Answer:
x = sqrt(17) - 1 or x = -1 - sqrt(17)
Step-by-step explanation:
Solve for x:
x^2 + 2 x + 1 = 17
Hint: | Factor the left hand side.
Write the left hand side as a square:
(x + 1)^2 = 17
Hint: | Eliminate the exponent on the left hand side.
Take the square root of both sides:
x + 1 = sqrt(17) or x + 1 = -sqrt(17)
Hint: | Look at the first equation: Solve for x.
Subtract 1 from both sides:
x = sqrt(17) - 1 or x + 1 = -sqrt(17)
Hint: | Look at the second equation: Solve for x.
Subtract 1 from both sides:
Answer: x = sqrt(17) - 1 or x = -1 - sqrt(17)
Owen is fishing from a dock he starts with the bait 2 feet below the surface he reels out the boat 19 feet then reels it back in 7 feet what is the final position of the bait relative to the surface of the water
Answer:
The bait is 14 feet below the water surface
Step-by-step explanation:
Here, we want to know the final position of the bait relative to the surface of the water.
Firstly, he starts with the bait at 2 feet below the water surface. The reels out the bait a further 19 feet, the new position of the bait relative to the water surface will be 2 + 19 = 21 feet
Now, he reels the bait back by 7 feet.
Thus, the new depth of the bait relative to the water surface will be 21-7 = 14 feet
1) f(x) = 3x - 4
g(x) – x2 + 3x
Find f(g(x))
Answer:
x=4/3
Step-by-step explanation:
What is the value of 6 x 90.6 ?
Answer:
543.6
Step-by-step explanation:
=> 6 x 90.6
=> 543.6
what is the value of x in the equation 3x-4y=65 when y=4 HELLP PLEEAASE !!!!
Answer: x=27
Step-by-step explanation:
Si la época prehistórica sucedió desde hace 2.5 millones de años a.C., hasta hace 2.500 años a.C.; el período Paleolítico (2.5 millones de años a.C. Hasta 10.000 a.C.; el Mesolítico 10.000 a.C. Hasta 5.000 a.C. Y, el Neolítico sucedió desde el 5.000 a.C. Hasta el 2.500 a.C. ¿A qué fracción de la época prehistórica corresponde el período paleolítico? *
Answer:
El período paleolítico corresponde a [tex]\frac{332}{333}[/tex] de la época prehistórica.
Step-by-step explanation:
En primer lugar, se determina la extensión de tiempo, medida en años, tanto de la época prehistórica como el período paleolítico: (Nótese que el signo negativo significa a.C.)
Época Prehistórica
[tex]\Delta T = -2500-(-2500000)[/tex]
[tex]\Delta T = 2497500\,years[/tex]
Período Paleolítico
[tex]\Delta t = -10000 - (-2500000)[/tex]
[tex]\Delta t = 2490000\,years[/tex]
La fracción de la época prehistórica que corresponde al período paleolítico es:
[tex]r = \frac{\Delta t}{\Delta T}[/tex]
[tex]r = \frac{2490000\,years}{2497500\,years}[/tex]
[tex]r = \frac{332}{333}[/tex]
El período paleolítico corresponde a [tex]\frac{332}{333}[/tex] de la época prehistórica.
C(x) = mx + 500
A company's total cost c(x), in dollars, to produce x shirts is given by the function above, where m is a
constant and x > 0. The total cost to produce 100 shirts is $800. What is the total cost, in dollars, to
produce 1000 shirts? (Disregard the $ sign when entering your answer.)
Total cost as the function of shirts is :
C(x) = mx + 500 .
It is given that , The total cost to produce 100 shirts is $800.
800 = 100m + 500
m = 3
So , cost is given by :
C(x) = 3x + 500 .
Now , putting x = 1000 .
We get :
C(x) = 3x + 500
C(x) = 3(1000) + 500
C(x) = $3500
Therefore , cost of producing 1000 shirts is $3500 .
Hence, this is the required solution .
Total cost to produce 1000 shirts will be $3500.
Linear equation: A linear equation with two variables 'x' and 'y' are given by,y = mx + b
Here, m = constant
Given in the question,
Equation representing company's total cost C(x) and number of shirts 'x' as,
C(x) = mx + 500
Here, m = constant
And x > 0
If C(x) = $800, x = 100,800 = m(100) + 500
m = 3
Equation for the total cost to produce the 'x' shirts will be,
C(x) = 3x + 500
If x = 1000,C(x) = 3(1000) + 500
x = $3500
Therefore, total cost to produce 1000 shirts will be $3500.
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Number of girls: 14 Number of boys: 12 Number of students in the class: 26 What is the ratio in simplest form of the number of boys to the number of students in this math class?
Answer:
6:13
Step-by-step explanation:
Which represents a function
Answer:
the one on the right
Step-by-step explanation:
one input cannot have more than one output
I need to know about the gradient
Answer:
Step-by-step explanation:
Using inductive reasoning, what number is the most reasonable conjecture for the next number in the pattern 27,23,19,15,
Answer:
11
Step-by-step explanation:
The pattern here is to subtract by 4, so 15-4=11
The table shows the height of the tree that Margo planted over an 11-month period.
A 2-column table with 6 rows titled Growth of Margo's Tree. The first column is labeled Month with entries 1, 3, 5, 7, 9, 11. The second column is labeled Height of Tree (feet) with entries 1.4, 1.5, 2.1, 2.7, 3.0, 1.8.
Which statement can be supported by the information in the table?
The tree increased in height each month during the entire 11-month period.
The tree decreased in height each month during the entire 11-month period.
The tree increased in height each month until the time period between month 9 and month 11.
The tree decreased in height each month until the time period between month 9 and month 11.
Answer:
The answer is c
Step-by-step explanation:
just did it on edg
Answer:
The answer is: C
PLEASE HELP meeeeeeee
======================================================
Explanation:
Let's find the x intercept of f(x). Replace f(x) with 0 and solve for x
f(x) = -2x+2
0 = -2x+2
2x = 2
x = 2/2
x = 1
Plugging x = 1 into f(x) leads to f(x) = 0. The x intercept of f(x) is 1.
-----------------------
Now onto g(x). If we were given a row that had y = 0, then we'd immediately find the x intercept. However, that isn't given, so we'll have to do a bit of work to find the equation for g(x).
First we need the slope. Pick any two rows to find the slope. I'll pick the middle two rows.
m = (y2-y1)/(x2-x1)
m = (3-6)/(1-0)
m = -3/1
m = -3 is the slope
The y intercept is b = 6 as the table shows this pairs with x = 0. The y intercept always happens when x = 0.
So with m = -3 and b = 6, we see that g(x) = -3x+6.
-------------------------
Plug in g(x) = 0 and solve for x. We'll use similar ideas done in the first section at the very top
g(x) = -3x+6
0 = -3x+6
3x = 6
x = 6/3
x = 2 is the x intercept of g(x)
--------------------------
In summary, we found...
x = 1 is the y intercept of f(x)x = 2 is the y intercept of g(x)Subtract the x intercept values to get 2-1 = 1, which is the distance between the x intercepts. The distance is never negative.
Please help, Solve Systems of Linear Equations
Answer:
x = 1 , y = 1 , z = -3
Step-by-step explanation using elimination:
Solve the following system:
{3 x + 2 y - z = 8 | (equation 1)
2 z + 2 x = -4 | (equation 2)
3 y + x = 4 | (equation 3)
Subtract 2/3 × (equation 1) from equation 2:
{3 x + 2 y - z = 8 | (equation 1)
0 x - (4 y)/3 + (8 z)/3 = -28/3 | (equation 2)
x + 3 y+0 z = 4 | (equation 3)
Multiply equation 2 by 3/4:
{3 x + 2 y - z = 8 | (equation 1)
0 x - y + 2 z = -7 | (equation 2)
x + 3 y+0 z = 4 | (equation 3)
Subtract 1/3 × (equation 1) from equation 3:
{3 x + 2 y - z = 8 | (equation 1)
0 x - y + 2 z = -7 | (equation 2)
0 x+(7 y)/3 + z/3 = 4/3 | (equation 3)
Multiply equation 3 by 3:
{3 x + 2 y - z = 8 | (equation 1)
0 x - y + 2 z = -7 | (equation 2)
0 x+7 y + z = 4 | (equation 3)
Swap equation 2 with equation 3:
{3 x + 2 y - z = 8 | (equation 1)
0 x+7 y + z = 4 | (equation 2)
0 x - y + 2 z = -7 | (equation 3)
Add 1/7 × (equation 2) to equation 3:
{3 x + 2 y - z = 8 | (equation 1)
0 x+7 y + z = 4 | (equation 2)
0 x+0 y+(15 z)/7 = -45/7 | (equation 3)
Multiply equation 3 by 7/15:
{3 x + 2 y - z = 8 | (equation 1)
0 x+7 y + z = 4 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Subtract equation 3 from equation 2:
{3 x + 2 y - z = 8 | (equation 1)
0 x+7 y+0 z = 7 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Divide equation 2 by 7:
{3 x + 2 y - z = 8 | (equation 1)
0 x+y+0 z = 1 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Subtract 2 × (equation 2) from equation 1:
{3 x + 0 y - z = 6 | (equation 1)
0 x+y+0 z = 1 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Add equation 3 to equation 1:
{3 x+0 y+0 z = 3 | (equation 1)
0 x+y+0 z = 1 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Divide equation 1 by 3:
{x+0 y+0 z = 1 | (equation 1)
0 x+y+0 z = 1 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Collect results:
Answer: {x = 1 , y = 1 , z = -3
Henry needs 2 pints of red paint and 3 pints of yellow paint to get a specific shade orange. If he uses 9 pints of yellow paint and wants the same orange color, how many pints of paint will he need altogether. Explain how you know
Answer:
15 pints of paint 6 red 9 yellow
Step-by-step explanation:
3x3=9 so 9 yellow pints
and 2x3=6 so 6 red pints
6+9=15 so 15 pints of paint in total
The ratio of yellow to blue skittles in a bag 5:9 if there are 12 more blue skittles in the bag than yellow skittles how many yellow skittles are in the bag
Answer: 15
Step-by-step explanation: 5/9=15/27. 27-15=12
The number of yellow skittles in the bag are 15 skittles while the number of blue skittles in the bag are 27 skittles.
What is Ratio?A ratio is an ordered pair of numbers x and y which can be written as x / y where y does not equal 0. A proportion is an equation in which two ratios are set equal to each other.
For given information,
The ratio of yellow to blue skittles in the bag is 5:9
The number of blue skittles in the bag = 12 + The number of yellow skittles in the bag= 12+Y
Fraction of the total skittles that are yellow = 5/(5 + 9) = 5/14
Fraction of the total skittles that are blue = 9/(5+9)= 9/14
The total number of skittles = Yellow + Blue
in this Y as yellow; Y+12 as blue.
Y + Y + 12 = 2·Y + 12
The fraction of the total skittles that are blue = 9/14
we have 9/14 × (2·Y + 12) = Y + 12
-> 9 × (2·Y + 12) = 14 × (Y + 12)
-> 18·Y + 108 = 14·Y + 168
-> 18·Y - 14·Y = 168 - 108 = 60
-> 4·Y = 60
-> Y = 60/4 = 15
∴ The number of yellow skittles in the bag = 15
The number of blue skittles is given as = Y + 12 = 15 + 12 = 27.
Thus, the number of yellow skittles in the bag are 15 skittles while the number of blue skittles in the bag are 27 skittles.
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I NEED SERIOUS HELP NOW PLZ
The expression (y – 9)2 is equivalent to which expression. Simplify and write in standard form. Show your work.
Answer:
Step-by-step explanation:
Hello,
[tex](y-9)^2=(y-9)(y-9)=y^2-2*9*y+9^2=y^2-18y+81[/tex]
thanks
Answer:
yes
Step-by-step explanation:
How do you divide 506 in the ratio 2:4:5 ?
Answer:
Step-by-step explanation:
If the ratio is 2:4:5 there are 2+4+5=11 equal parts...
506/11=46
So each part is equal to 46 so 506 in a ratio of 2:4:5 is:
92:184:230
Find the distance between each pair of points
L(-7,0) ,Y(5,9)
Answer: The distance is 15
Step-by-step explanation:
To find the distance between L and Y find the difference in the x and y coordinates then square them and add them to find their square root.
-7-5= -12
0-9 = -9
12^2 + 9^2 = d^2 where d is the distance
144 + 81 = d^2
225 = d^2
d= [tex]\sqrt{225}[/tex]
d= 15
2x-30+5x+2=2 plz help
Answer:
30/7
Step-by-step explanation:
So we have the equation:
[tex]2x-30+5x+2=2[/tex]
Combine like terms:
[tex](2x+5x)+(-30+2)=2[/tex]
Add:
[tex]7x-28=2[/tex]
Add 28 to both sides:
[tex]7x=30[/tex]
Divide both sides by 7:
[tex]x=30/7[/tex]
So, our answer is 30/7
Or approximately 4.2857 :)
What is the unit rate if a student reads 81 pages in 3 hours?
Answer:
27 pages per hour
Step-by-step explanation:
81 pages divide by 3 hours. think of it as a fraction and divided 3 on both bottom and top then it gives you 27pages per hour as a fraction
А
B
1. Village A, B and C lie on the edge of the Namib Desert.
Village A is 30 km due North of Village C. Village C is 65 km
due East of A.
Calculate the shortest distance between village C and B,
giving your answer to the nearest 0.1km
A water tank is 2/3 full. 40 litres of water are taken from the tank. The tank is now 1/2 full. How many litres does the tank hold when full?
⅔ - ½ = 4/6 - 3/6 (make denomenator the same)
= 1/6
Thus, 1/6 = 40 litres
A full tank is 6/6 which equals to 1 whole
So,
1 unit (from 1/6) = 40 litres
6 units (from 6/6) = 40 × 6
= 240 litres
Therefore, the tank holds 240 litres when it is full.
( i hope my solution helps :3 )
The number of liters does the tank hold when full is 240 liters.
Number of litersFormulate
x=40÷⅔ - ½
Let find the common denominator
x=40÷4-3/6
Calculate the sum or the difference
x=40÷1/6
Divide the fraction
x=40×6
x=240 liters
Inconclusion the number of liters does the tank hold when full is 240 liters.
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The length of a rectangle is 2 yards less than 3 times the width.The perimeter is 68 yards. Find the width
Answer:
length = (3*width) -2
length + 2 = 3*width
width = (length +2) / 3
2*length + 2*width = 68
OR: 2*length = 68 -2*width
If length = (3*width) -2 then
2*length = 6 * width -4
therefore,
6 width -4 = 68 -2 width
8 width = 72
width = 9
Since 2 length + 2 width = 68
then 2 length = 68 -2 width
2 length = 68 -18
length = 25
Step-by-step explanation:
Jesse loves to go hiking on rustic trails through trees and along rivers. One day in 20 minutes of hiking she hiked 1 mile. If Jesse hike at a constant rate what would the rate be
Answer:
0.05 mile per minutes
Step-by-step explanation:
Jesse's rate of hiking (miles per minute) = Total miles covered / Time covered
Miles covered = 1 mile
Time covered = 20 minutes
Jesse's rate of hiking (miles per minute) = Total miles covered / Time covered(minutes)
= 1 mile / 20 minutes
= 0.05 mile per minutes
20 minutes
= 20 × 60 seconds
= 1200 seconds
Jesse's rate of hiking (miles per seconds) = Total miles covered / Total time taken (seconds)
= 1 mile / 1200 seconds
= 0.0008333333333 miles per seconds
Approximately 0.000833 miles per seconds
Simplify: -3(y+2)^2-5+6y
Answer:3y^2+18y+7
:) happy to help
1.5r+15=2.25 just need help to show steps
Answer:
Step-by-step explanation:
Step 1: Subtract 15 from both sides.
1.5r+15−15=2.25−15
1.5r=−12.75
Step 2: Divide both sides by 1.5.
1.5r
1.5
=
−12.75
1.5
r=−8.5
Answer: r=-8.5
Step-by-step explanation:
1.5r+15=2.25
1.5r+15-15=2.25-15
1.5r=-12.75
1.5r/1.5=-12.75/1.5
r=-8.5
Danny is trying to determine the product between a rational and irrational number
Answer:
2√3=2√3, which is irrational
How much should Jenna save up to prepare for car repairs and maintenance? (A lump sum emergency fund just for car repair/maintenance that may come up in the future)
Answer:
$500 per year.
Step-by-step explanation:
Car repairs and maintenance expense is based on the usage of car as well as its present condition. If the car is bought from showroom and is new then it will incur only small amount of expense as its maintenance but if the car is used by various owners then it is likely that maintenance expense can be huge. The average car repair expense is $500 to $800 per year depending on car condition. Since Jenna car is new she should keep the repair estimate to be minimum that is nearly $500 per year or $42 per month.
A 12.5 oz box of cereal has a price of $2.07. What is the unit ratio of price to weight rounded to the nearest cent?
Answer:
16 cents
Step-by-step explanation:
The answer is 16 cents because 207 cents divided by 12.5 oz equals 16 cents.
Solve for d. dt=v What is d equal to? A. d=vt B. d=t/v C. d=v-t D. d=v/t
Answer: I think the answer is "d = vt"
Step-by-step explanation:
Multiply both sides of the equation by;
t * d = v * (t)
Multiply, v by t
Answer; d = vt
Hope this helps :)
The value of d, is equivalent to d = v/t.
What is a function?
An expression in mathematics defines a relationship between one variable (the independent variable, x) and another variable (the dependent variable, y). For example -
f(x) = 4x + 6
Given is the following equation -
dt = v
We have -
dt = v
d = v/t
Therefore, the value of d, is equivalent to d = v/t.
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