What is the area of trapezoid ABCD ? (Enter your answer as a decimal or whole number)
Answers
bear in mind that, the "bases" are the two parallel sides, and the height is the distance between them.
[tex]\bf \textit{area of this trapezoid}\\\\ A=\cfrac{AB(BC+AD)}{2}\\\\ -------------------------------\\\\ \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) A&({{ -1}}\quad ,&{{ 5}})\quad % (c,d B&({{ 3}}\quad ,&{{ 2}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ AB=\sqrt{[3-(-1)]^2+[2-5]^2}\implies AB=\sqrt{(3+1)^2+(2-5)^2} \\\\\\ AB=\sqrt{16+9}\implies AB=\sqrt{25}\implies \boxed{AB=5}[/tex]
[tex]\bf -------------------------------\\\\ \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) B&({{ 3}}\quad ,&{{ 2}})\quad % (c,d C&({{ 0}}\quad ,&{{ -2}}) \end{array} \\\\\\ BC=\sqrt{(0-3)^2+(-2-2)^2}\implies BC=\sqrt{9+16} \\\\\\ BC=\sqrt{25}\implies \boxed{BC=5}[/tex]
[tex]\bf -------------------------------\\\\ \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) A&({{ -1}}\quad ,&{{ 5}})\quad % (c,d D&({{ -13}}\quad ,&{{ -11}}) \end{array} \\\\\\ AD=\sqrt{[-13-(-1)]^2+[-11-5]^2} \\\\\\ AD=\sqrt{(-13+1)^2+(-16)^2}\implies AD=\sqrt{144+256} \\\\\\ AD=\sqrt{400}\implies \boxed{AD=\sqrt{20}}[/tex]
so, the area for this trapezoid is then
[tex]\bf A=\cfrac{5(5+20)}{2}\implies A=\cfrac{125}{2}\implies A=62\frac{1}{2}[/tex]
Area of the trapezoid ABCD is
[tex]62\frac{1}{2}[/tex]
Given :
The diagram of a trapezoid ABCD
Area of trapezoid is [tex]\frac{base1+base2}{2} \cdot height[/tex]
Lets find the length of base 1 and base 2 using distance formula
Base 1 is AD. find the distance AD
[tex]AD=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\\AD=\sqrt{\left(-13-\left(-1\right)\right)^2+\left(-11-5\right)^2}\\AD=20[/tex]
Now we find out BD that is base 2
[tex]BD=\sqrt{\left(0-3\right)^2+\left(-2-2\right)^2}\\BD=5[/tex]
Now find out height AB
A is (-1,5) and B(3,2)
[tex]AB=\sqrt{\left(-1-3\right)^2+\left(5-2\right)^2}\\AB=5\\[/tex]
[tex]Area =\frac{AD+BC}{2} \cdot AB\\Area=\frac{20+5}{2} \cdot 5\\Area=\frac{125}{2}\\Area=62\frac{1}{2}[/tex]
Area of the trapezoid ABCD is
[tex]62\frac{1}{2}[/tex]
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Related Questions
For a laboratory assignment, if the equipment is working, the density function of the observed outcome x is f(x) = 2(1 − x), 0
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The Variance is [tex]\int\limits^1_0 {(x- \mu)^2(2(1-x))} \, dx[/tex].
What is Variance?Variability is measured by the variance. The average of the squared deviations from the mean is used to calculate it. The degree of spread in your data set is indicated by variance. The variance is greater in respect to the mean the more dispersed the data.
Given:
E(x) = [tex]\int\limits^1_0 {x(2(1-x))} \, dx[/tex]
= [tex]\int\limits^1_0 {(2x - 2x^2)} \, dx[/tex]
For the variance, if μ is the mean, then
Var(x) = E( x- μ)²
= [tex]\int\limits^1_0 {(x- \mu)^2(2(1-x))} \, dx[/tex]
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A problem states
there are 5 more girls than boys and girls there are 27 students in the class in all How many boys are in the class
What are the unknowns in this problem
A Number of students in the class
B The number of boys in the class
C The number of girls in class
D The number of boys and the number of girls in class
Answers
the problem only stats there are 27 students and that there are 5 more girls than boys
it does not say how many boys or how many girls there are so D should be the answer
A reasonable APR to pay for a 3-year automobile loan is
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Which of the following is a function equivalent to f(x) = 4(1.8)2x?
f(x) = 4(3.24)x
f(x) = 4(3.24x)
f(x) = 12.96x
f(x) = 51.84x
Answers
Answer:
A: f(x) = 4(3.24)x
(you forgot to put the "^" symbol before the X to show it is rising to "2x",, AKA an exponent, but that's ok <3
Step-by-step explanation:
Please do not listen to the other answer! It is wrong and i will show you why.
First we need to take a look at the exponent and the number in parentheses. If anyone remembers, we need to use the distributive property to distribute the '2' in the exponent '2x' to the number(s) inside the parentheses.
So you would go: 1.8 x 2 = 3.24
You would then put the 3.24 in the place of the 1.8 to give you:
f(x) = 4(3.24)^x
Now, you may ask, 'biscuit, why do we keep the exponent 'x'? shouldn't we put it inside the parentheses?',, and to that i say no! We only used the 2 from the exponent, so the x stays in it's place.
You also might ask 'biscuit, why don't we go a step further and multiply the 4 by the 3.24?',, and to that I also say no! Remember, the question asked us to find a function equivalent to our original equation, not solve the whole equation <3
If you have any questions please don't hesitate to ask!
-Biscuit08
Trigonometric area formula: Area = 1/2 ab sin(c)
What is the area of triangle DEF? Round to the nearest tenth of a square unit.
10.3 square units
18.0 square units
20.0 square units
20.6 square units
Answers
Answer:
1. 10.3 square units.
Step-by-step explanation:
The general formula for area of triangle is [tex]\frac{1}{2}(\text{ Base}\times\text{ Height}})[/tex]. We can also find area of a triangle using trigonometric area formula.
[tex]Area=\frac{1}{2} ab\text{ sin}(c)[/tex], where a represents length of base and height of triangle is represented by [tex]b\text { sin}(c)[/tex].
We have been given two angle measures but we can only use sine of included angle whose two side lengths are given. In our triangle the angle that measures 31 degrees in included angle of sides EF and DF.
Now let us substitute our given values in the above formula.
[tex]Area=\frac{1}{2}\times 8\times 5\text{ sin}(31)[/tex]
[tex]Area=\frac{1}{2}\times 8\times 5\times 0.51503807491[/tex]
[tex]Area=4\times 5 \times 0.51503807491[/tex]
[tex]Area=20 \times 0.51503807491[/tex]
[tex]Area=10.3007614982\approx 10.3[/tex]
Therefore, the area of triangle DEF is 10.3 square units and 1st option is the correct choice.
Answer:
10.3= the awnser
Step-by-step explanation:
just took test and got it right.
Find the interest rate for the given deposit and compound amount. $4600 accumulating to $5994.78, compounded monthly for 4 years.
Answers
A = P (1 + r/n)^nt
where P is the intial amount (i. e., the principal), r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.
Then $5994.78 = $4600 (1 + r/12)^(4*12)
or ... $5994.78 = $4600 (1 + r/12)^48
We must solve for r.
Divide both sides of this equation by $4600:
1.303 = (1 + r/12)^48
Take the 48th root of both sides of this equation:
1.0056 = 1 + r/12
0.0056 = r/12 Solve for r: r = 12(0.0056) = 0.0672
The annual interest rate was 6.72%.
The rate of interest monthly is 0.55%.
Given that,
The deposit amount is $4,600.The future value is $5,994.78The number of months = 4(12) = 48.The payment i.e. PMT = $0Based on the above information, the calculation is as follows:
The formula is
= RATE(NPER,PMT,-PV,FV,TYPE)
After applying the above formula, the rate of interest monthly is 0.55%.
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a telephone pole needs a wire attached to its top and anchored to the ground at a point that is 56 feet less than the height of the pole. if the wire is to be 16 feet longer than the height of the pole what is the height of the pole
Answers
[tex]\bf (y+16)^2=(y-56)^2+y^2 \\\\\\ \underline{y^2}+32y+16^2=y^2-112y+56^2+\underline{y^2} \\\\\\ 32y+256=y^2-112y+3136\implies 0=y^2-144y+2880 \\\\\\ 0=(y-24)(y-120)\implies y= \begin{cases} \boxed{120}\\ 24 \end{cases}[/tex]
it cannot be 24, because then the ground base area will be 24 - 56, which is a negative amount and unfeasible for the phenomena.
Illinois State tax is 4.98%. How much did Brody pay for a post card that cost $1.19?
Answers
[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 1.19&100\\ a&4.98 \end{array}\implies \cfrac{1.19}{a}=\cfrac{100}{4.98}\implies \cfrac{1.19\cdot 4.98}{100}=a[/tex]
that much. close to 6 pennies.
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Answer:
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Answers
So it's 2, or 200%.
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100/0.5=x
200=x
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To get price after fee is included
multiply the 3,187.50 by (1+fee percentage)
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3,187.50x(1.09)
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"Eighty" represents the digit 8 in the tens place.
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A .8 + b
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8 is the total amount of bottles that they started out with.
b is the amount that Nora and her friends drank.
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C. 8 - b is your answer
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Final answer:
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Explanation:
The question pertains to genetics, specifically the inheritance patterns of eye color in fruit flies (Drosophila melanogaster), which is a classic example in the field of genetics. When crossing a white-eyed male (mutant allele) with a female that is heterozygous for red eye color (one red allele and one white allele), the offspring will have a 1:1 ratio of red-eyed to white-eyed if eye color is an X-linked trait. This is because the male passes on his Y chromosome without the eye color allele to half the offspring, and his X chromosome with the white eye color allele to the other half. The female passes on one of her X chromosomes to all the offspring—half of these will carry the red allele and the other half will carry the white allele.
If the trait follows simple Mendelian inheritance, assuming red eye color is dominant over white, the offspring ratio will be 50% red-eyed (having one red allele from the mother and one white allele from the father), and 50% white-eyed (having one white allele from the mother and one from the father).
it's 3 to 6 your welcome have a nice day :>
what is the value of x in 7(3x - 13)=224 ?
Will mark brainliest!
Answers
7(3x-13)=224
21x-91 = 224
21x = 315
x = 315 / 21
x = 15
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Using the first derivative test, find all relative extrema for f(x) g
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Volume of a conce with radius R and height H, Vcone = (1/3) π (R^2) * H
Vcone = Vc => (1/3)π (R^2)*H = π(r^2)*H
=> R^2 = 3 * (r^2)
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Answer: R = r √3
What would a frog do if he could not find scissors to cut a coupon out of the newspaper?
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use mental math to solve the equation z/-12 = -5
Answers
because
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A Sum of $14 is made of 92 coins consisting of dimes and quarters. How Many are there of each kind of coin
Answers
So 92 coins * 10 cents = $9.20
So it's 4.80 dollars away from 14 dollars.
So if we were to switch one to a quarter, it would increase by 0.15 cents.
So we want to see how many increases we need to reach 4.80 dollars more.
4.80/0.15 = 32
So there are 32 quarters and 60 dimes.
There are 60 dimes and 32 quarters.
Given that a sum of $ 14 is made of 92 coins consisting of dimes and quarters, to determine how many are there of each kind of coin, the following calculation must be performed:
0.10 x 92 + 0.25 x 0 = 9.20 0.10 x 72 + 0.25 x 20 = 12.20 0.10 x 52 + 0.25 x 40 = 15.20 0.10 x 62 + 0.25 x 30 = 13.70 0.10 x 60 + 0.25 x 32 = 14
Therefore, there are 60 dimes and 32 quarters.
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Which of these r-values represents the weakest correlation?
A. –0.75
B. –0.15
C. –0.55
D. –0.35
Answers
Answer: B. -0.15
Step-by-step explanation: It is the farthest from -1 so it would be -0.15.
The correct r - value which represents the weakest correlation is, - 0.15.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Now, Apply the absolute value to each number.
In other words, remove the negative sign to determine the positive version of that number.
-0.75 turns into 0.75
-0.15 turns into 0.15
-0.55 turns into 0.55
-0.35 turns into 0.35
Here, The smallest result is 0.15, which is closest to 0.
Thus, The closer r is to 0, the weaker the correlation.
Hence, The correct r - value which represents the weakest correlation is, - 0.15.
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