Given:
The equations of a system of equations are
[tex]y=-2x^2+3x-1[/tex]
[tex]x+y=-1[/tex]
To find:
The solution of the given system of equations.
Solution:
We have,
[tex]y=-2x^2+3x-1[/tex] ...(i)
[tex]x+y=-1[/tex] ...(ii)
Using (i) and (ii), we get
[tex]x+(-2x^2+3x-1)=-1[/tex]
[tex]x-2x^2+3x-1+1=0[/tex]
[tex]-2x^2+4x=0[/tex]
Taking out the common factors.
[tex]2x(-x+2)=0[/tex]
Using zero product property,we get
[tex]2x=0[/tex] and [tex]-x+2=0[/tex]
[tex]x=0[/tex] and [tex]2=x[/tex]
For x=0, we have
[tex]0+y=-1[/tex]
[tex]y=-1[/tex]
For x=2, we have
[tex]2+y=-1[/tex]
[tex]y=-1-2[/tex]
[tex]y=-3[/tex]
Therefore, the two solutions of the given system of equations are (0,-1) and (2,-3).
A middle school took all of its 6th grade students on a field trip to see a symphony. The students filled 855 seats, which was 45% of the total number of seats in the theater. How many total seats were in the theater?
Answer:
1900
Step-by-step explanation:
let a = total seats
the number of students that filled the theatre can be represented with this equation
0.45 x a = 855
divide both sides by 0.45
a = 855/0.45 = 1900
Answer:
1900
Step-by-step explanation:
Big brain and mental math
Which of the following rational functions is graphed below?
Answer:
B
Step-by-step explanation:
The function's zeroes results in vertical asymptotes. As one is at x = 1 and the other at x = -2, the zeroes must be (x-1) and (x+2), which only B contains in the numerator.
1.17375 rounded to nearest tenth
Answer:
1.2
Step-by-step explanation:
Since we are rounding it by the tenth, it means we are rounding to the 1st digit to the right of the decimal.
We know 7 is greater then 5 meaning we round up
.1 + .1 is equal to .2 meaning its 1.2
If you still don't understand, I recommend you talk to your teacher
Answer: The answer is 1.2
Step-by-step explanation: Since this is to the nearest tenth we are looking at the first two numbers after the decimal point the second number 7 is greater then 5 the first number will be greater if it was less then 5 or 5 we would round down now we discard the rest including the second number which leaves us with the rounded first number of 2 now it's 1.2
Please help! This is for my math class its due tomorrow
Answer:
negative one third
Step-by-step explanation:
So you go to the 1 and half
HELP SOMEONE PLEASEEE
Answer:
It is the first answer choice
Please can someone give me the answers to all three of them. THIS IS TIMED PLEASE HELP ME QUICK! (30 points)
Answer:
1. equation
2. inequality
3. inequality
Step-by-step explanation:
please help me with this i’m stuck
Answer:
A ) Substitute the side lengths of a and b in the equation
Step-by-step explanation:
The hypotenuse which is opposite the right angle it always the length of C in the cosine rule.
Anthony went shopping for a new pair of pants because of a sale. The store was offering a 5% discount. If the price on the tag was $32, what would be the price after the discount but before tax, to the nearest dollar and cent?
Answer:
$30.4
Step-by-step explanation:
fist we figure out what 5% of 32 is which is 1.6 then we subtract it from the total cost 32 - 1.6 = 30.4
what is
10-5?
10-3+4?
5+6-3
Answer:
5
11
8
Step-by-step explanation:
Answer:
10-5=5
10-3+4=11
5+6-3=8
Step-by-step explanation:
The heights of all the newborns in a certain country are normally distributed,
with a mean of 19 inches and a standard deviation of 0.5 inches. A mother
just delivered a baby that is 18 inches long. Which of the following represents
the z-score of the baby's height? (Round your answer to two decimal places.)
Answer:
c
Step-by-step explanation:
I need help very fast please!
9+10=?
Guys pls help
Answer:
19
Step-by-step explanation:
9 + 10 = 19
solve for x 7|x + 3| + 5 = 40
Answer:
4.6 or 4.57
Step-by-step explanation:
A data set that consists of many values can be summarized using the five-number summary. Arrange these five values in order from least to greatest. median maximum minimum Q1 Q3
Answer:
minimum, Q1, median, Q3, maximum.
Step-by-step explanation:
i did the test
Answer:
minimum, Q1, median, Q3, maximum.
1) In Alameda County, the sales tax is 11%. What would the difference in sales tax between a video game that costs $31.99 and a book that costs $18.99 be? 2) In Contra Costa County, the sales tax is 11.5%. What would the difference in sales tax between the same video game and book be in Contra Costa County? 3) A customer returns an item to a toy store in Contra Costa County, but the store has another location in Alameda County. If the customer's receipt shows that he paid $3.22 in tax on an item that costs $27.99, was the item purchased in Contra Costa County or Alameda County?
Answer:
Step-by-step explanation:
1. 3.52 tax for the game, 2.09 for the book
difference between the two, 1.43
2. 3.68 in tax for the book, 2.18 for the book
difference between the two, 1.50
3. It was purchased in Contra Costa county with 11.5% sales tax
Kate writes an algebraic expression using each of the variables x and y only once. they first expression she writes uses x and y as factors. Than she writes another expression that uses x and y as terms. if x and y are both negative integers, write a comparison between the two expressions
Choice A: More information is needed.
Choice B: Using x and y factor results in an expression of greater value than using x and y as terms.
Choice C: None of the other answers are correct.
Choice D: The two expressions are of equal value.
Answer:
B: Using x and y factor results in an expression of greater value than using x and y as terms.
Step-by-step explanation:
For her first expression, x and y are factors;
xy
For her second expression, x and y are written as terms;
x + y
For x and y are both negative integers, then;
-x * -y = xy ............... 1
-x + (-y) = - x - y
= - (x + y) .............. 2
Therefore, the value of x and y factors is greater than that when x and y are as terms. Thus the correct option is B.
Find the equation of the line shown
Answer:
y = x+1
Step-by-step explanation:
Slope-intercept form
(y = mx+b)
m = slope and b = y-intercept
The line crosses the y-axis at (0, 1), therefore the y-intercept (b) = 1
The slope (m) = 1
Because the slope is 1, it does not need to be written in the equation, as any number multiplied by 1 is that number.
richard klein works as auto mechanic and earns the following commission rates 3.00 percent for oil changes 5.00 percent for tune ups and 6.25 percent on auto parts sales he is guaranteed a minimum salary of $2,450.00 per month last month he brought in $2,500.00 in oil changes $4,500.00 in tune ups and sold $28,200.00 in parts what is his gross pay for the month
Answer:
Richard's gross pay for the month was $ 4,512.5.
Step-by-step explanation:
Given that Richard Klein works as auto mechanic and earns the following commission rates: 3.00 percent for oil changes, 5.00 percent for tune ups and 6.25 percent on auto parts sales; and he is guaranteed a minimum salary of $ 2,450.00 per month, if last month he brought in $ 2,500.00 in oil changes, $ 4,500.00 in tune ups and sold $ 28,200.00 in parts, to determine what is his gross pay for the month the following calculation must be performed:
2,450 + (2,500 x 0.03) + (4,500 x 0.05) + (28,200 x 0.0625) = X
2,450 + 75 + 225 + 1,762.5 = X
2,450 + 2,062.5 = X
4,512.5 = X
Thus, Richard's gross pay for the month was $ 4,512.5.
pls I need the answer with steps
Answer:
x = - 3.75
y = 28.75
Step-by-step explanation:
[tex] \begin{cases} x + y = 25\\\\ 5x + y = 10 \end{cases} [/tex]
Since, x + y = 25
Therefore, y = 25 - x..... (1)
5x + y = 10......(2)
Plug y = 25 - x in equation (2), we find:
5x + 25 - x = 10
5x - x = 10 - 25
4x = - 15
x = - 15/4
x = - 3.75
Plug x = - 3.75 in equation (1), we find:
y = 25 - (- 3.75)
y = 25 + 3.75
y = 28.75
(x, y) = (-3.75, 28.75)
I need help plz anyone
Answer:
e
Step-by-step explanation:
Angharad is buying a new 50-inch screen TV (remember that TV screens are measured along the diagonal )
a) If it is 30 inches tall, how wide is the screen ?
b) Her TV cabinet is 30 inches wide .will the TV fit inside it ?
Answer:
a) 40 inches
b) No it will not fit inside
Step-by-step explanation:
Angharad is buying a new 50-inch screen TV (remember that TV screens are measured along the diagonal )
a) If it is 30 inches tall, how wide is the screen ?
Diagonal ² = Width² + Height²
Diagonal = 50 inches
Height = 30 inches
50² = Width² + 30²
Width² = 50² - 30²
Width = √50² - 30²
Width = √(1600)
Width = 40 inches
b) Her TV cabinet is 30 inches wide .will the TV fit inside it ?
No it will not fit inside
This is because, the width of the TV is the above calculation is 40 inches. This is wider than the width of the TV cabinet, hence, it won't fit inside
Remy was on vacation in New France, Canada. He went to the Ratatouille restaurant and had an excellent dinner. How much did
he pay if the dinner cost $32 and he gave a 18% tip? How much was the tip?
Answer:
See both answers in the explanation
Step-by-step explanation:
Given data
Cost of dinner= $32
TIp=18%
Let us find the amount of the tip
=18/100*32
=0.18*32
=$5.76
Hence the total amount paid is
=5.76+32
=$37.76
The Tip is
=$5.76
what is the scale factor pls help
Answer:
im pretty sure its 2
Step-by-step explanation:
Answer:
4
Step-by-step explanaiton:
B is 4x bigger than A
the diagram shows the distance between city P and city S and city T. which measurement is closest to x, than the distance between city P and city T in miles?
Answer:
1352 miles
Step-by-step explanation:
since city t, s, and P make a right angle we can use the Pythagorean theorem to find the hypotenuse (distance from t to p) 1180 squared=1,392,400 and 660 squared =435,600 so now we add them together and take its square root which is 1352.0
Which trinomials are perfect square trinomials?
Select each correct answer.
O y2 + 18y + 81
O y2 + 20y + 100
O y2 + 25y + 200
Oy + 6y + 36
Mrs. Higgins's was hoping to make some extra cash, so she invested 12000 in equipment to print yearbooks, each year book cost her $5 to print and she sells them for $15. how many yearbooks must she sell before she breaks even?
Answer: im pretty sure it’s the first one
Step-by-step explanation: )
1/3 is what percent of 5/6
Answer:
1/3 is 40% of 5/6
Step-by-step explanation:
40%
(5/6)*(x/100)=1/3
x=(600)/15
x= 40
Write the word sentence as an equation. Then solve the equation. A number $k$ increased by 7 is 34. An equation that represents this word sentence is . The solution is $k=$ .
Answer: k = 27
Step-by-step explanation:
Here's the complete question:
Write the word sentence as an equation. Then solve the equation. A number k increased by 7 is 34.
An increase in k simply means that there's an addition. This will be:
k + 7 = 34
k = 34 - 7
k = 27
Therefore, the value of k is 27
Allison runs for 1 3/4 minutes and travels 1/5 mile. What is her speed in miles per minute?
how do you write 8.683 as a percentage?
Answer:
868.3%
Step-by-step explanation:
8.683 x 100 = 868.3%
Answer: 868.3%
All you need to do to convert a decimal to a percentage is multiply by 100. In this case we have to multiply 8.683 by 100 which gives us 868.3%