The dimensions of a trapezoid are halved.
a) How will the area be affected?
b) If the area of the original trapezoid is 28 cm?, then what will the area of the smaller
trapezoid be?
Draw or add images here
Answers
Answer:
a) area will be 1/4 of the original
b) 7 cm²
Step-by-step explanation:
a)Consider the equation for the area of a trapezoid:
A = 1/2(b1 +b2)h
Now, halve each of the dimensions:
A' = 1/2((1/2)b1 +(1/2)b2)((1/2)h)
A' = (1/4)(1/2(b1 +b2)h) = 1/4A
The area is multiplied by the square of the scale factor: (1/2)² = 1/4.
__
b)The area of the smaller trapezoid will be ...
A' = 1/4A = (1/4)(28 cm²) = 7 cm²
Related Questions
A company manufactures and sells personalized stationery. The weekly fixed cost is $3850 and it cost $3.00 to produce each package of stationery. The selling price is $6.50 per package. How many packages of stationery must be produced and sold each week for the company to generate a profit?
The company will generate a profit if;
more than or equal to
more than
less than or equal to
less than
|blank|packages of stationery are produced and sold each week.
(sorry forgot to add that part in last question, hope this one is better)
Answers
Answer:
more than 1100
Step-by-step explanation:
The contribution margin for each package sold is ...
$6.50 -3.00 = $3.50
The number of packages that must be sold to cover fixed costs is ...
3.50n > 3850
n > 1100 . . . . . . . divide by 3.50
The company will generate a profit if more than 1100 packages are produced and sold each week.
_____
Additional comment
If exactly 1100 packages are sold, then costs are covered, but profit is 0. In order for profit to be positive, more than 1100 packages must be sold.
2 2/6 is equivalent to what?
Answers
What is the sales tax on a jacket priced at $275 if the sales tax rate is 7%?
Answers
Four times a number, minus 4, is equal to three times the number, plus 6. Find the number
Answers
Answer:
42
Step-by-step explanation:
Suppose theta is an angle in the standard position whose terminal side is in Quadrant II and tan0= -sqrt3 Find the exact values of the remaining five trigonometric functions of theta
Answers
The exact values of the remaining five trigonometric functions of theta are
sinθ = √3/2cosecθ = 2/√3cosθ = -1/2secθ = -2 cotθ = -1/√3Since tanθ = -√3.
The remaining five trigonometric functions of theta are sinθ, cosecθ, cosθ, secθ and cotθ.
The next trigonometric function of θ is cotθ.
cotθ = 1/tanθ
= 1/-√3
= -1/√3.
Also, tan²θ + 1 = sec²θ
Substituting tanθ = -√3 into the equation, we have
(-√3)² + 1 = sec²θ
3 + 1 = sec²θ
sec²θ = 4
secθ = ±√4
secθ = ±2
Since θ is in the quadrant II,
secθ = -2
Also, cosθ = 1/secθ
= 1/-2
= -1/2
Also, cot²θ + 1 = cosec²θ
Substituting cotθ = -1/√3 into the equation, we have
(-1/√3)² + 1 = cosec²θ
1/3 + 1 = cosec²θ
cosec²θ = 4/3
cosecθ = ±√(4/3)
cosecθ = ±2/√3
Since θ is in the quadrant II,
cosecθ = +2/√3
Also, sinθ = 1/cosecθ
= 1/2/√3
= √3/2
So, the exact values of the remaining five trigonometric functions of theta are
sinθ = √3/2cosecθ = 2/√3 cosθ = -1/2secθ = -2cotθ = -1/√3.Learn more about trigonometric functions here:
https://brainly.com/question/4515552
The population of certain city is projected to grow at the rate of r(t) = 400 1+ people/ 24 +7 year in interval (Osts 5) t years from now. The current population is 60 000. What will be the population 5 years from now?
Answers
The population 5 years from now would be 60482
The population growth rate is given as:
[tex]r(t) = 400(1 + \frac{2t}{24 + t^2})[/tex]
The value of t, 5 years from now is represented as:
t = 5
Substitute 5 for t in the function r(t).
So, we have:
[tex]r(5) = 400(1 + \frac{2 \times 5}{24 + 5^2})[/tex]
Evaluate the exponent
[tex]r(5) = 400(1 + \frac{2 \times 5}{24 + 25})[/tex]
Evaluate the products
[tex]r(5) = 400(1 + \frac{10}{24 + 25})[/tex]
So, we have:
[tex]r(5) = 400(1 + \frac{10}{49})[/tex]
Divide 10 by 49
[tex]r(5) = 400(1 + 0.204)[/tex]
This gives
[tex]r(5) = 400(1.204)[/tex]
Expand
[tex]r(5) = 481.6[/tex]
The current population is given as 60000.
So, the population (P) 5 years from now would be
[tex]P = 60000 + 481.6[/tex]
[tex]P = 60481.6[/tex]
Approximate
[tex]P = 60482[/tex]
Hence, the population (P) 5 years from now would be 60482
Read more about population functions at:
https://brainly.com/question/20115298
the number of Significant Figures in 13410000 *
Answers
Answer:
hhhhhhhhhhhhhhhhhhh
Step-by-step explanation:
hhhhhhhhhhhh
Answer:
4
Step-by-step explanation:
13410000
Sig Figs4
13410000
Decimals0
Scientific Notation1.341 × 107
E-Notation1.341e+7
Words thirteen million four hundred ten thousand
This question has two parts. First, answer Part A. Then, answer Part B.
Part A
Fill in the blank question.
Cassie wants to purchase a pair of binoculars that is on sale for $155.75. The sales tax rate in his county is 7%.
Calculate the amount of sales tax Cassie will pay on the purchase. Round to the nearest cent if necessary.
sales tax: $
Listen to the complete question
Part B
Fill in the blank question.
How much will Cassie pay in all for the pair of binoculars after sales tax is included? Round to the nearest cent if necessary.
total cost: $
Answers
Answer:
$10.12
Step-by-step explanation:
Step one:
given data
we are told that the cost of binoculars is $155.75
and also the sales tax is 7%
Step two:
We want to first solve for the sales tax which is 7% of $155.75
=7/100* 155.75
=0.070*155.75
=10.12
Cassie will pay a tax of $10.12
Also Cassie will pay a total amount of
= 155.75+10.12
=$165.87
Order each set of rational numbers from least to greatest 2.1,-0.3,0.261,-2.5
Answers
Answer:
i think -2.5 -0.3 0.261 2.1
If I is parallel to m. Find x and y
Answers
Answer: make me brainlist
Step-by-step explanation: x=104
As Earth circulates the sun, it travels at a
speed of 20 miles per second. Convert
this speed to kilometers per second. At
this speed, how many kilometers will
Earth travel in 8 seconds? Assume that 1
mile is equal to 1.6 kilometers.
Answers
So it travels 32 kilometres per second
For the second part, if the earth travels 32 kilometres in 1 second, then it will travel 32 x 8 kilometres in 8 seconds, which is equal to 256 km
Solve the Inequality for x.
-5x + 20 < 5
A) x > 5
B) x < 3
C) x > 3
D) x < -5
Thanks!!! :D
Answers
Answer:
x>3
Step-by-step explanation:
-5x+20<5
-5x<5-20
-5x<-15
5x>15
x>15/5
x>3
Answer:
A) x > 3
Step-by-step explanation:
[tex]-5x + 20 < 5\\\rule{150}{0.5}\\-5x + 20 - 20 < 5 - 20 \\\\-5x < -15 \\\\\frac{-5x < -15}{-5}\\\\\boxed{x > 3}[/tex]
The table shows the final score of four golfers.
Golfer Final Score
Joe
-2
Allen
-5
Tara
-8
Violet
-4
Whose score was the lowest? Whose was the highest? Select your answers from the drop-down lists.
score was the lowest.
score was the highest.
Students, draw anywhere on this slide!
PER Deck eractive Skoe
Answers
Lowest is Tara because it the most far from 0
Answer:
Joe score was the highest. Tara score was the lowest.
Step-by-step explanation:
What is the answer to y=-2(-3/2)-9
Answers
Answer:
-6
Step-by-step explanation:
y = -2 x -3/2 - 9
3 - 9 = -6
Hey there!
y= -2 (-3/2) - 9
-2(-3/2) = [3]
y = 3 - 9
y = -6
Therefore, your answer is: y = -6
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
6+√27/4-√3 can be written in the form r +s√3/13
where are both r and s integers
what are the values of r and s
Answers
[tex]r = \left(\dfrac{33}{13}\right)[/tex]
[tex]s = \left(\dfrac{10}{13}\right)[/tex]
Step-by-step explanation:
Let's multiply and divide the given fraction by the conjugate of the denominator:
[tex]\dfrac{6+\sqrt{27}}{4-\sqrt{3}}×\dfrac{4+\sqrt{3}}{4+\sqrt{3}}[/tex]
[tex]\;\;\;\;= \dfrac{24 + 6\sqrt{3} + 4\sqrt{3} + \sqrt{27}\sqrt{3}}{13}[/tex]
[tex]\;\;\;\;=\frac{1}{13}(24 + 10\sqrt{3} + \sqrt{81})[/tex]
[tex]\;\;\;\;=\frac{1}{13}(33 + 10\sqrt{3})[/tex]
[tex]\;\;\;\;=\left(\dfrac{33}{13}\right) + \left(\dfrac{10}{13}\right)\dfrac{\sqrt{3}}{13}[/tex]
We can see here that
[tex]r = \left(\dfrac{33}{13}\right)[/tex]
[tex]s = \left(\dfrac{10}{13}\right)[/tex]
The value of the variable 'r' and 's' will be 33 and 18, respectively.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The two equations are given below.
(6 + √27) / (4 - √3) and (r + s√3) / 13
Simplify the expression (6 + √27) / (4 - √3), then we have
[tex]\rightarrow \dfrac{6 + \sqrt{27}} { 4 - \sqrt3} \times \dfrac{4 + \sqrt3} { 4 + \sqrt3} \\\\[/tex]
⇒ [(6 + 3√3)(4 + √3)] / (4² - 3)
⇒ [(24 + 6√3 + 12√3 + 9)] / (16 - 3)
⇒ (33 + 18√3) / 13
Compare the expression (33 + 18√3) / 13 with (r + s√3) / 13, then the value of r and s will be given as,
r = 33
s = 18
The value of the variable 'r' and 's' will be 33 and 18, respectively.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ2
Which quantity is proportional to 40/8?
Answers
Answer:
5/1
10/2
15/3
20/4
25/5
30/6
35/7
Step-by-step explanation:
Set up an algebraic equation then solve. 1. When 3 is subtracted from the sum of a number and 10 the result is 2. The sum of 3 times a number and 12 is equal to 3. Find the number. 3. Three times the sum of a number and 6 is equal to 5 times the number. Find the number. 4. The width of a rectangle is 4 inches less than its length. If the perimeter measures 72 inches, find the dimensions of the rectangle. 5. The perimeter of a square is 48 inches. Find the length of each 2. Find the number. side.
Answers
Answer:
( x+10)-3= 2
x+10= 5
x= -5
3x+12= 3
3x= -9
x= -3
3( x+6 )= 5x
3x+ 18 = 5x
2x= 18
x =9
w= l-4 y= x-4
perimeter= 2l+ 2w
2(2x) + 2( x-4)
4x+2x-8 = 72
6x= 72+8
6x= 80
x= 13.3 width = 9.3 length = 13.3
4x=48
x = 12
each 2= 24
Change 3/4 to a decimal! Please explain step by step to get marked as brainliest
Answers
Answer:
The answer is 0.75
Step-by-step explanation:
The line in a fraction that separates the numerator and denominator can be rewritten using the division symbol. So, to convert a fraction to a decimal, divide the numerator by the denominator. If required, you can use a calculator to do this. This will give us our answer as a decimal.
Another method without a calculator is:
Step 1: Find a number you can multiply by the bottom of the fraction to make it 10, or 100, or 1000, or any 1 followed by 0s.
Step 2: Multiply both top and bottom by that number.
Step 3. Then write down just the top number, putting the decimal point in the correct spot (one space from the right hand side for every zero in the bottom number)
Example:
Convert 3/4 to a Decimal:
Step 1: We can multiply 4 by 25 to become 100
Step 2: Multiply top and bottom by 25. It gives us 75/100.
Step 3: Write down 75 with the decimal point 2 spaces from the right (because 100 has 2 zeros);
Answer = 0.75
When solving a quadratic in the form ax2 + bx + c = 0 we are really finding the x–intercepts. These x–intercepts are also called roots. What is another term for roots or x-intercepts? put it in a full sentence for me please
Answers
Answer:
solutions
Step-by-step explanation:
Another term for the roots or x-intercepts of the standard-form quadratic equation is "solutions." These are the values of x that make the equation true.
Madie drove 200 miles at a speed of 50 miles per hour. Which equation will help you find the number of hours she was driving?
StartFraction 50 miles Over 1 hour EndFraction = StartFraction 200 miles Over question mark hours EndFraction
StartFraction 50 miles Over 1 hour EndFraction = StartFraction question mark hours Over 200 miles EndFraction
StartFraction 200 miles Over 1 hour EndFraction = StartFraction 50 miles Over question mark hours EndFraction
StartFraction 200 miles Over 1 hour EndFraction = StartFraction question mark hours Over 50 miles EndFraction
Answers
she drove for 4 hours
Answer:
the person above me is wrong its not an option for me ;-;
Step-by-step explanation:
Mary has 18 ounces of apple chips she evenly portions the apple chips between four containers how many ounces of apple chips are in one container
Answers
Answer:
4.5 ounces
Step-by-step explanation:
18/4=4.5
4.5•4=18
Last week, the price of oranges at the farmers market was $1.75 per pound. This week, the price has decreased by 15%. What is the price of
oranges this week?
Answers
Answer:
11.6 (6 is repeating)
Step-by-step explanation:
1.75 divided by 15% of 75
URGENNTTT PLEASE ILL GIVE 50
Take Triangle ABC, A(2,-1), B(1,4) and C(-2,2). Do
the series of mappings to find A'B'C'.
First translate
it 3 units to the right and 2 units up, next reflect
about the x-axis, and finally rotate 180 degrees.
Answers
Answer:
(3-2)
Step-by-step explanation:
Algebra 1
What is the greatest possible error for a measurement of 4 inches?
inches
Answers
( I will give brainliest! ) What is the simplified expression of
4x + 2(3x + 7) - 7x?
Answers
Answer:
[tex]3x + 14[/tex]
Step-by-step explanation:
Step 1: Distribute
[tex]4x + 2(3x + 7) - 7x[/tex]
[tex]4x + (2 * 3x) + (2 * 7) - 7x[/tex]
[tex]4x + 6x + 14 - 7x[/tex]
Step 2: Combine like terms
[tex]4x + 6x + 14 - 7x[/tex]
[tex](4x + 6x - 7x) + 14[/tex]
[tex]3x + 14[/tex]
Answer: [tex]3x + 14[/tex]
LAST ATTEMPT MARKING AS BRAINLIEST!! (Pythagorean theorem )
Answers
Your welcome
The hypotenuse AB of the right triangle ABC is parallel to the axis of the abscess. Find the length of the hypotenuse if A (-1; 1) and C (3; -4)
Answers
Answer:
10.25
Step-by-step explanation:
The slope of AC is given by the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (-4 -1)/(3 -(-1)) = -5/4
Then the slope of CB is the opposite reciprocal, 4/5. The equation of line CB in point-slope form is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
y -(-4) = 4/5(x -3) . . . . line CB
When y = 1 (to match the y-value of A), then ...
1 +4 = 4/5(x -3)
5(5/4) = (x -3) . . . . . multiply by 5/4
6.25 +3 = x = 9.25 . . . . add 3
Point B is (9.25, 1).
The length of the hypotenuse is ...
9.25 -(-1) = 10.25
the price of an article is Marked 25% above the cost price .if it is solid the profit of Rs.500 after allowing 15% discount .what will be it's selling price
Answers
Answer:
Rs 8500
Step-by-step explanation:
For a cost price of c, the marked price is ...
marked = c +25%·c = 1.25c
After the 15% discount, the sale price will be ...
s = marked -15%·marked = 0.85·marked = (0.85)(1.25c) = 1.0625c
The profit will be the difference between the sale price s and the cost c:
p = s -c
500 = (1.0625c) -c = 0.0625c
Then the cost is ...
500/0.0625 = c = 8000
and the sale price is ...
s = c +p = 8000 +500 = 8500 . . . rupees
The selling price will be Rs 8500.
Três torneiras enchem uma piscina em 10 horas quantas horas levarão 10 torneiras para encher 2 piscinas
Answers
Answer:
Step-by-step explanation:
Choose the equation that has m = 5 as the solution.
m + 4 = 20
m – 3 = 8
22 + m = 25
12 = m + 7
HElP ASAP!
Answers
Answer:
12 = m + 7
Step-by-step explanation:
When you plug in 5 to the above equation, you get 12 = 5 + 7. This is a true statement, so the answer is 12 = m + 7. Hope this helps!