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KATRIN_1 [288]
3 years ago
10

Solve this quadratic equation by completing the square.

Mathematics
1 answer:
erastova [34]3 years ago
5 0

Answer:

C

Step-by-step explanation:

x² + 6x = 18

To complete the square, take the coefficient of the x term, halve it, square the result, then add to both sides.

(6/2)² = 3² = 9

x² + 6x + 9 = 18 + 9

(x + 3)² = 27

x + 3 = ±√27

x = -3 ± √27

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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
matrenka [14]

Answer: Area of  ΔABC = 56m².

Explanation:

Since we have given that

point P∈ AB, such that AP:BP=1:3

Point M is the midpoint of segment CP.

Now, we have given that

Area of ΔBMP=21 m²

Since M is the mid-point of CP, so,

Area of ΔCMP= 21 m².

So, Area of ΔBCP = 21+21=42 m²

According to question,

\frac{3}{4}\times x= 42\\\\x=\frac{42}{3}=14\\\\\text{ Area of }\triangle APC=14m^2\\\\

So, area of ΔABC is given by

42+14=56m^2

Hence, area of  ΔABC =56m².

3 0
3 years ago
Read 2 more answers
Complete the table of ordered pairs for the given liners equation
Papessa [141]

Answer:

Step-by-step explanation:

Given equation of the line is,

y = -x + 1

We will get the output values (y-values) from the given equation for different input values (x-values).

For x = 0,

y = 0 + 1

y = 1

For x = -1,

y = -1 + 1

y = 0

For x = -6,

y = -6 + 1

y = -5

So the table of the ordered pairs will be,

x        0         -1          -6            

y       1           0         -5

5 0
3 years ago
Write the vector u as a sum of two orthogonal vectors, one of which is the vector projection of u onto v, proj,u
11Alexandr11 [23.1K]

Answer:

Take b = \frac{-17}{25}(7,1) as the projection of u onto v and w \frac{1}{25}(-31,217) as the vector such that b+w =u

Step-by-step explanation:

The formula of projection  of a vector u onto a vector v is given by

\frac{u\cdot v}{v\cdot v}v, where cdot is the dot product between vectors.

First, let b ve the projection of u onto v. Then

b = \frac{u\cdot v}{v\cdot v}v= \frac{-6\cdot 7+8\cdot 1}{7\cdot 7+1\cdot 1}(7,1) = \frac{-34}{50}(7,1) = \frac{-17}{25}(7,1)

We want a vector w, that is orthogonal to b and that b+w = u. From this equation we have that w = u-b = (-6,8)-\frac{-17}{25}(7,1)= \frac{1}{25}(-31,217)[/tex]

By construction, we have that w+b=u. We need to check that they are orthogonal. To do so, the dot product between w and b must be zero. Recall that if we have vectors a,b  that are orthogonal then for every non-zero escalar r,k the vector ra and kb are also orthogonal. Then, we can check if w and b are orthogonal by checking if the vectors (7,1) and (-31, 217) are orthogonal.

We have that (7,1)\cdot(-31,217) = 7\cdot -31 + 217 \cdot 1 = -217+217 =0. Then this vectors are orthogonal, and thus, w and b are orthogonal.

5 0
3 years ago
John can reach 60 centimeters above the top of his head. If John is 2 meters tall, how high can he reach?
zlopas [31]
He can reach 2.6 meters or 260 centimeters
8 0
3 years ago
can Consider the expresion 6348 how you use distruptive propert and the Gcf to find the equielovent expression? Explain how you
mario62 [17]

Answer:

63+48= 3(21+16)

Step-by-step explanation:

Check answer:

Distribute 3(21+16)

3(21)+3(16)

63+48

8 0
3 years ago
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