The area of the triangle is 16.
You can find this by plotting each of the points and drawing the triangle. You can then use the distance formula to determine each side length. The rectangle will be 2 on one side and 4 on the other. When multiplied together, it will give you the above answer
The coordinates of the midpoints for each side are (2.5, 5.5) , (4.5, 2.5), (1.5, 4.5), and (- 0.5, 7.5).
And, yes, the midpoints are the vertices of a rectangle, as its opposite sides are the same in length.
Use the formula for the midpoint of two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are,
[tex][\dfrac{(x_1 + x_2)}{2} , \dfrac{(y_1 + y_2)}{2} ][/tex]
Given that,
Vertices of the rectangle are (0, 8), (5, 3), (4, 2), and (- 1, 7).
Hence, the coordinates of the midpoints for each side are calculated by using the above formula,
The midpoint of two points (0, 8) and (5, 3) are,
[tex](\dfrac{(0 + 5)}{2} , \dfrac{(8 + 3)}{2} )[/tex]
[tex](2.5, 5.5)[/tex]
The midpoint of two points (5, 3) and (4, 2) are,
[tex](\dfrac{(5 + 4)}{2} , \dfrac{(3 + 2)}{2} )[/tex]
[tex](4.5, 2.5)[/tex]
The midpoint of two points (4, 2) and (-1, 7) are,
[tex](\dfrac{(4 - 1)}{2} , \dfrac{(2 + 7)}{2} )[/tex]
[tex](1.5, 4.5)[/tex]
The midpoint of two points (-1, 7) and (0, 8) are,
[tex](\dfrac{(-1 + 0)}{2} , \dfrac{(8 + 7)}{2} )[/tex]
[tex](-0.5, 7.5)[/tex]
Therefore, the coordinates of the midpoints for each side are (2.5, 5.5) , (4.5, 2.5), (1.5, 4.5), and (- 0.5, 7.5).
When the coordinates of vertices are rectangular then opposite sides are equal to each other.
So, we can check the length of each side of the coordinates of the midpoints (2.5, 5.5), (4.5, 2.5), (1.5, 4.5), and (- 0.5, 7.5).
Used the distance formula,
The distance between two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is,
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
So, The distance between the two points [tex](2.5, 5.5)[/tex] and [tex](4.5, 2.5)[/tex],
[tex]d = \sqrt{(4.5- 2.5)^2 + (2.5 - 5.5)^2}[/tex]
[tex]d = \sqrt{4 + 9}[/tex]
[tex]d = \sqrt{13}[/tex]
The distance between the two points [tex](4.5, 2.5)[/tex] and [tex](1.5, 4.5)[/tex],
[tex]d = \sqrt{(4.5- 1.5)^2 + (2.5 - 4.5)^2}[/tex]
[tex]d = \sqrt{9 + 4}[/tex]
[tex]d = \sqrt{13}[/tex]
The distance between the two points [tex](1.5, 4.5)[/tex] and [tex](-0.5, 7.5)[/tex]
[tex]d = \sqrt{(1.5+ 0.5)^2 + (7.5 - 4.5)^2}[/tex]
[tex]d = \sqrt{4 + 9}[/tex]
[tex]d = \sqrt{13}[/tex]
The distance between the two points[tex](-0.5, 7.5)[/tex] and [tex](2.5, 5.5)[/tex]
[tex]d = \sqrt{(2.5+ 0.5)^2 + (7.5 - 5.5)^2}[/tex]
[tex]d = \sqrt{9 + 4}[/tex]
[tex]d = \sqrt{13}[/tex]
Clearly, All the lengths of each side of the coordinates of the midpoints (2.5, 5.5), (4.5, 2.5), (1.5, 4.5), and (- 0.5, 7.5) are the same.
Hence, it forms a rectangle, as its opposite sides are also the same in length.
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56. Mikayla is filling a glass sphere with water.
If the diameter of the sphere is 12 inches,
what is the minimum amount of water she
needs to completely fill the sphere?
The minimum amount of water she needs to completely fill the sphere is; 904.32 inches³
How to find the Volume of a Sphere?
The formula for Volume of a Sphere is given as;
V = ⁴/₃πr³
We are given;
Diameter; d = 12 inches
Thus;
Radius; r = 12/2 = 6
To get the minimum amount of water she needs to completely fill the sphere, we just plug in the relevant values into the volume equation to get;
V = ⁴/₃π(6)³
V = 904.32 inches³
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In a lottery daily game, a player picks four numbers from 0 to 9 (without repetition). How many different choices does the player have
a) If order matters?
b) If order does not matter?
Answer:
a) If order matters, choices the player have = 5040
b) If order does not matter, choices the player have = 210
Step-by-step explanation:
n = 10, r = 4
When the order matters, its permutation.
permutation without repetition = P(n, r) = [tex]\frac{n!}{(n - r)!}[/tex]
= [tex]\frac{10!}{(10 - 4)!}[/tex]
= [tex]\frac{10!}{6!}[/tex]
= 5040
When the order doesn't matter, its combination.
combination without repetition= C(n, r) = [tex]\frac{n!}{r!(n - r)!}[/tex]
= [tex]\frac{10!}{4!(10 - 4)!}[/tex]
= [tex]\frac{10!}{4! × 6!}[/tex]
= 210
If order matters, there are 5,040 different choices. If order does not matter, there are 210 different choices.
Explanation:a) If order matters, the player has 10 choices for the first number, 9 choices for the second number (since it cannot be the same as the first), 8 choices for the third number, and 7 choices for the fourth number. Therefore, the total number of different choices is 10 * 9 * 8 * 7 = 5,040.
b) If order does not matter, the player is selecting a combination rather than a permutation. The number of combinations of four numbers chosen from a set of ten is given by the formula nCr = n! / (r!(n-r)!). In this case, n = 10 and r = 4, so the number of different choices is 10! / (4!(10-4)!) = 210.
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3. I need help with question in the attached picture!
ANSWER
p
[tex]{f}^{ - 1} (x) = 3x + 4[/tex]
EXPLANATION
The line r has equation,
[tex]f(x) = \frac{x - 4}{3} [/tex]
The line that represents
[tex] {f}^{ - 1} [/tex]
is p.
To find the equation of p, we let
[tex]y = \frac{x - 4}{3} [/tex]
We now interchange x and y.
[tex]x= \frac{y - 4}{3} [/tex]
We solve for y,
[tex]3x=y - 4[/tex]
[tex]y = 3x + 4[/tex]
Therefore
[tex] {f}^{ - 1} (x) = 3x + 4[/tex]
solve for x X - 47 = 192
Answer: x = 239
Step-by-step explanation:
You need to get rid of everything else except the x = #
So, to do that you need to take the -47 and add 47 on each side.
That would get you x = 239
Answer:
239
Step-by-step explanation:
X - 47 = 192
X = 192 + 47
X = 239
The independent variable in the relationship is the and should be placed on the . The dependent variable in the relationship is the and should be placed on the .
The independent variable is manipulated or controlled by the experimenter and is usually placed on the horizontal axis of a graph. The dependent variable is the variable that is measured to see the effect of the independent variable and is usually placed on the vertical axis of a graph.
Explanation:In a scientific study, the independent variable is the variable that is manipulated or controlled by the experimenter, and it is usually placed on the horizontal axis of a graph. The dependent variable is the variable that is measured to see the effect of the independent variable, and it is usually placed on the vertical axis of a graph.
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Carlos is half as old as Andre Andre is 15 years older than Carlos how old is Andre
Carlos is 15 years old and Andre is 30 years old.
Explanation:Let's represent Carlos' age as 'x', and Andre's age as 'y'.
We are given that Carlos is half as old as Andre, so we can write the equation:
x = (1/2)y
We are also told that Andre is 15 years older than Carlos, so we can write the equation:
y = x + 15
Substituting the value of y from the second equation into the first equation, we get:
x = (1/2)(x + 15)
Now, we can solve for x:
2x = x + 15
x = 15
Therefore, Carlos is 15 years old. Andre's age can be found by substituting the value of x into the second equation:
y = 15 + 15
y = 30
So, Andre is 30 years old.
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which sampling method starts with a random number and then selects every “k”th number thereafter?
A. simple random sampling
B. systematic random sampling
C. stratified random sampling
D. Cluster sampling
Answer:
B. Systematic Random Sampling
Step-by-step explanation:
The process of systemic random sampling involves randomly selecting the starting point but the succeeding points will be based on the interval in between each point. The interval is computed by dividing the population by the sample size.
Answer:
B. Systematic Random Sampling
Step-by-step explanation:
none that i can explain
please answer me x and my step correct please
Answer:x=4√6
Step-by-step explanation:
In ∆DCB, cos30°=BC/DB
√3/2*16=BC
BC=8√3
Applying PYTHAGORAS THEOREM in ∆BAC,
(8√3)^2=2x^2
x=4√6
Answer:
[tex]x=4\sqrt6}[/tex]
Step-by-step explanation:
Look at the picture.
ΔACD it's a triangle 30° - 60° - 90°. The sides are in ratio 1 : √3 : 2.
Therefore
CD : CB : DB = 1 : √3 : 2.
If BC = 16, then CD = 16 : 2 = 8 and CB = 8√3
ΔABC it's a triangle 45° - 45° - 90°. The sides are in ratio 1 : 1 : √2.
Therefore
AC : AB : CB = 1 : 1 : √2
If CB = 8√3, then AB = x = (8√3)/(√2)
[tex]x=\dfrac{8\sqrt3}{\sqrt2}\cdot\dfrac{\sqrt2}{\sqrt2}=\dfrac{8\sqrt6}{2}=4\sqrt6[/tex]
Graph f(x)=x2 +2x-3 label x and y intercept and vertex with their coordinates and draw axis of symmetry
Answer:
f(x) = x² + 2x - 3 ..….equation1
The graph of function will be a parabola
Standard form of parabola:
y=ax²+bx+c
x-coordinate of the vertex can be found using
x = [tex]\frac{−b}{2a}[/tex]
from equation 1 find values for a, b, and c.
a = 1, b = 2, c = -3 ⇒ x=−2/2(1) ⇒ x = -1
substitute the value of x into equation 1 for y-coordinate
f(-1) = (-1)² + 2(-1) – 3 ⇒ −4
vertex =(-1,−4)
Axis of symmetry = x = -1,
Axis of symmetry is vertical and passes through the vertex with equation
x = -1
For x-intercept, put y = 0
x² + 2x - 3=0 ⇒ x² + 3x -x - 3=0 ⇒ x( x + 3 ) -1 ( x + 3 ) ⇒ ( x − 1 )( x + 3 ) = 0
equate each factor to zero and solve for x
x − 1 = 0 ⇒ x = 1, x + 3 = 0 ⇒ x = -3
x-intercept = { 1, -3 }
For y-intercepts put x = 0
y = (0)² + 2(x) - 3
y = -3
y-intercept = ( 0 , -3 )
The points for the vertex, x-intercepts, and y-intercept and axis of symmetry are plotted on the graph.
use the formula a=p(1+r/n)nt to find the compound interest account . zakk deposited $5600.0in an account which compounded 1.9%quarterly and left there for ten years. what was the amount in the account at the end of ten years,?
Answer:
[tex]A=\$6,768.75[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=10\ years\\ P=\$5,600\\ r=0.019\\n=4[/tex]
substitute in the formula above
[tex]A=\$5,600(1+\frac{0.019}{4})^{4*10}[/tex]
[tex]A=\$5,600(1.00475)^{40}=\$6,768.75[/tex]
Fiona’s school has three hallways that make up three sides of a triangular building design. In the morning, Fiona walks 90 yards through the first hallway to get to the next. In the afternoon, she walks 60 yards through a second hallway to exit the building. What are the possible lengths of the third hallway that she did not walk through? between 30 yards and 60 yards between 30 yards and 90 yards between 30 yards and 120 yards between 30 yards and 150 yards
Answer:
"between 30 yards and 150 yards"
Step-by-step explanation:
Let one side of a triangle be x and another side be y. To find the possible lengths of the third side, it is given by:
Possible length of 3rd side would be between "x - y" and "x + y"
Here, given x = 90 and y = 60, so the possible length of 3rd side would be:
90 - 60 = 30,
90 + 60 = 150
Hence, in between 30 and 150
Answer:
its D between 30 and 150 just took test on ed got a 100
Step-by-step explanation:
Someone left me a ______ message on my voicemail; I had no idea what it meant.
Cryptic
Boisterous
Petulant
Jovial
Answer:
It is cryptic
Step-by-step explanation:
It is cryptic bc it means secretive and with hidden meaning
Answer:
Cryptic
Step-by-step explanation:
Cryptic means "having a meaning that is mysterious or obscure," so this would be the right answer
Why the others aren't correct:
Boisterous- Noisy, energetic, cheerful, rowdy [This doesn't fit the sentence]
Petulant- Childishly sulky [pouty] or bad tempered [This doesn't fit the sentence]
Jovial- Cheerful and friendly [This doesn't fit the answer]
Thus, the answer is cryptic.
I hope this helps!
Jay went to an amusement park. The park charges an entrance fee of $10.50 and $4.50 for every ride. Jay spent $46.50 on entrance fees and rides. Which fuction can be used to find the number of rides he went on?
10.50+4.50x=46.50
This is the fuction to use to solve the problem.
The function that can be used to find the number of rides he went on is
46.50 = 4.5x + 10.50
What is linear equation?A linear equation is a mathematical expression involving variables raised to the first power only.
It takes the form ax+b=0, where
a and b are constants, and x is the variable.
Represent the number of rides he went on by x
the total amount on rides will be
4.5x
The entrance fee = $10.50
Total amount = 45x + 10.50
Therefore, the equation that represents the number of rides he went on is
46.50 = 45x + 10.50.
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Solve 2.02W = -3.636
Answer: W=-1.8
Step-by-step explanation:
Divide both sides by 2.02 and you are left with W=-1.8.
Hope this helps!
Answer:
W = -1.8
Step-by-step explanation:
Step 1: Divide 2.02 on both sides.
W = -1.8
How many complex roots does the equation below have?
x 6 + x 3 + 1 = 0
The number of complex roots is
Answer:
The number of complex roots is 6.
Step-by-step explanation:
Descartes's rule of signs tells you that the number of positive real roots is 0. The number of negative real roots will be at most 2. The minimum value of the left side will be between x=0 and x=-1, but will never be negative. Thus all six roots are complex.
_____
The magnitude of x^3 will exceed the magnitude of x^6 only for values of x between -1 and 1. Since the magnitude of either of these terms will not be more than 1 in that range, the left-side expression must be positive everywhere.
Answer:
6
Step-by-step explanation:
The price of a ring was increased by 8% to £486. What was the price before the increase?
Step-by-step explanation:
price before increased be x
After it is increased by 8% it becomes1.08x
equal to 486
so 1 .08x=486
x=£450
The price of the ring before the increase was £450.
What is the Selling Price?
This refers to the value given to a product when sold to consumers from the retailers or wholesalers.
Hence,
Given that the price before the increase is X
If increased by 8%,
It becomes 1.08x=486
Collect like terms
x= £450
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Write the slope-intercept form of the equation for the line.
let's use those two endpoints in the line of (-5 , 2) and (5 , -1)
[tex]\bf (\stackrel{x_1}{-5}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-2}{5-(-5)}\implies \cfrac{-3}{5+5}\implies -\cfrac{3}{10}[/tex]
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-2=-\cfrac{3}{10}[x-(-5)]\implies y-2=-\cfrac{3}{10}(x+5) \\\\\\ y-2=-\cfrac{3}{10}x-\cfrac{3}{2}\implies y=-\cfrac{3}{10}x-\cfrac{3}{2}+2\implies y=-\cfrac{3}{10}x+\cfrac{1}{2}[/tex]
Answer:
y=-(3/10)x+(1/2)
Step-by-step explanation:
Let
A(-5,2),B(5,-1)
step 1
Find the slope m
m=(-1-2)/(5+5)
m=-3/10
step 2
Find the equation of the line into slope point form
we have
m=-3/10
point A(-5,2)
y-2=(-3/10)(x+5) ----> equation of the line into slope point form
Convert to slope intercept form -----> isolate the variable y
y=-(3/10)x-(15/10)+2
y=-(3/10)x+(5/10)
simplify
y=-(3/10)x+(1/2)
The mean absolute deviation is a measure of . This value represents the average distance each value is from the .
Previous
Answer:
I am not sure i am sorry if i was smart i would know but ya sorry
Step-by-step explanation:
::::::::::::::
30 POINTS,NEED HELP ASAP !!!
Which rule yields the dilation of the figure CDEF centered at the origin?
A) (x, y) → (4x, 4y)
B) (x, y) → (0.25x, 0.25y)
C) (x, y) → (x + 4, y + 4)
D) (x, y) → (x + 0.25, y + 0.25)
Answer: OPTION A.
Step-by-step explanation:
You can observe that in the figure CDEF the vertices are:
[tex]C(-2,-1),\ D(-2,0),\ E(2,2)\ and\ F(2,1)[/tex]
And in the figure C'D'E'F' the vertices are:
[tex]C'(-8,-4),\ D'(-8,0),\ E'(8,8)\ and\ F'(8,4)[/tex]
For this case, you can divide any coordinate of any vertex of the figure C'D'E'F' by any coordinate of any vertex of the figure CDEF:
For C'(-8,-4) and C(-2,-1):
[tex]\frac{-8}{-2}=4\\\\\frac{-4}{-1}=4[/tex]
Let's choose another vertex. For E'(8,8) and E(2,2):
[tex]\frac{8}{2}=4\\\\\frac{8}{2}=4[/tex]
You can observe that the coordinates of C' are obtained by multiplying each coordinate of C by 4 and the the coordinates of E' are also obtained by multiplying each coordinate of E by 4.
Therefore, the rule that yields the dilation of the figure CDEF centered at the origin is:
[tex](x, y)[/tex]→[tex](4x, 4y)[/tex]
Answer:
A. (x, y) => (4x, 4y) this will help you out ;-)
the volume of a cylinder is found by?
Answer:
Step-by-step explanation:
Base x width x height
For this case we have by definition that the volume of a cylinder is given by:
[tex]V = \pi * r ^ 2 * h[/tex]
Where we have to:
A: It is the radius of the cylinder
h: It is the height of the cylinder
To find the volume of a cylinder we must have the radius and the height. In an equivalent way we can have the diameter, the radius is obtained by dividing the diameter by 2.
Answer:
[tex]V = \pi * r ^ 2 * h[/tex]
Which graph shows the graph of a circle with equation x^2+(y-4)^2=16
Answer:
The option on the top left
Step-by-step explanation:
As the equation is [tex]x^2+(y-4)^2=16[/tex]
We know that the circle will have a radius of 4 and will be shifted 4 units up
The center and radius of given circle equation are (0, 4) and 6√6 units respectively.
What is a circle equation?The equation of circle provides an algebraic way to describe a circle, given the center and the length of the radius of a circle. The equation of a circle is different from the formulas that are used to calculate the area or the circumference of a circle.
The standard equation of a circle with center at (x₁, y₁) and radius r is (x-x₁)²+(y-y₁)²=r²
The given circle equation is x²+(y-4)²=216.
Find the properties of the conic section
Center: (0,4)
Radius: 6√6
Find the domain by finding where the equation is defined. The range is the set of values that correspond with the domain.
Domain:
[−6√6,6√6],{x∣∣−6√6≤x≤6√6}
Range: [4−6√6,4+6√6],{y∣∣4−6√6≤y≤4+6√6}
Therefore, the center and radius of given circle equation are (0, 4) and 6√6 units respectively.
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So I need to determine what he did wrong is this problem and what the correct step would be?
WORTH 59 POINTS
The top line has 4x^-2, they needed to move the x^-2 to the denominator using the negative exponent rule, so in line 1 instead of 1/y^-2, it should be 1/x^-2
Then the answer would become 4y^3 / x^3
My teacher dis the first one
Answer:
x² + 11x + 30
Step-by-step explanation:
Solve using the FOIL method. The FOIL method is:
FOIL =
First
Outside
Inside
Last
, and is the order in which you do the problem.
(x + 5)(x + 6)
Follow FOIL. First, solve First (multiply x with x)
(x)(x) = x²
Next, multiply Outside (multiply x with 6)
(x)(6) = 6x
Then, multiply Inside (multiply 5 with x)
(5)(x) = 5x
Finally, multiply Last (multiply 5 with 6)
(5)(6) = 30
Combine like terms (terms with the same amount of variables, and the same variables)
x² + 6x + 5x + 30
x² + (6x + 5x) + 30
x² + 11x + 30
x² + 11x + 30 is your answer.
~
PLEASE HELP RIGHT AWAY
Answer:
95
Step-by-step explanation:
Week Number of Beetles
0 16
1 16 + (16/4) = 20
2 20 + (20/4 ) = 20 + 5 = 25
3 25 + (25/4 ) = 25 + 6.25 ≈ 31
4 31 + (31/4) = 31 + 7.75 ≈ 31+8 ≈ 39
5 39 + (39/4) = 39 + 9.75 ≈ 39 + 10 ≈ 49
6 49 + (49/4) = 49+ 12.25 ≈ 49+12 ≈ 61
7 61 + (61/4) = 61 + 15.25 ≈ 61 + 15 ≈ 76
8 76 + (76/4) = 76 + 19 = 95
Hence there will be approximately 95 beetles by 8th week
Factorisation of ax^2 + bx + c
Answer:
-5(t+3)(t-6)
Step-by-step explanation:
-5²+15+90
= -5(t²-3t-18)
= -5(t+3)(t-6)
Maria solved the equation 34=+19
34
=
x
+
19
. Although her final answer was correct, she could have found it in a simpler way. Which sentence best explains why?
She could've subtracted 19 from both sides of the equation in the second step to find the value of [tex]x[/tex] immediately, rather then add 19 to both sides.
[tex]34=x+19 \\ \\ 34-19=x+19-19 \\ \\ x=15[/tex]
Answer:
19 should have been subtracted from, not added to, both sides of the equation.
Step-by-step explanation:
What would the mode be with this data set??
5,5,5,5,5
ANSWER=5
EXPLANATION
The Mode is known as the number that occurs most often in a set of data, so the data being 5,5,5,5,5 only has fives in it so the answer must be 5.
Hello There!
The mode is the number that occurs the most in a set of numbers. In this case, there is only 5 numbers but they are all the same so the mode of the data set shown would be 5.
x^y=p
Express in logarithmic form for the base.
ANSWER
[tex]y= log_{x}(p)[/tex]
EXPLANATION
The given expression is
[tex] {x}^{y} = p[/tex]
We take logarithm of both sides to base x.
[tex] log_{x}( {x}^{y} ) = log_{x}(p) [/tex]
Apply the power rule of logarithms to get:
[tex]ylog_{x}( {x}) = log_{x}(p)[/tex]
Logarithm of the base is 1.
This implies that,
[tex]y( 1) = log_{x}(p)[/tex]
[tex]y= log_{x}(p)[/tex]
.......Help Please......
Answer:
(7,5) is the vertex
Step-by-step explanation:
Anik is married and earns $29,560 per year. What is his
weekly federal withholding?
$44.89
$90.34
$82.88
$45.17
$41.44
90.34 because you divide 29,560 and 12 and then the answer to that by 12 and then divide by 4 and then divide by 7 and round