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natita [175]
3 years ago
14

Use the distributive property to create an equivalent expression to 42 + 6x

Mathematics
1 answer:
Brut [27]3 years ago
3 0
Hey there!
The distributive property is defined as:
a(b+c) = ab+ac.
Since a is being multiplied by b and c, it's a common factor. In this situation, our common factor is 6, as it goes into 6x and 42. So, we have:
6(7 + x)
Hope this helps!
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In ΔABC, the lengths of a, b, and c are 22.5 centimeters, 18 centimeters, and 13.6 centimeters, respectively.
Irina-Kira [14]
Given the values of the three sides of the triangle, we can apply the Cosine Law to find the angles of the triangle. Recall that for we can express the value of c through the equation below.

c^{2} = a^{2} + b^{2} - 2abcosC

Rearranging this equation, we can find the value ∠C as shown below.

\cos C = \frac{a^{2}+b^{2}-c^{2}}{2ab}
C = cos^{-1} (\frac{a^{2}+b^{2}-c^{2}}{2ab})

We can apply the same reasoning for finding the value of ∠B as shown.

B = cos^{-1} (\frac{a^{2}+c^{2}-b^{2}}{2ac})

Plugging in the values of the sides (see image attached) from the given. It will now be straightforward to compute for ∠B and ∠C.

C = cos^{-1} (\frac{22.5^{2}+18^{2}-13.6^{2}}{2(22.5)(18)})
C \approx 37.19

B = cos^{-1} (\frac{22.5^{2}+13.6^{2}-18^{2}}{2(22.5)(13.6)})
B \approx 53.13

Answer: ∠C = 37.19° and ∠B = 53.13°

7 0
3 years ago
Read 2 more answers
The value of a certain car decreases by 16% each year. What is the 1⁄2-life of the car?
svet-max [94.6K]

Answer:

The half life of the car is 3.98 years.

Step-by-step explanation:

The value of the car after t years is given by the following equation:

V(t) = V(0)(1-r)^{t}

In which V(0) is the initial value and r is the constant decay rate, as a decimal.

The value of a certain car decreases by 16% each year.

This means that r = 0.16

So

V(t) = V(0)(1-r)^{t}

V(t) = V(0)(1-0.16)^{t}

V(t) = V(0)(0.84)^{t}

What is the 1⁄2-life of the car?

This is t for which V(t) = 0.5V(0). So

V(t) = V(0)(0.84)^{t}

0.5V(0) = V(0)(0.84)^{t}

(0.84)^{t} = 0.5

\log{(0.84)^{t}} = \log{0.5}

t\log{0.84} = \log{0.5}

t = \frac{\log{0.5}}{\log{0.84}}

t = 3.98

The half life of the car is 3.98 years.

7 0
3 years ago
Let f(x) = x2- 3x - 7. Find f(-3)
Alexxx [7]
F(x) = x^2 - 3x - 7
f(-3) = (-3)^ 2 - 3(-3) - 7
f(-3) = 9 + 9 - 7
f(-3) = 18 - 7
f(-3) = 11
6 0
3 years ago
Find the simple interest on $2,219 principal, deposited for 6 years at a rate of 1.91%
Aleks04 [339]

Answer:

$13,568.30

Step-by-step explanation:

I = Prt

I = 2,219(1.0191)(6) = 13,568.30

6 0
3 years ago
Solve for x: −3|2x + 6| = −12
spayn [35]

Start with

-3|2x+6|=-12

Divide both sides by -3

|2x+6|=4

If the absolute value of a number is 4, that number can either be 4 or -4: we have the two solutions

2x+6=4 \iff 2x=-2 \iff x=-1

2x+6=-4 \iff 2x=-10 \iff x=-5

8 0
3 years ago
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