Answers
Answer:
Equation: 2x + x + 72 = 180m∠1 = 72°m∠2 = 108°Step-by-step explanation:
The angles lie on a straight line summing to total 180 degrees.
Form an equation:
m∠1 + m∠2 = 180
2x + x + 72 = 180
and solve:
3x + 72 = 180
3x = 180 - 72
3x = 108
x = 36
Find m∠1: 2(x) = 2(36) = 72°Find m∠2: x + 72 = 36 + 72 = 108°Answer:
see below
Step-by-step explanation:
We are here given a straight line which is splitted into two parts by a line , such that it makes two angles.
Also we know that the angle measure of a straight line is 180° . Therefore; here the sum of angles 1 and 2 will be 180° .
So that,
==> angle 1 + angle 2 = 180°
==> 2x + x + 72° = 180°
==> 3x = 180° - 72°
==> 3x = 108°
==> x = 108°/3
==> x = 36° .
The equation which we used to solve the problem is ,
==> Equation = 2x + x + 72° = 180°
For finding the individual angels substitute the value of x into their expressions , as ;
==> angle 1 = 2x = 2(36°) = 72°
==> angle 3 = x + 72° = 36° + 72° = 108° .
And we are done!
Related Questions
I need help on this one question, anyone know the answer?
Answers
4(43)+22= 194°
194 + 24 + 142 = 360
adjacent angles on a point
pls help find interval notation
Answers
Step-by-step explanation:
-2x - 7 > 1
-2x > 8
-x > 4
x < -4
that is a continuous line from -4 all the way to the left, and the dot on -4 is empty (meaning : it is not included due to the "<" symbol).
x - 2 >= -1
x >= 1
that is a continuous line from +1 all the way to the right, and the dot on +1 is filled (meaning : is IS included due to the ">=" symbol.
WILL GIVE THE BRAINLIEST
A graph of a quadratic function is shown. Use the graph for questions 1 through 4.
1. Use the graph to determine the value of for the function.
2. Write the equation of the parabola in vertex form.
3. Convert the vertex form of the parabola to standard form.
4. Use standard form of the parabola to identify the y-intercept of the function.
5. The factored form of a quadratic function is represented by () = 2(―4)(―6).
Write the equation in standard form.
For questions 6 through 9, a graph and table of values for () are shown.
6. Use the table or the graph to determine the value of for the function.
7. Write the equation in vertex form.
8. Write the equation in factored form.
9. Write the equation in standard form.
10. The function () is represented by () = 2(+ 3)^2 +4. Rewrite the function in
standard form.
Answers
The points where the graph intercepts the x-axis is the root of the function.
from the graph the points are 3.9 and 6.1
How to write the equation of the parabola in vertex formThe vertex v is at v ( 5, -4 ) this is equivalent to v ( h, k )
the equation of parabola in vertex form is y = a ( x- h )^2 + k
y = a ( x - 5 )^2 + {-4)
substituting point ( 4, -1 ) from the graph we have:
-1 = a ( 4 - 5 )^2 - 4
-1 = a - 4
a = 3
substituting the known values to y = a ( x- h ) + k
y = 3 ( x - 5 )^2 - 4
How to write the equation of the parabola in factored formy = 3 ( x - 5) ( x - 5 ) - 4
How to write the equation of the parabola in standard formy = 3 ( x - 5) ( x - 5 ) - 4
y = 3 ( x^2 - 10x + 25 ) - 4
y = 3x^2 - 30x + 75 - 4
y = 3x^2 - 30x + 71
Graph BHow to find the roots of the the function
The points where the graph intercepts the x-axis is the root of the function.
from the graph the points are 2 and 4
How to write the equation of the parabola in vertex form
The vertex v is at v ( 3, 2 ) this is equivalent to v ( h, k )
the equation of parabola in vertex form is y = a ( x- h )^2 + k
y = a ( x - 3 )^2 + 2
substituting point ( 0, -16 ) from the graph we have:
-16 = a ( 0 - 3 )^2 + 2
-16 = a - 9 + 2
-16 = a - 7
a = -9
substituting the known values to y = a ( x- h ) + k
y = -9 ( x - 3 )^2 + 2
How to write the equation of the parabola in factored formy = -9 ( x - 3) ( x - 3 ) + 2
How to write the equation of the parabola in standard formy = -9 ( x - 3) ( x - 3 ) + 2
y = -9 ( x^2 - 6x + 9 ) - 4
y = 3x^2 - 54x - 81 - 4
y = 3x^2 - 54x - 85
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Mia uses the formula πr2 to find the area of a circle. What is πr2 an example of?.
Answers
πr2 is an example of (D) a model.
What is a model?A mathematical model is a system description that employs math ideas and language. Mathematical modeling is the process of creating a mathematical model. Mathematical models are used in the natural sciences (physics, biology, earth science, chemistry), engineering disciplines (computer science, electrical engineering), and non-physical structures such as the social sciences (such as economics, psychology, sociology, political science). A large part of the field of operations research is the use of statistical equations to solve problems in business or military operations. Music, linguistics, and philosophy all use mathematical models (for example, intensively in analytic philosophy). A model is, for example, the method for the area of a circle, πr2.Therefore, πr2 is an example of (D) a model.
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The complete question is given below:
Mia uses the formula πr2 to find the area of a circle. What is πr2 an example of?
A. a robot
B. a car
C. a telescope
D. a model
What is the converse of the following statement?
"If cows make milk, then chickens make eggs. "
Answers
Answer:
"If chickens make eggs, then cows make milk."
Step-by-step explanation:
Answer: A: If chickens make eggs, then cows make milk.
Step-by-step explanation: Hope that helped
If you want to use the sin function in the math library, as x = math.sin(3.14), how should you write the import statement?
Answers
We use import math when we want to use the sin function in the math library, x= math. sin(3.14).
Similar to #include header_file in C/C++, that how to import function in python. The import statement brings in code from one module into another program, where modules are files that contain python code, and modules are used to group related code in a program, instead of rewriting the code again, you can reuse the same code in different files. To import code from a module a parameter is to be followed import module name ( where the import word is the keyword and the module name is the module you want to import ).
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2y-4+5y=4-3y+5
How to solve this?
Answers
Answer:
You would first move all of the y numbers to one side so it should look like this: 2y-4+5y+3y=4+5. Then you would all the numbers that don't have y at the end to the other side: 2y+5y+3y=4+5+4.
Then you would add them all up: 10y=13
So your answer is 10y=13
Step-by-step explanation:
For the function g defined above, a is a constant and g(4)=8. What is the value of g(-4)?
Answers
The value of g(-4) is 8.
A set of inputs and outputs that are connected to one another in some way is referred to as a relation. We refer to the relations as a function when each input results in a single output. However, you must be certain that no input leads to more than one output in order to determine if a relation is a function or not.
Only when each element of a nonempty set M has a single range to a nonempty set N is a function a relation.
g(x) = ax^2 + 24
⇒ g(4) = a (4)^2 + 24
⇒ 8 = 16a + 24
⇒ 8 − 24 = 16a
⇒ −16 = 16a
⇒ a = −1
Since, g(−4) = a(−4) ^2 + 24
∴ g(−4) = 16(−1) + 24
⇒ g(−4) = 8
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HELP me ill give brainlist or whatever its called
Answers
Answer:
1 cm
Step-by-step explanation:
you multiply 3 by 1/3 and you get 3/3 which is 1
From nine cards numbered 1 through 9, two cards are drawn. consider the selection and classification of the cards as odd or even as an experiment. how many sample points are there for this experiment?
Answers
Probability= 5/9
Even cards = 2,4,6,8
Odd cards = 1,3,5,7,9
The number of ways of choosing one odd and one even number is 5C1 * 4C1
( 5!/ 1!* 4!) * (4!/1! * 3!)
5* 4= 20
Total number of ways of choosing 2 cards out of 9 = 9C2
9!/ 2! * (9-2)!
= 9!/ 2! * 7!
= 9*8/2
= 9 *4= 36
Thus, Probability is = 20/ 36
= 5/9
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Will give brainliest
Answers
answer:
3/4
explanation:
the side lengths of preimage abcd are all four units, whereas image abcd's lengths are all three. from this, we can surmise the scale factor is 3/4.
how to calculate scale factor:
scale factor = dimension of the new shape ÷ dimension of the original shape
What is the side length of a square with an area of 121 square centimeters?
In centimeters
Answers
The answer to this question is:
Size of a square's side = 11 cm
A Square is a flat geometric shape with four right angles and equal sides. The square's four sides are equal to one another or congruent. The square's opposing sides run parallel to one another. The square's diagonals form a 90° angle with one another. The two diagonals of the square are equivalent to one another. The square is made up of four vertices and four sides.
Area of square = ( Side )²
Given that:
Area of square = ( Side )² = 121 cm²
Dimensions of a square's side = √ Area
so, the length of the square's side = √ 121
= √ 11*11
= √ ( 11 )²
= 11
Thus, side of the square = 11 cm
Therefore, side length of square = 11cm
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c. Write an equation for which every real number is a solution. Choose the correct answer below.
OA. 7(x-2)=2(x-7)
OB. 2(x-7)=2(x-7)
OC. x+2=x+7
Answers
Is the statement the solution set of a linear system involving variables is a list of numbers that makes each equation in the system a true statement when the values are substituted for respectively true or false? explain.
Answers
False, because The singles answer fits the description. All potential solutions are included in the solution set.
There might not be a solution to a set of linear equations that makes sense. False. There is at least one answer for a consistent system.What makes up a linear system's solution set?
The answer to a system of equations is a set of values for a variable that concurrently satisfy each equation. Finding every feasible combination of the variable values that make up the system's solutions is necessary to solve an equation system.Is it true that a linear system's existence and uniqueness are two key issues? False or true?
In a linear system, existence and uniqueness are crucial considerations. Both conceptually and practically, it is frequently essential to know whether a system has a solution (exists) and, if it does, whether this solution is the only one available (uniqueness).Learn more about linear system.
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Luis has 1/2 quart of grape juice. he pours the same amount into each of 5 glasses. which equation represents the fraction of a quart of grape juice n that is in each glass?ll
Answers
The equation n = (1/2)(1/5) represents the fraction of a quart of grape juice n that is in each glass option (A) is correct.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The question is incomplete.
The complete question is:
Luis has 1/2 quart of grape juice. he pours the same amount into each of 5 glasses. which equation represents the fraction of a quart of grape juice n that is in each glass?
n = (1/2)(1/5)
n = (1/2)(5/1)
n = (1/2)(5)
n = (1/2)
From the data given in the question:
Let n be the fraction of a quart of grape juice n that is in each glass:
n = (1/2)(1/5)
Thus, the equation n = (1/2)(1/5) represents the fraction of a quart of grape juice n that is in each glass option (A) is correct.
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Find the average rate of change for the function f(x)=3^x+17
Using the intervals x=3 to x=6
Answers
Answer:
234
Step-by-step explanation:
the average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
here [ a, b ] = [3, 6 ] , then
f(b) = f(6) = [tex]3^{6}[/tex] + 17 = 729 + 17 = 746
f(a) = f(3) = 3³ + 17 = 27 + 17 = 44 , then
average rate of change = [tex]\frac{746-44}{6-3}[/tex] = [tex]\frac{702}{3}[/tex] = 234
a line with a slope equal to -2/3 passes through (-1, -4) and (3,y) what’s the value of y
Answers
Answer:
-20/3
Step-by-step explanation:
Using point-slope form, the equation is
[tex]y+4=-\frac{2}{3}(x+1) [/tex]
Substituting x=3,
[tex]y+4=-\frac{2}{3}(3+1) \\ \\ y+4=-\frac{8}{3} \\ \\ y=-\frac{20}{3}[/tex]
3. Solve the formula v + f -e = 2 for e
O Ae-v-f-2
O BC v+f-2
O ce-v-f+2
O De-u+f+2
Answers
Answer:
B is the correct answer.
Step-by-step explanation:
Add -2+e to both sides
v + f − e -2+e = 2 -2+e
Which will give you v + f -2 = e.
James has a square garden with sides of length 8feet. he plans to enlarge it to a rectangle by increasing the length by 4 feet and the width by 1 feet. how many square feet in area will be added to the garden?
Answers
The area in square feet that will be added to the garden is 44 square feet.
Length of square garden = 8 feet
Area of Square garden = [tex](side)^{2}[/tex] = [tex](8)^{2}[/tex] = 64 square feet
On enlarging the square to a rectangle, length rectangular garden is (8+4)feet i.e.,12feet and width of rectangular garden is (8+1)feet i.e.,9feet.
Area of rectangular garden = (length × width)
= (12 × 9) square feet
= 108 square feet
The area in square feet that will be added to the garden = (Area of rectangular garden - Area of Square garden)
= (108 square feet - 64 square feet)
= 44 square feet
The area in square feet that will be added to the garden is 44 square feet.
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find the measure of angle B.
Answers
Answer:
m <B = 41°
Step-by-step explanation:
Fact: complementary angles measures add to 90 degrees
Given: m < A = 2x-19, and m <B = x+7
Find: m <B = ?
Find x
2x-19 + x+7 = 90
2x+x = 90 +19-7
3x = 102
x = 34
Find m <B
m <B = x+7
m <B = 34+7
m <B = 41
Mia uses the formula πr2 to find the area of a circle. What is πr2 an example of?.
Answers
πr² an example of a model.
What are mathematical models?A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science).
Here, the area of a circle is calculated by the use of formula πr² where π is a constant 3.14 and r is a variable. Therefore this formula is used to find the area.
Thus, πr² an example of a model.
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please help i’m literally so stressed out
Luis has $420 to spend at a bicycle store for some new gear and biking outfits.
Assume all prices listed include tax.
• He buys a new bicycle for $209.67.
•He buys 2 bicycle reflectors for $6.04 each and a pair of bike gloves for $25.77.
•He plans to spend some or all of the money he has left to buy new biking outfits
for $37.16 each.
Which inequality can be used to determine x, the maximum number of outfits Luis
can purchase while staying within his budget?
Answers
The inequality that can be used to determine x, the maximum number of outfits Luis can purchase while staying within his budget is x ≤ 4
How to solve inequality?Luis has $420 to spend at a bicycle store for some new gear and biking outfits.
He buys a new bicycle for $209.67.He buys 2 bicycle reflectors for $6.04 each and a pair of bike gloves for $25.77.He plans to spend some or all of the money he has left to buy new biking outfits for $37.16 each.Therefore,
x = maximum number of outfits Luis can purchase while staying within his budget.
Hence, the inequality that can be used to represent the situation is as follows;
209.67 + 6.04(2) + 25.77 + 37.16x ≤ 420
235.44 + 12.08 + 37.16x ≤ 420
247.52 + 37.16x ≤ 420
37.16x ≤ 420 - 247.52
37.16x ≤ 172.48
divide both sides by 37.16
x ≤ 4.64155005382
x ≤ 4
Therefore, the inequality that can be used to determine x, the maximum number of outfits Luis can purchase while staying within his budget is x ≤ 4
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You invested a total of $50,000 in 2 funds earning 6.5% and 9% simple interest. during 1 year, the 2 funds earned a total of $3625 in interest. how much did you invest in each fund? amount at 6.5%
Answers
Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. The person has invested $35,000 in the fund returning at a rate of 6.5%.
What is simple interest?Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,
SI = PRT = (R% of P)T
where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.
Let the amount invested in the first fund be represented by x, then the amount invested in the second fund will be ($50,000 - x).
Now, if the 2 funds earn 6.5% and 9% simple interest. Also, in the first year, they earned a total of $3625 from the interest. Therefore, we can write the equation to represent the given situation as,
6.5% of x + 9% of ($50,000 - x) = $3625
0.065x + 0.09(50,000 - x) = 3625
0.065x + 4,500 - 0.09x = 3,625
0.065x - 0.09x = 3625 - 4500
0.025 = 875
x = 875/0.025
x = 35,000
Therefore, the person has invested $35,000 in the fund returning at a rate of 6.5%.
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solve 2x-9y=14 for y
Answers
The value of y in expression is 14-2x/-9
How to calculate the value of y ?The expression is written as
2x - 9y = 14
We are asked to calculate the value of y in the expression
2x - 9y = 14
-9y= 14-2x
Divide by the coefficient of y which is -9
y= 14-2x/-9
Hence the value of y is 14-2x/-9
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PLEASE HELP ASAPPP !!! WILL GIVE BRAINLIEST AND 5 STAR RATING
Answers
Answer:
12/15
Step-by-step explanation:
-1/3-4/5
Explanation:
We want to get -4/5 to the denominator /15.
You first want to multiply 5 by 3 to get to 15. This is your denominator.
Since we multiplied 5 by 3, we also need to multiply -4 by 3. This is your numerator.
Your total is -12/15. If you simplify this, you get to -4/5.
Plug your final answer to -1/3, and you get the equation to -1/3-4/5.
Hope that helped!!
i’m confused please help
Answers
Show ([tex]\frac{\sqrt{11} }{6} ,[/tex][tex]\frac{5}{6}[/tex]) is or is not on the unit circle. State the unit circle definitions and definitions in terms of other trig functions.
Answers
By using coordinates in rectangular form and Pythagorean theorem, we conclude that the point (x, y) = (√11 / 6, 5 / 6) is on the unit circle as its norm is equal to 1.
Is a given point on Cartesian plane lying on the unit circle?
We find a point in rectangular form, that is, a point of the form (x, y). Unit circles are circles with a radius 1 that are commonly used to represent graphically angles. The given point is in the units if and only if its norm is equal to 1. The norm of the point is determined by using the Pythagorean theorem:
r = √[(√11 / 6)² + (5 / 6)²]
r = √[(11 / 36) + (25 / 36)]
r = √(36 / 36)
r = √1
r = 1
By using coordinates in rectangular form and Pythagorean theorem, we conclude that the point (x, y) = (√11 / 6, 5 / 6) is on the unit circle as its norm is equal to 1.
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8. Olivia's brother is twice her age
minus 9 years. He is also as old
as half the sum of the ages of
Olivia and both of her 12 year-
old twin brothers. Write and
solve an equation to find the
ages of Olivia and her brother.
Answers
The ages of Olivia and her brother are 10 years and 11 years respectively
Let x₁, and x₂ be the ages of Olivia and her brother respectively.
Given that Olivia's brother is twice her age minus 9 years.
⇒ x₂ = 2x₁ - 9 → equation 1
Also given that Olivia's brother is as old as half the sum of the ages of Olivia and both of her 12-year-old twin brothers.
⇒ x₂ = 1/2 × (x₁ + 12) → equation 2
Using equation 1 in equation 2, we get
2x₁ - 9 = 1/2 × (x₁ + 12)
⇒ 4x₁ - 18 = x₁ + 12 (multiplying by 2 on both sides)
⇒ 4x₁ - x₁ = 12 + 18
⇒ 3x₁ = 30
⇒ x₁ = 10 (dividing by 3 on both sides)
Using the value of x₁, in equation 1,
⇒ x₂ = 2(10) - 9
⇒ x₂ = 20 - 9
⇒ x₂ = 11
Therefore the ages of Olivia and her brother are 10 years and 11 years respectively.
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b) The angle of elevation of a tower at a distance of 27 meter from the foot of the tower is 60°, find the height of the tower. Speedy Additional Mathematics - Book VIII 98
Answers
The height of the tower is approximately 46.765 feet
Step-by-step explanation:
The given parameters are;
The distance from the foot of the tower where the angle of elevation is
measured = 27 feet
The angle of elevation to the top of the tower from a point 27 feet from the foot of the tower, θ = 60°
Therefore, by trigonometric ratio, we have;
tan 60= the height of tower / distance from foot of tower
[tex]\sqrt{3}[/tex]= height of tower /27
1.73205 *27 = height of tower
46.765 feet is the height of tower
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The function h is defined by the following rule
h(x)=-5x+5
Complete the function table down below
Answers
Check out the attached photo