2.) The information in the table below shows the
distance a car traveled during a number of hours.
Hours (h)
Miles (m)
1
45
2
90
3
135
4
180
Write an equation using the variables h and m that
represents the information in the table
Answers
Answer:
m = 45h
Step-by-step explanation:
Calculate the difference in y-values (miles):
[tex]45 \underset{+45}{\longrightarrow} 90\underset{+45}{\longrightarrow} 135\underset{+45}{\longrightarrow} 180[/tex]
As the number of miles increases by the same amount for every increase of an hour, the equation is linear.
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Given variables:
x = Hours (h)y = Miles (m)As the number of miles increases by 45 miles for each increase of an hour, the slope of the linear equation is 45:
[tex]\implies m=45h+b[/tex]
To find b, substitute one of the ordered pairs into the equation and solve for b:
[tex]\implies 45=45(1)+b[/tex]
[tex]\implies 45=45+b[/tex]
[tex]\implies b=45-45[/tex]
[tex]\implies b=0[/tex]
Therefore, the equation using the variables h and m that represents the information in the given table is:
[tex]\boxed{m=45h}[/tex]
Related Questions
A science teacher prepares an activity for her class. She cuts 3/4 yard of ribbon into 6 pieces of equal size. Write and solve an equation to find the length of each piece of ribbon.
Answers
The equation that represents the given situation will be (x=3/4÷6) and the length of each piece of ribbon will be 1/8 yards.
What is an equation?The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions. An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. As in 3x + 5 = 15, for example. There are many different types of equations, including linear, quadratic, cubic, and others. The three primary forms of linear equations are point-slope, standard, and slope-intercept.So, the equation that recipients the given situation:
The ribbon is 3/4 yards.Cuts into 6 equal pieces.Then, the equation will be:
x = 3/4 ÷ 6Now, calculate the equation for x as follows:
x = 3/4 ÷ 6x = 3/4 × 1/6x = 1/4 × 1/2x = 1/8
Therefore, the equation that represents the given situation will be (x=3/4÷6) and the length of each piece of ribbon will be 1/8 yard.
Know more about equations here:
https://brainly.com/question/28937794
#SPJ1
3. (02.02 MC)
The beginning mean bi-weekly wage in a certain industry is $2,498.00. If the mean bi-weekly wage grows by 3.25%, what is the new mean annual wage? (4 points)
$62,903.63
$64,948.00
$67,058.81
$69,079.13
Answers
If the mean bi-weekly wage grows by 3.25%, the new mean annual wage is: C. $67,058.81.
What is annual wage?Annual wage can simply be defined as the amount a person is paid annually as wages . Wages can be paid daily or weekly.
Using this formula to find the new mean annual wage
New mean annual wage = [Beginning mean bi-weekly wage × ( 1+ mean bi-weekly wage ) ]× Number of weeks per year /2
Let plug in the formula
New mean annual wage = [$2,498.00 × (1+ 0.0325)] × 52 weeks /2
New mean annual wage = [$2,498.00 × (1.0325)] × 26 weeks
New mean annual wage = $2,579.185 × 26 weeks
New mean annual wage = $67,058.81
Therefore the correct option is C.
Learn more about New mean annual wage here:https://brainly.com/question/16823998
#SPJ1
Can someone help me on this I’m confused
Answers
Step-by-step explanation:
if the goal is to have both numbers with denominator 6, then the first one is totally simple :
3 1/6 = 3 1/6
what else could it be ... ?
and the second, well, how many thirds are in a whole ?
right, 3, that's why we call them "thirds".
how many 6ths are in a whole ?
right, 6.
do you notice something ? it is easy to get from 3 to 6 by multiplying 3 by 2.
in order to keep the overall value of a fraction unchanged, when we multiply one part of the fraction by something we need to multiply the other part by the same number too.
so,
5 2/3 = 5 2/2×2/3 = 5 4/6
in short : yes, every third contains 2 6ths.
therefore, 2/3 = 4/6
the basketball game had 600 people in attendance if the ratio of hawk fans to cyclone fans is 2:10 how many more cyclone fans were there
Answers
Variables:
x: hawk fans
y: cyclone fans
The basketball game had 600 people in attendance means:
x + y = 600
The ratio of hawk fans to cyclone fans is 2:10 means
[tex]\begin{gathered} \frac{x}{y}=\frac{2}{10} \\ 10x=2y \\ \frac{10x}{2}=y \\ 5x=y \end{gathered}[/tex]Substituting the last equation into the first equation, we get:
x + 5x = 600
6x = 600
x = 600/6
x = 100
And the value of y is:
y = 5*100
y = 500
There were 500 - 100 = 400 more cyclone fans
The circumference of a circle is 24π in. What is the area, in square inches? Express your answer in terms of π.
Answers
Given
[tex]circumference\text{ of circle = 24}\pi\text{ in}[/tex]Recall that the formula for the circumference of a circle C is:
[tex]C\text{ = 2}\pi r[/tex]Using the formula, we can find the radius of the circle as shown:
[tex]\begin{gathered} 2\pi r\text{ = 24}\pi \\ Divide\text{ both sides by 2}\pi \\ r\text{ = }\frac{24\pi}{2\pi} \\ r\text{ = 12 in} \end{gathered}[/tex]The area A of a circle can be found using the formula:
[tex]A\text{ = }\pi r^2[/tex]Substituting the value obtained:
[tex]\begin{gathered} A\text{ = }\pi\text{ }\times\text{ 12}^2 \\ =\text{ 144}\pi\text{ in}^2 \end{gathered}[/tex]The area is 144π square in
Find the measure of the angle between the two vectors.
7) u = (6,-2)
v = (8,-8)
9) u =(2, 6)
v = (-5, -8)
8) u = (-2, 3)
v = (4, -6)
10) u = (-9, 4)
v = (-7, -1)
Answers
Answer:
780
Step-by-step explanation:
I need help with this and I need it explained to me how to do it
Answers
Answer:
14.42 feet
Explanation:
In the figure, we can see that the pole form a right triangle with legs equal to 12 feet and 8 feet, where 8 ft is half the wide or 16 ft/2 = 8 ft.
Then, by the Pythagorean theorem, the length of the slanted pole square is equal to the sum of the square of the legs, so
[tex]x^2=12^2+8^2[/tex]Where x is the minimum length of the slanted pole. Therefore, x is equal to
[tex]\begin{gathered} x^2=144+64 \\ x^2=208 \\ x=\sqrt[]{208} \\ x=14.42 \end{gathered}[/tex]Therefore, the answer is 14.42 feet.
Ruben bought 6 comic books for $21 Each comic book was the same price.
What was the cost for 1 comic book?
Answers
-3, -6, -12, -24,.... Next 3 2, 4, 8-12, -6, -3-48, -96, -192 -36, -48, -60
Answers
We can see that the ratio between consecutive numbers is
[tex]\frac{-6}{-3}=\frac{-12}{-6}=\frac{-24}{-12}=2[/tex]this means that, the nex number is
[tex]\begin{gathered} -24\cdot2=-48 \\ \text{and next} \\ -48\cdot2=-96 \\ \text{and finally} \\ -96\cdot2=-192 \end{gathered}[/tex]Hence, the answer is -48, -96, -192
х1451°Find the value of x. Round to the nearest tenth.x=
Answers
To solve this question, we employ the sine relation;
[tex]\begin{gathered} \frac{14}{x}=\sin 51 \\ \end{gathered}[/tex]Rearranging the equation, we obtain ;
[tex]x=\frac{14}{\sin 51}=20.88\approx20.9[/tex]Therefore, x = 20.9
Find the distance between the two points.|(1,4)✓ [?](-2,-3)Enter the number thatgoes beneath theradical symbol.Enter
Answers
The distance between two points is given as;
[tex]D=\sqrt[]{(y_2-y_{1_{}})^2+(x_2-x_1)^2}[/tex][tex]\begin{gathered} \text{Where x}_1=-2 \\ y_1=-3 \\ x_2=1 \\ y_2=4 \end{gathered}[/tex][tex]\begin{gathered} D=\sqrt[]{(4-(-3)^2+(1-(-2)^2} \\ D=\sqrt[]{7^2+3^2} \\ D=\sqrt[]{49+9} \\ D=\sqrt[]{58} \end{gathered}[/tex]The number beneath the radical symbol is 58.
1/3b+11/18 when b=1/6
Answers
To answer this question, we have that the expression is:
[tex]\frac{1}{3}b+\frac{1}{18}[/tex]Answer:
Solve for b by simplifying both sides of the equation, then isolating the variable. Exact Form:
b = 3/17 Decimal Form: b=0.17647058
Step-by-step explanation:
Which number lines have a point that is equal to point
P? Check all that apply.
←
H
-
-60
-60
-60
-60
0
0
0
0
0
Answers
Answer:
Step-by-step explanation:
-60 -60 -60 0 0
14 08.08LCChoose the brand of chips with the lowest price per ounce.Brand A 20 ounces for $2.50Brand 6 32 ounces for $3.25 (1 point)O Brand ABrandBoth brands have the same price per ounce.Not enough information is given
Answers
Brand 6
1) In this problem, we need to find the unit rate. So let's do it and then compare for both brands
2) Brand A
[tex]\begin{gathered} 20oz----2.5 \\ 1oz-----x \\ 20x=2.5 \\ \frac{20x}{20}=\frac{2.5}{20} \\ x=\$0.125 \end{gathered}[/tex]So for Brand A, 1 oz is approximately 13 cents ( rounding up to the nearest hundredth)
3) Brand 6
We can write out another proportion:
[tex]\begin{gathered} 32oz----3.25 \\ 1oz----y \\ 32y=3.25 \\ \frac{32y}{32}=\frac{3.25}{32} \\ y=\$0.101 \end{gathered}[/tex]So brand 6, 1 oz is approximately 10 cents.
Which of the following notations correctly describe the end behavior of the polynomial graph below?
Answers
The end behaviour of the polynomial graph is (b) x ⇒ +∝, f(x) ⇒ -∝ and x ⇒ -∝, f(x) ⇒ -∝
How to determine the end behaviour of the polynomial graph?The polynomial graph represents the given parameter
This polynomial graph is a quadratic function opened downwards
Polynomial function of this form have the following end behaviour:
As x increases, f(x) decreasesAs x decreases, f(x) decreasesThis is represented as
x ⇒ +∝, f(x) ⇒ -∝ and x ⇒ -∝, f(x) ⇒ -∝
Hence, the end behaviour is (b)
Read more about end behaviour at
https://brainly.com/question/1365136
#SPJ1
Combined gas law
Please reply with the steps, I'm confused
Answers
Answer:
V₂ = 1.0 L
Step-by-step explanation:
Combined Gas Law
[tex]\sf \dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}[/tex]
where:
P₁ is the initial pressure.V₁ is the initial volume.T₁ is the initial temperature.P₂ is the final pressure.V₂ is the final volume.T₂ is the final temperature.Temperature must be in kelvins (K).
To convert Celsius to kelvins, add 273.15.
Volume can be in any unit.
Given values:
P₁ = 5 atmV₁ = 1 LT₁ = 300 KP₂ = 10 atmT₂ = 600 KRearrange the equation to isolate V₂:
[tex]\implies \sf V_2=\dfrac{P_1V_1T_2}{P_2T_1}[/tex]
Substitute the given values into the equation:
[tex]\sf \implies V_2=\dfrac{5 \cdot 1 \cdot 600}{10 \cdot 300}[/tex]
[tex]\sf \implies V_2=\dfrac{3000}{3000}[/tex]
[tex]\sf \implies V_2=1.0\;L[/tex]
Therefore, the volume of V₂ is 1.0 L.
Learn more about the Combined Gas Law here:
https://brainly.com/question/28143218
guys can u help me with this question, please
Answers
The cross marked at the points (-2.5 , -5) and (0 , -1.5) is shown below .
The x and y coordinate helps in identifying a point in the coordinate axis and it is written as a ordered pair (x,y) .
where x represents the position of point with reference to the x-axis
and y represents the position of point with reference to the y axis .
In the question ,
points are given , we have to plot them and mark a cross .
Part(a)
point is (-2.5 , -5)
So , the x coordinate is -2.5
means the point is 2.5 units left from the origin ,
and y coordinate is -5 .
means the point is 2.5 units down from the origin .
the cross mark on the point is shown below .
Part(b)
point is (0 , -1.5)
So , the x coordinate is -2.5
means the point is 0 units units from the origin ,
and y coordinate is -1.5 ,
means the point is 1.5 units down from the origin .
the cross mark on the point is shown below .
Therefore , The cross marked at the points (-2.5 , -5) and (0 , -1.5) is shown below .
Learn more about Graphs here
https://brainly.com/question/4619801
#SPJ1
I need help with this check the picture
Answers
The numbers 7 in the domain and 10 in the range don't belong there.
Describe the domain and range of a function.The domain is the set of values over which the provided function is defined. The range is the set of all values that the function that is provided can return.
How are intervals in numbers understood?[a,b] refers to all values between a and b as well as a and b themselves.
With the exception of b, all values between a and b are referred to as (a,b).
We cannot write about them since we cannot include infinity or negative infinity since they are symbols for arbitrary enormous or tiny numbers, respectively.
Another thing to keep in mind is that when we plot functions, the inputs are typically on the x-axis and the outputs are typically on the vertical axis (y-axis).
Given : (2,7). (8, 12). (5,9). (10.15)
Domain: The initial value of numbers will always apply; 2, 8, 5, 10
Range: Numbers will always have a second value; 7, 12, 9, 15.
What you have here is :
Domain: (2,5, 7, 8, 10)
Range: (7.9. 10. 12. 15)
The problem is that 10 is in the range but 7 is in the domain. They shouldn't be there, those two. There is also an additional number there that you have. Only 4 digits should be in the Domain and Range. Given that there are four sets or pairs of values.
To know more about the domain and range, visit:
https://brainly.com/question/10197594
#SPJ1
help meeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
Diagonal = 9m
Step-by-step explanation:
area of a rectangle=L×W.-----------(I)
L=2W---------------(ii)
from (1)
32=2W×W
32=2W²
W²=32/2
W²=16
W=√16
W=4
from (ii)
length(L)=2W=2(4)=8m
Width(W)=4m
ii)Diagonal of a rectangle involves the use of Pythagoras theorem
Hyp²=opp²+Adj²
Hyp²=8²+4²
Hyp²=64+16
Hyp²=80
Hyp=√80
Hyp=8.94427191
Hyp=9m
:-The diagonal =9m
the lenght, l , of a rectangle is twice its width, w and the premiter is p
which mathematical relationship(s) this senerio
select all that apply
A L=W-P
B2L=W
C 2W=L
D 2(L+2W)=P
E 2(L+W)=P
F p=6W
Answers
The perimeter for the length L and width W that is 2L will be 2W=L as the definition of perimeter says, "The total length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges".
What is perimeter?The total length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. The perimeter of a shape is the space surrounding its edge. A closed path that encompasses, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. We must add up the lengths of the rectangle's four sides in order to determine its perimeter. Since there are two of each side length, it is easy to accomplish this by simply adding the length and width and multiplying the result by two. The perimeter formula is defined as perimeter=2(length + width).
Here,
Perimeter=2(length + width)
Length=L
Width=W=2L
2(L+W)=P
In accordance with the definition of perimeter, the perimeter for a length L and a width W that is equal to 2L will be 2W=L "In geometry, a shape's perimeter is referred to as its overall length. The perimeter of a shape is determined by adding all of its sides' and edges' lengths ".
To know more about perimeter,
https://brainly.com/question/6465134?referrer=searchResults
#SPJ1
The rectangle below has an perimeter of 50 units.2x - 2What is the length, in units, of the shorter side?
Answers
The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(length + width)
From the diagram,
length = 2x - 2
width = x
Perimeter = 50
Thus,
50 = 2(2x - 2 + x)
Dividing both sides of the equation by 2, it becomes
50/2 = 2x + x - 2
25 = 3x - 2
3x = 25 + 2 = 27
x = 27/3
x = 9
The length of the shorter side is 9
There are 348 identical plastic chips numbered 1 through 348 in a box. What is the probability of reaching into the box and randomly drawing a chip number that is smaller than 213? Express your answer as a simplified fraction or a decimal rounded to four decimal places
Answers
We have to find the probability of randomly drawing a chip number that is smaller than 213.
As the chips are numbered from 1 to 348,this probability will be equal to the proportion of chips that have a number that is less than 213.
We have 212 chips in the bag that have a number less than 213, so we can calculate the probability P as:
[tex]P=\frac{X}{N}=\frac{212}{348}=\frac{53}{87}\approx0.6092[/tex]Answer: the probability is 53/87 or approximately 0.6092.
can someone help me with this assignment
Answers
Answer:
6
Step-by-step explanation:
On the coordinate plane, it shows that the y axis is 6. Therefore, (16, 6)
Answer:
5
Step-by-step explanation:
If cos B = 7/8, then what is the positive value of tan 1/2 B, in simplest radical formwith a rational denominator?
Answers
Let us use the rule of the double of the angle
Since
[tex]\cos B=2\cos ^2\frac{B}{2}-1[/tex]Substitute cos B by 7/8
[tex]\frac{7}{8}=2\cos ^2\frac{B}{2}-1[/tex]Add 1 to both sides
[tex]\begin{gathered} \frac{7}{8}+1=2\cos ^2\frac{B}{2}-1+1 \\ \frac{15}{8}=2\cos ^2\frac{B}{2} \end{gathered}[/tex]Divide both sides by 2
[tex]\begin{gathered} \frac{\frac{15}{8}}{2}=\frac{2\cos ^2\frac{B}{2}}{2} \\ \frac{15}{16}=\cos ^2\frac{B}{2} \end{gathered}[/tex]Take a square root for both sides
[tex]\begin{gathered} \sqrt[]{\frac{15}{16}}=\cos \frac{B}{2} \\ \cos \frac{B}{2}=\frac{\sqrt[]{15}}{4} \end{gathered}[/tex]let us find sin B
Since
[tex]\sin ^2\frac{B}{2}+\cos ^2\frac{B}{2}=1[/tex]Then
[tex]\sin ^2\frac{B}{2}+\frac{15}{16}=1[/tex]Subtract 15/16 from both sides
[tex]\begin{gathered} \sin ^2\frac{B}{2}+\frac{15}{16}-\frac{15}{16}=1-\frac{15}{16} \\ \sin ^2\frac{B}{2}=\frac{1}{16} \end{gathered}[/tex]Take a square root for both sides
[tex]\begin{gathered} \sin \frac{B}{2}=\sqrt[]{\frac{1}{16}} \\ \sin \frac{B}{2}=\frac{1}{4} \end{gathered}[/tex]Since
[tex]\tan \frac{B}{2}=\frac{\sin \frac{B}{2}}{\cos \frac{B}{2}}[/tex]Then
[tex]\begin{gathered} \tan \frac{B}{2}=\frac{\frac{1}{4}}{\frac{\sqrt[]{15}}{4}} \\ \tan \frac{B}{2}=\frac{1}{\sqrt[]{15}} \end{gathered}[/tex]The value of tan(1/2 B) is
[tex]\frac{1}{\sqrt[]{15}}\times\frac{\sqrt[]{15}}{\sqrt[]{15}}=\frac{\sqrt[]{15}}{15}[/tex]26,862 divided by 407
Answers
Answer:
66
Step-by-step explanation:
it is 66
graph the function, not by plotting points, but by starting from the graph of y=e^x in the figure below.
the function is: y= e^-x -1
?? I need help finding the asymptote??
Answers
The given function has a horizontal asymptote and the equation of the horizontal asymptote is y = -1.
What is an asymptote of a function?
An asymptote is a line that a function's graph approaches as x or y approaches positive or negative infinity. Asymptotes are classified into three types: vertical, horizontal, and oblique. That is, the function approaches positive or negative infinity as approached from either the positive or negative side.
The given function is [tex]y=e^{-x}-1[/tex]
Exponential functions have a horizontal asymptote. The equation of the horizontal asymptote is y = -1
Horizontal Asymptote: y = -1.
The graph of the function [tex]y=e^{-x}-1[/tex] can be drawn as
Hence, the given function has a horizontal asymptote and the equation of the horizontal asymptote is y = -1.
To learn more about Asymptotes of a function, visit:
https://brainly.com/question/4138300
#SPJ1
TIME REMAINING56:5412.Which points are reflections of each other across both axes?Ty24-2(-2.8) and (2. -8)(-7 -1) and (-7. 1)(5.-6) and (-5, -6)NelSubSave and ExitMark this and return
Answers
a point is reflected against both axes when the two signs of the point are opposite
for example the reflexion against both axes for the point(-2,8) is (2,-8)
among the options there is none that meets this condition
7/10 3/10 solve complex fraction
Answers
The value of the complex fraction 7/10/3/10 is
2 1/3
What is a complex fraction?A fraction is made up of two parts, a numerator and a denominator; the number above the line is the numerator and the number below the line is the denominator. The line or slash in that separates the numerator and the denominator in a fraction represents division.
A complex fraction can be defined as a fraction in which the denominator and numerator or both contain fractions. For example( 5/2)/(6/4).
Therefore the fraction (7/10)/(3/10) can be simplified as 7/10÷3/10= 7/10×10/3 = 7/3= 2 1/3
Therefore the simplified value of the complex fraction is 2 1/3.
learn more about complex fraction from
https://brainly.com/question/28702241
#SPJ1
Jan takes her three children and two neighbor's childrento a matinee. All of the children are under age 13. Writan expression for the total cost of admission. Howmuch in all did Jan pay for admission?(Matinee: 3$)
Answers
There are 6 people going to the movie
Jan, her 3 children, 2 neighbor children
(1+3+2)
Each costs 3 dollars to get in
Total cost = number of people * cost
Total cost = (1+3+2) * 3
= 6*3
= 18
Solve the system of linear equations using matrices.4y-z=-5X+ 5y +z=-32x-y + 3z =13
Answers
The given system expressed as a matrix would be
0 4 -1 -5
1 5 1 -3
2 -1 3 13
To solve this, first, we have to change the first row for the second
1 5 1 -3
0 4 -1 -5
2 -1 3 13
Now, we multiply the first row by 2, then subtract it from the third row.
1 5 1 -3
0 4 -1 -5
0 -11 1 19
Then, we multiple the second row with -11/4 to subtract it from the third row.
1 5 1 -3
0 4 -1 -5
0 0 -7/4 21/4
The resulting system would be
[tex]\mleft\{\begin{aligned}x+5y+z=-3 \\ 4y-z=-5 \\ -\frac{7}{4}z=\frac{21}{4}\end{aligned}\mright.[/tex]We solve for z
[tex]\begin{gathered} \frac{-7}{4}z=\frac{21}{4} \\ z=\frac{21}{-7}=-3 \end{gathered}[/tex]Therefore, z is equal to -3.
We use z to find y in the second equation.
[tex]\begin{gathered} 4y-(-3)=-5 \\ 4y+3=-5 \\ 4y=-5-3 \\ 4y=-8 \\ y=\frac{-8}{4}=-2 \end{gathered}[/tex]Therefore, y is equal to -2.
We use y and z to find x in the first equation.
[tex]\begin{gathered} x+5(-2)+(-3)=-3 \\ x-10-3=-3 \\ x=-3+10+3=10 \end{gathered}[/tex]Therefore, x is equal to 10.