B
rearrange into standard form : ax² + bx + c = 0 (a≠ 0)
2x² - 3x - 2 = 0
(x - 2)(2x + 1) = 0 ( equate each factor to zero and solve for x )
x - 2 = 0 ⇒ x = 2
2x + 1 = 0 ⇒ x = - 0.5
HELP NEEDED!!! WILL GIVE 5 STARS!
A snack of an apple, a brownie, and a cheese stick has 270 calories. Two brownies and an apple have 290 calories. Two apples and three cheese sticks have 420 calories. How many calories are in each item?
Let a=calories in an apple, b=calories in a brownie, and c=calories in a cheese stick.
Which function is represented by the graph?
f(x) = −|x − 3| + 4
f(x) = −|x + 3| + 4
f(x) = −|x − 4| + 3
f(x) = −|x + 4| + 3
Answer:
Step-by-step explanation:
It is f(x) = −|x + 4| + 3 because the +4 in the absolute value sign moves the graph 4 spots to the left and the +3 moves the graph 3 spots up.
Answer:
f(x) = −|x + 4| + 3
Step-by-step explanation:
since, the value of the function at x=0 is -1
so, we will check which functions gives the same value
f(x) = −|x − 3| + 4 at x=0 it gives 1
f(x) = −|x + 3| + 4 at x=0 it also gives 1
f(x) = −|x − 4| + 3 at x=0 it gives -1
f(x) = −|x + 4| + 3 at x=0 it also gives -1
so, we have discarded first two options
Now at x=4 function gives negative value
f(x) = −|x − 4| + 3 at x=4 it gives 3
f(x) = −|x + 4| + 3 whereas at x=4 it gives -5
Hence, the function represented by the graph is:
f(x) = −|x + 4| + 3
A train traveled 325 miles in 5hrs. What was the trains average rate of speed in miles per hr ?
Hi there!
To find the average speed of a moving object all you need to do is divide the distance traveled by the object by amount of time it took the object to reach its final destination. So for this problem it would go like this:
325 ÷ 5 = 65
So for this problem in particular the answer is 65 MPH was the average speed of the train.
Your friend, ASIAX
please help on this one
its d to check answer use symbolab its a great sight
The density of mercury is 13.6 grams per cubic centimeter. Complete the steps for converting 13.6 g/cm^3 to kg/m^3
1 cubic meter = 100 cm * 100 cm * 100 cm = 1 x 10^6 cc
1 kilogram = 1,000 grams
13.6 g / cc
If we had a cubic meter of mercury, its mass would be (or it would "weigh") 13.6 * 1,000,000 = 13,600,000 grams or 13,600 kilograms.
And so its density would be 13,600 kg / cubic meter.
13600 kg/m³. To convert 13.6 g/cm³ to kg/m³, multiply by the conversion factor 1000 kg/m³.
Explanation:To convert from grams per cubic centimeter (g/cm³) to kilograms per cubic meter (kg/m³), we need to use conversion factors.
1 g/cm³ = 1000 kg/m³.
So, to convert 13.6 g/cm³ to kg/m³, we multiply by the conversion factor:
13.6 g/cm³ x 1000 kg/m³ = 13600 kg/m³
BRAINLIEST!PLEASE HELP ME
-12x - 0.4 > 0.2(36.5x + 80) - 55 Remove the brackets.
-12x - 0.4 > 7.3x + 16 - 55 Combine the like terms on the right
-12x - 0.4 > 7.3x - 39 Add 12x to both sides
- 0.4 > 7.3x + 12x - 39
- 0.4 > 19.3x - 39 Add 39 to both sides.
-0.4 + 39 > 19.3x Combine like terms on the left
38.6 > 19.3x Divide by 19.3
38.6 / 19.3 > x
2 > x
every sixth visitor to an animal shelter gets a free animal calendar every 20th visitor gets a free animal toy which visitor each day will be the first want to get both the calendar and the animal toy
Algebra 2: Factoring The Polynomial. Some are guess and test.
10w^2-37w+15
4z^2+4z-3
18v^2-15v-18
Multiply the first and last term. Now find two numbers that when you multiply gives you that product and when you add them gives you the middle term. Replace the middle term with those two numbers and factor using the grouping method.
10w² - 37w + 15
10 x 15 = 150 (1 x150, 2 x 75, 3 x 50, 5 x 30, 6 x 25, 10 x 15)
None of those pairs have a sum of -37 so this polynomial is prime.
************************************************************************************
4z² + 4z - 3
4 x -3 = -12 ( -1 x 12, -2 x 6, -3 x 4) ⇒ -2 + 6 = 4
= 4z² - 2z + 6z - 3
= 2z(2z - 1) +3(2z - 1)
= (2z + 3)(2z - 1)
************************************************************************************
18v² - 15v - 18
= 3(6v² - 5v - 6)
6 x -6 = -36 (1 x -36, 2 x -18, 3 x -12, 4 x -9, 6 x -6) ⇒ 4 x -9 = -5
= 3(6v² + 4v -9v - 6)
= 3[2v(3v + 2) -3(3v + 2)]
= 3(2v - 3)(3v + 2)
Anya has base salary of $200 per week for her part-time job. She earns $10 commission for sales for over $500. This week, her gross pay was $400
Answer:
Step-by-step explanation:
500+400+200+10
Which of the following graphs represents the equation y=-2x+3?
The graph which represents the equation y = -2x+3 is Option (B)
Plotting graph of a straight line -A straight line , say y = mx + c can be plotted on the graph by checking its y intercept (c), slope of the following curve (m) and satisfying the points on the x and y coordinates of the following graph.
Following these simple steps, we can easily plot the graph for any straight line.
How to identify the given straight line from the following options in the question ?The equation given is y = -2x + 3 .
First of all the graph will have a negative slope as the slope of the straight line is -2 .
Checking the graph in Option (B), we have
Slope of the curve = -2
Putting the points (0,3) and (1,1) in the following equation of curve ,
y = -2x + 3 , both satisfies.
Thus the graph in Option (B) represents the equation of the straight line.
To learn more about plotting graph of a straight line, refer -
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Need Help Asap!!!!!!
a right triangle has side lengths of 15,36, and 39 cm. what is the area of the triangle
This is a right triangle (you can confirm by using Pythagorean Theorem: 15² + 36² = 39²)
A = [tex]\frac{1}{2} b * h[/tex]
A = [tex]\frac{1}{2} 15 * 36[/tex]
= 15 * 18
= 270
Answer: 270 cm²
How long does it take a snail to crawl 89 inches
2 hours and 13 mins hope this helps
The area of a rectangular park is 24 square miles. If the length of the park is 6 miles, what is the width of the park?
You travel at an average speed of 20 km/h in a straight line to get to your grandmother's house. It takes you 3 hours to get to her house. How far away is her house from where you started ?
Distance = Speed x Time
Therefore distance = 20 x 3
Grandma's house is 60 km away from where you started.
Carmella turns on her oven, which heats up at
80
degrees per minute. The temperature of her house, and therefore her oven, is
70
degrees. Let
x
be the number of minutes that it will take for her oven to reach
390
degrees.
It will probably be 390 / 70
How can you use partial quotients to find 684 divided by 57?
Answer: 684 divided by 57=12
Step-by-step explanation:(with reference to the figure)
To find 684 divided by 57 by partial quotients .
Here dividend= 684 and divisor =57
Step 1: Write easy factors of divisor that is nearest to the dividend as follows
57×2=114
57×3=171
57×5=285
57×10=570(nearest easy factor)
Step 2: Now subtract 570 from 684 ,we get 114 then subtract 114=57×2 from it we get 0.
Step 3: Adding the factors we have used in step 1 and 2 ,it will give required quotient=10+2=12
i.e. 684=57(10)+57(2)
LOTS OF POINTS! PLEASE HELP!
Lena is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.
Company A charges $111 and allows unlimited mileage.
Company B has an initial fee of $75 and charges an additional $0.90 for every mile driven.
For what mileages will Company A charge less than Company B?
Use m for the number of miles driven, and solve your inequality for m.
Company A = 111
Company B = 75 + 0.90m ( 75 plus 0.90 per mile)
Set the 2 to equal and solve for m ( miles)
111 = 75 + 0.90m
Subtract 75 from each side:
36 = 0.90m
Divide both sides by 0.90:
m = 36 / 0.90
m = 40
At 40 miles both Company A and Company B would cost the same.
So for Company A to cost less than Company B, you would have to drive more than 40 miles.
m>40
There are 1000 toothpicks in a regular-sized box. If a jumbo box is made by doubling all the dimensions of the regular-sized box, how many toothpicks will the jumbo box hold?
Hi, here is the solution.
The doubling each dimensions increases the volume by 8. That is (2 * 2* 2)
There 1000 toothpicks in a regular box.
The jumbo box hold 8 *1000 = 8000 toothpicks.
Thank you.
How to solve this ?
-x-3y=-26
6x+3y=21
---------------
3y cancels out.
-x=-26
6x=21
--------------
5x=-5
x=-1
Increasing the price of an item decreases the amount of people willing to buy it
Independent....
Dependent ...
In economic theory, the price of a product is considered the independent variable, and the quantity of the product demanded by consumers is considered the dependent variable. As price (independent variable) increases, the quantity demanded (dependent variable) decreases.
Explanation:In the context of economics and specifically, the law of demand, the price of a commodity is the independent variable and the quantity demanded is the dependent variable. This means that the amount of a product that consumers are willing to buy (dependent variable) can change based on the price of the product (independent variable). If a price changes, if all other factors remain constant, the quantity demanded will react accordingly. For example, if the price of an item increases, the quantity demanded decreases because consumers are less willing to buy the item due to its high price. Conversely, if the price decreases, the quantity demanded increases because the product becomes more affordable to consumers.
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A store buys 77 1/2 pounds of mulch in a large shipment. They divide the mulch up into bags that can each hold 2 1/4 pounds. The store sells one bag of mulch for $2.25. For each part of the question, show your work.
a. How many full bags of mulch will the store make?
b. Considering only the full bags, what is the total sales price of all the bags of mulch?
Answer: a. The store will make 34 full bags of mulch.
b. Considering only the full bags, the total sales price is $76.50
Step-by-step explanation:
The total amount of mulch is [tex]77\frac{1}{2}[/tex] pounds or [tex]\frac{155}{2}[/tex] pounds.
Each bag can hold [tex]2\frac{1}{4}[/tex] pounds or [tex]\frac{9}{4}[/tex] pounds of mulch.
a. Suppose, the store will make [tex]x[/tex] number of bags of mulch.
So, the equation will be.........
[tex]x*\frac{9}{4}=\frac{155}{2}\\ \\x=\frac{155}{2}*\frac{4}{9}=\frac{310}{9}=34.44... \approx 34[/tex]
So, the store will make 34 full bags of mulch.
b. The store sells one bag of mulch for $2.25
So, the total sales price of 34 full bags of mulch will be: [tex](\$2.25*34)=\$76.50[/tex]
Which point represents the ordered pair (-3,2)?
Select one:
a. Point C
b. Point A
c. Point D
d. Point B
Answer:
Point B
Step-by-step explanation:
(X,Y)
(-3,2) If you first look on the x line, all the way to the negative section. You'll find -3, starting there you will go up to 2. Following the y line.
Answer:
B
Step-by-step explanation:
Please help asap 27 pts
[tex]3x\geq3\qquad|\text{divide both sides by 3}\\\\x\geq1\\---------------------------------\\\\9x < 54\qquad|\text{divide both sides by 9}\\\\x < 6\\\\Answer:\ 1\leq x < 6\to\ graph\ c)[/tex]
The answer is C. Because A. has the wrong length for its numbers, B. has to much space in between it for negative numbers, and D. is just so wrong I can not even explain it! Hope that this was helpful have an awesome day!
Will someone please help me with these questions. The table shows the average annual cost of tuition at 4-year institutions from 2003 to 2010.
1.) Find the least squares regression equation using the school year (in number of years after 2000) for the input variable and the average cost (in thousands of dollars) for the output variable.
2.)What is the best estimate for the average cost of tuition at a 4-year institution starting in 2000. (Hint: look at the y-intercept)
3.)What is the best estimate for the average cost of tuition at a 4-year institution starting in 2020.
4.)What does the slope mean in context of the situation? 5.)Most students are not able to afford this tuition for 4 years. What are some ways that you can lower the cost of your college tuition? If you don’t plan to attend college, what things can do you post- HS graduation to continue your education or provide for yourself financially?
Step-by-step explanation:
1.) The equation for the line of least squares regression is given by
[tex]Y=mX+c[/tex]
where Y = Output Variable = Average Cost (in thousands of dollars)
X = Input Variable = Number of years after 2000
Thus, the given data table transforms as follows:
No. of years after 3 4 5 6 7 8 9 10
after 2000 (X)
Average Cost (Y) 15.505 16.510 17.451 18.471 19.363 20.409 21.093 22.092
To determine the equation precisely, we need to calculate the values of 'm' (Slope) and 'c' (Y-intercept)
Let us take any two random values of X and Y from the above table, so that we have
X₁ = 3; Y₁ = 15.505 and X₂ = 8; Y₂ = 20.409
Plugging in these two sets of values, we get the following two equations:
15.505 = (3)m + c and
20.409 = (8)m + c
Let us subtract the upper one from the lower one so that we have
20.409 - 15.505 = 8m + c - 3m - c
4.904 = 5m
Hence, m = 0.9808
Using this value and plugging it in one of the above equations yields the value of c as
20.409 = 8(0.9808) + c
Therefore, c = 12.563
So, the required equation for the line of least squares regression is
Y = (0.9808)X + 12.563
2.) To estimate the cost of tuition at a 4-year institution in 2000, we can put the value of X to be 0.
We have Y = 0 + 12.563
Thus, the cost of tuition in 2000 was $12,563.
3.) To estimate the cost of tuition in 2020, we put the value of X as 20 so that we have
Y = (0.9808)(20) + 12.563 = 32.179
Therefore, we can expect the cost of tuition to be as high as $32,179 by 2020.
4.) The slope tells us the factor by which the tuition increases each year, starting with the base of 12,563 dollars in 2000.
One way to lower the cost of college tuition is by applying for a waiver based on income level. Alternatively, one can also work at the school.
One can join a part-time graduation program while working for the rest of the day so that one may support oneself as well as pay for their courses. Alternatively, one can opt for Online Courses and get some Diploma in their area of interest while working part-times so that they may pursue a degree later on in their life.
The least squares regression equation is Average cost = 14.5 + 1.24 * School year. The best estimate for the average cost of tuition at a 4-year institution starting in 2020 is 33.3 thousand dollars. The slope of the regression line means that the average cost of tuition increases by 1.24 thousand dollars for every year after 2000.
1. To find the least squares regression equation, we can use the following steps:
Calculate the mean of the independent variable (school year) and the dependent variable (average cost).
Calculate the deviations from the mean for both variables.
Calculate the product of the deviations from the mean for both variables.
Calculate the variance of the independent variable.
Calculate the slope of the regression line:
slope = sum of the product of the deviations from the mean / variance of the independent variable
Calculate the y-intercept of the regression line:
y-intercept = mean of the dependent variable - slope * mean of the independent variable
Calculations:
Mean of school year: 5.5
Mean of average cost: 19.0
Deviations from the mean for school year: -1.5, -0.5, 0.5, 1.5, 2.5
Deviations from the mean for average cost: -3.5, -2.5, -1.5, -0.5, 1.5
Product of the deviations from the mean: 5.25, 1.25, -0.75, 0.75, 3.75
Variance of the independent variable: 4.25
Slope of the regression line: 5.25 / 4.25 = 1.24
Y-intercept of the regression line: 19.0 - 1.24 * 5.5 = 14.5
Least squares regression equation:
Average cost = 14.5 + 1.24 * School year
complete the statement about how to prove that the medians of an isosceles triangle meet at a point. To prove that the medians of an isosceles triangle meet at a point, show that the of a side lies on the line containing the opposite and the point where the other two intersect.
Answer:
It is midpoint, vertex, and medians in that order.
Hope this helps!
I know these are correct because I got them correct!
Answer:
midpoint, vertex, and medians
Step-by-step explanation:
To prove that the medians of an isosceles triangle meet at a point, show that the
✔ midpoint
of a side lies on the line containing the opposite
✔ vertex
and the point where the other two
✔ medians
intersect.
Edginuity
What number multiplied by itself 2 times equals 49
You're basically looking for the square root of 49. In fact, if a number [tex] x [/tex] gives [tex] y [/tex] when multiplied by itself two times, then you have [tex] x^2 = y [/tex], which also means that [tex] x [/tex] is the square root of [tex] y [/tex], i.e. [tex] x = \sqrt{y} [/tex]
In your case, the answer is 7, because you have
[tex] \sqrt{49}=7 \iff 7^2 = 49 [/tex]
which is indeed true
Answer:
Step-by-step explanation:
You want the square root of 49, which is 7
6. Dawn lingua bought three yards of cloth to make some curtains. The cloth was on sale for $2.25 per yard. How much did dawn pay for the cloth if the sales tax was 5%?
7.25 u need to add 2.25+5=7.25
URGENT MATH HELP NEEDED!!! WILL MARK BRAINLIEST!!! PLEASE HELP!!! URGENT!!!
The table shows the number of touchdowns Luis scored during his football games.
Touchdowns scored (X) 0 1 2 3
Number of games (f) 6 10 7 5
(a) Create a probability distribution table. Show your work.
(b) What is the probability of Luis scoring 2 touchdowns?
(c) What is the probability of Luis scoring more than 1 touchdown?
(d) What is the estimated (expected) value of the number of touchdowns Luis scores?
SHOW YOUR WORK PLEASE!!!
Solution-
The table shows the number of touchdowns Luis scored during his football games.
Touchdowns scored (X) 0 1 2 3
Number of games (f) 6 10 7 5
Total games played = 6+10+7+5=28
1.
[tex]Probability\ of\ an\ event=\frac{Number\ of\ Favorable\ Outcomes}{Total\ Number\ of\ Possible\ Outcomes}[/tex]
[tex]P(X=0)=\frac{6}{28} \\ P(X=1)=\frac{10}{28} \\ P(X=2)=\frac{7}{28} \\ P(X=3)=\frac{5}{28}[/tex]
Probability Distribution Table,
Touchdowns scored (X) 0 1 2 3
Probability P(X) 6/28 10/28 7/28 5/28
2.
The probability of Luis scoring 2 touchdowns(i.e when X=2),
P(scoring 2 touchdowns) = P(X=2)
[tex]=\frac{7}{28}=0.25[/tex]
3.
The probability of Luis scoring more than 1 touchdown(i.e when X>1)
P(scoring more than 1 touchdowns) = P(X>1) = P(X=2) + P(X=3)
[tex]=\frac{7}{28}+\frac{5}{28}=0.42[/tex]
4.
Estimated number of touchdowns is calculated by multiplying the number of touchdowns by their respective probabilities and adding the result.
Estimated number of touchdowns is,
[tex]=0\times \frac{6}{28}+1\times \frac{10}{28}+2\times \frac{7}{28}+3\times \frac{5}{28}[/tex]
[tex]=0+\frac{10}{28}+\frac{14}{28}+\frac{15}{28}[/tex]
[tex]=\frac{39}{28}=1.39[/tex]
Use synthetic division to find the quotient and remainder. Express your answer as a polynomial.
1. 2x^3-11x^2+13x-21*x-3
2. 3x^3+7x^2-13x+10*x+2
3. 2x^3+13x^2-21x+9*x-1
4. 7x^3-8x+16/x-2
5. 8x^4-14x^3-71x^2-10x+24/x-4
1. 2x³ - 11x² + 13x - 21 ÷ x - 3
x - 3 = 0 ⇒ x = 3
3 | 2 -11 13 -21
| ↓ 6 -15 -6
2 -5 -2 -27
1. Answer: 2x² - 5x - 2 - [tex]\frac{27}{x - 3}[/tex]
*************************************************************
2. 3x³ + 7x² - 13x + 10 ÷ x + 2
x + 2 = 0 ⇒ x = -2
-2 | 3 7 -13 10
| ↓ -6 -2 30
3 1 -15 40
2. Answer: 3x² + x - 15 + [tex]\frac{40}{x + 2}[/tex]
3. 2x³ + 13x² - 21x + 9 ÷ x - 1
x - 1 = 0 ⇒ x = 1
1 | 2 13 -21 9
| ↓ 2 15 -6
2 15 -6 3
3. Answer: 2x² + 15x - 6 + [tex]\frac{3}{x - 1}[/tex]
4. 7x³ + 0x² - 8x + 16 ÷ x - 2
x - 2 = 0 ⇒ x = 2
2 | 7 0 -8 16
| ↓ 14 28 40
7 14 20 56
4. Answer: 7x² + 14x + 20 + [tex]\frac{56}{x - 2}[/tex]
5. 8x⁴ - 14x³ - 71x² - 10x + 24 ÷ x - 4
x - 4 = 0 ⇒ x = 4
4 | 8 -14 -71 -10 24
| ↓ 32 72 4 -24
8 18 1 -6 0
5. Answer: 8x³ + 18x² + x - 6
Amanda is adding the numbers below.
3.7 x 10^20 + 4.45x10^20
What is the sum written in scientific notation?
add 3.7 and 4.45 make sure to change it back to standard you'll get 815000000000000000000. move decimal between first and second digit which means you moved it to the left 18 times and your answer will be 8.15 x 10 ^18 I hope its right :( please don't judge if wrong :((( lol
Answer: 8.15 x 10²⁰
Step-by-step explanation:
In order to add or subtract, they must both have the same power - think of the power as "like terms". In this problem they already have the same power (10²⁰) so we don't need to manipulate them to have the same power. We can just add their coefficients (3.7 and 4.45).
3.7 x 10²⁰
+ 4.45 x 10²⁰
8.15 x 10²⁰