suppose you go to a concert and purchase 3 identical t-shirts and a hat. the hat cost $21 and you spend $60 in all how much does each t-shirt cost ?
the function y = 3.75 + 1.5(x-1) can be used to determine the cost in dollars for a taxi ride of x miles. what is the rate of change of the cost in dollars with respect to the number of miles?
Answer:
rate of change of the cost in dollars with respect to the number of miles= 1.5
Step-by-step explanation:
We have been given the function y = 3.75 + 1.5(x-1)
Let us simplify this equation
y = 3.75 + 1.5(x-1)
y= 3.75+1.5x-1.5
y = 1.5x+2.25
On comparing this equation withe the slope intercept form y = mx + b, we get
m = 1.5
b = 2.25
here x represents distance in miles and y represents the cost in dollars. So, the rate of change of the cost in dollars with respect to the number of miles would be equal to the slope of the line.
Thus, we have
rate of change of the cost in dollars with respect to the number of miles
= slope
= 1.5
The rate of change of a function is the slope of the function.
The rate of change of the function is $1.5 per miles
The function is given as:
[tex]\mathbf{y= 3.75 + 1.5(x - 1)}[/tex]
Open bracket
[tex]\mathbf{y = 3.75 + 1.5x - 1.5}[/tex]
Collect like terms
[tex]\mathbf{y = 1.5x - 1.5 + 3.75}[/tex]
[tex]\mathbf{y = 1.5x +2.25}[/tex]
A linear equation is represented as:
[tex]\mathbf{y = mx +b}[/tex]
Where: m represents the slope
So, by comparison:
[tex]\mathbf{m =1.5}[/tex]
Hence, the rate of change of the function is $1.5 per miles
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Subtract using the number line.
−113−16
−1 5/6
−1 1/2
−1 1/6
1 1/2
The value of -1 1/3 - 1/6 is -1 1/2.
Option B is our correct answer.
Given,
-1 1/3 - 1/6
We need to find the value.
What is a fraction?A fraction contains two parts:
Numerator and denominator.
Fraction = Numerator / Denominator
How do subtract fractions?Example:
2/3 - 2/4
We will find the LCM of 3 and 4.
= (2x4 - 2x3) / 12
= (8 - 6) / 12
= 2 / 12
= 1/6
How to convert a fraction into a mixed fraction?Example:
b/a
a x m + n = b
= [tex]m\frac{n}{a}[/tex]
Find -1 1/3 - 1/6
We can write -1 1/3 as:
= - 4/3
Now,
-4/3 - 1/6
=( -4x2 - 1) / 6
= (-8 - 1 ) / 6
= -9 / 6
= -3x3 / 3x2
= -3/2
Converting into a mixed fraction.
= -1 [tex]\frac{1}{2}[/tex]
Thus the value of -1 1/3 - 1/6 is -1 1/2.
Option B is our correct answer.
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The Pythagorean Sea, in Southern Antarctica has a depth that varies quadratically with its width. The width of the sea is 1000 meters. Two hundred meters from shore, the depth is 20 meters. Find the particular quadratic equation for the sea. Compute the depth of the deepest portion of the sea.
When filing separately, both Melvin and Sylvia have a standard deduction of $5700, and each can claim him/herself as an exemption for $3650. Neither has any additional adjustments to income. What is Melvin's taxable income? How about Sylvia's taxable income?
Melvin and Sylvia's taxable income is calculated by subtracting the sum of the standard deduction ($5,700) and the personal exemption ($3,650) from their adjusted gross income. Since the adjusted gross income was not provided, the exact taxable income cannot be determined without that information.
Explanation:When calculating Melvin and Sylvia's taxable income, we first need to use the given standard deduction and personal exemption to determine their taxable income. According to the information, the standard deduction is $5700 and the personal exemption is $3650 Therefore, we subtract the sum of these deductions from their adjusted gross income to find their taxable income.
Assuming Melvin and Sylvia both have the same adjusted gross income and ignoring any typos or irrelevant parts of the questions being asked, we have:
The formula for each individual's taxable income is as follows:
taxable income = adjusted gross income - (standard deduction + personal exemption)
To find Melvin or Sylvia's taxable income, simply plug their adjusted gross income into the formula.
the average person's stride length ,the distance covered by one step ,is approximately 2.5 feet long.How many steps would the average person take to travel 50 feet?
Answer:
20 steps
Step-by-step explanation:
It is given that distance covered by one step is approximately 2.5 feet long.
⇒ 2.5 feet long = One step
⇒ 1 feet long = [tex]\frac{1}{2.5}[/tex]
∴ 50 feet = [tex]50\times\frac{1}{2.5} = 20 steps [/tex]
Hence, person has to take 20 steps for travelling 50 feet.
a robot can complete 8 tasks in 5/6 hour. each task takes the same amount of time.
a. how long does it take the robot to complete the task?
b. how many tasks can the robot complete in one hour?
Answer:
A robot can complete 8 tasks in hour = [tex]\frac{5}{6}[/tex]
A robot can complete 1 task in hour = [tex]\frac{\frac{5}{6}}{8}[/tex]
A robot can complete 1 task in hour = [tex]\frac{5}{48}[/tex]
So, it take [tex]\frac{5}{48}[/tex] hours the robot to complete the task
A robot can complete tasks in [tex]\frac{5}{6}[/tex] hour = 8
A robot can complete tasks in 1 hour = [tex]\frac{8}{\frac{5}{6}}[/tex]
=[tex]9.6[/tex]
So, the robot complete 9 tasks in one hour.
9.086 minus 2.419 rounded to the nearest one
The Weight of water is 62 1/2 lb per cubic foot how many cubic feet would be occupied by 235 lb of water
30. The perimeter of a rectangle is 292 feet. The length of the rectangle is 4 feet less than 5 times the width. What is the length and width of the rectangle? a. length = 121, width = 25b. length = 114.3, width = 23.7 c. length = 25, width = 121d. length = 121.7, width = 24.3
A pair of shoes weighs 650 grams.How many decigrams does it weigh?
a rational function, a value is _________ from the domain if it would create a 0 in the function's denominator.
A sequence is defined by dividing the term number by the power of 2 raised to the term number. What is the seventh term?
A. 1/4
B.7/32
C.7/64
D.7/128
show how you round 1345/99 to the nearest integer
1.1 1 1/10 and 1.101 least to greatest
A computer programmer charges $45 an hour for coding projects plus a start up fee of $150.
Write an equation in standard form to represent the total cost t of a project that takes h hours.
An equation in standard form is C(t) = 150 + 45t
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here, A computer programmer charges $45 an hour for coding projects plus a start-up fee of $150. Let t be the time in hours then we can construct an equation as C(t) = 150 + 45t
Hence, An equation in standard form representing the information is C(t) = 150 + 45t
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The graph of g(x) is a parabola with a vertex at (0, 2).
Which statement is true?
Neither function is an even function.
Only the function g(x) is an even function.
Both functions are even functions.
Only the function f(x) is an even function.
Thank you!
Eduardo counted 10 seconds between seeing lightning and hearing thunder, and he knew that the lightning was about 2 miles away. If he counted four seconds between the next flash of lightning and hearing thunder, about how far away was the lightning
Eduardo used the time difference between seeing lightning and hearing thunder to determine the distance of the lightning. Given that sound travels a mile every five seconds, the second lightning was 0.8 miles away, based on a time difference of 4 seconds.
Explanation:Eduardo is using a method to measure the distance of lightning by noting the time difference between the visible flash of light and the audible sound of thunder. The speed of light is much faster than the speed of sound, which is why we see lightning before we hear thunder. This method works because it is known that sound travels approximately one mile every five seconds.
So, in Eduardo's first observation, he counted 10 seconds between seeing the lightning and hearing thunder. Given that sound travels a mile every five seconds, the lightning was 10 seconds/5 = 2 miles away.
In the second observation, he counted four seconds between the flash and the thunder. Using the same calculation, this means the lightning was 4 seconds/5 = .8 miles away. This is in agreement with the given information.
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I need to know what the term 8 means or represents in this expression
A triangle has an area of 10.5 square feet. The base of the triangle is 6 feet. What is the height?
Answer:3.5
Step-by-step explanation:
What is the equation of this graphed line?
if the product of 4 and a number is decreased by 12, the result is twice the opposite of the number. Find the number. EXPLAIN PLEASE ♥
math question down below
China has a population of approximately 1,322,000,000 people. Express this number in scientific notation. A) 1.322 x 109 B) 1.322 x 10-9 C) 1.322 x 10−8 D) 13.22 x 108
jim is at his house, and his car has 25 miles until it runs out of gas. would jim be able to make it from his house to the grocery store and back without stopping for gas? explain.
Answer:
No
Step-by-step explanation:
It would take 13 Miles to go to the store and 13 to go back. He only has 25 Miles so he would go over by 1.
a² + b² = c²
5² + 12² =
√169
c = 13
13 + 13 = 26 , He will not make it to to and back.
(I have this question as well so I already have the coordinate plane)
Jim would take 13 Miles to go to the store and 13 to go back. He only has 25 Miles so he would go over by 1.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given that jim is at his house, and his car has 25 miles until it runs out of gas.
We need to check whether jim be able to make it from his house to the grocery store and back without stopping for gas.
This we can find by using Pythagoras theorem.
a² + b² = c²
5² + 12² =√169
c = 13
13 + 13 = 26 ,
Hence, It would take 13 Miles to go to the store and 13 to go back. He only has 25 Miles so he would go over by 1.
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What represents the number written as 23 and 37 thousandths
The number written as 23 and 37 thousandths can be expressed in decimal form as 23.037.
What is Place value?The foundation of our whole number system is place value. In this approach, the value of a digit in a number is determined by where it appears in the number.
When we write a number like 23.037, each digit to the left of the decimal point represents a different place value. The place values start from the right with ones, then increase by a factor of 10 as we move to the left.
So in the number 23.037:
The digit 7 is in the thousandth place, meaning it represents 7/1000 or 0.007.
The digit 3 is in the hundredth place, meaning it represents 3/100 or 0.03.
The digit 0 is in the tenth place, meaning it represents 0/10 or 0.
The digit 2 is in the one's place, meaning it represents 2 ones, or simply 2.
Therefore, 23.037 can be written as:
23 + 0.037
or
23 and 37 thousandths
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Select from the drop-down menu to correctly identify the property shown.
5.2+(−2.4+(−3.9))=(5.2+(−2.4))+(−3.9)
what type of property is this??
I believe this would be the addition property of equality.
Hope this helps!
Which is the most accurate way to estimate 25% of 69?
Bert is planning to open a savings account that earns 1.6% simple interest yearly. He wants to earn exactly $192 in interest after 2 years. How much money should he deposit? A. $600 B. $60 C. $6,000 D. $3,072
Answer:
C. $6,000
Sorry this is late, this is 7th grade work and I wasn't in 7th till this year
Yeah welcome to 2020
compare 249 and 271. write the greater number in word form
Answer:
two hundred seventy-one
Step-by-step explanation:
Given: Two numbers 249 and 271.
To find: Word form of the greater number.
Solution:
We have two numbers 249 and 271.
To find the greater number, we need to compare the two numbers.
To compare the two numbers first of all we will compare the hundreds digit.
The hundreds digit of both the numbers is same that is 2.
Now, we will compare the tens digit of the two numbers.
The tens digit of the number 249 is 4 and the tens digit of the number 271 is 7.
As 7 is greater than 4.
271 is greater than 249.
Now, the word form of 271 is two hundred seventy-one.