Answers
There are a lot of questions here. I'll do problems 7 and 8 to get you started.
====================================================
Problem 7
The given equations are
y = x^2 + 5x - 2
y = 3x - 2
Since both right hand sides are equal to y, we can equate them, get everything to one side, and solve
x^2 + 5x - 2 = 3x - 2
x^2 + 5x - 2 - 3x + 2 = 0
x^2 + 2x = 0
x(x + 2) = 0
x = 0 or x + 2 = 0 ........ zero product property
x = 0 or x = -2
Now plug each x value back into one of the original equations given
If x = 0, then
y = 3x-2
y = 3*0-2
y = -2
Making (0,-2) as one solution. Repeat for the x value x = -2
y = 3x-2
y = 3(-2)-2
y = -8
The point (-2, -8) is the other solution to the system.
-------------------------------
Answer: There are two solutions and they are (0, -2) and (-2, -8)
====================================================
Problem 8
y = -x^2 - 3x + 2
y = x + 6
We'll use the same idea as before
y = -x^2 - 3x + 2
x + 6 = -x^2 - 3x + 2
x + 6 + x^2 + 3x - 2 = 0
x^2 + 4x + 4 = 0
Now factor the left side to solve for x
(x+2)(x+2) = 0
(x+2)^2 = 0
x+2 = 0
x = -2
Use this x value to find y
y = x+6
y = -2+6
y = 4
Or we can cay
y = -x^2 - 3x + 2
y = -(-2)^2 - 3(-2) + 2
y = 4
We get the same y value either way.
-------------------------------
Answer: There is one solution and it is (-2, 4)
Related Questions
Find the GCF from the two numbers, and rewrite the sum using the distributive property. 12+18= 42+14= 36+27= 16+72= 44+33= 6. 8 - 16 = 7. 54 + 24 = 8. 63 - 81 = 9. 25 - 60 = 10. 16 – 20 =
Answers
Answer:
65+7 too the test
Step-by-step explanation:
5
A bag of marbles had 16 red marbles and the rest were white. For a game, of the 16 red marbles were chosen, and 15 of the white marbles were also
chosen.
Use this information to answer the questions below.
If not enough information is given to answer a question, click on "Not enough information."
Answers
Roxanna has a collection of silver spoons from all over the world.
If the spoons are arranged in sets of 7, there are 5 left over.
If the spoons are arranged in sets of 8, there is 1 left over.
If the spoons are arranged in sets of 15, there are 14 left over.
If she has at least 50 spoons, what is the smallest possible number of spoons in her collection?
Answers
Answer: 89
Step-by-step explanation: 8 x 11 + 1 = 89, 7 x 12 + 5 = 89, 15 x 5 + 14 = 89
5) (4 points each) Consider picking ONE card from a standard deck of cards.
a) What is the probability of picking a Jack or a
b) What is the probability of picking a Spade or
Queen?
a Face Card?
c) What is the probability of picking a Face Card d) What is the probability of picking a Face Card
and a Heart?
Answers
A) 4/52
B) 16/52
C) 12/52
D) 25/52
Hope this is right, I did my best!
Solve for x: -2x + 14 = 20
Answers
Answer:
x = -3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesStep-by-step explanation:
Step 1: Define equation
-2x + 14 = 20
Step 2: Solve for x
Subtract 14 on both sides: -2x = 6Divide -2 on both sides: x = -3Step 3: Check
Plug in x into the original equation to verify it's a solution.
Substitute in x: -2(-3) + 14 = 20Multiply: 6 + 14 = 20Add: 20 = 20Here we see that 20 does indeed equal 20.
∴ x = -3 is a solution of the equation.
Help me with this question pleaseee
Answers
Answer:
13
Step-by-step explanation:
In the figure provided,
∠(9y + 7) = ∠(2y + 98) [vertically opposite angles]
7y + 7 = 98 [subtracting 2y from both sides]
7y = 91 [subtracting 7 form both sides]
y = 13 [dividing both sides by 7]
the area of a rectangular wall of a barn is 154 square feet. it's length is 8 feet longer than twice its width. find the length and the width of the wall of the barn.
Answers
Answer:
the length = 22 and width =7
Which city experiences a larger absolute change between the high temperature and low temperature, Nuuk in January or Isla Hoste in August?
Answers
Answer:
I believe it is Isla Hoste in August
Answer: it is Isla Hoste in August
Step-by-step explanation:
i am sure pls give me brainliest
You build a model of Laurel Park using the scale 1.5 inches:10 feet. If the model 94.5
inches wide, what is the width of the school campus?
Answers
Answer:
The width of the school campus is:
[tex] \boxed{ \underline{ \rm{630 \: feet}}}[/tex]
Step-by-step explanation:
Scale = 1.5 inches : 10 feet
That means, 1.5 inches is equals to 10 feet in real.
Then for 1 inch:
⇛ 10 / 1.5 feet
⇛ 10/3 feet
We need to find for 94.5 inches,
⇛ 94.5 inches = 94.5 × 2/3 feet
⇛ 94.5 inches = 63 feet
Thus, the width of the school campus is 63 feet.
There are 12 boys and 16 girls in a classroom. Which represents the simplified ratio of girls to students in the
classroom?
Answers
Answer: 2:3
Step-by-step explanation:
12/6=2
18/6=3
Answer:
Option A.
Step-by-step explanation:
Options:
A. 3 to 4
B. 4 to 3
C. 4 to 7
D. 7 to 4
In order to simplify a fraction the numerator and the denominator have to have common factors that they can be divided by.
[tex]\frac{12}{16}[/tex]
Divide
[tex]CF=4[/tex]
[tex]12\div4=3[/tex]
[tex]16\div4=4[/tex]
[tex]=\frac{3}{4}[/tex]
Hope this helps.
A lawn-mowing company is trying to grow its business. It had 26 clients when they started its business and wants to increase by 3 new clients each week. Use an arithmetic sequence to write a function to represent this real-world situation and determine the range of the function for the first four weeks of data.
A. f(x) = 3x + 26; 0 ≤ y ≤ 4
B. f(x) = 3x + 23; 26 ≤ y ≤ 35
C. f(x) = 3x + 26; 26 ≤ y ≤ 35
D. f(x) = 3x + 23; 0 ≤ y ≤ 4
Answers
Answer:
B
Step-by-step explanation:
I took had this question in my test and im pretty sure I got this correct
The range of the function for the first four weeks of data f(x) = 3x + 26; 26 ≤ y ≤ 35. The correct option is C.
What is the range of the function?The range of a function in mathematics can refer to one of two closely related ideas: The function's codomain a representation of the action A binary relation f between two sets X and Y is a function if there is exactly one y in Y such that f connects x to y for every x in X.
It is given that a lawn-mowing company is trying to grow its business. It had 26 clients when it started its business and wants to increase by 3 new clients each week.
The equation will be represented as follows:-
Let x be the number of the weeks then the expression will be written as:-
f(x) = 3x + 26
For the first four weeks, the range will be:-
26 ≤ y ≤ 35
Therefore, range of the function for the first four weeks of data f(x) = 3x + 26; 26 ≤ y ≤ 35. The correct option is C.
To know more about the range follow
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simpifly 54/27
..................
Answers
Answer:
2/1
Hope this helps.
Answer:
2/1
Step-by-step explanation:
continue dividing the denominator and numerator by 3
Khan Academy
Factor using polynomial division
The polynomial p(x) = x3 + 7x2 – 36 has a known factor of (x + 3).
Rewrite p(x) as a product of linear factors.
p(2) =
Answers
Answer:
Rewriting p(x) as a product of linear factors: [tex]\mathbf{f(x)=(x+3)(x-2)(x+6)}[/tex]
Step-by-step explanation:
The polynomial [tex]p(x) = x^3 + 7x^2 - 36[/tex] has a known factor of [tex](x + 3)[/tex]
We need to find other factors.
First we find quotient of [tex]p(x) = x^3 + 7x^2 - 36[/tex] divided by [tex](x + 3)[/tex]
The division is shown in image attached.
The quotient is: [tex]x^2+4x-12[/tex]
Now, factoring the quotient [tex]x^2+4x-12[/tex]
[tex]x^2+4x-12\\=x^2+6x-2x-12\\=x(x+6)-2(x+6)\\=(x-2)(x+6)[/tex]
The other two factors are (x-2)(x+6)
So, Rewriting p(x) as a product of linear factors: [tex]f(x)=(x+3)(x-2)(x+6)[/tex]
Coordinate plane with triangle EFG with E at 0 comma 5, F at 1 comma 1, and G at negative 2 comma 1. Point H at 1 comma 1 is on segment GF, and points E and H are connected with a segment.
Triangle EFG is dilated by a scale factor of 2 centered at (0, 2) to create triangle E'F'G'. Which statement is true about the dilation?
segment EG ≅ segment E prime G prime.
The slope of segment EF is the same as the slope of segment E prime H prime.
segment H prime F prime will overlap segment HF.
segment EH and segment E prime H prime both pass through the center of dilation.
Answers
Answer:
The answer is A
Step-by-step explanation:
I'm taking the test
Answer:
Either way, dilations wont cause congruency, the triangles will be similar (Invalidates A)
Step-by-step explanation:
What is the exact angle measure in radians?
495°
Answers
Answer:
495° × π/180 = 8.639
Step-by-step explanation:
The exact angle measure in radians of 495 is; 8.64radians
From convention;We can say that 360° is equal to 2πrad.
On this note, we can evaluate the value of 495° in rads as; x.
Therefore;
x = (495 × 2 πrad)/360x = 8.64 radians.
Read more on angle measures:
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(Who ever helps get brainly :D )
Solve two times five eighths.
Leave your answer as an improper fraction.
A) seven sixteenths
B) ten sixteenths
C) seven eighths
D) ten eighths
Answers
Answer:
c
Step-by-step explanation:
The improper fraction is ten eighths(10/8).
What is improper fraction?Improper fractions are ones that have been divided improperly for any number, object, or element, as indicated by the term. A fraction is a portion of a whole in mathematics. Denominator and numerator are the two components of fractions.
A fraction whose numerator exceeds the denominator is referred to as an improper fraction. Consider the case where x/y is an improper fraction and x exceeds y. The incorrect fraction is consequently always bigger than one.
Given two times five eighths.
we need to multiply 2 by 5/8
First, remember that 2 is equal to 2/1 since 2 divided by 1 equals 2. Therefore, frame the issue as follows to begin:
2/1 x 5/8
Combine the denominators (1 x 8) and the numerators (2 x 5 = 10) to create a single fraction, as seen below:
10/8
Hence two times five eighths is 10/8 in improper fraction.
Learn more about improper fraction;
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Roxanna has a collection of silver spoons from all over the world.
- If the spoons are arranged in sets of 7, there are 5 left over.
- If the spoons are arranged in sets of 8, there is 1 left over.
- If the spoons are arranged in sets of 15, there are 14 left over.
If she has at least 50 spoons, what is the smallest possible number of spoons in her collection?
Answers
a person is earning 600 per day to do a certain job. express the total salary S as a function of the number N of days that the person works.
Answers
Answer:
As im pretty sure the equation would be S=600N
Step-by-step explanation:
Answer this right and i will mark you brainliest hellllllpppp meeee ❤️
Answers
Answer:
y represents the money raised for charity
Step-by-step explanation:
A store pays $1.50 for a bag of candy. If the store wants to mark-up the price 60%,
for how much will the store sell the bag of candy?
Answers
Answer:
Selling price = $2.4
Step-by-step explanation:
Given:
Purchase price = $1.50
Increase in price = 60%
Find:
Selling price
Computation:
Selling price = Purchase price + (Purchase price)(Increase in price)
Selling price = $1.5 + (1.5)(60%)
Selling price = $1.5 + 0.9
Selling price = $2.4
You are given 3 to 1 odds against tossing three tails with three coins, meaning you win $3 if you succeed and you lose $1 if you fail. Find the expected value (to you) of the game. Would you expect to win or lose money in 1 game? In 100 games? Explain. Find the expected value (to you) for the game.
Answers
Step-by-step explanation:
To find the E(X) expected value, you come up with the different probabilities for each outcomeyour set of outcomes after 3 tosses would be = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} where H is heads and T is tailsEach element has a probability of 1/8 so let x represent number of tails[tex]Probability(x)=P(x)\\P(0)=\frac{1}{8} \\P(1)=\frac{3}{8} \\P(2)=\frac{3}{8} \\P(3)=\frac{1}{8}[/tex] The E(x)=Summation (x times P(x))[tex]E(X)=(0)(0.125)+(1)(0.375)+(2)(0.375)+(3)(0.125)=1.5[/tex] Now which probability is 1.5 tails? None, so it is either 2 tails or 1 tailsSo you can expect to lose money in 1 gameBut as you play more games the probability of getting 3 tails becomes more and more likely, so you can expect to win in a 100 gamesThe expected value is the value of winning made on a game when played overtime. Hence, the expected value of the game is -$0.5 ; with the player losing -$0.5 in the long run.
A coin toss :
{H, T}Sample space for 3 tosses :
{HHH, HHT, HHT, HTT, HHT, HTT, HTT, TTT}Toss required to win = 3 tails :
Amount won on success = $3 Amount lost otherwise = $1 = - $1Creating a discrete probability table :
X _____ 3 _______ - 1P(X) ___ 1/8 _____ 7/8The expected probability can be defined as :
E(X) = ΣX×P(X)E(X) = 3 × (1/8) + (-1) × 7/8
E(X) = 3/8 - 7/8 = - 4/8 = -1/2
Therefore, the expected value of the game = - 0.5 ; meaning that, I'll lose 0.5 in the long run.
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Written expression for (9x5)+(24-9)
Answers
Victor read 2 1/3 books over 14 days last summer. Assume it took him the same amount of time to read each book. How many days did it take him to read a full book?
I answered 1/6. Is this correct? I need explanation and answer. Will give the branliest!
Answers
Answer:
It took 6 days for Victor to read a full book.
Step-by-step explanation:
Given that Victor read 2 1/3 books in 14 days, and that it took him the same time to read each book completely, to determine the number of days it took him to read a complete book it is necessary to perform the following calculation:
1/3 = 0.333
14 / (2 + 1/3) = X
14 / 2.333 = X
6 = X
So, it took Victor 6 days to read a full book.
What is the constant of proportionality in the equation y=5/9 x?
Answers
Answer:
In your question, the constant of proportionality already jump out at us which is to get y, we have to multiply x by 5/9. Therefore the constant of proportionality is y=5/9x.
don't be putting random stuff and that's on period
Answers
Answer:
126 divided by 6 which is 27
Step-by-step explanation:
The answer is C
Answer is C!
Sawarasenaikimiwa⛓shoujonano?~
✨BöKùWâÿARiçHiñBįCChīńOoŠuDàYO!~~
Beach Hotel in Cancun is offering two weekend specials. One includes a 2-night stay with 3 meals and costs $195. The other includes a 3-night stay with 5 meals and cost $300. Which of the following shows the correct system to model this scenario?
Answers
Answer:
Step-by-step explanation:
-3 (2n+3m= 195)
2 (3n+5m= 300)
-6 - 9m= -585
6n + 10m= 600
m=5
Review: Key Concepts
.
Multiplication and division of rational__________ is similar to multiplication and division of rational numbers.
Answers
Answer:
Not helpful
Step-by-step explanation:
which of these is positive values and which have negative values
7-(-4)
-3+(-2)
5-8
-10+12
Answers
Answer:
Positive: 7-(-4) and -10+12
Negative -3+(-2) and 5-8
Step-by-step explanation:
Addition and subtraction rules
need help on this one please
Answers
Multiply and simplify the product.
(3 – 5i)(–2 + 4i)
Select the product.
14+ 2i
14 + 22i
15 + 22i
26+2i
Answers
Answer:
B
Step-by-step explanation:
We have the expression:
[tex](3-5i)(-2+4i)[/tex]
Distributive Property:
[tex]=(3-5i)(-2)+(3-5i)(4i)[/tex]
Distribute:
[tex]=(-6+10i)+(12i-20i^2)[/tex]
Simplify:
[tex]=(-6+10i)+(12i-20(-1))[/tex]
Simplify:
[tex]=-6+10i+12i+20[/tex]
Combine like terms:
[tex]=(-6+20)+(10i+12i)[/tex]
Simplify:
[tex]=14+22i[/tex]
Hence, our answer is B.
Answer:
14+22i
Step-by-step explanation: