Answer:
x=12
Step-by-step explanation:
Because they are similar triangles you can set up proportions. 12/18=8/x Then you solve that and get 12.
Answer:
the width is 9 23/30 feet ≈ 9.767 ft
Step-by-step explanation:
Let w represent the width of the train car. Then 6 times the width is 6w, and 8 ft less than that is (6w-8). We are told this amount is 50.6 feet, so we have ...
6w -8 = 50.6
6w = 58.6 . . . . . . . add 8; next divide by 6
58.6/6 = w = 586/60 = 293/30 = 9 23/30 . . . . feet
This is a repeating decimal: 9.766666...
The width of the train car is 9 23/30 ft, about 9.77 ft.
The justifications are 1. Distributive Property 2. Combine like terms 3. Addition Property of Equality 4. Division Property of Equality (Option 3 and 4).
<h3>What is a linear equation?</h3>
- It is described as the relationship between two variables, and a straight line results from plotting the graph of the linear equation.
- The equation is referred to as a linear equation in one variable if just one variable is contained in the equation.
Now,
We are given the linear equation: 
- 4x + 5x -2 = 6 (Distributive property)
- 9x - 2 = 6 (combining the like terms)
- 9x = 8 (additive property of equality)
- x = 8/9 (division property of equality)
Hence, The third and fourth solutions are correct when using the division property of equality, i.e., The justifications are 1. Distributive Property 2. Combine like terms 3. Addition Property of Equality 4. Division Property of Equality (Option 3 and 4).
To learn more about linear equations, refer to the link: brainly.com/question/11897796
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Answer:
f(x)=-18x^2
Step-by-step explanation:
Given:
1+Integral(f(t)/t^6, t=a..x)=6x^-3
Let's get rid of integral by differentiating both sides.
Using fundamental of calculus and power rule(integration):
0+f(x)/x^6=-18x^-4
Additive Identity property applied:
f(x)/x^6=-18x^-4
Multiply both sides by x^6:
f(x)=-18x^-4×x^6
Power rule (exponents) applied"
f(x)=-18x^2
Check:
1+Integral(-18t^2/t^6, t=a..x)=6x^-3
1+Integral(-18t^-4, t=a..x)=6x^-3
1+(-18t^-3/-3, t=a..x)=6x^-3
1+(6t^-3, t=a..x)=6x^-3
That looks great since those powers are the same on both side after integration.
Plug in limits:
1+(6x^-3-6a^-3)=6x^-3
We need 1-6a^-3=0 so that the equation holds true for all x.
Subtract 1 on both sides:
-6a^-3=-1
Divide both sides by-6:
a^-3=1/6
Raise both sides to -1/3 power:
a=(1/6)^(-1/3)
Negative exponent just refers to reciprocal of our base:
a=6^(1/3)
