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By AAS criteria, ΔABC ≅ ΔADC.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given is CA bisects ∠BAD, AB ⊥ BC and AD ⊥ DC.

In ΔABC and ΔADC -

∠ABC = ∠ADC = 90°

∠ACB = ∠ACD     {bisected angle ∠BCD}

AC = AC  {Common}

By AAS criteria, ΔABC ≅ ΔADC.

Therefore, by AAS criteria, ΔABC ≅ ΔADC.

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[Complete questions

Given: CA bisects ∠BAD, AB ⊥ BC and AD ⊥ DC . Prove: △ABC≅△ADC.]

Answer:

Option (3)

Step-by-step explanation:

Since, flowerbed is in the shape of a right triangle,

By applying Pythagoras theorem in the given right triangle,

(Hypotenuse)² = (leg 1)² + (leg 2)²

(Hypotenuse)² = (12)² + (12)²

(Hypotenuse)² = 144 + 144

Hypotenuse = √288

Hypotenuse = 16.97

                     ≈ 17 ft

Perimeter of the triangle = Sum of the measures of three sides of the triangle

= 12 + 12 + 17

= 41 ft

Therefore, Option (3) will be the correct option.

Answer:

41ft

Step-by-step explanation:

because i got 100% on the lesson

Answer:

25.5 / 3 = 8.5

Step-by-step explanation:

8.5 times more student prefer basketball over soccer

Answer:

d

Step-by-step explanation:

Answer:

472

Step-by-step explanation:

Answer:

huh

Step-by-step explanation:

?

The exponential function that best describes the total number of artifacts found in archaeological sites in the country after x years = T(x) = [tex]2(1.1)^{6x+2}[/tex]

An exponential function is defined by the formula f(x) = a×, where the input variable x occurs as an exponent.

Time period = x years

The number of archaeological sites discovered in a country  in x years = S(x) = [tex]2(1.1)^{x}[/tex]

The approximate number of artifacts found in each site over time = A(x) = [tex](1.1)^{5x+2}[/tex]

The total number of artifacts found in archaeological sites in the country after x years = T(x) = S(x).A(x) = [tex]2(1.1)^{x}(1.1)^{5x+2} = 2(1.1)^{6x+2}[/tex]

Learn more about exponential function here

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Answer: The number of people can be expected to have cold = 34

Step-by-step explanation:

Given: The ratio of people who actually have the flu to the people who have flu-like symptoms is 1:6.

If a doctor sees 40 patients, then the number of people can be expected to have cold = [tex]40\times\dfrac{6}{1+6}[/tex]

[tex]=40\times\dfrac6{7}[/tex]

[tex]=\dfrac{240}{7}\\\\=34.29\approx34[/tex]

Hence, the number of people can be expected to have cold = 34

Answer:

6

Step-by-step explanation:

6(1×2) - 3(2)

6×2 - 6

12-6

= 6

here you go

please help with mine

Answer:

y=3x-1

Step-by-step explanation:

Not enough context

Hope this helps!

:)

Answer:

Angle 3 and 4 are supplementary angles.

The equation (3x+4) + (2x+11) = 180 can be used to solve for x.

m 5 = 77

Step-by-step explanation:

Answer:

3x-2=25

x=9. .

Answer:

9

Step-by-step explanation:

Answer:

494018

Step-by-step explanation:

you are trying to find the diameter of the circle, it is usually half the length of a radius, but since 497 squared is how long a radius is (unless the question asked that the area if 497 inches squared), i can't really give you a clear answer, but the diameter is 247009 times 2 which is 494018

Answer:

Option A

Step-by-step explanation:

x-7>2

x>9

Therefore, A is correct since 9 isn't included in the solution set.

Answer:

First option is correct

Step-by-step explanation:

x-7 > 2

x > 7+2

x > 9

Answer:

y = 7/2 x+16

Step-by-step explanation:

The equation for a line is y = mx+b where m is the slope and b is the y intercept

y = 7/2 x+b

Substitute the point into the equation

9 = 7/2(-2)+b

9 = -7+b

9+7 = b

16 = b

y = 7/2 x+16

Answer:

12.2

Step-by-step explanation:

Answer:

4:1

Step-by-step explanation:

We know 1/5 of the marbles are red.

There are 10 marbles.

1/5 is also 2/10, so:

2 of the 10 marbles are red.

To find the blue marbles, lets subtract the red marbles from the total marbles:

10-2=8

So 8 of the marbles are blue.

This is a ratio of 8 blue to 2 red marbles.

Or

4 blue to 1 red marbles.

This can be shown as:

4 : 1

Hope this helps!

Answer:

113mm^2

Step-by-step explanation:

Firstly work out the area of the pink circle using πr^2, which is the area of a process.

So we do πx12^2, which gives us 144π mm we have to divide this by two to get half of a circle hence giving us the area of the semi-circle. 72π mm is the area of the semicircle.

Then we must find the area of the white circle to subtract it from our semicircle. Since we know the radius is 12 from the center to anywhere, we know that the white circles diameter is 12, using our formula for the area all we need to do is πx6^2. This gives us 36π.

72π - 36π = 36π

36π is equal to 113.0973355 and since we need it too 3sf it will be 113mm^2

Answer:

7.6 ft

Step-by-step explanation:

The volume of a sphere is

V = 4/3 pi r^3

A hemisphere is 1/2 of  a sphere

V = 1/2 (4/3 pi r^3)

V = 2/3 pi r^3

920 = 2/3 pi r^3

Multiply each side by 3/2

920 * 3/2 = 3/2 * 2/3 pi r^3

1380 = pi r^3

Divide each side by pi

1380/pi = pi r^3 / pi

1380/ pi = r^3

Using pi as 3.14

1380/3.14 = r^3

439.4904459= r^3

Taking the cube root of each side

(439.4904459)^(1/3)= r^3^(1/3)

7.602967711=r

To the nearest tenth

7.6 = r

radius=7.6ft

Answer:

Solution given:

radius [r]=?

Volume of hemisphere=920ft³

⅔*πr³=920

r³=920*3/(2π)

r³=439.267

r=[tex]\sqrt[3]{439.267}=7.6ft[/tex]

4,756 rounded to the nearest thousand is 5,000.

Answer:

rounded to the nearest thousands 4,756 is 5,000 since 7 is higher then 4 so it rounds up

Answer:

[tex]area = length \times width \\ 9 = (x + 3)(x + 2) \\ {x}^{2} + 2x + 3x + 6 = 9 \\ {x}^{2} + 5x + 6 = 9 \\ {x}^{2} + 5x + (6 - 9) = 0 \\ {x}^{2} + 5x =3[/tex]

Answer:

x + 1 y+1

Step-by-step explanation:

it translated 1 unit up the x axis and 1 unit y axis

Answer:

reflected across the y-axis and translated 1 to the right and 1 up

Step-by-step explanation:

Answer:

451.7in^2

Step-by-step explanation:

You first need to determine the radius of the circle. This can be done by taking the circumference and dividing it by 2pi:

[tex]r=\frac{75.36in}{2\pi } = 11.99 in[/tex]

Now that you have the radius, you can plug it into the formula for the area of a circle (this is assuming the pizza is perfectly round):

[tex]A=\pi r^2=\pi (11.99^2)=451.7in^2[/tex]

The area that covers the circular pizza is: 451.64 in.²

Area = πr²

Perimeter = 2πr, where r is the radius of the circle.

Given the following:

Perimeter of the circular pizza = 75.36 in.

Find the radius:

2πr = 75.36

r = 75.36/2π

r = 11.99 in.

Find the area:

Area = π(11.99)²

Area = 451.64 in.²

Learn more about the area of a circle on:

https://brainly.com/question/12269818

Answer:

i cant read it..

Step-by-step explanation:

2×12=24

24+3= 27

12*12=144

144/24=6

Answer:

42

Step-by-step explanation:

From the question, we have it that 63 cups were emptied

That means the sum of both cup sizes is 63

Thus;

x + y = 63 ••••••(i)

Since each small cup is of size 8 oz and a total of x was used. The total volume from the small sized cup is 8 * x = 8x oz

similarly for the medium sized, we have 12 * y = 12y oz

The sum of both is 4(147)

8x + 12y = 4(147 )•••••(ii)

We want to get the value of x

from equation i;

y = 63-x

Substitute this into equation ii

8x + 12(63-x) = 4(147)

8x + 756 - 12x = 4(147)

12x-8x = 756-4(147)

4x = 168

x = 168/4

x = 42 small sized cups

Answer:

The distance from the house to the school is 500 units

Step-by-step explanation:

The distance we want to calculate represents the hypotenuse of the right triangle

So, to use the Pythagoras’ theorem, we need the two other side lengths apart from the hypotenuse

The base side measures (350-50 = 300 units)

The measure of the height is (450-50 = 400 units)

Mathematically, the theorem states that the square of the hypotenuse equals the sum of the squares of the two other sides

Thus, we have it that;

h^2 = 300^2 + 400^2

h^2 = 90,000 + 160,000

h^2 = 250,000

h = √250,000

h = 500 units

Answer:

4x⁴-3x⁴+5x³-3x²+1

Step-by-step explanation:

Given that p (x) = 3x^3+2x^2+4x^4+3 and q (x) = 3x^4-2-x+5x^2

p (x) - q (x)​ = 3x^3+2x^2+4x^4+3 - (3x^4-2-x+5x^2)

p (x) - q (x)​ = 3x^3+2x^2+4x^4+3 - 3x^4 + 2 + x - 5x^2

Collect the like terms

p (x) - q (x)​ = 4x⁴-3x⁴+3x³+2x²-5x²+x+3-2

p (x) - q (x)​  = 4x⁴-3x⁴+5x³-3x²+1

This givess the difference