Which side in the figure on the right corresponds to the segment WU and what it the scale factor?
1 answer:
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1. It is given that f(x) is 16 times the square root of x.
Putting that in mathematical terms we have,
f(x) = 16 *
also, y = f(x)
So, we have the function
y= 16
4. We need to solve the inequality equation : 4x + 2y ≤ 6
Let us take the equation,
4x+2y ≤ 6
2y ≤ 6-4x
y ≤
y ≤ 3-2x
So, any point (x,y) lies on the given inequality region, where y≤ 3-2x
5. Solving system of equations using addition method
Given:
-5x-y =38 ------> a
-6x-3y =60 -------> b
Divide the equation b by no. 3
(-6x-3y)/3 = 60/3
-2x-y = 20 -------> c
Subtracting equation c from a we have,
-5x-y - (-2x-y) = 38 - 20
-5x-y+2x+y = 18
-3x = 18
x = -6
Now, substituting the value of x in equation a, we get
-5(-6) - y =38
30-y =38
y= 30-38 = -8
y=-8
∴ x = -6 and y = -8
6. Finding composition of functions
Given : f(x) =15x + 7 ; g(x) = x² - 5x
To find : (f+g)(x)
(f+g) (x) = f(g(x))
So, replace the value of x in f(x) by g(x), where g(x)= x² - 5x
(f+g)(x) = 15(x²-5x) +7 =15x²-75x+7
∴ (f + g)(x) = 15x²-75x+7
7. System of 3 equations must be solved to find the solution
-8x-8y-5z=-6
7x-8y-9z =17
9x+2y+6z =-1
Solving by substitution method.
Isolate x from first equation :
x= (-6+8y+5z)/(-8)
Substitute this value of x in 2nd and 3rd equations.
Now, isolating y from the 2nd equation rewritten above, we have
y= -
Now substituting this value of y in the 3rd equation rewritten above, we have
Isolating z from above equation, we have
z = -2
Substitute z= -2 in the equation of y, we have
y= - = 1
y = 1
Substituting the value of y and z, in the equation of x, we have
x= (-6+8(1)+5(-2))/(-8) = 1
x = 1
∴ x=1 ; y = 1 ; z = -2
8. 5x ≤ 7
Solving the above equation, we have
x ≤ 7/5
Please see attachment for the graph.
9. The given function is : g(y) = -6
The domain is the set of values of y for which there can be a value of g(y).
Here g(y) can be real only if y is greater than or equal to 0.
∴ The domain of the given function is [0,∞) .
10. Given : y is a function of x.
Definition of function : A function is a relation that associates each element in the domain to one element of another set, the co-domain of the function.
∴ For each element x, in the domain, there is only one value of y in the range.
Answer:
See explanation
Step-by-step explanation:
The given trigonometric equation is .
We take the inverse cosine of both sides to get:
to the nearest degree
None of the options satisfies the given equation.
But if the question is actually;
Then;
.
.
.
.
Or
.
In this case the answer will be B
Answer: y= - 4x+18
Step-by-step explanation:
Equation: y=mx+b
***remember: b is the y-intercept and m is the slope.
m=
3= x1
2= x2
6= y1
10=y2
m==
= -4
m=-4
Now we have y=-4x+b , so let's find b.
You can use either (x,y) such as (3,6) or (2,10) point you want..the answer will be the same:
(3,6). y=mx+b or 6=-4 × 3+b, or solving for b: b=6-(-4)(3). b=18.
(2,10). y=mx+b or 10=-4 × 2+b, or solving for b: b=10-(-4)(2). b=18.
Equation of the line: y=-4x+18
Answer:
The number of tickets they have sold in advance are summed up with the following equation and solution:
Equation: [the final answer should be in dollars]
Solution: The Opera sold 391 tickets in advance.
Step-by-step explanation:
First: Review some background information:
Let's see what the problem gives us to answer it. I'll bold out the important parts:
The Opera is collecting monies in advance for ticket sales. The tickets cost $17.50 each. If they have collected $6842.50 already, then how many tickets have they sold in advance?
We know how much the tickets cost and how much money they have earned from selling tickets, we can find out how much tickets they have sold.
Second: Solve the problem:
We can solve this problem using many ways, but I'm just going to pick one. We will use proportions to answer this. Now thoughts might be going through your head like this: What is this guy saying? What in the world is proportions? Well hopefully you learn from this example (Please don't take offense if you <em>do</em> know how to do proportions).
First we set up two fractions. One ticket costs $17.50, so we will use it to set up our first fraction: . We don't know how many tickets all together cost $6842.50 so we will use the variable: x. Now, we can set up our second fraction. x tickets costs $6842.50 so our second fraction will be:
. Now we must use cross multiplication. We multiply the numerator of the first fraction times the denominator of the second fraction, and then we multiply the denominator o the first fraction times the numerator of the second fraction. That's what we would do usually. But now, since we have a variable, we must use cross multiplication to solve for this variable. So we multiply the the numerator of the first fraction times the denominator of the other fraction and then we divide that answer times the denominator of the first fraction (You don't have to set it up like this).So let's solve this question:
1 x 17.50 = 17.50
6842.50 ÷ 17.50 = 391
So our equation is 6842.50 ÷ 17.50, and our solution is 391 tickets
Topic: Proportions