Answers
- Two supplementary angles add up to 180°, forming a straight angle (the angle formed by a straight line)
- The interior angles of a triangle add up to 180°
Given those, we notice that the one unlabeled angle in the figure shares a line with 156°. In fact, this angle is supplementary to 156°, which means that the two add up to 180°. To find the measure of this mystery angle, we can subtract 156 from 180 to obtain 180 - 156 = 24°.
Now, let's look at the triangle. We already know the measure of one of the angles is 24°, and the other two are x°. What else do we know about the angles of a triangle? From the two facts listed at the beginning, we know their interior angles add up to 180°, so let's use that fact to solve for x.
We have:
[tex]x+x+24=180[/tex], or [tex]2x+24=180[/tex]
Solving for x:
[tex](2x+24)-24=180-24\\2x=156\\(2x)/2=(156)/2\\x=78[/tex]
So, x = 78°.
For question 5, the definition of a pair of parallel lines is a pair of lines which never intersect, so "always" would be the appropriate answer.
Related Questions
Tarting at home, Emily traveled uphill to the hardware store for 60 minutes at just 6 mph. She then traveled back home along the same path downhill at a speed of 12mph. What is her average speed for the entire trip from home to the hardware store and back?
Answers
18÷2=9
Emilys average speed is 9mph
The hypotenuse of a right triangle is 20 centimeters, and the shorter leg is 12 centimeters. Find the length of the other leg. 2 cm 4 cm 16 cm
Answers
The length of the other side is : 16cm
What is a right-angled triangle?A right-angled triangle is a triangle with one of its angle 90 degrees and has two adjacent sides and a hypotenuse which is the longest side.
Analysis:
Since it is a right-angled triangle, we use Pythagoras theorem
[tex]hypotenuse^{2}[/tex] = [tex]opposite^{2}[/tex] + [tex]adjacent ^{2}[/tex]
hypotenuse = 20cm, opposite = 12cm, adjacent = xcm
[tex]20^{2}[/tex] = [tex]x^{2}[/tex] + [tex]12^{2}[/tex]
[tex]x^{2}[/tex] = 400 - 144
[tex]x^{2}[/tex] = 256
x = [tex]\sqrt{256}[/tex] = 16cm
In conclusion, the length of the other side is 16cm
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Frank and Latoya each ran every day as part of an exercise routine. Frank ran
3 miles each day for x days. Latoya ran 5 miles each day for y days.
The total number of miles that Frank ran is at least the total number of miles that Latoya ran. Write an inequality describing this relationship.
Answers
5 miles each day for y days is 5y
Frank ran at least as many miles as Latoya is 3x >/= 5y
After the police track the monkey and his kidnapper for a while, something changes. After one hour, the location is 32 miles away from the zoo. But after 70 minutes, or 76 hours, the location is still 32 miles away. Write an equation in point-slope form that represents the distance of the monkey and kidnapper, assuming they are still traveling in a linear pattern.
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order the bussiness owners up from youngest to oldest... Mark: 23 3/8 Steve: 23.45 Jeff: 23 1/4
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mark, then
steve...
What is the solution to the inequality? 5t≤−15
Answers
to construct a line parallel to a given line m to a point not on m, you need to know how to construct_______angles?
A. right
B. acute
C. congruent
D. obtuse
Answers
Can someone please explain the concept of Algebra? Just give me some basic tips so I can solve questions like the ones in the picture. Thanks in advance!
Answers
for Example: 4x= 8
x= 8 divide by 4
x= 2
Step 1: isolate the variable (in this case,x).
Isolating the variable makes you narrow down what you are solving for.
Step 2: solve for the variable.
You can solve for the variable by making x alone (meaning with no coefficient).
If you have any questions on how you can do these while it still being mathematically legal, let me know and I will help.
There are 12 girls and 16 boys and Javier's math class or 26 girls and 14 boys and Javier's core class is the race ratio of girls to boys in the two classes equivalent
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And [tex] \frac{26}{14} [/tex] simplifies to [tex] \frac{13}{7} [/tex]
They are not equivalent in simplest form, so they are not equivalent.
Simplify the expression:
sqrt(4x^2/3y)
Answers
The expression √(4x^2/3y) simplifies to (2x)/√(3y), by taking the square root of the numerator and the denominator separately.
Explanation:To simplify the expression √(4x^2/3y), we will start by simplifying the square root of a fraction, which can be done by taking the square root of the numerator and the denominator separately. We have √(4x^2) = 2x because the square root of 4 is 2 and the square root of x^2 is x. For the denominator, we have √(3y), which cannot be simplified further without additional information about y. Therefore, the simplified form of the expression is (2x)/√(3y).
Remember, if we encounter an expression with a higher root like a fourth root, we would raise the number to the 0.25 power, which is equivalent to taking the square root twice. While simplifying expressions, we may also need to solve for variables in an equation or work with fractional powers, which represent roots, such as x^2 = √x.
HELLO,
FORMULA: Ax+By=C
The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, $5,050 is collected. If 1,000 adults attended the fair, write and solve a linear equation to find the number of children that attended
ANSWER IN STANDARD FORM!
AND IF YOU ARE GOING TO ANSWER JOSEPH OR JURGEON I NEED AN HONEST ANSWER WITH EXPLANATION!
Answers
y=adults
1.50x+4y=5050
after its solved
x=700 children
x = children
y = adults
1.50x +4.00y =5050
y = 1000
1.50x + 4.00(1000) = 5050
1.50x +4000.00 = 5050
1.50x= 1050
x = 1050 / 1.50 = 700 children atttended
Write the inverse of the conditional statement. If a polygon is regular, then it has congruent angles and congruent sides.
A. If a polygon has congruent angles and congruent sides, then it is regular.
B. If a polygon does not have congruent angles and congruent sides, then it is not regular.
C. A polygon has congruent angles and congruent sides, if and only if, it is regular.
D. If a polygon is not regular, then it does not have congruent angles and congruent sides.
Answers
Answer:
The answer is option D.
Step-by-step explanation:
A conditional statement is a statement where we can symbolize the given statements in a p and q parts. And this contains if-then clause. It says, if p, then q. Here p is a hypothesis and q is a conclusion. Inverse of a statement means the negative form of the statement in the same order. If not p, then not q.
Given statement is :
If a polygon is regular, then it has congruent angles and congruent sides.
The inverse is :
If a polygon is not regular, then it does not have congruent angles and congruent sides.
For what values of k does the function y = cos kt satisfy the differential equation 4y'' = −9y? (enter your answers as a comma-separated list.)
Answers
The values of k that satisfy the equation 4y'' = -9y for the function y = cos kt are k = ±3/2.
Explanation:This is a question in differential equations, where we are given a cosine function y = cos kt and asked to find values of k that satisfy the given equation 4y'' = −9y.
Recall, the second derivative of cos kt is -k²cos kt which is equivalent to -k²y.
Substituting that into the differential equation, we get 4(-k²y) = -9y. If we simplify this, we get k² = 9/4. Therefore, the values of k which satisfy the given equation are k = ±3/2.
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The values of k that satisfy the differential equation 4y'' = −9y are k = ±3/2.
We can find the values of k that satisfy the differential equation 4y'' = −9y by solving for k.
First, we can rewrite the differential equation in its general form:
ay'' + by' + cy = 0
where a = 4, b = 0, and c = -9.
Next, we can find the characteristic equation:
ar^2 + br + c = 0
Plugging in the values of a, b, and c, we get:
4r^2 + 0r - 9 = 0
Solving for r, we get:
r = ±3/2
Therefore, the general solution to the differential equation is:
y = Acos(3t/2) + Bsin(3t/2)
where A and B are arbitrary constants.
Finally, we can substitute y = cos kt into the original differential equation and solve for k:
4k^2cos kt + 9cos kt = 0
Dividing both sides by cos kt, we get:
4k^2 + 9 = 0
Solving for k, we get:
k = ±3/2
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round 2.125 to the nearest hundreth.
Answers
A train travels from Chicago,Illinois to Los Angeles, ca in 1 day and 15 minuets. The distance between the two cities is 2,015.3 miles. How fast was the train going on average
Answers
15 minutes is 0.25 of an hour
24 hours in a day
2015.3/24.25
83.1051546 mph
or 83 mph
A rose garden is designed by joining a rectangle and a semicircle, as shown below. The rectangle is 24ft long and 18ft wide. If the gardener wants to build a fence around the garden, how many feet of fence are required?
Answers
Because you would add:
24 + 24 + 18 + 18 = 84ft
If you multiplied 18 by 24 you'd get area not perimeter.
♥ Hope I helped ♥
According to the given rectangle, approximately 112.27 feet of fence are required to enclose the rose garden.
The perimeter of a rectangle is the sum of all its sides. In this case, the rectangle has two sides of length 24 feet and two sides of length 18 feet.
Therefore, the perimeter of the rectangle can be calculated as follows:
Perimeter of rectangle = 2 * (Length + Width)
= 2 * (24 ft + 18 ft) = 2 * 42 ft = 84 ft.
The circumference of a circle can be calculated using the formula:
Circumference = π * Diameter.
Diameter of the Semicircle: The diameter of the semicircle is equal to the width of the rectangle, which is 18 feet.
Circumference of the Semicircle: Using the formula mentioned above:
Circumference = π * 18 ft
≈ 56.5487 ft (rounded to four decimal places).
Perimeter of the Semicircle: As it is a semicircle, we only need half of the circumference:
Perimeter of semicircle = Circumference / 2
≈ 56.5487 ft / 2 ≈ 28.2744 ft (rounded to four decimal places).
Total Fence Length Required: Now, we add the perimeter of the rectangle and the semicircle to find the total length of fence required to enclose the rose garden:
Total fence length = Perimeter of rectangle + Perimeter of semicircle
= 84 ft + 28.2744 ft ≈ 112.2744 ft (rounded to four decimal places).
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A man invested $500 in the stock market. During the first week, he gained $200. During the second week, the market was strong and the man doubled his money. During the third week, stocks fell, and the man lost $650. How much money did the man have at the end of three weeks?
Answers
500 + 200 = 700 700 x 2 + 1400
1400 - 650 = 750
$750 at the end of three weeks
Certain hot water bottles hold up to 1500 milliliters of water. how many liters are in 1500 milliliters
Answers
please help!!! thx!!!
Answers
distance = (speed)*(time)
we're given the speed and time. If we multiply them together, we get the distance
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The number 1.3 x 10^6 is in scientific notation. The coefficient 1.3 rounds to 1
This means "1.3 x 10^6" turns into "1 x 10^6"
Similarly, with the number 2.8 x 10^3, the coefficient 2.8 rounds to 3
The number "2.8 x 10^3" turns into "3 x 10^3"
When we multiply the numbers (1 x 10^6) and (3 x 10^3), we will
multiply the coefficients 1 and 3 to get 1*3 = 3
add the exponents: 6+3 = 9
So overall, the final answer is 3 x 10^9 indicating that it is choice C
(this is an estimate because we rounded the coefficients)
Marlene rides her bicycle to her friend jon's house and returns home by the same route. marlene rides her bike at constant speeds of 9 mph on level ground, 6 mph when going uphill and 18 mph when going downhill. if her total time riding was 1 hours, how far is it to jon's house?
Answers
To solve the problem:
Let f = distance one way distance on level ground
Let h = distance rode on the hill
Write a time equation; where Time = distance/speed:
level time + uphill time + downhill time + level time = 1hr
f/9 + h/6 + h/18 + f/9 = 1 hr
Multiply equation by 18 to get rid of the denominators
2f + 3h + h + 2f = 18
4f + 4h = 18
Simplify by dividing this by 4
f + h = 4.5 miles is took her to get to Jon’s house.
Find the missing values x and y
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2) (3z + 18)° = 108° ( in a para llelogram opposite angles are equal)
Then 3z+18 = 108 and 3z° = 90° → z = 30°
3) (3y)° = 108° (vertical angles) , 3y° = 108 and y = 36°
4) 3y = x° (corresponding angles) but 3y = 108, then x = 108°
(Mind you I am calculating the ∠ x, y, and z. To find the angles of the parallelogram replace x,y and z by their respective values
Evaluate 4-(3+2)^2
A. -21
B. -9
C. 5
D. 1
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if -7k=-42, then k=6
Answers
because minus and minus gives you a positive answer you just put 6 instead of -6
What does y=mx+b the m mean?
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Which percent is equivalent to 2.5?
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Answer:
250%
Step-by-step explanation:
The value of percentage of a number 2.5 is,
⇒ 250%
We have to given that,
To change a number 2.5 into percent.
Since, A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Now, We can change it as,
⇒ 2.5 × 100%
⇒ 250%
Therefore, The value of percentage of a number 2.5 is,
⇒ 250%
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A prepaid cell phone charges a preset number of minutes to use text messaging. The graph represents y, the number of minutes used for x, the number of text messages sent and received. Is there a direct variation? Which equation represents the relationship? Yes, y = 2x. Yes, y = 20x. No, y = x + 10. No, y = x + 20.
Answers
Answer:
Yes, y = 2x
Step-by-step explanation:
I took it on edge and got it right!!!
There will be definitely a direct relation and the relation will be y = 2x.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b, will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Proportion is very useful to set relations between variables.
Given that the prepaid cell phone charges a preset number of minutes to use text messaging. The graph represents y, the number of minutes used for x, and the number of text messages sent and received
so it is clear that cell phone charge upon the number of minutes to use text messaging hence y = 2x will be the correct answer.
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Identify the graph of 4+2i. Is the point at (2,4), (4,2), (4,-2), or (-4,2)?
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The graph of the complex number 4 + 2i corresponds to the point (4, 2) on the complex plane, with 4 as the real part and 2 as the imaginary part.
To identify the graph of the complex number 4 + 2i, you can think of it as a point on the complex plane. In the complex plane, the horizontal axis represents the real part of a complex number, and the vertical axis represents the imaginary part. So, for the complex number 4 + 2i, the real part is 4, and the imaginary part is 2.
Now, let's locate this point on the complex plane:
The real part (4) corresponds to the horizontal axis.
The imaginary part (2) corresponds to the vertical axis.
So, the point (4, 2) on the complex plane represents the complex number 4 + 2i. Therefore, the correct answer is (4, 2).
In summary, the graph of the complex number 4 + 2i corresponds to the point (4, 2) on the complex plane, where 4 is the real part, and 2 is the imaginary part.
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Simplify the expression shown.3x + 2 – 3x + 7 +5xwhat is the coefficient in the simplified expression?
Answers
The expression 3x + 2 - 3x + 7 +5x simplifies to 5x
when the terms containing variable 'x' are combined. Therefore, the coefficient in the simplified expression is 5.
Explanation:The given expression is 3x + 2 – 3x + 7 +5x.
To simplify this expression, we need to combine like terms, which in this case are terms with x.
The like terms are 3x, -3x, and 5x. When added together, they simplify to: 3x - 3x + 5x = 5x.
The number part of the term, excluding x, is referred to as the coefficient. So the coefficient of x in this simplified expression is 5.
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Suppose your friend says the line y=-2x +3 is perpendicular to the line x+2y=8. Do you agree? Explain.
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y = 2x + 3 has slope of 2 ( because of the '2x')
x + 2y = 8
2y = -x + 8
y = -0.5x - 4
2 * -0.5 = -1 so they are perpendicular
So the friend was right
graph y> 1-3x, I really need someone to answer this.