ILL BRAINLIEST YOU PLEASE HELP ME

Point P lies on the diagonal AC of square ABCD with AP > CP. Let [tex]$O_1$[/tex] and [tex]$O_2$[/tex] be the circumcenters of [tex]$\triangle \mathrm{ABP}$[/tex] and [tex]$\triangle \mathrm{CDP}$[/tex] respectively. Given that AB = 12 and [tex]$\angle \mathrm{O}_1 \mathrm{PO}_2=120^{\circ}$[/tex], then [tex]$\mathrm{AP}=\sqrt{\mathrm{a}}+\sqrt{\mathrm{b}}$[/tex],

where a and b are positive integers.

The value of a + b is 96.

Let mid-point of DC be E and mid-point of AB be F.

Since [tex]$\mathrm{O}_1$[/tex] and [tex]$\mathrm{O}_2$[/tex] are circumcenters, therefore both lie on the perpendicular bisectors of DC and AB passing through E and F.

Now, [tex]$\mathrm{O}_1 \mathrm{P}=\mathrm{O}_1 \mathrm{~B}$[/tex] and [tex]$\mathrm{O}_2 \mathrm{P}=\mathrm{O}_2 \mathrm{D}$[/tex]

Also [tex]$\angle \mathrm{CAB}=\angle \mathrm{ACD}=45^{\circ}$[/tex]

Therefore [tex]\angle \mathrm{BO}_1 \mathrm{P}=2 \times 45^{\circ}=90^{\circ}=\angle \mathrm{DO}_2 \mathrm{P}$[/tex]

Angle subtended by an arc of a circle at its center = 2 × the angle subtended at its circumference

Therefore [tex]\angle \mathrm{O}_1 \mathrm{~PB}$[/tex] and [tex]$\angle \mathrm{O}_2 \mathrm{PD}$[/tex] are isosceles right triangles.

Using the above information and symmetry,

[tex]$\angle \mathrm{DPB}=120^{\circ}$[/tex]

Also, [tex]$\triangle[/tex]ABP is congruent to [tex]$\triangle[/tex]ADP (SAS)

and [tex]$\triangle[/tex]CPB is congruent to [tex]$\triangle[/tex]CPD (SAS)

Therefore [tex]\angle \mathrm{APB}=\angle \mathrm{APD}=60^{\circ}[/tex]

And [tex]\angle \mathrm{CPB}=\angle \mathrm{CPD}=120^{\circ}[/tex]

Now, [tex]$\angle \mathrm{ABP}=(180-60-45)^{\circ}=75^{\circ}$[/tex]

[tex]\Rightarrow \angle \mathrm{O}_1 \mathrm{BF}=30^{\circ}[/tex]

And [tex]$\angle \mathrm{PDC}=(180-120-45)^{\circ}=15^{\circ}$[/tex]

[tex]\Rightarrow \angle \mathrm{O}_2 \mathrm{DE}=30^{\circ}[/tex]

Therefore [tex]\triangle \mathrm{O}_1 \mathrm{BF}$[/tex] and [tex]$\triangle \mathrm{O}_2 \mathrm{DE}$[/tex] are right angled triangles.

BF = DE = [tex]\frac{12}{2}[/tex] = 6

[tex]\Rightarrow O_1 B=O_2 D=4 \sqrt{3}[/tex]

And  PB = PD = [tex]\frac{4 \sqrt{3}}{\cos 45^{\circ}}=4 \sqrt{6}[/tex]

Now, Let x = AP

Using law of cosine on [tex]$\triangle[/tex]ABP, we have

[tex]& 96=x^2+144-24 x \times \frac{1}{\sqrt{2}} \\[/tex]

[tex]& \Rightarrow x^2-12 \sqrt{2} x+48=0 \\[/tex]

[tex]& \Rightarrow x=\sqrt{72} \pm \sqrt{24}[/tex]

Taking the positive root, AP = [tex]\sqrt{72}+\sqrt{24}$[/tex]

Therefore a + b = 72 + 24 = 96

For more questions on square

https://brainly.com/question/21327969

#SPJ4

Point P lies on the diagonal AC of square ABCD with AP > CP. Let [tex]$O_1$[/tex] and [tex]$O_2$[/tex] be the circumcenters of [tex]$\triangle \mathrm{ABP}$[/tex] and [tex]$\triangle \mathrm{CDP}$[/tex] respectively. Given that AB = 12 and [tex]$\angle \mathrm{O}_1 \mathrm{PO}_2=120^{\circ}$[/tex], then [tex]$\mathrm{AP}=\sqrt{\mathrm{a}}+\sqrt{\mathrm{b}}$[/tex], where a and b are positive integers. Find a + b. (correct answer +5, wrong answer 0 )

answer: 47.5 cups

Step-by-step explanation:

2.50 x 19 = answer

Answer:

Step-by-step explanation:

For every 3 quetzals there are four axolotls and for every 8 axolotls there are 5 Mexican wolves, if there is a population of 150 quetzals, how many axolotls are there? And how many Mexican wolves are there?

Answer:

look at the photo x is the red and y is the blue

The measure of the missing length of the trapezoid is equal to 3√39 units.

Trapezoids are quadrilaterals with only one pair of congruent sides and two pairs of congruent angles. The relationship between the longest and shortest legs (D, d) in a trapezoid is defined below:

D = d + 2 · c

Where c is the length of the horizontal leg of the right triangle in a trapezoid.

And the missing leg can be found by means of Pythagorean theorem:

x = √(r² - c²)

Where:

First, determine the length of shortest leg: (D = 40, d = 26)

40 = 26 + 2 · c

14 = 2 · c

c = 7

Second, find the longest leg by Pythagorean theorem:

x = √(20² - 7²)

x = 3√39

To learn more on trapezoids: https://brainly.com/question/12623349

#SPJ1

Answer:

0.07

Step-by-step explanation:

lets make a chart first

           small | medium | large

hot     |   5      |     48     |    22

cold   |   8      |       1      |     5

1. add all the hot drinks

5+48+22=75

2. find 5/75,

5/75=0.0666666

The partial fraction expansion of (x³ + 4)/ ((x² - 1)(x² + 3x + 2)) is -3/ 4(x + 1) + 5/12(x - 1) + 4/3(x + 2) - 3/ 2(x + 1)². So the coefficients A = -3/4, B = 5/ 12, C = 4/3 and D = -3/2.

A partial fraction expansion is a way of expressing a rational function (a function that can be written as the ratio of two polynomials) as the sum of simpler fractions, each with a numerator that is a constant or a simple polynomial. The process of finding the partial fraction expansion of a rational function is also known as partial fraction decomposition.

The denominator is

(x² - 1)(x² + 3x + 2) = (x² - 1)(x² + x + 2x + 2)

(x² - 1)(x² + 3x + 2) = (x + 1)(x - 1)(x + 1)(x + 2)

So by  partial fraction expansion

(x³ + 4)/ ((x² - 1)(x² + 3x + 2)) = (x³ + 4)/ ((x + 1)(x - 1)(x + 1)(x + 2))

(x³ + 4)/ ((x + 1)(x - 1)(x + 1)(x + 2)) = A/ (x + 1) + B/(x - 1) + C/(x + 2) + D/ (x + 1)²

A(x - 1)(x + 1)(x + 2) + B(x + 1)²(x + 2) + C(x + 1)²(x - 1) + D(x - 1)(x + 2) = x³ + 4

(A + B + C)x³ + (2A + 4B + C + D)x² + (-A + 5B - C + D)x + (-2A + 2B - C - 2D) = x³ + 4

Thus from coefficients of x³, x², x and 1,

A + B + C = 1

2A + 4B + C + D = 0

-A + 5B - C + D = 0

-2A + 2B - C - 2D = 4

Solving

A = -3/4, B = 5/ 12, C = 4/3 and D = -3/2

--The question is not clear, the question is given below--

"Enter (A,B,C,D) in order below if A, B, C, and D are the coefficients of the partial fractions expansion of

[tex]$$12\cdot\frac{x^3 + 4}{(x^2-1)(x^2 +3x+ 2)}[/tex]  "

To know more on partial fractions expansion

https://brainly.com/question/30079928

#SPJ4

The percent discount on the new phone is 15%.

Discount refers to a reduction in the original price of a product or service. It is a way for businesses to incentivize customers to purchase their products by offering a lower price than the original price.

To find the percent discount, we need to divide the amount of the discount by the original price, and then multiply by 100 to express the answer as a percentage.

Discount = Original Price - Sale Price

Discount = $46 - $39.10

Discount = $6.90

Percent Discount = (Discount / Original Price) x 100

Percent Discount = ($6.90 / $46) x 100

Percent Discount = 15%

Therefore, the percent discount is 15%.

Learn more about discount here: https://brainly.com/question/3434137

#SPJ4

Answer:

yes

Step-by-step explanation:

according to pythagoras theorem = hypotenuse² = √ base²+perpendicular²

so 21² + 28² = 35²

Answer:

yes

Step-by-step explanation:

yes

yes

yes

yes

yeyed

yes

Answer: x = 3

Step-by-step explanation:

-3 +9x = 24

9x= 24+3

9x=27

9x/9= 27/9

x=3

Answer:

x = 3

Step-by-step explanation:

-3 + 9x = 24

rearrange:

9x - 3 = 24

Add 3 to both sides of the equation:

9x - 3 + 3 = 24 + 3

9x = 27

Divide both sides by 9:

9x/9 = 27/9

x = 3

Have a nice day!

Answer:

V  =  38.47 in^3

Step-by-step explanation:

The container base radius is half the diameter, that is, 1.75 in, and the height is 12 in.  The formula for the volume of a cylinder of radius r and height h is V = (1/3)(pi)(r)^2h, which in this particular case comes out to:

V = (1/3)(3.14)(1.75 in)^2*(12 in), or

V  =  38.47 in^3

Answer:

115.40 in3

that is the correct answer to this question.

Answer:

a season your welcome: ]

Answer:

Seasons shouldn't be capitalized

Answer:

A. 35 million

B. $1519 increase

$7719 year end

Step-by-step explanation:

Answer:

Axis of Symmetry = -4

Vertex = (-4,7)

Step-by-step explanation:

Answer:

2000

Step-by-step explanation:

1 kilometer is = 1000 meters

give brainliest pls

Step-by-step explanation:

[tex]midpoint = ( \frac{(2 + 8)}{2} , \frac{(3 + 9)}{2} ) \\ = (5,6)[/tex]

Answer:

√(x2-x1)²+(y2-y1)²

√(8-2)²+(9-3)²

√6²+6²

√36+36

√72

8.48528137424≈8.5

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

a^2 + b^ = c^2

x^2 + 24^2 = 26^2

x^2 = 100

x=10

Can i have brainliest please

Answer:

x = 10

Step-by-step explanation:

This is a right triangle problem

use the Pythagorean Theorem

a^2 + b^2 = c^2

x^2 + 24^2 = 26^2

x^2 + 576 = 676

Subtract 576 from both sides

x^2 = 100

Take the square root of both sides

x = 10

Answer:

114.12

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

[tex]6\frac{2}{3} *12[/tex]

First, write the fractions as improper fractions.

[tex]\sf\frac{20}{3} *\frac{12}{1}[/tex]

Multiply.

[tex]\sf\frac{240}{3}[/tex]

Divide.

80

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{6\dfrac{2}{3}\times 12}[/tex]

[tex]\mathsf{= \dfrac{6\times3+2}{3}\times\dfrac{12}{1}}[/tex]

[tex]\mathsf{= \dfrac{18 + 2}{3} \times\dfrac{12}{1}}[/tex]

[tex]\mathsf{= \dfrac{20}{3} \times\dfrac{12}{1}}[/tex]

[tex]\mathsf{= \dfrac{20\times12}{3\times1}}[/tex]

[tex]\mathsf{= \dfrac{240}{3}}[/tex]

[tex]\mathsf{= 240\div 3}[/tex]

[tex]\mathsf{= 80}[/tex]

[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{80}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

184ft^2

Step-by-step explanation:

W have to find the area of triangles and rectangles and add them together to get the total area of the figure:

Area of triangles = 1/2(b)(h)

Area of rectangles = l x w

6 x 10 = 60

1/2(6)(4) = 12 (We can make this 12 a 24 because there are two of these triangles)

5 x 10 = 50 (We can also make this 50 a 100 because there are two of these rectangles)

100 + 24 + 60 = 184ft^2

Answer:

tree = 8

snowman = 1

deer = 4

snowflake = 4

Step-by-step explanation:

say t = tree, s = snowman, d = deer, f = snowflake

1. For 2d + f, since you know d is equal to f, replace the snowflake with a deer, turning the equation into 3d = 12. To find the value of d divide by 3 on both sides. This will result in 4. So, the value of deer = 4.

2. Now, find the value of the snowman using the value of the deer.

4-3 = 1. This means the value of the snowman = 1.

3. Plug in the value of the snowman into 2t + s = 17.

     2t + 1 = 17

  Subtract on both sides to get 2t by itself and then simplify

      2t = 17 -1 --> 2t = 16

  Divide by 2 on both sides to find the value of the tree

      2t/2 = 16/2 --> t = 8

Answer:

300 words in 6 minutes

300/6 words in 1 minutes

50 words in 1 minutes

Therefore,Lee can type 50 words in 1 minute.

Answer:

its 80ft

Step-by-step explanation:

On solving the provided question, we can say that - here in the given equation we got x- 1 = 0; x = 1, y = 2

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

y = 2x +1

y = 3x - 1

x- 1 = 0

x = 1, y = 2

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

Answer:

9978

Step-by-step explanation:

10000 - 22 = 9978

9978 is the answer

Answer: 9978

Step-by-step explanation:

Stack the numbers up like this 10000

                                                          22

     borrow from the one make the zero a ten, and then borrow from that to make the next one and make it a nine and then do it to the last one and subtract. Hope this makes sense

Answer:

40,000

Step-by-step explanation:

can I have branliest

Answer: 40,000

Step-by-step explanation: Well it doubles every 440 minutes. Since it is asking for the size after 880 minutes, and the starting size is 20,000 just double 20,000 because 440 times 2 equals 880.