Answers
Answer:
a. (-2,-1)
b. y = -(1/2)x-2
Step-by-step explanation:
We will look for an equation of the form y=mx+c, where m is the slope and b is the y-intercept (the value of y when x = 0).
Put the two given points into a table to make it easier to calculate the slopes for Lines A and B. See the attachment for the table. Slope is the change in y for a change in x, often termed the "Rise/Run." Using Line A as the example, the change in y (the Rise) is obtained by taking the Point 2 value for y (7) and subtracting the Point 1 value for y (3): Rise = (7 - 3) = 4. The Run is obtained by taking the Point 2 value for x (2) and subracting the Point 1 value of x (0). The ratio of Rise/Run is 4/2, so the slope is 2. The same process is used for Line B to obtain a slope of 3 for that line.
The two equations can be written with these slopes:
Line A: y = 2x + c
Line B: y = 3x + c
We need to find a value of c for each equation that will force the line through either of their two given points. c can be determined by entering either of that line's points into the equation(s) above and solving for c:
Line A:
y = 2x + c
3 = 2*(0) + c for point (0,3)
c = 3
The equation for Line A is y = 2x + 3
Line B:
y = 3x + c
2 = 3*(-1) + c for point (-1,2)
c = 5
The equation for Line B is y = 3x + 5
The graph of these lines is attached. They intersect at point (-2,-1).
[As a note, the solution may also be found by using substitution and solving for both x and y:
y = 2x+3
y = 3x+5
The solution exists when both y's and x's are equal:
Assume y is equal:
2x+3 = 3x+5
-x = 2; x = -2
----
Assume x is equal:
Rearrange:
y = 2x+3
2x = y-3
x = (y-3)/2
Use this definition of x in the second line equation:
y = 3x+5
y = 3((y-3)/2)+5
y = (3y - 9)/2 + 5
2y = 3y - 9 + 10
-y = 1
y = -1
The solution is (-2,-1), the same as was found by graphing.]
==================================================
A perpendicular line has a slope that is the negative inverse of the referenced line. For Line A, the perpendicual line would be -(1/2). The equation for this line would take the form y = -(1/2)x + c. We want this perpendicular line to intersect the same point that is the solution to the first problem: (-2,-1). Enter this point to find c:
y = -(1/2)x + c
-1 = -(1/2)*(-2) + c for (-2,-1)
-1 = 1+ c
c = -2
The perpendicular line is y = -(1/2)x - 2
See the attached graph.
Related Questions
Solve each system by elimination: 3x-2y=19 5x+4y=17
Answers
Answer: x= 5 y= -2
Step-by-step explanation: Time 2 to eliminate the y
6x - 4y = 38
5x + 4y =17
11x = 55
x= 5
Then put 5 in for the x, and you will get, y = -2
3. Beth finished 40% of her weekly biking workout. She has traveled 24 miles. How long is her
workout for the entire week?
Answers
Answer:
I think you times both numbers
Step-by-step explanation:
time both number s
Find the distance between point P and line ℓ.
Line ℓ contains points (0, −3 ) and (7, 4). Point P has coordinates (4, 3).
Answers
The distance between the line containing the points (0,-3) and (7,4) and the point P(4,3) is d =√2 units.
What is the distance between a line and a point?The distance between the line ax +by +c =0 and the point (x₁, y₁) is given by:
[tex]d=\frac{|ax_{1}+by_{1}+c|}{\sqrt{a^2+b^2}}[/tex]
Given that, the line passes through the points (0,-3) and (7,4).
The equation of the line is given by:
[tex]y -(-3)=\frac{4-(-3)}{7-0}(x-0)\\\\y+3=x\\\\x-y-3=0[/tex]
Now, the distance between the line x - y - 3 = 0 and point (4,3) is:
[tex]d=\frac{|1\times4+(-1)\times3+(-3)|}{\sqrt{1^2 +(-1)^2}}\\\\d=\frac{2}{\sqrt{2}}\\\\d=\sqrt{2}[/tex]
Hence, the distance between the line containing the points (0,-3) and (7,4) and the point P(4,3) is d =√2 units.
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the triangle has a perimeter of 65 feet. what system of equation to use for the perimeter equals 65 feet? l= 1/3m, m, and n=l+m-15
Answers
Answer:
l = 10 feet
m = 30 feet
n = 25 feet
Total Perimeter = 65 feet
Step-by-step explanation:
The perimeter of a trianlge is the sum of its three sides, and in this case is equal to 65 feet.
65 feet = l + m + n
l + m + n = 65
We also know that:
l = (1/3)m, and
n = l+m-15
Substitute these definitions of l and n into the original equation:
l + m + n = 65
[(1/3)m] + m + [l+m-15] = 65
[(1/3)m] + m + [[(1/3)m]+m-15] = 65
Simplify:
(1/3)m + m + (1/3)m + m - 15 = 65
2m + (2/3)m = 80
(6/3)m + (2/3)m = 80
(8/3)m = 80
m = 80*(3/8)
m = (10)*(3)
m = 30 feet
Since l = (1/3)m, l = 10 feet
Since n = l+m-15, n = 10 + 30 - 15, or 25 feet
The three sides are
l: 10 feet
m: 30 feet
n: 25 feet
Total = 65 feet
If x + y = 7 and x - y = 9, find the product of x and y.
Answers
Answer:
x=8
y=-1
Step-by-step explanation:
What is the solution to the system of equations?
2x+6y=-28
x + 3y = -14
Answers
Because when two linear equations graph this very same line, a system of two linear simultaneous equations variables cannot be solved.
What in mathematics is a linear equation?A linear equation seems to be an algebraic equation of something like the form y=mx+b, where m is the slope as well as b is the y-intercept, and only a constant and an initial-order (linear) component are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Briefing:2x+6y=-28 (i)
x + 3y = -14 (ii)
Subtract 3y from both sides of the equation(ii)
[tex]\begin{matrix}&x=-14-3y\\&2x+6y=-28\\\end{matrix}[/tex]
Replace all occurrences of x with -14-3y in each equation.
Replace all occurrences of x in 2x+6y=-28 with -14-3y.
[tex]\begin{matrix}&2(-14-3y)+6y=-28\\&x=-14-3y\\\end{matrix}[/tex]
Simplify the left side.
Simplify 2(-14-3y)+6y.
[tex]\begin{matrix}&\ -28=-28\\&x=-14-3y\\\end{matrix}[/tex]
Remove any equations from the system that are always true.
[tex]x=-14-3 y[/tex]
there is no solution for the given equation.
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what common side do △ADE and △BED share?
Answers
Answer:
ED
Step-by-step explanation:
They both have side ED in their triangles!
solve for C
7(c-12)=-21
Answers
Answer: c=9
Step-by-step explanation:
Which system of inequality is represented on the graph?
Answers
By solving linear inequation, it can be calculated that
The system of linear inequation represented by the graph is
x - y ≥ -8
3x + y ≥ -8
What is linear inequation?
Inequation shows the comparison between two algebraic expressions by connecting the two algebraic expressions by >,<, ≥, ≤
A one degree inequation is known as linear inequation.
Here,
One line passes through (0, 8) and (-1, 7)
Slope of the line = [tex]\frac{7-8}{-1-0}[/tex] = 1
Equation of line
y - 8 = 1(x - 0)
y - 8 = x
x - y = -8
Other line passes through (-4, 4) and (-3, 1)
Slope of the line = [tex]\frac{1-4}{-3-(-4)}[/tex] = -3
Equation of line
y - 4 = -3(x - (-4))
y - 4 = -3x - 12
3x + y = 4 - 12
3x + y = -8
Now the lines are solid lines
So equality is maintained
(0, 0) is inside the shaded region
So the system of linear inequation represented by the graph is
x - y ≥ -8
3x + y ≥ -8
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5% of what number is 9?
Answers
Answer:
180
Explanation:
5% of x = 9
9 × 100 = 900
900 ÷ 5 = 180
So,
5% of 180 = 9
5Answer:
45
Step-by-step explanation:
9x0.5=4.5
please help
its just 7th grade math Im bad at math
Answers
Answer:
B
Step-by-step explanation:
since it is already finalized that 200 lbs worth of computers have been loaded onto the truck, that will be a number by itself in the equation. However, the number of boxes of books is not finalized, and the question is asking you to create an inequality that may help find the amount of full boxes that can be loaded onto the truck without exceeding the weight limit of 1400 lbs.
hope this helps!!! :3
Barbara wants to restore her '66 Mustang in 4 years. She puts $200 into an account every month that pays 1.05% interest, compounded monthly. How much interest did she gain in 4 years?
Answers
Using the formula of compound interest, the amount accumulated over 4 years is $15,849.46
Compound InterestCompound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period. In Mathematics, compound interest is usually denoted by C.I.
The formula is often given as;
C.I = P(1 + r/n)^nt
C.I = Compound InterestP = principal r = raten = number of times compoundedt = timeSubstituting the values into the formula
C.I = 200(1 + 0.0105/12)^12*4
However, over the period of 4 years, the Principal becomes
Principal = 200 * 4 * 12 = 9600
Rate = 1.05 * 12 = 12.6
C.I = 9600(1 + 12.6/12)^12 * 4
C.I = $15,849.46
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LMNO is a parallelogram. If NM =x+5 and OL =2x+3 then find the value of x
Answers
If LMNO is a parallelogram then NM=7=OL and the value of X is 7 unit
What is a Parallelogram?
A quadrilateral having two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.
A parallelepiped is a three-dimensional shape with parallelogram-shaped faces. The base (one of the parallel sides) and height (the distance from top to bottom) of the parallelogram determine its area. A parallelogram's perimeter is determined by the lengths of its four sides.
As it is a parallelogram so, the opposite sides of the parallelogram are equal so NM=OL and ON=LM ,
according to the question ;-
NM = x+5
OL=2x+3
and NM=OL
x+5=2x+3
x=2
So, NM= 7
OL=7
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Evaluate 10.2x + 9.4y when x = and y = 3
Answers
The expression 10.2x + 9.4y when x = and y = 3 is 38. 4
What is an algebraic expression?An algebraic expression can be defined as an expression that is composed of terms, constants, coefficients, variables and factors.
These algebraic expressions are also made up of mathematical operations such as;
DivisionAdditionSubtractionParenthesesMultiplicationBracket. etcFrom the information given, we have the algebraic expression;
10.2x + 9.4y
Now, let's substitute the values of x as 1 and y as 3 into the expression, we have;
10.2(1) + 9.4(3)
expand the bracket
10. 2 + 28. 2
Add the values
38.4
Hence, the value is 38.4
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round 163 to the nearest 10? round it to the nearest ten it would be 160 i think because 163 is close to 160 so it has to 160
Answers
Answer:
163 rounded to the nearest ten = 160.
Step-by-step explanation:
yes since 163 is not 165 or greater its 160 but if it the number was greater than 165 than it would be 170. in this case its not so the answer would be 160.
A line passes through point (-5,-1) and has a slope of -3.
Write an equation in Ax+By=C form for this line.
Use integers for A,B, and C.
Answers
Answer:
y+3x=-16
Step-by-step explanation:
y=mx+c
y=-3x+c
-3x is the gradient
-5 is the x value and -1 is the y value
-1=-3x-5+c
-1=15+c
-16=c
y=-3x-16
y+3x=-16
determine the measure of each missing angle in the triangle! HELPPP PLEASSEEEE!!!
Answers
Answer the statistical measures and create a box and whiskers plot for the following set of data.
1, 3, 3, 5, 6, 6, 6, 7, 7, 10, 10, 11, 14
1,3,3,5,6,6,6,7,7,10,10,11,14
Answers
For the box and whiskers plot for the following set of data the value of Min is 3, Q1 is 6, Med is 12, Q3 is 14.5 and Max is 17.
What is box and whiskers plot?Box and whiskers plot is the way of representation of data which gives the graphical image of the data set to understand better. In this the data is represented with the help of quartile.
The minimum and the maximum values in the box plot is plotted at the end points.
The following set of data which i s given in the problem.
3, 4, 5, 6, 6, 7, 7, 12, 13, 14, 14, 15, 15, 16, 17
Min: 3
The minimum value in the given data is 3. Thus, the min is 3.
Q1:6
First quartile appears at 6. Thus, the value of Q1 is 6.
Med:12
The middle value of the given data is 12 which appears at the center of all the values. Thus the med is 12.
Q3:14.5
Second quartile appears at 14.5. Thus, the value of second quartile Q2 is 6.
Max: 17
The minimum value in the given data is 17 as shown in the image attached below. Thus, the min is 17.
Hence, for the box and whiskers plot for the following set of data the value of Min is 3, Q1 is 6, Med is 12, Q3 is 14.5 and Max is 17.
The complete question is : Answer the statistical measures and create a box and whiskers plot for the following set of data. You may optionally click and drag the numbers into numerical order.
3, 4, 5, 6, 6, 7, 7, 12, 13, 14, 14, 15, 15, 16, 17
3,4,5,6,6,7,7,12,13,14,14,15,15,16,17
Min:
Q1:
Med:
Q3:
Max:
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Mr. Johnson wants to use the interest from his High Savings Account to buy his next TV. The TV will cost $900. He would like his investment to grow over for two and a half years. If he has a rate of 3.5%, how much will he need to invest in order to cover the cost of the TV?
Answers
now, we're assuming the rate of 3.5% is for a simple interest account, so
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$900\\ P=\textit{original amount deposited}\\ r=rate\to 3.5\%\to \frac{3.5}{100}\dotfill &0.035\\ t=years\dotfill &2.5 \end{cases} \\\\\\ 900=P[1+(0.035)(2.5)] \implies 900=P(1.0875) \\\\\\ \cfrac{900}{1.0875}=P\implies 827.59\approx P[/tex]
If ur good at geometry can u help Solve for m given that the perimeter of the triangle is 19 centimeters.
Answers
Answer:
m = 7
Step-by-step explanation:
6 + 6 + 7 = 19.
You're welcome.
In a fish tank, 4/9 of the fish have a red stripe on them. If 12 of the fish have red stripes, how many total fish are in the tank?
Answers
Answer: If 4/9 of the fish have a red stripe, we can determine the total number of fish in the tank by dividing the number of fish with red stripes by the fraction of fish with red stripes. This gives us 12 / (4/9) = 12 * (9/4) = 27 fish. So, there are 27 fish in the tank.
[tex] \frac{4}{9} x = 12[/tex]
[tex]x = 12 \times \frac{9}{4} [/tex]
[tex]12 \times 9 = 108[/tex]
[tex]4 \times 1 = 4[/tex]
[tex]x = \frac{108}{4} [/tex]
[tex]x = 27[/tex]
There are 27 fish in the tank. Hope this helps.
Khadia raie bee and ell honey. He give a dicount to hi neighbor. The table how price of ,n of buying honey that ha a regular price of r dollar
Answers
The equation for the relationship between the regular price (r) and the neighbor's price (n) will be r - n = 250.
What are equations?A mathematical expression with an equals sign is referred to as an equation.
Algebra is widely used in equations.
When performing calculations but unsure of the precise number, algebra is used.
Linear equations: Any equation that can be expressed as ax + by + c = 0, where a, b, and c are all real numbers and a and b are not equal to zero.
In light of the posed query.
Khalid keeps bees and sells honey from them.
Additionally, n stands for the neighbor's honey price in dollars and r stands for the ordinary honey price in dollars.
We can determine the discount from the provided information.
7 - 4.50 = 2.50
8 - 5.50 = 2.50
10 - 7.50 = 2.50
12 - 9.50 = 2.50
Khalid gives his neighbor $2.50.
The equation for the link between the regular price r and the neighbor's price n will therefore be: r - n = 250
Therefore, the equation for the relationship between the regular price (r) and the neighbor's price (n) will be r - n = 250.
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Complete question:
Khalid raises bees and sells the honey. He gives a discount to his neighbors. The table shows the neighbors' price, n, of buying honey that has a regular price of r dollars. Write an equation that represents the relationship. I put two pictures below to help. :)
Answer: r - n = 2.5
Step-by-step explanation: Took Quiz
In the order of operations, the absolute value sign is considered to be at which level?
Answers
Answer:
Note that with embedded parentheses (parentheses within parenthesis), you always perform operations inside out; do the math on the inside before the outside. Note that if you have an absolute value | | sign which means take the positive value only of a number inside.
Answer: Absolute Value is the first level.
Step-by-step explanation:
2 |-10|
2 * 10
20
Which situation can be represented by the equation 56 = 2x -10? A. Sammy's age is 10 more than twice Ted's age. Sammy is 56 years old. How old is Ted? B. Sammy's age 10 decreased by twice Ted's age. Ted is 56 years old. How old is Sammy? C. Ted's age is twice Sammy's age decreased by 10 years. Ted is 56 years old. How old is Sammy? D. Ted's age is 10 less than twice Sammy's age. Sammy is 56 years old. How old is Ted?
Answers
Answer:
I'll try here: 23
Step-by-step explanation:
X = Sam's age.
X-10 = Ted's age
X + X -10 = 56
2X -10 =56
2x = 66
X = 33 , Sam's age
33 - 10 = 23 Ted's age
3x+8 = x-6
x=?
pls help
Answers
Answer:
x = -7Step-by-step explanation:
3x+8 = x-6
x=?
3x + 8 = x - 6
2x = -14
x = -7
---------------------------
check
3 × (-7) + 8 = -7 - 6
-21 + 8 = -13
-13 = -13
the answer is good
A motorcycle covers 315 km distance with 7 liters of petrol.
i)how many kilometres does it cover with 12 liters of petrol in the same mileage?
ii)how much petrol is needed to cover 270 km in the same mileage?
Answers
Step-by-step explanation:
225 km travels in =25 ltr
1 km travel = 225 25
540 km will require = 22525 ×540=60 L
Was this answer helpful?
Answer:
1) 540 km
2) 6 liters of petrol
Step-by-step explanation:
To answer the two questions, it is easiest to fist find the relationship between kilometers (km) and liters of petrol. Since 7 liters (L) results in 315 km, we can find the km/liter petrol conversion factor (converts liters of petrol to km):
(315 km)/(7 liters) = 45 km/L
1) 12 liters times the conversion factor will tell us how many km the motorcycle will travel"
(12 liters)*(45 km/liter) = 540 km [Note that the liters unit cancles, leaving only km]
2) To find the liters of petrol to travel 270 km, we can use the same conversion factor, but now we need to divide to get the units we want, which is km:
(270 km)/(45 km/l) = 6 liters [Note that km cancels and l moves to the top, leaving liters as the only unit.
At a coffee shop, the first 100 customers' orders were as follows. Small Medium Large Hot un 48 22 Cold 8 12 5 What is the probability that a customer ordered a medium given that he or she ordered a hot drink? Rounded to the nearest percent, [? ]% Enter
Answers
The probability that a customer ordered a small given that he or she ordered a cold drink is 32%
How to determine the probability?
The probability is represented as:
P(Small | Cold)
This is calculated using:
P(Small | Cold) = n(Small and Cold)/n(Cold)
Using the data on the given table, we have:
P(Small | Cold) = 8/(8 + 12 + 5)
Evaluate
P(Small | Cold) = 0.32
Express as percentage
P(Small | Cold) = 32%
Hence, the probability that a customer ordered a small given that he or she ordered a cold drink is 32%
Which statements are not true and true?
statement 1: the sum of two negative integers is positive
Statement 2: the product of two negative integers is positive
Statement 3: the difference of two negative integers is positive
Statement 4: the quotient of two negative integers is positive
Answers
A company has a monthly time series that regularly shows sales being higher in the summer months. This is an example of which component?.
Answers
This is an example of a seasonal component in a time series. A seasonal component refers to regular, predictable patterns that are associated with the time of year, such as increased sales during the summer months.
What are the different components in sales?Selling products or services to clients in exchange for cash or other types of payment is known as ale. The sales process consists of a number of elements, such as:
Product: The items or services being sold are referred to here. A corporation must have a comprehensive grasp of its product offerings and how they fit the demands of its target market.
Price: The sum of money that a consumer must fork over in order to purchase the item or service. Price should be set to maximise profit while maintaining market competitiveness.
Locations where higher the good or service is sold are referred to here as "place." Physical storefronts, internet marketplaces, or a network of distributors may all fall under this category.
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PLEASE HELP ASAP!!!!
Answers
Answer:
Lie #3
b^6 is not b^8
Step-by-step explanation:
All the problems use the quotient rule of exponents, which says that you subtract the exponents when dividing by the same base.
If we plug in 2 for x on #3, we have
[tex]\frac{b^8}{b^2}=b^(^8^-^2^)=b^6\\ b^6\neq b^8[/tex]
Furthermore, x would need to be 0 to make #3 true since 8-0 = 8