Answer:
b
Step-by-step explanation:
The pairs of solutions are (2, 6) and (-4, 0).
It is required to find the solution of (x,y).
What is quadratic equation?Any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power. The quadratic formula to solve a quadratic equation ax2 + bx + c = 0 is x = [-b ± √(b2 - 4ac)]/2a.
Given:
The equations are
y = x2 + 3x − 4 --------------- eqn(1)
x = y − 4 --------------- eqn(2)
from eqn (2),
y = x + 4 ---------- eqn(3)
equating eqn (1) and eqn (3),
x2 + 3x − 4 = x + 4
x2 + 3x − 4 - x - 4 = 0
x2 + 3x - x − 4 - 4 = 0
x2 + 2x - 8 = 0 ------------- eqn(4)
eqn (4) is a quadratic equation and can be simplified either by factorization, completing the square or quadratic formula method of solving quadratic equation.
Using factorization method,
sum of root = 2
product of root = -8 x 1 = -8
Next, find two numbers whose sum and product are 2 and -8 respectively
Let the two numbers be 4 and -2
Replace the sum of root (2) in eqn (4) with these two numbers. That is,
x2 + 4x - 2x - 8 = 0
Group into two expressions
(x2 + 4x) - (2x + 8) = 0
By factorize each expression we get,
x(x + 4) - 2(x + 4) = 0
pick and group both terms outside the brackets and inside one of the two brackets. That is,
(x - 2)(x + 4) = 0
x - 2 = 0 and x + 4 = 0
x = 2 and x = -4
Substitute the values of x into eqn (3)
if x = 2,
y = 2 + 4
y = 6
(2, 6)
If x = -4,
y = -4 + 4
y = 0
(-4, 0)
Therefore, the pairs of solutions are (2, 6) and (-4, 0).
Learn more about quadratic equation here:
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A 3.5 gallon gas can contains 910 gallons. How much more gas can be poured in?
Answer:
-96.5
Step-by-step explanation:
The cost of a book is $8.00. What is the selling price of the book if the store's markup is 36%?
if a/3=b/2 what are the following ratios? 3a-3b/a-b
Answer:
[tex]\dfrac{3a-3b}{a-b}=\dfrac{3}{1}[/tex]
Step-by-step explanation:
[tex]\text{Given}\\\\\dfrac{a}{3}=\dfrac{b}{2}\qquad|\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup\cdot\dfrac{a}{3\!\!\!\!\diagup}=3\cdot\dfrac{b}{2}\\\\a=\dfrac{3b}{2}[/tex]
[tex]\text{Substitute to}\ \dfrac{3a-3b}{a-b}:\\\\\dfrac{3\cdot\frac{3b}{2}-3b}{\frac{3b}{2}-b}=\left(\dfrac{9b}{2}-3b\right):\left(\dfrac{3b}{2}-\dfrac{2b}{2}\right)=\left(\dfrac{9b}{2}-\dfrac{6b}{2}\right):\left(\dfrac{3b-2b}{2}\right)\\\\=\left(\dfrac{9b-6b}{2}\right):\dfrac{b}{2}=\dfrac{3b\!\!\!\!\diagup}{2\!\!\!\!\diagup}\cdot\dfrac{2\!\!\!\!\diagup}{b\!\!\!\!\diagup}=\dfrac{3}{1}[/tex]
Other method:
[tex]\dfrac{3a-3b}{a-b}=\dfrac{3(a-b)}{a-b}\qquad|\text{cancel}\ (a-b)\\\\=\dfrac{3}{1}[/tex]
Assume Jack works from 2:30 PM to 7:00 PM. Using the function f(x) = 10x + 8, how much would he earn?
Answer:
$53
Step-by-step explanation:
10(4.5) + 8= 53
$53
hope this helped!
The earnings of Jack by the function assuming x as time spent from 2.30 PM will be $53.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given function,
f(x) = 10x + 8
Time spent working x = 7:00 PM - 2:30 PM
x = 4.50 hour
f(4.30) = 10(4.50) + 8
f(x) = $53
Hence "The earnings of Jack by the function assuming x as time spent from 2.30 PM will be $53".
For more about the linear function,
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William has $25 to spend at the grocery store. He used $8 for meat. He
wants to spend the rest of the money on packs of cookies. If each pack
of cookies costs $3.45, how many packs of cookies can he buy?
Answer:
64
Step-by-step explanation: because he can at least steal 64 packs before the cops get him
Answer:
4
or
4.92753623188 **However you cannot just buy a portion of one pack so you round back down to 4 packs.
Step-by-step explanation:
First we have $25, since he spent $8, we can now claim he has $17, Divide 17 into 3.45, He can buy 4 packs.
24 of 30 workers take 1 hour lunch. What percent of the workers take 1 hour lunch?
Answer:
80%
Step-by-step explanation:
Divide 24 by 30
Answer: 80%
Step-by-step explanation:
How much does one slice of pumpkin pie cost if there are 8 servings per pie?
Ingredients
• Pumpkin 15oz can ($1.50 for 15oz can)
2 eggs ($2.59 for one dozen)
• 1 tsp pumpkin pie spice ($5.99 for 1.12oz Jar =
approx.6tsp)
• Evaporated Milk 14oz can ($1.25 for 14oz can)
• Pillsbury Pie Crust ($3.79 for two crusts)
Show Your Work Here:
Answer:
$0.76 per serving of pumpkin pie
Step-by-step explanation:
the total cost of the ingredients needed to prepare a pumpkin pie = $1.50 + ($2.59 / 6) + ($5.99 / 6) + $1.25 + ($3.79 / 2) = $6.075
if we cut 8 servings per pie, then the cost per serving = total cost of the pie / number of servings = $6.075 / 8 = $0.759375 ≈ $0.76 per serving of pumpkin pie
We want to find the cost of each slice of a pie given that we know the price of the ingredients that we use to make the whole pie. We will see that the cost of a single slice is $0.75.
First, we must get the cost of the whole pie. We have:
$1.50 for the 15oz can of PumpkinWe know that 12 eggs cost $2.59, then 2 eggs cost: (2/12)*$2.59 = $0.43.We know that 1.12 oz of pie spice costs $5.99, and we use only one teaspoon of this, remember that: 1tsp = 0.167 oz, Then the cost of 1tsp of pie spice is: (0.167 oz)/(1.12 oz)*$5.99 = $0.89.$1.25 for the 14oz can of evaporated milk.One pie crust, we know that two of them cost $3,79, then only one costs: $3.79/2 = $1.90The total cost is then:
C = $1.50 + $0.43 + $0.89 + $1.25 + $1.90 = $5.97
Now we know the total cost of the pie, and it has 8 slices, then each slice costs: $5.97/8 = $0.75
If you want to learn more, you can read: https://brainly.com/question/20005135
Could I please get some help on this?
Using dimensional analysis, how many kilometers are there in 34 inches?
34 inches have the same length of 0.0008636 kilometers.
Help me pleaseeeeee!!!!!
please help thank you
Answer:
Positive
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
The image point of A after a translation left 3 units and up 3 units is the point
B(−9,−5). Determine the coordinates of the pre-image point A.
Answer:
(-6, -8)
Step-by-step explanation:
PLS GIVE BRAINLIEST
can you please help me
Answer:
y=-3,000x+12,000
Step-by-step explanation
the number of tickets remaining decrease by 3,000 every hour, 12,000 is the number of tickets available at the beginig
The sum of 2 times a number and 8 is 7
Answer:
The number is -1/2
Step-by-step explanation:
Let x be the number
2x+8 = 7
Subtract 8 from each side
2x+8-8 = 7-8
2x = -1
Divide each side by 2
2x/2 =-1/2
x = -1/2
The number is -1/2
Answer:
2x + 8 = 7
x = -1/2
Step-by-step explanation:
"a number" can be signified by a variable.
So 2 times a number would give you 2x
And 8 would mean to add 8.
Is 7 means the end result is 7.
So 2x + 8 = 7
x = -1/2
PLEASE ANSWER
what does ok mean?
I use it as a short way to say "okay" but I don't know how others may use it.
Which of the following
represents a function?
PLEASE HELP 15 POINTS OR BRAINLIEST JUST ASK PLEASE HELP ME
Answer:
A: represents a function
Explanation:
Every other option, A, has two y for one x.
It can be a function if there is 1x for 1y.
If this was helpful, please mark brainliest. Have a beautiful day!
Choice A is not a function because x = 2 leads to more than one y value (y = 1 and y = 7 at the same time)
Choice B is not a function for similar reasoning. Here we have x = 1 lead to y = 2 and y = 5 simultaneously.
Choice D is also not a function because of the two points (5,2) and (5,4). This tells us we have x = 5 lead to y = 2 and y = 4 at the same time.
A function is only possible if you have any input lead to exactly one output. Choice C shows this. Note how it passes the vertical line test. It is impossible to draw a vertical line through more than two points on the function curve.
Find the 61st term of the arithmetic sequence
8, 7, 6, ...
Answer:
The 61st term is -52
Step-by-step explanation:
PLEASE HELP I NEED HELP
class<18
Step-by-step explanation:
not positive but its saying the class would have less than 18 kids. i would put the less than or = to sign instead. i just don't have that on my laptop.
3
A 30 kg dog speeds up at a rate of 4 m/s2. What is the force of the dog?
Answer:
n
Step-by-step explanation:
Answer:
120N
Step-by-step explanation:
F = ma
F = Force
m = Mass
a = acceleration
F = (30)(4)
F = 120
Joseph received a $20 gift card for downloading music. Each downloaded song costs $1.29. Explain how to write and solve an inequality that can be used to determine the number of songs that he can purchase. Interpret the solution.
Answer:
So he can buy 15 + he will have on his card left 0.65$
Step-by-step explanation:
20 / 1.29 = 15 song's
20 - 19.39 = 0.65
So he can buy 15 + he will have on his card left 0.65$
the person above me is correct.
Please help me work this out, it's not multiple choice. I'll mark you brainliest.
Answer:
the correct one is c
Step-by-step explanation:
pls mark me as brainliest
Plz helppppppppppppppppppppppppppppppppppppppppp
Answer:
??????????
Step-by-step explanation:
Dissolution of 2Y +9 equals four is
Answer:
11
Step-by-step explanation:
Please I need it tomorrow
Tina is considering two cell phone plans and wishes to decide, based on her expected phone usage,
which plan to purchase. Plan A has a monthly fee of $4995. Plan B costs $39.95 per month. Plan A
charges 5¢ per minute after 300 minutes of talk time. Plan B charges 10€ per minute for any talk time
beyond 500 minutes. Which pair of equations could Tina use to decide on the least costly plan for her
usage? Assume Tina always uses more than 500 minutes per month
(a) c = 39.95 + 0,10m - 300)
(b) c = 39.95 + 0.1(m - 500)
c = 49.95 + 0.050m - 500)
C = 49.95 + 0.05(m - 300)
(c) =3995+0.11 - 50
(d) =3995 +0.11 - 500
C = 49.95 + 0.05m - 15
c = 49.95 + 0.05m - 300
(e) bando
If f(x) = - 4x + 3 and g(x) = 3 x2 + 2x - 4, find (f+ g)(x).
Answer:
Step-by-step explanation:
(f+g)(x) = [tex]-4x + 3 + 3x^{2} + 2x - 4\\[/tex]
= [tex]3x^{2} - 2x - 1[/tex]
Simplify the expression: 2x – 3x (5x – 8) – 4r (x - 2)
13. Prove 6n + 3 is equivalent to 3n + 2 + 3n + 1 by substituting n = 5 into both
expressions.
Answer:
6 x 5 = 30 + 3 = 33
3 x 5 = 15 15 + 2 = 17 17 + 15 = 32 32 + 1 = 33
Step-by-step explanation:
On Sunday, Sheldon bought 412 kg of plant food. He used 123 kg on his strawberry plants and used 14 kg for his tomato plants. How many kilograms of plant food did Sheldon have left?
Answer:
...............................
what is 3/4 of 36 cupcakes
Answer:
27
Step-by-step explanation:
Answer:
27 cupcakes
Step-by-step explanation:
36 divided by 4 is 9, 9 times 3 is 27
ABCD~EFGH similar polygons
Answer:
3
Step-by-step explanation: