1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
umka21 [38]
3 years ago
15

In △ABC, point P∈ AB is so that AP:BP=1:3 and point M is the midpoint of segment CP . Find the area of △ABC if the area of △BMP

is equal to 21m2.

Mathematics
2 answers:
ddd [48]3 years ago
5 0

M is mid point of CP. M will divide the \Delta BPC in two equal parts \Delta BMC and    \Delta BMP.

Area of \Delta BMP is equal to 21m^2

Since, \Delta BMC = \Delta BMP

Area of  \Delta BPC = Area of  \Delta BMC +Area of \Delta BMP =  21 + 21 = 42m^2

and since ratio of AP:BP =1:3  so the area of \Delta BMP will be 1/3 of Area of \Delta ABC

hence, Area of \Delta ABC = 63m^2

OLga [1]3 years ago
3 0

Answer: 56 m^2


Step-by-step explanation:

  1. The areas of triangle BMP and CMB are equal because the base and height are the same. Therefore, <em>A</em>BMP=<em>A</em>CMB=21m^2 which is due to transitivity.
  2. <em>A</em>PCB=<em>A</em>BMP+<em>A</em>CMB=21+21=42m^2
  3. The ratio of the areas of triangles ACP to PCB is the same as their bases AP and BP which is 1:3. This is due to area of triangles.
  4. After that, we use Substitution and Algebra to calculate the area of: <em>A</em>ACP=42 / 3 * 1 = 14 * 1 = 14
  5. Finally, we add all of the areas together. (Or you could've just multiplied in the last equation by 4 rather than 3 to get the <em>A</em>ABC sooner.) <em>A</em>ABC=<em>A</em>ACP+<em>A</em>PCB=14+42=56m^2
You might be interested in
An article reported that for a sample of 52 kitchens with gas cooking appliances monitored during a one-week period, the sample
kolbaska11 [484]

Answer:

a) 654.16-2.01\frac{164.55}{\sqrt{52}}=608.29    

654.16+2.01\frac{164.55}{\sqrt{52}}=700.03    

And we can conclude that we are 95% confident that the true mean of Co2 level is between 608.29 and 700.03 ppm

b) n=(\frac{1.960(175)}{25})^2 =188.23 \approx 189

Step-by-step explanation:

Part a

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

In order to calculate the critical value t_{\alpha/2} we need to find first the degrees of freedom, given by:

df=n-1=52-1=51

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,51)".And we see that t_{\alpha/2}=2.01

Replacing we got:

654.16-2.01\frac{164.55}{\sqrt{52}}=608.29    

654.16+2.01\frac{164.55}{\sqrt{52}}=700.03    

And we can conclude that we are 95% confident that the true mean of Co2 level is between 608.29 and 700.03 ppm

Part b

The margin of error is given by :

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}    (a)

The desired margin of error is ME =50/2=25 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

n=(\frac{z_{\alpha/2} s}{ME})^2   (b)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got z_{\alpha/2}=1.960, and we use an estimator of the population variance the value of 175 replacing into formula (b) we got:

n=(\frac{1.960(175)}{25})^2 =188.23 \approx 189

6 0
3 years ago
Which set of values could be the side lengths of a 30-60-90 triangle?
Tju [1.3M]

Answer:

A

Step-by-step explanation:

I think you are in geometry I learned this a little back...

It's hard to explain but basically one side is just (n) another is (n(square root sign))and another is (2n.)    

So the answer Is a because in this case (n) is 4  

6 0
3 years ago
Find x:<br><br><br><br><br> explain if you can!
Sergio039 [100]

Answer:

x is 97

Step-by-step explanation:

the interior angles have to equal 180 and the exterior angles have to come to 360 degrees

so you already know 23 to find the one by the 106 degree you use the linear pair postulate ( angles on a straight line will equal 180) so 180-106 equals 74. Now you have 2 of the three interior angles. To find the third you take 180 - 74 - 23 which equals 83 then you can use the linear pair postulate again and take 180-83 to get your answer for x which equals 97

4 0
3 years ago
What are the intercepts of the equation <br><br> -2A+2y = -8
r-ruslan [8.4K]
X intercepts: (8,0)
y intercepts: (0,-4)
7 0
2 years ago
Convert the following improper fractions into mixed numbers.<br><br> 3 1/4
lara [203]

Answer:

7 and 3/4

Step-by-step explanation:

31/4=7-3

the remainder is 3/4

8 0
3 years ago
Other questions:
  • Can you show me the steps to find the equation for (3×10)×8= ×(10×8)
    5·1 answer
  • Y=2/3 when x=1/2 <br> can anyone please help me
    6·1 answer
  • Pease Help. Will mark Brainliest
    5·2 answers
  • Is this proportional?<br> Questions answered: 60<br> Questions asked: 6
    13·2 answers
  • Please help me with this please
    8·1 answer
  • -11t=15-6t, please help me.​
    5·1 answer
  • Is 0 a perfect square?
    10·2 answers
  • Please help quickly!!<br> What is the radius, diameter and r2 of a circle with a 3cm area?
    14·1 answer
  • Find the slope and y-intercept of the graph of the equation: y=9x+3
    8·1 answer
  • The input-output diagram represents F(x)=x+4. What is the missing output value? F(x) Input Output 3 7 4 11 15​
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!