These sides also follow the same ratio a/2 : (a√3)/2: a
We get 1:√3:2. This is the 30-60-90 triangle theorem.
Now, According to the question:
Let's consider an equilateral triangle ABC with a side length equal to 'a'.
Now, draw a perpendicular from vertex A to side BC at point D of the triangle ABC. The perpendicular in an equilateral triangle bisects the other side.
Triangle ABD and ADC are two 30-60-90 triangles. Both the triangles are similar and right-angled triangles. Hence, we can apply the Pythagoras theorem to find the length AD.
[tex](AB)^2 = (AD)^2 + (BD)^2[/tex]
[tex]a^2 = (AD)^2 + (a/2)^2[/tex]
[tex]a^2 - (a/2)^2 = (AD)^2[/tex]
[tex]3a^2/4 = (AD)^2[/tex]
(a√3)/2 = AD
AD = (a√3)/2
BD = a/2
AB = a
These sides also follow the same ratio a/2 : (a√3)/2: a
Multiply by 2 and divide by 'a',
(2a)/(2a) : (2a√3)/(2a): (2a/a)
We get 1:√3:2. This is the 30-60-90 triangle theorem.
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2x – 5 > 3 or 11 – 3x > -2
Answer:
x > 4 and x <3
Step-by-step explanation:
Given the system of inequalities
2x – 5 > 3 or 11 – 3x > -2
for 2x – 5 > 3
2x > 3+5
2x>8
x>8/2
x> 4
For 11-3x > -2
-3x > 2-11
-3x > -9
x < -9/-3
x<3
hence the result will be x > 4 and x <3
Find the values of x and y if l // m.
Show all work.
Answer:
x = 7, y = 24
Step-by-step explanation:
23x -16 + 8x - 21 = 180 because they are supplementary angles
31x - 37 = 180
31x = 217
x = 7
23(7)-16 = 7y - 23 because they are vertical angles
168 = 7y
y = 24
Rhonda planted green beans on 67% of her farm. Rhonda's farm has 598 acres of land. Estimate the number of acres of green beans on Rhonda's farm.
Answer: 400 acres.
Step-by-step explanation:
We know that 598 is very close to 600, so we can round that amount up.
We also know that 67% is very close to [tex]\frac{2}{3}[/tex] because 2÷3≈0.67 & 67%=0.67
So, we can estimate [tex]\frac{2}{3}[/tex] of 600, which is about 400.
3c+2d=-24 and 2c+5d= -38
Answer:
c=-4, d=-6
Step-by-step explanation:
The sum of the first 8 terms of a GP is five times the sum of first 4 terms. Find the common ratio.
Answer:
1Step-by-step explanation:
Sum of nth term of a GP is expressed as;
Sn = a(r^n-1)/r-1
The sum of the first 8 terms of a GP is expressed as;
S8 = a(r^8 - 1)/r-1
The sum of first 4 terms is expressed as;
S4 = a(r^4 - 1)/r-1
If the sum of the first 8 terms of a GP is five times the sum of first 4 terms then
S8 = 5S4
a(r^8 - 1)/r-1 = 5[a(r^4 - 1)/r-1]
r^8 - 1 = 5(r^4 - 1)
r^8 - 1 = 5r^4 - 5
r^8 - 5r^4 = -5+1
r^4(r^4 - 5) = -4
r^4 - 5 = -4
r^4 = -4+5
r^4 = 1
r = 1
Hence the common ratio is 1
Ms. Fleener's fish tank has a bottom area of 102 square
centimeters. If the height of the fish tank is 12 centimeters, how
many cubic centimeters of water does the fish tank hold?
I
Answer:
1224 cm^3
Step-by-step explanation:
volume = bottom area x height
102x12=1224
The fish tank holds 1224 cc of water.
What is volume?In mathematics, volume is the space taken by an object.
Here, given that,
The area of the bottom of the tank =A= 102 cm²
now, the height of the water in tank = h= 12cm
we know, volume of water= A× h
=102×12 cc
=1224 cc
Hence, required volume is 1224 cc
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Factor the expression.
(_q^2r+_s^2)(_q^4t^2-6q^2rs^2t+_s^4t^2)
Answer:
2
3
4
9
Step-by-step explanation:
I need help using the Expand Group and Factoring method on this problem.
27a^2+72a+28
Answer:
1 x (27a^2+72a+28) or 1(27a^2+72a+28)
Step-by-step explanation:
First find the GCF (greatest common factor) of 27a squared 72a and 28. It is 1 because there is nothing else that can go in.
So put 1 outside the parentheses and keep the terms
1 x (27a^2+72a+28)
Find the number of terms and the degree of this polynomial. -9
[tex]9 {r}^{9} [/tex]
Number of terms: Degree:
Answers:
Number of terms: 1Degree: 9===============================================
Explanation:
This is consider a monomial since we only have one term. Terms are separated by a plus sign, so something like 5x^2+10x has two terms.
The degree of a polynomial is the largest exponent when dealing with single variables. In the case of 9r^9, the largest exponent is 9, so the degree is 9. Going back to an example like 5x^2+10x, the largest exponent is 2 so this is the degree of this example.
What's the diameter of 2.5ft
Answer:
5
Step-by-step explanation:
On an inch ruler, which mark is halfway between the 12-inch mark and the 3-inch mark?
Answer:
8 and half 8/2 8.5, wait or 7/5 or 7.5
Step-by-step explanation:
Answer:
7 1/2
Step-by-step explanation:
A jar contains 6 yellow and 8 blue gumballs. Two gumballs will be drawn at random without being replaced. If the first gumball drawn is blue, what is the probability that the second gumball will also be blue?
Answer:
I believe the answer would be 8/13 or 61.5%.
Step-by-step explanation:
Hope this helps :))
You are reading a new book. On Monday you read 3 pages. On each day after that, you read 3 times the number of pages you read on the previous day. How many pages do you read on Thursday?
pages plz answer me
81 pages.
Step-by-step explanation:
Tuesday: 3 x 3 = 9
Wednesday: 9 x 3 = 27
Thursday: 27 x 3 = 81
Answer:
81
Step-by-step explanation:
3x3x3x3
what is -6x - 8 < 4
on a number line
Answer:
x > -2
Step-by-step explanation:
-6x - 8 < 4
-6x < 12
x > -2
plss help me il mark you brainly
Answer:
thisl give u extra credit: 2.29*20 = 45.80 and 3.49*35 = 122.15.
Step-by-step explanation:
Answer:
1. 78.54 (area)
2. 25.13 (circumference)
3. 4.5 (radius)
4. 13 (diameter)
Step-by-step explanation:
Consider the following two linear equations.
2x + y = 5
-2x + 2y = 4
Solve for the point of intersection using elimination
Point of intersection:
Answer:
(1,3)
Step-by-step explanation:
:)
Which of the following interpretations for the given expression is correct?
A.
The sum of 2 and the quotient of 9 and 3.
B.
The product of 2 + 9 and 3.
C.
The quotient of 2 + 9 and 3.
D.
The sum of 2 and the product of 9 and 3.
Answer:
the answer is the quotient of 2+9 and 3
Pls help me with this I have 5 minutes to do this I will give brainleast plzz
Answer:
The answer for the first one is 1/2.
The answer for the second one is -1/1
Step-by-step explanation:
Hope that helps you :)
algebra work needed please help
Question: Which set of directions correctly describes how to plot the point (6, 2) on the coordinate plane?
A.Start at the origin. Move 6 units to the right, then move 2 units up.
B.Start at the origin. Move 6 units up, then move 2 units to the right.
C.Start at the origin. Move 6 units to the left, then move 2 units up.
D.Start at the origin. Move 6 units up, then move 2 units to the left.
I GIVE BRAINLIEST!
Select the correct days. Gina tracks the low temperatures for a city over six days. Identify the days colder than -1.75°F.
Answer:
[tex]Monday = -2.5F[/tex]
[tex]Tuesday = -1.9F[/tex]
Step-by-step explanation:
Given
See attachment
Required
Days colder than -1.75°F
From the attachment, we have:
[tex]Monday = -2.5F[/tex]
[tex]Tuesday = -1.9F[/tex]
[tex]Wednesday = 0F[/tex]
[tex]Thursday = -1.5F[/tex]
[tex]Friday = 0.5F[/tex]
Days with temperature less than -1.75°F are colder.
-2.5 and -1.9 are less than -1.75
So, we have:
[tex]Monday = -2.5F[/tex]
[tex]Tuesday = -1.9F[/tex]
Answer:
:)
Step-by-step explanation:
Rewrite using the
distributive property.
14 + 35?
whats the answer plz
Answer 7+7+35
Step-by-step explanation:
Answer:
I think (10*1)+4+(10*3)+5??
Step-by-step explanation:
the * represents a multiplication sign btw
Need help please and thank you
Perimeter= 4x+8 and Area= 2x+1x^2+2
I posted a photo on how I found these two answer.
Hope this helped
1440 tons of grain where brought to a silo over two days. On the second day 80 percent of the amount of the amount of the grain delivered during the first day where brought in. How many tons where delivered on the first day
Answer:
1152 tons of grains
Step-by-step explanation:
We are told in the above question:
Total number of grains = 1440 tons of grain
On the second day 80 percent of the amount of the amount of the grain delivered during the first day where brought in.
Hence,
The number of grains brought in during the first day = 80% × 1440 tons
= 80/100 × 1440 tons
= 1152 tons of grains
The difference of x and 4 (Algebraic expression)
Answer:
x - 4
Step-by-step explanation:
The difference means subtraction
The algebraic expression of the phrase is x-4.
What is an expression?One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.
Given phrase:
The difference of x and 4.
Here, we have the phrase difference.
So, we will use the subtraction operation.
So, the algebraic expression,
x - 4.
Therefore, x -4 is the algebraic expression.
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Tell whether the two ratios form a proportion. 120 baskets made in 3 days and 720 baskets made in 18 days.
Answer:
Yes they form a proportion.
Step-by-step explanation:
120:3 = 720:18 because:
3x6=18 so multiply 120 by 6 and you get 720. Which means the ratios are proportionate.
what are the missing values, and what is the equation for the table
Answer:
Step-by-step explanation:
This is a linear equation. Mx+b=y.
m=slope
x=x coordinate
y=y coordinate
b=y intercept (where x=0)
For this problem, you need to plug in 2 "coordinates", ex (1,16), and (0,__). You would need to find the slope, which would be y2-y1/x2-x1 (find two "coordinates" and then put it in, order doesn't matter.)
Hope this helps!
9514 1404 393
Answer:
see attached for table valuesexponential equation: y = 8·2^x; linear equation: y = 60x -44Step-by-step explanation:
Two points are not sufficient to define a graph, so the equation could be anything that gives the listed values.
We note that the given y-values are powers of 2. Specifically, they are 2^4 and 2^8. These powers differ by 4, just as the corresponding x-values differ by 4. This suggests an exponential equation might be good fit:
y = 2^(x+3)
Simplified, this is ...
y = 8·2^x . . . . . exponential equation for table values
__
Alternate solution
Often, when only two points are given, a linear function is indicated. We can use the two given points in the 2-point form of the equation for a line to find what the linear equation might be.
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (256 -16)/(5 -1)(x -1) +16 . . . . with values filled in
y = 240/4(x -1) +16 . . . . . . . . . . . find the ratio
y = 60x -60 +16 . . . . . . . . . . . . . eliminate parentheses
y = 60x -44 . . . . . linear equation for table values
__
The two answers we looked at here are shown in the attached table. There are an infinite number of other possibilities.
What is the value of (-4) (68) (1/4
Answer:
The answer is A
Step-by-step explanation:
Answer:
the correct answer is -68
Solve for w.
2w+8=13
Answer:
w = 2.5
Step-by-step explanation:
do minus 8 on both sides making the formula
2w =5
then divide both sides by two so the 2w is now just w making it
w = 5÷2
w = 2.5
Find the are of the circle use 3.14 and round to your nearest hundredth using 14m
Answer:
The question is incorrect. Please rewrite the question.