Answer:4mph
5mph
Slower
Step-by-step explanation:
The average rate of change for the runner is 0.667 miles per hour².
How to calculate the average rate of change?To calculate the average rate of change, we follow the following formula:
[tex]a = \frac{v_{2} - v_{1}}{t_{2} - t_{1}}[/tex],
where a is the average rate of change, v₂ is the final speed, v₁ is the initial speed, t₂ is the time for v₂, and t₁ is the time for v₁.
How to solve the given question?In the question, we are asked to find the runner's average rate of change between the hours 0.5 and 2 with speeds of 1.5 mph and 2.5 mph.
So we take, the initial speed v₁ = 1.5 mph, the final speed v₂ = 2.5 mph, the time for v₁, t₁ = 0.5 hours, and the time for v₂, t₂ = 2 hours.
Thus, we can calculate the average rate of change a, using the formula:
[tex]a = \frac{v_{2} - v_{1}}{t_{2} - t_{1}}[/tex],
or, a = (2.5 -1.5)/(2 - 0.5) = 1/1.5 = 0.667 miles per hour².
Therefore, the average rate of change for the runner is 0.667 miles per hour².
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find the indicated angle. Round your answer to the nearest tenth. Part 2. Show work please
Answer: 5) 72.6° 6) 68.7° 7) 37.3° 8) 81.5°
Step-by-step explanation:
Law of Cosines: a² = b² + c² - 2bc · cos A
b² = a² + c² - 2ac · cos B
c² = a² + b² - 2ab · cos C
5) a = 27, b = 26, c = 20, A = ???
a² = b² + c² - 2bc · cos A
27² = 26² + 20² - 2(26)(20) · cos A
729 = 676 + 400 - 1040 cos A
729 = 1076 - 1040 cos A
-311 = -1040 cos A
[tex]\dfrac{311}{1040}=\cos A\\\\\cos^{-1}\bigg(\dfrac{311}{1040}\bigg)=A[/tex]
72.6° = A
6) a = 11, b = 13, c = 12, B = ???
b² = a² + c² - 2ac · cos B
13² = 11² + 12² - 2(11)(12) · cos B
169 = 121 + 144 - 264 cos B
169 = 265 - 264 cos B
-96 = -264 cos B
[tex]\dfrac{96}{264}=\cos B\\\\\cos^{-1}\bigg(\dfrac{96}{264}\bigg)=B[/tex]
68.7° = B
7) a = 19.2, b = 11.7, c = 16.5, B = ???
b² = a² + c² - 2ac · cos B
11.7² = 19.2² + 16.5² - 2(19.2)(16.5) · cos B
136.89 = 368.64 + 272.25 - 633.6 cos B
136.89 = 640.89 - 633.6 cos B
-504 = -633.6 cos B
[tex]\dfrac{504}{633.6}=\cos B\\\\\cos^{-1}\bigg(\dfrac{504}{633.6}\bigg)=B[/tex]
37.3° = B
8) a = 8.8, b = 12.4, c = 14.1, C = ???
c² = a² + b² - 2ab · cos C
14.1² = 8.8² + 12.4² - 2(8.8)(12.4) · cos C
198.81 = 77.44 + 153.76 - 218.24 cos C
198.81 = 231.2 - 218.24 cos C
-32.39 = -218.24 cos C
[tex]\dfrac{32.39}{218.24}=\cos C\\\\\cos^{-1}\bigg(\dfrac{32.39}{218.24}\bigg)=C[/tex]
81.5° = C
label the midpoint between 6.54 and 6.55
6.545, since it is the midpoint of 6.54 and 6.55.
Hopefully it helps!
Please mark brainliest :)
The mid - point between the numbers is 6.545.
We have two decimal numbers → 6.54 and 6.55
We have to determine their mid - point.
You have two numbers - 'x' and 'y'. Find the mid - point between these two numbers.The midpoint (n) between these two numbers will be -
[tex]$n=\frac{x+y}{2}[/tex]
According to the question, we have -
Number 1 → 6.54
Number 2 → 6.55
Assume the mid - point be n. Therefore -
n = [tex]\frac{6.54+6.55}{2}[/tex] = 6.545
Hence, the mid - point between the numbers is 6.545.
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the set of multiples of 8 which are greater than 20 but less than 40
Answer:the answer would be i do believe 32
a windshield wiper blade is 17 in Long. Calculate the area come by the blade as it rotates through an angle of 138 degrees.
Answer: 348 in²
Step-by-step explanation:
Area of a circle is πr². Area of a sector is the same formula but only for the section so you need to determine what fraction of the circle it is. You do this by dividing by 360° if degrees are provided or by 2π if radians are given.
[tex]A=\pi r^2 \bigg(\dfrac{\theta}{360^o}\bigg)[/tex]
Given: r = 17
Ф = 138°
[tex]A=\pi(17)^2\bigg(\dfrac{138^o}{360^o}\bigg)\\\\\\.\quad =289\pi \bigg(\dfrac{23}{60}\bigg)\\\\\\.\quad =\dfrac{6647\pi}{60}\pi\\\\\\.\quad =347.9\ in^2[/tex]
x+12=7 x= needing help with this
Answer:
x=−5
Step-by-step explanation:
x+12=7
Step 1: Subtract 12 from both sides.
x+12−12=7−12
x=−5
Answer:
x = -5
Step-by-step explanation:
We subtract 12 on both sides.
After that, we got x = -5
And we're done ^^
What is the answer for 10-6(5-2y)
Answer:
-20 + 12y
Step-by-step explanation:
Equation: 10 - 6(5 - 2y)
Step 1:
10 - 30 + 12y Multiply (5 - 2y) by -6 (distributive property)
Step 2:
-20 + 12y Subtract 10 by 30 (10 - 30 = -20)
Answer:
[tex]12y-20[/tex]
Step-by-step explanation:
First, we need to distribute.
[tex]= 10+(-6)(5)+(-6)(-2y)= 10+-30+12y[/tex]
Now, we need to combine these terms.
[tex]=10+-30+12y=(12y)+(10+-30)=12y+-20[/tex]
The answer is
[tex]12y-20[/tex]
David bought a baseball card for $40. the value of the card increased by 25%. what is the new value of the card?
Answer:
65 i think
Step-by-step explanation:
Answer:
65 Im preety sure
Step-by-step explanation:
5 4th power times 5 to the 2 power
Answer:
15625
Step-by-step explanation:
Answer:
(5⁴)(5²) or 15625
Step-by-step explanation:
When looking at a problem like this you need to look for keywords such as "Power" and "times"
5 to the 4th power looks like this 5⁴
And 5 to the 2nd power looks like this 5²
Making this (5⁴)(5²)
But if you want the answer after that the answer is 15625
Solve the compound inequality: 3x + 6 < 12 AND 6x + 24 < 12
Answer:
[tex]x < -2[/tex].
Step-by-step explanation:
It is given that [tex]3x + 6 < 12[/tex] and [tex]6x + 24 < 12[/tex].
For [tex]3x + 6 < 12[/tex],
[tex]3x < 12-6[/tex]
[tex]3x < 6[/tex]
Divide both sides by 2.
[tex]x < 2[/tex] ...(i)
For [tex]6x + 24 < 12[/tex],
[tex]6x< 12-24[/tex]
[tex]6x< -12[/tex]
Divide both sides by 6.
[tex]x < -2[/tex] ...(ii)
From (i) and (ii), we get
[tex]x < 2\text{ and }x<-2[/tex]
[tex]\Rightarrow x<-2[/tex]
Therefore, the required answer is [tex]x < -2[/tex].
Construct the perpendicular bisector for the segment in the following figure. What process did you use? Explain.
Answer:
Perpendicular bisector for the given segment AB is shown below.
Step-by-step explanation:
Construction steps for the perpendicular bisector for the given segment AB are:
1. Open your compass more than half of the distance between end points of the given segment, i.e., A and B.
2. Place the compass on point A and mark two arc on each side of line segment AB.
3. Place the compass on point B and mark two arc on each side of line segment AB, which intersect the previous arcs.
4. Arcs meet at two points. Mark them C and D.
5. Draw the line between C and D.
The perpendicular bisector for the given segment AB is shown below.
Think about your previous math courses. Identify one tope that you learned about which
you excelled
The answer for this question I don’t think could be answered by anyone but yourself. To help you figure this out, just simply think about all of the math courses you’ve had previous to your current course and think about which course you did best in.
A quality control manager randomly selects 40 bottles of orange juice that were filled on june 12 to assess the calibration of of the filling machine.What is the population in the study?a. bottles of orange juice produced in the plantb. the 40 bottles of orange juice produced in the plantc. the 40 bottles of orange juice produced in the plant on june 12d. bottles of orange juice produced in the plant on june 12
Answer:
Option D - bottles of orange juice produced in the plant on june 12
Step-by-step explanation:
The population describes the data from which the sample size is gotten.
Now, we are told that A quality control manager randomly selects 40 bottles of orange juice that were filled on june 12 to assess the calibration of of the filling machine.
This means that the sample size is 40 bottles. The population from which this sample is gotten is therefore:
bottles of orange juice that were filled on june 12.
Option D is correct
Find an equation of the line passing through the given points. Use function notation to write the equation. (1,-1) and (2,2) f(x) = ? PLEASE HELP!
Answer:
Good luck!
Step-by-step explanation:
Roots = 1, 2
Sum of roots = 3
Product of roots = 2
Use f(x) = ax^2 - bx + c
Therefore, f(x) = x^2 - 3x + 2
How does the area of the scale drawing where 1 centimeter represents 10 miles compare to the area of a the drawing where 1 centimeter represents 30 miles? Area if 1 cm= 10 mi: square miles Area if 1 cm = 30 mi: square miles The area would be times as great.
Answer:
100 square miles900 square miles9 times as greatStep-by-step explanation:
It seems rather obvious that ...
(1 cm)^2 ⇒ (10 mi)^2 = 100 mi^2 . . . on the first drawing
(1 cm)^2 ⇒ (30 mi)^2 = 900 mi^2 . . . on the second drawing
The area on the second drawing is 900/100 = 9 times as great.
_____
These are the areas represented by 1 square cm on the scale drawing. If the drawing is larger, then the represented area is correspondingly larger. The ratio of represented areas is still 9 times for drawings of the same size.
Determine whether the equation defines y as a function of x.
x+y=9 and x^2+y^2=1 and x=y^2
Answer:
Function: [tex]x+y=9[/tex]
Not Function: [tex]x^2+y^2=1[/tex] and [tex]x=y^2[/tex]
Step-by-step explanation:
Given
[tex]x+y=9[/tex]
[tex]x^2+y^2=1[/tex]
[tex]x=y^2[/tex]
Required
Determine if [tex]y[/tex] is a function of [tex]x[/tex]
Solving x+y=9
[tex]x+y=9[/tex]
Make y the subject of formula
[tex]y = 9 - x[/tex]
Hence; y is a function of x
Solving [tex]x^2+y^2=1[/tex]
[tex]x^2+y^2=1[/tex]
Subtract x² from both sides
[tex]y^2=1 - x^2[/tex]
Square root of both sides
[tex]y =\± \sqrt{1 - x^2}[/tex]
This implies that
[tex]y =\sqrt{1 - x^2}[/tex] or [tex]y =-\sqrt{1 - x^2}[/tex]
Because [tex]y[/tex] can be any of those two expressions, it is not a function.
Solving [tex]x=y^2[/tex]
[tex]x=y^2[/tex]
Reorder
[tex]y^2 = x[/tex]
Take square roots
[tex]y = \±\sqrt{x}[/tex]
This implies that
[tex]y = \sqrt{x}[/tex] or [tex]y = -\sqrt{x}[/tex]
Because [tex]y[/tex] can be any of those two expressions, it is not a function.
³√1,000,000 how do I solve this expression?
Answer:
100
Step-by-step explanation:
try to write it exponentially
³√10⁶
(10⁶)^⅓
(10)^6/3
(10)^2
10x10 = 100
which expression is equivalent to x^6 - 5
Answer:
there are no options given
Step-by-step explanation:
The entire collection of individuals about which information is sought is called a
Answer: u may want to look at your vocabulary
Step-by-step explanation:
anyways: The entire collection of individuals about which information is being sought is called a. population.
Apply the distributive property to the expression 3(2 + x).
The length of a rectangle is 6 meters more than three times the width. The perimeter of the rectangle is 44 meters. What are the dimensions of the rectangle?
Answer:
width=4
length=18
Step-by-step explanation:
length-6=3width
length=3width+6
also:
perimeter of the rectangle=2(length+width)
44/2=width+length
22=width+length
now put the length we found in the 1st equation, in 22=width+length
=>22=width+3width+6
22-6=4width
width=4
now do the exact same thing with one of these equations:
22=width+length
length=3width+6
I'd do it with the 1st one:
22=4+length
22-4= length
length=18
Please help. Don’t understand this math problem!!!
Answer:
1). Option (C)
2). Option (A). degree of 3 = 0
Step-by-step explanation:
A polynomial having one term is called 'Monomial' in algebraic terms.
3 is a number that is a polynomial with a single term.
Therefore, the given expression is a polynomial.
Hence Option (C) is the answer.
3 can be written as 3x⁰ (Since x⁰ = 1)
Therefore, degree of the polynomial is 0.
Option (A). degree of the polynomial = 0
Enter the answer to the problem below, using the correct number of
significant figures.
125.6.1
Answer:
126
Step-by-step explanation:
because after point no. greater than 5 will definitely
be 1 no. more than that
Help please no one helps me
Answer:
The answer would be B because Ms. Shah's class planted four more trees so you would subtract 36 by 4 to get your answer
0.456(456 repeating) as a fraction
Answer:
Try 57/125
Step-by-step explanation:
Step 1: 0.456 = 456⁄1000
Step 2: Simplify 456⁄1000 = 57⁄125
Answer:
Step 1: 0.456 = 456⁄1000
Step 2: Simplify 456⁄1000 = 57⁄125
Hope this helps! （づ￣3￣）づ╭❤～
Dimensional analysis. How many years of your life will you be sleep if you live 3.95 x 10^7 minutes and average 8 hours sleep/night.
Answer:
The total years of sleep = 25.05 years
Step-by-step explanation:
Given total time in minutes = 3.95 x 10^7
Now convert the total time in hours = (3.95 x 10^7) / 60 = 658333.333 hours
Now covert the total hours into the day. Since a day has 24 hours so divide the total hours by 24 = 658333.333 / 24 = 27430.5555 days.
A person sleeps 8 hours a day, so total hours of sleep = 8 × a number of days.
A person sleeps 8 hours a day, so total hours of sleep = 8 × 27430.5555 days.
Thus, total sleeping hours = 219444.444
Now convert it into a number of years.
Convert total hours into the day and then years.
Number of days = 219444.444 / 24 = 9143.5185 days.
Now covert the total days in to years = 9143.5185 / 365 = 25.05 years
You mix soda water, fruit punch concentrate, and ginger ale in the ratio of 1 : 2 : 5 to make fruit punch. How many pints of each ingredient should you use to make 4 gallons of fruit punch?
Please help :)
Answer:
ggtr
Step-by-step explanation:
GIMME THOSE POINTS
Tammy made a shirt using
1/4 yards of green fabric and
1/3 yards of red fabric. How many more yards of red fabric did Tammy use?
Write your answer as a fraction in simplest form.
The number of more yards of red fabric Tammy used will be 1/12 yards.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
Tammy made a shirt using 1/4 yards of green fabric and 1/3 yards of red fabric.
Then the number of more yards of red fabric Tammy used will be
⇒ 1/3 - 1/4
⇒ (4 - 3) / 12
⇒ 1 / 12
The number of more yards of red fabric Tammy used will be 1/12 yards.
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what number increase by 25 become s 150
Answer:
125
Step-by-step explanation:
n+25 = 150.
150-25= 125.
n must equal 125.
answer is 125.
Can anybody help with these two problems for me please this for algebra finding slope
Answer:
Step-by-step explanation:
1. the slope is -7/2
2. the slope is 2/3
y = mx + b
m is the slope
Slope is the number before the x so
1. -7/2
2. 2/3
Find 7/8 divided by 1/3