Let:
x = Colored markers
y =
What is the equation of a line with slope 7/12 and y-intercept -3?
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m represents slope
c represents y intercept
Given that m = 7/12 and c = - 3, the equation of the line would be
y = 7x/12 - 3
A 9-foot roll of waxed paper costs $4.95. What is the price per yard ?
Answer:
$0.55 per yard
Step-by-step explanation:
a 9 foot roll is 4.95 so you divide the cost by the amount to get the unit rate which is $0.55 per yard
Mai is filling her fish tank water flows into the tank at a constant rate. 2.&- 0.5 1.6 time (minutes) water (gallons) 0.5 0.8 1 x1.6 1.6 x1.6 4.8 25 G 3 40 1) How many gallons of water will be in the fish tank after 3 minutes? Explain or show your reasoning. 2) How long will it take to fill the tank with 40 gallons of water? Explain or show your reasoning. 3) What is the constant of proportionality? What does it tell us about this situation?
Given
x = 0.5; y = 0.8
The constant of proportionality has to be calculated to estimate the other values.
The constant of proportionality "k" determines the relation of x and y, which can be represented as: y = kx.
So, in this exercise,
[tex]\begin{gathered} 0.8=k\cdot0.5 \\ \frac{0.8}{0.5}=k \\ k=1.6 \end{gathered}[/tex]y = 1.6y
(1) From this, we can estimate the value of y when x = 3.
[tex]\begin{gathered} y=1.6\cdot3 \\ y=4.8\text{gallons} \end{gathered}[/tex](2) If we want how long it will take to fill the tank with 40 gallons:
[tex]\begin{gathered} 40=1.6\cdot x \\ \frac{40}{1.6}=x \\ 25=x \end{gathered}[/tex]It will take 25 minutes.
(3) Finally, the constant of proportionality is 1.6 (as calculated above).
It tells us that the ratio between the gallons water of water and time. In other words, it tells us that for each 1 minute, 1.6 gallons are filled.
A square has a perimeterof 8,000 centimeters. Whatis the length of each side ofthe of the square inmeters?
Answer:
20 meters
Explanation:
The formula for calculating the perimeter of a square is expressed as
perimeter = 4s
where
s is the length of each side of the square
From the information given,
perimeter = 8,000 centimeters
Recall,
1 cm = 0.01 m
8000cm = 8000 x 0.01 = 80 m
Thus,
80 = 4s
s = 80/4
s = 20
The length of each side of the square is 20 meters
In a newspaper, it was reported that the number of yearly robberies in Springfield in 2013 was 180, and then went down by 40% in 2014. How many robberies were there in Springfield in 2014?
As given that the number of yearly robberies in Springfield in 2013 was 180
And then went down by 40% in 2014.
So robberies were there in Springfield in 2014:
[tex]\begin{gathered} N=180-180\times\frac{40}{100} \\ N=180-72 \\ N=108 \end{gathered}[/tex]So robberies were there in Springfield in 2014 are 72
May I please get help with this. I have tried multiple times but still could not get the correct answer or at least answer to them
SOLUTION:
Step 1:
In this question, we have the following:
Step 2:
The details of the solution are as follows:
Parallelogram:
a) Two pairs of parallel sides: Yes
b) Only one pair of parallel sides: NO
c) Four right angles: NO
d) All sides congruentnt: NO
Rectangles:
a) Two pairs of parallel sides: Yes
b) Only one pair of parallel sides: NO
c) Four right angles: Yes
d) All sides congruentnt: NO
Trapezoid:
a) Two pairs of parallel sides: NO
b) Only one pair of parallel sides: NO
c) Four right angles: NO
d) All sides congruentnt: NO
Consider the following statement:
If Paul is older than Bill and Fred is younger than Bill, then Bill's age is between Paul's and Fred's.
Write the Given statement
Paul is the oldest and Fred is the youngest of the three.
What is mean by younger?Younger is a comparative adjective that generally indicates more youthful.
Similar to old, elder simply indicates older in age. It is a comparative version of old.
Given that x is a natural number, let Bill's age equal x years.
Paul's age is thus calculated as (x + a) Years, where an is any positive integer.
Fred is also younger than Bill.
So, Fred's age is equal to x - k, where k is any positive integer.
As a result, if we arranged Fred, Bill, and Paul's ages, they would be
Bill, Fred, and Paul
x-k < x < x+a
As a result, we can conclude that Paul is the oldest and Fred is the youngest of the three.
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Solve for x and then give the m
x = 38
Step-by-step explanation:
(x + 6) + (3x - 16) + x = sum of angles in a triangle
(x + 6) + (3x - 16) + x = 180
(x + 3x + x ) + (6 - 16) = 180
5x +(-10) = 180
5x - 10 = 180
5x = 180 + 10
5x = 190
5x/5 = 190/5
x = 38
Answer:
x = 38 and m∠M = 98
Step-by-step explanation:
Angles in any triangle will always add up to 180 :
So angle O + Angle N + Angle M = 180
(x+6)+(3x-16)+(x) = 180
Simplify:
5x-10 = 180
Add 10 to both sides :
5x = 190
Divide both sides by 5 :
x = 38
Angle M will therefore
= 3(38) - 16
= 114 - 16
= 98
Hope this helped and have a good day
rag the red and blue dots along the x-axis and y-axis to graph 10x - 7y=40
We were given the equation:
[tex]10x-7y=40[/tex]We will proceed to graph this equation as shown below:
[tex]\begin{gathered} 10x-7y=40 \\ \text{Make ''y'' the subject of the equation, we have:} \\ \text{Subtract ''10x'' from both sides, we have:} \\ -7y=-10x+40 \\ \text{Divide through each term by ''-7'' to obtain the equation in terms of ''y'', we have:} \\ y=\frac{-10}{-7}x+\frac{40}{-7} \\ y=\frac{10}{7}x-\frac{40}{7}_{} \\ \\ y=\frac{10}{7}x-\frac{40}{7}_{} \\ when\colon x=-7 \\ y=\frac{10}{7}(-7)-\frac{40}{7} \\ y=-10-\frac{40}{7} \\ y=-\frac{110}{7} \\ \\ when\colon x=0 \\ y=\frac{10}{7}(0)-\frac{40}{7} \\ y=-\frac{40}{7} \\ \\ when\colon x=7 \\ y=\frac{10}{7}(7)-\frac{40}{7} \\ y=10-\frac{40}{7} \\ y=\frac{30}{7} \end{gathered}[/tex]We will proceed to plot these ordered pairs on a graph, we have:
Which statement about the graph below is true?
Answer:
a. The relation is a function because every input has an output.
Step-by-step explanation:
a relation in which for every input there is exactly one output (for every x there is just one y)
quizlet
Answer:
A. The relation is a function because every input has an input
Step-by-step explanation:
A relation is a function as long as there are not multiple outputs for one input. It's okay if there are multiple inputs for one output, like we can see here with points (-6, 1) and (2, 1).
Another way to test if a graphed relation is a function is the vertical line test. Draw vertical lines at multiple spots on the graph and if any of the vertical lines touches 2 points, the graphed relation is not a function.
:)
write an equation that gives the proportinal relationship of the graph
Answer:
y=5x
Explanation:
The slope-intercept form of the equation of a line is:
[tex]y=mx+b\text{ where }\begin{cases}m=\text{slope} \\ b=y-\text{intercept}\end{cases}[/tex]First, we find the slope of the line by picking two points from the line.
• The points are (0,0) and (3,15).
[tex]\begin{gathered} \text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}=\frac{15-0}{3-0}=\frac{15}{3} \\ \implies m=5 \end{gathered}[/tex]Next, the line crosses the y-axis at y=0.
Therefore, the y-intercept, b=0.
Substitute m=5 and b=0 into the slope-intercept form:
[tex]\begin{gathered} y=5x+0 \\ \implies y=5x \end{gathered}[/tex]The equation that gives the proportional relationship of the graph is y=5x.
The figure below shows a rectangular court. 74 ft (a) Use the calculator to find the area and perimeter of the court. Make sure to include the correct units. Area: 93 ft Perimeter: (b) The court will have a wood floor. Which measure would be used in finding the amount of wood needed? Perimeter O Area (c) A strip of tape will be placed around the court. Which measure would be used in finding the amount of tape needed? Perimeter O Area ft X ft² Ś ft³ ?
Given a rectangle with sides "a" and "b":
The area of the rectangle is:
[tex]A=ab[/tex]The perimeter of the rectangle is:
[tex]P=2a+2b[/tex]Given the sides of the rectangle:
a = 74 ft
b = 93 ft
(a)
The area of the rectangle is:
[tex]\begin{gathered} A=74ft*93ft \\ A=6882ft^2 \end{gathered}[/tex]The perimeter of the rectangle is:
[tex]\begin{gathered} P=2*74ft+2*93ft \\ P=148ft+186 \\ P=334ft \end{gathered}[/tex](b) The wood will cover all the area of the court, then the area must the used.
(c) The tape will be placed around the court, then the perimeter must be used.
Answer:
(a)
(b)
(c) Perimeter
You have two spinners each with three sections of equal size labeled with numbers 1,2,3. You spin both and observe the numbers. Let x be the sum of the two numbers. Find the probability distribution for X.
From the given problem with two spinners with three sections of equal size labeled as 1, 2, and 3.
Spinner 1 : 1 2 3
Spinner 2 : 1 2 3
The sum is as follows :
1+1 = 2
1+2 = 3
1+3 = 4
2+1 = 3
2+2 = 4
2+3 = 5
3+1 = 4
3+2 = 5
3+3 = 6
There are 9 total outcomes
There are (1) 2,
(2) 3's
(3) 4's
(2) 5's
and
(1) 6
and their corresponding probability can be calculated by :
[tex]\text{probability}=\frac{\text{ quantity}}{\text{ total quantity}}[/tex]Probability of 2 = 1/9
Probability of 3 = 2/9
Probability of 4 = 3/9 or 1/3
Probability of 5 = 2/9
Probability of 6 = 1/9
Construct the probability distribution :
To check if your probability distribution is correct.
The sum of P(X) must be equal to 1
1/9 + 2/9 + 1/3 + 2/9 + 1/9 = 1
Therefore the distribution is correct.
8. A plane uses a certain amount of fuel based on the number of miles it travels as shown in thetable.Miles Traveled 0 30 60 90 120Gallons of Fuel0156312468624a. What is the slope of the table, and what does it mean in the situation?b. What is the y-intercept of the table, and what does it mean in the situation?c. Write an equation for the table.
Remember the formua to calculate the slope of a line between to points
[tex]\begin{gathered} A(x_1,y_1) \\ \text{and} \\ B(x_2,y_2) \end{gathered}[/tex]is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So to calculate the slope of the table, let's use the points
A(0 , 0) and B(30 , 156). Thus,
[tex]\begin{gathered} m=\frac{156-0}{30-0}\rightarrow m=\frac{156}{30} \\ m=5.2 \end{gathered}[/tex]You can check that this slope works for any consecutive pair of points of the table, since the data is related with a straight line (constant slope)
To get a better sense of what a slope means, let's think about the original units of measurement of the data. Notice that the units for x data is "Miles traveled" and the units for y data is "Gallons of fuel".
In the formula for slope, we divide y data by x data. Therefore, the whole slope, with units of measurement, would be
[tex]m=5.2\text{ }\frac{\text{Gallons of fuel}}{\text{Mile(s) traveled}}[/tex]Thus, the slope of the table would mean the gallons of fuel consumed per each mile traveled
Now, remember the y-intercept occurs when x = 0.
In this case, the y-intercept would be 0, meaning that the plane didn't use any fuel until it started the journey. Perhaps it was parked and with the engines off.
To come up with an equation for the table, lets use the slope we calculated, point A(0 , 0) and the slope-point form of a line, as following:
[tex]\begin{gathered} y-0=5.2(x-0) \\ \rightarrow y=5.2x \end{gathered}[/tex]Answers:
a)
[tex]m=5.2[/tex]The slope of the table means the gallons of fuel consumed per each mile traveled.
b) The y-intercept is 0. It means the plane didn't use any fuel until it started the journey.
c)
[tex]y=5.2x[/tex]I’m stuck on this one need a push in Wright direction
In the graph it is observed that staright line is drawn between y-axis and x-axis. The graph of a linear function is always a straight line. So function represented in graph is linear.
Answer: Yes function is linear
Facot the expression 81x^2-25 ?
Apply difference of two square
[tex]x^2-y^2\text{ = (x - y)(x + y)}[/tex][tex]\begin{gathered} 81x^2\text{ - 25} \\ =(9x)^2-5^2 \\ \text{Apply difference of two square} \\ =\text{ (9x - 5)(9x + 5)} \end{gathered}[/tex]How would I convert 900,000km to miles?
EXPLANATION
Since we have 900,000 kilometers, and 1 kilometer is equivalent to 0.621371 kilometers, we can apply the unitary method in order to get the needed conversion as shown as follows:
[tex]\text{?miles}=900,000\operatorname{km}\cdot\frac{0.621371}{1\text{kilometer}}=559233\text{ miles}[/tex]?miles = 900,000 km * (0.621371/ 1 km) = 559,233 miles
The solution is 559,233 miles
graph a line that is parallel to the given line. determine the slope of the given line and the one you graphed in simplest form. click and drag on the graph to draw a line. Click and drag to plot a parallel line. The line will change colors when a parallel or perpendicular line is drawn accurately.
Choosing two points of the line given ( Lg ):
• A( ,0, -4, )
,• B( -,1.5, 0, )
Procedure:
0. Finding the slope ( ,m ,) of ,Lg:
[tex]m_{Lg}=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]m_{Lg}=\frac{0_{}-(-4)_{}}{-1.5_{}-0_{}}=\frac{4}{-1.5}=-\frac{8}{3}[/tex][tex]m_{Lg}=-\frac{8}{3}[/tex]Also, based on point (0, -4), we can determine the intersection in y - axis ( b = -4). Therefore, the equation of the line given is:
[tex]y=mx+b[/tex][tex]y=-\frac{8}{3}x-4[/tex]To determine the parallel slope ( mp ), we know that parallel lines have the same slope:
[tex]m_p=m_{Lg}=-\frac{8}{3}[/tex]For the new graph, you would have to choose a different parameter b, all the equation would be the same except b. Choosing b = 3 as an example:
[tex]y=-\frac{8}{3}x+3[/tex]Answer:
• Original slope: -8/3
,• Parallel slope: -8/3
Covert the decimal into a fraction and reduce to the lowest terms
Solution
- The number given to us can be rewritten as follows:
[tex]92.698=92+0.698[/tex]- Thus, we already know what is in the whole number bracket; 92.
- The fraction representation of 0.698 is what will occupy the fraction brackets.
- 0.698 can be rewritten as:
[tex]0.698=\frac{698}{1000}[/tex]- Let us simplify this fraction as follows:
[tex]\begin{gathered} \frac{698}{1000}=\frac{349\times2}{500\times2} \\ \\ 2\text{ crosses out.} \\ \\ =\frac{349}{500} \end{gathered}[/tex]- Thus, the answer is
A toy car that is 0.5 ft long is used to model the actions of an actual car that is 15 ft long. Which ratio shows the relationship between the sizes of the model and the actual car? A. 2:5 B. 5:2 C. 30:1 D. 1:30
A toy car that is 0.5 ft long is used to model the actions of an actual car that is 15 ft long. Which ratio shows the relationship between the sizes of the model and the actual car?
A. 2:5
B. 5:2
C. 30:1
D. 1:30
_____________________
0.5 ft the toy car: 15 the actual car
0.5*2 =1
15 *2 = 30
1: 30
_____________________________________
The ratio1:30 shows the relationship between the sizes of the model and the actual car
____________
Do you have any questions regarding the solution?
propriate symbols and/or words in your submissionSolve for the indicated measure.5. R = 19°, ZB = 56°, find mZT.6. R = 19, ZB'S 56°, find mZS.7. R = 19°, ZB = 56°, find mZC.8. True or false?AABC = AZXY9. Are the two triangles congruent?Yes or no?10. Use the image below to complete the proof.Identify the parts that are congruent by the given reason in the proof.STATEMENTS REASONSAB = DC GivenAB || DC Given2.Alternate Interior Angles TheoremReflexive Property of CongruenceSAS Congruence Theorem3.4.
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The sum of the internal angles in a triangle equals 180°
R + B = T = 180
Substitution
19 + 56 + T = 180
T = 180 - 19 - 56
T = 105°
Result:
T = 105°
Adam is working in a lab testing bacteria populations. After starting out with a population of 390 bacteria, he observes the change in population and notices that the population quadruples every 20 minutes.Step 2 of 2 : Find the population after 1 hour. Round to the nearest bacterium.
The given information is:
The starting population of bacteria is 390.
The population quadruples every 20 minutes.
To find the equation of the population in terms of minutes, we can apply the following formula:
[tex]P(t)=P_0\cdot4^{(\frac{t}{20})}[/tex]Where P0 is the starting population, the number 4 is because the population quadruples every 20 minutes (the 20 in the power is given by this), it is equal to 4 times the initial number, and t is the time in minutes.
If we replace the known values, we obtain:
[tex]P(t)=390\cdot4^{(\frac{t}{20})}[/tex]To find the population after 1 hour, we need to convert 1 hour to minutes, and it is equal to 60 minutes, then we need to replace t=60 in the formula and solve:
[tex]\begin{gathered} P(60)=390\cdot4^{(\frac{60}{20})} \\ P(60)=390\cdot4^3 \\ P(60)=390\cdot64 \\ P(60)=24960\text{ bacterias} \end{gathered}[/tex]Thus, after 1 hour there are 24960 bacterias.
Two rectangles overlap, as shown below. Find the area of the overlapping region (which is shaded) if AB = BE = 2 and AD = ED = 4.
The area of the overlapping region is of: 6.25 units squared.
Area of a rectangleThe area of a rectangle of length l and width w is given by the multiplication of the dimensions, as follows:
A = lw.
The dimensions of the right triangle as follows:
Leg x.Leg 2.Hence the remaining leg on the overlapping region is:
4 - x, as AD = 4.
By symmetry, the other dimension of the overlapping region is also of:
4 - x.
Being also the hypotenuse of the right triangles.
The value of x can be found applying the Pythagorean Theorem as follows:
x² + 2² = (4 - x)²
x² + 4 = 16 - 8x + x²
8x = 12
x = 1.5.
Then the two dimensions of the shaded region are:
4 - 1.5 = 2.5.
Meaning that the area is of:
A = 2.5 x 2.5 = 6.25 units squared.
Missing information
The figure is missing and is given by the image at the end of the answer.
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For each equation in the table, give the slope of the graph.
Solving the Question
Linear equations are typically organized like this: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept.
When the equation is like [tex]y=b[/tex], it means that it is a horizontal line and the slope is 0.
When the equation is like [tex]x=d[/tex], it is a vertical line and the slope is undefined.
AnswerFirst equation: 0
Second equation: undefined
Third equation: [tex]\dfrac{4}{5}[/tex]
drag and drop the matching inequality from the left into the box on the right
The first problem is modeled by the following inequality:
[tex]40+5x\ge95-4x[/tex]The second problem is represented by
[tex]95+4x<40+5x[/tex]The third problem is represented by
[tex]95-4x<40+5x[/tex]Observe that, "spending" refers to subtraction, "earnings" refers to addition. Also, the variables represent time. Additionally, "less than" is expressed as "<", "as much as or more than" is expressed as >=.
Hello I would like to know what is the answer to the question 3/4x 3 < 6
the coordinates of two points on a line are (-4,8) and (2,2). Find the slope of the line.
the coordinates of two points on a line are (-4,8) and (2,2). Find the slope of the line.
Applying the formula to calculate the slope
we have
m=(2-8)/(2+4)
m=-6/6
m=-1
slope is -1Triangle KLM has KL = 28, KM = 28, and LM = 21. What is the area of the triangle?The area of AKLM is about(Simplify your answer. Round to one decimal place as needed.)
Area = (b * h)/2, b = 21 bu we don't know h, s we have to calculate it
To calculate the height "h" we can use pythagoras with a triangle rectangle with base = 21/2 = 10.5 and hypothenuse = 28, so the height "h" is:
28² = h² + 10.5² ==> h² = 28² - 10.5² = 784 - 110.25 = 673.75
h² = 673.75
h = 25.96
Now that we have the height, the Area of the triangle = (b * h)/2 = (21 * 25.96)/2 = 272.5
Answer:
272.5
Find the equation for thefollowing parabola.Vertex (0,0)Focus (2, 0)A. 2x^2 = yB. y^2 = 8x2C. X^2 = ByD. y^2 = 8x
To answer this question we need the equation of a parabola that uses the distance from the focus to the vertex.
This formula is,
[tex]4p(y-k)=(x-h)^2[/tex]where,
p is the distance from the focus to the vertex, and the point (h,k) is the vertex.
[tex]\begin{gathered} \text{focus (2,0)} \\ \text{Threrefore} \\ p=2 \end{gathered}[/tex][tex]\begin{gathered} \text{vertex (0 , 0)} \\ \text{Therefore,} \\ h=0 \\ k=0 \end{gathered}[/tex]Let us now substitute the data into the equation of the parabola,
[tex]\begin{gathered} 4\times2(y-0)=(x-0)^2 \\ 4\times2(y)=x^2 \\ 8y=x^2 \end{gathered}[/tex]Hence, the equation for the parabola is, x² = 8y.
Option C is the correct answer.
Since January 1, 1960, the population of Slim Chance has been described by the formula P = 27000(0.95)^t, where P is the population of the city t years after the start of 1960. At what rate was the population changingon January 1, 19702?numerical rate of change= ___ people per year
We have to calculate the rate of change of the population P(t) at January 1, 1970 (t = 10).
The expression for P(t) is:
[tex]P(t)=27000\cdot0.95^t[/tex]The rate of change will be given by the first derivative of P(t):
[tex]\frac{dP}{dt}=27000\cdot\ln (0.95)\cdot0.95^t[/tex]Then, we can calculate the value of the rate of change when t = 10, by replacing t with 10 in the last expression. We then will get:
[tex]\begin{gathered} \frac{dP}{dt}(100)=27000\cdot\ln (0.95)\cdot0.95^{10} \\ \frac{dP}{dt}(100)\approx27000\cdot(-0.0513)\cdot0.5987 \\ \frac{dP}{dt}(100)\approx-829 \end{gathered}[/tex]The population, on January 1st 1970, is decreasing at a rate of 829 people per year.
Answer: numerical rate of change= -829 people per year
