There are two pieces of wires, each of length 66 cm. One wire is bent into a square and the other wire is bent into a circle. Find (a) the area of the square, (b) the area of the circle.
Answer:
Area of Circle = 346.5 cm².
Area of square = 272.25 cm ² .
Step-by-step explanation:
So , 2πR = 66
2 × 22 / 7 × R = 66
R comes out is 21/2 cm .
Area of Circle = 22/7 × 21/2 × 21/2 = 33×21/2
= 693 / 2 = 346.5 cm².
If bent into the shape of a square ;
4 a = 66
a = 33/2 . ( Side of a square )
Area of square = a ² = 33×33/4 = 1089/4
= 272.25 cm ² .
A ball is kicked upward with an initial velocity of 52 feet per second. The ball's height, h (in feet), from the ground Is
modeled by h= -16t^2 +52t where t is measured in seconds. How much time does the ball take to reach its highest
point? What is its height at this point?
Check the picture below.
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+52}t\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 52}{2(-16)}~~~~ ,~~~~ 0-\cfrac{ (52)^2}{4(-16)}\right) \implies \left( - \cfrac{ 52 }{ -32 }~~,~~0 - \cfrac{ 2704 }{ -64 } \right)[/tex]
[tex]\left( \cfrac{13}{8}~~,~~\cfrac{169}{4} \right)\implies \underset{\stackrel{\uparrow \hspace{3em}}{seconds\qquad }}{\stackrel{\stackrel{\qquad feet}{\hspace{3em}\downarrow }}{\left( 1\frac{5}{8}~~,~~42\frac{1}{4} \right)}}[/tex]
PLEASE HELPPP ITS WORTH 20 points!!!
Answer:
tanD =4/7
Step-by-step explanation:
tanD = P/B
Where P=4 and B=7
So;
tanD=4/7
Please Help I Don't Understand!
Answer:
5.3
Step-by-step explanation:
Since they are similar triangles, we assume the ratio between AM/AN is equal to the ratio between MB/NC.
AM/AN = 6/8 = 3/4
If MB is 4
3/4 = MB/NC = 4/NC
3/4 = 4/NC
3NC = 16
NC = 16/3
16/3 = 5.333333
My sister needs help on this question and I am too lazy to figure this out please help ASAP
The question was: Which figure has exactly one line of symmetry?
Answer:
its the Pentagon, the other shaps have 2 lines if symmetry
8- Determine the midpoint of a line segment with the endpoints (8, 0) and
(4,6)
A. (3,6)
B. (7,3)
C. (6,3)
D. (7.6)
Can someone help pls ?
Answer:
C. (6, 3)
Step-by-step explanation:
Use the midpoint formula!
Midpoint Formula
[tex]\text{midpoint} = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})[/tex]
x₁, x₂ ... x-coordinates of the endpoints
y₁, y₂ ... y-coordinates of the endpoints
Given endpoints:
(8, 0)
(4, 6)
Points are in form (x, y).
Now let's substitute the variables in the formula with our values.
[tex](\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})[/tex]
[tex](\frac{8 + 4}{2}, \frac{0+ 6}{2})[/tex]
[tex](\frac{12}{2}, \frac{6}{2})[/tex]
[tex](6, 3)[/tex]
(6, 3) is our midpoint!
Mrs. Yamaguchi's class weighed the potatoes that they grew in their garden and recorded the data on a table. Determine how many dots are above each data value in a line plot of this data.
Weights of Potatoes (in pounds)
1
4
3
8
5
8
1
2
5
8
1
2
1
2
3
4
1
4
1
8
3
4
1
2
3
8
1
2
3
4
3
8
The value
1
8
will have
Choose...
dots above it.
The value
1
4
will have
Choose...
dots above it.
The value
3
8
will have
Choose...
dots above it.
The value
1
2
will have
Choose...
dots above it.
Using a dot plot, it is found that the number of dots of each point are given as follows:
The value [tex]\frac{1}{8}[/tex] will have one dot above it.The value [tex]\frac{1}{4}[/tex] will have two dots above it.The value [tex]\frac{3}{8}[/tex] will have three dots above it.The value [tex]\frac{1}{2}[/tex] will have five dots above it.The value [tex]\frac{5}{8}[/tex] will have two dots above it.The value [tex]\frac{3}{4}[/tex] will have three dots above it.What does a dot plot shows?The dot plot shows the number of times each measure appears in the data-set.
In this problem, one measure has a value of 1/8, hence:
The value [tex]\frac{1}{8}[/tex] will have one dot above it.
Two measures have a value of 1/4, hence:
The value [tex]\frac{1}{4}[/tex] will have two dots above it.
Three measures have a value of 3/8, hence:
The value [tex]\frac{3}{8}[/tex] will have three dots above it.
Five measures have a value of 1/2, hence:
The value [tex]\frac{1}{2}[/tex] will have five dots above it.
Two measures have a value of 5/8, hence:
The value [tex]\frac{5}{8}[/tex] will have two dots above it.
Three measures have a value of 3/4, hence:
The value [tex]\frac{3}{4}[/tex] will have three dots above it.
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Answer:
1 2 3 5 2 3
Step-by-step explanation:
2. Mikaela counted 2 more turtle nests
on a North Carolina beach than
Diego. If Mikaela counted 38 turtle
nests, which equation could you use
to find the number of turtle nests
Diego counted?
A 2x = 38
B x÷2=38
C x - 2 = 38
D x + 2 = 38
expression equivlant (x+5)^2
Answer:
(x+5) (x+5)
Step-by-step explanation:
it's just (x+5)^2 twice
I NEED HELP ASAPPPPPP
Its height (in feet) as a function of time (in seconds after the timer was started) is given by the equation h(t)=−(t−12)2+81
. Which of the following statements is true?
The airplane reaches its minimum height of 12 feet in 81 seconds.
The airplane reaches its maximum height of 81 feet in 12 seconds.
The airplane reaches its minimum height of 81 feet in 12 seconds.
The airplane reaches its maximum height of 12 feet in 81 seconds.
Considering the given quadratic equation, the correct statement is given by:
The airplane reaches its maximum height of 81 feet in 12 seconds.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
In this problem, the equation is given by:
h(t) = -(t - 12)² - 81.
The vertex is (12,81), with a negative leading coefficient, hence it is a maximum point and the correct statement is given by:
The airplane reaches its maximum height of 81 feet in 12 seconds.
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A stack of 30 science flashcards includes a review card for each of the following: 10 insects, 8 trees, 8 flowers, and 4 birds.
What is the probability of randomly selecting an insect?
Express the probability as a reduced fraction
Answer:
1/3
Step-by-step explanation:
[tex]|\Omega|=30\\|A|=10\\\\P(A)=\dfrac{10}{30}=\dfrac{1}{3}[/tex]
A standard die is rolled and a month
of the year is chosen at random.
What is the probability of rolling a
number that is at least
then
choosing a month that does not
begin with the letter M?
200
Answer:
The probability is [tex]\frac{5}{9}[/tex]
Step-by-step explanation:
First we will find the probability of having a roll that is at least 3
1 2 3 4 5 6
this means there is a [tex]\frac{4}{6}[/tex] chance we will roll at least 3
Next we will find which months of the year are applicable
January February March April May June July August September October November December
This means there is a [tex]\frac{5}{6}[/tex] chance we will pick a month that does not begin with the letter M.
Now we can multiply these chances together to see what the total probability is.
[tex]\frac{4}{6} * \frac{5}{6} = \frac{20}{36} \rightarrow \boxed{\frac{5}{9}}[/tex]
That is the answer
- Kan Academy Advance
What is x in the figure?
im not sure I'd need to see the figure
HELLPPPPP ASAAPPPP.
What is the length of EF? (Giving 45 points, please hurry!)
Reflect the shape A in the line y
=
y
(-5, 6)
(4,3)
(-3, 1)
-8-7 -6 -5 -4 -3 -2 -1
4 5 6 7 8
-1
-2
-3
-4
-5
-6
-7
-8
What are the coordinates of the vertices
of the image?
A
00
8
7
6
LO
5
4
3
2
-
1
Đ
1
-2
3
-X.
2
(-5,6)
Step-by-step explanation:
What is the value of x?
(Round your answer to
the nearest tenth.)
Answer:
x ≈ 8.7
Step-by-step explanation:
given 2 secants from an external point to the circle, then
the product of the external part of one secant and the entire secant is equal to the product of the external part of the other secant and the entire secant , that is
6(6 + x) = 4(4 + 18) ← distribute parenthesis on both sides
36 + 6x = 4 × 22 = 88 ( subtract 36 from both sides )
6x = 52 (divide both sides by 6 )
x ≈ 8.7 ( to the nearest tenth )
Question in the picture 1-5
how to understand next steps what will be anyone give me explains
Step-by-step explanation:
remember a few things :
a × -1 = -a
-a × -1 = a
-1 × -1 = 1
1 × a = a
therefore,
-1 × -1 × a = 1 × a = a
and finally
c × (a + b) = c×a + c×b
so, we can say
(1 - 5) = -1 × -1 × (1 - 5) =
= -1 × (-1×1 + -1×-5) = -1 × (-1 + 5) =
= -1 × (5 - 1) = -(5 - 1)
Solve each equation.
1. x+6=4
2.x- -4 = -6
3.2(x-1)=-200
4.2x+-3=-23
Step-by-step explanation:
1) x+6 =4
x. =4-6
x. =-2
2) x-(-4) =-6
x+ 4. =-6
x. =-6-4
x. =-10
3)2(x-1)=-200
2x-2 =-200
2x. = -200+2
2x. = -198
x. = -198/2
x. = -99
4)2x+(-3) =-23
2x-3. =-23
2x. =-23+3
2x. =-20
x. =-20/2
x. = -10
please help me thank you :)
The function on the table is decreasing on the interval [-2, 0).
Over what interval is the function shown in the table decreasing?
A function is decreasing if, as x increases, f(x) decreases.
We can see that at x = -2, f(-2) = 12.
Then at x = 0, f(0) = 0.
And for the value after that:
x = 1, f(1) = 3
So now the function increases. Then we conclude that the function is decreasing on the interval [-2, 0), and after that the function increases.
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What is the discriminant of the quadratic equation 0 = -x² + 4x − 2?
Answer: 8
Step-by-step explanation:
The discriminant is [tex]b^2-4ac[/tex]
in the equation:
[tex]-x^2+4x-2[/tex]
A = -1, B = 4, C = -2
plug into equation
[tex]4^2-4(-1)(-2)[/tex]
[tex]16-8[/tex]
⇒ [tex]8[/tex]
please help with math
Which of the following functions best models the data represented by the scatterplot shown below?
A: y=160x-100
B: y=2^x+12
C: y=8x^2+10
D: y=25x+20
Answer:
C: y = 8x^2 + 10.
Step-by-step explanation:
It looks close to being a parabola so I think it is probably a function in x^2.
Try 8x^2 + 10
Checking against the plot
When x = 5 , y = 8(5)^2 + 10 = 210 , and on graph its 200
Calculating y for other values:
When x = 7, y = 8(7)^2 + 10 = 402, and on graph y = 400.
When x = 11, y = 978 , and on graph = 1000.
When x = 17, y = 2322, and on graph y = about 2350.
f(x) = 5 + 4x2, then f(3) =
Step-by-step explanation:
To answer this, we need to plug in 3 as x in the equation f(x) = 5 + 4x².
That would look like this: f(3) = 5 + 4(3)²
f(3) = 5 + 4(3)²
f(3) = 5 + 36
f(5)=41
Therefore, the answer is 41.
I hope this helps!! :)
To identify the most efficient model for a windmill, Gandalf Engineering Company designs the windmill shown. The design consists of four right triangles arranged equally around point O such that point O is the midpoint of BF¯¯¯¯¯ and DH¯¯¯¯¯¯.
Deductive Reasoning is the practice of arriving at a mathematical conclusion by simply analyzing the facts using the knowledge of the related concepts.
What is the proof that ∠A ≅ ∠E?Looing at ΔOAB and ΔOEF
It is clear that
OB = OF (O is the midpoint)
∠OBA = ∠OFE = 90°
Therefore
∠AOB = ∠EOF (Vertically Opposite Angles)
⇒ ΔOAB ≅ ΔOEF and
∠ A ≅ ∠E.
QED
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) The gym teacher divided a class into four teams with 7 students per team. How many students are in the class?
Answer:
28 students
Step-by-step explanation:
7 times 4 = 28
there are are seven students in 4 teams, so that means there are 4 groups of seven, and you multiply them together to get how many students in the class
Answer:
28
Keyword(s):
divided, four, 7, per team, how many
Step-by-step explanation:
7 × 4 = 28
dependent or independent
The probability of coin landing with heads is an independent event.
The probability of winning 1st and 2nd prize is a dependent event.
What are independent and dependent events?
Independents events are events whose occurrence do not depend on each other. They are random events. The probability of a coin landing on heads is a random event.
Dependent events are events that are not random. The outcome of one event depends on the outcome of another event.
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for each sequences, find the first 4 term and the 10th term the sequences are
(a) n^2+3
(b)2n^2
Answer:
see explanation
Step-by-step explanation:
to find the first 4 terms substitute n = 1, 2, 3, 4 into the sequence rule
to find the 10th term substitute n = 10 into the rule
(a)
a₁ = 1² + 3 = 1 + 3 = 4
a₂ = 2² + 3 = 4 + 3 = 7
a₃ = 3² + 3 = 9 + 3 = 12
a₄ = 4² + 3 = 16 + 3 = 19
a₁₀ = 10² + 3 = 100 + 3 = 103
(b)
a₁ = 2(1)² = 2(1) = 2
a₂ = 2(2)² = 2(4) = 8
a₃ = 2(3)² = 2(9) = 18
a₄ = 2(4)² = 2(16) = 32
a₁₀ = 2(10)² = 2(100) = 200
Which graph can be used to find the solution(s) to x2 – 4x + 4 = 2x + 1 + x2?
The solution to the equation x² – 4x + 4 = 2x + 1 + x² is x = 2.5 and the graph is shown in the picture.
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.
We have an equation:
x² – 4x + 4 = 2x + 1 + x²
After solving:
-4x + 4 = 2x + 1
6x = 3
x = 1/2 = 0.5
Thus, the solution to the equation x² – 4x + 4 = 2x + 1 + x² is x = 2.5 and the graph is shown in the picture.
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pls help... Prove (1+tanx)/(1+cotx)=tanx by algebra
[tex]\text{L.H.S}\\\\=\dfrac{1+\tan x}{ 1+ \cot x}\\\\\\=\dfrac{1+ \tan x}{ 1+ \tfrac 1{\tan x}}\\\\\\=\dfrac{1+\tan x}{\tfrac{\tan x+1}{\tan x}}\\\\\\=(1+\tan x) \times \dfrac{\tan x}{1+ \tan x}\\\\=\tan x\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]