Answer:
f(g(x)) = 15x + 2
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Distributive Property
<u>Algebra I</u>
- Functions
- Function Notation
- Composite Functions
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
f(x) = 5x + 7
g(x) = 3x - 1
<u>Step 2: Find</u>
- Substitute in functions: f(g(x)) = 5(3x - 1) + 7
- [Distributive Property] Distribute 5: f(g(x)) = 15x - 5 + 7
- [Addition] Combine like terms: f(g(x)) = 15x + 2
<span>A
cross section is formed by the <em>intersection</em> of a<em> three-dimensional object</em> and a <em>plane.</em>
So the right answers are 4 and 5. Let's explain each case.
First. A prism and a horizontal planeThe representation of this statement is shown in Figure 1. A prism has the following characteristics:
1. These objects have identical ends.
2. They have flat faces.
3. They have </span><span>the same </span>cross section<span> all along its length </span><span>
So in the figure, you can see how the horizontal plane intersects the prism. <em>The cross section</em> of this object <em>is a</em> <em>triangle</em>. Thus, </span><span>it has the same cross section all along its length and this object is called <em>a triangular prism.</em></span><span>
Second. A vertical plane and a pyramid
As shown in Figure 2 you can see the representation of this statement. </span><span>If the pyramid is cut with a plane that passes through the top vertex and it is perpendicular to the base, then the intersection of this pyramid and the plane becomes a <em>triangular cross section</em>.</span>
Step 1
Let the first consecutive integer be n
Then the second will be n+1
The third will be n+2
Step 2
Write an inequality for the problem
![n+n+1+n+2\leq15](https://tex.z-dn.net/?f=n%2Bn%2B1%2Bn%2B2%5Cleq15)
Step 3
Solve the inequality
![\begin{gathered} 3n+3\leq15 \\ 3n\leq15-3 \\ 3n\leq12 \\ \frac{3n}{3}\leq\frac{12}{3} \\ n\leq4 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%203n%2B3%5Cleq15%20%5C%5C%203n%5Cleq15-3%20%5C%5C%203n%5Cleq12%20%5C%5C%20%5Cfrac%7B3n%7D%7B3%7D%5Cleq%5Cfrac%7B12%7D%7B3%7D%20%5C%5C%20n%5Cleq4%20%5Cend%7Bgathered%7D)
Step 4
Find the possible set of three integers to satisfy the inequality.
![\begin{gathered} n=4---\text{ first integer} \\ n+1=4+1=5---\text{ second integer} \\ n+2=4+2=6---\text{ Third integer} \\ \text{check} \\ 4+5+6\leq15 \\ \text{Hence the set of thr}ee\text{ integers are; }\mleft\lbrace4,5,6\mright\rbrace \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20n%3D4---%5Ctext%7B%20first%20integer%7D%20%5C%5C%20n%2B1%3D4%2B1%3D5---%5Ctext%7B%20second%20integer%7D%20%5C%5C%20n%2B2%3D4%2B2%3D6---%5Ctext%7B%20Third%20integer%7D%20%5C%5C%20%5Ctext%7Bcheck%7D%20%5C%5C%204%2B5%2B6%5Cleq15%20%5C%5C%20%5Ctext%7BHence%20the%20set%20of%20thr%7Dee%5Ctext%7B%20integers%20are%3B%20%7D%5Cmleft%5Clbrace4%2C5%2C6%5Cmright%5Crbrace%20%5Cend%7Bgathered%7D)
One possible set of three integers that satisfy the inequality is;
{4,5,6}
Answer:
![(x-4)^2+(y+7)^2=43](https://tex.z-dn.net/?f=%28x-4%29%5E2%2B%28y%2B7%29%5E2%3D43)
Step-by-step explanation:
The standard equation of a circle is given by:
![(x-h)^2+(y-k)^2=r^2](https://tex.z-dn.net/?f=%28x-h%29%5E2%2B%28y-k%29%5E2%3Dr%5E2)
Where (<em>h, k</em>) is the center and <em>r</em> is the radius.
We are given that the center is (4, -7) and that the radius is √(43).
So, <em>h</em> = 4, <em>k</em> = -7, and <em>r</em> = √(43). Substitute:
![(x-(4))^2+(y-(-7))^2=(\sqrt{43})^2](https://tex.z-dn.net/?f=%28x-%284%29%29%5E2%2B%28y-%28-7%29%29%5E2%3D%28%5Csqrt%7B43%7D%29%5E2)
Simplify. Hence, our equation is:
![(x-4)^2+(y+7)^2=43](https://tex.z-dn.net/?f=%28x-4%29%5E2%2B%28y%2B7%29%5E2%3D43)
Answer:
ok so c is 5 + 1. that is 6. and d is 3 x 5 which is 15 + 6, so 21. I dont know about a or b though, sorry.
Step-by-step explanation: