Answers
Rule: For any triangle, the three angles add to 180 degrees.
The angles are: 'a', 'a-30', and 90 degrees
Add them up and set the result equal to 180. Then solve for 'a'
( a ) + ( a - 30 ) + 90 = 180
(a + a) + (-30 + 90) = 180
2a + 60 = 180
2a + 60 - 60 = 180 - 60 ..... subtract 60 from both sides
2a = 120
2a/2 = 120/2
a = 60
Side Note: Since a = 60, this makes a-30 = 60-30 = 30. So the two other angles of the triangle are 60 and 30. Add up the three angles to get 30+60+90 = 90+90 = 180 so that confirms we have the right answer.
Related Questions
If f(x)= 3x - 1 and g(x) = x+2, find (f +g)(x)
A. 3x-3
B. 4x+1
C. 2x-1
D. 2x-3
Help Please
Answers
3x+x-1+2
4x+1
If f(x)= 3x - 1 and g(x) = x+2, (f +g)(x) is 4x+1.
(3x-1)+(x+2)
=3x+x-1+2
=4x+1.
What are the operations of functions?A function operation guidelines that are accompanied as a way to remedy functions. Learn the definition of a feature operation such as the guidelines for addition, subtraction, multiplication, and division.
What are the different types of functions?One – one function (Injective function)Many – one function.Onto – function (Surjective Function)Into – function.Polynomial function.Linear Function.Identical Function.Quadratic Function.Learn more about functions here: https://brainly.com/question/6561461
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Of all numbers x and y whose sum is 50, the two that have the maximum product are xequals=25 and yequals=25. that is, if xplus+yequals=50, then xequals=25 and yequals=25 maximize qequals=xy. can there be a minimum product? why or why not?
Answers
x + y = 50
Q = x * y
Combining the two:
Q = x * (50 - x)
Q = 50x - x^2
Q = -x^2 + 50x
Q = -(x^2 - 50x)
Q = -(x^2 - 2 * 25x + 25^2 - 25^2)
Q = 25^2 - (x - 25)^2
Q = 625 - (x - 25)^2
So what we got is an equation for parabola with a vertex at
(25 , 625) and it opens downward. We know that parabolas only have one critical
value, so if x and y are unrestricted, then there's no minimum product.
No, there cannot be a minimum product. The product of two numbers is maximized when the numbers are equal or close to each other.
Explanation:The student is asking if there can be a minimum product when x and y are numbers whose sum is 50 and we are trying to maximize the product xy. The answer is no, there cannot be a minimum product. This is because the product of two numbers is maximized when the numbers are equal or close to each other. In this case, when x = 25 and y = 25, the product xy is maximized at 625. If x and y were further apart, the product would be smaller.
Thus,
Q = x * (50 - x)
Q = 50x - x^2
Q = -x^2 + 50x
Q = -(x^2 - 50x)
Q = -(x^2 - 2 * 25x + 25^2 - 25^2)
Q = 25^2 - (x - 25)^2
Q = 625 - (x - 25)^2
A car is traveling at a speed of 75 km/h. Compute the speed of the car in m/s.
A.5.6m/s
B.12.5m/s
C.20.8m/s
D.208m/s
Answers
Les bought 6 pairs of shorts for s dollars each and a blazer that cost three times as much as a pair of shorts.He Spent a total of $139.50.How much did the blazer cost?
Answers
6s+b=139.5
b=3s
Substitite for b
6s+3s=139.5
9s=139.5
s=15.5
Now multiply by 3 to get the blazer price
15.5*3= 46.5
Final answer: $46.50
s = 139.50 / 9 = $15.50
The blazer cost 3s dollars = 3 * 15.50 = $46.50 Answer
Ten less the quotient of a number and 3 is 6
Answers
Add 10 to both sides
x/3= 16
Multiply both sides by 3
x=48
Final answer: x=48
If f(x) = x + 8 and h(x) = 3x − 3, find a function g such that g ∘ f = h.
Answers
If f(x) = x + 8 and h(x) = 3x − 3,
g ∘ f = h
g ∘ (f ∘ f ^-1) = h ∘ f ^-1 ( proprety associative)
but ;
(f ∘ f ^-1) = x
g ∘ x = g
g(x) = (h ∘ f ^-1)(x)
calculate : (f ^-1)(x)
f(x) = x +8
x= f(x) - 8
so : (f ^-1)(x) = x - 8
g(x) = (h ∘ f ^-1)(x) = h((f ^-1)(x)) = h(x - 8) = 3(x - 8) -3
g(x) = 3x - 27
Find x if segment A B is perpendicular to segment C D in the figure below.
Answers
7x + 27 = 90
7x = 63
x = 9
The value of the segment 'x' is 9° as ∠ABC is a right angle.
What is a right angle?When the value of an angle is 90°, then it is called right angle.
Here, AB is perpendicular to CD.
Therefore, ∠ABC = 90°.
Again, ∠ABC = (7x + 27)° = 90°.
Therefore, 7x + 27 = 90
⇒ 7x = 63
⇒x = 9
Learn more about a right angle here: https://brainly.com/question/17201660
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A loaf of bread costs $1.79. how much would five loaf costs?
Answers
Answer:
8.95
Step-by-step explanation:
Because 1.79x5=8.95 You can look it up too
:)
what's the pattern for 1,3,5,7,5,3,1,3
Answers
The pattern 1,3,5,7... represents odd numbers, as each number cannot be evenly divided by 2.
The correct option is (A).
The pattern 1,3,5,7... represents odd numbers. These numbers are considered odd because they cannot be evenly divided by 2. Every number in the sequence is one greater than an even number, which means adding 1 to an even number gives you an odd number. For instance, the number 1 is odd because 0 (an even number) plus 1 equals 1. Similarly, 2 (which is even) plus 1 equals 3, and so on. This pattern of numbers is used to represent all numbers that, when divided by 2, have a remainder of 1.
complete question given below:
The pattern 1,3,5,7... represents numbers.
A.odd
B.even
C.whole
What!!!?!?! Could someone help me with the first two I don't understand and it's due tomorrow
Answers
-4(z-12)=42 how can I solve?
Answers
-4(z-12)=42
you can distribute but it's easier to divide both sides by -4
z-12=-10.5
add 12 both sides
z=22.5
First, we will get rid of the brackets by multiplying each term within the brackets by -4 as follows:
-4(z) - -4(12) = 42
-4z + 48 = 42
Then, we will isolate the term with the variable. To do so,we will simply subtract 48 from both sides as follows:
-4z+48-48 = 42-48
-4z = -6
Finally,we will get rid of the coefficient next to the variable by dividing both sides by -4.
The final result will thus be:
z = 3/2
1.) 2x + y = 3
2.) x - 2y = -1
If equation 1 is multiplied by 2 and then the equations are added, the result is
3x = 2
3x = 5
5x = 5
Answers
If it was any other solution, the equations would'nt make sense
What is the radius of Circle C?
Answers
radius = length of BC = x
Triangle ABC is a right triangle. The right angle (aka 90 degree angle) is at angle B as shown by the square marker.
Because we have a right triangle, we can use the pythagorean theorem
(leg1)^2 + (leg2)^2 = (hypotenuse)^2
(AB)^2 + (BC)^2 = (AC)^2
(22)^2 + (x)^2 = (x+14)^2
484 + x^2 = x^2 + 28x + 196
484 + x^2-x^2 = x^2 + 28x + 196-x^2
484 = 28x+196
484-196 = 28x+196-196
288 = 28x
28x = 288
28x/28 = 288/28
x = 72/7
x = 10.285714
The exact value of x, as a fraction is 72/7
Using a calculator, the approximate value of x is roughly 10.285714
So the radius is exactly 72/7 units long.
The radius is approximately 10.285714 units long.
The radius of a circle in Euclidean geometry is the distance from its center to any point on the circumference, and it can be calculated by dividing the circumference by 2π. In physics, the radius is also the radius of curvature for an object's circular path, determined by position data and the Pythagorean theorem.
Explanation:In mathematics, especially in Euclidean geometry, the radius of a circle is a fundamental concept that refers to the distance from the center of the circle to any point on its circumference.
Referring to the examples provided, one method to find the radius (r) is by understanding the relationship between the circumference of a circle (C) and its radius. In a flat, Euclidean space, the ratio C/r is a constant 2π, where π (pi) is approximately 3.14159. Therefore, if you know the circumference, you can calculate the radius by rearranging the formula to r = C/(2π).
In one of our more practical examples, the radius of curvature is used in the context of circular motion. When dealing with the path of an object in a circular trajectory, the radius of the circle also represents the radius of curvature. For instance, using position data where x = 3 m and y = 4 m, we can use the Pythagorean theorem to find the radius, r = √(3² + 4²) = 5 m.
Understanding these principles is crucial in fields such as physics, where the radius is directly related to calculating velocities and accelerations in circular motions as seen with centripetal acceleration.
Which rigid transformation does NOT result in reversed orientation of the original image?
Answers
How many subsets does set a have if the set a has 3 elements? 3 6 8?
Answers
The 8 subsets are { }, {a}, {b}, {c}, {a,b}, {a,c}, {b,c} and {a,b,c}.
If a set has n elements, the number of subsets is 2^n.
This should help
Let's say Set A = {1,2,3}, Set A can have subsets of:
{1}, {2}, {3}, {1,2}, {1,3}, {2,3}
And so there is 6 subsets.
Help me please I don't understand
Answers
Queenbee2005
The situation that is best modeled by a discrete graph is
Answers
Which equation could be used to solve for the length of side c, given a = 5, b = 12, and c = 72°?
Answers
c=sqrt(a^2+b^2-2abcos(c))
c=sqrt((5)^2+(12)^2-2(5)(12)cos(72))
c=sqrt(25+144-120cos(72))
c=sqrt(169-120cos(72))
c=sqrt(169-37.08)
c=sqrt(131.92)
c=11.49
Answer:
[tex]c=11.49[/tex]
Step-by-step explanation:
It is given that a = 5, b = 12, and c = 72°, then using the cosine formula, we get
[tex]c^2=a^2+b^2-2abcosC[/tex]
[tex]c^2=(5)^2+(12)^2-2(5)(12)Cos72^{\circ}[/tex]
[tex]c^2=25+144-2(60)(0.309)[/tex]
[tex]c^2=169-37.08[/tex]
[tex]c^2=131.92[/tex]
[tex]c=\sqrt{131.92}[/tex]
[tex]c=11.49[/tex]
Therefore, the value of the length of the side c is 11.49.
I have the answer but I have to show work help?
the circled is the question and the uncircled is the simplified answer, or so I'm told.
Answers
A car is traveling at a speed of 79 feet per second. (a) what is its speed in kilometers per hour?
Answers
0.0240792 x 60 = 1.444752 km/minute
1.444752 x 60 = 86.68512 km/hour
Ans: 86.69 km/h
Please answer the question please
Answers
Find the probability of pulling a yellow ball out of a box if the box contains two red balls, three yellow balls, and one green ball. A. 1/4 B. 1/3 C. 1/2 D. 3/4
Answers
62 is 112% of what number? find the base and round to the nearest hundredth
Answers
Answer: Hello there!
if 62 is the 112% of some number, this means that if the number is x; then the 100% of this number is x, and the 112% of this number is x + 0.12*x = 1.12*x
then this means that 62 = 1.12x
now we want to find the number x:
62 = 1.12x
x= 62/1.12 = 55.35714
now we need to round it to the nearest hundredth:
the hundredth place is the second number after the decimal point, in this case, is a 5, and we want to round it; if the next number is 5 or bigger, we round up, if it is less than 5, we round down.
We can see that the next number is a 7, so we should round up; then our number x is: 55.36
Which distribution exhibits a negative skew?
Answers
Answer:
In PLATO the answer is B
Step-by-step explanation:
Notice that all of the values start high at 0 and gradually get lower until 8
Answer: took the test
Step-by-step explanation:
Factor completely 3y^4 - 2y^2 - 5
Answers
(3y^2 -5)(y^2 +1)
PLEASE HELP Which is the equation of a line that is parallel to the line represented by y=3/4x-1/2?
Answers
parallel lines have same slope, so new line has slope = 3/4
answer
A. y = 3/4x + 1/2 (slope = 3/4)
Devonte used the change of base formula to approximate log8 (21). Which expression did Devonte use?
Answers
Answer:
[tex]log_8(21)=\frac{log21}{log8}[/tex]
Step-by-step explanation:
Given : Log expression [tex]log_8(21)[/tex]
To find : Write the expression using the change of base formula.
Solution :
Logarithmic change of base rule formula is
[tex]log_ab=\frac{log_eb}{log_ea}[/tex]
Now, using logarithmic rule in [tex]log_8(21)[/tex]
where a=8 and b=21
[tex]log_8(21)=\frac{log_{10}21}{log_{10}8}[/tex]
[tex]log_8(21)=\frac{log21}{log8}[/tex]
Therefore, The expression Devonte use [tex]log_8(21)=\frac{log21}{log8}[/tex]
a pizza with a diameter of 24 inches is cut into 16 equal slices. to the nearest square inch, what is the area of each slice of the pizza?
Answers
Answer:
Area of each slice of pizza is 28.27 square inches.
Step-by-step explanation:
The formula calculating the area of circle is
A = π[tex]r^{2}[/tex] where r is radius ( half of the diameter )
A = [tex](12)^{2}[/tex]
A = 452.38934 [tex]inches^{2}[/tex]
pizza cut into 16 equal slices
Therefore 452.38934 ÷ 16 = 28.27433 [tex]inches^{2}[/tex]
So the total area of the pizza is 452.39 square inches and the area of each slices are 28.27 square inches approximately.
Answer:
About 28 in ^2
Step-by-step explanation:
write an equation for each line. y intercept of -2,1, x intercept of 3.5
Answers
HELP PLEASE!! GIVE EXPLANATION! 15 PTS!!
What is the value of p?
10p+5=18p–62
A. –8
B. –18
C. 4
D. 8
Answers
10p+5=18p-62
10p-18p=-62-5
-8p =-67
p= 8.375
the answer should be
p= 8.375. but however it is not in the option.
The value of p is [tex]\frac{67}{8}[/tex], which is approximately 8.375. Therefore, the correct option is D. 8
To solve for p in the equation 10p + 5 = 18p - 62, we first need to isolate p on one side of the equation.
First, we'll subtract 10p from both sides to move the variable terms to one side:
10p + 5 - 10p = 18p - 62 - 10p
This simplifies to:
5 = 8p - 62
Next, we'll add 62 to both sides to isolate the term with p on one side:
5 + 62 = 8p - 62 + 62
This simplifies to:
67 = 8p
Finally, we divide both sides by 8 to solve for p:
[tex]\frac{67}{8} = p[/tex]
In conclusion, the value of p is 8.