Answer: ABCD is a quadrilateral
To prove : ∠AOB=
2
1
(∠C+∠D)
AO and BO is bisector of A and B
∠1=∠2∠3=∠4...(1)
∠A+∠B+∠C+∠D=360
(Angle sum property)
2
1
(∠A+∠B+∠C+∠D)=180...(2)
In △AOB
∠1+∠3+∠5=
2
1
(∠A+∠B+∠C+∠D)
∠1+∠3+∠5=∠1+∠3+
2
1
(∠C+∠D)
∠AOB=
2
1
(∠C+∠D)
Explanation: In a quadrilateral ABCD. AO and BO are bisectors of angle A and angle B respectively. Prove that ∠AOB=
2
1
{∠C+∠D}.
Kevin has a rectangular
swimming pools that is 12
feet by 16 feet. He wants
to put a rope diagonally
across the pool. How long
does the rope need to
be?
Answer:
20 feet long
Step-by-step explanation:
To solve this you need to use the Pythagorean theorum, [tex]a^2+b^2=c^2[/tex], where c is the length of rope needed and A and B are the side lengths. Think of it like a right triangle.
So, the equation is
[tex]12^2+16^2=c^2[/tex]
Which is then
[tex]144+256=c^2[/tex]
[tex]c^2=400[/tex]
And the possible values of c are 20 and -20.
From here we know the answer cannot be -20 because you cannot have a negatively long length of rope, so the answer must be 20 feet.
Answer:
20 feet
Step-by-step explanation:
Use Pythagoras's theorem.
[tex]A^{2}+B^{2} =C^{2} \\12^{2} +16^{2}= C^{2} \\400 = C^{2} \\\sqrt{400}= \sqrt{C^{2}\\\\[/tex]
20 = C
The function P(x) = –0.015x^2 + 1.2x – 11.5 gives the profit, in thousands of dollars, when a company sells a new product at x dollars per unit. Which of the following statements best interprets the average rate of change of this function from x = 50 to x = 55?
The profit increases by $375 for every $1 increase in the selling price.
The profit decreases by $375 for every $1 increase in the selling price.
The profit increases by $1875 for every $1 increase in the selling price.
The profit decreases by $1875 for every $1 increase in the selling price.
Answer:
The profit decreases by $ 375 for every $ 1 increase in the selling price.
Step-by-step explanation:
From the definition of the secant line we get that the average rate of change of [tex]P(x) = -0.015\cdot x^{2}+1.2\cdot x -11.5[/tex], where [tex]x[/tex] is the selling price of the product, measured in dollars per unit, is:
[tex]r = \frac{P(55)-P(50)}{55-50}[/tex] (1)
Now we evaluate the function at each bound:
x = 50
[tex]P(50) = -0.015\cdot (50)^{2}+1.2\cdot (50)-11.5[/tex]
[tex]P(50) = 11[/tex]
x = 55
[tex]P(55) = -0.015\cdot (55)^{2}+1.2\cdot (55)-11.5[/tex]
[tex]P(55) = 9.125[/tex]
Then, the average rate of change is:
[tex]r = \frac{9.125-11}{55-50}[/tex]
[tex]r = -0.375[/tex]
Hence, the profit decreases by $ 375 for every $ 1 increase in the selling price.
The statements that best interprets the average rate of change from x = 50 to x = 55 is (b) The profit decreases by $375 for every $1 increase in the selling price.
The profit function is given as:
[tex]P(x) = -0.015x^2 + 1.2x - 11.5[/tex]
Calculate P(x), when x = 50.
So, we have:
[tex]P(50) = -0.015(50)^2 + 1.2(50) - 11.5[/tex]
[tex]P(50) = 11[/tex]
Calculate P(x), when x = 55.
So, we have:
[tex]P(55) = -0.015(55)^2 + 1.2(55) - 11.5[/tex]
[tex]P(55) = 9.125[/tex]
The average rate of change from x = 50, to 55 is then calculated using:
[tex]m = \frac{P(55) - P(50)}{55-50}[/tex]
So, we have:
[tex]m = \frac{9.125 - 11}{55-50}[/tex]
[tex]m = \frac{-1.875}{5}[/tex]
Divide
[tex]m = -0.375[/tex]
The function is in 1000 units.
So, we have:
[tex]m = -0.375\times 1000[/tex]
[tex]m = -375[/tex]
-375 implies a decrease of $375 for every $1 increase in sales
Hence, the correct statement is (b)
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Eight year-old Alex is learning to ride a
horse. The trainer says that a horse
ages 5 years for every 2 human years.
The horse is now 50 years old in human
years. How can you determine the age
of the horse, in human years, when Alex
was born?
Hint: Use a table or a graph to
help you find the solution.
Show your work.
Answer:
The age of the horse, in human years, when Alex was born can be determined by simply deducting the Current age of Alex from the Current age of the horse in human years.
Therefore, the age of the horse, in human years, when Alex was born was 42 years.
Step-by-step explanation:
Current age of Alex = 8
Current age of the horse in human years = 50
Since the age of the horse is already stated in human years, it implies there is no need to convert the age of the horse again.
Therefore, since Alex is a human who was born 8 years ago, the age of the horse, in human years, when Alex was born can be determined by simply deducting the Current age of Alex from the Current age of the horse in human years as follows:
The age of the horse, in human years, when Alex was born = 50 - 8 = 42
Therefore, the age of the horse, in human years, when Alex was born was 42 years.
This can be presented in a table as follows:
Age of Alex Age of the Horse (in human years)
Eight years ago 0 42
Current age 8 50
WILL GIVE BRAINLIEST!!!!! Given the equation y = x – 2, you substitute 3 for y. Check all true statements below.
A. You replaced y with 3 temporarily.
B. This is wrong because you can only substitute for x.
C. The equation becomes 3 = x – 2
D. The value of x is 5.
E. The equation y = x – 2 is still true, just with specific values.
Answer:
y=x-2
a. 3=x-2
b. this isn't wrong??
c. 3=x-2
d. add 2 to both side so taht x is on its own so 5=x
e. yes
Answer:
C and E
Step-by-step explanation:
Im not entirely sure about A, because you are substituting so technically you changed it but the equation is still true (just as E says) but with more specific values.
B is not right because you can replace either y or x
D is not right because if you switch the equation to get the value of x you would make x= -3-2 which would be -5, not 5.
Hope this helped :)
Select the correct locations on the graph. Select the lines that represent functions.
Answer:
bruh there isnt a graph or anything we cant answer it
Step-by-step explanation:
Answer:
where is it
Step-by-step explanation:
In ΔBCD, the measure of ∠D=90°, BC = 81 feet, and DB = 52 feet. Find the measure of ∠C to the nearest tenth of a degree.
Answer:
39.9°
Step-by-step explanation:
m∠C = β
sin β = [tex]\frac{52}{81}[/tex] ⇒ β = arcsin [tex]\frac{52}{81}[/tex] ≈ 39.9°
Answer:
39.9
Step-by-step explanation:
sinC=
sin C = \{52}{81}
sinC=
81
52
C=\sin^{-1}{52}{81})
C=sin −1 ( 81 /52 )
C=39.9393\ 39.9^
C=39.9393≈39.9∘
A baseball camp is held at a complex that has 6 baseball diamonds. The coaches would like each diamond to have the same number of campers. Use divisibility rules to determine whether this is possible if 152 kids show up for the camp.
Answer:
Using divisibility rules, it is impossible to have exactly the same number of kids in each of the diamonds
Step-by-step explanation:
Here, we want to use divisibility rule to check for the possibility of 152 kids showing for the kids
Since we need exactly equal number of kids in each of the diamonds, we are going to test the possibilities that we can share 152 to have the same number of campers in each of the diamond
Mathematically 152/6 = 25.3333
Since we have a remainder for the division, it is impossible to share the campers equally in the six diamonds if 152 kids show up for the camp
We call a natural number "nice" if there are only even digits in its recording. How many "nice" four-digit numbers are there?
Answer:
I suppose that this refers to numbers like:
N = abcd
Where a, b, c and d are single digits.
We want to find the number of 4-digit numbers such that:
a, b, c and d are even numbers.
So let's count the number of options for each digit, where we impose that the possible digits must be even.
a: Here we have the options {2, 4, 6, 8} ( 0 is an even digit, but if we take a = 0, then this would be a 3 digit number) Then we have 4 options for a.
b: Here we have the options {0, 2, 4, 6, 8}. 5 options in total.
c: Here we have the options {0, 2, 4, 6, 8}. 5 options in total.
d: Here we have the options {0, 2, 4, 6, 8}. 5 options in total.
The total number of possible combinations will be equal to the product of the number of options for each selection.
C = 4*5*5*5 = 500
There are 500 "nice" numbers of 4-digits.
Johanna can jog 3,000 feet in 5 minutes. If she jogs at the same rate, how many feet can she jog in 8 minutes?
Answer:
4800
Step-by-step explanation:
3000\5=600
600*8=4800
What is the y-intercept. Describe how you know in both the table and the graph.
Answer:
(4,0)
Step-by-step explanation:
90 POINTS! PLEASE HELP!
Select the correct answer What is the solution for x in the equation 5/3 * x + 4 = 2/3* x Ο Α x = 12/7 OB B. x = -4 OC 12/7 OD x = 4
x=-4 hope it helps! good luck
In the 48 years between 1842, the average rate of erosion at horseshoe falls was 33 divided by 50 metre per year. In the 22 years between 1905 and 1927 the rate of erosion was 7 divided by 10 meter per year . Approximately how much total erosion occurred during these two time periods
Answer:
47. 08 meters
Step-by-step explanation:
Given that:
In 48 years between 1842 :
Rate of erosion = 33/50 meters per year
Between 1905 - 1927 (22 years)
Rate of erosion = 7/10 meters per year
Approximately how much total erosion occurred during these two time periods ;
Total erosion that occured within 1842:
Rate of erosion * number of years
(33/50)m * 48
0.66 meters * 48
= 31.68 meters
Total erosion that occured between 1905 - 1927:
Rate of erosion * number of years
(7/10)m * 22
0.7 meters * 22
= 15.40 meters
total erosion which occurred during these two time periods ;
31.68 meters + 15.40 meters
= 47.08 meters
Answer:
47. 08 meters
Step-by-step explanation:
Given that:
In 48 years between 1842 :
Rate of erosion = 33/50 meters per year
Between 1905 - 1927 (22 years)
Rate of erosion = 7/10 meters per year
Approximately how much total erosion occurred during these two time periods ;
Total erosion that occured within 1842:
Rate of erosion * number of years
(33/50)m * 48
0.66 meters * 48
= 31.68 meters
Total erosion that occured between 1905 - 1927:
Rate of erosion * number of years
(7/10)m * 22
0.7 meters * 22
= 15.40 meters
total erosion which occurred during these two time periods ;
31.68 meters + 15.40 meters
= 47.08 metersStep-by-step explanation:
A line passes through (2, -1) with slope 3.
What is the equation of the line in point-slope form?
A. y - 1 = 3(x + 2)
B. 3(y + 2) = x - 1
C. y - 2 = ( 1/3 x + 1)
D y + 1 = 3(x - 2)
Question 2 (1 point)
A video game has three villains who appear on screen at different intervals. One villain appears every 2 seconds, a second villain appears every
19 seconds, and a third villain appears every 10 seconds. How much time passes between the occasions when all three villains appear at the
same time?
Answer:
3 minutes tens seconds or 190 seconds
Step-by-step explanation:
Find the LCM.
Can you determine the solution of the |4x−2|≥−6 without solving?
Answer:
|4x-2|">"-6
add 2 to both sides
4x">"-4
divide both sides by 4
x">"-1
the ">" means greater than or equal to, I just don't have that character on my keyboard
Step-by-step explanation:
so the answer is x is greater than or equal to -1
IN: (-∞,-1]
for number line: You would write the number line from -1-10
then, you would put a closed dot on negative one, with an arrow going to the right!
Hope this helped! <3
Shannon's rain-catcher has 8 inches of water in it. Each day, 3 inches of water are added to the rain-catcher. Let y represent the total number of inches of water in the rain-catcher after x days. Express the equation in the form of y=mx+b .
Answer:
y= 3x + 8
Step-by-step explanation:
y = mx + b
m = 3 inches of water added each day
x = 8 inches of water at start
y= 3x + 8 is the required equation.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, Shannon's rain-catcher has 8 inches of water in it. Each day, 3 inches of water are added to the rain-catcher.
We have,
m = 3 inches of water added each day
x = 8 inches of water at start
Converting in y = mx + b, we get,
y = 3x+8
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pls give the answer
Answer:
It should be 245 m
Step-by-step explanation:
Separate it like this:
chop of the rectangle part and find the area of that and then add it to the trapezoid part
10*20 = 200.
Area of a trapezoid = 5+10/2 *6.
5+10 = 15. 1
5/2 = 7.5.
7.5*6 = 45.
45 + 200 = 245
What will be the slope of (3,-4) and (1,2)
Answer:
[tex]\boxed {m = 1}[/tex]
Step-by-step explanation:
Use the Slope Formula to determine the slope of two given points:
[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
First Point: [tex](x_{1}, y_{1})[/tex]
Second Point: [tex](x_{2}, y_{2})[/tex]
-Substitute both points:
First Point: [tex](3, -4)[/tex]
Second Point: [tex](1, 2)[/tex]
[tex]m = \frac{2 + 4}{1 - 3}[/tex]
-Solve for the slope:
[tex]m = \frac{2 + 4}{1 - 3}[/tex]
[tex]m = \frac{-2}{-2}[/tex]
[tex]\boxed {m = 1}[/tex]
Therefore, the slope is [tex]1[/tex].
17 points
Jeremy drove 18.04 miles on Monday, 18.4 miles on Tuesday, 17.68 miles
on Wednesday, and 17.86 miles on Thursday. Which shows the distances
written in order from greatest to least? *
17.68, 17,86, 18.04, 18.4
18.04, 18.4, 17.86, 17.68
17.86, 17.68, 18.4, 18.04
O 18.4, 18.04, 17.86, 17.68
Answer:
D. 18.4, 18.04, 17.86, 17.68
Step-by-step explanation:
Very Easy!
whats the answer to this I need this asap
will give brainliest
Answer:
I think is C
Step-by-step explanation:
PLEASE MARK ME AS BRAINLIEST
Mrs. Wally cut a 21 foot long ribbon into four equal lengths. How many feet long was each length of ribbon
the answer is:
Each equal length of ribbon is 5.25 ft
Step-by-step explanation:
21 divided by 4 is 5.25
To find the number of distributed quantities division operator is used. Each length of ribbon was 5.25 foot long.
What is division ?Division is a mathematical operation used to divide a number into equal parts. When a number is divided by another number, a quotient and remainder is obtained.
Given length of ribbon = 21 foot
Number of parts it has to be divided = 4.
So, to get the length of each part divide the total length by 4.
Thus, the length of each part is 21/4 = 5.25 foot.
Hence, the length Mrs. Wally' s each ribbon is 5.25 foot.
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Adult tickets to a basketball game cost $5. Student tickets cost $1. A total of $2,791 was collected on the sale of 1,275 tickets. How many of each type of ticket were sold?
9514 1404 393
Answer:
379 adult tickets896 student ticketsStep-by-step explanation:
Let 'a' represent the number of adult tickets sold. Then (1275-a) is the number of student tickets sold. The total revenue was ...
5a +1(1275 -a) = 2791
4a = 1516 . . . subtract 1275 and simplify
a = 379 . . . . . divide by 4
1275-a = 896
379 adult and 896 student tickets were sold.
which expression is equivalent to 2^3 square root x^2 • square root 16x if x > 0
Answer:
A
Step-by-step explanation:
The question is actually: 2 \sqrt[3]{x^3} ·\sqrt{16x}
The expression is equivalent to option A, [tex]\rm 8x \sqrt[6]{x}[/tex].
What is an Expression?An expression is a mathematical statement that consists of variables, constants, and mathematical operators.
The expression is [tex]\rm 2\sqrt[3]{x^2} . \sqrt{16x}[/tex]
The expression can be simplified as
[tex]\rm = 2 . 4 x^{2/3} x^{1/2}\\\\\=8 x ^{ 7/6}\\\\\\ = 8x x^{1/6}\\\\= 8x \sqrt[6]{x}[/tex]
Therefore, the expression is equivalent to option A, [tex]\rm 8x \sqrt[6]{x}[/tex].
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I need to know 2/7 divided by 6 =
Answer: 1/21
[tex]\frac{2}{7}:6=\frac{2}{7}.\frac{1}{6}=\frac{2}{42}=\frac{1}{21}[/tex]
Step-by-step explanation:
The sum of the ages of Martin and his son Sherwin is 47 years. Martin's age is 2 years more than 4 times the
age of Sherwin. Find their present age.
Answer:
In the picture above it shows how to answer the questions step by step. If there's a mistake, pls inform me.
what is 2.99 x 0.6 in dollars and cents plz help:(
Answer:
the answer is 1. 794
Step-by-step explanation:
Answer:1.794 is the answer to you question.
Step-by-step explanation:
What is accounting? What is the role of accounting in values?
Answer:
Found this on google, "Accounting creates values by maintaining transparency of accounts. Since man lives in the society, he has got a social life. For leading a social life he has to perform financial and material transactions daily. For carrying out these transactions successfully the existence of a sound environment is necessary."
Answer: Accounting is the process of recording financial transactions pertaining to a business.
Step-by-step explanation: The purpose of accounting is to accumulate and report on financial information about the performance, financial position, and cash flows of a business. This information is then used to reach decisions about how to manage the business, or invest in it, or lend money to it.
Find the slope I’m sorry I need help with this one I’m finding the answer but don’t understand it sorry
4x =64 find x in exponential equations
Answer:
X=16
Step-by-step explanation:
4/64
x=16
Find the value of a. The diagram is not to scale.
Answer: B. a = 144 degrees
Step-by-step explanation:
180=36+a
144=a
Step-by-step explanation:
hope it's obvious both the reason is being cointerior angle
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