Answer:A 30-60-90 right triangle is a special right triangle in which one angle measures 30 degrees and the other 60 degrees. The key characteristic of a 30-60-90 right triangle is that its angles have measures of 30 degrees (π/6 rads), 60 degrees (π/3 rads) and 90 degrees (π/2 rads). The sides of a 30-60-90 right triangle lie in the ratio 1:√3:2.
Step-by-step explanation:
The side lengths of a 30-60-90 triangle can be expressed as x, x√3, and 2x, where x is a positive constant.
We have,
In a 30-60-90 triangle, the angles measure 30 degrees, 60 degrees, and 90 degrees.
The side lengths of a 30-60-90 triangle have a specific ratio.
Let's denote the length of the shortest side as x, the length of the side opposite the 60-degree angle as y, and the length of the hypotenuse as z.
The ratios of the side lengths in a 30-60-90 triangle are as follows:
Shortest side: x
Side opposite 60-degree angle: y = x√3
Hypotenuse: z = 2x
Given this ratio, we can determine which set of values could be the side lengths of a 30-60-90 triangle.
The values must satisfy the above relationships.
Possible sets of values for the side lengths of a 30-60-90 triangle are:
Set 1:
x = 1
y = x√3 = √3
z = 2x = 2
Set 2:
x = 2
y = x√3 = 2√3
z = 2x = 4
Set 3:
x = 3
y = x√3 = 3√3
z = 2x = 6
Set 4:
x = k (where k is any positive constant)
y = x√3 = k√3
z = 2x = 2k
These sets of values satisfy the ratios for a 30-60-90 triangle.
Remember that the ratios are consistent, so any positive constant can be chosen for the length of the shortest side (x), and the other side lengths (y and z) will follow accordingly.
So,
Any set of values that satisfy the ratios given above could be the side lengths of a 30-60-90 triangle.
Thus,
The side lengths of a 30-60-90 triangle can be expressed as x, x√3, and 2x, where x is a positive constant.
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Find the slope of the line that passes through (9,4) and (4,11)
Solve the System of Equations -4x + 9y = 14 12x - 10y = - 8
Answer:
(1, 2)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtract Property of EqualityAlgebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
-4x + 9y = 14
12x - 10y = -8
Step 2: Rewrite Systems
-4x + 9y = 14
Multiply everything by 3: -12x + 27y = 42Step 3: Redefine Systems
-12x + 27y = 42
12x - 10y = -8
Step 4: Solve for y
Elimination
Combine 2 equations: 17y = 34Divide 26 on both sides: y = 2Step 5: Solve for x
Define equation: 12x - 10y = -8Substitute in y: 12x - 10(2) = -8Multiply: 12x - 20 = -8Isolate x term: 12x = 12Isolate x: x = 1Step-by-step explanation:
HERE,
two equation are,
●-4x+9y=14••••••••••••(equation I)
●12x-10y=-8•••••••••••(equation II)
First multiplying 3 in equation I
we get,
[tex]\bold{3×(-4x+9y=14) }[/tex]
=[tex]\bold{ -12x+27y=42 }[/tex]••(equation III)
Then,
we combine the equationii and equation III.
we get that,
[tex]\bold{12x-10y-12x+27y=-8+42 }[/tex]
[tex]\bold{\cancel{12x}-10y\cancel{-12x}+27y=-8+42 }[/tex]
[tex]\rightsquigarrow[/tex] [tex]\bold{17y=34 }[/tex]
[tex]\rightsquigarrow[/tex] [tex]\bold{ y=\dfrac{34}{17} }[/tex]
[tex]\rightsquigarrow[/tex] [tex]\boxed{ y=2 }[/tex]
Then,
put the value of y in equation II.
WE get,
[tex]\rightsquigarrow[/tex] [tex]\bold{12x-10×2=-8 }[/tex]
[tex]\rightsquigarrow[/tex] [tex]\bold{ 12x-20=-8 }[/tex]
[tex]\rightsquigarrow[/tex] [tex]\bold{ 12x=-8+20 }[/tex]
[tex]\rightsquigarrow[/tex] [tex]\bold{ 12x=12 }[/tex]
[tex]\rightsquigarrow[/tex] [tex]\bold{ x=\dfrac{12}{12} }[/tex]
[tex]\rightsquigarrow[/tex] [tex]\boxed{ x=1 }[/tex]
So,
solution of the two equation (-4x+9y) and (12x-10y=-8) is (1,2)
I neeed help , can somebody please tell the answer . ?
Answer:
x=39 degrees
Step-by-step explanation:
28+33+x=100
61+x=100
George collects 25 baseball cards each month. How many cards will he have at the end of one year? Complete the equation to help you solve the problem. 25 × = n
Answer:300
Step-by-step explanation:
25 times 12
Ramon owed $850.00 on his car loan. Two months later, he owed $510.00
on the loan. By which percent did Ramon's car loan amount decrease?
Answer:
40%
Step-by-step explanation:
(850-510)/850 = 340/850 = 2/5 = 40%
Answer: 40% I looked it up
Step-by-step explanation:
Simplify the following expression:
4x - (+3x)
Answer:
Step-by-step explanation:
1x
Hope it helped you
Answer: x!
Step-by-step explanation:
plz help !!!!!!!!!!!!
Answer:
A.) $0.89
Step-by-step explanation:
2(4x+3y=7.43)
-3(5x+2y=7.03)
8x+6y=14.86
-15x-6y=-21.09
add the two equations
-7x=-6.23
divide by -7
x=.89
Answer:$0.89
Step-by-step explanation:
Solution by substitution method
4n+3p=7.43
5n+2p=7.03
Suppose,
4n+3p=7.43→(1)
5n+2p=7.03→(2)
Taking equation (1), we have
4n+3p=7.43
⇒4n= -3p+7.43
⇒n = -3p+7.43/4
→(3)Putting n= -3p+7.43/4 in equation (2), we get
= 5n+2p=7.03
= 5(-3p+7.43/4)+2p=7.03
⇒-15p+37.15+8p=28.12
⇒-7p + 37.15=28.12
⇒-7p=28.12 - 37.15
⇒-7p=-9.03
⇒p=9.03/7
⇒p= 1.29→(4)
Now, Putting p=1.29 in equation (3), we get
n=-3p+7.43
n= -3(1.29)+7.43 / 4
⇒n= -3.87+7.43 / 4
⇒n= 3.56 / 4
⇒n=0.89
∴n= $0.89 and p=1.29
State all the integer values of x in the interval -2 ≤ x ≤ 4 that satisfy the following inequality 5x+5 ≥3
Answer:
0, 1, 2, 3, 4
Step-by-step explanation:
solving 5x + 5 ≥ 3 we get x ≥ -2/5
all values above, and including, zero are solutions
Mikayla downloaded 64
pictures from the cloud to her laptop.
These pictures took up 192 megabytes
of space on her laptop. Each picture
took up the same amount of space.
How many megabytes do 25
of these pictures take up?
Answer:
25 pictures will take up 75 Megabytes of space.
Step-by-step explanation:
Given that:
Number of pictures downloaded = 64
Space taken by pictures = 192 MBs
Unit rate = [tex]\frac{192}{64}[/tex]
Unit rate = 3 Megabytes per picture
Now,
The space 25 pictures would take,
25 pictures = 3*25
25 pictures = 75 Megabytes
Hence,
25 pictures will take up 75 Megabytes of space.
Help. I have a D in this class.
Complete the square to re-write the quadratic function in vertex form:
Answer:
y = (x - 4)² - 26
Step-by-step explanation:
To complete the square, all we need to do is take term -8x, and add enough to make the equation come out to the square of half that. Half of -8 is -4, so we need to add 26 to the equation to end up at 16:
[tex]y = x^2 - 8x - 10\\y + 26 = x^2 - 8x + 16\\y + 26 = (x - 4)^2\\y = (x - 4)^2 - 26[/tex]
Giving us the final result
3 = m/12
What is m?
It is for math
Answer:
m is equal to 36.
Step-by-step explanation:
To get rid of division, all you need to do is multiply both sides of the equation by the denominator, which is 12 in this case:
[tex]3 = \frac{m}{12}\\\\3 \times 12 = \frac{m}{12} \times 12\\\\36 = m[/tex]
So m is equal to 36
Please Help Quick ASAP Hurry
Find the constant of variation for the relationship shown in the following table:
x 1 2 3 4
y 4 8 12 16
A. 1
B. 2
C. 3
D. 4
Answer:
vfca
Step-by-step explanation:
vaddavavthui sn fa
Simon bought furniture for his apartment for a total of $2,900. The store financed his purchase for 18 months at 0% interest, and there is no minimum monthly payment amount. Simon decides to pay nothing the first month, and then $180 per month after the first month towards the total until it's paid off.
Complete question :
Simon bought furniture for his apartment for a total of $2,900. The store financed his purchase for 18 months at 0% interest, and there is no minimum monthly payment amount. Simon decides to pay nothing the first month, and then $180 per month after the first month towards the total until it's paid off.
Set up an equation such that Tn represents the total amount Simon still owes after n months.
Calculate the amount Simon still owes at the end of one year after his purchase.
Answer:
Tn = 2900 - 180(n - 1)
Tn = $920
Step-by-step explanation:
Cost of furniture = $2900
Assume no interest
Amount paid in first month = 0
Constant amount to be paid after first month = $180
T amount owed after n, months :
Tn = Cost of furniture - amount to be paid per month * (Number of months - 1)
Hence,
Tn = 2900 - 180(n - 1)
Amount owed at the end of one year after purchase :
Tn = 2900 - 180(12 - 1)
Tn = 2900 - 180(11)
Tn = 2900 - 1980
Tn = $920
The Simon decides to pay nothing the first month, and then $180 per month after the first month towards the total until it's paid off is :
Tn = 2900 - 180(n - 1)
Tn = $920
"To understand the calculation, check below."
InterestWhat all information we have ?
Cost of furniture = $2900
Assume no interest
Amount paid in first month = 0
Constant amount to be paid after first month = $180
T amount owed after n, months :
Tn = Cost of furniture - amount to be paid per month * (Number of months - 1)
Tn = 2900 - 180(n - 1)
Tn = 2900 - 180(12 - 1)
Tn = 2900 - 180(11)
Tn = 2900 - 1980
Tn = $920
The Simon decides to pay nothing the first month, and then $180 per month after the first month towards the total until it's paid off is Tn = $920.
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Describe in words the translation represented by the vector (2. – 1).
A. 2 units to the right and Duunit down
B. 1 unit to the right and 2 units down
C. 2 units to the left and Duunit down
D. 2 units to the left and 1 unit up
Romeo paid 380.75 in car repairs the sales tax is 7.5%. What is the total that Romeo has to pay
Step-by-step explanation:
Answer: $380.75x0.075%=28.55625 28.55625+380.75%-D409.30625 $409.30625 $409.31 Answer: $409.31
6 + √ 2x + 4 = 14
ill give brainliest
Answer:
X=8
Step-by-step explanation:
Move numbers to the right
[tex] \sqrt{2x} = 14 - 10 \\ \sqrt{2x} = 4 \\ 2x = 4 {}^{2} \\ 2x = 16 \\ x = 16 \div 2 \\ x = 8[/tex]
The value of x is 8.
Given that,
Equation; [tex]\rm 6+\sqrt{2x} +4 = 14\\[/tex]
We have to determine,
The value of x.
According to the question,
To determine the value of x following all the steps given below.
Equation; [tex]\rm 6+\sqrt{2x} +4 = 14\\[/tex]
Step1; Adding the terms 6 and 4,[tex]\rm 6+\sqrt{2x} +4 = 14\\\\ 10 +\sqrt{2x} = 14\\[/tex]
Step2; Taking the term 10 right-hand sides and simplifying the equation,[tex]\rm 10+\sqrt{2x} = 14\\\\ \sqrt{2x} = 14-10\\\\ \sqrt{2x} = 4\\[/tex]
Step3; Square both the sides and solve for the value of x,[tex]\rm \sqrt{2x} = 4\\\\Squaring \ on \ both \ the \ sides\\\\2x = 16\\\\x = \dfrac{16}{2}\\\\x = 8[/tex]
Hence, The required value of x is 8.
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Which is a possible turning point for the continuous function f(x)?
Answer:
We are given coordinates of a continuous function f(x)
(–2, 0)
(0, –2)
(2, –1)
(4, 0).
We need to find the possible turning point for the continuous function.
Note: Turning point is a point on the graph where slope of the curve changes from negative to positive or positive to negative.
A turning point is always lowest or highest point of the curve (where bump of the graph seen).
For the given coordinates we can see that (–2, 0) and (4, 0) coordinates are in a same line, that is on the x-axis.
But the coordinate (0, –2) is the lowest point on the graph.
Therefore, (0, –2) is the turning point for the continuous function given.
hoped this was helpful!
WILL MARK BRAINLIST!!! only for correct answer
NEED CORRECT ANSWER ASAPPP
Answer:
B
Step-by-step explanation:
The answer is B because the slope is [tex]\frac{4}{1}[/tex] and there is no y- intercept
Answer:
A.
Step-by-step explanation:
It starts from 32 on the y-axis and goes up 4 times on x-axis.
i need help with this (introduction to prove triangles congruent using sss or sas)
Answer:
Below:
Step-by-step explanation:
Given:
Line QR≅Line SR
Line PQ≅Line PS
Reflexive Property:
Line RP≅Line RP
SSS Theorem:
ΔPQR≅ΔPSR
Compare each side of the equation 56 ÷ 4 = 45 ÷ 3 to determine if it is true or false. (2 points)
True
False
Determine the value for x
Answer:
option 2) is correct
angle a and angle x are supplementary angles
so x=180-140
x=40°
3+(7-5)to the power of 2 x 6
Answer:
27
Step-by-step explanation:
PEMDAS
That is the order that you should solve complex equations
You first do equations in Parentheses
Then exponents
Then Multiplication or Division (whichever comes first in the equation)
Then Addition or Subtraction (again, whichever comes first in the equation)
So we first do the equation in parentheses, 7 - 5
7 - 5 = 2
Then we do the exponent (to the power of 2)
2 to the power of 2 is 4 (fun fact. 2 + 2 is the only equation that is the same in addition form and multiplication form)
Next, we multiply 4 by 6
4 x 6 = 24
And finally addition
3 + 24 = 27
subject: [Mathematics]
Since the rational numbers are in parenthesis next to each other it means you have to multiply both of the numbers together.
______________________________________Hope this helped at least a little bit!~
Also fun fact!
Your a beautiful person, and worth so much.
You deserve the world and more!
So please don't let anyone say otherwise, there are so many people in this world who love you.
And if someone can't see your beauty then their rather blind or your just to bright for them!
Your amazing, so keep on with life, stay strong, and live long because I love you!
Answer:
-12.98
Step-by-step explanation:
Uhhhhh.... I dunno lol
Someone please help me for good points
Answer:
The answer is C
Step-by-step explanation:
Graph the system of linear inequalities.
y > 3x + 2
y ≤ 3x − 4
Step-by-step explanation:
this is what i according to the calculator
Plzz help me ill give u brainlist
Answer:
B. A 100° angle
Step-by-step explanation:
Im pretty sure its an 100 degree angle :)
B.
Do my boys got me? Also giving brainliest ! Need D, E, and F
Answer:
Darn, I could have helped you but I'll leave it to the boys :) goodluck!!
(HELP NEEDED PLEASE) A claw arcade machine contains stuffed animals and mystery boxes. There are 44 items in the machine. Winning a stuffed animal has three times as many favorable outcomes as winning a mystery box. How many of each item is in the machine?
Solve for x. Look at the image attached thanks.
Answer:
x=2.2
Step-by-step explanation:
You know that for triangle ABC, side AB=10, CB=2 and AD=AB+BD=10+1=11. Given that triangles ABC and AED have the same angles, they are similar triangles.
So we can use the following ratios to solve for ED=x:
P
Find the surface area of a closed box with base width 3 cm, base length 5 cm and height 4 cm.
5 cm
1
4 cm
3 cm
4 cm
5 cm
3 cm
O 74 cm
O 15 cm
O 79 cm
O 94 cm
Answer:
Surface area of box = 94cm²
Step-by-step explanation:
Given that:
Width of box = 3 cm
Length of box = 5 cm
Height of box = 4 cm
Surface Area = 2lw + 2lh + 2hw
Surface area = 2( lw + lh + hw )
Surface area = 2(5*3 + 5*4 + 4*3) = 2(15+20+12)
Surface area = 2(47) = 94 cm²
Hence,
Surface area of box = 94cm²