Answers
Answer:
1. x = 24
2. x = 31
Step-by-step explanation:
For number 1, 3x - 1 = 71 because opposite angles are congruent. Solving that gives us x = 24.
For number 2, 2x + 4x - 6 = 180, because they lie on the same line and a straight line is 180 degrees. Solving that gives you 6x - 6 = 180, x = 31 degrees.
Answer:
1. 24
2. 31
Step-by-step explanation:
1. opposite angles are equal
( 3x-1)°=71°
3x=72
x=24
2. remember opposite angles are equal,
180°= (2x)°+(4x-6)°
186=6x
x=31
Related Questions
Ella bought a 2 bedroom unit 12 years ago for $95 000 and recently sold it for $280 000 (after deducting selling costs).
a) Find the profit.
b) Find the profit as a percentage of the buying price.
c) Find the profit as a percentage of the selling price.
d) Which percentage profit sounds better as far as Ella is concerned?
pls explain, thanks!!!!
Answers
C.P. = $95000
S.P. = $280000
a. Profit
= S.P. - C.P.
= $280000 - $95000
= $185000
b. Let the profit% of C.P. be x.
(x/100) × $95000 = $185000
=> x/100 = $185000/$95000
=> x/100 = 37/19
=> x = (37/19) × 100
=> x = 3700/19
=> x = 194 14/19
So, profit percent of buying price is 194 14/19%.
c. Let the profit% of S.P. be x.
(x/100) × $280000 = $185000
=> x/100 = $185000/$280000
=> x/100 = 37/56
=> x = (37/56) × 100
=> x = 3700/56
=> x = 925/14
=> x = 16 1/14
So, profit percent of selling price is 16 1/14%.
d. Buying price percentage profit sounds better as far as Ella is concerned.
Lorraine writes the equation shown. x²+4-15=0 She wants to describe the equation using the term relation and the term function. The equation represents a relation and a function a relation but not a function a function but not a relation neither a relation nor a function
Answers
Answer:
Neither a relation nor a function
Step-by-step explanation:
A relation in mathematics is a relationship between two or more set of values in an ordered pair, such as related x and y-values
An equation is a statement that gives declare the equality between two expressions
A function is a mapping rule that maps each element in the domain set to only one element in the range set
Therefore, the given equation in one variable, x, that asserts the equality of the expressions on the left and right hand side, is neither a relation nor a function
Convert 5π∕6 radians to degrees. Question 1 options: A) 25° B) 150° C) 150π° D) 1080°
Answers
Step-by-step explanation:
Hi there!
Given;
= 5(π\6)
We have;
π = 180°
Keeping value of π in the question;
= 5(180°/6)
= 5*30°
= 150°
Therefore, answer is option B.
Hope it helps!
Find all complex numbers z such that z^4 = -4.
Note: All solutions should be expressed in the form a+bi, where a and b are real numbers.
Answers
Rob cuts a circular hole out of a rectangular piece of paper. The paper measures 20 centimeters by 30 centimeters. The hole is 10 centimeters in diameter. How much of the piece of paper, in square centimeters, is left over after the hole is cut out?
Answers
Answer:
521.25
Step-by-step explanation:
the circle is 78.75 in area and the square is 600 so 600- 78.75 = 521.25
The first term of a sequence is 1 and every term after the first one is 1 more than the square of the preceding term. What is the fifth term?
Answers
Answer:
677
Step-by-step explanation:
the sequence is 1, 2, 5, 26, 677
the first term is 1
to find the 2nd term, do: [tex]1^{2} +1=2[/tex]
3rd: [tex]2^{2} +1=4+1=5[/tex]
4th: [tex]5^{2} +1 =25 +1=26[/tex]
5th: [tex]26^{2} +1=676+1=677[/tex]
How many solutions does the system have?
⎪
⎪
⎨
⎪
⎪
⎧
x+y=3
5x+5y=15
Answers
5(3-y) + 5y=15
15y-5y+5y=15
15y=15
Y= 15/15
Y= 1
X+(1)=3
X=3-1
X=2
Final answer: x=2 and y=1
Method: simultaneous equations
please answer this question!!
Answers
Answer:
a
Step-by-step explanation:
all angles of an equilaterall triangle are equal therefore 180÷3 = 60
Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles.
This is a triangle. side a has a length of 6 yards. side b has a length of 10 yards. side c has a length of 14 yards. The altitude to side c has a length of X yards. what is x
Answers
Answer:
3.71 yd
Step-by-step explanation:
Heron's formula:
area = 0.25 * √((a + b + c) * (-a + b + c) * (a - b + c) * (a + b - c))
so h = 0.5 * √((a + b + c) * (-a + b + c) * (a - b + c) * (a + b - c)) / c
a = 6
b = 10
c = 14
a+b+c = 30
-a+b+c = 18
a-b+c = 10
a+b-c = 2
x = h = 0.5×sqrt(30×18×10×2)/14 = sqrt(30×18×10×2)/28 =
= sqrt(10800)/28 = sqrt(400×9×3)/28 =
= 20×3×sqrt(3)/28 = 60×sqrt(3)/28 = 15×sqrt(3)/7 =
= 3.711537 yd
Determine the measure of the interior angle at vertex E.
A. 135
B. 45
C. 225
D. 75
Answers
Answer:
135
Step-by-step explanation:
The sum of the interior angles of a pentagon is 540
3x+3x+2x+2x+2x = 540
12x = 540
Divide by 12
12x/12 = 540/12
x = 45
E = 3x = 3*45 = 135
Answer:
135
Step-by-step explanation:
Using the following equation, find the center and radius:
x2 + 2x + y2 + 4y = 20
Answers
Answer:
centre = (- 1, - 2 ) , radius = 5
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given
x² + 2x + y² + 4y = 20
To obtain equation in standard form use method of completing the square
add ( half the coefficient of the x/y terms )² to both sides
x² + 2(1)x + 1 + y² + 2(2)y + 4 = 20 + 1 + 4
(x + 1)² + (y + 2)² = 25 = 5² ← in standard form
with centre = (- 1, - 2 ) and r = 5
Radius -5
YOUR WELCOME:)))
Which inequality is represented by this graph?
Answers
Answer:
x> 0
Step-by-step explanation:
There is an open circle at 0 so this means it is not equal to
The line goes to the right so x is greater than
x> 0
what is the slope in the linear equation y = 2x=1?
Answers
Answer:
The slope of the line is 2
Step-by-step explanation:
y=2x+1, compare it to the slope intercept form of a line, y=mx+c, the slope will be 2
Answer:
its 2
comment for more understanding
Good luck
1a.-14,____,-6,____,2,____,10
b. ____, - 2,4,____,16,____,64
2.Factor of 60=
1,2,3,4,5,6,10,x,15,20,y,z
Find the sum of the values of x, y and z
Please help me to solve these question, thank you.
Answers
Answer:
102
Step-by-step explanation:
x= 12
y= 30
z= 60
Hope u got it
Answer:
Hello,
a) -6
b) -39
c) 102
Step-by-step explanation:
I suppose this are sequence arithemical or geometrical
[tex]a)\\u_1=-14\\u_2=x\\u_3=-6\\u_4=y\\u_5=2\\u_6=z\\u_7=10\\\\We\ see\ that\ :\\u_3-u_1=-6-(-14)=-6+14=8\\u_5-u_3=2-(-6)=2+6=8\\u_7-u_5=10-2=8\\\\We\ may \imagine\ that\ the\ difference\ bethween\ 2\ terms\ is\ =8/2=4\\\\so\ x=-10, y=-2, z=6 \ and\ x+y+z=-10+(-2)+6=-6\\[/tex]
[tex]b)\\u_1=x\\u_2=-2\\u_3=4\\u_4=y\\u_5=16\\u_6=z\\u_7=64\\\\We\ see\ that\ :\\\\\dfrac{u_5}{u_3}=\dfrac{16}{4} =4\\\dfrac{u_8}{u_6}=\dfrac{64}{16} =4\\\dfrac{u_3}{u_2}=\dfrac{4}{-2} =-2\\\\The\ common\ factor\ is\ -2\\\\u_1=x=\dfrac{u_2}{-2} =1\\\\u_4=y=\dfrac{u_5}{-2} =-8\\\\u_6=z=\dfrac{u_7}{-2} =-32\\x+y+z=1+(-8)+(-32)=-39\\[/tex]
c)
All those numbers are divisor of 3*4*5=60
x=12, y=30, z=60
x+y+z=12+30+60=102
A graph shows minutes on the horizontal axis from 0 to 10 and miles from start on the vertical axis from 0 to 1.5. The blue line labeled Andy begins at 0 miles in 0 minutes and ends at 1.25 miles at 10 minutes. The red line labeled Berta begins at 0.5 in 0 minutes and ends at 1.12 miles in 10 minutes. The green line labeled Caedin begins at 1.5 miles in 0 minutes, to 0 miles in 6 minutes, and ends at 1 mile in 10 minutes. [NOTE: character count is 425; possible visual bias in graph]
Three runners run along a 1.5 mile trail one Saturday morning. The graph shows the runners’ locations starting at 9:00 a.m.
Answers
Answer:
Who is at the trail start at 9:00 a.m.? : Andy
Who runs fastest? : Caedin
When do Andy and Berta cross paths? : 9:08 am
Who is closest to the 1.5 mile mark after 6 minutes? : Berta
Step-by-step explanation:
assignment
Which of these products is negative? Select all that apply.
-8 ÷ (-3)
-2 ÷ 8
0 ÷ (-2)
15 ÷ (-5)
-8 ÷ (-9)
Answers
Answer:
Positive/negative = negative
Negative/positive = negative
So -2 ÷ 8 and 15 ÷ (-5) are going to have negative quotients.
Let me know if this helps!
Another of Bhaskara's problems results in a quadratic equation Parthava was enraged and seized a certain number of arrows to slay Karna. He expended one-half of them in defending himself. Four times the square root of the number of arrows were discharged against the horses. With six more, he transfixed Shalya, the charioteer. With three more, he rent the parasol, the standard, and the bow; and with the last one he pierced the head of Karna. How many arrows did Parthava have?
Answers
Answer:
Parthava had 100 arrows.
Step-by-step explanation:
Let's define N as the number of arrows that Parthava originally has.
He uses one-half of them in defending himself, so he used N/2 arrows
Now he uses four times the square root of the number of arrows, so now he uses:
4*√N
Then he uses 6
Then he uses 3
Then he uses the last one.
If we add all these numbers of arrows that he used, we should get the initial number of arrows that he used, then:
N/2 + 4*√N + 6 + 3 + 1 = N
Now we have an equation that we can try to solve.
First, let's move all the terms to the same side:
N/2 + 4*√N + 6 + 3 + 1 - N = 0
now we can simpify it:
(N/2 - N) + 4*√N + (6 + 3 + 1) = 0
-(1/2)*N + 4*√N + 10 = 0
Now we can define a new variable x = √N
Then we have: x^2 = N
now we can replace these new variables in our equation to get:
-(1/2)*x^2 + 4*x + 10 = 0
Now we just have a quadratic equation.
Remember that for a quadratic equation of the form:
0 = a*x^2 + b*x + c
The solutions were given by:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4*a*c} }{2a}[/tex]
Then in our case, the solutions will be:
[tex]x = \frac{-4 \pm \sqrt{4^2 - 4*(-1/2)*10} }{2*(-1/2)} = \frac{-4 \pm 6 }{-1} = 4 \pm 6[/tex]
So there are two solutions:
x = 4 + 6 = 10
x = 4 - 6 = -2
And remember that x = √N
Then x should be positive, then we take x = 10 as our solution here.
then we can use the equation:
x = 10 = √N
then
10^2 = √N^2 = N
10^2 = 100 = N
Parthava had 100 arrows.
An electricity post is supported by a 12 m long strut(wire). If the strut makes an angle of 53° with the ground level, how far from the post is the strut attached to the ground?
Answers
Step-by-step explanation:
I do hope that you understand through the steps in the attachment, if not kindly reach out!
I need help with this question...
Q: Five days last month it rained 6.5 inches. It rained 3.5 inches in 7 days last month. How many inches did it rain those 12 days?
Answers
Answer:
57 inches
Step-by-step explanation:
It rained 5*6.5+7*3.5=32.5+34.5=57 inches in the past 12 days
Find the values of x and y if (-x + 5, 1) = (-y, 2x - 5y).
Answers
Answer:
x = 8, y = 3
Step-by-step explanation:
Equating corresponding x and y coordinates , then
- y = - x + 5 ( multiply through by - 1 )
y = x - 5 → (1)
2x - 5y = 1 → (2)
Substitute y = x - 5 into (2)
2x - 5(x - 5) = 1 ← distribute and simplify left side
2x - 5x + 25 = 1
- 3x + 25 = 1 ( subtract 25 from both sides )
- 3x = - 24 ( divide both sides by - 3 )
x = 8
Substitute x = 8 into (1) for corresponding value of y
y = 8 - 5 = 3
Date: Pages The recent price of a car is Rs. 10.00,000: If its price reduces by to1 yearly after how many year its price will be Rs 7, 29,000?
Answers
Answer:
729000 year it's price will Rs 729000
On a sunny day, a building and its shadow form the sides of a right triangle. If the hypotenuse is 34 m long and the shadow is 24 m, how tall is the building
Answers
Answer:
Step-by-step explanation:
h=√[34²-24²]=√[(34-24)(34+24)]=√[10×58]=√(5×29)=√145 ≈12 m
The height of the building is 10 meters.
What is the Pythagorean theorem?Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We can apply this theorem only in a right triangle.
Example:
The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.
Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm
We have,
Let's call the height of the building "h".
We can use the Pythagorean theorem to relate the height, shadow, and hypotenuse of the right triangle:
h² + 24² = 34²
Simplifying and solving for h.
h² = 34² - 24²
h² = 676 - 576
h² = 100
h = 10
Therefore,
The height of the building is 10 meters.
Learn more about the Pythagorean theorem here:
https://brainly.com/question/14930619
#SPJ2
what’s the scale reading
Answers
Answer:
0.026
Step-by-step explanation:
6 out of 10 steps between 0.02 and 0.03.
If a wheel has a radius of 5cm
how much is one rotation of the wheel
How many rotations can the wheel do within a distance of 50km
Answers
Answer:
circumference = 2*PI*radius
circumference = 2 * PI * 5 cm
circumference = 31.4159265358979 cm
50 km = 500,000 centimeters
rotations = 500,000 / 31.4159 cm
15,915.51 rotations
Step-by-step explanation:
Find the area of the bolded outlined sector.
Answers
Outlined sector:
2 πr x 225/360 +2r
=2x3.14x10 x 225/360 +20
=59.25 cm
Hope this helped!
NEED HELP ASAP!!!!!!!
Answers
Will give brainliest to the first person
Answers
Step-by-step explanation:
Area=b×h
= (x+5)×(x+6)
=x^2+6x+5x+30
=x^2+11x+30
If u simplify u will get (x+5)(x+6) as answer.
Keep smiling and hope u are satisfied with my answer.Have a good day :)
Find the missing side of this right
triangle.
Х
7
12
X =
V[?
Answers
Answer:
[tex]\sqrt{193}[/tex]
Step-by-step explanation:
[tex]a^{2} +b^{2} =c^{2}[/tex]
a = 7
b = 12
[tex]7^{2} + 12^{2}[/tex] = 193
I hope this helped!! :)have a great day! :)convert f(x) = 5x(x – 6) to standard form
Answers
Answer:
[tex]5x^{2} - 30x[/tex]
Step-by-step explanation:
Taylor wirtes a exppersion with five terms all 5 terms are like terms how many terms are in equivilent exppersions with the least numbers of terms ?
Answers
Answer:
1 term
Step-by-step explanation:
Writing an expression of 5 terms such that all 5 terms are like terms ;
Using the analogy :
x, 2x, 4x, 3x, 5x
Writing as an expression :
x + 2x + 4x - 3x + 5x
7x - x + 5x
6x + 5x
11x
The least number of terms in its equivalent expression is 1 ;
As the expression x + 2x + 4x - 3x + 5x is equivalent to 11x
