Which could be the value of the third side of a triangle with sides 3 and 4? A. 3 B. 7 C. 12 D. 20

Given:

The three points are W(0,-2), I(2,0) and L(5,k).

To find:

The value of k for which the given points are collinear.

Solution:

We know that, three points are collinear if the area of the triangle formed by these three points is 0.

[tex]\dfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|=0[/tex]

[tex]x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)=0[/tex]

The three points are W(0,-2), I(2,0) and L(5,k). So,

[tex]0(0-k)+2(k-(-2))+5(-2-0)=0[/tex]

[tex]0+2(k+2)+5(-2)=0[/tex]

[tex]2k+4-10=0[/tex]

[tex]2k-6=0[/tex]

Adding 6 on both sides, we get

[tex]2k=6[/tex]

[tex]k=\dfrac{6}{2}[/tex]

[tex]k=3[/tex]

Therefore, the correct option is E.

Answer:

The answer is (0, 2)

Step-by-step explanation:

Ive also had this question and viewed iver it and said it was right this was some time ago but im glad to help :)

Answer:

the amount paid by Sarah is $20.64

Step-by-step explanation:

Given that

The total cost of the dinner is $61.92

And her friends pay 2 by 3

We need to find out the amount paid by Sarah

Since her friends pay 2 by 3 of the total cost

That means the remaining should be paid by Sarah i.e. 1 by 3

So, we need to multiply 1 by 3 with the total cost of the dinner i.e.

= 1 ÷3 × $61.92

= $20.64

Hence, the amount paid by Sarah is $20.64

Answer:

I believe they're the same because the last part of the equation is the same

Step-by-step explanation:

because 3/x-4+4 they both are the same

Answer:

85.13 inches^2 (2dp)

Step-by-step explanation:

Area semi circle:

πr^2/2

π * 4^2 / 2

25.1327412

Area parallelogram

bh

b x h

10 x 6 = 60

60 + 25.1327412 = 85.1327412

Answer:

3.24m

Step-by-step explanation:

SOH

sin(26)=O/7.4

O=7.4 sin(26)

O=3.24 (3sf)

Answer:

Step-by-step explanation:

The first four

Answer:

its 7x+3=x-3

Step-by-step explanation:

it is

Answer:

Step-by-step explanation:

Let the horizontal leg = 4√41 and the hypotenuse = 41 as

Then the vertical leg is:

Since the vertical leg is below the x-axis, its value is -5√41

Then we have:

Correct choice is A

Answer:

Step-by-step explanation: i just take the test

Answer: [tex]171.4\%[/tex]

Step-by-step explanation:

Given

Time is extended from 28 days to 76 days

The percentage increase is given by

[tex]\Rightarrow \dfrac{\text{New-original value}}{\text{original value}}\times 100[/tex]

Putting values

[tex]\Rightarrow \dfrac{76-28}{28}\times 100=\dfrac{48}{28}\times 100\\\\\Rightarrow 171.4\%[/tex]

Thus, the percentage increase in time is [tex]171.4\%[/tex]

Answer: b

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

Given that

There are 126000 people living in a town

Out of which 52920 people in the town own a car

So based on this, the group announces that fewer than 40% of residents own a car

We need to find out the statement is correct or not

So here we determine the percentage

= 52,920 ÷ 126,000

= 42%

Since it is more than 40%

So the given statement is false

Answer:

Step-by-step explanation:

32

Answer:

I do not understand ummmm

Answer:

C: 8.06

Step-by-step explanation:

c=a^2+b^2=42+72≈8.06226

Answer:

8.06

Step-by-step explanation:

C2= a2+ b2

C2= 7 squared + 4 squared

C2= 49+16

C2=65

C is the square root of c2

square root 65

C= 8.06

c= 8

An equivalent rational expressions with denominator (x+3), (x−4) and (x+4) is (3x²+6x-16)/(x³+3x²-16x-48).

The given denominator are (x+3), (x−4) and (x+4).

A mathematical expression that may be rewritten to a rational fraction, an algebraic fraction such that both the numerator and the denominator are polynomials.

Here, an equivalent rational expressions is

[tex]\frac{1}{x+3}+\frac{1}{x-4} +\frac{1}{x+4}[/tex]

The LCM of denominators is (x+3)(x-4)(x+4)

= (x+3)(x²-16)

= x(x²-16)+3(x²-16)

= x³-16x+3x²-48

= x³+3x²-16x-48

Now, [tex]\frac{(x-4((x+4)+(x+3)(x+4)+(x+3)(x-4)}{x^3+3x^2-16x-48}[/tex]

= (x²-16+x²+7x+12+x²-x-12)/(x³+3x²-16x-48)

= (3x²+6x-16)/(x³+3x²-16x-48)

Hence, an equivalent rational expressions with denominator (x+3), (x−4) and (x+4) is (3x²+6x-16)/(x³+3x²-16x-48).

Learn more about the rational expressions here:

https://brainly.com/question/19585906.

#SPJ1

Answer:

30%

Step-by-step explanation:

Answer: Its 18%

Step-by-step explanation: To get the answer subtract 96 from 78

Answer:

f(x)= (x-5)(x+6)

Step-by-step explanation:

First, we find the factors of -30 that add up to +1

We can use 6 and -5

6+(-5)=1

f(x)= x^2+6x - 5x-30

then, we do group factorization

f(x)= x(x+6)- 5(x+6)

f(x)= (x-5)(x+6)

i hope this helps <3

Answer:

I'm not sure of the answer

Answer:

-6.5cm/s

Step-by-step explanation:

-19.5/3

answer is in attachment!

Answer:

[tex]Area = 30[/tex]

Step-by-step explanation:

Given

Rectangle coordinates

[tex]A = (0,4)[/tex]

[tex]B = (4,2)[/tex]

[tex]C = (1,-4)[/tex]

[tex]D =(-3,-2)[/tex]

Required

The area of the rectangle

The area is calculated as:

[tex]Area = Length* Width[/tex]

The length of the rectangle will be represented as:

[tex]Length = AB = CD[/tex]

And the width is:

[tex]Width = BC = AD[/tex]

Calculate distance AB using:

[tex]AB = \sqrt{(x_1 - x_2)^2 +(y_1 - y_2)^2 }[/tex]

Where:

[tex]A = (0,4)[/tex] --- [tex](x_1,y_1)[/tex]

[tex]B = (4,2)[/tex] [tex]--- (x_2,y_2)[/tex]

[tex]AB = \sqrt{(0 - 4)^2 +(4 - 2)^2 }[/tex]

[tex]AB = \sqrt{(- 4)^2 +(2)^2 }[/tex]

[tex]AB = \sqrt{16 +4 }[/tex]

[tex]AB = \sqrt{20}[/tex]

Calculate distance BC using:

[tex]BC = \sqrt{(x_1 - x_2)^2 +(y_1 - y_2)^2 }[/tex]

[tex]C = (1,-4)[/tex] [tex]---(x_1,y_1)[/tex]

[tex]B = (4,2)[/tex] [tex]--- (x_2,y_2)[/tex]

[tex]BC = \sqrt{(1 - 4)^2 +(-4 - 2)^2 }[/tex]

[tex]BC = \sqrt{(- 3)^2 +(-6)^2 }[/tex]

[tex]BC = \sqrt{9 +36}[/tex]

[tex]BC = \sqrt{45}[/tex]

So, the area is:

[tex]Area = Length * Width[/tex]

[tex]Area = AB * BC[/tex]

[tex]Area = \sqrt{20} * \sqrt{45}[/tex]

[tex]Area = \sqrt{20 * 45}[/tex]

[tex]Area = \sqrt{900[/tex]

[tex]Area = 30[/tex]

Answer:

use ma th wa y (its all together)

Step-by-step explanation:

Answer:

10. The number of cupcakes Sheldon would have to buy to recieve the same number of cupcakes in a package would be 30 cupcakes in a package.

Step-by-step explanation: Find the least common denominator (LCD) of six and ten which is, 30.

11.  The greatest number of necklaces Samuel would have to make is four.

Step-by-step explanation: Divide 148 necklaces by 36 strings and the answer will be four necklaces.

12. The greatest length, in feet, of each piece of ribbon Karen, would have to cut is six feet.

Step-by-step explanation: Find the greatest common denominator (GCD) of 18 and 12 which is, six.

13. Find the least common denominator of five and three which is, 15 minutes.

Step-by-step explanation:

Jacob will finish his laps in these following minutes, supposing he starts at zero.

3 minutes, 6 minutes, 9 minutes, 12 minutes, 15 minutes...

That is, all instants of time which are multiples of three.

Betty

5 minutes, 10 minutes, 15 minutes, 20 minutes, 25 minutes, ...

That is, all instants of time which are multiples of five.

Answer: $26901

Step-by-step explanation:

From the information given, we are informed that Walter's home was originally valued at $29,275 but that after some improvement, it is now valued at $56,176.

Therefore, the increase in the worth of Walter's home will now be the difference in the values given above. This will be:

= $56,176 - $29275

= $26901

Answer:

D

Step-by-step explanation:

above the third quartile. because it is upper 25% of the data.

Answer:

C.between the 2nd and 3rd quartile

Answer:

x=4

Step-by-step explanation:

7(2x+8)=4(28)

14x+56=112

14x=112-56

14x=56

x=4

Answer:

what do u need help with there isn't anything attached

Step-by-step explanation:

Answer:

please put correct question

Answer:

k = 6.5

Step-by-step explanation:

The question relates to the association of the association of the equation of a graph point(s) on the graph

The given equation of the graph, is y = 2·x + c

The value of 'c' is a constant

We note that the value of 'c' can be found when x = 0, as follows;

y = 2·x + c = 2 × 0 + c = c

∴ When x = 0, y = c

From the graph, when x = 0 we have the y-intercept, the point the graph crosses the y-axis, which is the point y = -3

Therefore;

When x = 0, y = -3 = c

∴ c = -3

The equation of the graph becomes, y = 2·x + (-3) = 2·x - 3

y = 2·x - 3

The other given point on the graph is the point (k, 10)

The value k is the x-value when y = 10

Substituting y = 10 in the equation for the graph gives the x-value at the point y = 10 as follows;

10 = 2·x - 3

2·x = 13

x = 13/2 = 6.5

x = 6.5 (when y = 10)

Therefore the point (k, 10) = (6.5, 10)

By comparing the two equal coordinates, we have;

k = 6.5.