Answers
Answer:
1.) x={1,−2}
2.) x={3,-9}
3.) x = {4, 4}
4.) x={0, 12}
5.) x = {6, 8}
Step-by-step explanation:
1.) x2+x-2=0
Step-1 : Multiply the coefficient of the first term by the constant 1 • -2 = -2
Step-2 : Find two factors of -2 whose sum equals the coefficient of the middle term, which is 1 .
-2 + 1= -1
-1+ 2= 1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -1 and 2
x2 - 1x + 2x - 2
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-1)
add up the last 2 terms, pulling out common factors :
2 • (x-1)
Step-5 : Add up the four terms of step 4 :
(x+2) • (x-1)
(x + 2) • (x - 1) = 0
Hope this Helps!!!!
Related Questions
What is an equation of the line that passes through the point (6, 1) and is
perpendicular to the line 2x + 3y = 18?
Answers
Answer: y=1,5x-8
Step-by-step explanation:
At first transform the equation
2x+3y=18
3y= 18-2x
y= 6 - (2/3)x
The linear function has general form, which looks like that:
y=mx+n
perpendicular means that m1*m2=-1
In our case m1= -(2/3) and m2 is unknown
(-2/3)*m2= -1
m2=3/2 so m2=1,5
The line has to go through the point (6,1)
so 1=6*1,5+n
1=9+n
n= -8
so the function looks like that y=1,5x-8
Graph both equations. What point do they intersect at?
y = x + 3
y = -x-1
Answers
Answer: y= -1-1 = (0,-1) y= x + 3=(0,3)
Step-by-step explanation:
On average, Americans consume 13.9 pounds of ice cream per person over an entire year. Ben loves ice cream, but limits himself to one 6 ounce (oz) serving each week. Find the difference between the amount of ice cream that Ben consumes compared to the national average.
Answers
Answer:
5.6 pounds
Step-by-step explanation:
13.9 pounds of ice cream are consumed per year by individual.
Ben consumes 6 ounce serving per week.
The amount of ice cream consumed by Ben in a year can be determined by;
since there is an average of 52 weeks in a year, then;
6 ounces x 52 = 312 ounces
But,
1 ounce = 0.0625 pounds
So that,
312 ounces = x pounds
x = 312 x 0.0625
= 19.5
x = 19.5 pounds
Thus, Ben consumes 19.5 pounds of ice cream per year. He consumes more than the average value per person in a year.
The difference = Amount Ben consumes - National average
= 19.5 - 13.9
= 5.6 pounds
Which product is equivalent to -7 × 2/5?
Answers
Answer:
-2.8 or -14/5
Step-by-step explanation:
All you have to do is put the -7 over 1 and multiply across. So it'd look like:
-7/1 x 2/5 which works out across as -14/5 or you can convert it to a decimal to be -2.8. Hope this helps! :)
Triangular numbers can be represented with equilateral triangles formed by dots the first fire triangle numbers are 1 3 6 10 and 15 is there a direct variation between a triangle number and its position in the sequence explain your reasoning
Answers
Answer:
There's no direct variation
Step-by-step explanation:
Required
Determine if there's a direct variation between the number and its position
I'll start by giving an illustration of how the triangle is represented using stars (*)
*
**
***
****
*****
Represent the line number with y and it's position with x
On line 1:
y = 1, x = 1
On line 2:
y = 2, x = 3
On line 3:
y = 3, x = 6
On line 4:
y = 4, x = 10
On line 5:
y = 5, x = 15
Note that, x is gotten by calculating the accumulated number of stars while y is the line number.
Direct variation is represented by
y = kx
Or
kx = y
Where k is the constant of variation
For line 1:
Substitute 1 for y and 1 for x
k * 1 = 1
k = 1
For line 2:
Substitute 2 for y and 3 for x
k * 3 = 2
Divide through by 3
k = ⅔
Note that the values of k in both computations differ.
This implies that there's no direct variation and there's no need to check further.
No, the triangular numbers are not a direct variation. There is not a constant of variation between a number and it's position in the sequence. The ratios of the numbers to their positions are not equal. Also, the points (1, 1), (2, 3), (3, 6), and so on, do not lie on a line.
Step-by-step explanation:
Please help me out!! :c
Katie has f fish. Alejandro has 11 fish, which is 3 fewer than twice the number Katie has.
Which equation shows an equality between two different ways of expressing how many fish Alejandro has?
A. f + 3 = 11
B. f – 3 = 11
C. f/2 - 3 = 11
D. 2f – 3 = 11
Answers
Answer:
The answer would be D
Step-by-step explanation:
To find how many Katie has, you would have to double it ( times by 2 ). Then subtract 3, since Alejandro has three less than twice as many as Katie.
Answer:
the answer is d just did the test got it right
Step-by-step explanation:
divisibilty by 2 5 and 10
Answers
Step-by-step explanation:
if the number ends in a 0,it is divisible by 10.Also if number and s divisible by 2 and 5 it is divisible by 10
What number makes the equation true? Enter the answer in the box.
÷3 = 6
Answers
Answer:
18
Step-by-step explanation:
multiply 6 by 3
Hope this helps. Pls give brainliest.
please help me!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
dm me for help
Step-by-step explanation:
Kim creates a model of a building. The scale of her model building is 1 foot to 8 inch. Some of the measurements are shown in the table. 11 Enter numbers in the empty boxes to correctly complete the table.
Answers
Answer:
Left
50 feet
Right
16 inches
10 inches
Step-by-step explanation:
Here, we want to make a conversion and fill in the empty spaces
The scale is 1 foot is 1/8 inch
To convert from foot to inch, we multiply by 1/8
To convert from inch to foot, we multiply by 8
Thus, we have ;
Let’s fill in the left spaces first;
6.25 * 8 = 50 feet
Right spaces, top to bottom;
128 * 1/8 = 16 inches
80 * 1/8 = 10 inches
1) 12/10-2/10 =
2) 18/6- 24/12=
3) 3/5 - 1/10=
4) 1/3 - 1/12=
Answers
Answer:
1: 1
2: 1
3:2/5
4:1/4
Okay ive been stuck on this for 30 minutes what is 2+2+?
Answers
ok i need yall help please
15=x+23-2x
Answers
Round the following numbers to 1 decimal place.
a) 65.874
b) 326.59
c) 13.555
d) 7.959
Answers
Answer:
a)65.9
b)326.6
c)13.6
d)8.0
Answer:
a)65.9
b)326.6
c)13.6
d)8.0
Please I rlly need this help!
Use operations of decimal, fraction, and percent numbers to model the following scenarios. In your final answer, include only an equation or proportion modeling the scenario. Do not solve the problems.
1 A family dines in a popular franchise restaurant. At the end of the meal, they decide to leave their server a monetary tip that is equal to 20% of the total bill amount, $60.50. How much will the family leave their server as a tip?
2 A family dines in a popular franchise restaurant. They plan to use a coupon that will give them a discount of 15% off of their total dinner bill, not including applicable sales tax or their server’s tip. If the family’s dinner bill totaled $34.00 before tax and tip, how much money will they save by using the coupon?
3 A family dines in a popular franchise restaurant. They plan to use a coupon that will give them a discount of 10% off of their total dinner bill, not including applicable sales tax or their server’s tip. The bill totals $157.30 before tax and tip. What is the new total after the server applies the 10% off coupon?
4 A family of eight dines in a popular franchise restaurant. The restaurant has a policy of automatically including a standard tip to the final bill for parties larger than six people. The bill for the meal included a total of $58.25 in food and beverage sales, plus a standard tip of $10.49. What percent of the food and beverage sales does the restaurant consider to be a standard tip for parties larger than six?
5 A family dines in a popular franchise restaurant that has a policy of automatically including a 20% tip on all food and beverage sales before coupon discounts are applied. What is the family’s total bill amount if their food and beverages totaled $94.20 and they used a 15% off coupon? (HINT: Create more than one model.)
Answers
Answer:
more details about this?
Step-by-step explanation:
The teacher said we could estimate but give a good reason for that estimate
Answers
Answer:
$11, even if you do work a job thats not that hard you should still be making a good amount of money
Step-by-step explanation:
I just used my opinion
Michael record the number of miles he runs each week for the nine weeks 6,11,13,8,15,9,11,5,9 which box plot represents the data
Answers
Five number summary
min = 5Q1 = 7median = 9Q3 = 12max = 15===============================================
Explanation:
The given list of values is {6, 11, 13, 8, 15, 9, 11, 5, 9}
It sorts to {5, 6, 8, 9, 9, 11, 11, 13, 15}
The middle most value is the second 9. We have four items below or at the median {5,6,8,9} and four values above the median {11,11,13,15}
The middle item of {5,6,8,9} is (6+8)/2 = 14/2 = 7. This is the value of Q1.
The middle item of {11,11,13,15} is (11+13)/2 = 24/2 = 12. This is Q3.
The min is 5 since it is the smallest of the original list.
The max is 15 because it is the largest of the original list.
The five number summary is
min = 5Q1 = 7median = 9Q3 = 12max = 15The boxplot that matches with this five number summary is the boxplot in the upper right corner.
The min is the left whisker. The max is the right whisker.
The left edge of the box is Q1. The right edge of the box is Q3.
The middle vertical line inside the box is the median.
Answer:
upper right corner
Step-by-step explanation:
An 8-Bar Package Of Soap Sells For $4 What Is The Unit Rate In Cost Per Bar?
Answers
Answer:
2 dollars
Step-by-step explanation:
If it’s an 8 pack, that is 4 dollars then if you divid, every bar should cost 2 dollars each.
.50 cents per bar of soap
Replace the blank with a number that makes the inequalities equivalent.
- 6v < ____;v>-0.5
-5.5
30
3
6.5
Answers
Answer:
3
Step-by-step explanation:
[tex] - 6v < 3[/tex]
when dividing by a negative number the sign is switched
[tex]v > - 0.5[/tex]
Point A is located at -4.5, and point B is 3.25 units from point A. Write two additional equations that could be used to determine the location of point B.
Answers
Answer:
The equations are B = -4.5 + 3.25 and B = -4.5 - 3.25
Step-by-step explanation:
Since point A is located at -4.5 and point B is 3.25 units away from A, point B can either be located on the left or on the right of point A.
If point B is located at the right of A, the equation for point B is -4.5 + 3.25.
If point B is located at the left of A, the equation for point B is -4.5 - 3.25.
So, the equations are B = -4.5 + 3.25 and B = -4.5 - 3.25
3) A product is marked down 15%; the sale price is $127.46. What was the
original price?
Answers
Answer:elling price (S.P) = (100 - m)% ⋅ Original price -----(1)
Here,
S.P = 127.46, m = 15
Substitute 127.46 for S.P and 15 for m in (1).
127.46 = (100 - 15)% ⋅ Original price
127.46 = 85% ⋅ Original price
127.46 = 0.85 ⋅ Original price
127.46 / 0.85 = Original price
149.95 = Original price
So, the original price is $ 149.95.
Step-by-step explanation:
The original price of product when the product is market down by 15% and the sales price is given so it is $149.95.
Calculation of price:Price is down by 15%, so m = 15% or 0.15.
So, Original price = [tex]\frac{Selling price}{( 1 - m)}[/tex]
By putting the value, we get
Original price = [tex]\frac{127.46}{(1 - 0.15)}[/tex]
= [tex]\frac{127.46}{0.85}[/tex]
= $149.95
Hence the original price of of the product was $149.95
Learn more about sale here : brainly.com/question/24321449
Please help and look at the image. (The table shows the transportation method of employees at a certain company. What percent of the employees walk to work?
)
Answers
First find town many employees in total. Add all the numbers to find it. We get 1400. Next we find the percentage of 1400 that gets us the number 7. 0.5% of 1400 is 7 so 0.5% is the answer :)
Answer:
0.5% to walk to work.
Step-by-step explanation:
First, find town many employees in total, Add all the numbers to find it. We get 1400, next we find the percentage of 1400 that gets us the number 7.
0.5% of 1400 is 7 so 0.5% is the answer :)
the sixth one. thanks for all the help!
Answers
Answer: The answer is 8 because if you divide each total cost by it’s number of tickets, you will always get 8.
Answer:
sorry gchgfcghhhghhhj
12 gallons of gas cost $30. How much will it cost to get an additional 4 gallons of gas?
Answers
Answer:
the answer is 40
Step-by-step explanation:
The point (5, 5) is in Quadrant.
The point (3, –2) is in Quadrant.
The point (–4, –4) is in Quadrant.
Answers
Answer:
A coordinate plane.
The point (5, 5) is in Quadrant
✔ I
.
The point (3, –2) is in Quadrant
✔ IV
.
The point (–4, –4) is in Quadrant
✔ III
.
Step-by-step explanation:
give me branliest pls
The point (5, 5) is in Quadrant I, the point (3, –2) is in Quadrant IV, and the point (–4, –4) is in Quadrant III.
What is an ordered double?It is defined as a representation of coordinates in a two-dimensional coordinate plane. It has a list of two elements in it, such as (x, y).
The area using the ordered double:
[tex]\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|[/tex]
As we know the coordinate plane is divided into four parts.
The first part is known as I quadrant; in this quadrant both values of x and y are positive.
In the second quadrant II value of x is negative and the value of y is positive.
In the third quadrant III values of x and y are negative.
In the fourth quadrant IV value of x is positive and the value of y is negative.
From the above information:
The point (5, 5) is in Quadrant I
The point (3, –2) is in Quadrant IV
The point (–4, –4) is in Quadrant III
Thus, the point (5, 5) is in Quadrant I, the point (3, –2) is in Quadrant IV, and the point (–4, –4) is in Quadrant III.
Learn more about the order double here:
brainly.com/question/10757890
#SPJ5
A pair of designer sneakers was purchased for $120. Since they were purchased, their price has increased by 15%. Write an equation that can help you find the new price. What is the new price?
Answers
Answer:
$138
Step-by-step explanation:
The price increased by $18
52 degrees times x+56 time 78 degrees please help quickly WILL MARK BRAINLESS
Answers
Answer:
Com on grl i am textin u like crazy man
Step-by-step explanation:
HELP ILL GIVE 10 PTS quick pleaseee
Answers
Answer: I’m pretty sure it’s the 4th one.
Step-by-step explanation: because 1 and 2 have infinity solutions but 3 has no solution 4 comes up with x=-11
Can you give brainiest? :)
State the slope and y-intercept of y=5x+2
Answers
y-intercept: (0,2)
Answer:
5 is the slope
(0,2) is the y intercept
Step-by-step explanation:
The equation y = 5x + 2 appears to be written in the y = mx + b form of a linear equation.
m represents slope and b represents the y value of the y intercept.
Here, m = 5 and b = 2.
This means 5 is the slope and (0,2) is the y intercept.
I need help with this question can someone please help me?
Answers
Okay, to find the equation you must find the y-intercept and the slope.
To find the y-intercept, you must find (0,y). This is the point on the y-axis where x is 0. So, where along the y-axis is there a point? There is a point at (0,-1). Therefore, your y-intercept is -1.
To find the slope, you must do rise/run. Go to a point on the line, such as (0,-1). You must go up (or down) until you get lined up with next point on the line. You go up one time. Then, you must go right (or left) to get to the exact point. In this case, the point would be (-1,0). You go left one time.
If you go down or left when doing rise/run, the number would be negative. Since you went left, that number would be negative.
So, our slope would be 1/-1, which can also be written as -1/1.
Now, write the equation. There is always an x next to the slope. y= -1/1x
Then, put the y-intercept next to it. If it is positive, use a +. If it is negative, use a -. It is negative.
Therefore, the answer is y= -1/1x -1.