Answer:
Part 1) The equation in slope intercept form is 
Step-by-step explanation:
Part 1) Write an equation in slope-intercept form for a line that passes through (3,4) (and has a y intercept of -8)
we know that
The equation of a line in slope intercept form is equal to
where
m is the slope
b is the y-intercept
we have
substitute
solve for m
therefore
First Problem:
angle R and angle S are complementary which means they add to 90 degrees. Think "C" for "Complementary" and "Corner" as in a sharp 90 degree corner. That's how I remember it.
Let's solve for x
(angle R) + (angle S) = 90
(12x-3) + (7x-2) = 90
12x-3 + 7x-2 = 90
(12x+7x)+(-3-2) = 90
19x-5 = 90
19x-5+5 = 90+5
19x = 95
19x/19 = 95/19
x = 5
Since x = 5, we can say
angle R = 12x - 3
angle R = 12*5 - 3
angle R = 60 - 3
angle R = 57 degrees
Final Answer: 57 degrees
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Second Problem:
Angle 1 and angle 2 "form a linear pair". This means they are adjacent and supplementary (add to 180 degrees). Put another way, they combine to form a single straight angle or line.
Let's make
x = measure of angle 1
y = measure of angle 2
We're also told that "the measure of angle 2 is six more than twice the measure of angle 1", which basically translates to
y = 2*x + 6
Because the angles (x and y) are supplementary, we can also say
x+y = 180
So we have this system of equations
y = 2x+6
x+y = 180
Start with equation (2). Plug in the equation (1) and solve for x
x+y = 180
x+2x+6 = 180 ... note how y has been replaced with 2x+6
3x+6 = 180
3x+6-6 = 180-6
3x = 174
3x/3 = 174/3
x = 58
Now that we know x, we can find y
y = 2x+6
y = 2*58+6
y = 116+6
y = 122
Final Answer: 122 degrees
Answer:
13
Step-by-step explanation:
because you have to divide 13 divide by 1 and eat equals 13 then if you spin it the posibility might be 13
The amount of quarts of water to fill the jar is 10.6875 quarts
To solve this problem effectively, we need to understand the concept of word problems.
<h3>What are word problems in mathematics?</h3>
Word problems in mathematics are questions that require a crucial understanding and application of mathematical principles to solve them effectively.
From the parameters given:
- If 114 ounces of water is poured three times to fill the jar
Then, the total amount of ounces that fills the water is:
= 114 ounces × 3
= 342 ounces
From the dimensional analysis of measurements:
1 ounce = 0.03125 quarts
Thus, in quarts, 342 ounces will be:
= 10.6875 quarts
Learn more about word problems in mathematics here:
brainly.com/question/21405634
