he figure shows a parallelogram inside a rectangle outline:
A parallelogram is shown within a rectangle. The length of the rectangle is 3 over 5 foot, and the width of the rectangle is 2 over 5 foot. The two equal bases of the triangles outside the parallelogram are labeled 1 over 5 foot.
What is the area of the parallelogram?
1 over 25 square foot
11 over 25 square foot
3 over 25 square foot
4 over 25 square foot
Answers
Answer:
4/25 foot²
Step-by-step explanation:
Refer to attachment*
Consider the attachment first for a better understanding, now after considering the attachment you will gotta know that, the height of the parallelogram is just same as the width of the rectangle i.e (2/5) foot and but for the base of the parallelogram we can subtract the base of one triangle from the length of the rectangle, so it will give us (3/5) - (1/25) = (2/5), so now we have breadth as well as height of the parallelogram, so now, as area of a parallelogram is given by it's height times it's base, so we will be having
[tex]{:\implies \quad \sf Area_{(Parallelogram)}=\dfrac{2}{5}\times \dfrac25}[/tex]
[tex]{:\implies \quad \boxed{\bf{Area_{(Parallelogram)}=\dfrac{4}{25}\:\: sq.\:\:foot}}}[/tex]
Hence, Option D) is correct
Well, we have another method for it, we can subtract the area of both the triangles from the area of rectangle, and now,as their base of the triangle is (1/5) foot and height is same as the width of rectangle i.e (2/5) foots, so its area will be (1/2) times base times height, but as here are two triangles, so multiplying the area of one triangle by 2 will vanish 2, so now we just have
[tex]{:\implies \quad \sf Area_{(Parallelogram)}=\bigg(\dfrac{2}{5}\times \dfrac{3}{5}\bigg)-\bigg(\dfrac{1}{5}\times \dfrac{2}{5}\bigg)}[/tex]
[tex]{:\implies \quad \sf Area_{(Parallelogram)}=\dfrac{6}{25}-\dfrac{2}{25}}[/tex]
[tex]{:\implies \quad \boxed{\bf{Area_{(Parallelogram)}=\dfrac{4}{25}\:\: sq.\:\:foot}}}[/tex]
This also, proves that the correct answer is D)
Related Questions
A rectangle has one side equal to (2x+4) cm and a perimeter of (6x+4) cm. What is the area of the rectangle in terms of x?
Answers
The area of the rectangle in terms of x is 2x² - 8
A rectangle is a quadrilateral with four right angles in the Euclidean plane.
A region's size on a flat or curved surface is expressed in terms of area, a unit of measurement. A surface region or plane area is the area of an open surface or the boundary of a three-dimensional object, whereas a plane region or area refers to the area of a form or planar lamina.A perimeter is a closed path that surrounds, encircles, or defines a length in one dimension or a shape in two dimensions.Given one side of the rectangle is 2x+4 and the perimeter is 6x+4
Let the other side be y.
We know that:
perimeter = 2 × (sum of two sides)
or, 6x + 4 = 2 (2x+4+y)
or,6x + 4 = 4x + 8 + 2y
or, 2x - 4 = 2 y
or, y = x - 2
Now area of the rectangle = product of sides = (x - 2)(2x+4)
Area = 2x² - 4x + 4x - 8
or, Area = 2x² - 8
Hence the area of the rectangle in terms of x is 2x² - 8
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Assume z is a standard normal random variable. What is the value of z if the area between –z and z is 0.7580?
Answers
to the right is P(z> Z)
so P(z>Z) = 0.9909
P(z< Z) = 1- 0.9909 = 0.0091
Closest values from a z-table
P(z< -2.37) = 0.00889 (-0.00011 away)
p(z< -2.36) = 0.00914 (+0.00014 away)
so the answer must be (c) since it is between -2.36 and -2.37
In which direction does the parabola defined by the equation x = 2y^2 – 4 open?
Answers
Answer:
Upward
Step-by-step explanation:
Upward the graph looks like the above picture.
PLEASE HELP i realy don’t understand this at all
Answers
Check the picture below, recall that the radius of a circle is always the same length in the circle.
The manufacturer of color televisions can sell 1900 sets to his dealers at $575 each. If the price is $470, he can sell 2600 sets. The total cost of producing x television sets is C(x)=3300+608x−0.09x^2. Assuming the demand function is linear, find the price per set that will maximize profit. Round your answer to the nearest cent, if necessary.
Answers
Answer:
$545
Step-by-step explanation:
Finding the price that maximizes profit requires several steps. We need the demand function that tells quantity sold in terms of selling price. With this, we can express the cost and revenue functions in terms of selling price. The profit will be the difference between revenue and cost.
__
demandThe demand (q) is said to be a linear function of price (p). The equation for that can be written ...
q(p) = (q2 -q1)/(p2 -p1)(p -p1) +q1 . . . . . for two points (p1, q1) and (p2, q2)
Using the given demand points, this can be ...
q(p) = (1900 -2600)/(575 -470)(p -470) +2600
q(p) = -20/3(p -470) +2600
q(p) = -20/3p +5733 1/3
__
costThe cost function in terms of selling price can be found by substituting the q(p) equation for x in c(x). For the purpose of finding the maximum profit, we only need the marginal cost function:
c(q(p))' = c'(q(p))·q'(p) = (608 -0.18(q(p)))·(-20/3) = (608 -0.18(-20/3p +5733 1/3))(-20/3)
c'(p) = -8p +2826 2/3
__
revenueAs with cost, the function we need for finding the maximum profit is the marginal revenue function. Revenue is the product of price and demand, so the marginal revenue is ...
r(p) = p·q(p)
r'(p) = q(p) +p·q'(p) = (-20/3p +5733 1/3) +p(-20/3)
r'(p) = -40/3p +5733 1/3
__
maximum profitThe maximum profit is found where the marginal profit is zero. In turn, that is found where the difference between marginal revenue and marginal cost is zero:
P = R -C
P'(p) = 0 = r'(p) -c'(p) = (-40/3p +5733 1/3) -(-8p +2826 2/3)
0 = -16/3p +2906 2/3
16p = 8720 . . . . . multiply by 3, add 16p
p = 545 . . . . . . . price for maximum profit
The price per set that maximizes profit is $545.00.
Help help help math math
Answers
Answer:
Yes
Step-by-step explanation:
The relation here is we see that the y value is 1 less than the x value.
So, the function can be written as :
y = x - 1And this is clearly a linear functionThe table below represents the scores of ten students in Ms. Williams’s class on a math and science test.
Answers
Answer: the answer is A or the 1st one
Step-by-step explanation:
Answer:
the answer is the frist one
Step-by-step explanation:
Find the volume of the prism.
A drawing of a rectangular prism. It has length 1 foot, width mixed number one and one third feet and height one-half foot.
The volume is
cubic feet.
Answers
Answer:
2 thirds, or 0.666666666667
Step-by-step explanation:
The sum of two number is −16. One number is 20 less than the other. Find the numbers.
Answers
Answer:
-50 is your answer it is really easy just try to get -50
50 PTS I WILL MARK BRAINLIEST PLS HELP! A book store manager took several random surveys of customers to determine which book genre they purchased most frequently. This table shows the average of each survey.
Based on the data shown in the table, which conclusions can be made about the frequency that customers purchase a genre?
Select each correct answer.
On average, 1 out of 6 customers purchase fantasy books most frequently.
On average, 24% of the customers purchase autobiographies most frequently.
On average, 22% of the customers purchase romance books most frequently.
On average, 2 out of 10 customers, purchase health and wellness books most frequently.
Book Genre Average of Surveys
Autobiographies 24
Mystery 11
Romance 22
Health and Wellness 18
Fantasy 15
Answers
In an arithmetic sequence of numbers a1 = -4 and a6 = 46. Which of the following is the value of a12?
Answers
Answer:
a₁₂ = 106
Step-by-step explanation:
Given
a₁ (first term) = -4a₆ = 46Formula for nth term
aₙ = a₁ + (n - 1)dUsing that to expand a₆ and find d
a₆ = a₁ + (n - 1) d46 = -4 + (6 - 1)d50 = 5dd = 10Finding a₁₂
a₁₂ = a₁ + 11da₁₂ = -4 + 11(10)a₁₂ = 110 - 4a₁₂ = 106Answer:
[tex]a_{12}=106[/tex]
Step-by-step explanation:
Arithmetic sequence
General form of an arithmetic sequence: [tex]a_n=a+(n-1)d[/tex]
where:
[tex]a_n[/tex] is the nth terma is the first termd is the common difference between termsGiven:
[tex]a_1=-4[/tex][tex]a_6=16[/tex]To find the common difference (d), substitute the given values into the general formula and solve:
[tex]\begin{aligned}\implies a_6=(-4)+(6-1)d & =46\\ 5d-4 & =46\\ 5d & = 50\\ d & =10\end{aligned}[/tex]
Therefore, the equation for the nth term is:
[tex]\begin{aligned}a_n &=-4+(n-1)10\\& =10n-14 \end{aligned}[/tex]
To find the 12th term, substitute n = 12 into the equation:
[tex]\implies a_{12}=10(12)-14=106[/tex]
Base in your answer on exploration, what relationship exist between 30o
and 150o, 45o, and135o, and 60o and 120o?
Answers
Answer:
they all have a factor of 5
Step-by-step explanation:
fifty million of 94 million households watched the last episode of a popular television show. What percentage of households were not watching the show?
Answers
The percentage of households that were not watching the show were 46.81%.
Step-by-step explanation:In this case, we need to find the percentage of households that don´t watch the show. First, we need to know how much households don´t watch the show, this is:
[tex]94,000,000-50,000,000=44,000,000[/tex]
So, the households that were not watching the show were 44 million.
Now we can calculate the percentage, to find a percentage we use a division and to introduce the percentage units we multiply by 100.
[tex]\frac{44,000,000}{94,000,000}[/tex] × [tex]100=46.81[/tex]The percentage of households that were not watching the show were 46.81%.
If a kid is 120 cm tall and grows 4 percent taller how tall is he
Answers
im so sorry if im wrong, i hope u have a amazing day:)
Natalie Albert deposited checks totaling $1,735,97 into her savings account. She withdrew $100.00 while
depositing some coins. If her total deposit was $1,668.71, how much did Natalie deposit in coins?
Answers
1735.97-100=1635.97
1668.71-1635.97=32.74
Natalie Albert deposited checks totaling $1,735,97 into her savings account, she withdrew $100.00 while depositing some coins. If her total deposit was $1,668.71 then Natalie deposited $32.74 in coins.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let's call the amount Natalie deposited in coins "x".
We know that her total deposit was $1,668.71,
so we can write an equation:
1,735.97 - 100.00 + x = 1,668.71
Simplifying, we get:
1,635.97 + x = 1,668.71
Subtracting 1,635.97 from both sides, we get:
x = 32.74
Therefore, Natalie deposited $32.74 in coins.
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A pipe needs to be cut into pieces that are each 2/5 feet long. If the pipe is 10 feet long, how many pieces can be made from the pipe? Write your answer in simplest form.
Answers
Answer:
you can get 4 pieces
Step-by-step explanation:
2.5+2.5+2.5+2.5=10. or 2.5×4=10
NEED HELP WITH THIS QUESTION QUICK!!!
Answers
Answer:
56 degrees
90-34=56
Right-angle triangle, so the 2 angles should add to 90 to make 180 degrees
Hope this helps!
i need serious help lol
Answers
Answer:
A, C, can't see full answers
Step-by-step explanation:
a. 15/3=5 plus 10 is 15
Help picture below problem 12 will give brainlest
Answers
Answer:
68°
Step-by-step explanation:
triangle ODB is congruent to triangle FIL. Therefore, angle L is equal to angle B. So angle L is 68°
PLS HELP Use the net to find the lateral area of the prism. 8 15 17 9
answer choices 473 440 275 352
Answers
The lateral area of the prism is the area of the three rectangles in the middle of the net. (The two triangles are the bases of the prism, which don't count toward lateral area.) The total length of the three rectangular prism faces is (8 +15 +17) cm = 40 cm. The width of those rectangles is 9 cm. The lateral area will be the product of this length and width:
... lateral area = (40 cm)(9 cm) = 360 cm²
What are the domain and range of y=-5/6(x+2)^2-8?
PLEASE HELP WILL MARK BRAINIST AND GIVE OUT FREE MORE POINTS IF YOU ARE CORRECT I DO CHECK IT PLEASE AND THANK YOU !!
Answers
Answer:
Domain: allrealnumbers
Range: f(x) <= -8
Step-by-step explanation:
This equation shows that this shape is a parabola that is opening downwards (because of the negative in the -5/6)
This means it has a highest point. The x+2 means the curve is shifted/slid/tranlated to the right 2 units and the -8 at the end shows that it is slid/shifted/translated down 8 units. So the curve only exists starting from -8 and going down. That is the range f(x) <= -8
All upward and downward opening parabolas have a domain of all real numbers.
Let's see
[tex]\\ \rm\rightarrowtail y=\dfrac{-5}{6}(x+2)^2-8[/tex]
[tex]\\ \rm\rightarrowtail x\in R[/tex]
As x lies on numerator for all real numbers its true and never gets undefinedDomain is R
Now
[tex]\\ \rm\rightarrowtail y=\dfrac{-5(x+2)^2}{6}-8[/tex]
Vertex form of parabola:-
y=a(x-h)²+kOn comparing with this
Vertex=(h,k)=(-2,-8)Hence
Range :-
y≤-8Aldreba 2
Show all work
Answers
Answer:
rewrite f(g(-2))
plug in -2 in g(x)
g(x)=-2-3
g(x)=-5
now plug in -5 into f(x)
f(x)=-5^2
f(x)=25
25 is the answer
Answer:
-2x^3+6x^2
or simplified : -2x^2(x-3)
Step-by-step explanation:
Rewrite the statement as:
[tex]((x^2)(x-3))(-2)\\[/tex]
Distribute:
[tex](x^2*x-3*x^2)(-2)\\(-2)(x^3-3x^2)\\-2x^3+6x^2[/tex]
simplify by taking a common factor out, in this case, -2x^2:
[tex]-2x^2(x-3)[/tex]
A tabletop in the shape of a trapezoid has an area of 7,367 square centimeters. Its longer base measures
127 centimeters, and the shorter base is 85 centimeters. What is the height?
The height of the tabletop is
centimeters.
Answers
Answer:
69.5 cm
Step-by-step explanation:
Area trapezoid = 1/2 (b1+b2) * h = 7367
1/2(127+85) h = 7367 h=
(-x^2 -2) + (2x^2 + -1)
Answers
Answer:36
Step-by-step explanation:
x2 - 10x + 25 = 0 2x2 - 2x - 5 = 0 x2 - 16x = 36. This problem has been solved!
In 3x2 + 1 = 13, what is x called?
A
Coefficient
B
Expression
C
Variable
D
Range
Answers
Answer:
According to this problem, i would say the answer is c
Step-by-step explanation:
a variable examples are letters such as x, y, z, n
A researcher is studying the relationship between stress and diet among college students. The researcher recruits students by sending out an e-mail blast, and then includes in the sample the first 100 male and 100 female students who volunteer to participate. What type of sampling did the researcher use
Answers
Using sampling concepts, it is found that convenient sampling was used by the researcher to find the volunteers to participate.
How are samples classified?Samples may be classified as:
Convenient: Drawn from a conveniently available pool.Random: All the options into a hat and drawn some of them.Systematic: Every kth element is taken. Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.Stratified: Also divides the population into groups. Then, a equal proportion of each group is surveyed.In this problem, the first 100 male and first 100 female students sampled are the ones who volunteer to participate, and volunteering is associated with convenient sampling.
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Sophia goes to an icecream shop to get a medium ice cream that costs $4.50, Sophia only has $6.40 and toppings are $0.75 each. Write an inequality to find how many toppings Sophia can get .
Answers
Answer:
x ≤ 2
Step-by-step explanation:
4.5 = medium ice cream
0.75x = toppings, x = amount of toppings
Sophia has $6.4, so 4.5+0.75x has to be less or equal to that.
4.5 + 0.75x ≤ 6.4, solve
0.75x ≤ 1.9
x ≤ 2 8/15
BUT you cannot get half a topping or a fraction of a topping,
so, x ≤ 2 toppings.
Sophia can get 2 or less toppings.
Lucia has 48 markers and 64 stickers that she wants to give as favors for a party. She wants to put an equal number of markers and an equal number of stickers into each favor bag. She uses all the markers and stickers.
Use the drop-down menus to complete the statements below about the number of bags Lucia can make.
CLEARCHECK
The greatest number of bags Lucia can make is
. Each of these bags will have
markers and
stickers.
If she used more bags,
.
She could use
bags, but this is not the greatest number she could use.
Answers
The computation of the factors shows that the greatest number of bags that Lucia can make will be 16.
How to illustrate the factor?From the information given, Lucia has 48 markers and 64 stickers that she wants to give as favors for a party.
The computation of the factors shows that the greatest number of bags that Lucia can make will be calculated through then factors. This goes thus:
Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48
Factors of 64 = 1, 2, 4, 8, 16, 32, and 64.
Therefore, the highest common factor is 16.
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Answer:
16
Step-by-step explanation:
Marcus builds a brick wall that is 23 bricks across and 130 bricks high. Which is the best estimate of about how many bricks Marcus will use to build the wall
Answers
Answer: 2,990 Is the amount of Bricks Marcus will use for the wall
Step-by-step explanation:
If the wall is 130 bricks high and 23 bricks across then all you have to do is 130 x 23 which gives you 2,990
but since the question asks for best estimate just choose the answer closest to 2,990 unles they have 2,990 as an answer
Hope this Helps!
What is the surface area, in cm2, of the figure shown above ? Round your answer to the nearest tenth .
Answers
Answer:
Hope it helps................