Answer:
C(1,3) and D(1,4).
Step-by-step explanation:
The given quadrilateral ABCD has vertices at A (3,7) and B (3,6). The diagonals of this quadrilateral ABCD intersect at E (2,5).
Recall that, the diagonals of a parallelogram bisects each other.
This means that; E(2,5) is the midpoint of each diagonal.
Let C and D have coordinates C(m,n) and D(s,t)
Using the midpoint rule:
[tex](\frac{x_2+x_1}{2}, \frac{y_2+y_1}{2})[/tex]
The midpoint of AC is [tex](\frac{m+3}{2}, \frac{n+7}{2})=(2,5)[/tex]
This implies that;
[tex](\frac{m+3}{2}=2, \frac{n+7}{2}=5)[/tex]
[tex](m+3=4, n+7=10)[/tex]
[tex](m=4-3, n=10-7)[/tex]
[tex](m=1, n=3)[/tex]
The midpoint of BD is [tex](\frac{m+3}{2}, \frac{n+7}{2})=(2,5)[/tex]
This implies that;
[tex](\frac{s+3}{2}=2, \frac{t+6}{2}=5)[/tex]
[tex](s+3=4, t+6=10)[/tex]
[tex](s=4-3, t=10-6)[/tex]
[tex](s=1, t=4)[/tex]
Therefore the coordinates of C are (1,3) and D(1,4).
Final answer:
To ensure ABCD is a parallelogram with given vertices A (3,7) and B (3,6), and diagonals intersecting at E (2,5), the coordinates of C and D must be C (1,3) and D (1,4), derived using the midpoint formula.
Explanation:
To ensure that quadrilateral ABCD is a parallelogram, the diagonals AC and BD must bisect each other at the point E (2,5). Given vertices A (3,7) and B (3,6), and knowing that E is the midpoint of the diagonals, we can find the coordinates of C and D. Since E is the midpoint, for diagonal AC we have E's x-coordinate as the average of A and C's x-coordinates, and the same for the y-coordinate.
The coordinates of C can be found using the midpoint formula:
2 = (3 + xC)/2
5 = (7 + yC)/2
Solving these equations gives us C's coordinates:
xC = 2*2 - 3 = 1
yC = 2*5 - 7 = 3
Thus, point C is (1,3). For diagonal BD, we repeat the process:
2 = (3 + xD)/2
5 = (6 + yD)/2
Solving these equations gives us D's coordinates:
xD = 2*2 - 3 = 1
yD = 2*5 - 6 = 4
Point D is then (1,4). With vertices at A (3,7), B (3,6), C (1,3), and D (1,4), ABCD is a parallelogram because both pairs of opposite sides are parallel and equal in length, as indicated by their coordinates.
Subtract (5x + 3) from (9x – 7).
A. 4x – 4
B. 4x + 10
C. 4x – 10
D. –4x + 10
D is the correct answer
the result of subtracting (5x + 3) from (9x - 7) is 4x - 10. Therefore, the correct option is C: 4x - 10.
To subtract (5x + 3) from (9x - 7), we need to distribute the negative sign to all the terms in (5x + 3) and then perform the subtraction term by term.
(9x - 7) - (5x + 3)
= 9x - 7 - 5x - 3
Now, combine like terms:
= (9x - 5x) + (-7 - 3)
= 4x - 10
So, the result of subtracting (5x + 3) from (9x - 7) is 4x - 10. Therefore, the correct option is C: 4x - 10.
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True or false:
1) If f'(c)=0, then f has a local maximum or minimum at x=c.
I think this one is false, but I'm not sure.
2) If f is continuous on [a, b] and differential on (a, b) and f'(x) = 0 on (a, b), then f is constant on [a, b].
3) The Mean Value Theorem can be applied to f(x) = 1/x^2 on the interval [-1, 1].
I'm pretty sure the last one is false.
1. False. [tex]f'(c)=0[/tex] does not necessarily mean that [tex]f(c)[/tex] is a maximum or minimum. It could just as easily be a saddle point. For example, consider the function [tex]f(x)=x^3[/tex] with [tex]f'(x)=3x^2=0[/tex] when [tex]x=0[/tex], yet [tex]f(x)<0[/tex] for [tex]x<0[/tex] and [tex]f(x)>0[/tex] for [tex]x>0[/tex].
2. True. If [tex]f'(x)=0[/tex] for all [tex]x[/tex] in [tex](a,b)[/tex], then [tex]f[/tex] must be constant on that interval.
3. False. In order for the MVT to apply, [tex]f[/tex] must be continuous on the closed interval. But [tex]\dfrac1{x^2}[/tex] does not exist at [tex]x=0[/tex].
The first statement about f'(c)=0 implying a local maximum or minimum is true. The second statement that if f'(x)=0 on an interval implies the function is constant is also true. Lastly, the Mean Value Theorem cannot be applied to f(x) = 1/x² on the interval [-1, 1] because the function is not continuous at x=0.
Explanation:True or false:
The statement 'If f'(c)=0, then f has a local maximum or minimum at x=c' is true. As part of calculus, this is the concept of the first derivative test. If the derivative of a function at a given point is zero, it means that point is a local minimum or maximum, or it could also be a point of inflexion.The statement 'If f is continuous on [a, b] and differential on (a, b) and f'(x) = 0 on (a, b), then f is constant on [a, b]' is true. This is based on the fact that if the derivative of a function is zero over an interval, the function will be constant in that interval.The statement that 'The Mean Value Theorem can be applied to f(x) = 1/x² on the interval [-1, 1]' is indeed false. The Mean Value Theorem requires the function to be continuous over the closed interval and differentiable over the open interval. The function f(x) = 1/x² is not defined at x=0, hence it is not continuous in the interval [-1,1].Learn more about Calculus here:https://brainly.com/question/32512808
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A wall map is 45 cm high and 27 cm wide. Ashley wants to proportionately shrink it so its height is 12 cm. How wide would it be then?
Answer:
To shrink the height it has to be shrunk by:
27 / x = 12
x = 2.25 times
The width would be 45 / 2.25 =
20 centimeters.
Step-by-step explanation:
Answer:
7.2 cm wide
Step-by-step explanation:
Set it up as a proportion.. (45/27) = (12/x)
Cross multiply and solve for x.
I am running out of points!! Please help me!!
ANSWER
[tex]165.6 \degree[/tex]
EXPLANATION
The measure of arc AC corresponds to 22% + 24%=46%
The complete angle of the circle is 360°.
Therefore the measure of arc AC is
[tex] = \frac{46}{100} \times 360[/tex]
This simplifies to
[tex]165.6 \degree[/tex]
The correct answer is A.
Suppose that a laser light, positioned 100 ft from the base of a flag pole, illuminates a flag that is 85 ft above the ground.
What is the angle of inclination (angle of elevation) of the light beam?
Express your answer in degrees rounded to the nearest hundredth.
Enter your answer in the box.
Answer:
The angle of elevation is [tex]40.36\°[/tex]
Step-by-step explanation:
Let
[tex]\theta[/tex] ----> the angle of elevation
we know that
The tangent of an angle is equal to divide the opposite side to the angle by the adjacent side to the angle
we have that
[tex]tan(\theta)=\frac{85}{100}[/tex]
[tex]\theta=arctan(\frac{85}{100})=40.36\°[/tex]
if m AD=98 and m CD=120 Whats is m
Answer:
The measure of arc BC is 44°
Step-by-step explanation:
we know that
m arc AD+m arc DC+m arc BC+m arc AB=360° ----> by complete circle
substitute the given values and solve for m arc BC
98°+120°+m arc BC+98°=360°
m arc BC+316°=360°
m arc BC=360°-316°=44°
Answer:
109Step-by-step explanation:
You drop a ball from a height of 10ft. Each bounce the ball gains only 90% of its height back. How high does the ball bounce on its 6th bounce? Starting amount: decay rate: equation: answer:
Answer:
6th bounce: 40%
Starting amount: 100%
Decay rate: 10%
Equation: 100% - 10% - 10% - 10% - 10% - 10% - 10% =
Step-by-step explanation:
100% - 10% - 10% - 10% - 10% - 10% - 10% = 40%. 40% is the answer.
Using an exponential function, it is found that on the 6th bounce, the ball bounces up 5.31 ft.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem:
You drop a ball from a height of 10ft, hence A(0) = 10.Each bounce the ball gains only 90% of its height back, hence r = 0.1.Then, the height after the nth bounce is given by:
[tex]A[n] = 10(0.9)^n[/tex]
After the 6th bounce, we have that:
[tex]A[6] = 10(0.9)^6 = 5.31[/tex]
On the 6th bounce, the ball bounces up 5.31 ft.
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Please help! Will mark brainiest!!!!
Answer:
This is the alternate exterior angle theorem
Step-by-step explanation:
This is because angle 2 and angle 7 are in the outer part of each side of opposite lines
Help please I don’t know and I really need to finish
Answer:
2) First option
3) Second option
Step-by-step explanation:
5² = 625
13 × 8 × 5 = 520
write the expression in complete factored form 5u(n+6)+x(n+6)
Answer:
[tex](n+6)(5u+x)[/tex]
Step-by-step explanation:
The given expression is;
[tex]5u(n+6)+x(n+6)[/tex]
The greatest common factor is (n+6).
Let us factor the GCF to obtain:
[tex](n+6)(5u+x)[/tex]
Therefore the completely factored form of
[tex]5u(n+6)+x(n+6)[/tex]
is
[tex](n+6)(5u+x)[/tex]
Solve the triangle.
A = 32°, a = 19, b = 14
Answer:
A = 32°, a = 19, b = 14, B=22.98°, C = 125.02°, c = 29.36
Step-by-step explanation:
We have two sides of the triangle and we have an angle.
A = 32 °, a = 19, b = 14
We use the sine theorem to find the angle B.
We know that according to the sine theorem it is true that:
[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}[/tex]
[tex]\frac{sin(32\°)}{19}=\frac{sin(B)}{14}[/tex]
[tex]sin(B)=14*\frac{sin(32\°)}{19}\\\\B=Arcsin(14*\frac{sin(32\°)}{19})\\\\B=22.98\°[/tex]
We know that the sum of the internal angles of a triangle is always equal to 180.
So:
[tex]C=180-32-22.98\\\\C=125.02\°[/tex]
Finally we find the c side
[tex]\frac{sin(A)}{a}=\frac{sin(C)}{c}[/tex]
[tex]\frac{sin(32\°)}{19}=\frac{sin(125.02)}{c}[/tex]
[tex]0.02789=\frac{sin(125.02)}{c}[/tex]
[tex]c=\frac{sin(125.02)}{0.02789}\\\\c=29.36[/tex]
In ⊙L, m∠NMO=9x−3 and m∠NPO=4x+12. Find mNO.
Answer:
arc NO has measure 48
Step-by-step explanation:
We assume all measures are in consistent units (degrees or something similar). The two inscribed angles intercept the same arc, so are congruent:
9x -3 = 4x +12
5x = 15 . . . . . . . add 3-4x
x = 3 . . . . . . . . . divide by 5
The measure of the inscribed angle is then ...
4x +12 = 4(3) +12 = 24
That is half the measure of the arc, so the measure of arc NO is ...
arc NO = 2·24 = 48
Answer:
48°
Step-by-step explanation:
I'm actually just assuming that you mean arc NO. Proceeding with that...
Angle NMO is an inscribed angle which intercepts arc NO. Angle NPO is also an inscribed angle that intercepts arc NO. Because they both intercept the same arc, both inscribed angles have the same measure. Therefore,
9x - 3 = 4x + 12
Solving for x:
5x = 15
x = 3. Plug 3 in for x in either one of the equations to get that angles NMO and NPO measure
9(3) - 3 = 24°
The rule is that inscribed angles measure HALF of the arcs they intercept, so the measure of arc NO is 48°
Find the Geometric Mean of 8 and 50. Be sure to show your work!
Answer:
20
Step-by-step explanation:
The geometric mean of n numbers is the n-th root of their product. For two numbers, it is the square root of their product:
geometric mean = √(8·50) = √400 = 20
The answer is: 20
My work: √8*50 = √400 = 20
You have to take the square root of 8 multiplied by 50. With that, you would get 400, which is still squared because you have to get the numbers inside of the square root to one number. After that, you can now take the square root of the number that is inside of it, which in this case it is 400. The square root of 400 is 20.
I hope this helps!
PLEASE HELP SHOW ALL YOUR WORKING OUT MARK BRAINLIEST
Answer:
y=1/1 x+6
Step-by-step explanation:
y=mx+b
m=slope
b=y-intercept
the slope from one point to another is rise up one and go the the right one, therefore the slope of the line is 1/1.
The y-intercept is 6 which is shown on the graph
A principal of $3100 is invested at 5.5% interest, compounded annually. How much will the investment be worth after 7 years?
Answer:
$4501.51
Step-by-step explanation:
Because you're compounding annually, which is only once per year, you can use a simple formula:
[tex]A(t)=P(1+r)^{t}[/tex]
Filling in our info gives us
[tex]A(t)=3100(1+.055)^7[/tex]
Do the adding inside the parenthesis and then raise 1.055 to the 7th power to get
A(t)= 3100(1.454679161)
A(t)= $4509.51
John and George together raked 7/8 if the yard. John raked 3/4 of that amount. What part of the yard did john raked?
Answer:
1
8
Step-by-step explanation:
What do we know:
John and George raked 7/8 of the yard.
John raked 3/4 of 7/8
What we need to know is:
How much did George rake?
How? Subtract the fractions given.
7 - 3
8 4
To do this we must make the denominator (bottom) number the same. How? Find the least common denominator for 8 and 4. Basically what is the lowest number that both 8 and 4 can be divided.
Answer is 8
8 divided by 8 is 1
4 divided by 8 is 2
so
7 - 3 ×2 6
8 4 ×2 = 8
7 _ 6 = 1
8 8 8 is how much George raked.
Two consecutive perfect squares have a difference of $99$. what is the value of the larger perfect square?
Answer:
2500
Step-by-step explanation:
Let the first square number be [tex]x^2[/tex] then the next square number is [tex](x+1)^2[/tex].
The difference between these two consecutive numbers is 99.
This implies that:
[tex](x+1)^2-x^2=99[/tex]
We expand to get:
[tex]x^2+2x+1-x^2=99[/tex]
Simplify:
[tex]2x=99-1[/tex]
[tex]2x=98[/tex]
Divide both sides by 2
[tex]x=49[/tex]
Therefore the value of the larger perfect number is
[tex](49+1)^2=50^2=2500[/tex].
Please help me out please
Answer:
400 units³
Step-by-step explanation:
The volume (V) of the square pyramid is
V = [tex]\frac{1}{3}[/tex] area of base × height (h)
where h is the perpendicular height.
Consider the right triangle formed by a segment from the vertex to the midpoint of the base and the slant height ( the hypotenuse )
Using Pythagoras' identity on the right triangle
h² + 5² = 13²
h² + 25 = 169 ( subtract 25 from both sides )
h² = 144 ( take the square root of both sides )
h = [tex]\sqrt{144}[/tex] = 12
Area of square base = 10² = 100, hence
V = [tex]\frac{1}{3}[/tex] × 100 × 12 = 4 × 100 = 400
The double number lines show the ratio of minutes to days. How many minutes are in 222 days? minutes
2880
Step-by-step explanation:
Final answer:
To find out how many minutes are in 222 days, multiply the number of days (222) by the number of hours in a day (24) and then by the number of minutes in an hour (60). The result is 319,680 minutes.
Explanation:
The student is asking how many minutes are in 222 days. We begin the conversion using the provided information:
There are 24 hours in 1 day
There are 60 minutes in 1 hour
Now, we just need to multiply the number of days by the number of hours in a day, and then by the number of minutes in an hour, to get our answer.
222 days × 24 hours/day × 60 minutes/hour = 319,680 minutes
There are 319,680 minutes in 222 days.
Ameekah is working with consecutive integers
Consecutive numbers: 1, 2, 3, 4, 5.
As we can see it's the latest plus 1
So,
x, x + 1, x + 1 + 1, x + 1 + 1 + 1
x, x + 1, x + 2, x + 3 and so on
So it's x + 1.
For this case we have that by definition, a consecutive number is obtained by adding a unit to the previous one.
Example:
n, n + 1, n + 2, n + 3 ...
So:
If "x" is the first number of Ameekah, its second number to form a series of consecutive integers must be:
x + 1, that is, add "1" to the previous number.
Answer:
x + 1
Option B
What is the value of s if 8.25s - 2.375 = 10 ?
Answer:
s = 1.5
Step-by-step explanation:
10 + 2.375 = 12.375 = 8.85
12.375/8.25 = 8.25s/8.25
s = 1.5
Please help me with this!!!!!!!!!!
Answer:
True
Step-by-step explanation:
The incentre is equally distant from the triangles 3 sides and like centroids is always inside the circle.
A manager samples the receipts of every fifth person who goes through the line. Out of 50 people, 6 had a mispriced item. If 1,600 people go to this store each day, how many people would you expect to have a mispriced item?
Answer:
48 people
Step-by-step explanation:
1. 4/50 = x/600 do 4x600 and 50 times x
2.50x=2400
3. divide both sides by 50 to get a result of x=48.
Which is equivalent to 216^1/3
For this case we must find an expression equivalent to:
[tex]216 ^ {\frac {1} {3}[/tex]
So, we can rewrite the 216:
[tex]216 = 6 * 6 * 6 = 6 ^ 3[/tex]
Rewriting the expression:
[tex](6 ^ 3) ^ {\frac {1} {3}=[/tex]
By definition of power properties we have:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
So:
[tex]6 ^ {\frac {3} {3}} =\\6 ^ 1 =\\6[/tex]
Answer:
[tex]216 ^ {\frac {1} {3}}= 6[/tex]
The equivalent expression of [tex]216^{1/3}[/tex] is determined as 6.
What is simplification of an expression?Simplification refers to the process of reducing an expression, equation, or fraction into its simplest or most concise form.
The equivalent expression is determined by converting the exponents into roots as follows.
The given expression;
[tex]216^{1/3}[/tex]
This expression is simplified as follows;
[tex]216^{1/3}[/tex] = ∛ 216
The final expression becomes;
6³ = 216
So 6 is the answer
Thus, the equivalent expression of [tex]216^{1/3}[/tex] is determined as 6.
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Find the domain and range of the graph below:
Answer:
Domain is all real numbers; Range is all numbers less than or equal to 0
Step-by-step explanation:
Domain covers x values, range covers y values. The domain of an x^2 parabola, which is what this is, has a domain of all real numbers. Meaning that while the branches of the function keep going up and up and up or down and down and down, the values of x will never stop growing.
The range here is indicative of the lowest y value to the highest that the function covers. In this case, since the parabola is upside down, we have the highest to the lowest. The highest that the function goes up the y axis is right at the origin, where y = 0. Then it drops down into forever. So the range is all values of y less than or equal to 0
The Domain of [tex]f(x)[/tex] is all the real numbers, and
The Range of [tex]f(x)[/tex] is [tex]y\le0[/tex] or [tex]f(x)\le0[/tex]
The diagram shows the graph of the quadratic function
[tex]f(x)=-x^2[/tex]
The domain of [tex]f(x)[/tex] is all the real numbers, since the function has defined values for all real values of [tex]x[/tex].
The range of [tex]f(x)[/tex] is the set of values that [tex]f(x)[/tex] can assume. The square function has a range
[tex]\{y \text{ }|\text{ }y=x^2\text{ and }y\ge0\}[/tex] or the half-open interval [tex][0,\infty)[/tex].
This means that the negative of the square function will have the range
[tex]\{y \text{ }|\text{ }y=-x^2\text{ and }y\le0\}[/tex] or the half-open interval [tex](-\infty,0][/tex].
So, the domain of [tex]f(x)[/tex] is the open interval [tex](-\infty,\infty)[/tex] (all the real numbers), and the range of [tex]f(x)[/tex] is the half-open interval [tex](-\infty,0][/tex] (or, [tex]y\le0[/tex])
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PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
What is the inverse of h?
Answer: [tex]\bold{D)\quad h^{-1}(x)=\dfrac{1}{6}(x-1)}[/tex]
Step-by-step explanation:
Inverse is when you swap the x's and y's and then solve for y
y = 6x + 1
x = 6y + 1 swapped the x's and y's
x - 1 = 6y subtracted 1 from both sides
[tex]\dfrac{1}{6}[/tex] (x - 1) = y divided both sides by 6
Find function of f(-1)
f(-1) means the x value is -1 and you need to find what the Y value is.
Find -1 in the set of parenthesis and see what the Y value is.
When x = -1, y = 3
The answer would be 3.
Determine the rate of change and what the rate of change represents in this situation.
Answer:
The first answer is the one you want
Step-by-step explanation:
The rate of change is the slope. Here it is represented by the dollar value/number of tickets sold. This will give you the 1:1 ratio, meaning it will give you the number of dollars generated by the sale of 1 ticket. That's what rate of change is.
Use the slope formula and 2 points on the table. I chose the points (225, 250) and (200, 0):
[tex]\frac{0-250}{200-225} =\frac{-250}{-25} =10[/tex]
That translates to $10 per ticket.
Please please help me
Answer:
a) Acute
Step-by-step explanation:
To clasify the triangle as Acute, Right, or Obtuse, we use the converse of the pythagorean theorem and see if c^2 is greater, less than, or equal to b^2+a^2.
So 16^2 ? 11^2 + 12^2
Since 11^2 +12^2 = 265 and 16^2 is 256, c^2 is less than b^2+a^2. So the triangle is acute.
Answer:
a) Acute
Step-by-step explanation:
If 11 and 12 were the legs of a right triangle, the length of the hypotenuse would be ...
√(11² +12²) = √(121 +144) = √265 ≈ 16.3
The actual length of the longest side is shorter, so the opposite (largest) angle measure will be less than 90°. The triangle is acute.
A ladder leans against a building. The angle of elevation of the ladder is 70 degrees. The top of the ladder is 25ft from the ground.
To the nearest tenth of a foot, how long is the ladder?
Using law of sines:
Sin(angle) = opposite leg (height) / hypotenuse ( length of ladder)
Sin(70) = 25/x
x = 25 * sin(70)
x = 26.6 feet