R, P, Q act on the base AB, BC, CA triangles ABC in alphabetical order, respectively. Show that P sec A + Q sec B + R sec C = 0, if the fluid of this power system passes through the center of the triangle.​

Answers

Answer 1

Answer:

(i) In △ABD and △ACD,

AB=AC ....(since △ABC is isosceles)

AD=AD ....(common side)

BD=DC ....(since △BDC is isosceles)

ΔABD≅ΔACD .....SSS test of congruence,

∴∠BAD=∠CAD i.e. ∠BAP=∠PAC .....[c.a.c.t]......(i)

(ii) In △ABP and △ACP,

AB=AC ...(since △ABC is isosceles)

AP=AP ...(common side)

∠BAP=∠PAC ....from (i)

△ABP≅△ACP .... SAS test of congruence

∴BP=PC ...[c.s.c.t].....(ii)

∠APB=∠APC ....c.a.c.t.

(iii) Since △ABD≅△ACD

∠BAD=∠CAD ....from (i)

So, AD bisects ∠A

i.e. AP bisects∠A.....(iii)

In △BDP and △CDP,

DP=DP ...common side

BP=PC ...from (ii)

BD=CD ...(since △BDC is isosceles)

△BDP≅△CDP ....SSS test of congruence

∴∠BDP=∠CDP ....c.a.c.t.

∴ DP bisects∠D

So, AP bisects ∠D ....(iv)

From (iii) and (iv),

AP bisects ∠A as well as ∠D.

(iv) We know that

∠APB+∠APC=180

....(angles in linear pair)

Also, ∠APB=∠APC ...from (ii)

∴∠APB=∠APC=

2

180

=90

BP=PC and ∠APB=∠APC=90

Hence, AP is perpendicular bisector of

Step-by-step explanation:

HOPE ITS HELP YOU


Related Questions

Help find initial value for graph PLSSSSSS the dotted points are (0,8) and (16,20)

Answers

Answer:8

Step-by-step explanation:

The initial value, or y-intercept, is the output value when the input of a linear function is zero, as you've already pointed out, the function crosses the y- axis at (0,8)

pls help this a math question. image below

Answers

Answer:

D

Step-by-step explanation:

Same X, but different Y value, it is five apart in D

The answer is d your welcome

If b = the number of boys, which algebraic expression represents the phrase
below?
the sum of the number of boys and 15 girls
A. b + 15
B. b. 15
C. b - 15
D.
b
15

Answers

Answer:

A. b + 15

Step-by-step explanation:

b = the number of boys, substitute below:

The sum of the number of boys and 15 girls → The sum of b and 15 → b + 15

Correct choice is A

x+1=x+2 is there a solution

Answers

Answer:

No Solution

Step-by-step explanation:

This is impossible. x+1 is not x+2

Variables are always the same: x=x

Answer:

No their isn't

Step-by-step explanation:

Please Help Me please

Answers

Answer:

the 3 one

Step-by-step explanation:

0.12 to the nearest tenth

Answers

Answer:

0.1

Step-by-step explanation:

hope this helps

Answer: 0.1 / 0.10

Step-by-step explanation:

since the 2 is lower than 5 - it turns into 0

hope this helped ! :>

549.5 to 1 decimal place

Answers

Answer:

It is still 549.5

Step-by-step explanation:

Rounding to 1 decimal place is just rounding by the tenth place

So it is still 549.5

Hope this helps!

549.5 (still the same answer)

Anthony is gathering workout clothes. There are 4 pairs of running shoes and 10 workout shirts to choose from. How many different workout outfits can Anthony make?

Answers

Answer:

40

Step-by-step explanation:

But he doesn’t have pants so 0 but yeah 40 sounds right

if x is reduced by 25%. the result will be

Answers

[tex]\huge\color{skyblue}\boxed{\colorbox{black}{Answer♡}}[/tex]

[tex]a \: number \: x \: is \: reduced \: by \: 25\%[/tex]

[tex]25\% \: of \: x \: means \: ( \frac{25}{100} )(x) = 0.25x \\ \\=> x - 0.25x \\ = > 0.75x[/tex]

hope helpful~

The reduced quantity if x is reduced by 25% is 0.75x.

What is percentage?

A percentage, often known as percent, is a division by 100. Percentage, which means "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.

Given:

x is reduced by 25%,

Calculate the 25% of x as shown below,

25 / 100 × x

0.25x

Calculate the reduced quantity,

Reduced quantity = x - 0.25x

Reduced quantity = x(1 - 0.25)

Reduced quantity = 0.75x

To know more about percentages:

brainly.com/question/20818421

#SPJ2

Please help me with this

Answers

Answer:

it is -16

Step-by-step explanation:

I did the math i know for sure

Plz help me with this

Answers

Answer:

sorry cant see the question

Step-by-step explanation:

30 POINTS!!! A catfish weights about 0.2 pound and its weight increases by about 15% each week. Write an exponential equation that represents the weight of the catfish after t weeks.

Answers

Answer:

0.30 15 times 2 easy 30 and this percent so 0.30

Step-by-step explanation:

Evaluate:
[tex] {8}^{ - \frac{2}{3} } [/tex]
with steps please​

Answers

[tex]8^{-\tfrac 23}\\\\\\=\left(8^{\tfrac 13 }\ \right)^{-2}\\\\\\=\left[\left(2^3\right)^{\tfrac 13} \right]^{-2}\\\\\\=\left(2^{\tfrac 33} \right)^{-2}\\\\\\=2^{-2}\\\\=\dfrac 1{2^2}\\\\\\=\dfrac 14[/tex]

[tex] {8}^{ - \frac{2}{3} } \\ = {2}^{3 \times - \frac{2}{3} } \\ = {2}^{ - 2} \\ = \frac{1}{2^{ 2}} \\ = \frac{1}{4} [/tex]

Hope you could get an idea from here.

Doubt clarification - use comment section.

6 O
Which function is graphed on the coordinate plane below?
Ty
x
f(x) = 2x - 6
Of(x) = 2x + 6
f(x) = -2x + 6
Mark this and retum
Save and Exit
Next
Submit

Answers

Step-by-step explanation:

we don't see all possible answer options.

but it does not matter.

the line is clearly

y = 2x - 6

why ?

the slope is always the factor of x.

and the slope is defined as ratio of "y coordinate change / x coordinate change".

and we can clearly see, for every change in x by +1, y changes by +2. zu, the slope is 2/1 = 2.

and when x = 0, the graph shows us the y-intercept with y = -6.

hence the above mentioned equation.

The Function is graphed on the coordinate plane is y= 2x- 6.

What is Slope?

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

We have points from the graph as (3, 0) and (0, -6).

So, the slope of line is

slope= (-6 -0)/ (0-3)

slope = -6/ (-3)

slope= 2

Now, using the slope intercept form

y= mx + b

y= 2x + b

Now, put x= 3 and y= 0 we get

0= 6 + b

b = -6

So, the required function is

y= 2x - 6.

Learn more about Slope here:

https://brainly.com/question/3605446

#SPJ7

If 5/3 liters of water is enough to water ⅕ of your yard, 5 3 how much water is needed to water the entire yard?

Answers

Answer:

8 1/3 liters

Step-by-step explanation:

create a proportion from water : yard

let 'y' = water for entire yard

5/3 ÷ 1/5 = y ÷ 5/5

5/3 · 5/1 = y/1

25/3 = y/1

3y = 25

y = 8 1/3

Is this the right question

Answers

Answer:

no, ssa is the incorrect one

no it’s not A is correct i think

The areas of two similar
squares are 16 m2 and 49 m2.
What is the scale factor of
their side lengths?
[?]:[ ]

Answers

4:7

Take the square root of each square to get the side lengths

4*4=16
7*7=49

Answer:

4:7

Step-by-step explanation:

We know that

Area of square = s²

For square 1

16 = s²

√16 = s

4 = s

For square 2

49 = s²

√49 = s

7 = s

Scale factor = 4:7

How I can answer this question, NO LINKS, if you answer correctly I will give u brainliest!

Answers

Answer:

It is the first one.

Select the equation that contains the points (-1, -8) and (3, 4).

Answers

show us the equations
show us the equation

the given cube has a mass of 173 grams, what is it’s density

Answers

Answer:

I think the density is 4cm.

Hope that helps you.

Step-by-step explanation:

Find the product:
[tex] \frac{1}{8} \times \sqrt{8} [/tex]

Answers

Answer:

≈ 0.35

Step-by-step explanation:

First simplify [tex]\sqrt{8}[/tex] and [tex]\frac{1}{8}[/tex] :

[tex]\sqrt{8}[/tex] ≈ 2.83

[tex]\frac{1}{8}[/tex] = 0.125

Now multiply them as shown in the original equation:

0.125 x 2.83 = 0.35375 ≈ 0.35

HURRY IN TEST!!
Which of the following number lines shows the solution to the inequality given below?

2x − 3 < -9 OR 2x − 3 > 3

Answers

Answer: B.

Steps:

solve the inequalities

x <= -3

x>3

match to number line

answer B

Answer:

#LINE B

Step-by-step explanation:

(make sure to look at the color and direction of the arrow)

Solve for x.
-8 =X/4

Answers

x = −32

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How many twelfths make one whole






How many twelfths make one whole

Answers

Answer:

12

Step-by-step explanation:

1/12x1/x

1x=12x1

x=12

Answer:

12 twelfths make a whole.

Step-by-step explanation:

when the numerator and the denominator of a fraction are the same, they always equal one. 12/12 would simply to one, just like 3/3 or 200/200.

I hope this helps

How do I solve this problem?

Answers

Here is the work! The zeros of the graph are at -1 and 3

what is 72=2x+16x
please please helppppp meeee

Answers

Answer:

x = 4

Step-by-step explanation:

72 = 2x + 16x , that is

72 = 18x ( divide both sides by 18 )

4 = x

Answer:

x=4

Step-by-step explanation:

72=18x

72/18=4

x=4

Write your own formula. List the first 4 terms and solve for the 10th term using the formula.

Answers

Answer:

Below

Step-by-step explanation:

Formula for an arithmetic sequence is an = 4n - 5

First 4 terms are

-1, 3, 7, 11.

10th term = 4(10) - 5

= 35.

simplify the quotient. Write the answer in sn.

Answers

Answer:

2.4*10^4

Step-by-step explanation:

write in scientific notation

first i would simplify the 3.6/1.5

=2.4

then you get (2.4*10^7)/10^3

formula: (m^x)/(m^y)= m^(x-y)

(2.4*10^7)/10^3

=2.4*10^(7-3)/1

=2.4*10^4

This is a function?

O True
O False

Answers

Answer:

true

Step-by-step explanation:im not really sure

Jonah uses 1/2 of a cup of vinegar in his salad dressing recipe. How much vinegar would
Jonah use to make 1/2 of a recipe?
Write your answer as a fraction or as a whole or mixed number.
cups

Answers

Answer:

1/4 cup

Step-by-step explanation:

Assuming that the recipe makes 1 cup of dressing, Jonah would need 1/4 cup of vinegar. Half of 1/2 is 1/4.

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