Answer:
i. 
+ 26x + 144 - 299 = 0
ii. x = 5
Step-by-step explanation:
The area of the figure = 299 cm²
The figure has a shape of a rectangle, so that;
Area of rectangle = length x width
length of the figure = 18 + x
width of the figure = 8 + x
Area of the figure = (18 + x) x (8 + x)
299 = (18 + x) x (8 + x)
299 = + 26x + 144
+ 26x + 144 - 299 = 0
+ 26x - 155 = 0
applying the trigonometric formula;
x = (-b ± 
) ÷ 2a
= (-26 ± 
) ÷ 2
= (-26 ± 
) ÷ 2
= (-26 ± 
) ÷ 2
= (-26 ± 36) ÷ 2
x = (-26 + 36) ÷ 2 OR x = (-26 -36) ÷ 2
= 10 ÷ 2 OR -62 ÷ 2
= 5 OR -31
Thus, x = 5
Step-by-step explanation:
since x=2 and z=-2
4+4=8 [ because -2* -2=+4 ]
Answer:
To find c you know that angles on a straight line equal 180° (supplementary angles). So 70+30+∠C=180.
Now we can solve this.
100+c=180.
Move the 100 over to the other side.
100-100+c=180-100
Simplify.
∠C=80°
Because we know that the two lines with double arrows are parallel, we can use the rule that alternate interior angles are congruent. This means that ∠E=70.
∠E=70°
Since the total sum of the angles in a triangle are equal to 180°, we know that ∠D+∠C+∠E=180. Because we already know ∠C and ∠E we can put those numbers in for them. 80°+70°+∠D=180°. Now we can solve this.
80+70+D=180
Simplify this.
150+D=180
Now we move the 150 over to the other side to get D by itself.
150-150+D=180-150
Simplify.
D=30
∠D=30°
Now we can find the vertical angle opposite ∠A by using the alternate interior angles rule again this time using the parallel lines with only one arrow on them. The vertical angle opposite ∠A=30°. Since vertical angles are congruent ∠A=30°.
∠A=30°
We are going to use the alternate angles rule one more time to solve for ∠B (this rule is very important when dealing with parallel lines), we could also use the corresponding angles rule but for simplicity we will just stick with the alternate angles rule. Because the vertical angle opposite ∠A is equal to 30°, we can see that the supplementary angle opposite ∠B=30°. Because this angle is supplementary with B we know that 30+B=180.Now we can solve this.
30+B=180
Now we move the 30 over to the other side.
30-30+B=180-30
Simplify.
B=150
∠B=150°
I hope this helps!
Solving <span>8x-5y=10 for y helps us to identify the y-intercept:
-5y = -8x + 10. Dividing both sides by -5, we get (8/5)x -2. Therefore, y = (8/5)x - 2; the y-intercept is (0,-2).
The equation </span><span>-6x-7y=-6 can be solved for its slope in the same manner.
7y = -6x + 6; then y = (-6/7)x + 6/7. Its slope is -7/6. A line perpendicular to this line has slope equal to the negative reciprocal of -7/6, which is 6/7.
So, using the slope-intercept form, y = mx + b becomes y = (6/7)x -2.</span>
First solve for the other angles.
You know one angle is 15º.
The one across from it is also 15º since it is a vertical angle to the known 15º angle.
Both of those together gets 30º.
The whole thing is 360º, so just subtract 30 from 360 and divide.
360 - 30 = 330
Do the same for the 15x angle.
The one under/across to it is a vertical angle so is also 15xº.
Now you are left with 30xº = 330.
Just divide now.
330 / 30 = 11
x = 11
15x = 165
Checking your work:
15x = 165
15x = 165
15
15
Those are the angles.
Add those numbers together and make sure it adds up to 360º.
165 + 165 + 15 + 15 = 360
So this is correct.
