Answer:
A ≈ 21.22 m²
Step-by-step explanation:
The area (A) of a triangle using Heron's formula is
A = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
where s is the semi perimeter and a, b, c the sides of the triangle.
Here the perimeter of the equilateral triangle is 21 m , then
a = b = c = 21 ÷ 3 = 7 m
s = 21 ÷ 2 = 10.5
Then
A = [tex]\sqrt{10.5(10.5-7)(10.5-7)(10.5-7)}[/tex]
= [tex]\sqrt{10.5(3.5)(3.5)(3.5)}[/tex]
= [tex]\sqrt{450.1875}[/tex]
≈ 21.22 m² ( to 2 dec. places )
State the equation, in slope-intercept form, of each of the following graphs of linear relations.
Explain how the equation was determined.
Answer: y=80/5x+80
Step-by-step explanation:
At one point graph goes from (0,400) to (25,800). So the y intercept is 400 because that’s where the line was at x=0. 0 to 25 is 25. 400 to 800 is 400. So the equation would be y=400/25x+400. But you can divide all of it by 5 to get y=80/5x+80.
Daisy (5,9,2,6,14,3)
Milkweed (10,8,22,12,12,9)
Coneflower (3,7,2,10,16,7)
A biology class took a field trip. The students counted the number of daisy, milkweed, and coneflower plants in six different locations. The data sets are shown above. What is the overall range in the number of plants for all three types of plants?
Answer:
The overall range is 20
Step-by-step explanation:
Given
The above dataset
Required
The overall range
Range is calculated as
[tex]Range = Highest - Lowest[/tex]
The highest of the dataset is 22, and it can be found in Milkweed.
The lowest of the dataset is 2, and it can be found in Daisy
So, the range is:
[tex]Range = 22 - 2[/tex]
[tex]Range = 20[/tex]
Nia solved the equation -1.98 = 5.2v + 13.1. Her answer was v = -2.9. She is fairly confident about her answer, but wants to do a quick check of her solution using estimation to make sure her answer is reasonable.
Which of the following shows a good check of her answer?
Answer:
substitute for v, when v = -2.9
Step-by-step explanation:
[tex]-1.98=5.2v+13.1[/tex]
subtract 13.1 on both sides.
[tex]-15.08=5.2v[/tex]
divide by 5.2 to isolate v
[tex]\frac{-15.08}{5.2} = \frac{5.2v}{5.2}[/tex]
[tex]-2.9=v[/tex]
substitute for v
[tex]-1.98=5.2(-2.9)+13.1[/tex]
[tex]-1.98=-15.08+13.1[/tex]
[tex]-1.98=-1.98[/tex]
secA-tanA=(cosA/2-sinA/2)/(cosA/2+sinA/2)
Answer:
Step-by-step explanation:
SecA - TanA
= 1/CosA - SinA/CosA
= 1 - SinA/CosA
We know that Sin2A = 2SinACosA and Cos2A = Cos²A - Sin²A
Thus SinA = Sin2(A/2) = 2Sin(A/2)CosA/2
CosA = Cos2(A/2) = Cos²A/2 - Sin²A/2
Now substituting the values back,
=> 1 - 2Sin(A/2)Cos(A/2) / Cos²(A/2) - Sin²(A/2)
// we know that Sin²θ + Cos²θ = 1
=> Sin²(A/2) + Cos²A/2 - 2Sin(A/2)Cos(A/2) / Cos²(A/2) - Sin²(A/2)
//We know that numerator is of form a² + b² - 2ab which is (a - b)².
//Similarly denominator is of form a² - b² which is (a - b)(a + b)
=> [Sin(A/2) - Cos(A/2)]² / [Cos(A/2) + Sin(A/2)][Cos(A/2) - Sin(A/2)]
=> [ - {Cos(A/2) - Sin(A/2)}]² / [Cos(A/2) + Sin(A/2)][Cos(A/2) - Sin(A/2)]
=> [Cos(A/2) - Sin(A/2)]² / [Cos(A/2) + Sin(A/2)][Cos(A/2) - Sin(A/2)]
=> [Cos(A/2) - Sin(A/2)] / [Cos(A/2) + Sin(A/2)]
= R.H.S
Hence proved.
It takes four or three hours to get a pair of socks and seven hours to get a pair of clothes as he spends 89 hours kidding a total of 15 pairs of socks and gloves how many pairs of each does she kinit?
Answer:
Gloves = 11 pairs
Socks = 4 pairs
Step-by-step explanation:
Given that :
Time taken to knit pair of socks = 3 hours
Time taken to knit pair of gloves = 7 hours
Total time taken to knit 15 pairs of gloves and socks = 89 hours
Let :
number of socks = x and number of gloves = y
x + y = 15 - - - - (1)
3x + 7y = 89 - - - (2)
From (1):
x = 15 - y
Put x = 15 - y in (2)
3(15 - y) + 7y = 89
45 - 3y + 7y = 89
45 + 4y = 89
4y = 89 - 45
4y = 44
y = 44/4
y = 11
From :
x = 15 - y
x = 15 - 11
x = 4
What is 51809 rounded to 1,2 and 3 significant figures?
PLSS HELP
Answer:
1 significant figure: 50,000 2 significant figures: 52,000 3 significant figures: 51,800
Step-by-step explanation:
FIrst, a significant figure is basically a non-zero digit (at least in your case). Basically, the 1 significant figure in your case would be to the nearest 10 thousand, which would be 50,000. Now, for 2 significant figures. This would be the nearest thousand, 52,000. Finally, 3 significant figures is to the nearest hundred, aka 51,800. Note: If you find a problem like this again 0 in between two digits that aren't 0 is a significant digit, aka the 0 in 51809. Hope this helped!
Solve for x:
( x - 6 ) ^ 2 = 7
Answer: x= 6 +/- root of 7
Step-by-step explanation:
1. Expand the left hand side: e.g, 3^2 = 3×3 =9
(x-6)(x-6) = 7
2. Multiply the brackets first by "separating" one of them, and take 7 to the left hand side:
x(x-6) - 6(x-6) =7
x^2 - 6x -6x +36-7=0
Simplify by adding like terms
x^2 -12x +29=0
3.Now your equation is in the form ax^2+bx + c =0, it means you can use the quadratic formula which is x= [-b +/- root of (b^2 - 4ac)]÷ 2a
Then SUBSTITUTE where:
a=1
b= -12
c=29
Therefore, x should be 6+ root of 7 OR 6- root of 7
Answer:
uhhhh okay thank you for removing my answer
Step-by-step explanation:
ANSWER QUICK !!
Yuri is participating in a tund-raiser at school. She will receive donations from 2 people. A cousin will donate $0.40 for every 1/8 mile that Yuri walks.
A friend will give Yuri a one-time donation of $30
What is the minimum number of miles Yuri needs to walk to raise at least $507 Enter the answer in the box,
507 - 30 = 477
477 / 0.4 = 1192.5
1192.4 / 8 = 149.0625 miles or 150 miles
i don't know if this is right cause the answer seems so absurd
*HELP*
calculate the pay for the following day of a weekly time card given a wage of $12 an hour
Answer:
96 dollars and 50 cents
Step-by-step explanation:
Hello!! Please help me ASAP
Using special right triangles show and explain all work for each problem. Each solution and work should demonstrate your understanding of Special Right Triangles (30-60-90 and 45-45-90)
Find the missing side length and angle of this triangle. I've attached the triangle.
Answer:
Step-by-step explanation:
The basic 30-60-90 triangle ratio is:
Side opposite to 30° angle is : x
Side opposite to 60° angle is : x √3
Side opposite to 90° angle is : 2x
From the diagram we learn that
x√3 = 10
[tex]x = \frac{10}{\sqrt{3}}=\frac{10*\sqrt{3} }{\sqrt{3}*\sqrt{3}}\\\\x=\frac{10\sqrt{3}}{3}= 5.77\\[/tex]
∠T = 30°, Side opposite to ∠T is AC = 5.77
∠A = 90°, side opposite to ∠A is TC = 2x = 2*5.77 = 11.54
(PICTURE) 15 Points and marking Brainliest could someone please answer/explain this for me
Answer:
9. Hypotenuse = √(19.1²+11.3²) = √492.5 = 22.2 m²
10. Area = (34×40)/2 + (17²×π/2)
= 680 + 453.96
= 1133.96 cm²
Answered by GAUTHMATH
Your best friend made 60% of the 40 shots he took. how many shots did your friend make?
Answer:
24
Step-by-step explanation:
We need to find 60% of 40
60% * 40
.60 *40
24
He makes 24 shots
Step-by-step explanation:
60%/100%×40
60%/10%×4 (0 is cancelled)
6×4 (60 and 10 Cancelled)
24 Answer
x2 +15-8x entre 3-x ayuda pliz
Lúc 6 giờ, một ô tô xuất phát từ A đến B với vận tốc trung bình 40km/h. Khi đến B,
người lái xe làm nhiệm vụ giao nhận hàng trong 30 phút rồi cho xe quay trở về A với vận
tốc trung bình 30km/h. Tính quãng đường AB, biết rằng ô tô về đến A lúc 10 giờ cùng
ngày.
Answer:
Đáp án:
60km
Step-by-step explanation:
30 phút
=
1
2
giờ
Ô tô đi từ A đến B rồi từ B về A mất số thời gian là:
10
−
6
−
1
2
=
3
,
5
giờ (không tính thời gian nhận hàng)
Gọi độ dài quãng đường AB là
x
(km)
Ta có:
Thời gian đi từ A đến B là
x
40
(quãng đường chia vận tốc)
Thời gian đi từ B đến A là
x
30
Ta có phương trình:
x
40
+
x
30
=
3
,
5
⇔
x
=
60
(km)
Vậy quãng đường AB là 60km.
How many solutions does 6 - 3x = 4 - X-3 - 2x have?
O A. Infinitely many solutions
O B. No solutions
C. Two solutions
D. One solution
Answer:
6 - 3x = 4 - X-3 - 2x
-3x+x+2x=4-6-3
0x=-5
No solutions
5×12÷[-12÷{15+(4-3)}]
Answer: -80
Step-by-step explanation:
Marking brainliest please explain if you can (PICTURE)
The two bases of a trapezoid measure 14 inches and 10 inches respectively. The trapezoid's height is 8 inches. What is the area of the trapezoid?
192 square inches
1120 square inches
140 square inches
96 square inches
Answer:
A = 96 inches ^2
Step-by-step explanation:
The area of a trapezoid is given by
A = 1/2 ( b1+b2)h where b1 and b2 are the bases and h is the height
A = 1/2( 14+10)*8
A = 1/2(24)*8
A = 12*8
A = 96 inches ^2
The area of trapezoid is given
A = 1/2 (b1+b2)h where b1 and b2 is base and h is height
A = 1/2 (14+10)*8
A = 1/2 (24)*8
A = 12 * 8
A = 96 square inches ....which of the following represents x= 1/2 y written in general form?
2x-y = 0
=============================================
Work Shown:
x = (1/2)y
2x = y ... multiply both sides by 2
2x-y = 0 ... subtract y from both sides
This is in standard form Ax+By = C, where A,B,C are integers. In this case, A = 2, B = -1, C = 0.
Within 9 hours, the number of stars seen went from 190 to 33 as the sun started to rise. Find out how many stars are getting hidden by the sunlight each hour.
Answer:
Approximately 17 stars
[tex]2 \sqrt{75} - \sqrt{108} + 5 \sqrt{48}[/tex]
[tex]\\ \sf\longmapsto 2 \sqrt{75} - \sqrt{108} + 5 \sqrt{48} \\\\ \sf\longmapsto 2 \sqrt{25 \times 3} - \sqrt{36 \times 3} + 5 \sqrt{16 \times 3} \\ \\ \sf\longmapsto 2 \times 5 \sqrt{3} - 6 \sqrt{3} + 5 \times 4 \sqrt{3} \\ \\ \sf\longmapsto 10 \sqrt{3} - 6 \sqrt{3} + 20 \sqrt{3} \\ \\ \sf\longmapsto (10 - 6 + 20) \sqrt{3} \\ \\ \sf\longmapsto 24 \sqrt{3} [/tex]
Answer:
24aprtment3
Step-by-step explanation:
A 16-ounce package of frozen peas costs
85¢. Give the unit price in cents per ounce. Round to the nearest tenth of a cent.
The peas cost ___ cents per ounce.
Note: Rounding to the nearest tenth of a cent is the same as rounding to the nearest thousandth of a dollar.
Answer:
5.3 cents
Step-by-step explanation:
85/16
because all 16 ounces cost 85 cents
Answer:
5.3 cents.
Step-by-step explanation:
Write the equation of the line that passes through the points (−4,1) and (−9,5). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
Help plz
Step-by-step explanation:
gradient(m)=change in y/change in x
=5-1/-9-(-4)
=4/-9+4
=4/-5
equation now
y-y1=m(x-x1)
y-1=4/-5[x-(-4)]
y=4/-5(x+4)+1
y=-4/5x-16/5+1
y=-4/5x-21/5
Answer:
y = -4/5x - 11/5
Step-by-step explanation:
First, find the slope using the slope formula.
[tex]m=\frac{y_1-y_2}{x_1-x_2}\\\\m=\frac{1-5}{-4-(-9)}\\\\m=-\frac{4}{5}[/tex]
Then, use the point-slope formula and substitute the values for the variables. I'll use (-4, 1) in this instance.
[tex]y-y_1=m(x-x_1)\\\\y-1=-\frac{4}{5}(x+4)\\\\y-1=-\frac{4}{5}x-\frac{16}{5}\\\\y=-\frac{4}{5}x-\frac{11}{5}[/tex]
Find the area of the regular polygon. Round your answer to the nearest hundredth.
Answer:
Step-by-step explanation:
The central angle of a hexagon is 60 degrees. Drop a line from the center to the middle of the side marked 7.
Use the tan of the angle so formed (which is 30 degrees)
Tan(30)= opposite / height (which is the line you just drew).
Tan(30) = 3.5 / h
Tan(30) = 0.5774
Tan(30) = 3.5 / h multiply both sides by h
h*Tan(30) = 3.5 Divide by tan30
h = 3.5 / Tan(30)
h = 3.5 / 0.5774
h = 6.062
Now from both ends of the given side, draw 2 lines to the center. Find the area of that triangle.
Area of 1 triangle = 1/2 * b * h
area of 1 triangle = 1/2 * 7 * 6.062
Area of 1 triangle = 21.2176
There are 6 such triangles so multiply that number by 6
Answer: 6 * 21.2176
Answer: 127.31
Solve the inequality: (x −3)12+ 2 ≥4
Question 14 options:
A)
x ≥ 35
B)
x ≥ 13
C)
x ≥ 11
D)
x ≥ 7
Answer:
Its c
Step-by-step explanation:
QUESTION 2 Write the slope-intercept form of the equation of the line through the gran point micia the grea slope through: (5,-2), siope--1 Oay=-2=6 Oby=-2-3 O cy=-x=3 Ody=-z-6
Answer:
y = -x+3
Step-by-step explanation:
Slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = -1x +b
Using the point for x and y we can calculate b
-2 = -1(5)+b
-2 = -5+b
Add 5 to each side
-2+5 = b
3 = b
y = -x+3
ASAP!! can i get help on this one and can i please get a vivid explanation thank you.
Answer:
3x + 11
Step-by-step explanation:
1) Remove Parentheses:
x + 4 + 2x + 7
2) Combine Like Terms:
(2x + x) and (4 + 7)
3) Simplify:
3x + 11
Hope this helps, good luck! Have a good day. :)
I'LL GIVE BRAINLIEST !!! FASTER
please explain how do you get the answer !
Answer:
70
Step-by-step explanation:
we have the angle of vertex in the isosceles triangle = 180-2*bottom coner= 180-65/2=50
3 angles in the equilateral triangle are equal to 60
we have 50 + 60 +h =the angle of PQR =180
h=70
Answer: h = 70°
In the triangle with Angle R = 65
It is a isoceles triangle as two sides are equal
So base angles will be equall too
Then the third angle will which is the q one will be
65+65+q = 180
q = 180 - 130
q = 50
In the other triangle with all sides equal will be equilateral triangle which means all angles equal = 60
So
Now ATQ
60 + 50 + h = 180
h = 180 - 110 (Angles on a straight line adds upto 180)
h = 70
Must click thanks and mark brainliest
kendra is 3 times her dauters age plus 7 years kendra is 49 years old. write an equation to find he duaghters age?
Answer:
3x+ 7 =49
Step-by-step explanation:
49-7= 42
42 divided by 3 = 14
her daughter is 14 years old
I truly hope this helped, it makes sense to me. I wasn't sure whether or not you needed a more detailed equation, but that's one.
have a great day!
D.2 please help I’ll mark brainliest
Answer:
At 2
Step-by-step explanation:
I think it is because it slants down instead of going up. That is the reason why I say my answer is at 2.
HOPE THIS HELPED
