PQ and RS are two lines that intersect at point T, as shown below:
Two lines PQ and RS intersect at point T. Angles PTR and STQ are shown congruent.
Which statement is used to prove that angle PTR is always equal to angle STQ?
a. Lines PQ and RS do not have a fixed length.
b. Angle PTR and angle PTS are supplementary angles.
c. Lines PQ and RS intersect at an angle less than a right angle.
d. Angle PTR and angle PTS are complementary angles.
Answers
Related Questions
For every real number x, y, and z, the statement (x – y)z = xz – yz is _____ true. An algebraic expression in simplest form _____ has like terms.
Answers
The statement (x – y)z = xz – yz is always true due to the distributive property in mathematics. Moreover, an algebraic expression in the simplest form does have like terms. Like terms are grouped together to simplify the expression.
Explanation:For every real number x, y, and z, the statement (x – y)z = xz – yz is always true. This is an illustration of the distributive property in mathematics, which states that for all real numbers, the equation a(b + c) = ab + ac holds true. In the given equation, the place of 'a' is taken by 'z', while 'x' and 'y' replace 'b' and 'c' respectively.
On the other hand, an algebraic expression in simplest form does have like terms. Like terms are terms with the same variable part. For instance, in the expression 3x2 + 2x - x2 + 4 +5x - 2, the like terms can be combined to simplify the expression to 2x2 + 7x + 2.
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How is the sentence "10 more than P is -3" written as an equation
p-3=10
P+10=-3
P+10=3
P=10-3
Answers
The correct expression is P + 10 = -3
We have a sentence - "10 more than P is -3".
We have to determine the expression that represents the sentence.
Express the statement - "The difference of x and y is equal to n" in the form of expression.The expression representing the above statement is -
n = x - y
According to the question, we have -
10 more than P is -3
We can write it as a expression -
P + 10 = -3
Hence, the correct expression is P + 10 = -3
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For what values of b does the value of the fraction 5−2b /4 belong to the interval [−2; 1]?
Answers
[tex]-2 \leq {\frac{5-2b}{4}}\leq1[/tex]
First, multiply everything by 4 to clear the denominator:
[tex]-8\leq5-2b\leq4[/tex]
Subtract 5 from both sides:
[tex]-13\leq-2b\leq-1[/tex]
In the last step, we need to divide everything by -2 which will flip both inequality signs, so we have:
[tex]\frac{13}{2}\geq b \geq \frac{1}{2}[/tex]
So b is in the interval [tex][\frac{1}{2},\frac{13}{2}][/tex].
Answer: The required value of b lies in the interval [0.5, 6.5].
Step-by-step explanation: We are given to find the value of b so that the following fraction belong to the interval [−2, 1] :
[tex]f=\dfrac{5-2b}{4}.[/tex]
According to the given information, we can write
[tex]-2\leq f\leq 1\\\\\Rightarrow -2\leq \dfrac{5-2b}{4}\leq1\\\\\Rightarrow -8\leq 5-2b\leq 4\\\\\Rightarrow -8-5\leq-2b\leq 4-5\\\\\Rightarrow -13\leq -2b\leq -1\\\\\Rightarrow 13\geq 2b\geq 1\\\\\Rightarrow \dfrac{13}{2}\geq b\geq \dfrac{1}{2}\\\\\Rightarrow 6.5\geq b\geq 0.50[/tex]
Thus, the required value of b lies in the interval [0.5, 6.5].
How to rotate a triangle 90 degrees counter clockwise about the origin
Answers
Plot the point M (-2, 3) on the graph paper and rotate it through 90° in a clockwise direction, about the origin. Find the new position of M. Solution: When the point is rotated through 90° clockwise about the origin, the point M (h, k) takes the image M' (k, -h).
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It took a cheetah 45 minutes to run from Jungle A to Jungle B. If the average speed for the trip was 80 km/h, what is the distance between the two jungles.
PLZ HELP! ITS HOMEWORK!!!!
Answers
Day Temperature
1 13
2 15
3 22
4 12
5 22
6 18
7 18
8 22
9 11
10 13
11 20
12 21
You record the temperature for 12 days. Which number summarizes all of the data with a single number?
A) 4.2
B) 11
C) 16
D) 17.25
Answers
Answer:
D) 17.25
Step-by-step explanation:
If you want to summarize all the data points with a single number you want a measure of center such as mean. The mean for the data set is 17.25. All the others represent a measure of spread.
Answer:
17.25
Step-by-step explanation:
Write 5,256 divided into 52 and show your work
Answers
how to solve for x for a parallelogram
Answers
Answer:
11) 11x-10
x=10
Step-by-step explanation:
SPEED RUN
Carmella sells homemade pies for $10 a pie. It costs $2 for the ingredients to bake each pie. Carmella bought a new oven for $600. How many pies must Carmella bake and sell before she recovers the cost of the oven?
Answers
the steps i did were
1. i added 10 and 2 to get 12
2. i divided 12 into 600
3. then i got the answer 50
so that's how i found out the total of pies she needed to sell i hope this worked for you.
Webster Digital received a promissory note of $8,000 for 9 months at 7% simple interest from one of its customers. After 4 months, the note was discounted at Bank of Aventura at a discount rate of 10%. What are the proceeds Webster Digital will receive from the discounted note? (Round to the nearest cent)
Answers
[tex]FV=P(1+rt)[/tex]
where: P is the initial value of the promissory note, r is the simple interest rate, and t is the time period (in years).
Given that Webster Digital received a promissory note of $8,000 for 9 months at 7% simple interest from one of its customers.
P = &8,000; t = 9 months = 9 / 12 = 0.75 years; r = 7% = 0.07
[tex]FV=8000(1+(0.07\times0.75)) \\ \\ =8000(1+0.0525)=8000(1.0525) \\ \\ =\$8,420[/tex]
The proceed from a discounted promisory note is given by
[tex]X=FV(1-dt)[/tex]
where: FV is the maturity value of the promissory note, d is the discount rate and t is the number of years remaining from the time the note was discounted to the maturity date.
Given that after 4 months, the note was discounted at Bank of Aventura at a discount rate of 10%.
t = 9 months - 4 months = 5 months = 5 / 12 years; d = 10% = 0.1; FV = $8,420
[tex]X=8420\left(1-\left(0.1\times \frac{5}{12} \right)\right) \\ \\ =8420\left(1- \frac{1}{24} \right)=8420\left( \frac{23}{24} \right) \\ \\ =\$8,069.17[/tex]
Therefore, the proceed is $8,069.17
math help will give brainliest
X is 7 but I got m angle D wrong
Answers
x = 7
The measure of angle D is 14 degrees
-----------------------------------------------
-----------------------------------------------
Angle C and angle D are complementary, which means they add to 90 degrees.
(angle C) + (angle D) = 90
(12x-8) + (3x-7) = 90
12x-8 + 3x-7 = 90
(12x+3x) + (-8-7) = 90
15x-15 = 90
15x-15+15 = 90+15
15x = 105
15x/15 = 105/15
x = 7
So you have the correct x value. Nice work.
Now use this x value to find the measure of angle D
angle D = 3*x - 7
angle D = 3*7 - 7
angle D = 21 - 7
angle D = 14 degrees
12s + 4 + 4s - 2 simplified need help with school work
Answers
Just combine your like terms [tex]12s + 4s \\ \\ and \\ 4 + (-2) \\ \\ Let's\\ Solve\\ The\\ S's:\\ 12s + 4s = 16s \\ \\ \\ \\ Now \\ Solve\\ The\\ Other\\Numbers:\\ 4 + (-2) = 2 \\ \\ \\ \\ \\ Your \\ Answer: \\ 16s + 2 [/tex]
Good luck on your assignment and enjoy your day!
~[tex]MeIsKaitlyn:)[/tex]
Can someone help with numbers 15 and 16
Answers
I had x before the movie.
x - 13.50 = 26.50
Add 13.50 to both sides of the equation:
x = 40
I had $40 before the movie.
16.
The original balance was x.
x - 161.15 = 423.28
Add 161.15 to both sides:
x = 584.43
The previous balance was $584.43
Divide. −5 5/8÷5
a) −1 1/8
b) −5/8
c) 5/8
d) 1 1/8
Answers
Answer:
I believe the answer is A, but I can't be completely sure.
Step-by-step explanation:
To determine the diameter of the sun, an astronomer might sight with a transit (a devise used by surveyors for measuring angles), first to one edge of the sun and then to the other, finding that the included angle equals 32 minutes (32'). Assuming that the distance from the Earth to the sun is 92,919,800 miles, calculate the diameter of the sun.
Answers
Final answer:
The astronomer calculates the diameter of the Sun using trigonometry and the given angle and distance, arriving at an approximate value of 1,727,804 miles which is a reasonable estimate when compared to the actual diameter of the Sun.
Explanation:
To calculate the diameter of the Sun, the astronomer uses the given angular size and the distance from the Earth to the Sun. Since we have the angle of 32 minutes (which is about 0.533° when converted to degrees), we can set up the following relationship using trigonometry:
diameter of the Sun = 2 × (distance to the Sun) × tan(½ × angular size in radians)
Let's convert the angular size from minutes to degrees and then to radians:
32 minutes = 32' / 60 = 0.533°
To convert degrees to radians, we use the fact that 180° is equivalent to π radians:
0.533° × (π radians / 180°) = 0.0093 radians
Now, we can use the distance to the Sun which is given as 92,919,800 miles and apply the formula:
diameter of the Sun = 2 × 92,919,800 miles × tan(0.0093 radians)
Performing the calculation:
diameter of the Sun ≈ 2 × 92,919,800 × 0.0093
diameter of the Sun ≈ 1,727,804 miles
This is an approximation because the angular size varies slightly due to the elliptical orbit of Earth. Comparing to the actual diameter of the Sun, which is about 1.39 million kilometers (or about 864,000 miles), we can see that our calculated value is a reasonable estimate, keeping in mind that trigonometric calculations rely on a circular orbit assumption and ideal conditions.
show the numbers in order from least to greatest? 323 , 3.7, 3.65
Answers
What is the value of the function at x = −2?
Answers
Answer:
3.
Step-by-step explanation:
We have been given graph of a function. We are asked to find the value of our given function at [tex]x=-2[/tex].
To find the value of our given function at [tex]x=-2[/tex], we need to find the y-value of our given function when [tex]x=-2[/tex].
We can see that value of y-coordinate is 3, when [tex]x=-2[/tex], therefore, at [tex]x=-2[/tex] the value of the function is 3.
what percent of 32 is 4
Answers
To find the percent, just divide.
4/32 -> 1/8 -> 0.125
Now, 0.125 as a percent is:
12.5%
what is another way to write 4 hundreds
Answers
Another way to write 4 hundred is to express it in scientific notation which is 4.0 × 10²
Scientific notation is another way of expressing figures in standard form. It is a proper form of writing a large number in simpler ways.
Another way to 4 hundred is to express it in a standard form or scientific notation.
400 hundred in scientific notation = 4.0 × 10²
Therefore, we can conclude that 4 hundred is to express it in scientific notation which is 4.0 × 10².
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Tia kayaked 2400 meters at a constant rate in 1.5 hours on Saturday. On Sunday, she kayaked 200 meters per hour faster. What was Tia’s average rate on Sunday? A. 1600 meters per hour B. 1800 meters per hour C. 2000 meters per hour D. 2200 meters per hour
Answers
Since Tia kayaked 2400 meters at a constant rate in 1.5 hours on Saturday. On Sunday, she kayaked 200 meters per hour faster. Tia’s average rate on Sunday is B. 1800 meters per hour
What is average rate?Average rate is the change of quantity with time.
Since Tia kayaked 2400 meters at a constant rate in 1.5 hours on Saturday. On Sunday, she kayaked 200 meters per hour faster. To find Tia’s average rate on Sunday, we proceed as follows
To find Tia's average rate on Sunday, we first need to find Tia's average rate or speed on Saturday.
Tia's speed on Saturday, s = d/t where
d = distance kayaked on Saturday and t = time kayaked on SaturdaySince
d = 2400 m andt = 1.5 hSubstituting the values of the variables into the equation, we have that
s = d/t
= 2400 m/1.5 h
= 1600 m/h
Sine Tia kayaked 200 meters per hour faster on Sunday, Tia's average rate or speed on Sunday is s' = 1600 meters per hour + 200 meters per hour = 1800 meters per hour
So, Tia’s average rate on Sunday is B. 1800 meters per hour
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Tia's average rate on Sunday was 1800 meters per hour, as she kayaked at a speed that was 200 meters per hour faster than her speed on Saturday which was 1600 meters per hour.
Explanation:To calculate Tia's average rate on Sunday, we first need to find her speed on Saturday. Given that she kayaked 2400 meters in 1.5 hours, we can apply the formula speed = distance/time to find that her speed on Saturday was 1600 meters per hour (2400m/1.5h = 1600 m/h). On Sunday, Tia kayaked 200 meters per hour faster than her Saturday's speed, making her average rate on Sunday 1800 meters per hour (1600 m/h + 200 m/h).
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9x*2 + 16y*2 - 108x -64y - 188 = 0
Answers
Ross drove 300 miles at r miles per hour and 360 miles at r+10 miles per hour. If the time needed to drive 300 miles was equal to the time needed to drive 360 miles, find the rates at which Ross drove (Express the time needed for each part of the trip as t=d/r)
Answers
t = d/r
t = 300/r
For the 360 mile part:
t = d/r
t = 360/(r + 10)
The times were equal, so
300/r = 360/(r + 10)
360r = 300(r + 10)
360r = 300r + 3000
60r = 3000
r = 50
r + 10 = 60
He drove 300 miles are 50 mph and 360 miles at 60 mph.
He drove
In if 5/7 of students are wearing jeans today and there are about 27 students in the class how many students are wearing the jeans today
Answers
Final answer:
By calculating 5/7 of 27, we find that approximately 19 students are wearing jeans today after rounding down to the nearest whole number.
Explanation:
To find out how many students are wearing jeans, we need to calculate 5/7 of the 27 students in the class.
First, we determine the value of one seventh of the class by dividing the total number of students by 7:
27 ÷ 7 = 3.8571 (we can round this to 3.86 for simplicity)
Next, we multiply this result by 5 to find five sevenths:
3.86 × 5 = 19.3
Since we cannot have a fraction of a student, we round down to the nearest whole number. Therefore, approximately 19 students are wearing jeans today.
It's important to understand and apply fractions and division to solve such mathematical problems. This example showcases the practical application of these concepts.
The inverse of a function occurs when _____.
Answers
Final answer:
The inverse of a function occurs when the roles of x and y are interchanged, reflecting the function's graph across y = x.
Explanation:
The inverse of a function occurs when the roles of x and y are interchanged, which involves reflecting the function's graph across the line y = x. For a function to have an inverse, it must pass the horizontal line test, meaning each output value corresponds to a unique input value.
Which equation demonstrates the distributive property?
A) 81 + 18 = 99
B) 81 x 18 = 18 x 81
C) 81 + 18 = 9(9 + 2)
D) (9 + 2)9 = 9(9 + 2)
Answers
Hope this helped!
(9+2)9=9(9+2)
81+18=9(9+2)
81+18=81+18
81+18=99
Subtract. 125−(−35) Enter your answer, in simplest form, in the box.
Answers
Answer:
The answer is 2 actually, this is a fraction question.
Step-by-step explanation:
When we subtract 125−(−35) the result will be 160.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given expression is 125−(−35)
Subtraction is an operation that represents removal of objects from a collection.
Minus is the operator of subtraction.
One hundred twenty five minus of minus thirty five.
We know that when minus is multiplied with minus operator the result will be positive.
So 125+35
When one hundred twenty five is added with thirty five the result will be one hundred sixty
160
Hence, when we subtract 125−(−35) the result will be 160.
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Write equation that describes the function
Answers
The equation that describes the function is f(x) = -x + 1
Function:A function is just a relationship between an input and an output values.The table represents a linear function. Therefore, let's use slope formula to
write the equation;
y = mx + bwhere
m = slope
b = y-intercept
m = -2 - 0 / 3 - 1 = - 2 / 2 = -1
y = -x + b
let's find b using (1, 0)
0 = -1 + b
b = 1
Therefore,
y = -x + 1
The function can be written as f(x) = -x + 1
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AT&T charges $76.00 for 500 minutes or Sprint charged $54.00 for 450 minutes which is the better deal
Answers
To determine the better deal between AT&T and Sprint, we need to compare the cost per minute for each plan. Sprint offers a lower cost per minute, making it the better deal.
Explanation:To determine which deal is better, we need to compare the cost per minute for each plan. For AT&T, the cost per minute is $76.00/500 minutes = $0.152 per minute. For Sprint, the cost per minute is $54.00/450 minutes = $0.12 per minute.
Therefore, the better deal is Sprint because it offers a lower cost per minute compared to AT&T.
Simplify 2 to the fifth power over 3 squared all raised to the fourth power. 2 to the twentieth power over 3 to the eighth power 2 to the ninth power over 3 to the eigth power 8 to the fifth power over 12 squared 2 over 3 squared
Answers
2 to the fifth power over 3 squared all raised to the fourth power
[tex]\left(\dfrac{2^5}{3^2}\right)^4=\dfrac{(2^5)^4}{(3^2)^4}=\dfrac{2^{5\cdot4}}{3^{2\cdot4}}=\dfrac{2^{20}}{3^8}[/tex]
Answer: 2 to the twentieth power over 3 to the eighth power
Used:
[tex]\left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\(a^n)^m=a^{n\cdot m}[/tex]
Answer:
yes
Step-by-step explanation:
The function f(x)=40,000(0.75)x represents the number of bacteria present in a petri dish after x hours. What is the average rate of change in the number of bacteria between Hour 2 and Hour 5?
Question 1 options:
A.−6102 bacteria/h
B.4336 bacteria/h
C.−4336 bacteria/h
D.6102 bacteria/h
Answers
f(b) - f(a)
The average rate of change (arc) is --------------
b - a
Here that comes to 40000 [0.75^5 - 0.75^2]
--------------------------------
5-2
or arc = -13007.81 / 3 = -4335.9 bacteria per year.
The average rate of change in the number of bacteria between Hour 2 and Hour 5 is approximately -3,482 bacteria/hour.
Explanation:To find the average rate of change in the number of bacteria between Hour 2 and Hour 5, we need to calculate the difference in the number of bacteria at Hour 5 and Hour 2, and then divide it by the difference in time (3 hours).
At Hour 2, substitute x = 2 into the function f(x) = 40,000(0.75)^x:
f(2) = 40,000(0.75)^2 = 40,000(0.5625) = 22,500 bacteria.
At Hour 5, substitute x = 5 into the function:
f(5) = 40,000(0.75)^5 = 40,000(0.3164) = 12,656 bacteria.
Now we can calculate the average rate of change:
Average rate of change = (f(5) - f(2)) / (5 - 2) = (12,656 - 22,500) / 3 = -3,482 bacteria/hour. The average rate of change in the number of bacteria between Hour 2 and Hour 5 is approximately -3,482 bacteria/hour.