Square OPQR is inscribed in triangle ABC. The areas of △AOR, △BOP, △CRQ are 1, 3, and 1, respectively. What is the area of square OPQR?

Answer:

Ans = 76

Step-by-step explanation:

10y + [tex]x^{2}[/tex]

=> 10 * 4 + [tex]6^{2}[/tex]

=> 40 + 36

=> 76

Hope it helps :)

Answer:

PJ = 41.34

Step-by-step explanation:

P is incenter, three angles bisector meet

∠MJP ≅ ∠OJP

PM = PN = PO = 22   (radius: property of incenter)

∠JPM = 90 - ∠MJP = 90 - OJP = ∠JPO

ΔJPM ≅ ΔJPO   (ASA) or (SAS)

LM = JO

2x + 3 = 5x - 45

3x = 48

x = 16

JM = 35

PJ = √35²+22² = √1709 = 41.34

The value of PJ in triangle KJL is 41.32 units.

The point formed at the intersection of the three angle bisectors of a triangle; also the centre of the incircle.

Given that, P is incenter of the triangle KJL,

Considering the triangles ΔMJP and ΔOJP

PM = PO (property of incenter)

∠ JMP ≅ ∠ JOP

JP is common segment.

ΔJPM ≅ ΔJPO  (by SAS rule)

JM = JO  (CPCTC)

2x + 3 = 5x - 45

3x = 48

x = 16

JM = 35

Using the Pythagoras theorem,

PJ² = PM²+JM²

PJ = √35²+22² = √1709 = 41.34

Hence, The value of PJ in triangle KJL is 41.32 units.

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Answer: first one

Step-by-step explanation:

Answer:

yes, school is hard

thanks for points

have a good day ....❤

Answer:

Read explanation

Step-by-step explanation:

A)The slope is the number before the X so 0.25, this represents the amount of money people have to pay for each mile driven over 150 miles.

B) The y-intercept is the number after the X so 32, this number represents the amount people have to pay rent the car before actually using it.

Well the distance from the two points is 15 so that means the midpoint in -10+7.5=-2.5. There you go! Have a nice day.

Where exactly are the alleged statements?

Answer:

a) The location of the center of the ellipse is [tex](4,-6)[/tex]. It is determine by knowing the location of foci and Midpoint formula.

b) The standard equation of the ellipse is [tex]\frac{(x-4)^{2}}{31}+\frac{(y+6)^{2}}{81} = 1[/tex].

c) Major semiaxis ([tex]a[/tex]): [tex]a = 9[/tex], Minor semiaxis ([tex]b[/tex]): [tex]b = \sqrt{31}[/tex]

Step-by-step explanation:

a) Foci are located in the major axis of the ellipse, given the locations of ends of the major axis and locations of the foci. We can determine the location of the center of the ellipse by Midpoint formula:

[tex](h,k) = \frac{1}{2}\cdot F_{1}(x,y) + \frac{1}{2}\cdot F_{2} (x,y)[/tex] (1)

Where [tex]F_{1} (x,y)[/tex] and [tex]F_{2} (x,y)[/tex] are the locations of the foci.

If we know that [tex]F_{1}(x,y) = (4, -6-5\sqrt{2})[/tex] and [tex]F_{2} (x,y) = (4,-6+5\sqrt{2})[/tex], then the location of the center of the ellipse is:

[tex](h,k) = (4, -6)[/tex]

The location of the center of the ellipse is [tex](4,-6)[/tex]. It is determine by knowing the location of foci and Midpoint formula.

b) Now we need to determine the length of each semiaxis:

Major semiaxis ([tex]a[/tex])

[tex]a = \sqrt{[V_{2}(x,y)-(h,k)]\,\bullet\,[V_{2}(x,y)-(h,k)]}[/tex] (2)

[tex]V_{2}(x,y)-(h,k) = (4,3)-(4,-6)[/tex]

[tex]V_{2}(x,y) - (h,k) = (0, 9)[/tex]

[tex]a = 9[/tex]

Please notice that [tex]V_{2}(x,y)[/tex] is one of the vertices of the ellipse in the major axis.

Distance between focus and center ([tex]c[/tex])

[tex]c = \sqrt{[F_{2}(x,y)-(h,k)]\,\bullet\,[F_{2}(x,y)-(h,k)]}[/tex]

[tex]F_{2}(x,y) -(h,k) = (4-4,-6+5\sqrt{2}+6)[/tex]

[tex]F_{2}(x,y) - (h,k) = (0, 5\sqrt{2})[/tex]

[tex]c = 5\sqrt{2}[/tex]

Minor semiaxis ([tex]b[/tex])

[tex]c^{2} = a^{2}-b^{2}[/tex] (3)

[tex]b = \sqrt{a^{2}-c^{2}}[/tex]

If we know that [tex]a = 9[/tex] and [tex]c = 5\sqrt{2}[/tex], then the length of the minor semiaxis is:

[tex]b = \sqrt{31}[/tex]

In this case, the standard equation of the ellipse is defined by this formula:

[tex]\frac{(x-h)^{2}}{b^{2}}+\frac{(y-k)^{2}}{a^{2}} = 1[/tex]

If we know that [tex]a = 9[/tex], [tex]b = \sqrt{31}[/tex] and [tex](h,k) = (4, -6)[/tex], then the standard equation of the ellipse is:

[tex]\frac{(x-4)^{2}}{31}+\frac{(y+6)^{2}}{81} = 1[/tex]

The standard equation of the ellipse is [tex]\frac{(x-4)^{2}}{31}+\frac{(y+6)^{2}}{81} = 1[/tex].

c) The lengths of the axes are, respectively:

Major semiaxis ([tex]a[/tex]): [tex]a = 9[/tex]

Minor semiaxis ([tex]b[/tex]): [tex]b = \sqrt{31}[/tex]

Answer:

a) The location of the center of the ellipse is . It is determine by knowing the location of foci and Midpoint formula.

b) The standard equation of the ellipse is .

c) Major semiaxis (): , Minor semiaxis ():

Step-by-step explanation:

Answer:

1,436.8

Step-by-step explanation:

Answer:

3,2

Step-by-step explanation:

3 is equal to 3 which can be it and 2 is less than 3

Answer:

Step-by-step explanation:

x+110=180

x=70 degrees

y+40+110=180

y=30 degrees

z+70+90=180

z=20 degrees

Answer: The answer should be 39 yard line

Step-by-step explanation: If you start at the 50 and remove 11 yards you will have 39 yards left

Answer: 50 inches

Step-by-step explanation:

Answer:

75 student tickets and 10 chaperone tickets

Step-by-step explanation:

First find out how many groups there are total by dividing 85 by 1 group total of 17 (15 students 2 chaperones).

85 / 17 = 5

Since you now know there are five groups of 15 students and 2 chaperones all you have to do is multiply 5 time 15 students and 5 times 2 chaperones.

15 x 5 = 75 for students

5 x 2 = 10 for chaperones  

Answer:

(-2, 6)

Step-by-step explanation:

Plug in one of the equations into the y-variable (doesn't matter which):

2x + 10 = -4x - 2

Combine like terms by adding the 4x to both sides. This makes it cancel out on the right side, and 2x + 4x on the right side is 6x:

6x + 10 = -2

Combine like terms by subtracting 10 from both sides, making it cancel out on the left side, and on the right: -2 - 10:

6x = -12

Then isolate the x-variable by dividing both sides by 6:

x = -2

Taking the -2, plug it into an x-variable in either of the equations:

y = 2x +10

y = 2(-2) + 10

y = -4 + 10

y = 6

answer:

11x

step-by-step explanation:

x + 4x + 6x

= 11x

Answer:

11x

Step-by-step explanation:

just add them all together

x + 4x = 5x

5x + 6x = 11x

hope this helps :)

The other no. is:

32

As you can see that in the ratio given, 3 is the smaller no. and 12 too.

So when we divide 12 by 3, we get 4

Then to find the other no. we need to multiply 4 with 8 (which is the other no.          in the ratio given)

Therefore, we get the other no. as 32

And also when you divide 12 by 32,

You get the answer as 3 by 8 (which is the given ratio)

Hope you found this helpful!

THANK YOU!!

∝ Sidhdi

Answer:

200g

Step-by-step explanation:

24x2=48

100x2=200

Answer:

Part A is no because after subtracting it is 6/10 and 6/10 is not equal to 1/2

Step-by-step explanation:

First you make the fraction's denominator equal

2/5 = 4/10

Camen's water bottle is 1 8/10

Jorge's water bottle is 2 4/10

1/2 = 5/10

Make the fractions into a improper fraction

Camen's is 18/10

Jorge's is 24/10

subtract it

24 - 18 = 6

So Part A is no because after subtracting it is 6/10 and 6/10 is not equal to 1/2

Answer:

254.34 in^2

Step-by-step explanation:

Answer:

y = - 4x + 5

Step-by-step explanation:

(y-1)/ (5-1) = (x-1)/(-1)

y-1 / 4 = -x+1

y-1 = -4x+4

y = - 4x + 5

Answer:

it would take 12.5 or 12 and a half years

Step-by-step explanation:

Answer:

m∠ABC = 110°

Step-by-step explanation:

By the property of exterior angle of a triangle,

"Exterior angle of a triangle is equal to the sum of two opposite interior angles"

m∠BAC + m∠ABC = 135°

25° + m∠ABC = 135°

m∠ABC = 135° - 25°

             = 110°

Therefore, measure of angle ABC is 110°.

Answer: 240 m

Step-by-step explanation:

Given

Football field measures [tex]100\ m\times 72\ m[/tex]

Another similar field of length

[tex]L=30\ m[/tex]

and width, say W is marked

So, their area must be the same

[tex]\Rightarrow 100\times 72=30\times W\\\\\Rightarrow W=\dfrac{7200}{30}=2540\ m[/tex]

The width of the football field is 41.7m

The football measures 100m by 72 m. The school football field is similar.

For similar rectangles, the corresponding sides have common ratios. Therefore, let's establish the proportion as follows:

cross multiply

3000 = 72w

divide both sides by 72

w = 3000 / 72

w = 41.6666666667

w = 41.7 m

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Answer:

280 Cubic inches

Step-by-step explanation:

When finding the volume, the equation is V=l*w*h

Therefore, the equation should be:

10.1*3.9*6.8

This is equal to exactly 267.852

However, the answer is 280 cubic in. because it's a larger number and it's about 13 from the actual answer. On the other hand, 250 cubic in. is about 17 from the actual number.

Answer:

There were 176 pitchers at the camp.

Step-by-step explanation:

Given that,

The ratio of pitchers to catchers at a baseball camp was 11:4.

Let pitchers be 11x and catachers be 4x.

Total catchers = 64

4x = 64

x = 16

So,

Pitchers = 11x

= 11(16)

= 176

Hence, there were 176 pitchers at the camp.

Answer:

√8x^7y^8

= 2x^3y^4 √2x

answer is C. third choice

Step-by-step explanation:

The expression is equivalent to given expression is [tex]2^{\frac{3}{2} }x^{\frac{7}{2} }.y^4[/tex].

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given expression is √(8x⁷y⁸).

Here, √(8x⁷y⁸)

= [tex](8x^7y^8)^{\frac{1}{2} }[/tex]

= [tex]2^{\frac{3}{2} }x^{\frac{7}{2} }.y^{\frac{8}{2} }[/tex]

= [tex]2^{\frac{3}{2} }x^{\frac{7}{2} }.y^4[/tex]

Therefore, the equivalent expression is [tex]2^{\frac{3}{2} }x^{\frac{7}{2} }.y^4[/tex].

To learn more about an equivalent expression visit:

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Answer:

Rhombus

Step-by-step explanation:

This undoubtedly has to be a rhombus. When you look at other quadrilaterals for example and want to judge and or differentiate, we see that in the case of a square, the diagonals are equal to one another and they are not congruent. Same can be applied to that of a rectangle as well, it's diagonals aren't congruent, even if they appear perpendicular.

On the other hand, the diagonals of a rhombus is both perpendicular, and at the same time congruent. And thus, that's our answer

Answer:

Step-by-step explanation:

Use Pythagorean

Answer:

in right angled triangle BCD

by using Pythagoras law

P²+B²=H²

A²+B²=C²

36²+18²=x²

x=√1620=18√5m

x=18√5 m is your answer