Another way to write this is:
x = 23y + 5
xy = 6732
Now plug in the first equation into the second:
(23y + 5)y = 6732
23y^2 + 5y - 6732 = 0
Either use quadratic equation or factor:
(y - 17)(23y + 396) = 0
y = 17 or -396/23
You know you can automatically eliminate the second y because it's negative and you need the two integers to multiply to a positive number (6732).
Plug y = 17 back into either equation (second might be easier):
17x = 6732
x = 396
<h3>step 1.</h3>
use graph paper.
<h3>step 2.</h3>
draw lines thru the graph wait go on my image above!
Answer:
D. A triangle with angles measuring 75°, 60°, and 45°
Step-by-step explanation:
Given various triangle descriptions, you want to know which one describes more than one triangle.
<h3>Triangle relations</h3>
The angles and sides of a triangle satisfy a few different relations:
- angle sum — the sum of angles is 180°
- triangle inequality — the sum of the two short sides exceeds the long side
- law of cosines — c² = a² +b² -2ab·cos(C)
- law of sines — a/sin(A) = b/sin(B) = c/sin(C)
<h3>Application</h3>
A. Two sides and the included angle can be used with the Law of Cosines to find the length of the third side. That is, a single triangle is created by these measurements.
B. Sides measuring 4, 8, and 15 do not satisfy the triangle inequality, so no triangle is created by these measurements.
C. Sides measuring 6, 8, and 10 satisfy the triangle inequality, so will create a single triangle. (That triangle is a right triangle.)
D. The given angles total 180°, so could be the angle measures of any number of triangles. At least one side length must be specified in order to completely define a single triangle. These measures create more than one triangle.
Explanation:
As we know that set is the collection of elements and set builder is the method of defining the set with the help of specific property in which we can use arithmetic operations as well
Generally,
It is the general form of any set in which we can construct the complete set with the help of equation in the given in set builder form.
Since we have the elements : 45,55,65,75
So, the set builder form will be { x: x =5(2n+1) ,4≤n≤7,x,n∈ N }
We will read it as it is the value of x which will be find with the help of given equation i.e. x=5(2n+1) where n goes from 4 to 7 only and x and n are natural numbers only.
Answer:
920*1.12^t
Step-by-step explanation:
Every year, we see that it goes up 12%.
12% in decimal form is 0.12.
Let's say we have "x" amount of cars one year. The next year, the number of cars will increase by 12%. 0.12x is added on after one year.
So in total, at the beginning of a new year, the number of cars is 0.12x+x = 1.12x.
In this case, we have 920 cars. So if every year the number of cars is multiplied by 1.12, then in "t" years we will have 920*(1.12)^t. We multiply by 920 because that's the current number of cars, and we add the ^t because we multiply by 1.12 every year.
You are very welcome!
:P
