Two lines are parallel if they do not intersect at any point.
Another way of thinking on parallel lines is: two lines are parallel if they have the same slope.
On the other hand, all horizontal lines have the same slope, which is equal to 0.
Since all horizontal lines have a slope equal to 0, this means that all horizontal lines are parallel.
Therefore, the answer is: yes. All horizontal lines are parallel.
Notice: This is only valid in 2D.
1. A train moves at a constant speed and travels 6 miles in 4 minutes. What is its speed in miles per minute? d/t = r time distance t d 4 mins. 6 miles
Answer: 1.5 miles / minute
Given that:
Distance travelled = 6
Time = 4 minutes
Speed = Distance / time
Speed = 6 / 4
1.5 mile / minute
The top of the hill rises 243 feet above checkpoint 2, which is -162. What is the altitude of the top of the hill?
The altitude of the top of the hill or the difference in elevation point is 406 feet.
Difference in Elevation PointThe vertical distance between two points is called the difference in elevation. The process of measuring differences in elevation is called levelling , and is a basic operation in topographical surveys.
To determine the difference in elevation between two points, determine the elevation at each point and then calculate the difference.
Point A = 243 feetPoint B = -162 feetThe difference in elevation between the two points is
Point A - Point B = 243 - (-162) = 243 + 162 = 406
The difference in the elevation point is 406 feet.
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I need help with this Tyler’s mom purchased a saving bond for Tyler. The value of the savings bond increases by 4% each year one year after it was purchased, the value of the savings bond was $156.00 find the value of the bond when Tyler’s mom purchased it. Explain your reason
Let x = value of the bond when Tyler’s mom purchased it.
After one year, this value increased by 4%. This new value is calculated as follows:
[tex]\text{new value = }x\cdot1.04[/tex]The new value is $156.00, then
[tex]\begin{gathered} 156.00=x\cdot1.04 \\ \frac{156.00}{1.04}=x \\ 150.00=x \end{gathered}[/tex]The value of the bond was $150.00 when Tyler’s mom purchased
the product of 4 and the diference of 9 and 2 find the value of your expression
Answer:
28
Step-by-step explanation:
4(9-2)
4(7)
28
16 - 2t = 5t +9 Can you help me solve this?
1=t
add 2t to the second side, so that it is going to be 16=7t+9
now, subtract 9 from the right side: 16-9=7t
7t=7
t=1
I am not good at word problems this is a project so need extra help
M = $6,400
C = $3,600
CD interest = $180
Money market interest = $256
Here, we want to start by completing the chart
We proceed as follows;
Let us take it line by line
a) The rate for the CD account is 5%
Writing this as decimal is 5/100 = 0.05
b) The time for the CD account is 1 year
Next line;
a) Principal invested in money market is $M
b) The time is also 1 year
Next line;
The interest earned on investment is the sum of both
That will be;
0.05c + 0.04m
So, let us write the equations to solve simultaneously;
[tex]\begin{gathered} c\text{ + m = 10,000} \\ 0.05c\text{ + 0.04m = 436} \\ \text{second equation multiplied through by 100;} \\ 5c\text{ + 4m = 43,600} \\ \text{From i;} \\ c\text{ = 10,000-m} \\ \text{put this into the multiplied equation} \\ 5(10,000-m)\text{ + 4m = 43600} \\ 50,000\text{ - 5m + 4m = 43600} \\ m\text{ = 50,000-43600} \\ m\text{ = 6400} \\ c\text{ = 10,000-6400} \\ c\text{ = 3,600} \end{gathered}[/tex]So, let us fill the last parts;
a) $3,600 + $6,400 = Total $10,000 invested
b) CD interest is 0.05 c = 0.05 (3,600) = $180
Money market interest = 0.04M = 0.04 (6,400) =$256
$180 + $256 = $436 total interest
Find the slope of the line that passes through (54, -61) and (8, -56).
Answer:
The slope m of the line that passes through the two given points is;
[tex]m=-\frac{5}{46}[/tex]Explanation:
We want to calculate the slope of the line that passes through the given point;
[tex](54,-61)\text{ and }(8,-56)[/tex]Recall that the slope formula can be written as;
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]substituting the given points;
[tex]\begin{gathered} (x_1,y_1)=(54,-61) \\ (x_2,y_2)=(8,-56) \end{gathered}[/tex]We have;
[tex]\begin{gathered} m=\frac{-56-(-61)}{8-54}=\frac{5}{-46} \\ m=-\frac{5}{46} \end{gathered}[/tex]Therefore, the slope m of the line that passes through the two given points is;
[tex]m=-\frac{5}{46}[/tex]
an alloy contains copper and zinc in the ratio 3:7. find the mass of the metal in 750g of alloy
Given:
An alloy contains copper and zinc in a ratio of 3:7. The total mass of the alloy is 750g.
Required:
Find the mass of the metal in 750g of alloy.
Explanation:
Let the mass of the metal is x gm.
The weight of copper = 3x
The weight of zinc= 7x
Total weight
[tex]\begin{gathered} 3x+7x=750 \\ 10x=750 \\ x=\frac{750}{10} \\ x=75\text{ gm} \end{gathered}[/tex]
Find the slope of the line that goes through the given points.
(-3,-2) and (– 15,13)
Answer:
Answer:
Slope m= [tex]-\frac{5}{4}[/tex]
As a decimal:
m = -1.25
Step-by-step explanation:
[tex]m=\frac{Rise}{Run} =\frac{y}{x} \\m=\frac{y2-y1}{x2-x1} \\m=\frac{13--2}{-15--3} \\m=\frac{15}{-12} \\m=-\frac{5}{4}[/tex]
3 Drag each equation to the correct location on the table. Determine the number of solutions to each equation. Then place each equation in the box that corresponds to its number of solutions. 35 = 2+ +1 2 – 1 = 45 + 3 31 – 2 35 + 1 2x + 3 = 35 – 1 1 2x + 1 = 21 No Solutions 1 Solution 2 Solutions Reset Next All rights reserved. i NE
Then, it has just 1 solution, and it should be placed in the second column.
[tex]\begin{gathered} 2^x-1=4^x+3. \\ \text{This has no solution} \end{gathered}[/tex][tex]\begin{gathered} 3x-2=3^x+1 \\ \text{This has no solution.} \end{gathered}[/tex]Next;
[tex]\begin{gathered} \frac{1}{2}x+3=3^x-1 \\ \text{This has no solution. It should be in the first column} \end{gathered}[/tex][tex]\begin{gathered} 2x+1=2^x \\ \text{Let x=0,} \\ 2(0)+1=2^0=1 \end{gathered}[/tex]This has one solution, and it should be placed in the second column.
Not everyone pays the same price for the same model of a car that the figure is the streets a normal distribution for the price paid for the particular model of a new car the meanest $24,000 and a standard deviation is $1000 user 68–95-99.7 Raw to find a percentage of buyers who paid more than $27,000
The Solution:
The correct answer is 0.15%
Given the data in the given question,
We are required to find the percentage of buyers who paid more than $27,000.
The percentage of the total buyers is 100%
The percentage of buyers that paid between $21,000 and $27,000 is given to be 99.7%
This means that the total percentage of buyers who paid less than $21,000 and the buyers who paid more than $27,000 is
[tex]100-99.7=0.3\text{ \%}[/tex]Since the distribution is a normal distribution, it follows that half of 0.3% is the percentage of buyers who paid more than $27,000.
[tex]\frac{0.3}{2}=0.15\text{ \%}[/tex]Thus, the percentage of buyers who paid more than $27,000 is 0.15%
7. 4×= 3yy=-4x + 39. y+2=0x+ 2 = 011.x-5y=45x + y = 4Determine if the graphs will show parallel or perpendicular lines, or neither.
Given:
[tex]\begin{gathered} 4x=3y \\ y=-4x+3 \end{gathered}[/tex]Sol:.
If the both line are perpendicular then multipilcation of slope is -1 then:
[tex]\begin{gathered} y=mx+c \\ m=\text{slope} \\ \end{gathered}[/tex][tex]\begin{gathered} 3y=4x \\ y=\frac{4}{3}x \\ m_1=\frac{4}{3} \end{gathered}[/tex][tex]\begin{gathered} y=-4x+3 \\ m_2=-4 \end{gathered}[/tex][tex]\begin{gathered} =m_1m_2 \\ =\frac{4}{3}\times-4 \\ m_1m_2\ne-1 \\ \text{That mean its not perpendicular } \end{gathered}[/tex]For parallel line slope are same then its not a parallel line
So line neither perpendicular or parallel.
Please find the coordinates and graph the points on the graph and rotate the image.Please demonstrate the pre image and the rotated image on the graph after finding the coordinates.
We have that the general rule for a counterclockwise rotation of 270 degrees is given by the following expression:
[tex]R_{270}(x,y)=(y,-x)[/tex]then, in this case,we have the following:
[tex]\begin{gathered} R_{270}(4,5)=(5,-4)=D^{\prime} \\ R_{270}(6,-2)=(-2,-6)=E^{\prime} \\ R_{270}(1,-2)=(-2,-1)=F^{\prime} \end{gathered}[/tex]and the graph would look like this:
which function has an inverse that is also a function horizontal line test
If the graph of a function y = f(x) is such that no horizontal line intersects the graph at more than one point, then f has an inverse function.
A. The absolute value function f(x) = | x | is intersected twice by any horizontal line at y > 0. Thus this function does not have an inverse
B. The quadratic function f(x) = x^2 has a graph called parabola. If we plot any horizontal line at y>0, that line will intersect the function twice. This function has no inverse function
I I need help solving problem number 8 please :)
Answer:
(8, -1)
Explanation:
Given the below system of equations;
[tex]\begin{gathered} y^2+x^2=65\ldots\ldots\ldots\text{.Equation 1} \\ y+x=7\ldots\ldots\ldots\ldots\text{.Equation 2} \end{gathered}[/tex]Let's go ahead and test each of the given solutions and see which of them is the correct one;
For (8, -1), we have x = 8 and y = -1;
Substituting the above values in Equation 1, we have;
[tex]\begin{gathered} (-1)^2+(8)^2=65 \\ 1+64=65 \\ 65=65 \end{gathered}[/tex]Substituting the values into Equation 2;
[tex]\begin{gathered} (-1)+8=7 \\ -1+8=7 \\ 7=7 \end{gathered}[/tex]We can see that (8, -1) is a solution to the given system of equations
What kind of transformation converts the graph of f(x)=(5x+6)^2 into the graph of g(x)=-(5x+6)^2
In order to get from
[tex]f(x)=(5x+6)^2[/tex]To
[tex]f(x)=-(5x+6)^2[/tex]You have to reflect across the x-axis.
Remember that the x-axis is the line with equation
[tex]y=0[/tex]Answer: Option A
A pair of bikes cost $89.99 and the sales tax is 8%.What is the total cost of the shoes including tax?
Answer
Total Cost of the bike including tax = $97.1892
Explanation
Cost of the bike = $89.99
Sales Tax = 8% of Cost of bike = 8% (89.99) = 0.08 (89.99) = $7.1992
Total Cost of the bike = (Cost of the bike) + (Sales Tax)
= 89.99 + 7.1992
= $97.1892
Hope this Helps!!!
write the linear equation that passes through the two given points (2,-2) and (0,-1)
Given the points:
(x1, y1) ==> (2, -2)
(x2, y2) ==> (0, -1)
To find the linear equation, use the form:
y = mx + b
where m is the slope.
To find the slope, use the formula below:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Thus, we have the slope as:
[tex]m=\frac{-1-(-2)}{0-2}=\frac{-1+2}{0-2}=\frac{1}{-2}=-\frac{1}{2}[/tex]Input 2 for x, -2 for y, and -1/2 for b to find b.
[tex]\begin{gathered} -2=-\frac{1}{2}(2)+b \\ \\ -2=-1+b \\ \\ -2+1=b \\ \\ -1=b \end{gathered}[/tex]Therefore, the linear equation is:
[tex]y=-\frac{1}{2}x-1[/tex]ANSWER:
[tex]y=-\frac{1}{2}x-1[/tex]Simplify.1,5m^7(-4m^50^2A. -6m^14B. 24m^17C. 24m^14D. 12m^17There is a picture too if you need it.
The expression can be simplified as,
[tex]\begin{gathered} 1.5m^7(-4m^5)^2 \\ =1.5m^7(16m^{10}) \\ =24m^{17} \end{gathered}[/tex]Thus, option (b) is the correct solution.
Which of the following shapes is the cross-section for a cylinder?A. SquareB. TriangleC. CircleD. Pentagon
Solution:
Concept:
The vertical cross-section of a cylinder is a rectangle, and the horizontal cross-section is a circle.
From the explanation above,
The final answer is CIRCLE
OPTION C is the right answer
Of the twenty-two students in a classroom, ten are transfer students, seven are nursing students, four are AAS students and one student is undecided.If three students are chose randomly, without replacement, find the probability that all three students are nursing students.
Given that:
• There are a total number of 22 students in the classroom.
,• 10 of them are transfer students.
,• 7 are nursing students.
,• 4 are AAS students.
,• 1 student is undecided.
,• Three students are chosen randomly.
Since you need to find the probability that all three students that are chosen randomly are nursing students, you need to set up that this is:
[tex]P(A)[/tex]Where Event A is that one of the students is a nursing student.
Therefore, the probability that three of the chosen students are nursing students can be set up as:
[tex]\begin{gathered} P=P(A)\cdot P(A)\cdot P(A)=P(A)^3 \\ \\ P=P(A)^3 \end{gathered}[/tex]Knowing that the total number of students is 22 and 7 of them are nursing students, you know that:
[tex]P(A)=\frac{7}{22}[/tex]Therefore:
[tex]P=(\frac{7}{22})^3[/tex][tex]P=0.0322[/tex]Hence, the answer is:
[tex]P=0.0322[/tex]Please help me i have been struggling for two days
we have the equation
[tex]\log _5(x+1)-\log _2(x-2)=1[/tex]using a graphing tool
see the attached figure
The solution is x=2.90y= 3(x-3)^2-12E) Find two more points on The Graph. You can choose what x-values to use. Write your points as coordinates x y
Given:
[tex]y=3(x-3)^2-12[/tex]The quadractic equation above is written in vertex form:
[tex]y=a(x-h)^2+k[/tex]Where:
(h, k) is the coordinate of the vertex of the parabola
We have
a = 3
h = 3
k = -12
Let's find the following:
A.) Identify the coefficients, a, h, and k
Comparing the equation with the vertex form, we have:
a = 3
h = 3
k = -12
B.) Identify whether the graph opens up or opens down.
If a is greater than zero, then the graph opens up
If a is less than zero, then the graph opens downwards
Here, a = 3
Since a is greater than zero, the graph opens up.
The graph of the equation opens up
C.) Find the vertex.
The coordinates of the vertex is = (h, k)
Given:
h = 3
k = -12
Therefore, the vertex is: (3, -12)
D.) Find the axis of symmetry.
The axis of symmetry is the line that passes through the vertex and the focus.
To find the axis of symmetry we have:
x = h
where h = 3
Thus, the axis of symmetry is:
x = 3
E.) Let's find two more points.
Point 1 ==> (x, y)
Let's take x = 1
Substitute 1 for x and solve for y:
[tex]\begin{gathered} y=3\mleft(x-3\mright)^2-12 \\ \\ y=3(1-3)^2-12 \\ \\ y=3(-2)^2-12 \\ \\ y=3(4)-12 \\ \\ y=12-12 \\ \\ y=0 \end{gathered}[/tex]When x is 1, y is 0.
Therefore, we have the point:
(x, y) ==> (1, 0)
Point 2:
Let's take x = 2
Substitute 2 for x and solve for y:
[tex]\begin{gathered} y=3\mleft(x-3\mright)^2-12 \\ \\ y=3(2-3)^2-12 \\ \\ y=3(-1)^2-12 \\ \\ y=3(1)-12 \\ \\ y=3-12 \\ \\ y=-9 \end{gathered}[/tex]When x is 2, y is -9.
Therefore, we have the points:
(x, y) ==> (2, -9)
ANSWER:
A.) a = 3
h = 3
k = -12
B.) The graph opens up
C.) (3, -12)
D.) x= 3
E.) (1, 0), (2, -9)
The number of cities in a region over time is represented by the function
For this question, in order to find T(x), we need to multiply the two given functions.
[tex]T(x)=(C\cdot P)(x)[/tex][tex]T(x)=C(x)\cdot P(x)[/tex][tex]=(2.9)(1.05)^x\cdot(1.05)^{3x+5}[/tex][tex]=(2.9)(1.05)^{x+3x+5}[/tex][tex]T(x)=2.9(1.05)^{4x+5}[/tex]Therefore, the answer must be option A.
Find all numbers whose absolute value is .4]
The numbers 4 and - 4 have an absolute value equal to 4.
What numbers are associated to a given absolute value?
In this question we need to find all the numbers such that absolute value is equal to 4. This can be found by using the definition of absolute value:
|x| = x for x ≥ 0.|x| = - x for x < 0.Absolute values are functions that contains only the magnitudes of the numbers, that is, their distances with respect to zero. Then, if the absolute value is 4, then, the number may be 4 or - 4.
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The absolute value is 4, then, the number may be 4 or - 4.
What are Absolute values?Absolute value describes the distance from zero that a number is on the number line, without considering direction
To find all the numbers such that absolute value is equal to 4.
By definition of absolute value we have
|x| = x for x ≥ 0.
|x| = - x for x < 0.
Absolute values contains magnitude which does not have direction.
|4|=4 for 4≥ 0.
|4| = -4 for x < 0.
Then, if the absolute value is 4, then, the number may be 4 or - 4.
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2625÷32 long division way
Answer: 82 R1 or decimal form 82.031
Step-by-step explanation:
0082
. --------
-0
26
. - 0
. 262
. -256
65
-64
. 1
write a linear equation to: slope=2 and goes through point (4, 11)
When you have to write a linear equation and you have the slope (m) and a point (4, 11) you:
1. Use the standard form of a linear equation:
[tex]y=mx+b[/tex]You know the value of:
m= 2
y= 11
x= 4
You make a substitution:
[tex]11=(2)(4)+b[/tex]You can find then the value of b:
[tex]11=8+b[/tex][tex]b=11-8=3[/tex]Then you have now the data to form the final linear equation:
[tex]y=2x+3[/tex]write each percent as a decimal 1%
You have the following percentage:
24.1%
In order to determine the associated decimal to this fraction you proceed as follow:
In certain deep parts of oceans, the pressure of sea water, P, in pounds per square foot, at a depth of dfeet below the surface, is given by the following equation:4dP = 14 +11If a scientific team uses special equipment to measures the pressure under water and finds it to be 318pounds per square foot, at what depth is the team making their measurements?Answer: The team is measuring atfeet below the surface.
1) Given this equation for Pressure, we need to plug into p the pressure of 318 lbs/ft² to get the depth according to the model described by this equation.
2) So, we can write out:
[tex]\begin{gathered} P=14+\frac{4d}{11} \\ 318=14+\frac{4d}{11} \\ 11\times318=11\times(14+\frac{4d}{11}) \\ 3498=154+4d \\ 3498-154=4d \\ 3344=4d \\ 4d=3344 \\ \frac{4d}{4}=\frac{3344}{4} \\ d=836ft \end{gathered}[/tex]Note that we multiplied both sides by 11 to get rid of the fraction.
Thus this is the depth below the surface that generates such pressure
I need help answering this question, if you can thank you very much.
Answer: We have to factor out the polynomial which is:
[tex]x^2+6x-16[/tex]The factorization is as follows:
[tex]\begin{gathered} \text{ Method:} \\ \\ (x+a)(x+b)=x^2+(a+b)x+ab \\ \\ \\ ----------------------- \\ \text{ Solution:} \\ \\ x^2+6x-16 \\ \\ \text{ The unknowns }\rightarrow\begin{cases}ab={-16} \\ a+b={6}\end{cases} \\ \\ \\ \text{ The possible values are:} \\ \\ \\ a=8 \\ b=-2 \\ \\ \\ \text{ Because:} \\ \\ \\ (8)\times(-2)=-16 \\ (8)+(-2)=6 \\ \\ \\ \text{ Therefore the factored form is:} \\ \\ \\ (x+8)(x-2)=x^2+6x-16 \end{gathered}[/tex]