The easiest variable you can solve for first is "z". Knowing that opposite angles of a quadrilateral inscribed in a circle are supplementary, subtract 93 from 180 to get z.
Z should equal 87.
The next variable we can solve for is "x". We know that inscribed angles are half the measure of their intercepting arc, so we know 93 is half of (112 + x). The equation would look like this:
93= (112 + x)/2
Multiply both sides by 2
186 = 112 + x
Subtract 112 from both sides
74 = x
Now we can apply the same method we used to find "x" to find y. Set up an equation like this:
80 = (y + x)/2
Substitute the value of x in
80 = (y + 74)/2
Multiply both sides by 2
160 = y + 74
Subtract 74 from both sides
86 = y
Hope this helps!
Answer:
0
Step-by-step explanation:
(1)^2(-1)^2 +(1)(-1) -(-1)^3 -(1)^3
= 1·1 -1 -(-1) -1
= 1 - 1 + 1 - 1 = 0
The equation for the first part would be 4.50p+40=112.
This is because he earns 40 dollars in wages which doesn't change but the number of shoes he commissions, which would be 4.50 per pair. varies based on how many he commissions.
The answer to your second part would be 16.
To find the number, you subtract 40 from each side which gets you 4.50 = 72. From there you just divide which gets you 16.
Another easy way to do it would just be substituting until you find the right number like on a calculator but if you don't have a calculator on hand (let's say for a test), than the first way would be more effective.
Answer:
Statement B and D are correct.
Step-by-step explanation:
The number of minutes Gabriel spends grading essays can be presented as a function: f(x) = 4x, where x is the number of graded essays and 4 is the number of minutes Gabriel spends on grading each essay.
By definition, domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes.
So in this case, domain of f(x) is the set of all values of x which is an integer going from 0 to 105. Statement D is accurate.
Range of f(x) is the set of all values that f takes and can be calculated by multiplying 4 with (0,105), equal (0,420). Statement B is accurate.
1.5 quarts of 20% fruit juice and 4.5 quarts of 100% fruit juice.
Step-by-step explanation:
Let x be the number of quarts of 100% fruit juice
Let y be the number of quarts of 20% fruit juice
The equation for amount of quarts is ;
x+y=6
x=6-y-------------------equation 1
The equation for the amount of quarts of fruit juice to get 80% fruit juice will be;
x(100%)+y(20%)=80%------however you need to make 6 quarts so divide first portion of equation by 6
{x(100%)+y(20%) }/6=80%
Multiply both parts of the equations by 6
x(100%)+y(20%)=480% --------------equation 2
Use equation 1 in 2
(6-y)(100%)+y(20%)=480%
600-100y+20y=480
600-80y=480
600-480=80y
120=80y
120/80 =y
1.5=y
Use the value of y in equation 1
x=6-y , x= 6-1.5=4.5
So you have,
1.5 quarts of 20% fruit juice and 4.5 quarts of 100% fruit juice.
Learn More
Mixtures equations;brainly.com/question/11898822
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