Solution
Note: When two lines are parallel to each other, their slopes are equal.
[tex]\begin{gathered} \text{ Given the line } \\ y=\frac{2}{5}-\frac{4}{3}x \\ y=-\frac{4}{3}x+\frac{2}{5} \\ \\ \text{The general form of the equation of a straight line} \\ y\text{ = mx + c} \\ \text{where m = slope and c = y- intercept} \\ \\ By\text{ comparing }y=-\frac{4}{3}x+\frac{2}{5}\text{ with y = mx + c} \\ m=-\frac{4}{3} \\ \\ \text{The slope of the line }y=\frac{2}{5}-\frac{4}{3}x\text{ is }-\frac{4}{3} \\ \\ \text{The slope of the line parallel to the line }y=\frac{2}{5}-\frac{4}{3}x\text{ is also }-\frac{4}{3} \end{gathered}[/tex]The answer is -4/3
Rachel practiced 1/2 of an hour on Monday, 1/3 of an hour on Tuesday, 1/4 of an hour on both Wednesday and Thursday, and 1/2 of an hour on Friday. Find how many minutes she practiced each day and then find how many minutes she practiced in all during the week.
ANSWER and EXPLANATION
We want to find the number of minutes she practiced each day and in total.
An hour is equal to 60 minutes.
On Monday, she practiced 1/2 of an hour. To convert this to minutes, multiply 1/2 by 60 minutes. That is:
[tex]\begin{gathered} \frac{1}{2}\cdot60 \\ \Rightarrow30\min \end{gathered}[/tex]On Tuesday, she practiced for 1/3 of an hour. That is:
[tex]\begin{gathered} \frac{1}{3}\cdot60 \\ \Rightarrow20\min \end{gathered}[/tex]On Wednesday, she practiced for 1/4 of an hour. That is:
[tex]\begin{gathered} \frac{1}{4}\cdot60 \\ \Rightarrow15\min \end{gathered}[/tex]On Thursday, she practiced for 1/4 of an hour. That is also equal to:
[tex]\Rightarrow15\min [/tex]On Friday, she practiced for 1/2 of an hour. That is equal to:
[tex]=>30\min [/tex]To find the total number of minutes that she practiced in all during the week, find the sum of the number of hours for all the days given.
[tex]\begin{gathered} 30+20+15+15+30 \\ \Rightarrow110\min \end{gathered}[/tex]She practiced for 110 minutes during the week.
4x+3y=14-yx-5y=23. IF (x, y) is a solution to the system of equationsabove, what is x - y?A) 1B)C) 3D) 18
C. 3
2. Determine the equation of the asymptote for the following exponential functions: *y=2x-3 b. y = (3)* + 2 c. ** y = 2(3)* d. 2 + 3x I *** a.
a) y = -3
b) y = 2
c) y = 0
d) y = 2
Explanation:The asymptote is the constant added to the expression of the variable
a) y = 2^x - 3
Theexpression of the variable = 2^x
The number after it is is - 3
So the asymptote is y = -3
b) y = (1/3)^x + 2
The number added to the expression of the variable is 2
Asymptote is y = 2
c) y = 2(3)^x
y = 2(3)^x + 0
The expression of the variable = 2(3)^x
There is no number added to the expression of the variable
Hence, Asymptote is y = 0
d) 2 + 3^x
[tex]\begin{gathered} The\text{ function is not equated to y} \\ Since\text{ we are told they are all exponntial function,} \\ \text{let 2 + 3}^x\text{ = y} \end{gathered}[/tex]The expression of the variable = 3^x
The number added to this expression is 2
Asymptote is y = 2
Prior to making deposits of $75 and $50 Marian had a balance of $102in her checking account. How much must she deposit so that her balance winbe at least $300 and she can avoid a service fee
Marian had a balance of $102
Then she made two deposits, one of $75 and the other for $50
We can calculate the balance of her checking account after the deposits were done
New balance = $102 + $75 + $50 = $227
The account needs to have at least $300 to avoid a service fee, so we calculate how much is needed to complete that amount
New deposit = $300 - $227 = $73
So, if Marian deposits at least $73, the account balance will be $300 or more
Answer: She must deposit at least $73
Our family has a small pool for relaxing in the summer that holds 1500 gallons of water. I decided to fill the pool for the summer. When I had 5 gallons of water in the pool, I decided that I didn't want to stand outside and watch the poik fill, so I had to figure out how long it would take so that I could leave, but come back to turn off the water at the right time. I checked the flow on the hose and found that it was filling the pool at a rate of 2 gallons every minute. Use a table, a graph, and a equation to create a mathematical model for the number of gallons of water in the pool ar minutes?
Let the volume, as a function of time t, be v:
v(t) = 5 + 2t
v(t) = 5 + 2t
The mathematical model is v(t) = 5 + 2t
can you please give me some more information about this
We can see that the segment is defined by the points (-5, 5) & (-3, -4).
Now, we calculate the mid-point by using the following expression:
[tex]mp=(\frac{x_2-x_1}{2},\frac{y_2-y_2}{2})[/tex]So, now we replace:
[tex]mp=(\frac{-5-(-3)}{2},\frac{-4-5}{2})\Rightarrow mp=(-1,\frac{1}{2})[/tex]So, the mid point is (-1, 1/2).
I need help with my math
Step 1: write out the formula for slope
[tex]\text{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]Step2: Identify the point in the diagram
[tex]\begin{gathered} (-2,-4)\text{ and (2,2)} \\ x_1=-1,x_2=2,y_1=-4,y_2=2 \end{gathered}[/tex]Step3: Substitute the value into the given formula above
[tex]\begin{gathered} \text{Slope}=\frac{y_2-y_1}{x_2-x_1} \\ =\text{ }\frac{2-(-4)}{2-(-2)} \\ =\frac{2+4}{2+2} \\ =\frac{6}{4} \end{gathered}[/tex][tex]\text{slope}=\frac{3}{2}[/tex]Hence the slope of the line is 3/2
What is the product?6 2/5, 5/6, 1 1/4
Given
[tex]6\frac{2}{5},\frac{5}{6},1\frac{1}{4}[/tex]Product means multplication
[tex]6\frac{2}{5}\times\frac{5}{6}\times1\frac{1}{4}[/tex]Change the mixed fraction to improper fraction
[tex]\begin{gathered} \frac{32}{5}\times\frac{5}{6}\times\frac{5}{4}=\frac{4}{1}\times\frac{1}{3}\times\frac{5}{1} \\ \frac{4}{1}\times\frac{1}{3}\times\frac{5}{1}=\frac{20}{3}=6\text{ }\frac{2}{3} \end{gathered}[/tex]The final answer
[tex]6\text{ }\frac{2}{3}\text{ or }6.6667[/tex]At a gas station each leader of gas cost $3 but there's a promotion that for every beverage you purchase you save 20 cents on gas is your total savings on gas proportional to the number of beverages you purchase?
Input data
$3 per gas
0.20 cents savings per beverages
Procedure
Yes, your total savings on gas proportional to the number of beverages you purchases.
For every beverage purchased, there is a saving of $0.20
s = savings
is 1/8 greater than 18%
Consider than 18% in decimal is 0.18.
Next, take into that 1/8 = 0.125
0.18 is great
Divide 180 into two parts such that the first part is 12 less thantwice the second part.a 100, 80b 90,90c 116, 64d 99. 81
You can find a math expression dividing the statment as follow:
Divide 180 into two parts such that: x and y
the first part: X
is 12 less than: X= -12
twice the 2(
second part: Y
the first (X) part is 12 less than twice the second part (Y):
X=2Y-12
You have 3 6 sided dice. One is red one is blue one is green What is the probability that you roll a one on the red die a 2 on the blue die and a 3 on the green
Solution
Step 1
[tex]Probability\text{ of any event = }\frac{number\text{ of required outcomes}}{number\text{ of sample space}}[/tex]Step 2:
For each die, the number of sample space is (1 ,2,3,4,,6)
Note: AND represent multiplication
Step 3:
The probability that you roll a 1 on the red die a 2 on the blue die and a 3 on the green
[tex]\begin{gathered} =\text{ }\frac{1}{6}\text{ }\times\text{ }\frac{1}{6}\text{ }\times\text{ }\frac{1}{6} \\ \text{= }\frac{1}{216} \end{gathered}[/tex]Final answer
[tex]\frac{1}{216}[/tex]The sales tax for an item was $6.80 and it cost $340 before tax. Find the sales tax rate. Write the answer as a percentage.
Answer: 1.788%
Explanation
Given
• Sales tax for an item: $6.80
,• Total cost before tax: $340
Procedure
To find the sales tax rate we have to divide the sales tax against the total cost as follows:
[tex]\frac{6.08}{340}=0.01788[/tex]To convert it to percent we have to multiply times 100%:
[tex]0.01788\times100\%=1.788\%[/tex]If f(x) = (x + 3)4, find the inverse of f.f -1(x) = x1/4 - 3f -1(x) = x1/4 + 3f -1(x) = 3x1/4f -1(x) = x1/4 /3
Given:
The function
[tex]f(x)=(x+3)^4[/tex]Required:
FInd inverse of f.
Explanation:
Function inverse definition
[tex]\text{ A function }g\text{ is the inverse of function f if for }y=f(x),x=g(y).[/tex]Now,
[tex]\begin{gathered} y=(x+3)^4 \\ \text{ Replace x with y} \\ x=(y+3)^4 \\ \text{ Solve for y,} \\ x=(y+3)^4 \\ y=x^{\frac{1}{4}}-3 \end{gathered}[/tex]Answer:
Option A is correct.
Ernesto already has 6 flowers in his garden and his garden he will grow 4 more flowers per seed packet he plants.let s represent the number of seed packets he plants and f represent the total number of flowers he will have. Complete the equation that represent the relationship between s and f
Two sides of a triangle have the followingmeasures. Find the range of possiblemeasures for the third side.
The sum of the lengths of any two sides of a triangle must be greater than the third side.
So:
A+B>C
B+C > A
C+A > B
Given the 2 sides: 31 and 44, suppose they are sides A and B:
44-31 < c < 44+31
Range
13 < C < 75
NEED HELP ASAP!!!!!!!!
The values of y/x when y is -6 and x is -1 is 6, when y is 0 and x is 1 is 0 and when y is 6 and x is 3 is 2.
According to the question,
We have the following information:
y = 3x-3
Now, in order to solve this equation we have to fill the given table with the values of x and y:
So, we have x = -1 and y = -6:
y/x = -6/-1
6
We have x = 1 and y = 0:
y/x = 0/1
0
We have x = 3 and y = 6:
y/x = 6/3
2
Hence, the values of y/x when y is -6 and x is -1 is 6, when y is 0 and x is 1 is 0 and when y is 6 and x is 3 is 2.
To know more about values of y/x here
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1/4x+1/2=5(5/6x+5)x= ?
For this problem, we need to solve the following expression:
[tex]\frac{1}{4}x+\frac{1}{2}=5(\frac{5}{6}x+5)[/tex]For that, we need to isolate the x variable on the left side:
[tex]\begin{gathered} \frac{1}{4}x+\frac{1}{2}=\frac{25}{6}x+25\\ \\ \frac{25}{6}x-\frac{1}{4}x=\frac{1}{2}-25\\ \\ \frac{2\cdot25x-3x}{12}=\frac{1-50}{2}\\ \\ \frac{47x}{12}=-\frac{49}{2}\\ \\ x=-\frac{12\cdot49}{2\cdot47}\\ \\ x=-\frac{588}{94}=-\frac{294}{47} \end{gathered}[/tex]The value for x is equal to -294/47.
move the numbers to the blanket to order them from least to greatest value.
The given numbers from least to greatest are
• 1 - 21 = -20
,• -0.89
,• 0.4
,• 0.5
,• 9/8 = 1.125
To order the number from least to greatest, we just have to know the value of each one. For example, 1 - 21 equals -20, this will be the least number because it has the greatest absolute value as a negative number. Then, we have -0.89, which is greater than -20. And so on.
Ordered the sides in the triangle from shortest to longest?
The sine rule states that
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]Where a is the opposite side to angle A, b is the opposite side to angle B, and c is the opposite side to angle C
In our problem:
[tex]\frac{\sin(40degree)}{EF}=\frac{\sin(55degree)}{FG}=\frac{\sin(85degree)}{EG}[/tex]Remember that the function sine is growing in the interval [0,90°]; therefore, from the first 2 equalities
[tex]undefined[/tex]How do I write an equation of a line passing through
The equation is:
[tex]y=\frac{1}{2}x+2[/tex]Explanation:Given the point (2, 3), and the equation:
y - 4 = -2(x + 3) .............................................(1)
[tex]\begin{gathered} y=-2x-6+4 \\ =-2x-2 \end{gathered}[/tex]Comparing with the equation of a line:
[tex]y_{}=mx+b[/tex]where m is the slope, and b is the y-intercept
The slope in (1) is -2
Note that perpendicular lines have their slopes as negative reciprocals of each other.
The negative reciprocal of -2 is 1/2
The equation of a line perpendicular to (1) is:
[tex]y=\frac{1}{2}x+b[/tex]Applying the given point (2, 3), we have x = 2, y = 3
[tex]\begin{gathered} 3=\frac{1}{2}(2)+b \\ \\ b=3-1=2 \end{gathered}[/tex]The equation is therefore;
[tex]y=\frac{1}{2}x+2[/tex]what is the equation of the line that passes through the point[tex]( - 3 - 11)[/tex]y=2x-4
Answer
To check if a line passes through a point replace x in the equation
For example:
y= 2x-4
replacing
y = 2*( -3) -4
y= -6-4
y = -10
So then y= 2x-4 passes through the point (-3, -10)
I need help with this math problem I have a picture that I can show you of what it is
The 18 % off of the listed price x can be denoted as,
[tex]\frac{100-18}{100}x=0.82x[/tex]18% more than the amount x can be denoted as,
[tex]\frac{100+18}{100}x=1.18x[/tex]3/10 of the origianl voulme x drained out is denoted as,
[tex]x-\frac{3}{10}x=\frac{10x-3x}{10}=\frac{7x}{10}[/tex]3/10 stock is added,
[tex]x+\frac{3}{10}x=\frac{10x+3x}{10}=\frac{13x}{10}[/tex]Explain what a chord is and determine if a diameter is or is not a chord. Explain in 5-7 sentences.
Solution:
A chord is a line segment in a circle with both endpoints on the circle. It is a line whose both ends touch the circumference of a circle.
The diameter is a line that touches both ends of a circle and passes through the center of the circle. Hence, a diameter is a special chord that passes through the center of the circle and it is the longest chord in the circle.
Further explanation:
From the image shown, image 1 has a line that is not a chord because its ends do not touch the circle. Image 2 is a chord because its ends touch the circle. That is what differentiates a line from a chord. Its ends must touch the circumference of a circle.
A diameter is also a chord because it meets the condition of a chord. Its ends touch the circle.
What differentiates both is that a chord does not pass through the centre of the circle, while a diameter passes through the centre.
Therefore, a diameter is a chord.
3 5 6 Graphs and Tables: To determine matching graphs and tables you would use your answer choices to plug in x values and solve to see if you get the correct y value for each pair. 10. 9. Which linear equation matches the table shown? The equation y = 3x - 4 represents the relationship in which of the following tables? 3 10 5 7 6 9 2 11 2 10 y у 6 18 11 17 23 29 35 3 y - 2 3 A. y = x + 8 X - - O B. y = 4x - 1 y-10 -> - C. y = 3x + 2 14 17 20 D. y = 5x - 4
Determine the linear equation for the table.
[tex]\begin{gathered} y-17=\frac{23-17}{7-5}(x-5) \\ y-17=\frac{6}{2}(x-5) \\ y=3x-15+17 \\ y=3x+2 \end{gathered}[/tex]So equation for the table is y = 3x + 2.
Select all the expressions whichrepresent the total number of bookread by Joel, Lucas and Erica.x + (2x + 3) + (5 - 4x)6x + 87x+27X-2x + (2x + 3) + (4x - 5)
Given:
Joel read x books
Lucas read 3 more than twice the number of books Joel read
So,
Lucas read 2x + 3
Erica read 5 less than four times the number of books Joel read
So,
Erica read 4x - 5
So, the total number of books read by Joel , Lucas and Erica :
x + (2x + 3) + (4x - 5)
= 7x - 2
So, the correct options are:
[tex]\begin{gathered} 7x-2 \\ x+(2x+3)+(4x-5) \end{gathered}[/tex]
A quantity with only magnitude is called a what?can you please explain it.
A quantity with only magnitude is called an scalar.
Hence, the answer is B.
1. Identify the population and the sample of the following scenarios,Part A: A survey of 1353 American Households found that 18% of the households own acomputer,Part B: A recent survey of 2625 elementary school children found that 28% of thechildren could be classified obese,Part C: The average weight of every dh person entering the mall within three hourperiod was 146 lb.
Let's begin by listing out the information given to us:
The population refers to the entire group from which you want to make a conclusion
The sample refers to the specific subject from whom data is obtained
Part A
Population = 1353
Sample = 18% of the population = 18% * 1353 = 243.54 ≈ 244
Part B
Population = 2625
Sample = 28% of the population = 28% * 2625 = 735
Part C
Population = every person that came into the mall
Sample = every person that came into the mall within the 3 hour period
Suppose you roll a pair of six-sided dice and add their totals.(a) What is the probability that the sum of the numbers on your dice is 9 or 11? (b) What is the probability that the sum of the numbers on your dice is an even number or a number less than 6? (c) What is the probability that the sum of the numbers on your dice is a prime number or a number greater than 5?
Rolling a pair of six-sided dice, we have the following sample space:
(a) The probability that the sum of the numbers on your dice is 9 or 11 is
P(X = 9) + P(X = 11)
= 4/36 + 2/36
= 6/36
= 1/6
(b) The probability that the sum of the numbers on your dice is an even number or a number less than 6 is:
P(X = even) + P(X < 6)
= 21/36 + 10/36
= 31/36
(c) The probability that the sum of the numbers on your dice is a prime number or a number greater than 5?
P(X = prime) + P(X > 5)
= 14/36 +
Based on her recipe, Elena knows that 5 servings of granola have 1,750 calories. which equation can be used to represent the relationship between the number of calories, c, and the number of servings of granola, g?
Answer:
c = 350g
Explanation:
To find the relationship, we will use proportions. So, we know that 5 servings of granola have 1,750 calories and it will be equivalent to g servings of granola with c calories. Therefore, the proportion is:
[tex]\frac{\text{Granola}}{\text{Calories}}=\frac{5}{1,750}=\frac{g}{c}[/tex]So, using cross multiplication, we get:
[tex]5\cdot c=1,750\cdot g[/tex]Then, solving for c, we get:
[tex]\begin{gathered} 5c=1750g \\ \frac{5c}{5}=\frac{1750g}{5} \\ c=350g \end{gathered}[/tex]So, the answer is: c = 350g