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DiKsa [7]
3 years ago
14

Use substitutions to solve each system of equations.[y = 4x -6] [5x + 3y = 1]

Mathematics
1 answer:
boyakko [2]3 years ago
4 0

y=4x-6.....(1)

5x+3y=1....(2)

substitute y=4x-6 into equation 2

5x+3(4x-6)=1

5x+12x-18=1

17x=19

x=1.12

substitute x=1.12 into equation 1

y=4(1.12)-6

y=4.48-6

y=-1.52

x=1.12,y=1.52

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The function f is continuous on the closed interval [1,15] and has the values shown on the table above. Let g(x) = ∫f(t) dt [1,x
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We're looking for the two values being subtracted here. One of these values is easy to find:

<span>g(1) = ∫f(t)dt = 0</span><span>
since taking the integral over an interval of length 0 is 0.
 
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3 years ago
Read 2 more answers
Pls help me .question no 14
Alex_Xolod [135]

Question 14, Part (i)

Focus on quadrilateral ABCD. The interior angles add to 360 (this is true for any quadrilateral), so,

A+B+C+D = 360

A+90+C+90 = 360

A+C+180 = 360

A+C = 360-180

A+C = 180

Since angles A and C add to 180, this shows they are supplementary. This is the same as saying angles 2 and 3 are supplementary.

==================================================

Question 14, Part (ii)

Let

x = measure of angle 1

y = measure of angle 2

z = measure of angle 3

Back in part (i) above, we showed that y + z = 180

Note that angles 1 and 2 are adjacent to form a straight line, so we can say

x+y = 180

-------

We have the two equations x+y = 180 and y+z = 180 to form this system of equations

\begin{cases}x+y = 180\\y+z = 180\end{cases}

Which is really the same as this system

\begin{cases}x+y+0 = 180\\0+y+z = 180\end{cases}

The 0s help align the y terms up. Subtracting straight down leads to the equation x-z = 0 and we can solve to get x = z. Therefore showing that angle 1 and angle 3 are congruent. We could also use the substitution rule to end up with x = z as well.

4 0
3 years ago
what is the equation of the line that passes through the point (3,5) and is it parallel to the line y= - 2x+3
Alekssandra [29.7K]
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A box contains 8 two-inch screws. Four have a Phillips head and 4 have a slotted head. In how many ways can 4 screws be chosen s
hammer [34]

Answer:

There are 6\cdot 6=36 different ways to choose 4 screws such that 2 have a Phillips head and 2 have a slotted head.

Step-by-step explanation:

If 4 screws must be chosen so that 2 have a Phillips head and 2 have a slotted head, then you have to choose 2 screws with a Phillips head from 4 screws with a Phillips head and 2 screws with a slotted head from 4 screws with a slotted head.

You can choose 2 screws with a Phillips head from 4 screws with a Phillips head in

C^4_2=\dfrac{4!}{2!(4-2)!}=\dfrac{4!}{2!\cdot2!}=\dfrac{1\cdot2\cdot3\cdot4}{1\cdot2\cdot1\cdot2}=6

different ways.

You can choose 2 screws with a slotted head from 4 screws with a slotted head in

C^4_2=\dfrac{4!}{2!(4-2)!}=\dfrac{4!}{2!\cdot2!}=\dfrac{1\cdot2\cdot3\cdot4}{1\cdot2\cdot1\cdot2}=6

different ways.

In total there are 6\cdot 6=36 different ways to choose 4 screws such that 2 have a Phillips head and 2 have a slotted head.

7 0
3 years ago
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