The proof was completed by assuming that two supplementary angles could both be obtuse, which would mean that their sum is more than 180°. This contradicts the definition of supplementary angles, where their sum should always be exactly 180°, and hence proves that two supplementary angles cannot both be obtuse.
Explanation:To complete the indirect proof, we start by assuming that two supplementary angles, let's call them angle1 and angle2, can indeed both be obtuse angles. An obtuse angle is defined as an angle which measures more than 90°. Therefore, if both angle1 and angle2 are obtuse, they would each measure more than 90°, meaning that their sum (angle1 + angle2) would measure more than 180°.
However, the definition of supplementary angles is such that their sum should always be exactly 180°. Therefore, we reach a contradiction in our assumed scenario: the sum of angle1 and angle2 cannot be both more than 180° (by our assumption that they are both obtuse) and exactly 180° (by the known definition of supplementary angles).
This contradiction means that our initial assumption was incorrect, thus completing the proof. In other words, two supplementary angles cannot both be obtuse, as it would contradict the definition of supplementary angles.
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The height, h, of a falling object t seconds after it is dropped from a platform 300 feet above the ground is modeled by the function h(t)=300-16t2. Which expression could be used to determine the average rate at which the object falls during the first 3 seconds of its fall.
Answer:
-96 feet/sec.
Step-by-step explanation:
The height h of a falling object after t second when it is dropped from a platform 300 feet above the ground is modeled by the function h (t) = 300 - 16t²
Then speed or average rate by which the object falls from height h will be [tex]\frac{d[h(t)]}{dt}=\frac{d(300-16t)^{2} }{dt}[/tex]
Speed = [tex]\frac{d}{dt}(300)[/tex] - [tex]\frac{d}{dt}(16t^{2} )[/tex]
= -16 (2t)
Speed = -32t
After 3 second speed of object will be
Speed = -32(3)
= -96 feet/second
Therefore, the average rate will be -96 feet/sec. during the first 3 seconds of its fall.
6 ( y + 8 ) = 3 ( 2y - 7 )
Ray's gym charges an initial sign-up fee of $25.00 and a monthly fee of $15.00.
Write a function that describes the gym's total membership fee for x months.
what are the steps for using a compass and a straightedge to construct the bisector of
ANSWER:
How to construct a Line Segment Bisector AND a Right Angle
using just a compass and a straightedge.
STEP-BY-STEP EXPLANATION:
Steps:
1)Place the compass at one end of line segment.
2)Adjust the compass to slightly longer than half the line segment length
3)Draw arcs above and below the line.
4)Keeping the same compass width, draw arcs from other end of line.
5)Place ruler where the arcs cross, and draw the line segment.
Solve. 5t<-15
A) t > 3
B) t < 3
C) t > -3
D) t < -3
Which statements are true the ordered pair (1, 2) and the system of equations?
y=−2x+4
7x−2y=3
Select each correct answer.
When (1, 2) is substituted into the first equation, the equation is true.
When (1, 2) is substituted into the first equation, the equation is false.
When (1, 2) is substituted into the second equation, the equation is true.
When (1, 2) is substituted into the second equation, the equation is false.
The ordered pair (1, 2) is not a solution to the system of linear equations.
The ordered pair (1, 2) is a solution to the system of linear equations.
The linear pair postulate states that if two angles form a linear pair, then they are __________ angles.
Answer:
supplementary
Step-by-step explanation:
The solution to -5m = -20 is negative.
True or false
False
a negative number times a negative number would have a positive answer
What could the answer be?
When the federal reserve wants more money to be printed, which agency will be in charge of printing it?
Answer:
The U.S. Treasury.
Step-by-step explanation:
The coordinates of point D are (7, 4) and the coordinates of point E are (1, −3) .
What is the slope of the line that is perpendicular to DE¯¯¯¯¯?
Enter your answer as a simplified fraction in the box.
Use the information about sports in the photo to explain how inequalities can be used to describe school sports. Include an inequality describing the number of schools needed to add girls’ track and field so that the number is greater than the number of schools currently participating in girls’ basketball.
You have a rectangular vegetable garden in your backyard that measures 15 feet by 10 feet. You want to double the area of the garden by adding the same distance x to the length and width of the garden. Find the value of x and the new dimensions of the garden.
To double the area of the rectangular vegetable garden, we need to add the same distance, x, to the length and width. The value of x is 10 feet, and the new dimensions of the garden are 25 feet by 20 feet.
Explanation:To double the area of the garden, we need to add the same distance, x, to both the length and width of the garden. The original dimensions of the garden are 15 feet by 10 feet, with an area of 150 square feet. To double the area, we set up the equation 2(15+x)(10+x) = 2(15)(10). Solving this equation gives us the value of x and the new dimensions of the garden.
Expanding the equation, we have 30x + x² + 300 = 300. This simplifies to x² + 30x - 300 = 0. Factoring this quadratic equation, we get (x - 10)(x + 30) = 0. So x = -30 or x = 10. We discard the negative value since distance cannot be negative, so x = 10 feet.
The new dimensions of the garden are 15+10 = 25 feet and 10+10 = 20 feet.
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Rules for Plotting Points:
1) Start at the origin: _________
2) If your x-value is ___________, move right; if it is ___________, move left;
if it is _____, don’t move.
3) If your y-value is ___________, move up; if it is ___________, move down;
if it is _____, don’t move.
Solve the equation. How old is Sam?
Sam's age doubled plus 5 is the same as Sam's age tripled minus 1.
Question 5 options:
Sam is 6yrs old.
Sam is 4 yrs old.
Sam is 12 yrs old.
Sam is 5 yrs old.
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find the x and y intercepts -3x-6y=12
Answer:
x-intercept: -4y-intercept -2Step-by-step explanation:
The x-intercept is found where the graph crosses the x-axis, at y=0. Substituting that into the equation and solving for x, we get ...
-3x = 12
x = 12/-3 = -4 . . . . . x-intercept = -4
The y-intercept is found where the graph crosses the y-axis, at x=0. Substituting that into the equation and solving for y, we get ...
-6y = 12
y = 12/-6 = -2 . . . . . y-intercept = -2
_____
A graphing calculator confirms these values.
Given: M is the midpoint of LN; LM =8 prove:LN=16
The proof of LN= 16 is shown below:
What is midpoint?The midpoint formula is applied when one is required to find the exact center point between two defined points. So for a line segment, use this formula to calculate the point that bisects a line segment defined by the two points.
Given:
LM= 8
and M is the midpoint of LN
So, the line LN will be break into two equal parts LM and MN
then we can write
LM= MN= 8
Now,
LN= LM+ MN
LN= 8+8
L=16
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BRAINLIESTTTTTTTTTTTTT
Solomon is taking out a 5,320 two year loan with an APR of 10.25%. What will the finance charge be for this loan to the nearest dollar?
The table below represents a linear function f(x) and the equation represents a function g(x): x f(x) −1 −7 0 −1 1 5 g(x) g(x) = 5x − 4 Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points) Part B: Which function has a greater y-intercept? Justify your answer. (4 points)
What is the parents function of f(x)=3x-5
Of the birds in Monica's pet shop, 1/5 are pigeons. Of the pigeons, 1/3 are white. Look at each expression. Can it be used to find the fraction of birds in Monica's pet shop that are white pigeons?
1/15.
The expression that can be used to find the fraction of birds in Monica's pet shop that are white pigeons is:
1/5 x 1/3 = 1/15
This calculation is derived by multiplying the fraction of pigeons in the pet shop (1/5) by the fraction of white pigeons among pigeons (1/3).
Simplify this problem: X3 / X.
When adding two numbers, such as 123 and 423, care is taken to first line them up and then add like digits. How does expanding this expression to [(1 × 102) + (2 × 101) + (3 × 100)] + [(4 × 102) + (2 × 101) + (3 × 100)] make the operation more like a polynomial addition problem?
Rachel deposited $6,449.82 into a savings account with an interest of 6.9% compounded annually. About how long will it take for the accout to be worth $8,000?
Answer:
3 years and 3 months.
Step-by-step explanation:
Since, the amount formula in compound interest,
[tex]A= P(1+\frac{r}{100})^t[/tex]
Where,
P = principal amount,
r = rate per period,
t = number of periods,
Here, A = $ 8,000, r = 6.9%, P = $6,449.82,
By substituting the values,
[tex]8000 = 6449.82(1+\frac{6.9}{100})^t[/tex]
[tex]\frac{8000}{6449.82}=(1+\frac{6.9}{100})^t[/tex]
[tex]\ln (\frac{8000}{6449.82})=t\ln(1.069)[/tex]
[tex]\implies t = \frac{\ln (\frac{8000}{6449.82})}{\ln(1.069)}=3.228[/tex]
Hence, it would be take 3.228 years or 3 years and 3 months.
Factor the four-term polynomial.
xz + x + yz + y
A. (z - y)(x + 1)
B.(x - y)(z + 1)
C.(x + y)(z + 1)
jasmine has $15 dollars and save $2.50 every month . radha has $0 and save $3.50 every month. jasmines savings after x months can be represented by the function f(x)=2.5x+15. radahs savings after x months can be represented by the function g(x)=3.5x after how any moths will they both have the same amount in savings? find the value of x which f(x)=g(x)
2.5x+15 = 3.5x
subtract 2.5x from each side
15 = x
they will have the same amount after 15 months
Joel earns $1,700 per month. If he spends $425 on rent each month, what percent of his income does he spend on rent? A. 20% B. 331/3% C. 40% D. 25%
Kendall is stacking boxes that are 7.5inches tall. Explain how to find the height (in inches)
Final answer:
To find the height of stacked boxes, multiply the height of one box (7.5 inches) by the total number of boxes stacked.
Explanation:
Kendall is stacking boxes that are each 7.5 inches tall. To find the total height in inches of the stacked boxes, you would need to multiply the height of one box by the total number of boxes stacked. For example, if Kendall stacks 10 boxes, the calculation would be 7.5 inches x 10, which equals 75 inches. Therefore, the total height of the 10 stacked boxes would be 75 inches.
The length of a rectangle is 4.2 cm more than 2 times the width. If the perimeter of the rectangle is 42.6 cm, what are its dimensions?