Answers
Given:
In a right angle triangle, the measure of exterior angle is [tex](9x+16)^\circ[/tex].
The measure of opposite interior angle is [tex](5x-14)^\circ[/tex].
To find:
The value of x.
Solution:
Exterior angle theorem: In a triangle the measure of an exterior angle is equal to the measure of sum of two interior angles.
Using exterior angle theorem, we get
[tex](9x+16)^\circ=90^\circ+(5x-14)^\circ[/tex]
[tex](9x+16)^\circ=(5x+76)^\circ[/tex]
[tex]9x+16=5x+76[/tex]
Isolate the variable x.
[tex]9x-5x=-16+76[/tex]
[tex]4x=60[/tex]
[tex]x=\dfrac{60}{4}[/tex]
[tex]x=15[/tex]
The value of x is 15. So, the measure of the exterior angle is:
[tex](9x+16)^\circ=(9(15)+16)^\circ[/tex]
[tex](9x+16)^\circ=(135+16)^\circ[/tex]
[tex](9x+16)^\circ=151^\circ[/tex]
Therefore, the value of x is 15 and the measure of the exterior angle is 151 degrees.
Related Questions
What is the approximate circumference of a circle that has a diameter of 15 inches?
Answers
Answer:
[tex]{ \tt{circumference \approx\pi \: d}} \\ \approx{ \tt{3.14 \times 15}} \\ \\ \approx47.124 \: inches[/tex]
Which expression is the radical form of x^4/5?
Answers
Answer:
The picture is the answer
Step-by-step explanation:
Solve for x. Round to one decimal place
Answers
Answer:
x ≈ 27.2
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 Subtraction Property of EqualityTrigonometry
[Right Triangles Only] SOHCAHTOA[Right Triangles Only] sinθ = opposite over hypotenuseStep-by-step explanation:
Step 1: Define
Identify variables
Angle θ = 54°
Opposite Leg = 22
Hypotenuse = x
Step 2: Solve for x
Substitute in variables [sine]: sin54° = 22/x[Multiplication Property of Equality] Cross-multiply: x = 22/sin54°Evaluate: x = 27.1935Round: x ≈ 27.2A hose fills a small swimming pool at a rate of 15 cubic feet per 60 seconds. Which equation can be used
to find the amount of cubic feet, y, in x seconds?
Answers
Answer:
y = 1/4x
Step-by-step explanation:
y = amount of cubic feet = 15 cubic feet
x = time taken = 60 seconds
y = kx
Where,
k = constant of proportionality
y = kx
15 = k * 60
k = 15/60
k = 1/4
The equation
y = kx
Where
k = 1/4
Becomes,
y = 1/4x
A scatter plot is shown with the title Jordans Hot Chocolate Sales. The x axis is labeled High Temperature and the y axis is labeled Cups of Hot Chocolate Sold. Data points are located at 20 and 20, 30 and 18, 40 and 20, 35 and 15, 50 and 20, 45 and 20, 60 and 14, 65 and 18, 80 and 10, 70 and 8, 40 and 2.
Answers
Answer:
First Part;
As the temperature in the city increases, the number of cups of hot chocolate sold decreases
Second Part;
The approximate value of the slope in number of cups sold per change in temperature is -0.12222
The approximate value of the y-intercept is 20.944 degrees temperature
Step-by-step explanation:
Question;
First Part
What is the relationship between temperature in the city and the number of cups of hot chocolate sold, using your own words
Second Part
How can the line of best fit be made. Give the approximate values of the slope and the y-intercept of the line of best fit
Explanation
The data points are presented in the following table;
[tex]\begin{array}{lcl}x&&y\\20&&20\\30&&18\\40&&20\\35&&15\\50&&20\\45&&20\\60&&14\\65&&18\\80&&10\\70&&8\\40&&2\end{array}[/tex]
A scatter plot is formed from the given data using MS Excel
First part;
From the values of the number of cups sold, y, and the temperature at which they are sold, x, there is correlation between the x and y values, such that as the temperature increases, the number of cups sold decreases, the becomes more rapid as the temperature increases past 50, such that the reason for taking the hot chocolate decreases with increasing temperature
Second Part;
The line of best fit can be found using the least squares regression formula to draw a straight line from the regression equation as follows;
y = a + b·x
[tex]b = \dfrac{\sum \left(x_i - \bar x\right) \times \left(y_i - \bar y\right) }{\sum \left(x_i - \bar x\right )^2 }[/tex]
a = [tex]\bar y[/tex] - b·[tex]\bar x[/tex]
Where;
b = The slope
a = The y-intercept
From MS Excel, we have;
[tex]\bar y[/tex] = 15, [tex]\bar x[/tex] = 48.63636
[tex]\sum \left(x_i - \bar x\right) \times \left(y_i - \bar y\right) = -410[/tex]
[tex]\sum \left(x_i - \bar x\right )^2 = 3354.545[/tex]
Therefore;
[tex]b = \dfrac{-410}{3354.545} = -0.12222[/tex]
The approximate value of the slope, b = -0.12222 (number of cups sold per unit change in temperature)
a = 15 - (-0.12222)×48.63636 ≈ 20.944
The approximate value of the y-intercept, a = 20.944 (in degrees of temperature).
what is the value of k in which the expression k-22=13-61
Answers
Evaluate expressions-
If x=3 what is the value of 8x+23?
A.47
B.93
C.208
D.61
Answers
Explanation:
We replace x with 3 and use PEMDAS to evaluate
8*x+23
8*3+23
24+23
47
Answer:
[tex]47[/tex]
Step-by-step explanation:
[tex]8x + 23[/tex]
[tex]8(3) + 23[/tex]
[tex]24 + 23[/tex]
[tex]47[/tex]
Hope it is helpful...4. Un granjero tiene 57 puercos, que representan el 8 % del total de sus puercos. ¿Cuántos puercos tiene en total?
Answers
Answer:
713 puercos
Step-by-step explanation:
Sea T el número total de puercos
Número de cerdos = 57
Porcentaje = 8%
Para encontrar el número total de puercos;
Porcentaje = 8/100 * T = 57
8T/100 = 57
8T = 5700
T = 5700/8
T = 712,5 ≈ 713 puercos
Por lo tanto, el granjero tiene 713 puercos en total.
Randip had a balance of $86 in her checking account. She made deposits of $34 and $15. She then made withdrawals for $17 and $30. How much money does Randip now have in her account
Answers
Answer:
$88
Step-by-step explanation:
Randip's balance = initial deposit + sum of deposits - sum of withdrawals
sum of deposits = $34 + $15 = $49
sum of withdrawals = $17 + $30 = $47
$86 + $49 - $47 = $88
Answer:
88
Step-by-step explanation:
Is -14 greater than less than or equal to -3
Answers
Answer:
less than is the correct answer
[tex](2x + 3)(2 {x}^{2} - x - 2)[/tex]
simplify this question
Answers
4
x
3
+
4
x
2
−
7
x
−
6
Which item on the diagram below of a circle, with center
0, represents a radius of the circle?
Answers
Answer:
The answer is DE
Step-by-step explanation:
I learned about it in school.
The radius of a circle with center O is DO. Therefore, option B is the correct answer.
Given that, a circle, with center O, represents a radius of the circle.
What is the circle?A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius.
Radius of a circle is the distance from the center of the circle to any point on it's circumference.
Here, DO and OC is the radius of a circle with center O.
The radius of a circle with center O is DO. Therefore, option B is the correct answer.
To learn more about the circle visit:
https://brainly.com/question/11833983.
#SPJ2
Given that a²+b²=34 and ab=15 , find the value of (a+b²).
Answers
Answer:
The numbers are 3 and 5
HOPE THIS HELPS
- Todo ❤️
Step-by-step explanation:
3^2=9
5^2=25
25+9=34
3*5=15
Answer:
64
Step-by-step explanation:
(a+b)²= a²+b²+2ab = 34+(2×15)= 64
Multiply and combine like terms to determine the product of these polynomials (2x-3)(5x+6)
Answers
Answer:
10xsquared - 3x -18
Step-by-step explanation:
just multiply out and combine like terms
10xsqaured +12x -15x -18
= 10xsquared -3x -18
In converting 14 hours to minutes, what unit (omit the number) would you
place in the denominator of your ratio? Use the plural form in your answer.
Remember that there are 60 minutes in 1 hour.
Answers
Answer:
The unit I would place in the denominator of my ratio is minutes
Step-by-step explanation:
1 hour = 60 minutes
Converting 14 hours to minutes
= 14 hours/ x minutes = 1 hour /60 minutes
x minutes = 14 × 60 minutes
= 840 minutes
14 hours = 840 minutes
Therefore,
The unit I would place in the denominator of my ratio is minutes
Find the trigonometric ratio. Write your answer as a fraction in the simplest form
Answers
Answer:
sinB = [tex]\frac{12}{13}[/tex]
Step-by-step explanation:
sinB = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{12}{13}[/tex]
The Trigonometric ratios is 12/13
What is Trigonometry?The branch of mathematics concerned with specific functions of angles and their application to calculations.
We have,
H= 13, B= 5 and P=12
So,
sin B= Perpendicular/ Hypotenuse
= 12/13
hence, sin B= 12/13
Learn more about trigonometry here:
https://brainly.com/question/14746686
#SPJ2
Please help me URGENT! No links
Answers
Answer:
find the coordinates and then do subtract the first one, for example for line segment AB, do (1,6) and (5,1)
(1,6) (5,1)
1-6 = -5
5-1 = 4
answer is -5/4 and that is the slope of the line.
Continue with the rest please like how i did the example
PLS HELP WILL GIVE BRAINLIEST IF CORRECT♡
Rationalize the denominator of fraction with numerator square root of -36 and denominator the quantity of 2 minus 3i plus the quantity 3 plus 2i
Answers
Answer:
Here are the step require to divide complex numbers:
Step 1:To divide complex numbers, you must multiply by the conjugate. To find the conjugate of a complex number all you have to do is change the sign between the two terms in the denominator.Step 2:Distribute (or FOIL) in both the numerator and denominator to remove the parenthesis.Step 3:Simplify the powers of i, specifically remember that i2 = –1.Step 4:Combine like terms in both the numerator and denominator, that is, combine real numbers with real numbers and imaginary numbers with imaginary numbers.Step 5:Write you answer in the form a + bi.Step 6:Reduce your answer if you can.
Example 1 – Divide: 
Step 1: To divide complex numbers, you must multiply by the conjugate. To find the conjugate of a complex number all you have to do is change the sign between the two terms in the denominator.

Step 2: Distribute (or FOIL) in both the numerator and denominator to remove the parenthesis.

Step 3: Simplify the powers of i, specifically remember that i2 = –1.

Step 4: Combine like terms in both the numerator and denominator, that is, combine real numbers with real numbers and imaginary numbers with imaginary numbers.

Step 5: Write you answer in the form a + bi.

Step 6: Reduce your answer if you can. In this case you can’t reduce, so the final answer is:

Example 2 – Divide: 
Step 1: To divide complex numbers, you must multiply by the conjugate. To find the conjugate of a complex number all you have to do is change the sign between the two terms in the denominator.

Step 2: Distribute (or FOIL) in both the numerator and denominator to remove the parenthesis.

Step 3: Simplify the powers of i, specifically remember that i2 = –1.

Step 4: Combine like terms in both the numerator and denominator, that is, combine real numbers with real numbers and imaginary numbers with imaginary numbers.

Step 5: Write you answer in the form a + bi.

Step 6: Reduce your answer if you can. In this case you can reduce the answer, so the final answer is:

Click Here for Practice Problems
Example 3 - Divide: 
Step 1: To divide complex numbers, you must multiply by the conjugate. To find the conjugate of a complex number all you have to do is change the sign between the two terms in the denominator.

Step 2: Distribute (or FOIL) in both the numerator and denominator to remove the parenthesis.

Step 3: Simplify the powers of i, specifically remember that i2 = –1.

Step 4: Combine like terms in both the numerator and denominator, that is, combine real numbers with real numbers and imaginary numbers with imaginary numbers.

Step 5: Write you answer in the form a + bi.

Step 6: Reduce your answer if you can. In this case you can reduce the answer, so the final answer is:

Click Here for Practice Problems
Example 4 - Divide: 
Step 1: To divide complex numbers, you must multiply by the conjugate. To find the conjugate of a complex number all you have to do is change the sign between the two terms in the denominator.

Step 2: Distribute (or FOIL) in both the numerator and denominator to remove the parenthesis.

Step 3: Simplify the powers of i, specifically remember that i2 = –1.

Step 4: Combine like terms in both the numerator and denominator, that is, combine real numbers with real numbers and imaginary numbers with imaginary numbers.

Step 5: Write you answer in the form a + bi.

Step 6: Reduce your answer if you can. In this case you can reduce the answer, so the final answer is:

solve (x-4)^2=5 pls help me
Answers
Answer:
square root of 5 - 4
Step-by-step explanation:
Answer:
square root of 5 +4
I dont get the qustion
Answers
Answer:
1/2
Step-by-step explanation:
There are two possible outcomes when flipping a coin
heads or tails
P( tails) = number of favorable outcomes / total outcomes
= 1/2
Answer:
p is tails and its saying you flip a fair coin, meaning you have a 50 50 chance which means you have a 50% chance of getting heads and same with tails.
Step-by-step explanation:
therefore, p is 0.5
have a great day!!
3p²q - 6pq² help me please .
Answers
3p²q - 6 pq²
3pq (p - 2q )
I think this is the solution
A scale drawing of a room is shown below. In the drawing, the room is 7 inches long and 5 inches wide. What is the actual area of the room?
75ft^2
37 1/2 ft^2
150 ft^2
50 ft^2
please help TvT
Answers
Answer:
the actual area of the room is 35 inches
Step-by-step explanation:
you have to multiply 7 by 5.
Multiply 7 by 5 which is 35
what is the value of x
2/3x -32=35
Answers
Answer:
To find the value of x we need to simplify this.
The steps to simplifying are simple.
We need to take away, add and do a lot to a bunch of stuff, until we receive our answer.
___________________________
Let's continue.
___________________________
Alright, let's go ahead and show our steps.
[tex]\mathrm{Multiply\:both\:sides\:by\:}3x-32[/tex]
[tex]\frac{2}{3x-32}\left(3x-32\right)=35\left(3x-32\right)[/tex]
_____________________
[tex]Simplify = \\2=35\left(3x-32\right)[/tex]
_____________________
[tex]\mathrm{Switch\:sides}\\35\left(3x-32\right)=2[/tex]
_____________________
[tex]\mathrm{Divide\:both\:sides\:by\:}35\\\frac{35\left(3x-32\right)}{35}=\frac{2}{35}[/tex]
_____________________
[tex]\mathrm{Simplify}\\3x-32=\frac{2}{35}[/tex]
_____________________
[tex]\mathrm{Divide\:both\:sides\:by\:}3\\\frac{3x}{3}=\frac{\frac{1122}{35}}{3}[/tex]
_____________________
[tex]Simplify = \\x=\frac{374}{35}[/tex]
_____________________
Therefore, the answer is x = 374/35
Given the linear equation 2x + y = 6, write another linear equation in two variables such that these two equations when represented geometrically form parallel lines.
Answers
Answer:
The family of lines that are parallel to [tex]2\cdot x + y = 6[/tex] is of the form [tex]2\cdot x + y = k, \,k\neq 6[/tex]. A possible solution is [tex]2\cdot x + y = -2[/tex].
Step-by-step explanation:
Let be [tex]2\cdot x + y = 6[/tex] the equation of a line, another line is parallel to it if and only if it is of the form:
[tex]2\cdot x + y = k, \,k\neq 6[/tex] (1)
Then, a possible solution is [tex]2\cdot x + y = -2[/tex].
Help
Will
Give
Brainlist
Answer
Answers
Answer:
140 km
Step-by-step explanation:
according to scale on a map
1 m = 20 km
7 m = ?
7m = 20*7 km
=140 km
how do I solve this?
Answers
Answer: I cant see the problem
Step-by-step explanation:
Answer:
Where is the question?
Step-by-step explanation:
GUYS HELP please i dont know what to answer
Answers
Answer:
2nd one : y = -4/x
3rd one : y + x/2 = 9
4th one
5th one : y = x^2
6th : 5.8x - y = 2.3
Step-by-step explanation:
Not sure about these. You might want to wait for another person to answer
Have a nice day!
PLEASE HELP, and dont forget to show work!
Answers
Explanation:
- Divide the equation by 6 (x^2-7=0)
- Add 7 (x^2=7)
- Square root x to find solutions (x=rad7)
- Dont forget the radical means that there are two solutions!
If 120 learners took an examination, passes to fail is 17:3 : what percentage of learners passed
Answers
Answer:
85%
Step-by-step explanation:
First, let's add up the ratios and use it to divide 120. That way we can find out how many people each ratio is.
17 +3 = 20
120/20 = 6
Each individual ratio is equal to 6.
17 * 6 = 102
3 * 6 = 18
102/120 = percentage of who passed
= 0.85
85 percent of learners passed.
Circumference of the circle with the radius 10mm? Use pi 3.14
Answers
Answer:
62.8 mm
Step-by-step explanation:
pie = 3.14
radius = 10 mm
circumference of a circle = 2πr
=2*3.14*10
=62.8 mm