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Sloan [31]
3 years ago
8

Determine the answer to 3 + (-5) and explain the steps using a number line

Mathematics
1 answer:
Andreas93 [3]3 years ago
4 0

Answer:

-2

Step-by-step explanation:

3 - 5 = -2

Place the dot on -2 on the number line that is on your problem as the answer. To show the steps on the number line, use your jumps to go back. For example, your starting point will be on 3, and then use your jumps to go back by 5; that means you go into the negatives. For this case, it is -2.

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The total area of the figure to the right is 299 cm². Use this fact to write an equation involving x. Then solve the
Sliva [168]

Answer:

i. x^{2} + 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 = x^{2} + 26x + 144

x^{2} + 26x + 144 - 299 = 0

x^{2} + 26x - 155 = 0

applying the trigonometric formula;

x = (-b ± \sqrt{b^{2} - 4ac}) ÷ 2a

= (-26 ± \sqrt{(26)^{2} - 4(1*-155)}) ÷ 2

= (-26 ± \sqrt{676 +620}) ÷ 2

= (-26 ± \sqrt{1296}) ÷ 2

= (-26 ± 36) ÷ 2

x = (-26 + 36) ÷ 2  OR x = (-26 -36) ÷ 2

  = 10 ÷ 2 OR -62 ÷ 2

  = 5 OR -31

Thus, x = 5

5 0
3 years ago
X^2 + z^2<br><br>when, x= 2 and z= - 2​
victus00 [196]

Step-by-step explanation:

since x=2 and z=-2

4+4=8 [ because -2* -2=+4 ]

5 0
3 years ago
I need the angle measurements for each letter in this image
Blizzard [7]

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!

7 0
3 years ago
Read 2 more answers
Equation for the line perpendicular to the line -6x-7y=-6 having the same y-intercept as 8x-5y=10
PilotLPTM [1.2K]
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>
4 0
3 years ago
What is the value of x in the figure above? ^^
Zielflug [23.3K]
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.
7 0
3 years ago
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