Answer:
(a) [tex]y = 0.025x+15[/tex]
(b) 18.5 minutes
(c) 450.4 minutes
Step-by-step explanation:
Given
[tex]290\ minutes = \$22.25[/tex]
[tex]360\ minutes = \$24.00[/tex]
Solving (a): Determine the linear equation
First, we need to calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where
[tex](x_1,y_1) = (290,22.25)[/tex]
[tex](x_2,y_2) = (360,24.00)[/tex]
So, we have:
[tex]m = \frac{24.00 - 22.25}{360 - 290}[/tex]
[tex]m = \frac{1.75}{70}[/tex]
Multiply through by 100
[tex]m = \frac{1.75 * 100}{70 * 100}[/tex]
[tex]m = \frac{175}{7000}[/tex]
Next, is to calculate the equation of the line using:
[tex]y - y_1 = m(x - x_1)[/tex]
Recall that:
[tex](x_1,y_1) = (290,22.25)[/tex]
[tex]m = \frac{175}{7000}[/tex]
[tex]y - 22.25 = \frac{175}{7000}(x - 290)[/tex]
[tex]y - 22.25 = \frac{175x}{7000} - \frac{175}{7000} * 290[/tex]
[tex]y - 22.25 = \frac{175x}{7000} - \frac{50750}{7000}[/tex]
Add 22.25 to both sides
[tex]y = \frac{175x}{7000} - \frac{5075}{700} + 22.25[/tex]
[tex]y = \frac{175x}{7000} + \frac{-5075 + 15575}{700}[/tex]
[tex]y = \frac{175x}{7000} + \frac{10500}{700}[/tex]
[tex]y = 0.025x+15[/tex]
(b) Solve for y when x = 140
[tex]y = 0.025x+15[/tex]
Substitute 140 for x
[tex]y = 0.025 * 140 + 15[/tex]
[tex]y = 3.5 + 15[/tex]
[tex]y = 18.5[/tex]
(c) Solve for x when y = 26.25
[tex]y = 0.025x+15[/tex]
Substitute 26.25 for y
[tex]26.25 = 0.025x + 15[/tex]
Solve for 0.025x
[tex]0.025x = 26.26 - 15[/tex]
[tex]0.025x = 11.26[/tex]
Solve for x
[tex]x = 11.26/0.025[/tex]
[tex]x = 450.4\ minutes[/tex]
Use a model to divide. 4/5 divided by 6 Express the answer in simplest terms. 2/30 2/15 5/30 1/15
Answer:
2/30 or 5/30
Step-by-step explanation:
The simplest form of the expression is 1/6.
We have,
The concept used to solve the division problem 4/5 divided by 6 is the idea of dividing a fraction by a whole number.
To divide a fraction by a whole number, we can interpret it as finding a fraction of a fraction.
In this case, we want to find 4/5 divided by 6, which can be understood as dividing the fraction 4/5 into 6 equal parts.
To use a model to divide 4/5 by 6, we can represent 4/5 as a fraction bar and divide it into 6 equal parts.
If we divide the fraction 4/5 into 6 equal parts, each part would represent 1/6 of the original fraction.
Therefore,
The simplest form of the expression is 1/6.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ6
Can someone help due in an hour
figure 1 is 130 degrees because a whole line is 180 degrees subtract the 50 boom.
figure 2 is a bit more difficult all together it is 360 y is 30 degrees due to vertical angles and x and z are 150 degrees because 360-60=300 divided by 2 equals 150
figure 3 x is 135 due to vertical angles which makes w and y are 45 because 360-270 equals 90 divide by 2 equals 45
figure 4 is 106 because you add 172 and 82 and then subtract that by 360 there you go. hope this helps you out
1 Matt runs in the park every day at the average rate of c meters per minute.
Today Matt ran at triple his usual speed. What was his speed today?
2 Matt runs in the park every day at the average rate of c meters per minute.
If Matt runs triple his regular speed for 20 minutes, what distance would he cover?
3Matt runs in the park every day at the average rate of c meters per minute.
During these 20 minutes, Matt covers 2400 meters. Use this information to write an equation.
Answer:
The answer for the first one is 3c
Step-by-step explanation:
Because it is 3·c
Answer:
1. 3c
2. 3c·20
3. 3c·20=2400
Step-by-step explanation:
Here! Hope I could help :)
f(x) = 2x + 3 and g(x) = –x^2 + 5, find f(1) and g(1)
Answer: dont you need like a picture or sum to find g1 or something?
Step-by-step explanation:
Answer:
Step-by-step explanation:
f(1)= 2(1)+3= 2 + 3 =5
g(1)= -1^2 + 5 = -1 + 5 = 4
i need help on a math question pls help thank u
WOTH 50 POINTS
Answer:
C. 7 ft
Step-by-step explanation:
The radius and height of the cone are the legs of a right triangle. The slant height is the hypotenuse.
24² + h² = 25²
576 + h² = 625
h² = 49
h = 7
Answer: C. 7 ft
Q: use the number lines to write 0.9 as a binary fraction to the nearest sixteenth
Answer:
12
Step-by-step explanation:
A decimal is never a rational number
True or False
Answer: False
Step-by-step explanation: this is false because Rational Numbers: Any number that can be written in fraction form is a rational number. This includes integers, terminating decimals, and repeating decimals as well as fractions. ... So, any terminating decimal is a rational number.
ANSWER CORRECTLY FOR 25 POINTS
Fill in the table using this function rule.
y=2x-1
x | y
6 |
8 |
9 |
10 |
FIND 'y's VALUE FOR ALL LISTED
Answer:
(6, 11)(8, 15)(9, 17)(10, 19)
Step-by-step explanation:
ohhhh
sooo
y = 2(6) - 1
y = 12 - 1
y = 11
(6, 11)
y = 2(8) - 1
y = 16 - 1
y = 15
(8, 15)
y = 2(9) - 1
y = 18 - 1
y = 17
(9, 17)
y = 2(10) - 1
y = 20 - 1
y = 19
(10, 19)
A company has 15 employees with a salary of $22,000, 12 employees with a salary of $23,100, 16 employees with a salary of $26,300, 4 employees with a salary of $30,100, 4 employees with a salary of $39,000, and 1 employee with a salary of $148,500.
Find the mean salary for the employees
The mean is $5,563.56
What is Arithmetic mean?
Arithmetic mean is also called average it is calculated by summing the values then dividing by the number of sets
(22,000 + 23,100 + 26,300 + 30,100 + 39,000 + 148,500) / (15 + 12 + 16 + 4 + 4 + 1)
= 289,300 / 52
= 5563.46
Read more on mean here: https://brainly.com/question/1136789
Scarlett and her friends are going into a movie theater. How much would it cost to
buy 5 drinks and 4 candies if each drink costs $4.50 and each candy costs $5.00?
How much would it cost to buy 5 drinks and 4 candies if each drink cost $d and each
candy cost $c?
Answer:
5 drinks: $25.00 4 candies: $18.00 Total: $43.00
inn equation form: $5d+$4.5c=?
Step-by-step explanation:
5*5=25
4.5*4=18
25+18=43
Answer:
answer is on screenshot pls like so i could get points lol
Step-by-step explanation:
If the third term of geometric series is 3, find the product of its first five terms.
Answer:
Solution
Third term of G.P.=ar2=3
General term =arn−1
Product of first five terms =a5⋅r0+1+2+3+4
=a5r10=(ar2)5
=(3)5
=243.
G=-4. Quickly plzzzz. Evaluate expression :)
Answer:
11
Step-by-step explanation:
16 - | g+9|
Let g = -4
16 - | -4+9|
Evaluate inside the absolute value
16 - | 5|
The absolute value of 5 is 5
16 -5
11
One of the original Seven Wonders of the World, the Great Pyramid of Cheops was built about 2580 BC. Its original height was 480 feet 11 inches, but owing to the loss of it's topmost stones, it is now shorter. Find the current height of the Great Pyramid using the information given in the illustration.
This value is approximate.
========================================================
Explanation:
The entire paragraph of text given to you is not needed. It's interesting that the height used to be 480 ft 11 in, but we don't use that anywhere in our calculations to get the current shorter height. Instead we rely solely on the diagram.
Refer to the diagrams I have posted below. Figure 1 is the same diagram more or less, but I've added the variables x and h.
x = horizontal distance from the center of the pyramid to the left most part of the pyramid.h = current height of the pyramidBoth h and x are in feet.
I've also added the point labels A through E.
I've split figure 1 into two pieces. Figure 2 focuses on triangle ADE and figure 3 focuses on triangle BDE.
---------------------
Let's put our attention on triangle ADE in figure 2.
Set up the tangent ratio shown below and solve for h.
[tex]\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}\\\\\tan(\text{A}) = \frac{\text{DE}}{\text{AD}}\\\\\tan(40.3) = \frac{h}{x+200}\\\\h = (x+200)\tan(40.3)\\\\[/tex]
Now move onto triangle BDE in figure 3.
Set up the tangent ratio and apply substitution.
[tex]\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}\\\\\tan(\text{B}) = \frac{\text{DE}}{\text{BD}}\\\\\tan(46.27) = \frac{h}{x+100}\\\\\tan(46.27) = \frac{(x+200)\tan(40.3)}{x+100}\\\\[/tex]
---------------------
Let's solve for x.
[tex]\tan(46.27) = \frac{(x+200)\tan(40.3)}{x+100}\\\\(x+100)\tan(46.27) = (x+200)\tan(40.3)\\\\x\tan(46.27)+100\tan(46.27) = x\tan(40.3)+200\tan(40.3)\\\\[/tex]
[tex]x\tan(46.27)-x\tan(40.3)=200\tan(40.3)-100\tan(46.27)\\\\x(\tan(46.27)-\tan(40.3))=200\tan(40.3)-100\tan(46.27)\\\\x=\frac{200\tan(40.3)-100\tan(46.27)}{\tan(46.27)-\tan(40.3)}\\\\x\approx 329.87238475414\\\\[/tex]
Use this to find h.
[tex]h = (x+200)\tan(40.3)\\\\h \approx (329.87238475414+200)\tan(40.3)\\\\h \approx 449.364461010933\\\\h\approx 449.364[/tex]
The height of the pyramid is currently 449.364 feet approximately.
---------------------
Lastly we'll convert to feet,inches format since the "480 ft 11 in" figure is in that format.
h = 449.364 ft
h = 449 ft + 0.364 ft
h = 449 ft + (0.364 ft)*(12 in/1 ft)
h = 449 ft + 4.368 in
h = 449 ft + 4 in
h = 449 feet, 4 inches
what is the measure of
Answer:
56
Step-by-step explanation:
Like I said, all the angles of a triangle ALWAYS add up to 180 degrees (which is a straight angle). It might seem like they don't give angle A for us, but we can see that angle A is a right angle, which is 90 degrees. So, we can add 90 and 34 degrees, and then subtract that from 180.
90 + 34 = 124
180 - 124 = 56
I hope this helps! Have a lovely day! :)
Help asap please!!!
The temperature in Smallville is 30°F one morning. It rises 10 over 5 hours. The equation y = 2x+ 30 was given to represent this situation.
Which of the following tables demonstrates the relationship between the time and temperature in Smallville?
A x 0 1 2 . y 0 2 4
B x 0 1 2 . y 30 32 34
C x 30 35 40 . y 0 1 2
D x 30 32 34 . y 0 1 2
Considering the given linear function, it is found that table B represents the situation.
What is a linear function?A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0.In this problem, the function is given by:
y = 2x + 30.
Hence, the y-intercept is of b = 30, that is, when x = 0, y = 30, and the slope of m = 2 means that when x increases by 1, y increases by 2, hence table B is the answer for this question.
More can be learned about linear functions at https://brainly.com/question/24808124
On the third day, Anna and Tamara traveled well into the night and double their travel time. On the fourth day, Anna and Tamara lost 4 hours because Anna got sick. Write an algebraic expression that represents how many hours Anna and Tamara travel the last two days.
9514 1404 393
Answer:
3t -4
Step-by-step explanation:
If t represents their normal travel time (in hours), Anna and Tamara traveled 2t on the third day, and t-4 on the fourth day.
The number of hour traveled in the last two days (day 3 and day 4) are ...
2t +(t-4) = 3t-4
Please Help! I will give brainlest! It locks soon!
Answer:
Step-by-step explanation:
2cos²θ - 1 - cosθ = 0
(2cosθ + 1)(cosθ - 1) = 0
cosθ = -1/2, θ = 2π/3, 4π/3
cosθ = 1, θ = 0
so answer is 3rd choice
Angie opened a bank account She deposited $225 each
month for 4 months. Her bank charged her $5 each month
to use the account
How much money is in Angie's account after 4 months?
A $880
B. $920
C. $205
D. $220
Answer:
A $880
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
Which of the following is the best definition of the probability of a certain
outcome of an event?
Answer:
Sorry but wheres the rest?
Graph line y=-2x+5 with no x
Answer:
Step by Step Solution
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
y-(-2*x+5)=0
STEP
1
:
Equation of a Straight Line
1.1 Solve y+2x-5 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line y+2x-5 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 5/1 so this line "cuts" the y axis at y= 5.00000
y-intercept = 5/1 = 5.00000
Calculate the X-Intercept :
When y = 0 the value of x is 5/2 Our line therefore "cuts" the x axis at x= 2.50000
x-intercept = 5/2 = 2.50000
Calculate the Slope :
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 5.000 and for x=2.000, the value of y is 1.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 1.000 - 5.000 = -4.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = -4.000/2.000 = -2.000
Geometric figure: Straight Line
Slope = -4.000/2.000 = -2.000
x-intercept = 5/2 = 2.50000
y-intercept = 5/1 = 5.00000
How much sand will it take to fill a 8 by 9 square pyramid
A cylinder has a height of 3 centimeters and a radius of 4 centimeters. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
Answer:
151 Centimeters if using 3 centimeters or 158 Centimeters if using 3.14 Centimeters
Step-by-step explanation:
Sorry if this isn't what you asked for, but i tried my best ^^
X 3 4 x is 1/2 idk it .. if you can help thank you so much it’s math .
Answer:
1/32
Step-by-step explanation:
(1/2)^3 /4= (1/8)/ 4= 1/8 x 1/4= 1/32
e) A parent's age is 11 more than twice their child's age. The parent is 39 years old.
What equation represents the situation?
Answer:
done
Step-by-step explanation:
2x+11=39
A line passes through the points (-3, 7) and (6, 4). Which shows the graph of this line?
Answer:
y=-1/3x+6 is the equation of the graph so just use this to find the graph
Step-by-step explanation:
Answer:
where are the images
Step-by-step explanation:
What is the sum of 4mn | 7mn-5mn
Answer: the sum = 8
Step-by-step explanation:
Which of the following equations will produce the graph shown below?
y = 1/2 x² => C
we can see the point ( 2 ; 2)
x = 2
y = 1/2 * 2² = 1/2 * 4 = 2
Which statement best describes a cause and effect structure of a speech?
o It discusses similarities and differences between two different topics,
O It shows the challenges of a topic and explains how the issue can be solved.
O It provides the audience with the order in which events happened.
o It presents the reasons something happened and describes the result.
Answer:
Fourth option
Step-by-step explanation:
Cause and effect all starts with a reason for a certain event, for example perhaps a group of children going into an abandoned house that is rumored to be "haunted", which caused an effect. So, in this case the children going into an abandoned house that is rumored to be haunted (cause) which then lead into a result, a ghost started to chase them around the house in till they could manage an escape. (effect) Although creating a very good story for us to read, cause and effect has real life examples. The answer is the fourth option or "it presents the reasons something happened and describes the result."
Hope this helps.
Which option is equivalent to log 7 - log 2? A. log 5 B. log 7 C. log 9 D. log 7^2
5+5=?...........................
Answer:
10
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
because yes