Solve for the unknown variable
4y-2=8-2y+4y
y=?

​

Let a, b, and c be vectors each starting at the origin and terminating at the points (x, x + 1), (x + 2, x + 3), and (x + 3, 2x + 4), respectively.

Then the vectors a - b, a - c, and b - c are vectors that point in directions parallel to each of the legs formed by the triangle with these points as its vertices.

If this triangle is to contain a right angle, then exactly one of these pairs of vectors must be orthogonal. In other words, one of the following must be true:

(a - b) • (a - c) = 0

or

(a - b) • (b - c) = 0

or

(a - c) • (b - c) = 0

We have

a - b = (x, x + 1) - (x + 2, x + 3) = (-2, -2)

a - c = (x, x + 1) - (x + 3, 2x + 4) = (-3, -x - 3)

b - c = (x + 2, x + 3) - (x + 3, 2x + 4) = (-1, -x - 1)

Case 1: If (a - b) • (a - c) = 0, then

(-2, -2) • (-3, -x - 3) = (-2)×(-3) + (-2)×(-x - 3) = 2x + 12 = 0   ==>   x = -6

which would make a - c = (-3, 3) and b - c = (-1, 5), and their dot product is not zero. Then the triangles vertices are at the points (-6, -5), (-4, -3), and (-3, -8).

Case 2: If (a - b) • (b - c) = 0, then

(-2, -2) • (-1, -x - 1) = (-2)×(-1) + (-2)×(-x - 1) = 2x + 4 = 0   ==>   x = -2

which would make a - c = (-3, -1) and b = (-1, 1), and their dot product is also not zero. The vertices are the points (-2, -1), (0, 1), and (1, 0).

Case 3: If (a - c) • (b - c) = 0, then

(-3, -x - 3) • (-1, -x - 1) = (-3)×(-1) + (-x - 3)×(-x - 1) = x ² + 4x + 6 = 0

but the solutions to x here are non-real, so we throw out this case.

So there are two possible values of x that make a right triangle, x = -6 and x = -2.

Answer:

198 more people attended the play on Sunday than on Friday

Step bye step explanation:

638 - 438 = 198.

(438 Friday night

(438 Friday night 636 Sunday night)

Answer:

x^2+6x+9= (x+3)^2

Step-by-step explanation:

x^ 2 +6x+__ =(_)^ 2

The formula is a^2+2ab+b^2= (a+b)^2

x^2= a^2

x=a

6x=2ab where a=x

6x=2x*b

b=3

b^2=9

x^2+6x+9= (x+3)^2

Answer:

A.23

maaf kalosalah !(!)!(!)!(!)!(!)!(!)!(!)!(!)!(!)!

Answer:

x < -4

Step-by-step explanation:

-3x > 12

-----   ----

-3      -3

12 ÷ -3 = -4

Which means:

x < -4

(The sign changes because the equation is divided by a negative number)

Hope this helped.

Answer:

x <-4

Step-by-step explanation:

-3x > 12

Divide each side by -3. remembering to flip the inequality

-3x/-3 > 12/-3

x <-4

Answer:

V≈113.1

Step-by-step explanation:

V=πr2h

3=π·32·12

3≈113.09734

Answer:

I think: vol of h20 inside = side³ = (80cm)³ =512000 cm³

Please refer!

Step-by-step explanation:

I'm not sure but hope it helps.

Answer:  445.5 (choice C)

Work Shown:

[tex]S_n = \frac{n}{2}(a_1+a_n)\\\\S_{11} = \frac{11}{2}(8+73)\\\\S_{11} = 5.5(81)\\\\S_{11} = 445.5\\\\[/tex]

Adding the first 11 terms of this arithmetic sequence yields the sum 445.5

Answer:

no,  

(

1

,

0

)

is not an ordered pair of the function  

f

(

x

)

=

1

+

x

.

Step-by-step explanation:

Ordered pairs are usually written in the form  

(

x

,

y

)

by tradition.

so usingthe function,

f

(

x

)

=

1

+

x

we can rewrite it as,

y

=

1

+

x

any pair of x and y that satisfy this equation are solutions to the equation.

so subbing in  

(

1

,

0

)

,

0

=

1

+

(

1

)

0

=

2

which is not true so the point does not make the function true.

It might be easier to see graphically,

graph{1+x [-10, 10, -5, 5]}

any combination of x and y on this line make the equation true and as such are an ordered pair of the function.

Answer:

Step-by-step explanation:

Answer:

10 bucks

Step-by-step explanation:

Money=9*(1+0.05)^3

Money=9*(1.05)^3=10.41≈10

The measures of the angles between the peaks are;

m∠BSC = 22.5°

m∠ASB = 67.5°

The reason for arriving at the above angles is as follows:

The known values are;

The location of the surveyor = Point S

The angle between peaks A and B = m∠ASB = 3 times as large as the angle between peaks B and C = 3 × m∠BSC

The measure of angle m∠ASC = A right angle = 90°

Required:

To find m∠ASB and m∠BSC

From the given diagram, we have;

m∠ASC = 90°

m∠ASC = m∠ASB + m∠BSC (angle addition postulate)

m∠ASB = 3 × m∠BSC

∴ m∠ASC = 3 × m∠BSC + m∠BSC = 4 × m∠BSC

m∠ASC = 4 × m∠BSC = 90°

m∠BSC = 90°/4 = 22.5°

m∠BSC = 22.5°

m∠ASB = 3 × m∠BSC

∴ m∠ASB = 3 × 22.5° = 67.5°

m∠ASB = 67.5°

Learn more about angle addition postulate here:

https://brainly.com/question/4208193

Answer:

1) 3c+2s=19

4c+5s=30

2) c=5 s=2

3)42minutes

Step-by-step explanation:

The potter need 3c minutes to make three cups and 2s to make two saucers, then he needs 3c+2s minutes to make both of them

3c+2s=19

He needs 4c+5s minutes to produce 4 cups and 5 saucers

4c+5s=30 (half of an hour is 30 minutes)

So the equations are

3c+2s=19

4c+5s=30

2) to solve you should express c from the first equation and use it in the second equation

3c=19-2s

c=19/3-(2/3)*s

4(19/3-(2/3)*s) +5s=30

76/3-(8/3)*s+5s=30

(7/3)*S= (14/3)

s=2

3c=19-4

3c=15

c=5

3) 6c+6s= 6(c+s)= 6(5+2)=6*7=42

The maximum no of fruits that could be put in each box is 48

For determining the maximum no of fruits, we have to find out the highest common factor i.e. HCf between two numbers i.e. 240 and 288

So,

For 240 = [tex]2 \times 2 \times 2 \times 2 \times 3 \times 5[/tex]

And, for 288, it is = [tex]2 \times 2 \times 2 \times 2 \times 2 \times3 \times 3[/tex]

So, the highest common factor between two numbers is

= [tex]2\times 2\times 2\times 2\times 3[/tex]

= 48

So we can conclude that the maximum no of fruits that could be put in each box is 48

Learn more about numbers here: brainly.com/question/17429689?

Answer:

the maximum number of fruits that can be put in each box=48

Given :

Total number of oranges = 240

Total number of apples = 288

we find maximum number of fruits by finding highest common factor HCF

Step-by-step explanation:

Lets find out HCF of 240 and 288

Write the prime factors for 240 and 288

[tex]288=2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3\\240=2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5[/tex]

Now write the common factor for both numbers

[tex]2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 =48[/tex]

So, GCF is 48

We have to  put 48 fruits in each box.

Learn more :

brainly.in/question/8084599

Answer:

44.8

Step-by-step explanation:

Using the Cosine formula, we first have Cos 48 = 30/x. So then we just solve for x and get 44.8342965, which rounds to 44.8

I hope this helped! :D

Answer:

70

Step-by-step explanation:

1+9+40-40+40+10*2

----------------------- 20

10+40-40+40+20

50 (-40+40 cancels out to 0) +20

50+20= 70

(Following PEMDAS)

Multiply, add, subtract.

if you were to instead go through it left to right, you would get 120, which is incorrect.

Answer: 2.08 km

Step-by-step explanation:

Side of Square = 520 m

Perimeter of Square = Side × 4

                                  = 520 × 4

                                  = 2080 m

1000 m = 1km

2080 m = 2080 ÷ 1000

              = 2.08 km

Answer:

The addition should be divided by 4 and not 3 since there are 4 meals.

Step-by-step explanation:

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

[tex]\\ \sf\longmapsto \sqrt{(-9-0)^2+(1-10)^2}[/tex]

[tex]\\ \sf\longmapsto \sqrt{(-9)^2+(-9)^2}[/tex]

[tex]\\ \sf\longmapsto \sqrt{81+81}[/tex]

[tex]\\ \sf\longmapsto \sqrt{162}[/tex]

[tex]\\ \sf\longmapsto 12.42[/tex]

Answer:

37.68

Step-by-step explanation:

Formula for finding the circumference of a circle is C = 2πr

If you substitute the numbers in you should get 37.68.

Answer:

Hello,

Step-by-step explanation:

[tex]LUB(E)=0.2=\dfrac{1}{5} \\\\GUB(E)=0.2 34 34 34 ....=0.2+\dfrac{1}{10} *0.343434....\\\\=\dfrac{1}{5} +\dfrac{1}{10} *\dfrac{34}{99} \\\\=\dfrac{198+34}{990} \\\\=\dfrac{116}{495}[/tex]

Answer:

NO

Step-by-step explanation:

6312/8= 789

here, 6312 is devisable by 8.

Therefore, there will not be any water left in the tank.

Complete the square in the denominator to get

tan²(t ) + 14 tan(t ) + 48 = tan²(t ) + 14 tan(t ) + 49 - 1

… = (tan(t ) + 7)² - 1

Substitute u = tan(t ) + 7 and du = sec²(t ) dt. Then the integral becomes

[tex]\displaystyle \int \frac{2\sec^2(t)}{\tan^2(t)+14\tan(t)+48} \,\mathrm dt = 2 \int \frac{\mathrm du}{u^2-1}[/tex]

Separate the integrand into partial fractions:

[tex]\dfrac1{u^2-1} = \dfrac12 \left(\dfrac1{u-1}-\dfrac1{u+1}\right)[/tex]

Then we get

[tex]\displaystyle \int \frac{2\sec^2(t)}{\tan^2(t)+14\tan(t)+48} \,\mathrm dt =  \int \left(\frac1{u-1}-\frac1{u+1}\right)\,\mathrm du \\\\ =\ln|u-1|-\ln|u+1| + C \\\\ = \ln\left|\frac{u-1}{u+1}\right|+C \\\\ = \boxed{\ln\left|\frac{\tan(t)+6}{\tan(t)+8}\right|+C}[/tex]

Answer:

the addition properties of zero and multiplication properties of zero

zero is even, not odd not neutral.

zero is neither positive or negative.

Answer: One side could be 18 and the other side will be 33.

Step-by-step explanation:

One way of setting up the inequality is: Side #2 + Side #3 > Side #1

[tex]2x-3+x>18\\3x-3>18\\3x>18+3\\3x>21\\x>7[/tex]

Another way of setting up the inequality is: Side #1 + Side #3 > Side #2

[tex]18+x>2x-3\\18+3>2x-x\\x<21[/tex]

Final way of setting up the inequality is: Side #1 + Side #2 > Side #3

[tex]18+2x-3>x\\15>x-2x\\15>-x\\x>-15[/tex]

Therefore, we have the range for our value of x, which is between 7 and 21. Any possible value between works. Negative measurements are rejected. One of the sides would equal the x-value, while the other side would equal the value of 2x-3.

Answer:

C. 3 3/4

Step-by-step explanation:

just is

id k how to explain

Answer:

C: 3-a

Step-by-step explanation:

The answer is C because an algebraic expression needs to have a variable in it. The variable is "a," so the answer has to be C.

Answer:

Option C : as in algebraic expression there must a variable and constant.