Answer:
x = 18
Step-by-step explanation:
y = x + 8
2x + y = -10
Add 10 to 8, then subtract x from 2x leaving you with one x, and finally subtract y from y leaving you with X = 18
Answer: (A) The longer side in the rectangle is 45 units.
(B) The line LP measures 14 cm.
Step-by-step explanation: In the rectangle, two sides are given as 2x and 3x + 3, respectively. The perimeter is also given as 146 units. The formula to determine the perimeter is
Perimeter = 2(L + W)
We can now substitute for the values
146 = 2(2x + 3x + 3)
146 = 2(5x + 3)
146 = 10x + 6
Subtract 6 from both sides of the equation
140 = 10x
Divide both sides of the equation by 10
14 = x
With the value of x now known as 14, the sides of the rectangle are,
L = 2x
L = 2 x 14
L = 28
And the other side is
W = 3x + 3
W = 3(14) + 3
W = 42 + 3
W = 45
Therefore the longer side is 45 units.
In question B;
The rhombus has all sides congruent as one of its properties. This simply implies that the diagonal from point M to point O, is the same length as the diagonal from point L to point N. Hence, at point P, where both diagonals intersect, both diagonals are divided into two equal lengths each. If line LN is 28 cm, then line LP which is half of LN shall be 28 divided by 2, and that gives us 14 cm.
Answer:
See screenshot
Step-by-step explanation:
For this problem, to draw this polygon scaled down by a factor of a half, we simply will take the length of each side of the polygon and divide by 2.
Original side lengths:
6 - 4 - 2 - 4 - 4 - 8
Scaled side lengths:
3 - 2 - 1 - 2 - 2 - 4
Hence, you will get the new shape, shown in blue in the screenshot as your half scaled polygon.
Cheers
Answer:
(b) –4g^4 – 3g^3 + 4g^2 + 5g + 3
Step-by-step explanation:
The simplification process is described and partially carried out. We are to finish by combining like terms and writing the result in standard form.
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<h3>Combine Like Terms</h3>
g^2 + (–4g^4) + 5g + 9 + (–3g^3) + 3g^2 + (–6) . . . . given
The like terms are the g^2 terms and the constants.
= (1 +3)g^2 + (–4g^4) +5g +(9 +(–6)) +(–3g^3)
= 4g^2 +(–4g^4) +5g +3 +(–3g^3)
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<h3>Write in Standard Form</h3>
In this form, the terms are written in order of decreasing degree.
= –4g^4 –3g^3 +4g^2 +5g +3