The area of the quadrilateral is equal to √901 square units.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the quadrilateral in a two-dimensional plane is called the area of the quadrilateral.
Given that quadrilateral ABCD with A(-4,-2), B(-3,2), C(2,4) and D(4,-3). Calculate the sides of the quadrilateral by the distance formula,
AB = √[(2+2)² + (-3+4)²]
AB = √(16+1)
AB = √17
CD = √[(4-2)² + ( 4 + 3)²]
CD = √ (4+49)
CD = √53
The area will be calculated as,
Area = AB x CD
Area = √17 x √53
Area = √901 Square units
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Find the equation of the tangent line that crosses the function, f(x) = x^2-5, at x=-2
Answer:
We can use the point-slope formula to find the equation of the tangent line. The point-slope formula is given by:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line, and m is the slope of the line. To find the equation of the tangent line, we need to find the slope of the line and a point on the line.
To find the slope of the line, we can use the definition of derivative. The derivative of a function f(x) at a point x0 is defined as:
f'(x0) = lim(h->0) (f(x0 + h) - f(x0))/h
In our case, the function f(x) is given by f(x) = x^2 - 5, and the point x0 is -2, so we have:
f'(-2) = lim(h->0) (f(-2 + h) - f(-2))/h
Substituting the value of the function f(x) = x^2 - 5, we get:
f'(-2) = lim(h->0) (((-2 + h)^2 - 5) - ((-2)^2 - 5))/h
Simplifying the expression, we get:
f'(-2) = lim(h->0) (h^2 - 4h)/h
Since the limit is defined as h approaches 0, we can drop the h from the denominator since it will become insignificant in the limit:
f'(-2) = lim(h->0) (h^2 - 4h)
Now we can evaluate the limit as h approaches 0:
f'(-2) = lim(h->0) h^2 - 4h
In the limit, h^2 becomes 0, so we are left with:
f'(-2) = lim(h->0) - 4h
Since the limit is defined as h approaches 0, the value of the limit is simply -4 times 0, which is 0. Therefore, the slope of the tangent line is 0.
Now that we know the slope of the tangent line, we need to find a point on the line. We are told that the line passes through the point (-2, f(-2)) on the function f(x) = x^2 - 5. Substituting the value of the function, we get:
(-2, f(-2)) = (-2, (-2)^2 - 5) = (-2, -9)
So the point on the line is (-2, -9).
We now have the slope and a point on the line, so we can use the point-slope formula to find the equation of the line. Substituting the values into the point-slope formula, we get:
y - (-9) = 0(x - (-2))
Simplifying, we get:
y = -9
Therefore, the equation of the tangent line that passes through the point (-2, -9) with a slope of 0 is given by y = -9.
When naming a segment , wy is the same as yw
True or False ?
Answer:
Yes it is true.............
Find the equation of the tangent line to the graph of f(x) = e^2x-5 at the point (2, 1/e).
The tangent line to the graph of f(x) = 2e²ˣ-5 at the point (2, 1/e) is given by y=2e⁴+1-2e⁵/e
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The equation of the tangent line to the graph of f(x) = e²ˣ-5
To find the Equation of a tangent to any curve you must first find the derivative of the function.
y = e²ˣ-5
y'=2e²ˣ
sub x=2 into derivative function
y'(2)=2e⁴
so we have found that the tangent line is y=2e⁴+c
now we have to sub in the point and solve for c:
1/e=2e⁴+c
c=1/e-2e⁴
c=1-2e⁵/e
c=0 when x is 2.
The equation of tangent to the line is y=2e⁴+(1-2e⁵)/e
Hence, the equation of the tangent line to the graph of f(x) = 2e²ˣ-5 at the point (2, 1/e) is given by y=2e⁴+1-2e⁵/e
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a pineapple which was bought for $1.00 was sold at $1.30. calculate the profit percent
Answer: 30%
Step-by-step explanation:
HELP PLEASE INSTANT
Answer: number 3
Step-by-step explanation:
The radius of a moon is 798 miles. Use the formula for the radius r of a
A
4t
sphere given its surface area A, r =
moon.
to find the surface area of the
The surface area A of the moon is
(Round to the nearest whole number as needed.)
The total surface area of the moon is A = 79,98,258[tex]miles^{2}[/tex]
or A = 2.07153931 × [tex]10^{13} m^{2}[/tex]
as per given in the question,
the radius of the moon ( r) is 798 miles
to find the area of the total surface area of the cylinder
Area (A) = [tex]4\pi r^{2}[/tex] where r is radius of the sphere,
by substituting the radius in total surface area formula area,
A = [tex]4\pi (798) ^{2}[/tex]
( let [tex]\pi =3.14[/tex])
A = [tex]4\times3.14\times798\times798[/tex]
A = [tex]12.56\times63684[/tex]
A = 79,98,258.24
( by rounding to the nearest whole number we get )
A = 79,98,258[tex]miles^{2}[/tex]
or we can write in
A = 2.07153931 × [tex]10^{13} m^{2}[/tex]
( in terms of meters)
the total surface are of the sphere is A = 79,98,258[tex]miles^{2}[/tex]
A = 2.07153931 × [tex]10^{13} m^{2}[/tex]
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Hi, need fast answers and an explanation on how you got your answer please.
Answer:
x = 56
y = 124
z = 56
Step-by-step explanation:
The 124° angle and y° are vertical angles. vertical angles are congruent. they have equal measures.
y = 124
Angles 124° and x° form a linear pair. Angles in a linear pair are supplementary. Their measures add to 180°.
124 + x = 180
x = 180 - 24
x = 56
Angles x° and z° are vertical angles.
z = x = 56
Answer:
x = 56
y = 124
z = 56
50 POINTSSSSSS ASAP!!!! 50 POINTSSSSSS ASAP!!!! 50 POINTSSSSSS ASAP!!!! PLEASE HELP
A.
36°
B.
55°
C.
89°
D.
91°
Answer: I believe it would be 55 but It would help if it says what kind of triangle it is.
Step-by-step explanation:
Answer:
The answer is 91°
Step-by-step explanation:
In any triangle, the sum of all angles is equal to 180°
So,
35° + 54° + x = 180°
x = 180 - 89
x = 91°
Thus, The third angle is 91°
Find the measure of x
Answer: x = 7
Step-by-step explanation:
15(x+2) = R because they are equal angles.
set 135 = 15(x=2) because they are opposite each other so they equal each other
[tex]\frac{135}{15} =\frac{15(x+2)}{15} \\9 = x+2\\x=7[/tex]
NO LINKS!! Help me with the 2-Column Proof Part 1aa
3(x-4)+5=2(x-3)+4
3x-12+5=2x-6+4
3x-7=2x-2
x-7=-2
x=5
Here is the two column proof:
Statement Reason
3(x - 4) + 5 = 2(x - 3) + 4 Given3x - 12 + 5 = 2x - 6 + 4 Distribution property of multiplication3x - 7 = 2x - 2 Addition property of equality 3x - 2x = - 2 - (-7) Subtraction property of equality x = 5 ProvedFind the measure of ∠ 1
a 180°
b 30°
c 60°
d 120°
Answer:
120 degrees
Step-by-step explanation:
sum of all three angles of any triangle is 180
X+30+30=180
x+60=180
-60. -60
x=120
Hopes this helps
a rectangle is 14 inches long and 16 inches wide what’s its area
Multiply the width by the length:
14 • 16 = 224
Its area is 224.
R
What is the approximate distance between points A and B7 (5 points)
+
-5-4-3-2-10
2
34
-2
B
-3
-5
0723 45
IN
5
Answer:
7.62 units C
I need help with this question pls someone fast I’ll give brainliest and good amount of points
Answer:
Below
Step-by-step explanation:
180° rotation (clockwise OR counterclockwise)
Reflection across y axis would put the diagram in Q IV
90 degree rotation CCW would also be in Q IV
Translation R and up would be more centered around the origin
There are a adults at the fair. There are 20 more kids than adults. Write an expression
that shows how many kids there are.
a+
Submit
olo
The Number of kids in the fair is x + 12
What are Variables ?A variable is a symbol and a stand-in for any mathematical object in mathematics. A variable can specifically represent a number, a vector, a matrix, a function, its argument, a set, or one of its elements.
According to the given information
Let x be the variable
Let the number of adults in the fair = x
Number of kids in the fair is 12 more than the adults
So
Number of kids in the fair = 12 + Number of adults in the fair
= 12+x
Hence
The Number of kids in the fair is x + 12
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write the quadratic function in standard form (show steps)
Intercept form: y=(x+2) (x-2)
if g(x) is the image of y=-3x[tex]y=3x^{2}-24x+2[/tex] after a translation left 5 units and up 5 units write in starnded form
The image of y which is g(x) is 3x² + 60x + 82.
What are some transformation of functions?Suppose we have a function f(x).
f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).
f(x ± c) = Horizontal left/right shift by c units (x - + c, y).
(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).
f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).
f(-x) = Reflection over y axis, (-x, y).
-f(x) = Reflection over x-axis, (x, -y).
Given, y = 3x² - 24x + 2.
Now, g(x) is an image of y after a translation left 5 units and up 5 units.
∴ g(x) = 3(x + 5)² + 2 + 5.
g(x) = 3(x² + 20x + 25) + 7.
g(x) = 3x² + 60x + 75 + 7.
g(x) = 3x² + 60x + 82.
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50 POINTS HELP ASAP
Which algebraic rule describes the reflection of quadrilateral ABCD to quadrilateral A'B'C'D'?
An image displaying two quadrilateral ABCD and A'B'C'D' in a graph with vertices. ABCD with vertices A of -5 comma -1, B of -3 comma -3, C of -5 comma -5 and D of -7 comma -3 and A'B'C'D' with vertices A' of 5 comma -1, B' of 3 comma -3, C' of 5 comma -5 and D' of 7 comma -3.
A.
(x, y) → (1 – x, 1 – y)
B.
(x, y) → (–x, y)
C.
(x, y) → (x, –y)
D.
(x, y) → (x – 1, y – 1)
Answer:
B) (x, y) → (–x, y)-----------------------------------
From the picture we see this is a reflection across the y-axis.
From the coordinates we see all x-coordinates have changed to opposite and all y-coordinates remained as is.
The rule for such reflection is:
(x, y) → (–x, y)This is the option B.
Answer:
B) (x, y) → (–x, y)
Hope This Helps <33
--Jax
Jacob owns a small business selling bagels. He knows that in the last week 108
customers paid cash, 24 customers used a debit card, and 18 customers used a credit
card.
Based on these results, express the probability that the next customer will pay with a
debit card or a credit card as a decimal to the nearest hundredth.
The probability that the next customer pays with a debit card or a credit card will be 0.28.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
Jacob claims an independent venture selling bagels. He realizes that somewhat recently 108 clients paid cash, 24 clients utilized a charge debit card, and 18 clients utilized a credit card.
The total number of events is given as,
Total event = 108 + 24 + 18
Total event = 150
The probability that the next customer pays with a debit card or a credit card is written as,
P = (24 / 150) + (18 / 150)
P = 42 / 150
P = 0.28
The likelihood that the following client pays with a check card or a Visa will be 0.28.
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Answer:
Step-by-step explanation:0.28
During bowling practice, Marley rolled 28 strikes out of 70 attempts. What percent of Marley's
attempts were strikes?
40 percent of Marley's attempts were strikes, when Marley rolled 28 strikes out of 70 attempts.
Define percentage.Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage. A % is a number that indicates how many out of 100 it is, and it can also be expressed as a decimal or a fraction. Put the percentage value in the numerator and 100 in the denominator to convert a percentage to a fraction.
Given,
28 strikes rolled by Marley
Total attempts = 70
For percentage,
28/ 70 × 100%
0.4 × 100%
40%
40 percent of Marley's attempts were strikes, when Marley rolled 28 strikes out of 70 attempts.
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A college club has 20 members. Three of those members are officers of the club. What fraction of the members of the club are officers?
Answer: 3/20
Step-by-step explanation:
With our fraction, we will have officer members over total number of members. Three is a prime number, so this fraction cannot be simplified any more. This gives us the fraction;
3/20
Please look at the picture and answer the question, Thank you!
Inequality: x>12
Interval Notation: ( 12, ∞ )
Add the equations.
2 x-3 y=-1
+3 x+3 y=26
A. 5 x=25
B. 5 x=27
C. 5 x-6 y=-27
D. 6 y=25
Answer: 5x= 25
Step-by-step explanation:
Answer: The correct answer is A. 5x = 25
Step-by-step explanation:
Add the equations:
2x - 3y = -1
3x + 3y = 26
Add the like terms:
2x + 3x = 5x
3y + -3y = 0
26 + -1 = 25
The resulting equation:
5x = 25
Wile Coyote is chasing after the famous Road Runner one afternoon. The roadrunner sets off at a
speed of 72mph, while the coyote has issues with his rocket bike. It takes him 15 minutes to
repair it, then he shoots after him. The coyote is not worried at all because his ACME rocket bike
has a speed of 220mph. How long (in minutes) has the Road Runner been running once the
coyote catches up to him?
The time the Road Runner been running is 7.3 minutes
How to determine the time the Road Runner been running?From the question, we have the following parameters that can be used in our computation:
Roadrunner speed = 72mph
Time for repair = 15 minutes
Speed = 220mph
Represent the time the Road Runner been running with x
The speed is calculated using
Speed = Distance/Time
So, we have the following representations
Roadrunner speed = Distance/Time
Wile Coyote speed = Distance/Time
This gives
72 = Distance/(15 + x) -- for the roadrunner
220 = Distance/x for the Wile Coyote
So, we have
Distance = 72(15 + x)
Distance = 220x
Substitute the known values in the above equation, so, we have the following representation
220x = 72(15 + x)
Open the brackets
220x = 1080 + 72x
Evaluate the like terms
148x = 1080
So, we have
x = 7.3
Hence, the minutes is 7.3 minutes
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What are the vertex and range of y = |4x + 8| − 1? (0, −1); −∞ < y < ∞ (0, −1); −1 ≤ y < ∞ (−2, −1); −∞ < y < ∞ (−2, −1); −1 ≤ y < ∞
The vertex and range of y = |x + 1| + 3 will be (−1, 3); 3 ≤ y < ∞ respectively.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
You may get the vertex of y = |x + 1| + 3 as follows.
Where the absolute values are zeros are the vertex points of the absolute value function.
|x + 1| = 0
x + 1 = 0
x = -1
Substitute the value into an original function,
y = |-1 + 1| + 3
y= 0 + 3
y = 3
As a result, the vertex is at (-1, 3)
Remember that the domain is specified in the range of (-∞, ∞) while determining the range.
Given that |x + 1| ≥ 0 , (absolute value is always 0 or positive)
The result of adding 3 to the inequality's two sides is
|x + 1| + 3 ≥ 3
But since |x+1| + 3 is identical to f(x) = y, we have y = f(x) 3, which means that the range is specified for all values larger than 3.
So the range is 3 ≤ y < ∞
Thus,the vertex and range of y = |x + 1| + 3 will be (−1, 3); 3 ≤ y < ∞ respectively.
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43. Find the length of the midsegment.
45
45
74
126
74
Answer: hi
Step-by-step explanation:
what is 6 + 3 to the 4th power
Answer:
the answer is 87!
Answer: 6561
Step-by-step explanation: 6+3=9
9^4 = 9*9*9*9 = 81 * 81 = 6561
Naomi's electricity costs depend on the number of kilowatt hours she uses, as shown in the graph below. According to this graph, which expression can be used to calculate her electricity cost after using x kilowatt hours?
A. 0.06x + 40
B. 0.08x + 20
C. 0.1x + 10
D. 0.12x
Answer:
b. 0.08x + 20
Step-by-step explanation:
its B because the price goes up $40 every 500 KW's so
40 divided by 500 = 0.08
The expression used to calculate Naomi's electricity cost after using x kilowatt hours is 0.08x+20. Therefore, option B is the correct answer.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
From the graph we have, (500, 60), (1000, 100), (1500, 140) and (2000, 180).
We know that, slope of a line is Slope=(y2-y1)/(x2-x1)
= (100-60)/500
= 40/500
= 0.08
Substitute m=0.08 and (x, y)=(500, 60) in y=mx+c, we get
60=0.08(500)+c
60=40+c
c=20
Substitute m=0.08 and c=20 in y=mx+c, we get
y=0.08x+20
The expression used to calculate Naomi's electricity cost after using x kilowatt hours is 0.08x+20. Therefore, option B is the correct answer.
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What symmetries does the graph of f(x)=√2 x−1 have?
Answer:
Step-by-step explanation:
Find the asymptotes.
Vertical Asymptotes:
x
=
0
Horizontal Asymptotes:
y
=
0
No Oblique Asymptotes
Amy had 30 minutes to do a three-problem quiz. She spent 10
7/10 minutes on question A and 4 2/5 minutes on question B. How much time did she have left for question C?
The time Amy has left for the question C is 13.9 minutes.
How to write a mixed fraction into a fraction?The mixed fraction can be converted into a fraction by interchanging the numerator with the sum of the product of denominator and the whole number and the numerator of the mixed fraction. It can be shown as 2(¹/₂) = (2 × 2 + 1)/2 = 5/2.
Given that,
The total time for quiz is 30 minutes.
The time taken to do problem A is 10(⁷/₁₀) and for B is 4(²/₅).
Thus, the remaining time left can be calculated by the as follows,
30 - (10(⁷/₁₀) + 4(²/₅))
Change the mixed fraction into the fraction to obtain,
30 - (107/10 + 22/5) = 13.9
Hence, the time left for question C is given as 13.9 minutes.
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