The altitude of the equilateral triangle is [tex]\( \frac{9\sqrt{3}}{2} \)[/tex] centimeters.
In an equilateral triangle, all three sides are equal in length. Let's denote the length of each side of the equilateral triangle as s centimeters.
The perimeter of an equilateral triangle is given as the sum of the lengths of all three sides:
Perimeter = 3s
Given that the perimeter is 27 centimeters, we can set up the equation:
27 = 3s
Now, we can solve for the length of each side s:
[tex]\[ s = \frac{27}{3} = 9 \][/tex]
So, each side of the equilateral triangle is 9 centimeters long.
Now, to find the altitude of the equilateral triangle, we can use the formula for the altitude of an equilateral triangle, which is:
[tex]\[ \text{Altitude} = \frac{\sqrt{3}}{2} \times \text{Length of a side} \][/tex]
Substituting the length of a side s = 9 into the formula, we get:
[tex]\[ \text{Altitude} = \frac{\sqrt{3}}{2} \times 9 \\\[ \text{Altitude} = \frac{9\sqrt{3}}{2} \][/tex]
So, the altitude of the equilateral triangle is [tex]\( \frac{9\sqrt{3}}{2} \)[/tex] centimeters.
What is -5/8 times -8 plus 10
Answer:
The answer is 15.
Identify the like terms in the expression -4x2-2x+8+6x-9
Which statements are true about the ordered pair (−1,−4) and the system of equations?
x−y=3
7x−y=−3
Select each correct answer.
When (−1,−4)) is substituted into the second equation, the equation is true.
When (−1,−4) is substituted into the first equation, the equation is true.
When (−1,−4) is substituted into the second equation, the equation is false.
The ordered pair (−1,−4) is not a solution to the system of linear equations.
The ordered pair (−1,−4) is a solution to the system of linear equations.
When (−1,−4) is substituted into the first equation, the equation is false.
What are the real-number solutions of the equation 2x5 = 12x3 - 16x ?
The x-intercept of the line x = 3.5 is ____? and the y-intercept of the line y = -6.5 is ____? Enter your answer as an ordered pair.
Clovis wants to make a surprise visit to his uncle who lives out of town. He purchases an airline ticket for $69. There is a 15% sales tax on the price of the airline ticket. In addition he must pay a baggage fee of $20. When he arrives at the airport, Clovis takes a taxi to his uncle's house which is 8 miles from the airport. The taxi fee is $2.50 per mile. If Clovis has spent a total of $123.35 for the airline ticket and taxi, at what percent of his fare did Clovis tip the taxi driver?
a.
10%
b.
15%
c.
20%
d.
25%
Answer:
20%
Step-by-step explanation:
edge 2021
Zach is 4 years older than twice his sister Maya’s age.
Let m represent Maya’s age.
Which expression represents Zach’s age?
m + 4
2m + 4
4m + 2
2m
how many sides does a regular polygon have if each exterior angle measures 30 degree
Which expression represents the composition f(g(h(x))) for the functions below?
f(x) = 2x + 1
g(x) = 4x^2
h(x) = x^2
4x^4
8x^4 + 1
8x^2 + 1
(8x^2 + 1)^2
Simplify equation -2b^3 +2^3
Which relation is a function?
I. {(2, 4), (–1, 7), (3, 0), (5, 4)}
II. {(–3, 6), (–3, 6), (8, 6), (8, 10)}
III. {(4, 1), (–2, 5), (–8, 3), (4, 6)}
A. II only
B. I only
C. I and II
D. II and III
What is the measure of angle KML?
help me with algebra 2
Final answer:
Algebra 2 involves solving simultaneous equations through a multi-step process, simplifying where possible and carefully verifying solutions to ensure reasonableness.
Explanation:
Algebra 2, typically taught in high school, involves solving simultaneous equations for unknown values. The process includes several algebraic steps, where students are advised to eliminate terms where possible to simplify the algebra and carefully check their work at each step. After finding the potential solutions, it's crucial to check the answers to ensure they are reasonable within the context of the problem. This systematic approach to solving algebraic problems, such as equations in one variable, is a methodical and critical part of Algebra 2's curriculum.
If f(x) = 3a|2x – 4| – ax, where a is some constant, find f ′(2).
Answer:
so would the answer be DNE?
Step-by-step explanation:
. If you saved $2.00 on january 1, $4.00 on february 1, $8.00 on march 1, $16.00 on april 1, and so on. how much money would you save in one year?
By following a pattern of doubling the saved amount each month, the total amount saved in one year would be approximately $8190.00.
Use the concept of geometric sequence defined as:
A unique kind of sequence called a geometric sequence has a constant ratio between every two succeeding words. This ratio is regarded as one of the geometric sequence's frequent ratios.
Amount saved on January 1: $2.00
Amount saved on February 1: $4.00
Amount saved on March 1: $8.00
Continuing the pattern, the saved amount on April 1 would be $16.00
Since it can be seen that,
The pattern is that the saved amount doubles each month.
Therefore,
To calculate the total amount saved in one year,
Sum up the amounts for each month.
In this case, it would be
$2.00 + $4.00 + $8.00 + $16.00 + $32.00 + $64.00 + $128.00 + $256.00 + $512.00 + $1024.00 + $2048.00 + $4096.00 = $8190
Hence,
The saved amount in one year is $8190
To learn more about sequence visit:
brainly.com/question/12373434
#SPJ5
What is the slope of the line represented by the equation y+3=-4(x-5)
A. -4
B. 3
C. -3
D. 4
For tax reasons, I need to create a rectangular vegetable patch with an area of exactly 50 sq. ft. The fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot. What are the dimensions of the vegetable patch with the least expensive fence? ...?
Patty has a fish pond in her backyard. Even though the air temperature outside has change 35 degrees from sunrise to sunset, the water temperature in the fish pond has only changed 2 degrees. The reason for this lack of temperature change in the water is that it has a high
_____________.
Answer:
The reason for this lack of temperature change in the water is that it has a high specfic heat .
Step-by-step explanation:
Definition of specfic heat .
The amount of heat required per unit mass to raise the temperature by one degree Celsius .
Reason = The reason for this lack of temperature change in the water is due to hydrogen bonding present in water molecules .These hydrogen bonds takes large amount of heat gain for just 1 degree Celsius change in temperature. therefore water temperature increases slowly.
Simplify the expression.
(8 + 7a) + 4
Answer:
its 12+7a
Step-by-step explanation:
i used the answer that was below and it was backwards! please dont use it if you want it to be correct! the correct answer is 12+7a
Determine which two values the following number is between.
3√176
A. 5.59 and 5.6
B. 5.6 and 5.61
C. 5.62 and 5.63
one zero of f(x)=x^3-2x^2-5x+6 is 2 what are the zeros of the function
Answer:
Answer:
x=-2, x=1, x=3
Step-by-step explanation:
Step-by-step explanation:
one zero of f(x)=x^3-2x^2-5x+6 is 2 what are the zeros of the function
the following polynomials have the function
f(x)=x^3-2x^2-5x+6
note 2 is not a zero of the function
but x=-2
to find the other zeros we say
f(x)/x+2=x^3-2x^2-5x+6/(x+2)
we have the quadratic equation
x^2-4x+3
factorizing the above, using factorization method
(x^2-3x-x+3)
(x^2-3x)(-x+3)
x(x-3)-1(x-3)
(x-1)(x-3)
x=1, x=3
the zeros of the function are
x=-2, x=1,x=3
substituting the values back into the function
we have zero
f(1)=1^3-2(1)^2-5(1)+6
F(1)=0
Answer:
-1 and -3 are the other zeroes
solve for x... 4(-2x+3)=-5x
A farmer grows two types of grain in his fields. He has a seed budget of $15,000.00 and has spent $5,800.00 to plant wheat seed so far. If barley seed costs $53.00 per acre to plant, what is the maximum number of acres of barley the farmer can plant and still be under budget?
A.283 acres
B.109 acres
C.173 acres
D.174 acres
Answer:
The answer is option D.
Step-by-step explanation:
Total seed budget is = $15000
Amount paid for wheat seeds = $5800
So, amount left is = [tex]15000-5800=9200[/tex]
Now, lets suppose the number of acre of land to be planted by barley seeds be = x
Barley seed costs = $53 per acre.
This means for 53x acres $9200 will be used.
Therefore, [tex]x=\frac{9200}{53}[/tex] = 173.58 acres ≈ 174 acres
Santa has lots of mixed up socks in his sack! If he has 6 green socks, 4 gold socks, 8 black socks and 2 red socks, what is the minimum he needs to pull out of his sack to get a matching pair?
39% of 50 is what number
Mai's penny bank is 7/10 full. After she removes 200 pennies, it is 1/2 full. How many pennies can Mai's bank hold?
In one week, 103 students were absent,17 fewer students were absent than the week before. howe many students were absent in those two weeks?
In the first week, 120 students were absent, and in the second week, 103 students were absent. Total absentees in the two weeks are 223 students.
To determine how many students were absent in two weeks, we first need to find the number of students absent in the first week. We know that 103 students were absent in the second week and that this number is 17 fewer students than the number absent the week before.
Let the number of students absent in the first week be denoted as x.
According to the information given:
x - 17 = 103.To find x, we solve the equation:
x - 17 + 17 = 103 + 17 x = 120 students.Hence, 120 students were absent in the first week. Adding the absences from both weeks:
Total absentees in two weeks = 120 (first week) + 103 (second week) = 223 students
Raisins sell for $3.50 per pound, and granola sells for $5.90 per pound. Terri bought some raisins and some granola. The total weight was 2.1 pounds and cost $8.79.
How many pounds of raisins and how many pounds of granola did Terri buy?
A.
0.6 pounds of raisins; 1.5 pounds of granola
B.
1.1 pounds of raisins; 1 pound of granola
C.
1 pound of raisins; 1.1 pounds of granola
D.
1.5 pounds of raisins; 0.6 pounds of granola
The GCF of the numbers in the expression (32 + 16) is . The numbers left inside the parentheses after factoring out the GCF are and .
Answer:
The answer is :
2 and 1
Step-by-step explanation:
The GCF means greatest common factor between given numbers.
The GCF of the numbers in the expression (32 + 16) is 16.
Factor each with a common factor of 16:
[tex](16\times2+16\times1)[/tex]
After factoring out 16, we have:
[tex]16(2+1)[/tex]
So the answer is :
2 and 1
When Emma was born, she weighed 3.2 kilograms. In 2 months, she weighed
5.15 kilograms.
How much did Emma gain in her first 2 months?