7. A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and sides 6 cm each is to be made of three different shades as shown in Fig. 8.17. How much paper of each shade has been used in it?
Answers
Answer:
Step-by-step explanation:
diagonal = 32 cm
Area of square = [tex]\dfrac{d^{2}}{2}[/tex]
[tex]=\dfrac{32*32}{2}\\\\=512 \ cm^{2}[/tex]
Diagonal separate the square into two equal triangles.
Area of upper triangle that is shaded black = area of lower triangle = 512/2
= 256 cm²
Isosceles triangle:
a = 6 cm ; b = 6 cm c = 8cm
[tex]s = \dfrac{a+b+c}{2}\\\\=\dfrac{6+6+8}{2}\\\\=\dfrac{20}{2}\\\\=10\\\\s-a = 10 - 6 = 4 \ cm\\\\s-b = 10-6 = 4 \ cm\\\\c - c = 10 - 8 = 2 \ cm\\\\Area = \sqrt{s*(s-a)(s-b)(s-c)}\\\\=\sqrt{10*4*4*2}\\\\=\sqrt{2 * 2 * 4 * 4 * 5}\\\\=4*2\sqrt{5}\\\\=8\sqrt{5}\\\\=8*2.24\\\\=17.92 \ cm^{2}[/tex]
Area of black shade paper = 256 + 17.92 = 273.92 cm²
Area of white shade paper = 256 cm²
Area of the isosceles triangle = s(s-a)(s-b)(s-c)
Related Questions
How many significant figures does 4857.169 have?
Answers
Answer:
Significant Figures
7
4857.169
Decimals
3
4857.169
Scientific Notation
4.857169 × 103
E-Notation
4.857169e+3
Words
four thousand eight hundred fifty-seven point one six nine
Explanation: Mark Brainliest plz
Answer:
plz mark me as a brainliest i really need it
Step-by-step explanation:
4857.169
Sig Figs
7
4857.169
Decimals
3
4857.169
Scientific Notation
4.857169 × 103
E-Notation
4.857169e+3
Words
four thousand eight hundred fifty-seven point one six nine
The size of a population of fish in a pond is modeled by the function P, where P(t) gives the number of fish and t gives the number of years after the first year of introduction of the fish to the pond for 0≤t≤10. The graph of the function P and the line tangent to P at t=4 are shown above. Which of the following gives the best estimate for the instantaneous rate of change of P at t=4 ?
Answers
The slope (m) will be "279.33". A further solution to the question is provided below.
At one moment this same instantaneous modification rate would be the same with the functionality derivative assessed somewhere at the time. In certain other terms, the pitch of such tangent line towards the curvature is somewhere at a level equivalent to that as well.
According to the question,
(x₁, y₁) = (3, 0)(x₂, y₂) = (6, 838)As we know,
⇒ [tex]Slope (m) = \frac{y_2-y_1}{x_2-x_1}[/tex]
By substituting the values, we get
⇒ [tex]=\frac{838-0}{6-3}[/tex]
⇒ [tex]=\frac{838}{3}[/tex]
⇒ [tex]=279.33[/tex]
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The instantaneous rate of change is the rate of change at a particular point or instant in the graph. The instantaneous rate of change of P at [tex]t=4[/tex] is 250
I've added as an attachment, the graph that represents the population of the fish.
To determine the instantaneous rate of change at [tex]t=4[/tex], we simply calculate the slope (m) of the tangent line using:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Because of the scale of the graph, I will use the following estimated points from the tangent line
[tex](x_1,y_1) = (3,0)[/tex]
[tex](x_2,y_2) = (4,250)[/tex]
So, the slope is:
[tex]m = \frac{250 - 0}{4 - 3}[/tex]
[tex]m = \frac{250}{1}[/tex]
[tex]m = 250[/tex]
Hence, the instantaneous rate of change of P at [tex]t=4[/tex] is 250
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Show work please
[tex] \sqrt{ \frac{45}{5} } [/tex]
Answers
Answer: 3
Step-by-step explanation:
[tex]\sqrt{ \dfrac{45}{5}} =\sqrt{9}=\bold3[/tex]
Answer:
3
Step-by-step explanation:
We don't really need to simplify this, but if you do:
45/5 is the same as 45 ÷ 5 so
45/5 = 9
Now we have to find the square root of 45/5(or 9). The square root of a number(x for example) is the number(y) that multiplied by itself once will equal x or y · y = x.
For this you can use a calculator:
[tex]\sqrt{\frac{45}{5} }[/tex] = 3
or
[tex]\sqrt{9}[/tex] = 3
How would I prove the congruency of these triangles?
Answers
Answer:
SAS
Step-by-step explanation:
line AB = line CD S = SIDE
AB = CD because the shape is a parallelogram and opposite sides of a parallelogram are equal.
Hence, proved AB = CD
Answer:
Step-by-step explanation:
In ΔADC & ΔABC,
Statement Reason
AD = BC Given
∠DAC ≅ ∠ACB {AB // BC , AC is transversal, ⇒ alternate interior angles are equal}
AC = CA Reflexive property
ΔADC ≅ ΔABC SAS congruent
AB = CD CPCT -> Corresponding Part of Congruent Triangles
Solve 3x − x + 2 = 12.
Answers
2x=12_2 2x=10 x=5 that answer
5x + 2) mize
2.
P has coordinates (2, 4). Q has coordinates (-10, 12). Find the midpoint of PQ.
122
Answers
express each of the following in standard form 0.000000000221
Answers
Answer:
[tex]2.21 \times {10}^{ - 10} [/tex]
Step-by-step explanation:
When we shift (.) from left to right in scientific notarion, the power of 10 varies in negative numbers according to how many numbers we shift.
A boy is 12 years old his mother is four times as old as he is in x years time the mother will be three times as old as. the son form an equation in x and hence find x
plzzzzzzz help
Answers
Answer:
age of boy = 12
age of mother = 4 times age of boy = 4*12 = 48
let x = years time
3(12+x) = 48+x
36+3x = 48+x
3x-x = 48-36
2x = 12
x = 6
In 6 years time the mother will be three times as old as the son.
pleasexmark me as brainlist
PLS HELP WILL MARK AS BRAINLIEST
Answers
Answer:
SEE THE IMAGE FOR SOLUTION .
HAVE A GREAT DAY
Answer:
11. D
12. C
13. D
14. B
15. E
Step-by-step explanation:
11.
1/3 + 1/2 = 2/6 + 3/6 = 5/6
A is 3/4
B is 2/3
C is 9/10
D is 4/5
E is 2/5
the closest to 5/6 is 4/5.
12.
this is totally easy. just simply additions and one subtraction (to see what is left).
8+10+9 = 27
so, he has
60 - 27 = 33 hours left
13.
the mean value of a series of equal weighted numbers is simply their sum divided by the amount of numbers.
so,
(2+5+3+6+4)/5 = 20/5 = 4
14.
a scale factor is always applied to all dimensions, otherwise the result will be distorted. and that would be especially bad for a map.
so, clearly the width of the larger map is 3 times the width of the smaller map. therefore, the length of the larger map has to be also 3 fine the length of the smaller map.
3×6 = 18
15.
3t - 10 = 8
3t = 18
t = 6
answer choices:
A. 98
B. 72
C. 44
D. 42
Answers
Answer:
B
Step-by-step explanation:
The volume (V) of the triangular prism is calculated as
V = Bh ( B is the area of the triangular base and h the height )
B = [tex]\frac{1}{2}[/tex] bh
Here b = 8 and h = 6 ( perpendicular legs )
B = [tex]\frac{1}{2}[/tex] × 8 × 6 = 4 × 6 = 24 ft² , then
V = 24 × 3 = 72 ft³ → B
Change 3224in^2 to cm^3
Answers
Answer:
98
Step-by-step explanation:
show work
order of operations. please help!
Answers
Is -√15 irrational or rational
Answers
Explanation:
Square root that are not perfect square are considered irrational as sqrt(15) isn’t a perfect square thus it’s irrational.
Which of the following describes a correct process for solving the equation 3(x + 6) = 21 and arrives at the correct solution?
A. Divide both sides of the equation by 3, and then subtract 6 from both sides of the equation. The solution is x = 1.
B. Subtract 6 from both sides of the equation, and then divide both sides of the equation by 3. The solution is x = 5.
C. Distribute the 3, subtract 6 from both sides of the equation, and then divide both sides of the equation by 3. The solution is x = 5.
D. Add 6 to both sides of the equation, and then divide both sides of the equation by 3. The solution is x = 9.
Answers
Answer:
A. Divide both sides of the equation by 3, and then subtract 6 from both sides of the equation. The solution is x = 1.
Step-by-step explanation:
3(x + 6) = 21
Divide both sides by 3
(x + 6) = 7
Subtract 6 from each side
x = 7-6
x=1
Answer:
x=1
Step-by-step explanation:
multiply 3 with (x+6) resulting into 3x+18=21
cross-multiply and divide through by 3.
There u go
what is the constant of the proportionality in the equation y = 7x
Answers
Answer:
7
Step-by-step explanation:
The equation of direction variation is
y = kx where k is the constant of variation
y = 7x so 7 is the constant of variation
Answer:
7
Step-by-step explanation:
The equation of direction variation:-
y = kx where k is the constant of variation -> Eq 1
y = 7x -> Eq 2
Comparing Eq 1 and Eq 2,
k=7
Amaya wants to jog 8 Miles this week she has jog 2 1/2 miles on Monday and 3 2/5 miles on Wednesday how many miles does amaya still need to jog to meet her goal
Answers
Answer:
2 1/10 miles.
Step-by-step explanation:
She has already jogged 2 1/2 + 3 2/5 miles. This is 2 5/10 + 3 4/10 or 5 9/10. 8 miles is also equal to 7 10/10 miles. So, to find the remaining amount of miles, we can do 7 10/10 - 5 9/10 = 2 1/10.
Amaya still needs 2.1 miles to jog to meet her goal.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
Operators who let do basic mathematical calculations.
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
Given that this week she has jog 2 1/2 miles on Monday and 3 2/5 miles on Wednesday
She has already jogged 2 1/2 + 3 2/5 miles.
⇒ [tex]2\dfrac{1}{2} + 3\dfrac{2}{5} = \dfrac{5}{2} + \dfrac{17}{5}[/tex]
Convert fractions into decimals,
⇒ 2.5+3.4
Apply the arithmetic operation,
⇒ 5.9
So, to find the remaining amount of miles,
⇒ 8 -5.9 = 2.1
Hence, Amaya still needs 2.1 miles to jog to meet her goal.
Learn more about Arithmetic operations here:
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need some help with 8th grade math
Answers
Answer:
D = (3,3)
E = (-5,0)
F = (-2,2)
Step-by-step explanation:
the y axis is the vertical line of the graph so an example of flipping would be (-3,5) turns to (3,5) changing only the x value same the other way around (5,-9) turns to (-5,9) only the x value changes symbol
Answer:
D1 = (3, 3) E1 = (-5, 0) F = (-2, -2)
Step-by-step explanation:
D1 = (3, 3)
E1 = (-5, 0)
F = (-2, -2)
Refer to the number line. Find the coordinate of point H that is 1/5 of the distance from C to F.
A B C
DEF
-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7
Answers
Number lines are used to represent numbers on a line at regular intervals. The coordinate of point H is -2.2
From the number line, we have:
[tex]C = -4[/tex]
[tex]F = 5[/tex]
First, we calculate the distance between C and F using absolute functions
[tex]CF = |C - F|[/tex]
[tex]CF = |-4- 5|[/tex]
[tex]CF = |-9|[/tex]
Remove absolute bracket
[tex]CF = 9[/tex]
Point H is [tex]\frac 15[/tex] of the distance so, we have:
[tex]H = \frac 15 CF[/tex]
[tex]H = \frac 15 \times 9[/tex]
[tex]H = 1.8[/tex]
This means that point H is 1.8 from the right of C.
So, the coordinate of H is:
[tex]H = C + 1.8[/tex]
[tex]H = -4 + 1.8[/tex]
[tex]H = -2.2[/tex]
Hence, the coordinate of point H is -2.2
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IF A= { a, b, c d and B={a,b,c,d}
how can I solve this
Answers
Answer:
what we have to prove or equation ?
A(-2,3)
Triangle ABC has vertices at A(-2,3), B(-3,6), and
C(2,-1) Is triangle ABC a night triangle? If so, which
angle is the night angle?
O No, the triangle has no right angles.
O Yes, the right angle is angle A
O Yes, the right angle is angle B
O Yes, the right angle is angle C
VA
C (2-1)
B (-3,-6)
Answers
second choice i’m prolly wrong
A rectangle has perimeter 56 cm and length 21 cm. What is its width?
Answers
hhhhhhhhhhh
Answer:
width=7 cm
Step-by-step explanation:
perimeter=2(lengths+width)
56 =2(21+x)
56 =42+2x
56-42 =2x
2x = 14
x =7
therefore the width=7 cm
18
A company is expanding its building area from 16,500 square feet to 22,605 square feet. What is the percentage increase of the
area of the building space?
Answers
the answer is 37%
: 16500*37%= 6150
6150+16500=22605 :correct
what is the awnser y= 4x-9
Answers
Answer:
x = y+9/4
Step-by-step explanation:
if you were trying to rearrange to make x the subject. Take minus 9 to another side which will be plus 9, then divide y+9 by 4
If PQ = 6x - 1 and PR = 15x - 29,
then QR = ?
Answers
Explanation:
PR - PQ = QR
15x - 29 - 6x + 1 = QR
9x - 28 = QR
3 3/4÷3/4
pls I need this for my tuition in 5 min
Answers
Step-by-step explanation:
15/4÷3/4
15/4×4/3 (2 reciprocal of 3 upon 4)
5/1
or 4 1/1 Answer
4,4 will be cancelled 15 will be cancelled by 3
factorize the following questions
1. a^8-b^8
2. 32y^4 - 162
Answers
Answer:
1. [tex]2(16 {y}^{4} - 81)[/tex]
2. [tex]2(2y - 3) \times (2y + 3) \times (4 {y}^{2} + 9)[/tex]
Step-by-step explanation:
1. [tex] a^{8} - {b}^{8} [/tex]
➡️ [tex]( {a}^{4} - {b}^{4} ) \times ( {a}^{4} + {b}^{4} )[/tex]
➡️ [tex]( {a}^{2} - {b}^{2} ) \times ( {a}^{2} + {b}^{2} ) \times ( {a}^{4} + {b}^{4} )[/tex]
➡️ [tex](a - b) \times (a + b) \times ( {a}^{2} + {b}^{2} ) \times ( {a}^{4} + {b}^{4} )[/tex]
➡️ [tex]2(16 {y}^{4} - 81)[/tex] ✅
---------------------------------------------------
2. [tex] 32 {y}^{4} - 162[/tex]
➡️ [tex] 2(16y^{4} - 81)[/tex]
➡️ [tex]2(4 {y}^{2} - 9) \times (4 {y}^{2} + 9)[/tex]
➡️ [tex]2(2y - 3) \times (2y + 3) \times (4 {y}^{2} + 9)[/tex] ✅
Amy owes her mother $76. She pays her mother $14 on Sunday and $24 on Monday. Use an expression to describe the situation. How much does Amy still owe her mother?
Answers
Answer:
Amy still owes her mother $38.
Step-by-step explanation:
76 - 14 - 24
76 - 14 = 62
62 - 24 = 38
Please help me it's the lateral area of a cone along with the surface area
Answers
Answer:
the lateral area of cone is L=A﹣πr2
the surface area of cone is
[tex]a = \pi \: r \sqrt{h^{2} + r {}^{2} }[/tex]
A sailboat travels a distance of miles in of an hour. Which complex fraction represents the unit rate in miles per hour?
Answers
Answer: I think its D and A
Step-by-step explanation:
Answer:
im pretty sure its D and also A
Step-by-step explanation:
Cuanto da √(1 ÷ 6^2 - 1 ÷ 10^2)
Answers
Answer:
It is 2/15
Step-by-step explanation:
[tex] = \sqrt{ \frac{1}{ {6}^{2} } - \frac{1}{ {10}^{2} } } \\ \\ = \sqrt{ \frac{4}{225} } \\ \\ = \frac{ \sqrt{4} }{ \sqrt{225} } \\ \\ = \frac{2}{15} [/tex]