How would I graph these equations?
a. 2x + 3y = 12
b. x = 7
Answers
A
For Part A, we must first put this in Slope Intercept Form (SIF), which is y=mx+b where "m" is the slope and "b" is the y-intercept. To do this, we should solve like a normal equation for y.
2x+3y=12
-2x -2x
3y=-2x+12
/3 /3
y=-2/3x+4
Now that we have the proper equation, it is simply to graph! We should simply make a point at (0, 4), and then go down 2, right 3 until you are satisfied with your line.
B
Part B is a simple x value, which means you will draw a vertical line through 7 on the x-axis.
Below I have attached a clearly labeled graph that shows you examples of these lines. The red markings indicate x=7. The yellow circle shows you the y-intercept in Part A, while the yellow dots show you the slope in Part A.
Related Questions
what is the slope of a line that is parellel to the line represented by the equation y=2/5x+4/5
Answers
So, answer would be 2/5.
8. Find the congruence transformation that maps ∆ABC to ∆A’B’C’. Explain your reasoning
Answers
In this case, to flip any of the points to map up accurately to the other points, we would have to do a transformation of reflection about the y-axis. The reason behind this is that out of other transformation process, we can only achieve the image of triangle ∆A’B’C’ through reflection.
Dilation will not work since it only changes the size of the object. The shape and position will not affected.
A translation will not work because although the shape can move, it still needs to flip to achieve triangle ∆A’B’C’.
A rotation will also not work because when you rotate it, the shape will still not map over the new one.
Therefore the only answer to this question would be to
reflect triangle ∆ABC about the y-axis.
Joey has a full 40 coins consisting of only quarters and nickels if the total value is $5.00 how many of each does joey have.
Answers
0.25q + 0.05n = 5
0.25(40 - n) + 0.05n = 5
10 - 0.25n + 0.05n = 5
-0.25n + 0.05n = 5 - 10
- 0.20n = -5
n = -5 / -0.20
n = 25 <=== 25 nickels
q + n = 40
q + 25 = 40
q = 40 - 25
q = 15 <== 15 quarters
q=number of quarters
40 coins total so
n+q=40
total value is 500 cents
5n+25q=500
divide both sides by 5
n+5q=100
so we gots
n+q=40
n+5q=100
elimination
multily first equation by -1 and add to 2nd equation
-n-q=-40
n+5q=100 +
0n+4q=60
4q=60
divide both sides by 4
q=15
sub back
n+q=40
n+15=40
minus 15 both sides
n=25
25 nickles and 15 quarters
The base edge of an oblique square pyramid is represented as x cm. If the height is 9 cm, what is the volume of the pyramid in terms of x?
3x2 cm3
9x2 cm3
3x cm3
x cm3
Answers
Hence, the volume of pyramid is:
3x^2 cm^3
Step-by-step explanation:We know that a volume(V) of a oblique square pyramid with height 'h' and base area A is given by the help of formula:
[tex]V=\dfrac{1}{3}\times (Ah)[/tex]
Now, according to the ques we have:
The base edge of an oblique square pyramid is represented as x cm.
The height is 9 cm.
Hence, the base area (A) is calculated as:
[tex]A=x^2[/tex]
( Since the base is in the shape of a square and we know that the area of square with side length s is given as:
[tex]Area=s^2[/tex] )
So, the volume of the pyramid is calculated as:
[tex]V=\dfrac{1}{3}\times (x^2\times 9)\\\\V=3x^2 \ cm^3[/tex]
Hence, the volume of pyramid is:
3x^2 cm^3
A pyramid is a solid shape with several triangles and a base. The volume of the pyramid in terms of x is 3x^2 cm3
How to calculate the volume of a pyramid?The volume(V) of an oblique square pyramid with height 'h' and base area A is expressed according to the formula:
V = Bh/3
B is the base area = x * x = x^2
h is the height = 9cm
Substitute
V = x^2*9/3
V = 3x^2cubic cm
Hence the volume of the pyramid in terms of x is 3x^2 cm3
Learn more on volume of pyramid here: https://brainly.com/question/218706
What is the degree of this polynomial? 5y^4+y^3+2/3y^2+y+1
A. 5
B. 2
C. 1
D. 4
Answers
so.. notice, if the term has several variables, the degree of the term is, the sum of the exponents.
Answer: 4
Step-by-step explanation:
Complete the series: 3760, 1880, 360, 180, 45,?
Answers
Rex weighed 80 pounds a year ago. Now he weighs 92 pounds. What is the percent increase in his weight?
(A)12%
(B)13%
(C)15%
(D)16%
Answers
.15~15%
Answer is 15%
%change=100(92-80)/80
%change=1200/80
%change=15%
Find the equation of the linear function which passes through the points (-1, 3) and (4, -2). give your answer in y = mx + b form.
Answers
Hello : let
A(-1,3) B(4,-2)
the slope is : (YB - YA)/(XB -XA)
(-2-3)/(4+1) = -1
an equation is : y=ax+b a is a slope
y = -x +b
the line through
point B(4,-2) : -2 = -1(4)+b
b = 2
the equation is : y =-x+2
Please help!
A company has a $150 budget to provide lunch for its 20 employees. The options are to provide either roast beef sandwiches, which cost $5 apiece, or tuna sandwiches, which also cost $5 apiece. The company also wants to use the entire budget. Suppose r represents the number of roast beef sandwiches it provides and t represents the number of tuna sandwiches. Which statement is correct?
A. The company can provide lunch for all 20 employees and use the entire budget because there is a solution to the system of equations r-t=20 and 5r+5t=150.
B. The company can provide lunch for all 20 employees and use the entire budget because there is a solution to the system of equations r+t=20 and 5r+5t=150.
C. The company cannot provide lunch for all 20 employees and use the entire budget because there is no solution to the system of equations r-t=20 and 5r-5t=150.
D. The company cannot provide lunch for all 20 employees and use the entire budget because there is no solution to the system of equations r+t=20 and 5r+5t=150.
Answers
r+t = 20 and 5(r+t) = 150
If you sub in the first equation into the second, you will get: 100 = 150, which is incorrect
It means the system does NOT have solutions.
Answer will be the last choice
Answer: D. The company cannot provide lunch for all 20 employees and use the entire budget because there is no solution to the system of equations r+t=20 and 5r+5t=150.
Step-by-step explanation:
Let 'r' represents the number of roast beef sandwiches it provides and 't' represents the number of tuna sandwiches.
Then, the total number of roast beef sandwiches and tuna sandwiches is equal to the number of employees :
[tex]r+t=20[/tex]....................(1)
Also, the cost of each roast beef sandwich and cost of each tuna sandwich is same as $5.
If company wants to use the entire budget of $150, then we have another equation :-
[tex]5r+5t=150\\\5(r+t)=150[/tex]
If we divide 5 on both sides we get
[tex]r+t=30[/tex].............................(2)
When we compare equation (1) and (2) we get 20=30 but it is not possible therefore the system has no solution.
Therefore, the correct statement is "The company cannot provide lunch for all 20 employees and use the entire budget because there is no solution to the system of equations r+t=20 and 5r+5t=150."
A hotel chain charges $75 each night for the first two nights and $50 for each additional night’s stay. the total cost t is a function of the number of nights x that a guest stays.
Answers
you would need a function to determine whether to use a formula for 1 or 2 nights or a formula for more than 2 nights
T(x)={a if x <_ 2, b if x > 2}
if it's 2 nights or less use option a, a = 75x
if its longer than 2 days use option b, b= 50x + 50
Answer:
t = 75x {x ≤ 2}
t = 150 + 50x {x > 2}
Step-by-step explanation:
A hotel chain charges $75 per night for first two nights.
If the number of nights of the stay are x then charges for x nights
= 75x where x ≤ 2
If the stay is for than 2 nights then charges for x nights
= Charges for two first 2 nights(@$75 per night) + charges for other than initial 2 nights (@$50 per night)
= (75×2) + 50x where x > 2
Therefore total cost of the hotel if represented by t then the function will be
t = 75x {x ≤ 2}
t = 150 + 50x {x > 2}
Determine the equation of the graph and select the correct answer below.
parabolic function going down from the left and turning at the point negative three comma two and going up through the point zero comma twelve and continuing towards infinity
y = (x + 3)2 − 2
y = (x − 3)2 − 2
y = (x + 3)2 + 2
y = (x − 3)2 + 2
Answers
Answer:
The correct answer is [tex]y = \frac{10}{9}(x+3)^2+2[/tex]
Step-by-step explanation:
The correct answer to the question is not provided in the options listed below.
In order to find the equation of the quadratic function that you're looking for, you should identify the two points the parabola passes through: the vertex (that is point (-3,2)) and the y-intercept (the point (0,12)).
As we are given the vertex of the quadratic function, we can use the completed square form: [tex]y=a(x-h)^2+k[/tex], where h and k are, respectively, the x and y coordinates of the vertex.
As (-3,2) is the vertex, we have:
[tex]y=a(x+3)^2+2[/tex]
Now, as the graph passes through the point (0,12), we can replace x=0 and y=12 in the formula above in order to find the value of a. Then, we make a the subject of the equation:
[tex]12=a(0+3)^2+2[/tex]
[tex]12=9a+2[/tex]
[tex] 10=9a[/tex]
[tex] \frac{10}{9}=a[/tex]
So, the equation of the parabola is [tex]y=\frac{10}{9}(x+3)^2+2[/tex].
Read the following statement: 3x = 3x. This statement demonstrates:
the substitution property.
the reflexive property.
the symmetric property.
the transitive property.
Answers
Helllllllllllkklllllllkkkkkkkp
Answers
In other words, you can put it like this:
1(ab) + 1c = 1d
Since our answer choices, let's try to get a by itself.
ab + c = d
Subtract both sides by c.
ab = d - c
Now, a is being multiplied by b, so we need to perform the opposite order of operations (divide).
Divide both sides by b.
You're left with:
a = (d - c)/b
Your answer is D.)
I hope this helps!
A regular hexagon and an equilateral triangle have equal perimeters. what is the ratio of the area of the hexagon to the area of the triangle? express your answer as a common fraction.
Answers
Hexagon: s = (p/6) = p/6
Triangle: s = (p/3) = p/3
The areas of each polygon are also calculated below. It is noted that the polygons are regular (meaning, each side and angle are equal).
Area of Hexagon: A = 3√3/2 a²
Substituting the known values,
A = 3√3/2(P/6)²
Simplifying,
A = √3/24P²
For the triangle,
A = √3/4a²
Substituting,
A = √3/4 (P/3)²
Simplifying,
A = √3/36P²
The ratio is equal to:
ratio = (√3/24P²) / (√3/36P²)
ratio = 3/2
ratio = 1.5
A company sells boxes of cow bells (b) for $20 and boxes of air horns (h) for $30. They can make a batch of cow bells that fills 8 boxes or a batch of air horns that fills 9 boxes. The company only has 53 boxes. Which system of equations helps the company plan to make $275?
Answers
8b + 9h = 53
Solving a system of equations to help a company plan revenue and production constraints.
The system of equations:
20b + 30h = 275 (total revenue equation)
8b + 9h = 53 (total boxes equation)
By solving these equations simultaneously, the company can determine the number of cow bells and air horns to produce to make $275 while satisfying the box constraint.
the first term of the sequence is 13 the term to rule is take away -5 work out the 4th term
Answers
The student is trying to find the 4th term in a mathematical sequence where the first term is 13 and the rule for each term is to add 5. Thus, the 4th term of this sequence is 28.
Explanation:The student is asking about a mathematical sequence where the first term is 13 and the term to rule is 'take away -5', or in other words, add 5 (since subtracting a negative number is the same as addition). So, to find the nth term of this sequence, you subtract (or add in this case) -5 to the first term, and continue in the sequent term.
Using these rules, here are the first four terms of the sequence: 1st term - 13. 2nd term [tex]- 13 + 5 = 18[/tex]. 3rd term [tex]- 18 + 5 = 23[/tex]. 4th term[tex]- 23 + 5 = 28.[/tex]
So, the 4th term in this sequence is 28.
Learn more about Mathematical Sequence here:
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Solve the equation. 8d + 3d – 3d – 8 = 3d
Answers
D = - 1.6
this is the answer simplified
Answer:
1.6
Step-by-step explanation:
If 3x² -6=y for all real numbers x, then x² - 2 =
Answers
If 3(x² - 2) = y, then
[tex] \frac{3(x^2-2)}{3}= \frac{y}{3} \\ \\ x^2-2 = \frac{y}{3} [/tex]
Answer:
x² - 2 = y/3
If a and b are positive numbers such that 2b=3a, what's the value of ((a+b)/b)? I know you can plug in numbers for this, but i'm interested in solving this algebraically. Thanks.
Answers
What is the solution to this system of equations 2x-7=y y=2x+3
Answers
Answer:
No solution
Step-by-step explanation:
[tex]2x-7=y[/tex]
[tex]y=2x+3[/tex]
To solve the system of equations, we use substitution method
Lets substitute the second equation y=2x+3 for y in the first equation and solve for x
[tex]2x-7=2x+3[/tex]
Lets solve for x
subtract 2x on both sides
[tex]2x-2x-7=2x-2x+3[/tex]
[tex]-7=+3[/tex] is false
So, no solution for this system of equations
Find the dot product, a • b. a = 6i + 5j, b = -5i + 4j
Answers
If i is the constant i, then it is 20j^2 -i*j + 30
Answer:
the answer is -10
(05.01 MC)
The table and the graph below each show a different relationship between the same two variables, x and y:
How much more would the value of y be on the graph than its value in the table when x = 12?
20
30
60
70
Answers
For the table, y = 25x.
When x = 12, y = 25*12 = 300
For the graph, y = 30x
When x = 12, y = 30*12 = 360
When x = 12, the value of y on the graph is 60 more than its value in the table.
Answer:
The correct option is C. The value of y be on the graph than is 60 more than the y value in the table when x = 12.
Step-by-step explanation:
If a line passing through two points then the equation of line is
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
From the given table it is clear that the line passing thought the points (4,100) and (5,125).
[tex]y-100=\frac{125-100}{5-4}(x-4)[/tex]
[tex]y-100=25(x-4)[/tex]
[tex]y-100=25x-100[/tex]
[tex]y=25x[/tex]
The value of this function at x=12 is
[tex]y=25(12)=300[/tex]
From the given table it is clear that the line passing thought the points (0,0) and (2,60).
[tex]y-0=\frac{60-0}{2-0}(x-0)[/tex]
[tex]y=30x[/tex]
The value of this function at x=12 is
[tex]y=30(12)=360[/tex]
The difference between y value in the graph and in the table at x=12 is
[tex]360-300=60[/tex]
The value of y be on the graph than is 60 more than the y value in the table when x = 12. Therefore the correct option is C.
Find the measures of all of the angles in the parallelogram.
Answers
FED = DGF = 59x - 1
EDG = GFE = 121x + 1
And now since we know angles in a quadrilateral always add up to 360°, we can create an equation and solve for x:
2(59x - 1) + 2(121x + 1) = 360
118x - 2 + 242x + 2 = 360
360x = 360
x = 1
Now sub into our angle equations:
FED = DGF = 59(1) - 1 = 58°
EDG = GFE = 121(1) + 1 = 122°
A dress calls for 1 1/3 yards of material for a dress.if you have 21 3/4 yards of material,how many dresses can be made?
Answers
divide 21 3/4 by 1 1/3 = 16 5/16
she can make 16 dresses
I need help with this problem
Answers
Zeus Industries bought a computer for $2740. It is expected to depreciate at a rate of 24% per year. What will the value of the computer be in 3 years?
Round to the nearest penny. Do not type the "$" sign in your answer
Answers
A=p (1-r)^t
A ?
P 2740
R 0.24
T 3years
A=2,740×(1−0.24)^(3)
A=2,740×(0.76)^(3)
A=1,202.8 round your answer to get
A=1203
Using the given points, determine the slope.
(0, 32) and (100, 212)
Answers
To find the slope of two given points, subtract the y values, and subtract the x values, or..
[tex] \frac{(y2 - y1)}{(x2 - x1)} [/tex]
[tex] \frac{(212 - 32)}{(100 - 0)} [/tex]
[tex] \frac{180}{100} [/tex]
The answer is 9/5 or 1.8.
Hope this helps! :)
The slope is the change in y divided by the change in x.
or
The slope is the ratio of rise to run.
so:slope = (212-32) / (100-0) = 9/5 = 1.8
Triangle DEF is congruent to GHJ by the SSS theorem. Which rigid transformation is required to map DEF onto GHJ?
dilation
reflection
rotation
translation
Answers
Answer: The correct option is 4, i.e., translation.
Explanation:
It is given that the triangle DEF is congruent to GHJ by the SSS theorem.
From the given figure it is noticed that the triangle DEF and GHI are isosceles triangle.
Reason for correct option:
In transition the side and angles of the shape are not effected and the figure transfers from one place to another place without making any other change.
Since the both triangle are congruent and the position of all sides and angles are same, therefore option 4 is correct.
Reason for incorrect option:
In dilation the size of the figure is either stretched or compressed according to the scale factor k. But in the given figure the size of both triangles are same it means option A is incorrect.
In reflection the distance of all the point in preimage and all the image are same from the central line. Any central line does not exist in given figure. SO, the option B is incorrect.
In rotation the side length and angles are not affected but the position are not same, therefore the option C is incorrect.
Answer: Translation
Step-by-step explanation:
Given: Triangle DEF is congruent to GHJ by the SSS theorem.
From the given picture two sides of both triangles are equal therefore, the triangle DEF and GHI are isosceles triangle.
We know that a transition is a kind of rigid motion used in geometry to trace a function that moves an object a particular distance that maps produces images.
Since the both triangle are congruent and just position of triangle GHJ is shifted to the right and down.
Therefore, the transition is rigid transformation which is required to map DEF onto GHJ
A map of square piece of property is drawn at a scale of 1:500. If a side of the property on the map is 16 cm, what is the property's actual area?
Answers
s=500x
A=250000x^2, and since x=16cm
A=250000(16^2)
A=64000000 cm^2 But a more appropriate unit would be m^2 so:
A=64000000cm^2(m^2/10000cm^2)=6400 m^2
Answer:
Property's actual area = 6400 m²
Step-by-step explanation:
Scale = 1 : 500
Side on map = 16 cm
Side of property = scale x side on map = 16 x 500 = 8000 cm
Area of property = 8000 x 8000 = 64000000 cm²
Area of property = 6.4 x 10⁷ cm² = 6.4 x 10³ m²
Property's actual area = 6400 m²
Find the 6th term of a geometric sequence t3=444 t7=7104
Answers
Answer:
3552
Step-by-step explanation: