If the difference a number and four is tripled, the result is six less than the number. Find the number.

Mathematics

1 answer:

Lera25 [3.4K]3 years ago

3 0

3(x-4)=x-6
3x-12=x-6
3x-x = -6+12
2x=6
X= 3

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Find the values of x and y. The diagram is not to scale.

Aleksandr [31]

Step 1

Find the value of x

we know that

$(x-1)\°=74\°$ -------> by corresponding angles, because the given lines are parallel

Solve for x

$(x-1)\°=74\°\\x=74+1 \\ x=75\°$

Step 2

Find the value of y

we know that

$(x-1)+40+(y-2)=180$

substitute the value of x and solve for y

$(75-1)+40+(y-2)=180$

$74+40-2+y=180$

$112+y=180$

$y=180-112$

$y=68\°$

therefore

the answer is the option B

$x=75\°, y=68\°$

8 0

3 years ago

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Which is the graph of the solution set of −2x + 5y > 15? Image for option 1 Image for option 2 Image for option 3

Masteriza [31]

To make that graph you follow these steps.
1) Set the cartesian coordinate system:
- vertical axis: y
- horizontal axis: x
- positive x-semi axis: to the right
- negative x-semi axis: to the left
- positive y-semi axis: upward
- negative y semi axis: dwonward

2) solve the inequality for y:
given:                   -2x + 5y > 15
transpose-2x:            5y > 15 + 2x
divide by 5:                  y > 3 + (2/5)x

3) Graph

- draw the line y = 3 + (2/5)x, using a dotted line (i.e. - - - - - -)
- remember that 3 is the y intercept, and 2/5 is the slope
- the line is dotted because the solution does not include the points in the line.

- the solution is the region above and to the left of the dotted line.

4) See the figure attached for better visualization: the pink region is the solution of the inequality.