Justin's constant rate of running can be represented by the equation
=17/2 =8.5, where r is his speed in kilometers per hour. This indicates that Justin runs at a steady pace of 8.5 kilometers per hour.
To find the equation that represents Justin's constant rate of running, we can use the formula for speed, which is distance divided by time. Given that Justin travels 17 km in 2 hours, we can use these values to determine his speed.
Step 1: Identify the variables:
Let's denote:
d as the distance traveled (in kilometers)
t as the time taken (in hours)
r as the rate or speed (in kilometers per hour)
Step 2: Write down the formula for speed:
Speed =Distance/Time
Step 3: Plug in the given values:
We know that Justin travels 17 km in 2 hours. So,
d=17 km and t=2 hours.
Step 4: Calculate the speed:
=17/2=8.5 km/hr
Step 5: Write down the equation:
Now that we know Justin's speed is 8.5 km/hr, we can express it as an equation:r=8.5
So, the equation representing Justin's constant rate of running is:
r=8.5
This equation states that Justin's speed is always 8.5 kilometers per hour, regardless of the distance he travels. It's a linear equation because his speed remains constant over time
complete question=
Justin runs at a constant rate, traveling 17 kilometers in 2 hours. What is the equation that represents Justin's rate of running?"
Algebra 1 B Exponents and Exponential Functions Unit Portfolio?
Task 1?
Task 2?
Task 3?
Need an
Exponents and Exponential Functions Table?
Would be nice if you could help with all of it though. After all it is (30)points!!!
Exponents multiply a number by itself, while exponential functions contain variables in the exponent. Algebra 1B tasks involving these could include simplifying exponents, solving problems with exponential functions, and creating or interpreting an Exponential Functions Table. Studying, understanding rules, and practicing problems will aid success.
Explanation:It seems like you need help with understanding Exponents and Exponential Functions. Exponents are a way of multiplying a number by itself. For example, 2^3 means 2 is multiplied by itself twice (2 * 2 * 2).
On the other hand, exponential functions are a special type of functions where the variable is in the exponent. For instance, the function f(x) = 2^x is an exponential function.
For your Algebra 1B tasks, here's a sample process: for Task 1, you might be required to simplify numbers or expressions using exponents. Task 2 may require you to solve problems using exponential functions. And Task 3 could involve creating or interpreting an Exponential Functions Table, which is a table showing the values of an exponential function for different x-values.
Remember to follow your study guides, textbooks, and your teacher's instructions for each task. Practicing problems and understanding the rules of exponents and exponential functions will help you earn those 30 points!
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Which of the binomials below is a factor of this trinomial?
x2 + 4x + 4
A. x - 2
B. x + 2
C. x - 4
D. x + 4
The function h(x)=x^2+3 and g(x)=x^2-6.If g(x)=h(x)+k, what is the value of k
Answer:
g(x) = (x – 9 )2 + -8
Step-by-step explanation:
Find the surface area of a sphere with a radius of 8cm.
(use 3.14 for pi and round to the nearest tenth)
A. 267.9 cm^2
B. 803.8 cm^2
C. 2143.6 cm^2
D. 201.0 cm^2
By definition, the surface area of a sphere is given by:
[tex] A = 4 * \pi * r ^ 2
[/tex]
Where,
r: sphere radius
Substituting values in the given equation we have:
[tex] A = 4 * 3.14 * 8 ^ 2
[/tex]
Doing the calculations we have:
[tex] A = 803.84
[/tex]
Rounding to the nearest tenth:
[tex] A = 803.8 cm ^ 2
[/tex]
Answer:
The surface area of a sphere with a radius of 8cm is:
B. 803.8 cm ^ 2
write an equation that is parallel to y = -4x - 1 and passes through (-2 , 4)
PLEASE HELP STEP BY STEP
Jasmine and Carlotta are sisters and each have their own savings together they borrowed $28 from their brother to go to the movies.Each girl has to pay back an equal amount.Carlotta also owes her brother $6,which expression represents the change in Carlotta’s savings after she repays her brother
The expression which shows the change in Carlotta's savings is x-8 if her she owes her brother $6.
What is expression?An expression is a combination of numbers, symbols and variables but not in equal to form.
How to form an expression?In the problem Jasmine and Carlotta borrowed $28 from their brother. Since both need to pay back equally so Carlotta needs to pay back $14 but she owes 6 from her brother so she now has to pay only 8.
Let the savings be x
in this way only $8 needs to be subtracted from savings.
The expression will be = x-8.
Hence the expression which shows the change in savings is x-8.
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Write the first five terms of a sequence. Write both an explicit formula and a recursive formula for a general term in the sequence. recursive formula for arithmetic sequence recursive formula for geometric sequence how to write a recursive formula recursive formula calculator arithmetic sequence formula calculator geometric sequence formula recursive sequence write the first five terms of the arithmetic sequence Report inappropriate predictions
9, 12, 19, 30, ...
Therefore the whole formula for the nth term is;Answer with explanation:
⇒Arithmetic Sequence
11,21,31,41,51,......
First term[tex]a_{1}[/tex] =11
Common Difference(d)=21-11=10
[tex]\rightarrow a_{n}=a_{n-1}+10---{\text{Recursive formula}}\\\\\rightarrow a_{n}=a_{1}+(n-1)d\\\\a_{n}=11+(n-1)\times 10\\\\a_{n}=10n+1---{\text{Explicit formula}[/tex]
⇒Geometric Sequence
First five terms of the sequence are
[tex]4,4^2,4^3,4^4,4^5,.....\\\\\text{First term}=a_{1}=4\\\\ \text{Common ratio},r=\frac{a_{2}}{a_{1}}\\\\r=\frac{4^2}{4}\\\\r=4\\\\a_{n}=4\times a_{n-1}---\text{Recursive formula}\\\\a_{n}=a_{1}\times r^{n-1}\\\\a_{n}=4\times 4^{n-1}\\\\a_{n}=4^{1+n-1}\\\\a^n=4^n-----\text{Explicit formula}[/tex]
Simplify:
(x^3-8)
ok i know it simplifies to (x-2)(x^2+2x+4)
but i don't know why
Part 1.] The attached picture
Part 2.] What is the probability of getting 4 heads when tossing a coin 6 times (rounded to the nearest tenth).
Part 3.] A.) Describe the connection of the pattern of outcomes to Pascal’s triangle.
B.) Look at the increase in values. What is the pattern in the number of total possible outcomes?
Part 4.] Complete the table for powers of 11.
11^0=____
11^1=____
11^2=____
11^3=____
Using the pattern, what is the value of 11^4? _____
Calculate 11^5? _____
Calculate 11^6? _____
Part 5.] Can you use the values in Pascal’s triangle to find the powers of 11? Explain.
Determine whether the given measures can be the lengths of the sides of a triangle. write yes or no. explain. 9.2, 14.5, 17.1
Answer with explanation:
If the length of three segments are, 9.2, 14.5 and 17.1 ,it can be sides of triangle if , Sum of two segments is greater than the third segment.
1.→ 9.2 +14.5=23.7 >17.1
2.→ 14.5 +17.1=41.6 > 9.2
3.→17.1 +9.2=26.3 >14.5
As, sum of any two segment is greater than third segment, so the following measurements can be the the lengths of the sides of a triangle.
Which of the following interpretations for the given expression is correct?
the cube of the difference of 5 times the square of y and 7 divided by the square of 2 times y
the difference of the cube of 5 times the square of y and 7 divided by 2 times the square of y
the cube of the difference of the square of 5 times y and 7 divided by the square of 2 times y
the cube of the difference of 5 times the square of y and 7 divided by 2 times the square of y
Answer:
The cube of the difference of 5 times the square of y and 7 divided by the square of 2 times y.Step-by-step explanation:
The give expression is:
[tex]\frac{(5y^{2}-7)^{3} }{(2y)^{2} }[/tex]
In words, this expression would have all these statement referring to each operation:
The cube of the difference, because the difference is inside the cubic power.Of 5 times the square of y and 7, because these are the terms that are being subtracted.Divided by, because the expression described before is in a quotient.The square of two times y, because the both factor are inside the squared power.Therefore, the first statement is correct.
what set of transformations could be applied to rectangle ABCD to create A’B’C’D’?
A)Reflected over the x-axis and rotated 180 degrees
B)Reflected over the y-axis and rotated 180 degrees
C)Reflected over the x-axis and rotated 90 degrees counterclockwise
D)Reflected over the y-axis and rotated 90 degrees counterclockwise
Answer:
C)Reflected over the x-axis and rotated 90 degrees counterclockwise
Step-by-step explanation:
Reflection over the x-axis move point C from (-1, 1) to (-1, -1), point D from (-1, 2) to (-1, -2), point A from (-4, 2) to (-4, -2) and point B from (-4, 1) to (-4, -1). As can be seen, y-coordinate changes sign, so that, the distance between the original point and its reflection respect x-axis remains the same.
Rotation 90 degrees counterclockwise around origin means that x-coordinate and y-coordinate switches and x-coordinate is multiplied by -1. So, point (-1, -1) transforms into (1, -1) - point C' -, (-1, -2) transforms into (2, -1) - point D' -, point (-4, -2) transforms into (2, -4) - point A' - and point (-4, -1) transforms into (1, -4) - point B'.
Why do you switch the inequality sign when multiplying or dividing by a negative?
What is the measure of AC? Enter your answer in the box. ___°
Do not answer for points. If so, you WILL be reported and points be taken BACK. -.-
Answer:
AC = 21⁰
Step-by-step explanation:
arc AC has central angle 3x+9 n its inscribed angle <ABC is 3x-1.5
central angle = 2 * inscribed angle
3x+9 = 2 * (3x-1.5)
3x+9 = 6x -3
3x = 12
x = 4
so arc AC = (3*4 + 9) = 21⁰
15) Which equation does not represent a function?
A) y = 2x + 3
B) x = 4y + 7
C) 6x - 5y = 8
D) y2 = -5x - 8
look at the question below // 50 points // please help!!
Hi there!
I believe your answer is A. Asymptote. It wouldn't be focus or axis, those just don't make sense. This means it could be either asymptote or directrix. Directrix is a fixed line describing a curve or surface. An asymptote is a line that continually approaches a given curve but does not meet it at any finite surface. Therefore, your answer is asymptote.
Hope this helps!
- Chris
The base of a triangle is 9 inches more than 3 times the height. if the area of the triangle is 105 square inches, find the base and height.
HELP ASAP!!! ill mark brainliest! Which of the following graphs represents the function ƒ(x) = 2x?
A graph that correctly represents the exponential function [tex]f(x) = 2^x[/tex] include the following; B. graph B.
How to write and graph an exponential function?In Mathematics and Euclidean Geometry, an exponential function can be modeled by using this mathematical equation:
[tex]f(x)=a(b)^x[/tex]
Where:
a represents the initial value or y-intercept.x represents x-variable.b represents the rate of change or common ratio.Based on the information provided above, we would select the following exponential function to plot on a set of axes or cartesian coordinate;
[tex]f(x) = 2^x[/tex]
where:
The rate of change (b) is 2 and it represents an exponential growth.
The y-intercept (a) is 1 and it means the graph of this function would cross the y-axis at point (0, 1).
In conclusion, we can logically deduce that only graph B correctly represent an exponential function with these key features.
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Missing information:
Which of the following graphs represents the function [tex]f(x) = 2^x[/tex]?
please help idk this one !!Which represents the solution(s) of the system of equations, y + 4 = x2 and y – x = 2? Determine the solution set by graphing.
(–2, 0)
(–2, 0) and (2, 0)
(–2, 0) and (3, 5)
no solutions
Answer:
[tex](-2,0)[/tex] and [tex](3,5)[/tex]
Step-by-step explanation:
we have
[tex]y+4=x^{2}[/tex] -----> equation A
Is a vertical parabola open upward
[tex]y-x=2[/tex] ----> equation B
Is the equation of a line
we know that
The solution of the system of equations is the intersection point both graphs
Using a graphing tool
The intersection points are [tex](-2,0)[/tex] and [tex](3,5)[/tex]
see the attached figure
Paul, Colin and Brian are waiters. One night the restaurant earns tips totalling £71.10. They share the tips in the ratio 2:3:4. How much more does Colin get over Paul?
The amount that Colin will get more than Paul is $7.90.
From the information given, Paul's share will be:
= 2/9 × $71.10
= $15.80
The share of Colin will be:
= 3/9 × $71.10
= $23.70
The difference between Colin's share and Paul's share will be:
= $23.70 - $15.80
= $7.90
Therefore, the amount that Colin will get more than Paul is $7.90.
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my sister needs help on this! right answer ill choose as an "brainliest" person:)
Three cubes of edge 12 cm are joined together (end to end).Find the volume of the resultng cuboid
(-9,17); slope= -4/3
An equation of the line in slope-intercept form that passes through the point (-9, 17) and has a slope of -4/3 is y = -4x/3 + 5.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.At data point (-9, 17) and a slope of -4/3, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 17 = -4/3(x - (-9))
y - 17 = -4x/3 - 12
y = -4x/3 - 12 + 17
y = -4x/3 + 5
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Complete Question:
Write an equation in slope-intercept form of the line that passes through the point (-9,17) and had a slope of -4/3.
Solve the inequality.
–12m < –24
Karen is buying pens and pencils for the new school year. She wants to have no more than 25 writing utensils in all. She also wants the number of pencils to be greater than or equal to the square of 3 less than the number of pens. Create a system of inequalities to model the situation above, and use it to determine how many of the solutions are viable.
Karen's situation can be modeled by the following system of inequalities:
Total number of utensils: p + n ≤ 25 (p = number of pens, n = number of pencils)
Pencils vs. pens: n ≥ (3 - p)^2 (pencils must be at least the square of 3 less than the number of pens)
Viable solutions: All solutions within this system are viable.
Explanation:First inequality: This ensures that the total number of writing utensils (pens + pencils) doesn't exceed 25, Karen's desired maximum.
Second inequality: This accounts for Karen's preference for having at least as many pencils as the square of 3 less than the number of pens. It avoids solutions with fewer pencils than the squared difference.
Viable solutions: Since both inequalities are valid and independent, any solution that satisfies both is acceptable. This leaves a broad range of viable combinations of pens and pencils, allowing Karen flexibility within her limits.
Therefore, all solutions within the system of inequalities are valid possibilities for Karen's purchase. She can choose any combination of pens and pencils as long as their total is 25 or less and the number of pencils is greater than or equal to the square of 3 less than the number of pens.
If the area of an equilateral triangle is 9√3 sq ft, how long is a side?
6 ft.
9 ft.
18 ft.
Answer:
6ft.
Step-by-step explanation:
Which expression represents the sum of (2x-5y) and (x+y)?
A. 3x-4y
B.3x-6y
C.x-4y
Dx-6y
How many distinct and real roots can an nth-degree polynomial have?
Given the form D =ABC, what is the formula for C?