9 - 6 + 4 × 13
First, simplify 4 × 13 to get 52. / Your problem should look like: 9 - 6 + 52
Second, simplify. Subtract 9 - 6 then add 52 onto that. / Your problem should look like: 55
Answer: 55
The 2 on the right are single reflections. The top on the left is a rotation, and the bottom left is a translation.
Answer:
$2159.07
Step-by-step explanation:
The compound interest formula is used to find the balance for the $1000 investment:
A = P(1 +r/n)^(nt)
A = 1000(1 +.012/12)^(12·10) = 1000·1.001^120 ≈ 1127.43
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For a 2% loss, the multiplier of the investment value is 1-.02 = 0.98. The value of the first $500 investment is ...
A = 500(1 -.02) = 490.00
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The continuous compounding formula is used for the second $500 investment.
A = Pe^(rt)
A = 500e^(.008·10) = 500e^.08 = 541.64
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The total value of Albert's investments is ...
$1127.43 +490 +541.64 = $2159.07
Answer:
y=-2x+14
Step-by-step explanation:
If we are looking for a line parallel to 2x+y=5.
Then we are looking for an equation with the same slope as the equation 2x+y=5.
To obtain the slope of equaiton 2x+y=5 I will put it in slope-intercept form.
Luckily there is only one step which is to subtract 2x on both sides.
y=-2x+5
The slope of this line is -2
The slope of parallel line will also be -2.
So we know our equation is in the form y=-2x+b
To find b we will just use the point (x,y)=(5,4) we know is on the line.
Plug in and solve for b.
4=-2(5)+b
4=-10+b
14=b
So the equation that is parallel to 2x+y=5 and goes through (5,4) is y=-2x+14
Answer:
A is 55°
Step-by-step explanation:
To solve this, you need to remember that the sum of the angles inside a triangle is equal to 180 degrees.
Also, noting that this is an isosceles triangle. That means that a and b are equal. With that in mind, we can simply say:
a + b + c = 180
a ≡ b ∴ 2b + c = 180
2(4x + 31)° + (2x + 58)° = 180°
8x° + 62° + 2x° + 58° = 180°
Let's just stop right here, and note that normally you can treat symbols of measurements just like variables. We've done the same here, applying the distributive property with the ° symbol. Note though that it's currently part of every single term, so I'm going to factor it out:
(8x° + 62° + 2x° + 58°) / 1° = 180° / 1°
8x + 62 + 2x + 58 = 180
10x + 120 = 180
10x = 60
x = 6
Again noting that A and B are identical due to this being an Isosceles triangle, we can say:
A = (4x + 31)°
A = 24° + 31°
A = 55°
We can also check our answer. The sum of the angles should be 180, and two of those angles should be 55. That means that angle C should be 180 - 2 * 55, or 180 - 110 = 70. Let's test it:
70 = 2x + 58
70 = 12 + 58
70 = 70
So we know that our answer is correct.
