Given:
The figure of rectangle.
To find:
a. The diagonal of the rectangle.
b. The area of the rectangle.
c. perimeter of the rectangle.
Solution:
(a)
In a right angle triangle,
[tex]\sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]\sin 30=\dfrac{12}{Hypotenuse}[/tex]
[tex]\dfrac{1}{2}=\dfrac{12}{Hypotenuse}[/tex]
[tex]Hypotenuse=12\times 2[/tex]
[tex]Hypotenuse=24[/tex]
So, the diagonal of the of the rectangle is 24 units.
(b)
In a right angle triangle,
[tex]\tan \theta=\dfrac{Perpendicular}{Base}[/tex]
[tex]\tan 30=\dfrac{12}{Base}[/tex]
[tex]\dfrac{1}{\sqrt{3}}=\dfrac{12}{Base}[/tex]
[tex]Base=12\sqrt{3}[/tex]
Length of the rectangle is 12 and width of the rectangle is [tex]12\sqrt{3}[/tex]. So, the area of the rectangle is:
[tex]Area=length \times width[/tex]
[tex]Area=12 \times 12\sqrt{3}[/tex]
[tex]Area=144\sqrt{3}[/tex]
So, the area of the rectangle is [tex]144\sqrt{3}[/tex] sq. units.
(c)
Perimeter of the rectangle is:
[tex]P=2(length+width)[/tex]
[tex]P=2(12+12\sqrt{3})[/tex]
[tex]P=24+24\sqrt{3}[/tex]
[tex]P\approx 65.57[/tex]
Therefore, the perimeter of the rectangle is about 65.57 units.
A 29-foot rope is cut into two pieces. The longer piece is 2 feet longer than twice the shorter piece. How long is each piece?
Answer:
20 is the longer piece, 9 is the shorter piece
Step-by-step explanation:
9*2=18
18+2=20
20+9=29
LOOK AT THE PHOTO PLEASE
Answer:
The answer to the question provided is 4.
Step-by-step explanation:
[tex] \: \: \: \: \: \: \: \: \: \: 9x + 4 = 5x + 20 \\ \frac{ - 5x = - 5x}{4x + 4 = 20} \\ \frac{ \: \: \: \: \: \: \: \: - 4 = - 4}{ \frac{4x}{4} = \frac{16}{4} } \\ x = 4[/tex]
[I apologize if the answer to the question is inaccurate]
helppppppppppppppppp
Answer:
x[tex]\leq[/tex]1
Step-by-step explanation:
Which of the expressions are equivalent to the one below? Check all that
apply.
10x(3+4)
A. (3+4)x10
O B. (10x3) + 4
C. 10.3 + 10 - 4
D. 10. (4+3)
SUBMIT
The line of best fit for a set of data is y = 19.3232 – 0.7334x. What is the approximate x-value where the y-value is 15.654
Answer:
The answer should be 5.003, you can round if you want to 5
Step-by-step explanation:
During a 4-year period, 65% of snowstorms in a certain city caused power outages. 14 of the snowstorms did not cause power outages. Find the total number of snowstorms in this city over the 4-year period.
Answer:
40
Step-by-step explanation:
S x .35 = 14
S = 14/.35
S = 40
Verify:
40 x 35% = 14
Huh! Its me DaBaby and i need your help with this question. Yeah Yeah!
Answer:
the third one is the correct answer
[tex]b { }^{ - 16} [/tex]
Step-by-step explanation:
hope the helps
Answer:
b to power of -16
Step-by-step explanation:
By rounding to 1 significant figure estimate the answer to the question of these questions. a) 346x904
b) 2451x988
c) 3203x7756
Write the equation of the quadratic function shown in the graph.
Answer:
Step-by-step explanation:
y = a(x-h)² + k, where (h,k) is the vertex.
vertex is clearly (0,0), so y = ax².
Plug in (3,3) and solve for a:
3 = a3²
a = ⅓
y = ⅓x²
What’s the area of this polygon? Need to show work.
Thank you!
Step-by-step explanation:
area of traingle formed on right= 1/2*base*height
=1/2*5*6
= 15mi²
Help......................
Write the inequality for the description. Use x as your variable.
Mary has at least 14 pairs of shoes in her closet.
Answer:
x≤14
Step-by-step explanation:
≤ = greater than/equal to(at least)
It costs $29.50 to enter an amusement park and $0.25 to ride a ride. You have $30. Write an equation that represents the number of rides you can ride.
Answer: 120.
Step-by-step explanation: $30 divided by $0.25
A tennis tournament has 342 players. A single match involves 2 players. The winner of a match will play the winner of a match in the next round, whereas losers are eliminated from the tournament. The 2 players who have won all previous rounds play in the final game, and the winner wins the tournament. What is the total number of matches
Answer:
341 matches
Step-by-step explanation:
Given
[tex]Players = 342[/tex]
[tex]Match = 2\ players[/tex]
Required
Total number of matches.
The total number of matches is calculated by getting the number of matches in each round.
i.e.
[tex]Matches = \frac{Players}{2}[/tex]
So, we have:
Round 1
[tex]Matches = \frac{342}{2} = 171[/tex]
Round 2
[tex]Matches = \frac{171}{2} = 85\ R\ 1[/tex] [R 1 means remainder 1]
Round 3
[tex]Matches = \frac{85 + 1}{2} = \frac{86}{2} = 43[/tex]
[The remainder is added to each round]
Round 4
[tex]Matches = \frac{43}{2} = 21\ R\ 1[/tex]
Round 5
[tex]Matches = \frac{21+1}{2} = \frac{22}{2} = 11[/tex]
Round 6
[tex]Matches = \frac{11}{2} = 5\ R\ 1[/tex]
Round 7
[tex]Matches = \frac{5+1}{2} = \frac{6}{2} =3[/tex]
Round 8
[tex]Matches =\frac{3}{2} = 1 + 1[/tex]
Round 9
[tex]Matches = \frac{1+1}{2} =\frac{2}{2} = 1[/tex]
So, the total is:
[tex]Total = 171 + 85 + 43 +21 + 11 + 5 + 3 + 1+1[/tex]
[tex]Total = 341[/tex]
Apply the distributive property to create an equivalent expression.
I will give brainiest but if you put a link i won't
9514 1404 393
Answer:
12e -6f -8
Step-by-step explanation:
The factor outside parentheses multiplies each term inside parentheses.
= (6e)(2) +(-3f)(2) +(-4)(2)
= 12e -6f -8
Step by step explanation please
Step-by-step explanation:
of what where is the question
please help i don't even where to start
solve for x
The radius is 10, so the diameter is 20. This means the parts of the diameter (the chord through the center P) to the left and right of the vertical chord have lengths 16 and 4, respectively.
Because the horizontal chord is a diameter, the vertical chord is cut in half, so its parts above and below the diameter both have length x.
Now, by the intersecting chord theorem,
16×4 = x × x
or
x ² = 64
so that
x = 8
Lydia would like to have cake and pizza at her party the cake will cost $23, each pizza cost $15.00 the total budget for the food at her party is $75 what are the number of pizzas she can get and what is the equation and define your variable
Answer:
20
Step-by-step explanation:
fw3f2f3sf a
What is 6 ( 8 + w). Use the distributive property to remove the parentheses.
Answer:
42 + 6w
Step-by-step explanation:
Basically,
6(8+w) is 6 x (8+w)
OR 6(8) + 6(w)
Hence 42 + 6w
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find out the time at which the rocket will reach its max, to the nearest 100th of a second.
y=-16x^2+161x+108
y=−16x
2
+161x+108
Answer:
5.03secs
Step-by-step explanation:
Given the height reached by the rocket expressed as;
y = -16x^2 + 161x + 108
The rocket reaches it max height when its velocity is zero
Velocity is expressed as;
V(x) = dy/dx = 0
dy/dx = -32x + 161
0 = -32x + 161
32x = 161
x = 161/32
x = 5.03
Hence it will take 5.03secs for the rocket to reach its maximum height
Enter your answer in the box.
Find the value of the expression 4d - C + 3 when c = 3 and
d = 6.
Answer:
4d - c + 3
4(6) - 3 + 3
24 - 3 + 3
24
Step-by-step explanation:
24
Hope this helps :T
please help me fast! thanks
Answer:
the answer is 15
Step-by-step explanation:
Just add
Answer:
15 grams
Step-by-step explanation:
Given the points A (-3, -1), B (1, 4) C (4, -1) what is the x coordinate of D, if ABCD is a parallelogram?
Given:
ABCD is a parallelogram, A(-3,-1), B(1,4), C(4,-1).
To find:
The x-coordinate of point D.
Solution:
Let the point D be (x,y).
We know that the diagonals of a parallelogram bisect each other. So, third midpoints are same.
Midpoint formula:
[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
In parallelogram ABCD, AC and BD are two diagonals.
Midpoint of AC = Midpoint of BD
[tex]\left(\dfrac{-3+4}{2},\dfrac{-1+(-1)}{2}\right)=\left(\dfrac{1+x}{2},\dfrac{4+y}{2}\right)[/tex]
[tex]\left(\dfrac{1}{2},\dfrac{-2}{2}\right)=\left(\dfrac{1+x}{2},\dfrac{4+y}{2}\right)[/tex]
[tex]\left(\dfrac{1}{2},-1\right)=\left(\dfrac{1+x}{2},\dfrac{4+y}{2}\right)[/tex]
On comparing both sides, we get
[tex]\dfrac{1}{2}=\dfrac{1+x}{2}[/tex]
[tex]1=1+x[/tex]
[tex]1-1=x[/tex]
[tex]0=x[/tex]
Similarly,
[tex]-1=\dfrac{4+y}{2}[/tex]
[tex]-2=4+y[/tex]
[tex]-2-4=y[/tex]
[tex]-6=y[/tex]
The coordinates of point D are (0,-6).
Therefore, the x-coordinate of point D is 0.
A basket had 15 mangoes. A monkey came and took
away two-fifths of the mangoes. How many mangoes
were left in the basket
Answer: There are 9 mangoes left in the basket.
Step-by-step explanation:
(2/5) * 15 = 6.
15 - 6 = 9.
Emily grows flowers on part of her 2-acre farm. Her house
and barn cover half an acre, her vegetable gardens cover
1 1/4 acres, and her flower garden covers the rest of her
farm. She divides the flower garden into 16 equal-sized
plots and puts 4 kinds of flowers in each plot.
How large is each plot of flowers in Emily's garden?
Answer:
1/64 for each type f flowe
Step-by-step explanation:
what is the fraction form of .8
help me please i dont know what to do
Answer:
x = 14.4
Step-by-step explanation:
First of all, the triangle has three sides, so let's use hero's formula to find the area.
A = √[p(p - a)(p - b)(p - c)]
Where;
a, b and c are the 3 given sides of the triangle and;
p = (a + b + c)/2
p = (18 + 30 + 24)/2
p = 72/2
p = 36
Thus;
A = √(36(36 - 18)(36 - 30)(36 - 24))
A = √46656
A = 216 Sq.units
Now, we also know from general formula of a triangle that;
A = ½bh
Where;
b is base and h is height
In the given image;
b = 30
h = x
Thus;
½ × 30 × x = 216
Rearranging, we have;
x = 216 × 2/30
x = 14.4
Given that the quadrilateral shown is a parallelogram, which statements are correct?
A)
mZA = 950
B)
mZB = 65
C)
mZC = 959
D)
AD = 8
E)
DC = 12
Answer: I know that DC is 12 and AD=8 the others i dont know.
Step-by-step explanation:
This is because opposite sides of a parallelogram are parallel and congruent. therefore AB and DC are equal/congruent.
The equation has a solution of x = 5.
What is the value of k?
k =
Answer:
K= -11
Step-by-step explanation:
Can anyone help me out??
9514 1404 393
Answer:
p(1) = 6
Step-by-step explanation:
The basic idea is to put 1 wherever you see x. That gives you ...
p(1) = 2·1² +3·1 +1
The powers of x are all 1 when x=1, so the value of p(1) is just the sum of the coefficients:
p(1) = 2 + 3 + 1
p(1) = 6