Determine the y intercept for the linear function 3x - 4y = 24. Show all work for credit.
Answers
Answer:
y-intercept = -6
Step-by-step explanation:
y-intercept is the value of "y" where a line meets the Y coordinate.
The equation of the line
The linear function given to us is a straight line of equation:
[tex]\boxed{\mathsf{3x-4y=24}}[/tex]
We have two methods to determine the y intercept of the given line
Method #1(Intercept form)
The intercept form will benefit us with not only the y-intercept but also the x-intercept.
If a line makes an x-intercept "a" and a y-intercept "b", it's equation in intercept form is given by:
[tex]\boxed{\mathsf{\frac{x}{a} +\frac{y}{b} =1}}[/tex] . . . . . . . .. . . (¡)
Our main motive here is to get a 1 on one side and have separate denominators for x and y.
PROCESSING OUR CONVERSION:
[tex]=>\mathsf{3x-4y=24}[/tex]
taking 24 to the denominator on the LHS:
[tex]\implies\mathsf{\frac{3x}{24} -\frac{4y}{24} =1}[/tex]
reducing the fractions to their simplest form:
[tex]\implies\mathsf{\frac{x}{8} -\frac{y}{6}=1}[/tex]
getting a plus in between the two fractions and taking the leftover minus to 6 of " [tex]\frac{y}{6}[/tex]"
[tex]\implies\mathsf{\frac{x}{8} +\frac{y}{-6}=1}[/tex]
On comparing it with eqn. (¡), we get
a = 8 and b = -6
which are the x and y intercepts respectively
Since, the question's only asked for the y-intercept
ANSWER:
y-intercept = - 6
- - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - -
Method #2(slope-intercept form)
The given equation is in standard form. To convert it into slope-intercept you simply have to isolate y.
CONVERSION:
[tex]\implies \mathsf{3x-4y=24}[/tex]
taking y to the RHS and getting 24 to the LHS
[NOTE: Signs change in doing so]
[tex]\implies \mathsf{3x-24=4y}[/tex]
dividing both the sides by 4
[tex]\implies \mathsf{\frac{3x}{4} -6=y}[/tex]
This is the equation in slop-intercept form!
When a line meets the Y-axis it's x coordinate becomes 0.
[Check the attachment]
Substituting x with 0
[tex]\implies \mathsf{0-6=y}[/tex]
[tex]\implies \mathsf{-6=y}[/tex]
ANSWER:
x is 0 when y is -6.
Implies that the y intercept of the line is -6
Related Questions
Express in vertex form
Y=2x^2 - 2x - 5
Answers
Answer:
y = 2(x - [tex]\frac{1}{2}[/tex] )² - [tex]\frac{11}{2}[/tex]
Step-by-step explanation:
y = 2x² - 2x - 5 ← factor out 2 from the first 2 terms
= 2(x² - x) - 5
Using the method of completing the square
add/subtract (half the coefficient of the x- term)² to x² - x
y = 2(x² + 2(- [tex]\frac{1}{2}[/tex] ) x + [tex]\frac{1}{4}[/tex] - [tex]\frac{1}{4}[/tex] ) - 5
= 2(x - [tex]\frac{1}{2}[/tex] )² + 2(- [tex]\frac{1}{4}[/tex] ) - 5
= 2(x - [tex]\frac{1}{2}[/tex] )² - [tex]\frac{1}{2}[/tex] - 5
= 2(x - [tex]\frac{1}{2}[/tex] )² - [tex]\frac{11}{2}[/tex] ← in vertex form
Helpppppppppz it’s to harddd
Answers
Answer:
Try C hope this is right
Step-by-step explanation:
A Carpenter wants to build a elliptical table top from a 4 foot to by 6 foot sheet of plywood. she traces out the ellipse using a string attached to thumbtacks located at the foci of the ellipse.
Answers
The thumbstacks have an in-between distance of [tex]2\sqrt{5}[/tex] feet.
The distance between any focus and the center of the ellipse ([tex]c[/tex]), in feet, is described by the following expression:
[tex]c = \sqrt{a^{2}-b^{2}}[/tex] (1)
Where:
[tex]a[/tex] - Major semiaxis length, in feet.[tex]b[/tex] - Minor semiaxis length, in feet.If we know that [tex]a = 3\ft[/tex] and [tex]b = 2\,ft[/tex], then the distance between focus and center is:
[tex]c = \sqrt{3^{2}-2^{2}}[/tex]
[tex]c = \sqrt{5}[/tex]
The distance between the thumbstacks is described by this expression:
[tex]d = 2\cdot c[/tex]
[tex]d = 2\sqrt{5}\,ft[/tex]
The thumbstacks have an in-between distance of [tex]2\sqrt{5}[/tex] feet.
We kindly invite to check this question on ellipses: https://brainly.com/question/14281133
yo ill give brainliest if ur right help pls
Answers
Answer:
B or C. Im thinking C.
Step-by-step explanation:
Answer:
C, look at the problem and it says plus" directly look at the option and compare.
Step-by-step explanation:
pls help me for my geometry class
Answers
Answer:
I CANT SEE SRY
Step-by-step explanation:
simplify (-4x+4)(4x[tex]x^{2}[/tex]+2)
Answers
Answer:
−16x3+16x2−8x+8
Solve.
32.3 = 14.8 + 8.4x
Enter your answer as a mixed number in simplest form in the box.
x =
Answers
The value of x is 2.0833.
Given that,
The equation is 32.3 = 14.8 + 18.4x.We need to find the value of x.Based on the above information, the calculation is as follows:
32.3 = 14.8 + 8.4x
32.3 - 14.8 = 8.4x
17.5 = 8.4x
x =2.0833
Learn more: brainly.com/question/17429689
Answer:
2 1/12
Step-by-step explanation:
I took a math quiz and got it 100% correct!
Hope this helps!
Have a great day/night!
If P(t) = 5e 0.89t
Then what is p(3)?
please!
Answers
Answer:
15.989
Step-by-step explanation:
i dont think you care
The cube of twice a number.
Answers
Answer
?
Step-by-step explanation:
Wheres The Question
How do you solve 100^(5x+2)=1000^(4x-1)?
Answers
7⅕-2⅔x0,5 explain step by step
Answers
Step-by-step explanation:
7/5 - 2×2/3 × 0.5 = 1.4 - 2×0.5×2/3
= 1.4 - 1 ×2/3
=1/4 × 2/3
=1.5 - 0.6
Draw an ordered stem and leaf diagram to show this information.
245, 250, 251, 253, 258, 264, 267, 269, 273, 276
Key:24|5 means 245.
Answers
=========================================================
Explanation:
The key tells us how to set up the stem and leaf diagram. It says that [tex]24|5[/tex] represents the value 245.
This means that "24" is one of the stems. In fact, it's the smallest stem possible since there's nothing smaller than 240 on this given list of values.
The only leaf associated with this stem is 5. The stem 24 and the leaf 5 combine to form the number 245 as the key indicates.
--------------------------
In the next row is the stem 25. For this stem, we'll have the leaves of: 0, 1, 3, 8. The stem 25 and those leaves mentioned combine to form 250, 251, 253, 258 in that exact order. This time we'll use up four boxes for this row. The last box in this row is blank.
The remaining rows (stems 26 and 27) are handled in pretty much the same fashion. Let me know if you have questions how the boxes are filled in. It helps to start with sorted data from smallest to largest. Luckily, that's already been done for us.
The filled out chart is shown below. I replaced the stems 0,1,2,3 with 24,25,26,27.
Help me please save me from detention
Answers
Answer:
The answer is B.
Step-by-step explanation:
It would be B because,
2+2=4
4+2=6
6+4=10
10+6=16
Not A because,
1+1=2
2+1=3 not 4
There you go :) pls gime the crown... :)
i need the answer for
3-3 Mini Assessment | Constant of Proportionality in Graphs
Question
POSSIBLE POINTS: 1
The relationship between the number of ounces of tea purchased and the total cost of the tea is proportional as shown in the graph.
Which equation models this relationship?
y = 7/4x
y = 4/7x
y = 4/1x
y = 1/4x
Answers
Answer: y= (7/4)x
Step-by-step explanation:
Build a table of representative values and then calculate the slope between any 2 of the points. I'll pick (2,3.5) and (8,14) [See attachment. ]
The slope is the Rise/Run:
Rise = (14 - 3.5) = 10.5
Run = (8-2) = 6
Slope = Rise/Run: (10.5/6) = 1.75
The equation should read y = 1.75x.
None of the options works, as written, but note that 7/4 looks close to 1.75. In fact, 7/4 = 1.75.
Use the equation y = 1.75x and enter several values of x (the ounces purchased) and y (the total cost of the purchase). The attachment summarizes the results (Predicted), along with the actual values (Actual) taken from the graph. Excellent correlation, considering the difficulty in making precise graph readings.
Therefore y = (7/4)x
Class 10R sat a test.
The mean mark for the class was 70%.
There are 30 students in class 10R, 20 of whom are boys.
The mean mark for the boys in the test was 62%.
Work out the mean mark for the girls.
Answers
86%
Step-by-step explanation:30 students in the class with a mean average of 70% can be expressed as:
total class percent / 30 = 70%
Rearranged, this gives that the class achieved a total of 30x70 or 2100%.
20 boys in the class with a mean average of 62% can be expressed as:
total boys percent / 20 = 62%
Rearranged, this gives that the boys achieved a total of 20x62 or 1240%.
This means that the girls achieved 2100 - 1240 so 860%.
Because there are 30 students and 20 boys, there are 10 girls.
Then work out the mean with a total of 860% and 10 girls.
860/10 = 86%.
? 2x² – 3x - y = -5
-x+y=5
Answers
Answer:
2x^2- 3x - Y= -5 -x + Y = 5
there is no solve because it already is solved.
Step-by-step explanation:
PLEASE HELP ME ASAP!!!!
4 5/9 is the same as the sum of 2 1/3 and 5/6 times a number.
What is the number?
Enter your answer as a mixed number in simplest form in the box.
PLEASE ANSWER QUICK!!
Answers
Answer:
2 2/3
Step-by-step explanation:
Question 13 of 20
If fx) = 5x- 4 and g(x) = 4x+1, find (f- g)(x).
Answers
Answer:
Step-by-step explanation:
x-5
Last semester, Zachary earned an average score of 80 points on math tests. So far this semester, his average score is 15% lower. What is the average of Zachary's scores this semester?
Answers
Answer:
The answer would be 12
Step-by-step explanation:
15/100 = X/80
To solve the equation above for X, you first switch the sides to get the X on the left side, then you multiply each side by 80, and then finally divide the numerator by the denominator on the right side to get the answer.
The equation
15/100 = X/80
X/80 = 15/100
X*80/80 = 15*80/100
X = 1200/100
X = 12
randall wants to fill up 40 percent of the scare containers. what is this number as a fraction
Answers
Answer:
2/5
Step-by-step explanation:
Normally, percentage is expressed in 0 - 100 so for Randall to fill up 40% of his container, that means he'd fill out 40 out of a hundred. That's 40/100 which simplified will give you 2/5
line j passes through the point (-4,10) and (2,-8). Line k passes through the point (1,2) and is parallel to line j. Find an equation for line k.
Answers
Answer:
344444444433333338694
Step-by-step explanation:
Answer: y = -3x+5
Step-by-step explanation:
PLEASE HELPP and no pictures please i can't see them on a school computer. Ill appreciate a step by step explanation than you! IM GIVING 40 POINTS
Answers
Answer:
a.
The area of the large circle is 225π cm² [exact] or 706.9 cm² [approximate].
b.
area = 50π/6 cm² [exact]
area = 26.2 cm² [approximate]
Step-by-step explanation:
This problem is easier to solve than it looks.
a.
Area of the large circle.
Look at the top left small circle, the middle circle, and the bottom right circle. You can draw a single line segment that is a diameter of the large circle and also contains the diameters of the three small circles. That means that the diameter of the large circle is 3 times the diameter of each small circle.
R and D are the radius and diameter, respectively, of the large circle.
r and d are the radius and diameter, respectively, of the small circles.
D = 3d
D = 6r = 6(5 cm) = 30 cm
R = 15 cm
A = πr²
A = π(15 cm)²
A = 225π cm²
The area of the large circle is 225π cm² [exact] or 706.9 cm² [approximate].
b.
There are 6 congruent spaces between the small circles and the large circle, and there are another, different 6 congruent spaces between the center circle and the 6 circles around it. The region we need is made up of one space of each type.
The combined area of all 12 spaces is the area of the large circle minus the total area of all the small circles. The area we need to calculate is 1/6 of that combined area.
area = (1/6)(area of large circle - total are of all small circles)
area = (1/6)[225π cm² - 7π(5 cm)²]
area = (1/6)[225π - 175π]cm²
area = 50π/6 cm² [exact]
area = 26.2 cm² [approximate]
express the following ratio in the simplest form
2kg 250g :5kg
please give me answer
Answers
Step-by-step explanation:
5kgthe following ratio in the simplest form
Answer:
Below.
Step-by-step explanation:
2 Kg : 250g : 5 kg
Convert all to grams:
= 2000 : 250 : 5000
= 200 : 25 : 500
= 8:1:20.
If an atom has 5 protons, 7 neutrons and 5 electrons what is the mass number of the atom?
Please help quick!
No links!
Answers
Answer:
7+5=12
Step-by-step explanation:
To calculate the mass number of an atom, you have to add the protons and the neutrons. We have 7 neutrons and 5 protons, so your mass number would be 12. Let me know if you have any further questions. :)
I need help with this Pre-Cal question
Answers
Answer:
Step-by-step explanation:
helpppppppppppppppppppppppppppppppppppppp
Answers
Answer:
a). 10
b). 14
c).12
d). 10
Step-by-step explanation:
Answer:
a) 10/55
b) 12/14
c) 9/12
d) 10/15
Step-by-step explanation:
253 is what percent of 220
Answers
115%
A newspaper reports the following changes in the temperature of a city over 4 days: 3.24 degrees Celsius, -3/8 degrees Celsius, -0.15 degrees Celsius, 7/9 degrees Celsius Write an expression to show the average daily change in the temperature of the city. Write the steps to solve the expression. Round your answer to the nearest hundredth.
Answers
Answer:
It is 0.873 but rounded to hundredth is 0.87
Step-by-step explanation:
I included a picture on how to solve it, hoped I helped. :)Answer:
0.873 rounded to the nearest hundredth is 0.87
Step-by-step explanation:
express the followinf percentage as a fraction
a) 6 3/5%
Answers
Answer:
6.6/100 or 3.3/5
Step-by-step explanation:
6.6% or 6 3/5% now since those are all out of 100 (since percentages) you just put #/100 and get your fraction
Solving by Elimination
Answers
Answer:
unsolvable
Step-by-step explanation:
by elemination 14x+7y=-7 (1)
-14x-7y=7 (2)
x and y will be 0 then
