Given the information below, find the coordinates of the vertices L and P such that ABCD=NLPM. A(2,0), B(2,4,), C(-2,4), D(-2,0), M(4,0), N(12,0)
Answers
From the drawing it is clear that ABCD is a square with side length 4 units.
ABCD and NLPM are similar, and the side MN is 8 units. This means that NLPM is a square of side length 8 units.
The order of the letters is important, which means, after M comes N then comes L. With this in mind, there are 2 models we can draw, as drawn in the picture:
I) L(12, 8), P(4, 8)
II) L(12, -8), P(4, -8)
Answer: L(12, 8), P(4, 8) or L(12, -8), P(4, -8)
Answer:
Its B I just took the test
Related Questions
helpppppppppppppppppppppp
Answers
-2-0/2-1
-2/1
-2
Final answer: -2
The second term in a geometric sequence is 20. The fourth term in the same sequence is 11.25. What is the common ratio
Answers
so [tex]a_1[/tex] is the first term, [tex]a_2[/tex] the second term and so on...
In a geometric sequence with [tex]a_1=c[/tex], and common ratio r, the terms are as follows:
[tex]a_1=c[/tex]
[tex]a_2=cr[/tex]
[tex]a_3=c r^{2} [/tex]
[tex]a_4=c r^{3} [/tex]
.
.
that is, each term is its previous term times the common ratio r.
In our example
[tex]a_2=cr=20[/tex] and [tex]a_4=c r^{3}=11.25 [/tex]
[tex] \frac{a_2}{a_4}= \frac{cr}{c r^{3}}= \frac{1}{ r^{2}}= \frac{20}{11.25}= 1.778 [/tex]
so [tex]r^{2} =1/1.778=0.56[/tex]
[tex]r= \sqrt{0.56}= 0.75[/tex]
Answer: r=0.75
Using the given zero, 2 - 4i, find one other zero of f(x) = x4 - 4x3 + 21x2 - 4x + 20
Answers
The conjugate of the given zero 2 - 4i is 2 + 4i, which must also be a zero of the polynomial f(x) due to the Complex Conjugate Root Theorem.
Given the zero 2 - 4i of the polynomial function f(x) = [tex]x^4 - 4x^3 + 21x^2 - 4x + 20,[/tex] we know by the Complex Conjugate Root Theorem that if a polynomial has real coefficients, then any complex zeros must occur in conjugate pairs. Therefore, the conjugate of 2 - 4i, which is 2 + 4i, must also be a zero of the polynomial function.
As a result, the polynomial can be factored to include the factors (x - (2 - 4i)) and (x - (2 + 4i)). When these factors are multiplied out, they will give you a quadratic factor of the polynomial, which when multiplied with the remaining factors, will result in the original polynomial f(x). The two factors, when multiplied together, yield a quadratic with real coefficients, which means any remaining zeros must also satisfy this quadratic equation.
If f(x) = -2[x] + 8, what is f(-1.8) (PLS HELP ASAP)
Answers
in this the output is the closest right side integral value.
-2[-1.8]+8
=-2×-1+8
=2+8
=10
Answer:
option c)10
Step-by-step explanation:
Given is a least integer function as
[tex]f(x) =-2[x]+8[/tex]
We are to find out the function value when x = -1.8
Substitute for x the value -1.8
we have
[tex]f(x) =-2[-1.8]+8\\[/tex]
-1.8 has the integer -1 to the left of it.
Hence we get
[tex]f(x) =-2[-1]+8=10[/tex]
Hence answer is option c)10
The point $(r,\theta)$ in polar coordinates is $(7,5)$ in rectangular coordinates. what is the point $\left( 2r, \theta + \frac{\pi}{2} \right)$ in rectangular coordinates?
Answers
Final Answer:
The rectangular coordinates of the point[tex]$\left( 2r, \theta + \frac{\pi}{2} \right)$[/tex], where [tex]$(r, \theta)$[/tex] corresponds to the polar coordinates (7, 5), are approximately (-13.59, 11.54).
Step-by-step explanation:
In polar coordinates, a point is represented as [tex]$(r, \theta)$[/tex] , where [tex]$r$[/tex] is the distance from the origin, and $\theta$ is the angle with respect to the positive x-axis. In rectangular coordinates, the point is represented as (x, y).
Given that the point [tex]$(r, \theta)$[/tex] in polar coordinates is equivalent to the point (7, 5) in rectangular coordinates, we can express this relationship as:
[tex]\[ x = r \cos(\theta) \][/tex]
[tex]\[ y = r \sin(\theta) \][/tex]
For the given point $(7, 5)$, we have:
[tex]\[ x = 7 \cos(5) \][/tex]
[tex]\[ y = 7 \sin(5) \][/tex]
Now, you want to find the point [tex]$\left( 2r, \theta + \frac{\pi}{2} \right)$[/tex] in rectangular coordinates. This can be expressed as:
[tex]\[ x' = 2r \cos\left(\theta + \frac{\pi}{2}\right) \][/tex]
[tex]\[ y' = 2r \sin\left(\theta + \frac{\pi}{2}\right) \][/tex]
We know that [tex]$\cos\left(\theta + \frac{\pi}{2}\right) = -\sin(\theta)$[/tex] and [tex]$\sin\left(\theta + \frac{\pi}{2}\right) = \cos(\theta)$[/tex]. Substituting these into the equations:
[tex]\[ x' = -2r \sin(\theta) \][/tex]
[tex]\[ y' = 2r \cos(\theta) \][/tex]
Now, if we substitute the values of [tex]$r$[/tex] and [tex]$\theta$[/tex] from the given point (7, 5):
[tex]\[ x' = -2 \times 7 \times \sin(5) \][/tex]
[tex]\[ y' = 2 \times 7 \times \cos(5) \][/tex]
Calculating these values will give you the rectangular coordinates of the point $\left( 2r, \theta + \frac{\pi}{2} \right)$.
When 23 is subtracted from 4 times a certain number the result is 4
Answers
x = the 'certain number' we want to find
Then, we can formulate an equation:
4x - 23 = 4
Now, solve for x:
4x = 27
x = 27/4 = 6.25
Given,
4x - 23 = 4
4x = 27
x = [tex] \frac{27}{4} [/tex] = 6.75
Hence, the number is 6.75
Use the remainder theorem to determine the remainder when d4 + 2d2 + 5d − 10 is divided by d + 4.
Answers
The remainder theorem states that the answer when d + 4 is substituted into the whole equation, the remainder would be the answer divided by d + 4. Therefore:
d + 4 = 0
d = -4
Evaluating when d = -4:
d^4 + 2 * d^2 + 5 * d − 10
= (- 4)^4 + 2 * (- 4)^2 + 5 * (- 4) – 10
= 256 + 2 * 16 – 20 – 10
= 256 + 32 – 30
= 258
Therefore basing on the remainder theorem, the remainder would then be:
Remainder = 258 / (d + 4) ---> Answer
Brett wants to paint the exterior of his two-story home but does not know what length ladder he should buy. The top of his roof is 29 ft above ground level, and (for safety reasons) the ladder should not be at more than an 80° angle from the ground. How long, rounded up to the nearest foot, is the shortest ladder that Brett should buy?
Answers
so after rounding is 30 ft
Answer:
Brett should buy a ladder of minimum 30 ft length.
Step-by-step explanation:
Brett wants to paint his exterior of a double story home.
Height of the roof of the second story from the ground = 29 feet
Maximum angle between the ground and the ladder should be = 80°
Now from the figure,
sin 80° = [tex]\frac{AB}{AC}[/tex]
0.9848 = [tex]\frac{29}{AC}[/tex]
AC = [tex]\frac{29}{0.9848}[/tex]
AC = 29.45
≈ 30 ft
Therefore, Brett should buy a ladder of minimum 30 ft length.
Which mathematical statement represents “17 more than a number is 26”?
Answers
17 + x = 26
17 +n = 26
n + 17 = 26
something like those, you didn't give options to choose from.
Answer:
x + 17 = 26
Step-by-step explanation:
mathematical statement represents “17 more than a number is 26”
Let x be the unknown number
17 more means we add 17 with the unknown number x
so it becomes x+17
'is' represents an = sign
So the equation for the mathematical statement “17 more than a number is 26” becomes x + 17 = 26
Suppose? 30% of the people in your town talk on their cell phones and drive at the same time. if you stood on a busy street corner and watched 50 people drive? by, about what proportion would you expect to see talking on their cell? phones?
Answers
What is the sum of?
A. S=1.5
B.S=2
C.S=4.5
D.=8
Answers
∑4(0.5)ⁿ⁻¹
n=1
For n = 1 → 4(0.5)¹⁻¹ = 4(0.5)⁰ = 4(1) = 4
For n = 2 → 4(0.5)²⁻¹ = 4(0.5)¹ = 4(0.5) = 4(0.5)
For n = 3 → 4(0.5)³⁻¹ = 4(0.5)²
For n = 4 → 4(0.5)⁴⁻¹ = 4(0.5)³
We notice this is a geometric series with first term:
a=4 & r= 0.5
Since r<1, then the formula of the sum when n→∞ is:
Sum= a(1/1-r)
Sum = 4/(1-0.5)
Sum = 4/(1/2) = 4 x 2
∞
∑4(0.5)ⁿ⁻¹ = 8 (answer D)
n=1
A new truck that sells for 29,000 depreciates 12% each year. What is the decay factor b?
Answers
The highest temperature recorded in the town of Westgate this summer was 180°F. Last winter, the lowest temperature recorded was -15°F.
Find the difference between these two extreme temperatures.
Answers
Good luck and have nice day.
How do you solve and graph a piece wise function and state the domain and range?
Answers
now for 4) check the picture on the left-hand-side
if you notice the intervals, it goes from -∞ and stops at -2, then goes from 2 over to 3, then from 3 onwards, so the domain will also be (-∞ , +∞).
Now, the range...
the 1st subfunction 3-x is just a line coming down form -∞....
the 2nd subfunction is just 2x, also a line going up, now once you get to
the 3rd subfunction is just 5, meaning y = 5, or f(x) = 5, which is just a horizontal line at y = 5.
since the 3rd subfunction goes from x > 3 onwards to +∞, and is just a horizontal line, it doesn't go below 5, so one would think the range is -∞, 5.
however, from the 2nd subfunction if we use say x = -1.9999, 2x ---> 2(-1.9999) = -3.9998 , that's lower than 5, and that's the lowest the piece-wise goes, thus, the range comes from -∞ and goes as low as -3.9998, (-∞ ,-3.9998]
notice, we didn't use -2, because the 2nd subfunction 2x, doesn't include it in its range -2 < x ⩽ 3.
now, for 4) I used -1.9999 but your teacher might be expecting something like -1 or thereabouts, just an integer amount. But the idea being, the 2nd subfunction, does not include the -2.
Terry earns $22,500 annually. What is the total amount of each paycheck if she is paid biweekly?
Answers
52 weeks per year
biweekly means she gets paid every 2 weeks
so 52/2 = 27
22500/27 = 833.33 each paycheck
An equilateral triangle has sides of length s. If each side is increased by 3, represent the new perimeter in terms of s.
Answers
= 3s + 9
Solve the inequality. 4(p – 4) > 12
Answers
4(p - 4) > 12
First, we need to apply the Distributive Property to the left side of the inequality.
To apply the Distributive Property, we need to multiply the number/variable outside of the parenthesis by all inside numbers/variables inside of the parenthesis.
4(p - 4)
4(p) + 4(-4)
4p - 16 is what we're left with on the left side of the inequality.
Now, our inequality is this:
4p - 16 > 12
Add 16 to both sides.
4p > 28
Divide both sides by 4.
p > 7
p > 7 is your solution.
I hope this helps!
plz rate
An investment of $200 increases at a rate of 9.5% per year. What is the growth factor, b?
Answers
The standard form for rate equation is:
F = P (1 + r)^n
or
F = P b^n
So b = 1 + r
In this case, r is given as 9.5% or 0.095. Therefore:
b = 1 + 0.095
b = 1.095
The growth factor is 1.095.
Write an appropriate direct variation equation if y = 27 when x = 9
Answers
27 = k*9
k = 27/9 = 3
required variation is y = 3x
Answer: y=3x
Step-by-step explanation:
What is the common ratio in the sequence -27, 9, -3, 1....?
A. 3
B. -3
C. 1/3
D. -1/3
Answers
9/-27 = -1/3
to find the next term in a geometric sequence, u multiply by the common ratio....
-27 * -1/3 = -27/3 = 9
9 * -1/3 = -9/3 = -3
-3 * -1/3 = -3/-3 = 1
△DEF has vertices D (2,2), E (-2,-1), and F (-3,5). Complete the following charts indicating the location of △D′E′F′ and △D″E″F″.△DEF is reflected in the y-axis. Then it is translated along the vector ⟨3,−5⟩. Enter your answers as points using parenthesis and commas. Do not use any spaces.
Answers
the coordinate of D' (-2, 2)
the coordinate of E' (2, -1)
the coordinate of F' (3, 5)
Translating D'E'F' by the vector (3, -5) gives the following coordinate of D''E''F'' as follows
the coordinate of D'' (-2+3, 2-5) = (1, -3)
the coordinate of E'' (2+3, -1-5) = (5, -6)
the coordinate of F'' (3+3, 5-5) = (6, 0)
The diagram below shows the transformation of triangle DEF
A quadratic equation is shown below:
4x^2 − 12x + 10 = 0
Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)
Part B: Solve 2x^2 − 13x + 21 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)
Answers
the radicand is b²-4ac
if it is in form ax²+bx+c
when it is
greater than 0, then 2 real roots
equal to 0, then 1 real root
less than 0, then no real roots
so
a=4
b=-12
c=10
b²-4ac=(-12)²-4(4)(10)=144-160<0
so 0 real roots
B.
using quadratic formula because it is easier
for
ax²+bx+c=0
[tex]x=\frac{-b+/-\sqrt{b^2-4ac}}{2a}[/tex]
so
for 2x²-13x+21
a=2
b=-13
c=21
[tex]x=\frac{-(-13)+/-\sqrt{(-13)^2-4(2)(21)}}{2(2)}[/tex]
[tex]x=\frac{13+/-\sqrt{169-168}}{4}[/tex]
[tex]x=\frac{13+/-\sqrt{1}}{4}[/tex]
[tex]x=\frac{13+/-1}{4}[/tex]
x=(13+1)/4 or (13-1)/4
x=14/4 or 12/4
x=7/2 or 3
Exit Felix was given $125 for his birthday from his grandmother. He plans to put this money toward the purchase of a $250 skateboard. The remainder of the money he plans to earn mowing lawns for the rate of $35 each. What is the least number of lawns Felix will have to mow in order to have enough to buy the skateboard?
Answers
First let's set up an inequality.
35x ≥ 125
Now solve for x
125/35 = 3.6 (round up to nearest whole number)
x = 4
The answer is 4
Hope this helps! :)
What is the lateral area of the drawing?
A. 425 km2
B. 1021 km2
C. 200 km2
D. 114 km2
Answers
Answer: Option 'D' is correct.
Step-by-step explanation:
Since we have given 4 trapeziums with parallel sides :
[tex]a=8\ km\\b=4\ km[/tex]
For height 'h'. we will consider the right angled triangle with
Perpendicular = 4.3 km and base = 2 km ,
We need to find the hypotenuse:
[tex]H^2=B^2+P^2\\\\H^2=2^2+4.3^2\\\\H^2=4+18.49\\\\H=\sqrt{22.49}\\\\H=4.742\ km[/tex]
Now, Lateral surface area of the figure = 4 × Area of trapezium
[tex]4\times \frac{1}{2}\times (8+4)\times 4.742\\\\=113.81\ km^2\\\\=114\ km^2[/tex]
Hence, Option 'D' is correct.
There are 9 different positions on a baseball team. if a team has 18 players how many different line-ups can the team make?
Answers
Final answer:
To find the number of different line-ups a team can make, we use permutations. Using the formula for permutations, we arrive at the answer of 437,760 different line-ups.
Explanation:
To find the number of different line-ups a team can make, we need to use the concept of permutations. Since there are 9 positions on a baseball team and 18 players, we can arrange the players in a line-up using the formula for permutations:
P(n, r) = n! / (n-r)!
Where n is the total number of players (18) and r is the number of positions (9). Substituting the values, we get:
P(18, 9) = 18! / (18-9)! = 18!/9! = 437,760.
Therefore, there are 437,760 different line-ups that the team can make.
If f(x) = –x2 + 3x + 5 and g(x) = x2 + 2x, which graph shows the graph of (f + g)(x)?
Answers
(f + g)(x) = –x2 + 3x + 5 + x2 + 2x
(f + g)(x) = 5x + 5
Answer:
Given the functions: [tex]f(x)= -x^2 +3x+5[/tex] and [tex]g(x) = x^2+2x[/tex]
Now, calculate first [tex](f+g)(x)[/tex] ;
[tex](f+g)(x) = f(x) + g(x)[/tex]
Substitute the given values we have;
[tex](f+g)(x) = -x^2+3x+5+x^2+2x[/tex]
Combine like terms;
[tex](f+g)(x) =5x+5[/tex]
Let y = [tex](f+g)(x)[/tex]
Then, we have y = 5x+5
Now, Graph the equation of the line y =5x +5
Using slope intercept form: An equation of line is given by :
y = mx +b ; where m is the slope of the line and b is the y-intercept.
On comparing we get;
m = 5 (Since, slope is positive which means a line moves upward on a graph from left to right)
Now, find the intercepts of the equation: y=5x+5;
x-intercepts: The graph or line crosses the x-axis i.,e
Substitute y = 0 and solve for x;
0 = 5x +5
Subtract 5 on both sides we get;
-5 = 5x
Divide both sides by 5 we get;
x = -1
x-intercepts= = (-1, 0)
Similarly for y-intercept:
Substitute the value of x= 0 and solve for y;
y = 5(0)+5
y = 5
y-intercepts = (0, 5)
Now, using these point we can draw a graph of function [tex](f+g)(x) =5x+5[/tex] as shown below in the attachment.
A rectangular prism has a length of 8 feet, a width of 3 feet, and a height of 5 feet. What is the surface area of the rectangular prism?
Answers
surface area = 2(wl +hl+hw)
w=3
l=8
h=5
wl=3*8 =24
hl=5*8 =40
hw=5*3 =15
24+40+15 = 79
2*79 = 158 feet^2
The surface area of the rectangular prism is 158 square feet.
What is surface area?The surface area of any given object is the area or region occupied by the surface of the object.
Formula for finding the surface area of rectangular prism:Surface Area = 2{(h × l) + (h × w) +(l × w)]
Where,
l is the length of the rectangular prism
h is the height of the rectangular prism
w is the width of the rectangular prism
According to the given question
Length of the rectangular prism = 8 feet
width of the rectangular prism = 3feet
height of the rectangular prism = 5 feet.
Therefore,
the surface area of the rectangular prism = 2[(8 × 5)+ ( 5 × 3) + ( 8 × 3)]
surface area of rectangular prism = 2[ 40 +15 +24} = 158 square feet.
Hence, the surface area of the rectangular prism is 158 square feet.
Learn more about the surface area of rectangular prism here:
https://brainly.com/question/14987814
#SPJ2
Solve x2 – 4 = 5 by graphing the related function.
Answers
+4 +4
x2=9
square root both the x and 9
x=3
Answer:
Refer graph attached below
Step-by-step explanation:
Given equation [tex]x^2-4=5[/tex]
We have to Solve the given equation [tex]x^2-4=5[/tex] graphically.
We first solve the given equation [tex]x^2-4=5[/tex]
Consider the given equation [tex]x^2-4=5[/tex]
Adding 4 both sides, we have
[tex]\Rightarrow x^2-4+4=5+4[/tex]
Simplify, we get,
[tex]\Rightarrow x^2=9[/tex]
[tex]\Rightarrow x^2-9=0[/tex]
To plot the graph let [tex]x^2-9=y[/tex] be the equation
It will be a parabola with vertex (0,9).
Refer graph attached below
Write an algebraic equation for the following. The product of three and a squared number is twice the sum of the number and four.
Answers
x is the unknown number
Write the expression in standard form.
three divided by quantity three minus twelve i.
Answers
Answer:
What was the answer?!?!!?!? >-<