenagers d. 400 teenagers please select the best answer from the choices provided a b c d
Answers
According to the given statement the teenagers went to the zoo = 300
What is linear equation explain?First order equations include linear equations. In the coordinate system, the linear equations have been defined for lines. A linear equation throughout one variable is one in which there is a homogeneous variable having degree 1 (i.e., only one variable). many variables have present in a linear equation.
According tot the given information:6a+4c+5t = 5300......................(equation)
a+c+t = 1200
3c-8t = 0
So,
Putting the value a= 1/6
6a+4c+5t = 5300
0.333c+0.167t = 316.667
3c-8t = 0
solving for the value of t:
6a+4c+5t = 5300
3c-8t = 0
1.056t = 316.667
So,
t = 316.66666667/1.05555556
= 300
According to the given statement the teenagers went to the zoo = 300.
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Find the product and show your solution.
1. (x+9) (x²-9x+81)=
2. (y²-7) (y⁴-7y²+49)=
3. (x²-5) (x⁴+5x²+25)=
4. (8x-9y) (64x²+72xy+81y²)=
5. (10m-11) (100m²+110m+121)=
Answers
The solution to the expansion of each polynomial is;
1. (x + 9)(x² - 9x + 81) = x³ + 729
2. (y² - 7)(y⁴ - 7y² + 49) = y⁶ − 14y⁴ + 98y² - 343
3. (x² - 5)(x⁴ + 5x² + 25) = x⁶ - 125
4. (8x - 9y)(64x² + 72xy + 81y²) = 512x³ - 729y³
5. (10m - 11) (100m² + 110m + 121) = 1000m³ - 1331
How to expand polynomials?
1) We want to expand the polynomial;
(x + 9)(x² - 9x + 81)
= x³ + 729
2) We want to expand the polynomial;
(y² - 7)(y⁴ - 7y² + 49)
Multiplying out gives;
y⁶ −7y⁴ + 49y² −7y⁴ + 49y² - 343
Combining like terms gives;
y⁶ − 14y⁴ + 98y² - 343
3) We want to expand the polynomial;
(x² - 5)(x⁴ + 5x² + 25)
Multiplying out gives;
x⁶ - 125
4) We want to expand the polynomial;
(8x - 9y)(64x² + 72xy + 81y²)
Multiplying out gives;
512x³ - 729y³
5) We want to expand the polynomial;
(10m - 11)(100m² + 110m + 121)
Multiplying out gives;
1000m³ - 1331
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Write a quadratic function to model the graph to the right.
f(x)
Answers
The quadratic equation to model the graph is y = x² - 6 · x + 14.
How to derive the expression of a quadratic equation from a graph
The picture presents us the graph of a parabola, whose algebraic expression is a quadratic equation. In accordance with fundamental theorem of algebra, a quadratic equation can be derived by knowing three distinct points on Cartesian plane.
If we know that (x, y) = (0, 14), (x, y) = (3, 5) and (x, y) = (6, 14), then the coefficients of the quadratic equation in standard form:
14 = c (1)
5 = 9 · a + 3 · b + c (2)
14 = 36 · a + 6 · b + c (3)
The solution of the system of linear equations is (a, b, c) = (1, - 6, 14). Hence, the quadratic equation to model the graph is y = x² - 6 · x + 14.
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Someone help please
a
Answers
Answer:
see explanation
Step-by-step explanation:
f(x) × g(x)
= 3x(4x - 1) ← distribute parenthesis by 3x
= 12x² - 3x
when x = 1 , then
= 12(1)² - 3(1) = 12(1) - 3 = 12 - 3 = 9
Cookies are sold in the lunchroom for $2. Ana wants to buy cookies for a group of her friends. If she has $20, write an inequality to show the number of cookies cc she can buy. Use the variable c.
Answers
Answer: she could buy 10 cookies.
Step-by-step explanation:
In order to figure out how many cookies she can buy just do 20÷2.
If f(x) = -x³, g(x) = 3x² - 1, and h(x) = 2x + 5, what is the degree of [f o go h](x)?
2356
Answers
The degree of the polynomial formed is 6.
The degree of a polynomial is the highest degree of the variables present with non-zero coefficients.
For example the polynomial has three 7x³y²+9xy+4 terms. The first term has a degree of 5 (the sum of the powers 2 and 3), the second term has a degree of 1, and the last term has a degree of 0. Therefore, the polynomial has a degree of 5, which is the highest degree of any term.
Now the given functions are:
[tex]f(x)=x^3[/tex] ,g(x)=3x²-1 and h(x)=2x
Now we have to find (f ° g° h)(x). Let us first find (g°h)(x).
(g°h)(x) is equal to g[h(x)]
=g[2x+5]
=3(2x+5)²-1
=3(4x²+20x+25)-1
=12x²+60x+74
Now we find (f ° g° h)(x)
(f ° g° h)(x)=f[g(2x+5)]
f[g(2x+5)]=f(12x²+60x+74)
f(12x²+60x+74)=(12x²+60x+74)³
Now we have to simplify the expression:
(12x²+60x+74)³
=[tex]1728x^6+25920x^5+161568x^4+535680x^3+996336x^2+985680x+405224[/tex]
The largest degree of the variable x in the polynomial is 6.
hence the degree of [f o go h](x) is 6.
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please help with this qestion, I just need the answer in numbers
Answers
Answer:
Step-by-step explanation:
All that is needed here is the difference[tex]=0,738-0,585\\=0,153\\[/tex]Answer:
0.153 or 15.3%
Step-by-step explanation:
Subtract save percentage last season from save percentage this season:
0.738 - 0.585 = 0.153
Convert the decimal answer to a percent
0.153 x 100% = 15.3%
Can you solve please 8=2k-8-6k
Answers
Answer:
k = -4
Step-by-step explanation:
8 = 2k - 8 - 6k
Collect like terms
8 = -4k - 8
Add 4k to both sides (nice to have variable on left, constants on right)
8 + 4k = -8
Subtract 8 from both sides
4k = -16
Divide both sides by 4
k = -4
help would be very appreciated
Answers
Answer:
g(-6) = -6
g(0) = 5
g(7) = 8
h(-6) = 10
h(0) = -1
h(7) = -4
Step-by-step explanation:
g(x) = (1/3) f(x)
g(-6) = (1/3)(-18) = -6
g(0) = (1/3)(15) = 5
g(7) = (1/3) (24) = 8
h(x) = -g (x) + 4
h(-6) = -(-6) + 4 = 10
h(0) = -(5) + 4 = -1
h(7) = -(8) + 4 = -4
I hope this helps!
Write the rational numbers as a decimal:
7/8
1/1
-7/9
-17/40
1 and 5/6
-2 and 17/18
-5 and 7/12
8 and 15/22
Answers
Answer:
7.8
-7.9
-17.40
1. 5.6
-2. 17.18
-5. 7.12
.8 15.22
Step-by-step explanation:
Which symbol will make the statement true?
Answers
Answer:
∉
Step-by-step explanation:
10 is not a member of the set {6, 8, 13, 14} and ∉ is used to represent "not a member of"
Answer:
B ( if you talking about Mathematics enhancement )
Step-by-step explanation:
First one make the statement true but ( 6, 8, 13 ,14 ) didn't related to 10 According to a pattern
A lighthouse casts a revolving beam of light as far as the pier. what is the area that the light covers?
Answers
the area covered by the light of the lighthouse is given by: A = πx²
What is a circle?All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
Area of a circle having r as radius = πr²
Given: The revolving light beam that extends to the pier.
Let the distance to the pier x.
Typically, the rotating beam rotates 360 degrees.
Therefore, Its motion is circular.
The mathematical formula for the area that the light covers is: A = πx²
Hence, the area covered by the light of the lighthouse is given by: A = πx²
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a weding planner rented 13 tables and 104 chairs for an up coming wedding. What is the chair to table ratio?
Answers
Answer: 1:8
Step-by-step explanation:
13 tables
104 chairs
Ratio: 13:104
divide both sides by 13
13:104 = 1:8
4 + −1 2/3= i have no clue, send help asap.......
Answers
Answer:
2 1/3 :)
Step-by-step explanation:
This is because you just subtract lol
4 +- 1 2/3= 4- 1 2/3
What is the slope of the line that passes through the points (-9, 0) and (−17,4)? Write your answer in simplest form.
Answers
The slope of the line that passes through the points (-9, 0) and (−17,4) is -2
What is a good example of a line's slope?The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the location where the y-intercept is located (0, b). For instance, the slope and y-intercept of the equation y = 3x - 7 are 3 and 0, respectively.
The formula to calculate slope is -
m = x2 - x1 / y2 - y1
(-9, 0) and (−17,4)
m = -17 + 9 / 4 - 0
m = -8/4
m = -2
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