Answers
It will be the first option.
The statement is option (A) ∠ ADB and ∠CBD satisfies the alternate interior angle theorem.
What is a rectangle?A rectangle is one of the types of quadrilaterals in which all four angles are right angles or equal to 90 degrees. It is four-sided polygon in which the opposite sides are parallel and equal to each other.
For the given situation,
The diagram below shows the rectangle ABCD.
The diagonals AC and BD are drawn.
From the diagram,
According to alternate interior angle theorem, [tex]\angle ADB[/tex] and [tex]\angle CBD[/tex] are alternate interior angles .
Hence we can conclude that the statement is option (A) ∠ ADB and ∠CBD satisfies the alternate interior angle theorem.
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Related Questions
write in graphing form please! A parabola that opens down with no stretch factor that has a vertex of (-6,5)
Answers
(x+6)^2 + 5
Hope this helps!
Consider the equation 2x-3(2x-1)=3-4x. solve the equation for x. for each step, identity the property used to write an equivalent equation.
Answers
2x - 6x + 3 = 3 - 4x
Now, simplify.
-4x + 3 = - 4x
Cancel out the double "4x"
3 = 3
Since both side have an equal answer, there in an infinite number of answers.
Hope this helps! ☺♥
When matter changes state, what two things are always conserved?
Answers
In a change of state, mass and energy are the two things that are always conserved, in accordance with the law of conservation of matter and the first law of thermodynamics, respectively.
When matter changes state, the two things that are always conserved are mass and energy. This is explained by the law of conservation of matter, which states that the total mass of the products must equal the total mass of the reactants in a chemical reaction, and the law of conservation of energy, often referred to as the first law of thermodynamics.
In any given closed system, neither mass nor energy is created or destroyed, but can be transformed from one form to another. For example, when a substance burns, its matter is not lost but is instead transformed into other substances with the same total mass. Likewise, energy can be moved or transformed, but the total amount of energy remains constant. These principles apply to both living and non-living systems, keeping the total quantity of matter and energy fixed in the universe.
A restaurant charges an automatic gratuity of 18% on tables with more than 6 people. A party of 8 had a bill of p. Which expression can be used to find the total cost of the meal with the gratuity?
Answers
Answer: the answer is 1.18p
Step-by-step explanation:
It is trust me (;
If EG=25 and point F is 2/5 of the way between E and G, find the value FG. The drawing is not to scale.
a. 12.5
b. 10
c. 20
d. 15
d. 7
Answers
This can be done by multiplying the two numbers.
2/5 × 25 = 10
10 is the distance from E to F.
So now that you have EF and know the overall length of EG (25), you can easily find FG.
25 - 10 = 15
The answer is:
d. 15
Solve for x: −3 |x + 7| = −12
Answers
then you get |x + 7| = 4
what you do now is make two separate equations
drop the absolute value signs
x + 7 = 4 OR x + 7 = -4
subtract 7 from both sides AND BOTH EQUATIONS
x = -3 OR x = -11
lets check it!
-3 |-3 + 7| = -12 -3 |-11 + 7| = -12
-3 |4| = -12 -3 |-4| = -12
-3 (4) = -12 -3 (4) = -12
yep! your answers are x = -3 OR x = -11
i hope this helps!!
Thomas paid $5 for a multicolor file folders. There were 100 folders in the box .what was the cost of each folder?
Answers
5/100 = $0.05
Therefore, the cost of each folder was $0.05
Hope I helped :)
0.05
:))
Find f(x) and g(x) so that the function can be described as y = f(g(x)).
y = eight divided by x squared + 2
Answers
stella writes 1/7 of a page in 1/5 of a minute. how many minutes doesn’t it take her to write a full page?
Answers
It takes Stella 1.4 minutes to write a full page, calculated by setting up a proportion based on her rate of writing [tex]\frac{1}{7}[/tex] of a page in 1/5 of a minute.
Stella writes [tex]\frac{1}{7}[/tex] of a page in [tex]\frac{1}{5}[/tex] of a minute. To calculate how many minutes it takes her to write a full page, we can set up a proportion. Since 7/7 would make a full page, we'd need Stella to write seven times as much as she does in 1/5 of a minute. So, the math to find the time for a full page looks like this:
[tex]\frac{1}{7}[/tex] page : [tex]\frac{1}{5}[/tex] minute = 7/7 page : x minutes
Now multiply both sides by (1/5) minutes to isolate x:
[tex]\frac{1}{7}[/tex] / [tex]\frac{1}{5}[/tex] = 1/x
Cross multiply to solve for x:
[tex]\frac{1}{7}[/tex] * x = [tex]\frac{1}{5}[/tex]
x = [tex]\frac{1}{5}[/tex] / [tex]\frac{1}{7}[/tex]
x = [tex]\frac{1}{5}[/tex] * (7/1)
x = 7/5 minutes
x = 1.4 minutes
Therefore, it takes Stella 1.4 minutes to write a full page.
One number is 4 less than a second number. twice the second number is 19 less than 5 times the first. find the two numbers.
Answers
What is 334.54 + 198 grams
Answers
hope this helps
Question: Is this a significant figures question?
ANSWER round to the significant figures: 533 grams
When you do addition you use the number with the least number of decimals places to determine how many decimal places will be in your answer. There are no decimal places in 198 so you would round before the decimal place in the answer (ones place).
What is the slope of this graph?
Answers
Now, on the line, I plotted (0, 2) and (-2, 10).
You would now plug this into the rise/run formula.
The formula is [tex] \frac{y2 - y1}{x2 - x1} [/tex]
The equation would become,
[tex] \frac{10 - 2}{-2 - 0} [/tex] = [tex] \frac{8}{-2} [/tex] = -4
I believe the answer would be -4.
I hope this helps!
What is the best approximation for the measure of angle ABC?
Answers
cos(x) = 0.525
answer
C.
x = 58.3"
Find the angular velocity of a wheel that makes 30 revolutions in 10 seconds.
1.5π rad/sec
3π rad/sec
6π rad/sec
Answers
angular velocity in rads / sec = 60pi / 10 = 6pi Answer
The angular velocity of the wheel is 6π rad/sec.
What is angular velocity?Angular velocity is the speed at which the angle between two bodies changes as an item rotates or revolves around an axis.
In one revolution,
The angular velocity is 2π rad/sec.
In 30 revolutions,
The angular velocity is 2π x 30 rad/ 10sec.
The angular velocity is 60π rad/sec.
The SI unit of angular velocity is radians per second.
Hence, The wheel's angular velocity is 6 rad/sec.
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The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 3 cm/s. when the length is 20 cm and the width is 10cm, how fast is the area of the rectangle increasing
Answers
b = breadth of the rectangle,
a = area of the rectangle,
t = time,
So, [tex] \frac{dl}{dt} [/tex] = 8 cm/s &
[tex] \frac{dw}{dt} [/tex] = 3 cm/s
Area of the rectangle, a = l × w
Differentiate the equation with respect to t,
[tex] \frac{da}{dt} [/tex] = l × [tex] \frac{dw}{dt} [/tex] + w × [tex] \frac{dl}{dt} [/tex]
[tex] \frac{da}{dt} [/tex] = 20 × 3 + 10 × 8
[tex] \frac{da}{dt} [/tex] = 60 + 80
[tex] \frac{da}{dt} [/tex] = 140 [tex] cm^{2} [/tex]/s
Therefore, the correct answer is 140 [tex] cm^{2} [/tex]/s.
dl/dt = 8 (rate of length increasing)
dw/dt = 3 (rate of width increasing)
l = 20 (when the length is 20)
w = 10 (when the width is 10)
The unknown is dA/dt (the rate the area is increasing)
Start with the formula for the area of a rectangle
A = w*l
Find the derivative of it
d/dt(A) = d/dt(w*l) Use the multiplication rule
dA/dt = w(dl/dt) + l(dw/dt)
Substitute in what is known from above
dA/dt = 10(8) + 20(3) = 80+60 = 140
The area is increasing 140 square centimeters per second
What is the square root of 53 rounded to the nearest hundreth
Answers
7.28010988928
A right triangle has one angle that mesures 23. The adjacent leg measures 27.6 cm and the hypotenuse measures 30cm.
What is the approximate area of triangle? Round to the nearest tenth
Area of the triangle =1/2bh
A:68.7cm^2
B.161.7cm^2
c.381.3cm^2
D450.cm^2
Answers
tangent (23) = opposite/adjacent (TOA), where opposite is altitude and adjacent is base
So tangent (23) = alt/27.6cm
alt = 27.6×tan23 = 27.6×0.424
alt = 11.72cm
So now area = 1/2 (b)(h), where h=alt
area = 1/2 (27.6cm)(11.72cm) = 161.7cm^2
[tex] 161.7{cm}^{2} [/tex]
So the correct answer is [B.]
Se implicit differentiation to find an equation of the tangent line to the curve at the given point.7x2 + xy + 7y2 = 15, (1, 1) (ellipse)
Answers
(xy+14y)|dy/dx = -14x
dy/dx = -14x /(xy+14y)
dy/dx |(x=1,y=1) : -14(1) / (1+14) = -14/15
using
y-y1=/x-x1 = -14/15
y-1/x-1 = -14/15
15y-15 = -14x+14
15y+14x -15-14=0
14x +15y = 29
Kevin picked 13 more apples than Andy. if Kevin picked 30 apples, how many did Andy pick ? Let A= the apples sandy picked
Answers
30-13=17
Billie and Toni are driving from Chicago to Phoenix. The first day they drove 420 miles. They want to drive at 65 miles per hour for the rest of their trip. a. Write an algebraic expression to represent the situation. b. If they drive 8 hours a day for the next two days, how far have they traveled by the end of the third day?
Answers
A. We are given that they already drove 420 miles and an additional of 65 miles per hour. Therefore distance covered is:
d = 420 + 65 t
where d is distance and t is time
B. If they drove 8 hours per day for 2 days, then total time is t = 16 hours, hence:
d = 420 + 65 * 16
d = 1460 miles
1) Which statement about 5y = 2x is true?
A) The equation represents a direction variation whose consent of variations is 5/2.
B) The equation represents a direct variation whose consent of variations is 2/5.
C) The equation does not represent a direction variation.
D) The equation does not represent a line through the origin.
2) What is the equation of the graph of y = |x| shifted 3 units up?
A) y = |x| – 3
B) y = |x| + 3
C) y = |x + 3|
D) y = |x – 3|
3) Two parallel lines form an inconsistent system of equations that has no solution.
True
or
False
Answer all and Show or Explain your answer :)
Answers
2) B f(x) + k is a vertical shift up k units
3) True Because parallel lines have the same slope and different y - intercepts they do not touch thus called inconsistent. Since they do not touch they will not have a solution.
A bouncing ball reaches a height of 27 feet at its first peak, 18 feet at its second peak, and 12 feet at its third peak. Describe how a sequence can be used to determine the height of the ball when it reaches its fourth peak.
Answers
A= value of the first term
n= the number of the term you want to find
r= common ratio
value of r is = 2/3 because 27 times 2/3 = 18 which is the second term
n = 4 since you want to find the 4th term in the sequence
Plug it in and results are
4th term = 27(2/3)^(4-1) = 8
The answer is 8
Hope this helps!
[tex]a_n=a_{n-1}-\frac{a_{n-1}}{3}[/tex]
Here:
[tex]a_4=a_3-\frac{a_3}{3}=12-\frac{12}{3}=12-4=8[/tex]
Square tiles 9-inches on a side cover the floor of a rectangular room exactly. the border tiles are white and all other tiles are blue. the room measures 18 feet by 15 feet. how many tiles are white
Answers
18 ft × (12in/1ft)= 216 in
15 ft × (12 in/1ft)= 180 in
divide each side of the room by 9 inches to get number of white tiles per a wall
wall 1(18ft): 216in/9in= 24 white tiles
wall 2(15ft): 180in/9in= 20 white tiles
wall 3(18ft): 216in/9in= 24 white tiles
wall 4(15ft): 180in/9in= 20 white tiles
Lastly, add up all the white tiles and subtract 4 (the tiles that we counted twice because they were the corner tiles and touched both walls)
24+20+24+20-4= 84 white tiles total
PLEASE HELP!!! Will give brainliest!
Answers
Hope this helps!
Leena knits 10 rows in 12 min. At this pace, how long will it take her to knit the next 25 rows? Enter your answer in the box. min
Answers
10 rows = 12 mins
10 rows = 12 mins
5 rows = 6 mins
----- -----
25rows 30 mins
5r=6m
25r=?m
25r=30m
It will take her 30 minutes to knit 25 rows
Sandy bought a soft drink for 2 dollars and 6 candy bars. she spent a total of 20 dollars. how much did each candy bar cost
Answers
A warehouse is packing materials to ship out to a customer. A small box has the dimensions of x inches, (x+ 2) inches and (2x) inches. Where x is the length in inches of width. A large box has the dimensions of (x+5) inches, (x + 7) inches and (3x) inches.
*Recall that Volume = (Length)(Width)(Height)
Part 1: Write an expression that represents the dimensions of the small box.
Part 2: Write an expression that represents the dimensions of the large box.
Part 3: What is the difference in the volumes of the two boxes? Show or explain or work.
Answers
I ended up finding the first 2
vsmall=x(x+2)(2x)
vlarge=(x+5)(x+7)(3x)
I found those on answers . com
V=volume...
I just need #3
1. The expression that represents the dimensions of the small box is (2x³ + 4x²).
2. The expression that represents the dimensions of the large box is (3x³ + 36x² + 105x).
3. The difference in the volumes of the two boxes is (x³ + 32x² + 105x)
What is the volume of the box?1.
Small box:
x inches,
(x+ 2) inches and
(2x) inches
Volume = length × width × height
= x × (x + 2) × (2x)
= (x² + 2x) × 2x
= 2x³ + 4x²
2.
Large box:
(x+5) inches,
(x + 7) inches and
(3x) inches.
Volume = length × width × height
= (x + 5) × (x + 7) × (3x)
= 3x³ + 36x² + 105x
4.
Difference in volume = Large box - Small box
= (3x³ + 36x² + 105x) - (2x³ + 4x²)
= 3x³ + 36x² + 105x - 2x³ - 4x²
= x³ + 32x² + 105x
Therefore, x³ + 32x² + 105x is the expression which represents the volume of the box.
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The exchange rate is £1 = €1.12 how many £ would I get for €336
Answers
so 336€ = 336/1.12£ = 300£
Steven wants to buy a $500 bicycle. Steven has no money saved, but will be able to deposit $45 into a savings account when he receives his paycheck each Friday. However, before Steven can buy the bike, he must give his sister $85 that he owes her. For how many weeks will Steven need to deposit money into his savings account before he can pay back his sister and buy the bike?
Answers
If he first has to pay back $85 to his sister, then he'd be able to do that by the second week. 45+45 is 90 so he will have $5 once he pays back his sister. In 3 weeks, He'll have 50 dollars. In four weeks, he'll have 95 dollars. In five weeks, he'll have 140 dollars. In six weeks, he'll have 185 dollars. In several weeks, he'll have 230 dollars. In eight weeks, he'll have 275 dollars. I think you get the gist by now. I calculated that in 13 weeks he will have enough money to pay back his sister and buy his bike.
The town Atlanta needs $14,000 for a new playground Lanzetta Elementary school raise $5358 Lantana middle school race $2834 Atlanta high school raised eig The town Atlanta needs $14,000 for a new playground Lanzetta Elementary school raise $5358 Lantana middle school race $2834 Atlanta high school raised $4132 about how much more do they need to raise choose the best estimate
Answers
Lantana Mid. Sch raised 2834....round to 3,000
Atlanta High Sch. raised 4132...round to 4,000
they need 14,000...they have (5,000 + 3,000 + 4,000) = 12,000....so they will need (14,000 - 12,000) = 2,000 more....keep in mind, these are estimates...not exact answers
To find out how much more money is needed for the Atlanta playground, add the amounts raised by each school and subtract from the total amount needed. The schools have raised $12,324, so they still need about $1676. Therefore, $1676 more is required to meet the goal.
Let's calculate how much money the schools have already raised:
Lanzetta Elementary School raised $5358Lantana Middle School raised $2834Atlanta High School raised $4132First, add these amounts together:
$5358 + $2834 + $4132 = $12,324Next, subtract the total amount raised from the total money needed:
$14,000 - $12,324 = $1676Therefore, the town of Atlanta still needs to raise about $1676 for the new playground.