Can somebody give me an review over how to solve systems of equations by substitution and elimination? PLEASE HELP I forgot how to do it and my Algebra EOC is TOMORROW!! I provided an example question and I need LONG ACCURATE and HELPFUL explanations, not a one sentence response (or I will report you). PLEASE HELP ME!!!
Answer:
Price per large envelope = $1.42 (option A)
Price of each postcard = $0.35 (not asked for in this specific question)
Step-by-step process for solution given below
Step-by-step explanation:
The first thing to do for this problem and other similar problems is to set up the system of linear equations to be solved
We start with the unknowns and provide variable names for these unknowns
There are two unknowns here - the cost of each postcard and the cost of each large envelope
Let
x = cost of one postcard
y = cost of one large envelope
Customer 1 bought 14 postcards(cost = 14x) and 5 envelops(cost = 5y) for a total cost of $12
We can set up this as an equation:
12x + 5y = 12 ............ [1]
Customer 2 bought 10 postcards(cost = 10x) and 15 envelops(cost = 15y) for a total cost of $24.80
This translates to the following equation:
10x + 15y = 24.80 .... [2]
Let's re-write these equations one below the other for easier solution:
[tex]\begin{amatrix}14x+5y=12\dots[1]\\ 10x+15y=24.8\dots[2]\end{amatrix}[/tex]
Solving by substitution:
From any one of the above equations, express one variable in terms of the other variable and substitute for that variable in the other equation to solve.
Take equation [1]
[tex]14x+5y=12[/tex]
Let's express x in terms of y.
Move 5y to the right:
[tex]14x=12-5y[/tex]
[tex]x =\dfrac{12-5y}{14}[/tex]
Use this expression in y for x in equation [2]
[tex]10x + 15y = 24.8\\\\\implies 10 \cdot \dfrac{12-5y}{14}+15y=24.8\\\\\implies \dfrac{\left(12-5y\right)\cdot \:10}{14} + 15y = 24.8\\\\\implies \dfrac{\left(12-5y\right)\cdot \:10}{14} + 15y = 24.8\\\\[/tex]
Multiply throughout by 14:
[tex]14 \cdot \dfrac{\left(12-5y\right)\cdot \:10}{14} + 14\cdot 15y = 14 \cdot 24.8\\\\(12-5y)10 + 210y = 347.2\\\\120 - 50y + 210y = 347.2\\\\120 + 160y = 347.2\\\\160y = 347.2- 120\\\\160y = 227.2\\\\y = \dfrac{227.2}{160}\\\\y = 1.42[/tex]
Substitute y = 1.42 in equation [tex]x=\dfrac{12-5y}{14}[/tex]
[tex]x=\dfrac{12-5\cdot \:1.42}{14}\\\\x = 0.35\\\\[/tex]
So the cost of each large envelope was $1.42 and cost of each postcard was $0.35
Answer is option A
Solve by elimination
The idea here is to get the coefficients of one of the variables the same in both equations by multiplying / dividing one or both of the equations by some factor and then add/subtract to isolate the other variable and solve
For equations 1 and 2 do the following
Subtract the equations:
[tex]70x+105y=173.6\\-\\70x+25y=\;\;\;\;\;60\\\\[/tex]
-------------------------------
[tex]80y=113.6[/tex]
y = 113.6/80 = 1.42 as before
Substitute for y in equation 1 and solve for x
14x + 5y = 12 => 14x + 5(1.42) = 12
=> 14x + 7.1 = 12
=> 14x = 12 - 7.1
=> 14x = 4.9
=> x = 4.9/14 = 0.35 as before
I personally prefer solving by elimination since solving by substitution involves heavy duty fractional expressions
What is the range?
89 86 93 86 85 87
need help ASAP, would appreciate the assistance very much.
(Question 1)
What are Corresponding Angles?A pair of angles formed by two parallel lines and a transversal are said to be the corresponding angles.
Corresponding angles are formed only when,
One of them is interior and the other is exteriorThey are on the same side of the transversal andThey are not at the same vertexThe pairs of Corresponding Angles in the given figure are —
∠1 and ∠3∠2 and ∠4∠5 and ∠7∠6 and ∠8You can write any two of them because the question says to write any two Corresponding Angles.
(Question 2)
What are Alternate Interior Angles?Alternate angles that lie in the interior region of both the lines are called alternate interior angles.
Alternate Interior Angles are formed only when,
Each pair of alternate interior angles is equal.Each pair of co-interior angles is supplementary.The pairs of Alternate Interior Angles in this given figure are —
∠2 and ∠7∠3 and ∠6These are the only two pairs of Alternate Interior Angles.
(Question 3)
What are Alternate Exterior Angles?Alternate angles that lie in the exterior region of both the lines are called alternate exterior angles.
Alternate Exterior Angles are formed only when,
Both lie on the exterior side of the lines.They are placed on the opposite sides of the transversal.The pairs of Alternate Exterior Angles in this given figure are —
∠1 and ∠8∠5 and ∠4These are the only two pairs of Alternate Exterior Angles.
(Question 4)
In this given Figure, Line segment AB is parallel to Line segment CD.
∠1 = 154° [Alternate Interior Angles]
∠2 = 180 - 154° [Linear Pair]
= 26°
(Question 5)
In this given Figure, Line segment AB is parallel to Line segment CD.
∠1 = 97° [Corresponding Angles]
∠2 = 82° [Corresponding Angles]
∠3 = 180 - 97° [Linear Pair]
= 83°
Hope my answer helps you ✌️
Mark BRAINLIEST
PLEASE HELP ME POR FAVOR
I'm rlly bad at this kind of math please help and write how you did each question
Answer:
its to blurry , sorry cant give you answer , too blurry. Make it less blurry ty3n i can answer it
PLS HELP I NEED THIS NOW PLSSSSSSSSSSSSSSSSS
What does the symbol indicated by the arrows most likely represent?
a hurricane
low pressure
high pressure
high temperatures
this is sience ok
Answer:
Step-by-step explanation:
What does the symbol indicated by the arrows most likely represent?
high pressure there’s no picture.
-6+[tex]\frac{x}{4}\\[/tex]=-5
Please answer asap (it's due tomorrow), Mrs. Carter is preparing materials for a craft project. She needs to cut 5 meters of ribbon into pieces that are 0.5 meter long. How many 0.5-meter pieces can she cut from 5 meters of ribbon? Please check your answer, show your work.
Mrs. Carter can cut 10 pieces of 0.5-meter-long ribbon from 5 meters of ribbon.
Here's how you can calculate it:
- Divide the length of the ribbon by the length of each piece: 5 ÷ 0.5 = 10.
- Therefore, Mrs. Carter can cut 10 pieces of 0.5-meter-long ribbon from 5 meters of ribbon.
Answer:
10 pieces
Step-by-step explanation:
You take the total (5 meters) and divide it by the length she needs (0.5 meters) to get 10
....................
Answer: 350
Step-by-step explanation:
Divide it by the centimeter
Answer:
350 (*^▽^*)
Step-by-step explanation:
help pls will give brainliest
Answer:
s = 7
Concept Used:
Linear pair axiom
Step-by-step explanation:
(6s-8) + 90 + 8s = 180 (Linear pair axiom)
14s = 98
s = 7
Answer:
7
Step-by-step explanation:
The 3 angles are on a straight line, meaning the angle is 180°.
We know that one angle is 6s-8°, another is 8s°, and the middle angle is 90° because of the small box.
We can set up an equation to find s:
6s-8+8s+90=180
simplify
14s+82=180
subtract 82 from both sides
14s=98
divide both sides by 14
s=7
Hope this helps :)
pls helpppp box plot
Answer:
Hello the answer : C. :)
Step-by-step explanation:
H
Answer: c
Step-by-step explanation:
You start from the range so you subtract 34-24=10 and the median is 31
The equation shown describes a relationship between x and y.
y = 5x + 2
If the value of x increases by 1, what is the corresponding increase in the value of y?
y should increase by five every time
5x is just a multiple 5 but without knowing how many tines your multiplying. Now we know that x increases by 1 each time, so it should just be normal multiplying. 5(1) = 5, 5(2) = 10, 5(3) = 15 and so on. It's a constant increase of 5.
What is the scale factor from the large triangle to the small triangle?
A. 1/2
B. 2/3
C. 1/3
D. 3/4
What is the mode?
3 9 4 7 4 3 7 4 4 4
Answer:
it's 4
Step-by-step explanation:
4 appears more times than any number here
A store marks up their items by 30% to get the retail price. the store bought a bowl for $17. What is the retail price?
Answer:324
Step-by-step explanation:
ifdosfsf
Answer:
The retail price is $17 × 1.3 = $22.10.
The cell phone company allows all users 450 text messages a month. Any text messages over the allowed amount are charged $0.25 per message. Craig only has $26 extra to sped on his cell phone bill. how many messages can he go over the allowed amount for the month without breaking his budget of $26? Let p represent the amount of text messages Craig can go over.
Inequality: ___________
Craig can send and receive ______________ extra text messages without breaking his budget of $26
Let's first find the total cost of the text messages Craig can send in a month. Craig is allowed to send 450 text messages without any additional charges. If he sends more than that, he will be charged $0.25 per message. Let's say he sends x additional messages over the 450 allowed:
Cost of additional messages = $0.25 * x
So, the total cost of Craig's text messages in a month is:
Total cost = Cost of allowed messages + Cost of additional messages
Total cost = $0 + $0.25x
Total cost = $0.25x
We know that Craig has a budget of $26 for his cell phone bill. We can set up an equation to represent this:
Total cost ≤ $26
Substituting the expression for the total cost of Craig's text messages, we get:
$0.25x ≤ $26
Dividing both sides by $0.25:
x ≤ 104
Therefore, Craig can go over the allowed amount by at most 104 text messages without breaking his budget of $26.
Answer: he can go over by 104
Step-by-step explanation:Total cost = $0 + $0.25x
Total cost = $0.25x
Total cost ≤ $26
Substituting the expression for the total cost of Craig's text messages, we get:
$0.25x ≤ $26
Dividing both sides by $0.25:
x ≤ 104
Therefore, Craig can go over the allowed amount by at most 104 text messages without breaking his budget of $26.
have a good day
Can someone help?? Thanks
Answer:17.6
Step-by-step explanation:
If 60% was taken off then what woold be left would be 40%. 40% translated into a decimal is 0.4 if you multiply that by 44 you would get the answer of 17.6.
Answer: $17.6
Step-by-step explanation:
100%-60%=40%. 40/100=0.4 and then you multiply 0.4x44=17.6. The price is now $17.6
Anyone knows the answer???
Answer:b
Step-by-step explanation:
Answer:
#3 points are
(-4, 2)
(4, 2)
(-4, -2)
(4, 0)
#4 scale factor = 1/4
#5 scale factor = 1/2
Step-by-step explanation:
#3
take the given points and multiply the x and y by 2/3
#4 take any point and compare it to a similar point on the dilated graph. for example, you take a point from the original graph (-2, 4) and a point from the dilated graph (-1/2, 1) since you multiply -2 by 1/4 to get -1/2, that is your scale factor.
#5 same as #4 but with different points
Jill can make 50 flash cards every 20 minutes COMPLETE THE TABLE USING EQUIVALENT RATIOS.
MINUTES NUMBER OF CARDS
50
30
20 -----
-----
36
Answer:
minutes : # of cards made
20 50
40 100
60 150
80 200
100 250
120 300
140 350
160 400
180 450
200 500
220 550
240 600
260 650
280 700
300 750
320 800
340 850
360 900
380 950
400 1000
And please let me know if this helps.
Can someone answer this question for me? asap please
Answer:
a) If the volume of the prism on the left is 1029 m³, then the volume of the prism on the right is 1536 m³.
b) If the height of the prism to the left is 14 m, the height of the prism to the right will be 16 m.
c) If the surface area of the prism to the left is 392 m², the surface area of the prism to the right will be 512 m².
Step-by-step explanation:
a) To solve, set up a proportion. Volume is three-dimensional, so we need to cube.
(7/8)³=1029/x
Now we can solve using cross products to get 1536.
If the volume of the prism on the left is 1029 m³, then the volume of the prism on the right is 1536 m³.
b) To solve the second one, we also set up a proportion. Height is one-dimensional, so we will not need exponents here.
7/8=14/x
Solve using cross products to get 16.
If the height of the prism to the left is 14 m, the height of the prism to the right will be 16 m.
c) Now we are solving for area, which is two-dimensional. Therefore, we will need to square.
7/8²=392/x
Solve using cross products to get 512.
If the surface area of the prism to the left is 392 m², the surface area of the prism to the right will be 512 m².
Hope this helps and good luck on your homework! For additional resources, check out The Maths Prof: Similarity parts 1-3.
An employee at a grocery store was restocking shelves. He was restocking cans of beans and
cans of corn. The ratio of cans of beans to total cans on the shelf is 9 to 17.
Which of the following could be the number of cans of corn on the shelf?
A. 24
B. 27
C. 51
D. 78
Open this doc 2 (less blurry one!)
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{3}}x+16\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{1}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{1} \implies -3}}[/tex]
so we're really looking for the equation of a line whose slope is -3 and it passes through (-9 , 13)
[tex](\stackrel{x_1}{-9}~,~\stackrel{y_1}{13})\hspace{10em} \stackrel{slope}{m} ~=~ - 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{13}=\stackrel{m}{- 3}(x-\stackrel{x_1}{(-9)}) \implies y -13 = - 3 ( x +9) \\\\\\ y-13-3x-27\implies {\Large \begin{array}{llll} y=-3x-14 \end{array}}[/tex]
Answer:
m = 1/3
m⊥ = -3
x1 = -9
y1 = 13
point slope: y-13 = -3(x+9)
slope intercept: y= -3x-14
Step-by-step explanation:
Equation given is in y=mx+b form, so I think m=1/3 (or whatever is right before the x cause it is little hard to see)
To find a perpendicular slope, you use the negative reciprocal of the given slope, so the perpendicular slope would be m=-3
x1 and y1 would be the given coordinates so -9 and 13 respectively
Finally plug in all this info into point slope form equation (y-y1 = m(x-x1)
Point slope would be: y-13 = -3(x+9)
Slope intercept would be: y= -3x-14
Hope this helps!
Can someone help please I'm in a hurry
I NEED A GOOD GRADE SO I CAN BE A STEPPER NEXT YEAR !!!!!
Answer: It's 7
Step-by-step explanation: Since all the sides are the same and it says JK is 7 inches HL must also be 7 inches.
Hope It helped!
What is the area of Z?
Answer:
t = 5 kilometers
Step-by-step explanation:
From the given figure,
Perimeter = 18 kilometers
Now, the formula for perimeter of a rectangle = 2(l + b)
Where,
'l' is the length of the rectangle
and
'b' is the breadth of the rectangle.
Since length is the longest side of a rectangle, therefore from the given figure
=> l = t kilometers
and
=> b = 4 kilometers
Substituting values in the formula,
18 = 2(t + 4)
=> 18/2 = t + 4
=> 9 = t + 4
=> 9 - 4 = t
=> t = 5 kilometers
Answer:
5 km
Step-by-step explanation:
We know that the perimeter of this rectangle is 18km.
We also know that 1 side is 4km.
Given the perimeter formula:
[tex]P=2(l+w)[/tex]
We can substitute our given values:
18=2(4+w)
Solve the right side
18=8+2w
subtract 8 from both sides
10=2w
divide both sides by 2
5=w
This means that z, the width, is 5 km.
Hope this helps!
sdadagsdsdad please help meeeeeeeeeee
Help with number 4 please
Micah and Jason made a parallelogram-shaped stained glass windows. Micah's window has an area of 99 square inches. The height of Jason's window is 6 inches and its base is 15 inches. Apply a formula to find the area of Jason's window. Whose stain glass window has the greater area?
Help me please. Thanks in advanced
Answer:
Step-by-step explanation:
The sum of the interior angles of a triangle is 180 degrees. Therefore, we can set up an equation using the measures of the angles in triangle ABC:
ZABD + CBD + ABC = 180
Substituting in the given measures, we get:
(0.12x + 64) + (0.13x + 28) + ABC = 180
Simplifying and solving for x, we get:
0.25x + 92 + ABC = 180
ABC = 180 - 0.25x - 92
ABC = 88 - 0.25x
We know that the measure of angle ABC is 0.11x + 12. Substituting this into the equation for ABC, we get:
0.11x + 12 = 88 - 0.25x
Solving for x, we get:
0.36x = 76
x = 211.11
Therefore, the value of x is approximately 211.11.
Answer:
x = 352
Step-by-step explanation:
From the given Linear Pair, we can observe that ∠ABD and ∠CBD form a Straight Angle which is 180°.
∠ABD = 0.12x + 64°
∠CBD = 0.13x + 28°
Now we can understand that ∠ABD + ∠CBD = ∠ABC (Linear Pair)
∠ABC = 180°
So, ∠ABD + ∠CBD = 180°
(0.12x + 64°) + (0.13x + 28°) = 180°
(0.12x + 0.13x) + (64° + 28°) = 180° (Distribution Property)
0.25x + 92° = 180°
0.25x = 180° - 92°
0.25x = 88°
x = 88/0.25
x = 352
Hope my answer helps you ✌️
Mark BRAINLIEST
Manuela spins a spinner with four equal sections, labeled A, B, C, and D, twice. If letter B is spun at least once, she wins. Otherwise, Gabriela wins. Which shows the winning sample space for Manuela?
Answer:
B
Step-by-step explanation:
is b because its that and I did the assiment
Please help will give brainlest and special thanks
Answer:
To find the x-intercept, substitute in
0 for y
and solve for x. To find the y-intercept, substitute in
0 for x
and solve for y.
x-intercept(s): (−5,0)
y-intercept(s): (0,10)
Step-by-step explanation:
90 30 + 50 +(2x+10)=90
