Answers
Answer:
We only need one simple theorem for this.
Theorem 7 - The Exterior Angle Theorem: An exterior angle of a triangle is equal to the sum of the two remote interior angles.
So in this case, the measurement of the exterior angle is (45x)°, and the interior angles are (25x)° and (57 + x)°.
=> Therefore, we have:
25x + (57 + x) = 45x
25x + x - 45x = - 57
-19x = -57
x = -57/(-19) = 3
So x = 3
Outside angle = addition of the two inner angles.
45x = 25x + 57 + x
45x = 26x + 57
45x - 26x = 57
19x = 57
x = 57/19
x = 3
Did you follow the logic?
Related Questions
Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm? 1. acute, because 62 + 102 < 122 2.acute, because 6 + 10 > 12 3.obtuse, because 62 + 102 < 122 4.obtuse, because 6 + 10 > 12
Answers
Answer:
The best represents a triangle is obtuse, because 6 + 10 > 12 ⇒ answer 4
Step-by-step explanation:
* Lets talk about some facts in the triangle
- The triangle is formed when the sum of the lengths of the shortest
two side is greater then the length of the longest side
∵ The lengths of the sides are 6 cm , 10 cm , 12 cm
∵ 6 + 10 > 12
∴ 6 , 10 , 12 are the sides of a triangle
- Two know the type of the triangle use these rules
# The three sides of the triangle have lengths a , b , c where a and b
are the shortest sides means a , b < c, then
- If a² + b² > c² , the triangle is acute triangle (its 3 angles are acute)
- If a² + b² = c² , the triangle is right triangle (the angle opposite to c is a
right angle and the other 2 angles are acute angles)
- If a² + b² < c² , the triangle is obtuse triangle (the angle opposite to c is an
obtuse angle and the other 2 angles are acute angles)
∵ (6)² + (10)² = 36 + 100 = 136
∵ (12)² = 144
∵ 136 < 144
∴ (6)² + (10)² < (12)²
∴ The triangle is obtuse
* The best represents a triangle is obtuse, because 6 + 10 > 12
Express 256^-3/4 as a fraction. Write the fraction in the form a/b, where a and b are positive integers with no common factor greater than 1 .
Answers
Answer:
1/64
Step-by-step explanation:
[tex]256^{-\frac{3}{4}}=2^{8(-\frac{3}{4})}=2^{-6}=\dfrac{1}{2^6}=\dfrac{1}{64}[/tex]
256^-3/4 can be converted into a positive fraction by interpreting the negative exponent as a reciprocal and the fractional exponent as a root. It simplifies to 1/(4th root of 256^3), which equals 1/64.
Explanation:To express the numeral 256^-3/4 in the form of a fraction, we first need to understand how negative and fractional exponents work. The number is in the form of a^(-m/n) which is equivalent to the nth root of a^-m or 1/(nth root of a^m). The negative sign in the exponent implies a reciprocal of the number and the fractional exponent denotes a root of the number.
Now applying this understanding to our number which is 256^-3/4. Here, the base a is 256 and the fractions -m/n is -3/4. Therefore, it is equivalent to the 4th root of 256^-3, which can also be written as 1/(4th root of 256^3).
The 4th root of 256 is 4. So, the expression now becomes 1/(4^3), which after simplifying gives us the result 1/64.
So, the expression 256^-3/4 written as a positive fraction is 1/64.
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Alex takes a full-time position that pays a salary of $58,000 per year. What is her pre-tax monthly income? Do not include a "$" in your answer.
please explain
Answers
Answer:
4833.33
Step-by-step explanation:
The salary of $58,000 is Alex's pre-tax income. It is presumed to be divided evenly between the 12 months of the year, so his monthly income is ...
$58,000/12 = $4833.33
Keshawn is asked to compare and contrast the domain and range for the two functions. f(x) = 5x g(x) = 5x Which statements could he include in his explanation? Check all that apply. The domain of both functions is all real numbers. The domain of f(x) is x > 5. The domain of g(x) is x > 5. The range of both functions is y > 5. The range of f(x) is y > 0. The range of g(x) is y > 0.
Answers
Answer:
"The domain of both functions is all real numbers."
Step-by-step explanation:
Given
[tex]f(x) = 5x\\and\\g(x) = 5x[/tex]
We can see that the function will have some value for any value of x and is not undefined on any value of x. So the domain of f(x) is all real numbers.
Similarly, g(x) is also not undefined on any value of x so it also has domain of all real numbers.
The range of f(x) and g(x) will be all real numbers as the functions do not produce infinity on any of the input.
Only the statement that
"The domain of both functions is all real numbers."
is true for the given functions ..
PLS HELP WITH ALL QUESTIONS WILL GIVE BRAINLIEST TO THE CORRECT ANSWER
THANK YOU IN ADVANCE.
Answers
Answer:
see explanation
Step-by-step explanation:
(a)
The opposite sides of a rectangle are congruent, hence
x + 1 = 5 ( subtract 1 from both sides )
x = 4
Or
x - 1 = 3 ( add 1 to both sides )
x = 4
(b)
The sum of the 3 angles in a triangle = 180°, hence
3y + 2y + y = 180
6y = 180 ( divide both sides by 6 )
y = 30
Answer:
PART A "4"
PART B "30"
Step-by-step explanation:
PART A
If you refer to my picture below, then you will know that the sides are equal.
The x-1 side is equal to 3 and the x+1 sign is equal to 5. So it best makes sense that 4 is equal to x. That's because x-1 is 3 and x+1 is 5.
PART B
This is tricky. As you know all sides of a triangle add up to 180 degrees. I would divide by 3, but that would be incorrect. Whenever you see these y's, you have to divide by that amount. The y's are there for a reason, so that some sides are bigger than the other. Divide 180 by 6(number of y's). That is 30. This gives you the solution to one y so if it asks you for 2y or 3y, then you would multiply. But it's not. 30 is the answer
Which aspect of electronic commerce does the FTC regulate?
A.
encryption and transfer of data
B.
disposing of credit reports
C.
network security
D.
antivirus software updates
Answers
Answer:
The correct answer option is A. encryption and transfer of data.
Step-by-step explanation:
The business activities that take place through internet as the medium are referred to as electronic commerce.
The Federal Trade Commission [FCT] is one of the main functional bodies responsible for regulating such electronic commerce activities which includes encryption and transfer of data.
The risk of data theft from encryption and transfer of data is really high so FTC makes sure to prevent theft from the transaction made through e-commerce.
Answer:
Which aspect of electronic commerce does the FTC regulate?
A.
encryption and transfer of data
B.
disposing of credit reports
C.
network security
D.
antivirus software updates
Step-by-step explanation:
#platofam
Kim took out a $55,000 loan for college she is borrowing money from 2 banks bank a charges an interest rate of 8% and b charges an interest rate of 11% after one year Kim owes 5000 in interest how much money did she borrow from bank a.
Answers
Answer:
$35,000
Step-by-step explanation:
Let x represent the amount borrowed from Bank A. Then (55000-x) is the amount borrowed from Bank B. Kim's total 1-year interest is ...
0.08x + 0.11(55000 -x) = 5000
-0.03x + 6050 = 5000 . . . . . simplify
-0.03x = -1050 . . . . . . . . . . . . subtract 6050
x = 35,000 . . . . . . . . . . . . . . . divide by -0.03
Kim borrowed $35,000 from Bank A.
Please help, refer to picture
Answers
Answer:
99°
Step-by-step explanation:
∠7 and ∠8 are a linear pair, so are supplementary. Numbers are assumed to be degrees.
∠7 + ∠8 = 180
2x+15 + 3x = 180 . . . . . substitute given values
5x = 165 . . . . . . . . . . . . subtract 15, collect terms
x = 33 . . . . . . . . . . . . . . . divide by the coefficient of x
∠8 = 3x = 3·33 = 99 . . . . . degrees
Cylinder A has a volume of 100 cm and cylinder B has a height that two fifths of the height of cylinder A
Answers
You need more input here what even is the question
Need help with math question
Answers
Answer:
D
Step-by-step explanation:
This is a vertical opening parabola, since the focus is above the vertex on the axis of symmetry x = 2
The standard form of a vertically opening parabola is
(x - h)² = 4a(y - k)
where (h,k) are the coordinates of the vertex and a is the distance from the vertex to the focus.
here (h, k) = (2, - 1) and a = 4, hence
(x - 2)² = 16(x + 1) → D
Answer:
D
Step-by-step explanation:
The vertices of a hyperbola are located at (−4, 1) and (4, 1). The foci of the same hyperbola are located at (−5, 1) and (5, 1). What is the equation of the hyperbola?
Answers
The equation of the hyperbola is [tex]\frac{x^2}{16} - \frac{(y - 1)^2}{9} = 1[/tex]
How to determine the equation of the hyperbola?The vertices of the hyperbola are given as:
Vertices = (±4, 1)
The foci of the hyperbola are given as:
Foci = (±5, 1)
The coordinates of the vertices is represented as::
Vertices = (±a, n)
By comparing (±a, n) and (±4, 1), we have:
a = 4
n = 1
The coordinates of the foci is represented as::
Foci = (±c, n)
By comparing (±c, n) and (±5, n), we have:
c = 5
n = 1
Calculate b using:
b = √(c² - a²)
So, we have:
b = √(5² - 4²)
Evaluate
b = 3
The equation of a hyperbola is:
[tex]\frac{x^2}{a^2} - \frac{(y - n)^2}{b^2} = 1[/tex]
So, we have:
[tex]\frac{x^2}{4^2} - \frac{(y - 1)^2}{3^2} = 1[/tex]
Evaluate the exponent
[tex]\frac{x^2}{16} - \frac{(y - 1)^2}{9} = 1[/tex]
Hence, the equation of the hyperbola is [tex]\frac{x^2}{16} - \frac{(y - 1)^2}{9} = 1[/tex]
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Simplify the expression.
the quantity x to the two fifths power end quantity to the power of 10
Answers
Answer:
x^4
Step-by-step explanation:
(x^(2/5))^10 is what I understand the words to mean
x^(2/5*10)
x^(20/5)
x^4
Answer:
The simplified form of given expression is [tex]x^4[/tex].
Step-by-step explanation:
The given expression is
[tex](x^\frac{2}{5})^{10}[/tex]
According to the power of power property of exponent, if x, a and b are any real number, then
[tex](x^a)^b=x^{ab}[/tex]
Using power of power property of exponent, the given expression can be written as
[tex](x^\frac{2}{5})^{10}=x^{\frac{2}{5}\times 10}[/tex]
[tex](x^\frac{2}{5})^{10}=x^{\frac{20}{5}}[/tex]
[tex](x^\frac{2}{5})^{10}=x^{4}[/tex]
Therefore the simplified form of given expression is [tex]x^4[/tex].
Given the following linear functions determine the relationship
Answers
Answer:
Perpendicular
Step-by-step explanation:
Linear equations will describe parallel lines when the lines have the same slope. These equations are written in slope-intercept form, so we can easily determine that the slopes are ...
f(x): slope is 5/6
g(x): slope is -6/5
These are not the same, so the lines are not parallel.
__
The lines will be perpendicular when the product of their slopes is -1. Here, that product is ...
(5/6)(-6/5) = -30/30 = -1
These equations describe lines that are perpendicular.
A bag contains 7 pieces of paper numbered 1 to 7. P(2)=. Is this an experimental or theoretical probability and why?
CAN YOU GUYS PLEASE HELP ME I NEED TO TURN THIS IN IN 30 MINUETS!!!!!
Answers
Answer:
theoretical probability
Step-by-step explanation:
This is theoretical probability. The 7 pieces of paper each bear one number from {1, 2, ... , 6, 7}. There is only one piece of paper marked 7. So the probability of drawing a 2 is 1/7.
Point c is the center of the circle what is the measure of
A.
B.
C.
D.
Look at the circle down below
Answers
Answer:
93°
Step-by-step explanation:
Angle ACB is a central angle. The theorem regarding central angles and the arcs they intercept is that the angle and the arc are congruent. That means that arc AB is also 93°
What is the exponential form of log5 9 = x?
x^9 = 5
5^x = 9
x^5 = 9
9^x = 5
Answers
Answer:
B
Step-by-step explanation:
Using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
Hence
[tex]log_{5}[/tex] 9 = x ⇒ 9 = [tex]5^{x}[/tex] → B
Answer:
its d 5 < x ≤ 9 .
The area of a parking lot is 1710 square meters. A car requires 5 square meters and a bus requires 32 square meters of space. There can be at most 180 vehicles parked at one time. If the cost to park a car is $2.00 and a bus is $6.00, how many buses should be in the lot to maximize income? Please help :(
Answers
Answer:
To maximize the income should be 30 buses and 150 cars
Step-by-step explanation:
Let
x-----> the number of cars
y ----> the number of bus
we know that
[tex]5x+32y\leq1,710[/tex] ------> inequality A
[tex]x+y\leq 180[/tex] ----> inequality B
The function of the cost to maximize is equal to
[tex]C=2x+6y[/tex]
Solve the system of inequalities by graphing
The solution is the shaded area
see the attached figure
The vertices of the solution are
(0,0),(0,53),(150,30),(180,0)
Verify
(0,53) ---> [tex]C=2(0)+6(53)=\$318[/tex]
(150,30) ---> [tex]C=2(150)+6(30)=\$480[/tex]
therefore
To maximize the income should be 30 buses and 150 cars
Answer:
Givens
The area of the parking lot is 1710 square meters.A car requires 5 square meters.A bus requires 32 square meters.There can be a maximum of 180 vehicles.The cost for a car is $2.00.The cost for a bus is $6.00.To solve this problem we need to create a table to order all this information and express it as a system of inequations.
Car Bus Total Capcity
Sq. Meters 5c 32b 1710
N° vehicles c b 180
Therefore, the inequalities are
[tex]5c+32b\leq 1710\\c+b\leq 180[/tex]
The expresion which represents the income is
[tex]I=2c+6b[/tex], because a car is $2.00 and a bus is $6.00.
Now, we first need to find the critical points of the solution of the inequality system, which is attached. Observe that the only points that can be a solution is (150,30), because there can't be just car or just buses.
Then, we replace this point in the income expression
[tex]I=2c+6b\\I=2(150)+6(30)=300+180=480[/tex]
Therefore, in order to maximize incomes, we need to park 150 cars and 30 buses, to make $480 income.
what undefined term does a circle use
Answers
Answer:
The definition of a circle uses the undefined term Arc
Step-by-step explanation:
There are three terms generally considered to be undefined in geometry: point, line and plane. A circle is the set of all points in a plane the same distance from a given point called the center. The only of our options that is used in this definition is plane.
Becky is using the expression 2z + 3 to represent the number of chairs in her classroom. There are twice as many chairs as tables, and there are three extra chairs in the back. What does z represent?
The number of chairs.
The number of tables.
The number of chairs at tables.
The number of chairs and tables
Answers
Answer:
The number of tables
Step-by-step explanation:
Let
z ----> the number of tables
y-----> the number of chairs
we know that
[tex]y=2z+3[/tex]
therefore
z represent the number of tables
Answer:
the number of tables :]
Step-by-step explanation:
A rectangles length is 1.5 times its width. The perimeter of the rectangle is four more than 3 times the length. What are the dimensions of the rectangle
Answers
Answer:
8 by 12 units
Step-by-step explanation:
Let w represent the width of the rectangle. Then the length is 1.5w. The perimeter is 4 more than 3 times this, so is (3(1.5w) +4) = 4.5w+4
The perimeter is given by the formula ...
P = 2(length + width)
Filling in the given values for the variables, we have ...
4.5w +4 = 2(w +1.5w)
4 = 0.5w . . . . . . subtract 4.5w and collect terms
8 = w . . . . . . . . . multiply by 2
length = 1.5×8 = 12
The rectangle is 8 units wide and 12 units long. The perimeter is 40 units.
Answer:
Step-by-step explanation:
8x12
Tennis balls are packaged into cylindrical cans to ship and sell. Three tennis balls fit into one cylinder so that the height of the three balls is equal to the height of the cylinder. and the diameter of one ball is equal to the diameter of the cylinder. The radius of one tennis ball is 1.3 inches. How much air space is in the cylinder around the tennis balls?
Answers
Answer:
about 13.8 in³
Step-by-step explanation:
The volume of air is the difference between the volume of the cylinder of radius 1.3 inches and height 7.8 inches, and that of three spheres, each with a radius of 1.3 inches.
The formula for the volume of a cylinder is ...
V = πr²h
The formula for the volume of a sphere is ...
V = (4/3)πr³
For h = 6r, the difference is ...
(cylinder volume) - 3×(sphere volume) = πr²·(6r) - 3×(4/3)πr³
= πr³(6 -4)
= 2πr³ = 2π(1.3 in)³ = 4.394π in³
≈ 13.8 in³ . . . . air space in the cylinder of tennis balls
On a coordinate grid Ming's house is located 2 blocks to the right and 5 blocks up from (0,0). Joe house is located 3 blocks to the right and 2 blocks down from Ming's house. What ordered pair describes the location of joe house?
Answers
Answer:
(5, 3)
Step-by-step explanation:
Conventionally, the ordered pairs are (right, up). Then ...
Ming's = (0, 0) + (2, 5) = (2, 5)
Joe's = Ming's + (3, -2) = (2, 5) + (3, -2) = (2+3, 5-2)
Joe's = (5, 3)
Answer:
( 5,3 )
Step-by-step explanation:
i am doing this test too
15. What is the value of (1/2)3?
A. 1/6
B. 1/8
C. 1/2
D. 11/2
Answers
Answer:
(1/2)^3
= (1/2) (1/2) (1/2)
= 1/4 (1/2)
= (1)(1)/(4)(2)
= 1/8
Step-by-step explanation:
Please mark brainliest!
Alice and Will are measuring a liquid solution using graduated cylinders. Alice uses 6.5liters of the liquid solution, and Will uses 4,750milliliters of the liquid solution. What is the ratio of Alice's measurements to Will's measurements? Simplify your answer.
Answers
The simplified ratio of Alice's measurements to Will's measurements is 26:19 when both measurements are converted to milliliters.
Explanation:The ratio of Alice's measurements to Will's measurements can be found by converting both measurements to the same units and then simplifying the resulting fraction. Alice's measurement is in liters and Will's measurement is in milliliters. We know that 1 liter equals 1,000 milliliters, so Alice's measurement converted to milliliters is 6.5 liters * 1,000 = 6,500 milliliters.
Therefore, the ratio of Alice's measurement to Will's measurement in milliliters is 6,500:4750. To simplify this ratio, you can find the greatest common divisor (GCD) of the two numbers and divide both numbers by the GCD. In this case, the GCD of 6,500 and 4,750 is 250. Thus, the simplified ratio is 26:19.
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The ratio of Alice's measurements to Will's measurements is approximately [tex]\[ \frac{4750 \text{ milliliters}}{1000} = 4.75 \text{ liters} \][/tex]
To compare Alice's measurement to Will's, we need to express them using the same unit. Let's convert Will's measurement from milliliters to liters:
1 liter = 1000 milliliters
So, Will's measurement of 4750 milliliters is equivalent to:
[tex]\[ \frac{4750 \text{ milliliters}}{1000} = 4.75 \text{ liters} \][/tex]
Now, we can compare Alice's and Will's measurements:
Alice's measurement: 6.5 liters
Will's measurement: 4.75 liters
The ratio of Alice's measurements to Will's measurements is:
[tex]\[ \frac{\text{Alice's measurement}}{\text{Will's measurement}} = \frac{6.5}{4.75} \][/tex]
To simplify the ratio, we can multiply both the numerator and the denominator by 4 to get rid of the decimal in the denominator:
[tex]\[ \frac{6.5 \times 4}{4.75 \times 4} = \frac{26}{19} \][/tex]
So, the ratio of Alice's measurements to Will's measurements is [tex]\( \frac{26}{19} \)[/tex].
If you had a cube measuring 5 cm per side, what is its total surface area?
Answers
Answer:150 square cm
Step-by-step explanation:
Which of the following statements are true?
Answers
Answer:
Both graphs have been shifted and flipped
Both graphs have exactly one asymptote
Step-by-step explanation:
Choice A is incorrect since both graphs are not logarithmic functions. The graph of f(x) appears to be an exponential function.
Choice B is also incorrect since both graphs are not exponential functions. The graph of g(x) does not belong to the exponential family since y can take on negative values.
When the graph of f(x) is shifted downwards and flipped, we can obtain the graph of g(x).
Both graphs have exactly one horizontal asymptote
The potential and kinetic energy of a rock thrown into the air and falling back is misunderstood in statement 1. Voting rates are lower in the United States compared to some other democratic countries, and according to Kepler's laws, a satellite speeds up as it approaches its parent body and slows down as it moves away.
Explanation:For the given set of statements:
The statement that 'If a rock is thrown into the air, the increase in the height would increase the rock's kinetic energy, and then the increase in the velocity as it falls to the ground would increase its potential energy.' is False. The potential energy increases with height, not kinetic energy, and when the rock falls, its velocity increases which in turn increases its kinetic energy, not potential energy.The statement that 'Voting rates are higher in the United States than in most democratic industrialized countries, including Sweden and South Korea' is False. These countries are known to have higher voter turnouts compared to the United States.The statement, 'According to Kepler's laws of planetary motion, a satellite increases its speed as it approaches its parent body and decreases its speed as it moves away from the parent body' is True. As a satellite approaches the parent body, gravitational force pulls it in, causing it to speed up and as it travels further from the parent body, it decelerates. Learn more about Physics Statements here:https://brainly.com/question/30255438
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If log_3(x)=4.5 and log_3(y)=3, what is log_3(x^2/y)?
a. 3
b. 6.75
c. 6
d. 1.5
Answers
There all log base 3, the base won't matter as long as they're all the same.
log(x^2/y)=2log(x)-log(y)=2(4.5)-3=6
Answer: c. 6
Evelyn has a bag containing red (R), blue (B), and green (G) marbles as shown below. If each marble is replaced after it is drawn, what is the probability of randomly drawing three consecutive red (R) marbles
Answers
Answer:
the probability of drawing three consecutive red marbles is based on how many red marbles you have and many marble there is in total.
Answer:
27/512
Step-by-step explanation:
P(3 consecutive red)=P(red)×P(red)*P(red)=3/8*3/8*3/8=27/512.
The reason P(red)=3/8 for each picking of marble us because you are putting the marble back in and there are 3 red while you have 8 marbles in all.
Use the inverse properties of logarithms to simplify the expression.
10^ log 21
Answers
Answer:
21
Step-by-step explanation:
Rule of logs:
[tex] b^{\log_b x} = x [/tex]
Your problem:
[tex] 10^{\log_{10} 21} = 21 [/tex]
The value of the given logarithm expression will be 21.
What is a logarithm?Exponents can also be written as logarithms. A number base logarithm is similar to some other number. It is the exact inverse of the exponent expression.
The expression is given below.
[tex]\rightarrow 10^{\log 21}[/tex]
We know that
[tex]\rm a ^{\log_ab} = b[/tex]
Then the expression will be
⇒ 21
More about the logarithm link is given below.
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Need help with a math question
Answers
Answer:
b = 17
Step-by-step explanation:
The angle bisector of the apex angle of an isosceles triangle is also a median and altitude. PS=RS=17
b = 17