Final answer:
The y-intercept is the value of y when x is zero, represented by the constant b in the linear equation y = mx + b. In the example y = 55x + 75, the y-intercept is 75, indicating where the line intersects the y-axis and signaling the initial value of y before any changes in x.
Explanation:
An example of a y-intercept can be found in the linear equation y = mx + b, where b represents the y-intercept. This value is where the line crosses the y-axis on a graph. If we consider the equation y = 55x + 75, for instance, the y-intercept is 75. This means that when x (the independent variable) is zero, the y value, possibly indicating the starting point of a scenario such as labor charges before work begins, is 75.
A real-world example can be seen in a car repair scenario where the total labor charges (y) depend on the number of hours worked (x). Given the equation y = 55x + 75, when no hours are worked (x=0), the total charges start at $75, which is the y-intercept. The slope of the line is 55, indicating that for each additional hour worked, the labor charges increase by $55.
What's the distance between the points (-3,11) and (5,5)
This month, Kami sold 70 figures in 2 sizes. The large figures sold for $12 and the small figures for $8. The amount of money received from the sales of the large figures were equal to the amount he earned from the small figures. How many large figures did he sell?(options) A-20 B-28 C-35 D-42 E-50.
Kami sold 28 large figures, as their earnings equaled that of 42 small figures. (Option B)
Let's denote the number of large figures sold as [tex]\( L \)[/tex] and the number of small figures sold as [tex]\( S \).[/tex]
We know the following:
1. [tex]\( L + S = 70 \)[/tex] (Total figures sold)
2.[tex]\( 12L = 8S \)[/tex] (Amount earned from large figures equals the amount earned from small figures)
We can use these equations to solve for [tex]\( L \):[/tex]
From equation 2, we can express [tex]\( S \) in terms of \( L \):[/tex]
[tex]\[ S = \frac{12L}{8} = \frac{3L}{2} \][/tex]
Now, we can substitute this expression for [tex]\( S \)[/tex] into equation 1:
[tex]\[ L + \frac{3L}{2} = 70 \][/tex]
Multiplying both sides by 2 to clear the fraction:
[tex]\[ 2L + 3L = 140 \]\[ 5L = 140 \][/tex]
Now, divide both sides by 5:
[tex]\[ L = \frac{140}{5} = 28 \][/tex]
So, Kami sold [tex]\( 28 \)[/tex] large figures.
Therefore, the answer is option B - 28.
What is the length of a rectangle with a width of 18in and an area of 117in
9.
Which of these is a simplified form of the equation 6y + 4 = 8 + 2y + 2y? (5 points)
6y = 8
10y = 12
2y = 4
4y = 12
10.
The work of a student to solve the equation 2(3x – 4) = 8 + 2x + 4 is shown below:
Step 1: 2(3x – 4) = 8 + 2x + 4
Step 2: 5x – 6 = 12 + 2x
Step 3: 5x – 2x = 12 + 6
Step 4: 3x = 18
Step 5: x = 6
In which step did the student first make an error and what is the correct step? (5 points)
Step 2; 6x – 6 = 2(6 + x + 2)
Step 2; 6x – 8 = 12 + 2x
Step 3; 5x – 2x = 12 – 6
Step 3; 5x + 2x = 12 + 6
Explain how the Venn diagrams in this lesson show that all integers and all whole numbers are rational numbers
All integers in which real numbers are involved can be written as p/q such that p and q are integers so they will be a rational number.
What is an irrational number?Any real number that cannot be written as the quotient of two integers, p/q, where p and q are both integers, is referred to as an irrational number.
In another word, irrational numbers are those numbers that can not terminate.
For example, √2, and √3 are irrational numbers because they cannot be written as p/q where p and q both should be integers.
All integers are non-decimal numbers so they can be written as p/q such that p and q both will be integers so they will be a rational number.
The whole number is a positive integer so it will be in the category of integers only.
So,
In the given Venn diagram it is clear that in the real number all rational and irrational numbers are included in the rational number integer and in which the whole number is shown.
Hence "All integers in which real numbers are involved can be written as p/q such that p and q are integers so they will be a rational number".
For more about the irrational number,
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Order the following fractions from least to greatest: 5/16, 3/4, 1/2
A: 1/2, 3/4, 5/16
B: 3/4, 5/16, 1/2
C: 5/16, 1/2, 3/4
D, 1/2, 5/16, 3/4
A Fast food restaurant sold 30 burgers with cheese.If the ratio of burgers sold with cheese compared to without cheese was 10:7,How many burgers did they sell total?
To find the total number of burgers sold, we use the ratio of burgers with cheese to those without (10:7), determine the number of sets in the 30 burgers with cheese sold, and calculate the number of burgers without cheese accordingly. The restaurant sold a total of 51 burgers.
To determine the total number of burgers sold, we can use the given ratio of burgers with cheese to burgers without cheese, which is 10:7. This means for every 10 burgers with cheese, there are 7 burgers without cheese. We're told that the restaurant sold 30 burgers with cheese. Since these represent the '10' part of the ratio, we can find out how many sets of '10' there are in 30 burgers to then calculate the '7' part of the ratio.
First, we divide the number of cheeseburgers by 10:
30 burgers with cheese \/ 10 = 3 setsNext, we multiply the 7 parts of the ratio by 3 to find the number of burgers without cheese:
7 x 3 = 21 burgers without cheeseTo find the total number of burgers sold, we add the number of burgers with cheese and the number without cheese:
Total number of burgers = 30 (with cheese) + 21 (without cheese) = 51 burgersexplain the difference in meaning between |-3| and -3
The number is positive when measured in absolute value. So |-3| = 3. since distance cannot be calculated in negative quantities.
What is the number?A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
It is given that:
Two numbers are given:
|-3| and -3
As we know, the mod function has positive range.
Let f(x) = |x|
The range of the function is [0, ∞)
The value of |-3| will be 3 after removing the mod which is also called the absolute value of the mod function.
A number's distance from zero, or its absolute value, is expressed as the number of spaces.
Since distance cannot be calculated in negative quantities, it cannot be negative. A number is positive when measured in absolute value. So |-3| = 3.
Thus, the number is positive when measured in absolute value. So |-3| = 3. since distance cannot be calculated in negative quantities.
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I will give BRAINLIEST to whoever is correct.
If x^2=10,What is the value of x?
Solve 11 and 13 pleaseeeee
wich is the mean of the following numbers 5,6,4,6,4
How does the numbers of zeros in the product of 8 and 5000 compare to the number of zeros in the factors?
Teresa will rent a car for the weekend . She can choose one of two plans . The first plan has no initia fee but costs $0.70 per mile driven . The second plan has an initial fee of $65 and costs an additional $0.20 per mile driven . How many miles would Teresa need to drive for the two plans to cost the same ?
According to the dietary guidelines for Americans which of the following is important in order to maintain a healthy weight?
A. Get all the nutrients your body needs
B. Balance calories eaten with activity level
C. Wash hands when preparing food
D. Eat nutrient-dense food
Which of the following is an example of proper food handling?
A. only clean the surface when you are done cooking
B. place frozen foods on the countertop to thaw
C. keep all perishable foods inside cabinets
D. keep your hands clean while you are cooking
Which of the following is a good choice according to the dietary guidelines?
A. Diet Soft Drinks
B. Frozen Yogurt
C. Salmon
D. Fruit Snacks
wallace has a $50 bill. pizza pies cost 12.25 each. if p represents the number of pizzas he buys, write an expression for the change he recieves
To calculate the change Wallace receives, subtract the total cost of pizzas (12.25 times p) from the original $50.
To answer the question of how to write an expression for the change Wallace receives after buying p number of pizzas, we need to use a simple algebraic expression. Wallace has a $50 bill and each pizza cost $12.25. If p represents the number of pizzas, then the total cost of the pizzas would be 12.25 times p. To find the change he receives, we subtract this amount from the original $50.
The expression for the change Wallace receives is:
Change = 50 - (12.25 times p)
A triangle has a height of x meters and a base of 14 meters. Write and solve an inequality for the values of x that give an area of at most 112 m
Answer:
The values of x must be 16 meters or less to satisfy the inequality. (x ≤ 16 m)
Step-by-step explanation:
The area of a triangle is given by the formula:
A=[tex]\frac{bh}{2}[/tex]
Where 'b' is the base of the triangle (in this case is equals to 14 meters)
'h' is the height of the triangle (in this case is x)
As the area of the triangle must be less or equal to 112 m², the inequality is given by:
112m²≥[tex]\frac{(14m)x}{2}[/tex]
[tex]\frac{112m^{2}*2 }{14m}[/tex]≥x
16m ≥ x
a balloon pump and 3 packs of balloons cost £9 altogether. a balloon pump and 4 packs of balloons cost £11 altogether. how much dose a balloon pump anf 8 packs of balloons cost?
I need to know 37-45 and show work
If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to y from the second equation is substituted into the first equation. 2x − 7y = 4 3x + y = −17
Mandy is trying to subtract 4 - 12 and she has asked you for help how would you explain the process of solving a problem to Mandy using a number line
The length of a rectangle is 2 units shorter than one-fifth of the width, x.
Which expression represents the perimeter of the rectangle?
2/5x−8
12/5x−4
2/5x−4
12/5x−2
I just took the test and the answer is B. 12/5x - 4
In case anyone else has the same question
How many times heavier is a 16 1/2 pound rockthen a 10 1/2 pound rock
Answer: [tex]16\dfrac{1}{2}[/tex] pound rock is 1.571 times heavier than [tex]10\dfrac{1}{2}[/tex] pounds rock.
Step-by-step explanation:
Since we have given that
Quantity of rock = [tex]16\dfrac{1}{2}\ pounds=\dfrac{33}{2}\ pounds[/tex]
Quantity of another rock = [tex]10\dfrac{1}{2}=\dfrac{21}{2}\ pounds[/tex]
We need to find the number of times heavier is 16 1/2 pound rockthen a 10 1/2 pound rock.
so, number of times is given by
[tex]\dfrac{33}{2}\div \dfrac{21}{2}\\\\=\dfrac{33}{2}\times \dfrac{2}{21}\\\\=\dfrac{33}{21}\\\\=1.571[/tex]
Hence, [tex]16\dfrac{1}{2}[/tex] pound rock is 1.571 times heavier than [tex]10\dfrac{1}{2}[/tex] pounds rock.
what is the distance between A(3,-4) and B(-1,3) (distance formula)
math questions down below
Find the sum or difference of 8-6.38
what is the balance as a result of having a credit of $84 and a debit of $29
84-29=55
84 is your credit and 29 is your debit
Evaluate the expression 6x7-3^2x9+4^3
A yellow jacket can fly 4.5 meters in 9 seconds.find the unit rate in meters per second
7=14x-42y solve equation for y