Solve the following pair of linear equations using substitution method


[tex] x-3y = 13[/tex]

[tex]x+2y=8[/tex]
​

Answer:

x = 3

Step-by-step explanation:

Step-by-step explanation:

3(8x-8)/2=64

3(8x-8)=64×2

24x-24=128

24x=128+24

24x=152

24x/24=152/24

x=6.3

Answer:

A'(2,2) B'(3,4) C'(1,4) O'(Q,2)

Answer:

The probability of a person getting their own hat is 1/5 or 20%.

Step-by-step explanation:

If each person has one hat the chances (the probability) of them getting their own hat would be 20%. The chances (the probability) of them getting a hat that belongs to one of the other four students would be 80%. Due to there being 5 hats each person owns 1 hat so there would be a 1 out of 5 chance of them getting their own hat.

Answer:

[tex] \rm Numbers = 4 \ and \ -3.[/tex]

Step-by-step explanation:

Given :-

The sum of two numbers is 1 .

The product of the nos . is 12 .

And we need to find out the numbers. So let us take ,

First number be x

Second number be 1-x .

According to first condition :-

[tex]\rm\implies 1st \ number * 2nd \ number= -12\\\\\rm\implies x(1-x)=-12\\\\\rm\implies x - x^2=-12\\\\\rm\implies x^2-x-12=0\\\\\rm\implies x^2-4x+3x-12=0\\\\\rm\implies x(x-4)+3(x-4)=0\\\\\rm\implies (x-4)(x+3)=0\\\\\rm\implies\boxed{\red{\rm x = 4 , -3 }}[/tex]

Hence the numbers are 4 and -3

Answer:

Step-by-step explanation:

If the product of 2 integers is -12, then that equation looks like this:

xy = -12

If the sum of those same 2 integers in 1, then that equation looks like this:

x + y = 1

Let's solve the second equation for x and plug it into the first equation. Solving the second equation for x gives us

x = 1 - y and plug that into the first equation in place of x to get:

(1 - y)y = -12 and

[tex]y-y^2=-12[/tex] Now move everything over to one side and factor to find y:

[tex]-y^2+y+12=0[/tex] and the 2 values for y are

y = -3 and y = 4. Let's see what happens when we solve for x.

If xy = -12 and y is -3:

x(-3) = -12 so

x = 4

If xy = -12 and y is4:

x(4) = -12 so

x = -3

So it looks like the 2 integers are -3 and 4

Answer:

3

Step-by-step explanation:

We are going to be using cofunction identity cos(90-x)=sin(x).

Apply to either side but not both.

cos(22f − 1) = sin(7f + 4)

sin(90-[22f-1])=sin(7f+4)

90-[22f-1]=7f+4

Distribute

90-22f+1=7f+4

Combine like terms

91-22f=7f+4

Add 22f on both sides

91=29f+4

Subtract 4 on both sides

87=29f

Divide 29 on both sides

3=f

f=3 is between 0 and 90

Answer:

The answer is "3."

Step-by-step explanation:

Just submitted the test and got the answer correct!

Answer:

x < 0.5

Step-by-step explanation:

Given

2(1 - x) > 2x ( divide both sides by 2 )

1 - x > x ( add x to both sides )

1 > 2x ( divide both sides by 2 )

[tex]\frac{1}{2}[/tex] > x , that is

x < [tex]\frac{1}{2}[/tex] OR x < 0.5

Answer:

In picture

Step-by-step explanation:

Brainliest please~

[tex](0,3)[/tex] and [tex](1,-2)[/tex]

Equation: (refer the image below)

Slope:

[tex]m=\frac{3+2}{0-1}[/tex]

[tex]m=-5[/tex]

Equation:

[tex]y=5x-b[/tex]

[tex]3=b[/tex]

Substitute (0,3)

Point: [tex](1,-2)[/tex]

Answer:

0.09

Step-by-step explanation:

avg rate of change is:  change in y/ change in x

so it´d be   3.59 - 0.89 / 2014 - 1984

= 2.7/ 30

= 0.09

note:

The slope formula and the average rate of change formula are the same, just written a bit different, so you could also use:

y2 - y1 / x2 - x1

Answer:

2x+5x^2=1

2x+5x*5x=1

2x+25x=1

27x=1

1/27=x

Hope This Helps!!!

Answer:

D. 24

Hope it helps!

Answer:

2

Step-by-step explanation:

11.

[tex]6x = 30 \\ x = \frac{30}{6} \\ x = 5[/tex]

Missing angle:

[tex]6x \\ = 6 \times 5 \\ = 30[/tex]

_________________________________________

12.

[tex](4 + 5x) + (x + 2) = 180 \\ 6x + 6 = 180 \\ 6x = 180 - 6 \\ 6x = 174 \\ x = \frac{174}{6} \\ x = 29[/tex]

Missing angle 1:

[tex](4 + 5x) \\ = 4 + (5 \times 29) \\ = 4 + 145 \\ = 149[/tex]

Missing angle 2:

[tex]x + 2 \\ = 29 + 2 \\ = 31[/tex]

_________________________________________

13.

[tex]5x + (3x + 12) = 180 \\ 8x + 12 = 180 \\ 8x = 180 - 12 \\ 8x = 168 \\ x = \frac{168}{8} \\ x = 21[/tex]

Missing angle 1:

[tex]5x \\ = 5 \times 21 \\ = 105[/tex]

Missing angle 2:

[tex](3x + 12) \\ = (3 \times 21) + 12 \\ = 63 + 12 \\ = 75[/tex]

_________________________________________

14.

[tex]32 + (6x + 4) = 90 \\ 36 + 6x = 90 \\ 6x = 90 - 36 \\ 6x = 54 \\ x = \frac{54}{6} \\ x = 9[/tex]

Missing angle:

[tex](6x + 4) \\ = (6 \times 9) + 4 \\ = 54 + 4 \\ = 58[/tex]

_________________________________________

15.

[tex](2x + 1) + (x + 2) = 90 \\ 3x + 3 = 90 \\ 3x = 90 - 3 \\ 3x = 87 \\ x = \frac{87}{3} \\ x = 29[/tex]

Missing angle 1:

[tex](2x + 1 ) \\ = ( 2 \times 29) + 1 \\ = 58 + 1 \\ = 59[/tex]

Missing angle 2:

[tex]x + 2 \\ = 29 + 2 \\ = 31[/tex]

_________________________________________

16.

[tex](3x + 1) + (4 + 2x) = 90 \\ 5x + 5 = 90 \\ 5x = 90 - 5 \\ 5x = 85 \\ x = \frac{85}{5} \\ x = 17[/tex]

Missing angle 1:

[tex](3x + 1) \\ = (3 \times 17) + 1 \\ = 51 + 1 \\ = 52[/tex]

Missing angle 2:

[tex](4 + 2x) \\ = 4 + (2 \times 17) \\ = 4 + 34 \\ = 38[/tex]

Answer:

b . is the answer

Step-by-step explanation:

ha ahhgahga

Answer:

Probably 10

Step-by-step explanation:

10/5=2

Answer:

15 x 150 = 2250

2250 + 1000 = 3250

you make $3250,00

Answer:

Table 4 is the answer. Step-by-step explanation: Bethany is making trail mix with 3 cups of raisins for every 2 cups of peanuts. So, the ratio of peanuts to raisins is 2 : 3.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

GOT IT RIGHT edge 2021

Answer:

The equation of the line is, y = x

Step-by-step explanation:

The constraints of the required linear equation are;

The point through which the line passes = (2, 2)

The line to which the required line is parallel = y = x + 4

Two lines are parallel if they have the same slope, therefore, we have;

The slope of the line, y = x + 4 is m = 1

Therefore, the slope of the required line = 1

The equation of the required lime in point and slope form becomes;

y - 2 = 1 × (x - 2)

∴ y = x - 2 + 2 = x

The equation of the required line is therefore, y = x

Answer:

[tex]\implies \dfrac{ -4x+7}{2(x-2) }[/tex]

Step-by-step explanation:

The given expression to us is ,

[tex]\implies \dfrac{\frac{ 3}{x-1} -4 }{ 2 -\frac{2}{x-1}}[/tex]

Now take the LCM as ( x - 1 ) and Simplify , we have ,

[tex]\implies \dfrac{\frac{ 3 -4(x-1) }{x-1} }{ \frac{2-2(2x-1)}{x-1}}[/tex]

Simplifying further , we get ,

[tex]\implies \dfrac{ -4x+7}{2(x-2) }[/tex]

Hence the second option is correct.

Answer:

[tex] \frac{ \frac{3}{x - 1} - 4}{2 - \frac{2}{x - 1} } \\ = \frac{ \frac{3 - 4(x - 1)}{x - 1} }{ \frac{2(x - 1)}{x - 1} } \\ = \frac{3 - 4x + 4}{2x - 2} \\ \frac{ - 4x + 7}{2(x - 1)} \\ option \: b \: is \: your \: answer \\ thank \: you[/tex]

Answer:

plotting x = 2

see the x- axis look for the point x = 2(on right side of the origin ). Mark that point and draw a straight line parallel to the y- axis.

This is the graph of x = 2

plotting y = -4

see the y- axis and then look for the point y= -4 (that must be 4 units below the origin). Mark that point and draw a straight line parallel to the x- axis.

This is the graph of y = -4

we see that, the graph x = 2 is parallel to the y-axis whereas the graph y = -4 is parallel to the x- axis.

Answer:

1.12 Units

Step-by-step explanation:

1. Use cos(56°) = x/2

Make sure your calculator mode is in deg (degree) not rad(radians)

2.  2(cos(56°)) = x

3. x = 1.118385807

4. Round up to get 1.12 Units

[tex]\sf \bf {\boxed {\mathbb {GIVEN:}}}[/tex]

Sum of three consecutive odd integers = [tex]27[/tex]

[tex]\sf \bf {\boxed {\mathbb {TO\:FIND:}}}[/tex]

The values of the three integers.

[tex]\sf \bf {\boxed {\mathbb {SOLUTION:}}}[/tex]

[tex]\sf\purple{The\:three\:consecutive \:odd\:integers\:are\:7,\:9\:and\:11.}[/tex]

[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}[/tex]

Let us assume the three consecutive odd integers to be [tex]x[/tex], [tex](x+2)[/tex] and [tex](x+4)[/tex].

As per the condition, we have

[tex]Sum \: \: of \: \: the \: \: three \: \: consecutive \: \: odd \: \: integers = 27[/tex]

[tex]➺ \: x + (x + 2) + (x + 4) = 27[/tex]

[tex]➺ \: x + x + 2 + x + 4 = 27[/tex]

Now, collect the like terms.

[tex]➺ \: (x + x + x) + (2 + 4) = 27[/tex]

[tex]➺ \: 3x + 6 = 27[/tex]

[tex]➺ \: 3x = 27 - 6[/tex]

[tex]➺ \: 3x = 21[/tex]

[tex]➺ \: x = \frac{21}{3} \\[/tex]

[tex]➺ \: x = 7[/tex]

Therefore, the three consecutive odd integers whose sum is [tex]27[/tex] are [tex]\boxed{ 7 }[/tex], [tex]\boxed{ 9 }[/tex] and [tex]\boxed{ 11 }[/tex] respectively.

[tex]\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}[/tex]

[tex]⇢ 7 + 9 + 11 = 27[/tex]

[tex]⇢ 27 = 27[/tex]

⇢ L. H. S. = R. H. S.

[tex]\sf\blue{Hence\:verified.}[/tex]

[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35ヅ}}}}}[/tex]

Answer:

5 years

Step-by-step explanation:

(x+15)=4x

15=4x-x

15=3x

5=x

Answer:

38

Step-by-step explanation:

6⅓÷⅙

change 6⅓ to improper fraction

19/3÷1/6

keep the first fraction, change the division sign to multiplication and reciprocate/flip the second fraction

19/3× 6/1

the denominator 3 and numerator 6 will simplify/cancel each other

the new fraction is now: 19/1 × 2/1

there is no need to multiply the denominators because it will still be equal to 1 so we just need to multiply the numerators by each other

19×2=38 OR 38/1 (both answers are the same)

Answer:

The circumference of Earth's equator is 40,080 km.

Step-by-step explanation:

Given that every 24 hours, Earth makes a full rotation around its axis, and Earth's speed of rotation at the equator is 1,670 km per hour, to determine what is the circumference of Earth's equator the following calculation must be performed:

24 x 1,670 = X

40,080 = X

Therefore, the circumference of Earth's equator is 40,080 km.

Step-by-step explanation:

The question is not clear to me

Answer:

Traversable because it has exactly two odd nodes

Step-by-step explanation:

There is a rule that says it is traversable if it has exactly 2 odd nodes. The are other rule where it can be traversable is if has no odd nodes.

Also if we let the starting point be D and the ending point be B we can travel the network in such way that each edge is only traveled once which is the definition that the network is traversable.

So I will do this by starting at D, then travel to A using the outside edge, then travel to back to D using inside edge, then travel to C, then travel to B, then travel to A using outside edge, and then back to B from A using inside edge.

Within similar triangles, the angles are the same. So, we need to look at the side lengths then.

72 to 12

66 to 11

42 to 7

In each pair of corresponding side lengths, the original side length from triangle ABC is divided by 6 (or multiplied by 1/6) to get the smaller side length on triangle DEF.

The scale factor from ABC to DEF is 1/6.

Hope this helps!

Answer:

the angle <ABC is equal to 65°

Answer:

15, The answer is greater than 14 because when you multiply the 2 fractions you get a number that is greater than 15

Step 1: Set up equation

[tex]\frac{25}{1}*\frac{3}{5}[/tex]

Step 2: Cross reduce

you can cross reduce 25 and 5 because they are both share a common divisor

[tex]\frac{5}{1} *\frac{3}{1}[/tex]

Step 3: Multiply numerator and denominator together

[tex]\frac{15}{1}[/tex]

Final Answer:

15

The answer is greater than 14 because when you multiply the 2 fractions you get a number that is greater than 15

Answer:

Step-by-step explanation: