A rectangle has the following vertices. Find the area of the rectangle. (9, −1), (−1, 7), (−5, 2), (5, −6)
Answers
Answer: 82 sq. units .
Step-by-step explanation:
Let A (9, −1), B (−1, 7), C(−5, 2), D(5, −6) are the vertices of rectangle.
Then we plot them on graph ( as provided in attachment)
Length = AB [tex]=\sqrt{(9+1)^2+(-1-7)^2}[/tex] units [By distance formula : [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]]
[tex]=\sqrt{(10)^2+(-8)^2}=\sqrt{100+64}=\sqrt{164}=2\sqrt{41}[/tex] units
Width = BC = [tex]\sqrt{(-1+5)^2+(7-2)^2}[/tex] units
[tex]=\sqrt{4^2+5^2}\\\\=\sqrt{16+25}\\\\=\sqrt{41}[/tex]
Area = length x width
= [tex]2\sqrt{41}\times\sqrt{41}=2\times41= 82\text{ sq. units}[/tex]
Hence, the area of the rectangle is 82 sq. units .
Related Questions
logx+log(3x-5)=log2
Answers
Answer:
x=2
Step-by-step explanation:
please fine me the solution
Answers
Answer:
16/3a^22b^2
I used a calculator to solve this
A. 3/4=a/36
B.4/9=b/36
Answers
Answer:
A. = 27 B. = 16
Step-by-step explanation:
A. 36/4 = 9 3X9 = 27
B. 36/9 = 4 4X4 =16
(3+4i)+(8+2i) complex number in standard form
Answers
Answer:
(3 + 4i) + (8 + 2i) = 3 + 4i + 8 + 2i
(3 + 4i) + (8 + 2i) = (3 + 8) + (4i + 2i)
(3 + 4i) + (8 + 2i) = 11 + 6i
hope it helps if yes mark me BRAINLIEST!
Tysm!
:)
Answer:
11 + 6i
Step-by-step explanation:
Well, by the looks of it, you're combining like terms. Just add numbers that have the same variable or jut add coefficients:
(3 + 4i) + (8 + 2i)
= 3 + 4i + 8 + 2i
= (3 + 8) + (4i + 2i)
= 11 + 6i
Tan45degree - 10cos60degree
Answers
Answer:
- 4
Step-by-step explanation:
Tan(45°) - 10 * cos (60°) = - 4
Given the diagram below, Hannah writes m 1+ m 4 = 180°, m 2 + m 5 = 180°, and m 3+ m 26 = 180°. Which of the following reasons allows her to write these sums?
Answers
Answer:
A. Definition of linear pair
Step-by-step explanation:
A linear pair of angles is formed when two lines intersect. Since angle on a straight line = 180°, angles of a linear pair sum up to 180°.
angles 1 and 4, angles 2 and 5, angles 3 and 6 are all linear pairs. Each pair = 180°.
Answer:
a
Step-by-step explanation:
a pex
Evaluate the expression when x= -3 X^2+8x-7
Answers
9-24-7
= -22
Your answer is -22.
Which expression is the simplest form of...
Answers
Answer:
The answer is option A
Step-by-step explanation:
[tex]( {x}^{ - \frac{4}{7} } )^{7} [/tex]Using the rules of indices
That's
[tex]( { {a}^{x} })^{y} = {a}^{x \times y} [/tex]Simplify the expression
We have
[tex]( { {x}^{ - \frac{4}{7} } })^{7} = {x}^{ - \frac{4}{7} \times 7 } \\ = {x}^{ - 4} [/tex]Again using the rules of indices
That's
[tex] {x}^{ - y} = \frac{1}{ {x}^{y} } [/tex]The final answer is
[tex] \frac{1}{ {x}^{4} } [/tex]Hope this helps you
Draw a square with side-length x. Write an expression that represents the perimeter.
Answers
Answer:
4x
Step-by-step explanation:
Length of square = x cm
Perimeter; p = 4 × length of square
p = 4x
last one anyone know it?
Answers
Answer:
6/(-2) = -3
Step-by-step explanation:
rule - when you divide positive number by a negative number then it is negatie so with the same rule applied it is
6/-2
-3
6 + (-2) means we start at 0 and go up 6 units to arrive at 6 on the number line. In terms of a building, you can think of starting on the ground floor and then going up 6 floors. Then adding on the -2 means we go down 2 floors to arrive at 6 + (-2) = 6-2 = 4
Answer: Choice B) go up 6, then down 2What is the value of 4 in the number 45?
Answers
Answer:
40
Step-by-step explanation:
The 4 in 45 is 40 because it is in the tens place, 4 times 10= 40. The 5 is 5 becasue it's in the ones place. :)
It's just place value:
Answer:
The first digit i.e. 4 is called the tens' place. Here, there are 4 tens. The last or right digit i.e. 5 is called the ones' place. Therefore, in the number 45 = 4 tens plus 5 ones = 40 + 5 = 45
Simplify using a calculaor. Not sure how to plug it in
Answers
Hi there! Hopefully this helps!
----------------------------------------------------------------------------------------------------
Answer: 1000~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Calculate 10000 to the power of [tex]\frac{3}{4}[/tex].
[tex]\frac{3}{4} = 0.75[/tex]
[tex]10000^{0.75}= 1000[/tex].
Solve -4r + 18= 6 I need this equation
Answers
Answer:
r = 3Step-by-step explanation:
[tex]-4r + 18= 6\\\\\mathrm{Subtract\:}18\mathrm{\:from\:both\:sides}\\\\-4r+18-18=6-18\\\\\mathrm{Simplify}\\\\-4r=-12\\\\\mathrm{Divide\:both\:sides\:by\:}-4\\\\\frac{-4r}{-4}=\frac{-12}{-4}\\\\\mathrm{Simplify}\\\\r=3[/tex]
Binomial (-x + 3) and trinomial (-2x2 + 5x + 6) are the factors of what polynomial? (Hint: 4 and 2 are factors of 8. Multiply.)Binomial (-x + 3) and trinomial (-2x2 + 5x + 6) are the factors of what polynomial? (Hint: 4 and 2 are factors of 8. Multiply.)Binomial (-x + 3) and trinomial (-2x2 + 5x + 6) are the factors of what polynomial? (Hint: 4 and 2 are factors of 8. Multiply.)
Answers
Answer:
2x^3-11x^2+9x+18
Step-by-step explanation:
By multiplying both the binomial and the trinomial given, we obtain a polynomial which contains both as factors. We notice as well that the given trinomial doesn't have 3 as a root (so there is no multiple root x = 3 in the product we obtain:
[tex](-x+3)\,(-2x^2+5x+6)=2\,x^3-5x^2-6x-6x^2+15x+18=2x^3-11x^2+9x+18[/tex]
Then, this new polynomial
[tex]2x^3-11x^2+9x+18[/tex]
has both given polynomials as factors.
Consider the following. x = e4t, y = t + 7
Eliminate the parameter to find a Cartesian equation of the curve.
Answers
Answer:
y = 7 +ln(x)/4
Step-by-step explanation:
Maybe your parameterized equation is ...
(x, y) = (e^(4t), t +7)
Using t = y-7, we can substitute for t in the expression for x:
x = e^(4(y -7))
ln(x) = 4(y -7)
ln(x) +28 = 4y
y = 7 +ln(x)/4
Explain how to perform a two-sample z-test for the difference between two population means using independent samples with
σ1 and σ2 known.
Answers
Answer:
Z= (X1`-X2`)- (u1-u2)/[tex]\sqrt{ \frac{ s_1^2}{n_1^2} +\frac{ s_2^2}{n_2}[/tex] (here s1=σ1 and s2= σ2)
Step-by-step explanation:
Let X1` be the mean of the first random sample of size n1 from a normal population with a mean u1 and known standard deviation σ1.Let X2` be the mean of the second random sample of size n2 from another normal population with a mean u2 and known standard deviation σ2. Then the sampling distribution of the difference X1`-X2` is normally distributed with a mean of u1-u2 and a standard deviation of
[tex]\sqrt{ \frac{ s_1^2}{n_1^2} +\frac{ s_2^2}{n_2}[/tex] . (here s1=σ1 and s2= σ2) In other words the variable
Z= (X1`-X2`)- (u1-u2)/[tex]\sqrt{ \frac{ s_1^2}{n_1^2} +\frac{ s_2^2}{n_2}[/tex] (here s1=σ1 and s2= σ2)
is exactly standard normal no matter how small sample sizes are . Hence it is used as a test statistic for testing hypotheses about the difference between two population means.
The procedure is stated below.
1) Formulate the null and alternative hypotheses.
2) Decide on significance level ∝
3) Use the test statistic Z= (X1`-X2`)- (u1-u2)/[tex]\sqrt{ \frac{ s_1^2}{n_1^2} +\frac{ s_2^2}{n_2}[/tex] (here s1=σ1 and s2= σ2)
4) Find the rejection region
5)Compute the value of Z from the sample data
6) Rehect H0 if Z falls in the critical region, accept H0 , otherwise.
when the polynomial f(x)=2x^3+ax^2+b is divisible by (x+1) and that there is a remainder of 16 when it is divided by (x-3) find the values of a and b
Answers
Answer:
hjgyjgyjyjhhh
Step-by-step explanation:
ygjyjygyjjg
Two cities, Ashville and Boulder, are 2.5 inches
apart on a map. A third city, Wellspring, is
located exactly halfway between Ashville
and Boulder. If the map uses a scale of 0.5
inch = 15 miles, find the actual distance from
Wellspring to Boulder.
Answers
Answer:
The distance between W and B is 18.75 mi.
Step-by-step explanation:
2.5 inches converts to
2.5 in 15 mi
------------ * ---------- = 37.5 mi
1 1 in
Half of this distances places us at the midpoint between W and B:
37.5 mi
--------------- = 18.75 mi
2
You need a total of 60 pounds of two commodities costing $1.35 and $2.85 per pound.
A) Verify that the total cost is y = 1.35x + 2.85(60 - x), where x is the number of pounds of the less expensive commodity.
Let x be the number of pounds of the commodity costing $1.35 per pound. Because there are_____pounds total, the amount of the second commodity is______. The total cost, in dollars, is y = 1.35x + 2.85(60 - x).
B) Find the inverse function of the cost function.
What does each variable represent in the inverse function?
1) X represents the commodity costing $1.35 per pound and Y represents the commodity costing $2.85 per pound.
2) X represents pounds and Y represents cost.
3) X represents the commodity costing $2.85 per pound and Y represents the commodity costing $1.35 per pound.
4) X represents cost and Y represents pounds.
5) X represents the commodity costing $1.35 per pound and Y represents cost.
C) What is the domain of the inverse function?
Validate or explain your answer using the context of the problem.
1. The domain of the inverse function is equal to the range of the original function.
2. The domain of the inverse function is equal to the domain of the original function.
3. The domain of an inverse function is always R.
D) Determine the number of pounds of the less expensive commodity purchased when the total cost is $78.
Answers
Answer: provided in the explanation section
Step-by-step explanation:
We will take this problem step by step to ensure we have easy understanding of the problem at hand.
(a). taking x as the number of pounds of the commodity costing $1.35 per pound.
Also since we have 60 pounds as total
The amount of second commodity is 60 - x
then the total cost (in dollars) is
y = 1.35x + 2.85(60 - x)
(b). since we have that;
y = 1.35x + 2.85(60 - x)
solving for y gives
y = 1.35x + 171 - 2.85x
y = 171 - 1.5x
doing exchange of variables y and x we have;
x = 171 - 1.5y
where;
1.5y = 171 - x
y = 171 - x / 1.5
f(x) = y and y = f⁻¹(x)f⁻¹(x) = 2/3 [171 - x] ------------- (1)
Here x represents the cost and y represents the pounds
(c). Given that less commodity is purchased, the Cost will be at its lowest and will be 60 (1.35) = $81.
Also, if only the more expensive commodity is purchased, the Cost will be at its maximum and will be 60(2.85) = $171
Therefore the domain of inverse becomes [81,171]That is to say that the domain of inverse function is equal to the range of original function.
(d). plug in x = $78 in the inverse function
where y = 2/3 [171-78]
y = 2/3[93] = 2[31]
y = 62
The number of pounds of the less expensive commodity purchased when the total cost is $78 is given as
y = 62
cheeers i hope this solution was helpful
What the answer S4• s8 •s3
Answers
Answer:
s^15
Step-by-step explanation:
When multiplying exponents with the same base, add the exponents
Write the equation of a line with a slope of -2 and a y-intercept of 5
Answers
Answer:
y = - 2x + 5Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
From the question
Slope / m = - 2
y intercept / c = 5
Substitute the values into the general equation above
We have the final answer as
y = - 2x + 5Hope this helps you
What is the vertex for y=|x-3|-2
Answers
Answer:
The vertex is [3,0]
Step-by-step explanation:
y=a(x−h)2+k , where ( h,k ) is the vertex of the parabola. By comparing the two equations, we see that h=3 and k=0 . The vertex is at ( 3,0 ).
Answer:
The vertex is [3,0]
Step-by-step explanation:
y=a(x−h)2+k , where ( h,k ) is the vertex of the parabola. By comparing the two equations, we see that h=3 and k=0 . The vertex is at ( 3,0 ).
the ratio of Encik Arif's mass to his sons mass is 3:2 . If his son's mass is 42 kg, find Encik Arif's mass.
Answers
Answer:
Encik Arif's mass is 63kgStep-by-step explanation:
Let Encik Arif's mass be x
the ratio of Encik Arif's mass to his son's mass is 3:2
That's
[tex] \frac{3}{2} [/tex]The son's mass is 42, so the ratio of Encik Arif's mass to his son's is
x : 42
That's
[tex] \frac{x}{42} [/tex]Now equate the two fractions
That's
[tex] \frac{3}{2} = \frac{x}{42} [/tex]Cross multiply
3(42) = 2x
126 = 2x
Divide both sides by 2
We have the final answer as
x = 63Hope this helps you
50 points Its really geometry Distance Formula
Answers
Step-by-step explanation:
1) 51
2)32
3) 18
4)9
5)12
Answer:
slime tee
Step-by-step explanation:
charli damelio
refr
rt
gr
grt
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rgt
123ssroblFour different linear functions are represented below.
a) which function has the graph with the greatest slope?
b) which functions have graphs with y intercepts greater than 3?
c)which function has the graph with a y intercept closest to 0
Answers
Answer:
A) Function 4
B) Function 2
C) Function 3
Step-by-step explanation:
if i bought a product for $74.83 and get a 10% refund how much do i get back?
Answers
if you bought a stock last year for $59 and it risen 13% how much is the stock worth now
Answers
Answer:
$ [tex] \underline{ \underline { \sf{ \bold{66.67}}}}[/tex]Step-by-step explanation:
Price of stock bought = $ 59
% rise = 13%
Price of stock rise :
⇒[tex] \sf{13\% \: of \: 59}[/tex]
⇒[tex] \sf{ \frac{13}{100} \times 59}[/tex]
⇒$ [tex] \sf{7.67}[/tex]
New price is 13% more than $ 59
Hence, New price = $ 57 + $ 7.67
= $ 66.67
Hope I helped!
Best regards!!
Solve the following:
2x – 7 > 9
a
3> 8
b
x > 1
C
3 < 8
d
x>-1
Answers
Answer: x > 8
2x - 7 > 9
2x > 9+7
2x > 16
2x / 2 > 16 / 2
x > 8
How many times larger than the number (1 − 8 /15 ) is the number (1.2 + 2/ 3 )?
Answers
Answer:
1- 8/15= 7/15 = 0.4(6)
1.2 + 2/3 = 28/15 = 1.8 (6)
If y varies inversely with x and y=11 when x=3, find the equation that relates x and y.
Answers
Answer:
y = [tex]\frac{33}{x}[/tex]
Step-by-step explanation:
Use the inverse relationship equation, y = [tex]\frac{k}{x}[/tex]
Plug in what we know to solve for k:
11 = [tex]\frac{k}{3}[/tex]
33 = k
Plug 33 in as k to find the equation:
The equation will be y = [tex]\frac{33}{x}[/tex]