ANSWER
[tex]x=\sqrt{3}-1[/tex] or [tex]x=-\sqrt{3}-1[/tex]
EXPLANATION
To complete the square for [tex]x^2+2x-2=0[/tex].
We rewrite the equation to get
[tex]x^2+2x=2[/tex].
We now add [tex](1)^2[/tex] to both sides to get
[tex]x^2+2x+1^2=2+1^2[/tex].
The expression on the Left Hand Side of the equation is a perfect square.
So our equation becomes
[tex](x+1)^2=2+1[/tex]
This gives us,
[tex](x+1)^2=3[/tex]
We take square root of both sides to obtain,
[tex]x+1=\pm \sqrt{3}[/tex]
[tex]x=-1\pm \sqrt{3}[/tex]
We split the [tex]\pm[/tex] to obtain,
[tex]x=\sqrt{3}-1[/tex]
or
[tex]x=-\sqrt{3}-1[/tex]
Answer:
x = √3 - 1 and x = -√3 - 1
Step-by-step explanation:
x^2 +2x - 2 = 0
To solve this equation, keep the variables on one side and constants on the other
x^2 + 2x = 2
Now to complete the square, divide the coefficient of x by 2:
2x ---> coefficient of x is 2
so 2/2 = 1
Now add the square of 1 to both the sides of the equation:
x^2 + 2x + (1)^2 = 2 + (1)^2
which makes it
(x + 1)^2 = 3
To solve it, take square root of both sides which gives
x = √3 - 1 and x = -√3 - 1
Help ASAP!!! Problem is on the picture provided.
QUESTION 1
The volume of a cone is given by;
[tex]V=\frac{\pi r^2h}{3}[/tex]
From the given information,
[tex]r=12,h=6[/tex]
[tex]V=\frac{12^2\times 6}{3}\pi[/tex]
[tex]V=\frac{144 \times 6}{3}\pi[/tex]
[tex]V=288\pi[/tex]
QUESTION 2
The volume of a sphere is given by
[tex]V=\frac{4\pi r^3}{3}[/tex]
From the given information.\
[tex]r=\frac{Diameter}{2}= \frac{12}{2}=6[/tex]
Therefore the volume of the sphere is
[tex]V=\frac{4\times6^3}{3} \pi[/tex]
[tex]V=\frac{4\times216}{3} \pi[/tex]
[tex]V=288\pi[/tex]
QUESTION 3
The volume of a sphere is given by
[tex]V=\frac{4\pi r^3}{3}[/tex]
From the given information.\
[tex]r=9[/tex]
Therefore the volume of the sphere is
[tex]V=\frac{4\times 9^3}{3} \pi[/tex]
[tex]V=\frac{4\times 729}{3} \pi[/tex]
[tex]V=972\pi[/tex]
QUESTION 4
The volume of a cylinder is given by
[tex]V=\pi r^2 h[/tex]
From the given information,
[tex]r=\frac{Diameter}{2}= \frac{12}{2}=6[/tex]
and
[tex]h=27[/tex]
Therefore volume of the cylinder
[tex]V=6^2 \times 27 \pi[/tex]
[tex]V=36 \times 27 \pi[/tex]
[tex]V=972\pi[/tex]
QUESTION 5
The volume of a cylinder is given by
[tex]V=\pi r^2 h[/tex]
From the given information,
[tex]r=\frac{Diameter}{2}= \frac{8}{2}=4[/tex]
and
[tex]h=18[/tex]
Therefore volume of the cylinder
[tex]V=4^2 \times 18 \pi[/tex]
[tex]V=16 \times 18 \pi[/tex]
[tex]V=288\pi[/tex]
QUESTION 6
The volume of a cone is given by;
[tex]V=\frac{\pi r^2h}{3}[/tex]
From the given information,
[tex]r=\frac{18}{2}=9,h=36[/tex]
[tex]V=\frac{9^2\times 36}{3}\pi[/tex]
[tex]V=\frac{81 \times 36}{3}\pi[/tex]
[tex]V=972\pi[/tex]
Volume of a cone = [tex]\pi r^2\frac{h}{3}[/tex]
Volume of a sphere = [tex]\frac{4}{3} \pi r^3[/tex]
Volume of a cylinder = [tex]\pi r^2h[/tex]
With the help of these formulas, we can calculate the volumes.
A cone with a radius of 12 units and a height of 6 units = [tex]\pi 12^2\frac{6}{3}[/tex] = 288[tex]\pi[/tex]
A sphere with a diameter of 12 units = [tex]\frac{4}{3} \pi 6^3[/tex] = 288[tex]\pi[/tex]
A sphere with a radius of 9 units = [tex]\frac{4}{3} \pi 9^3[/tex] = 972[tex]\pi[/tex]
A cylinder with a diameter of 12 units and a height of 27 units = [tex]\pi 6^227[/tex] = 972[tex]\pi[/tex]
A cylinder with a diameter of 8 units and a height of 18 units = [tex]\pi 4^218[/tex] = 288[tex]\pi[/tex]
A cone with a diameter of 18 units and a height of 36 units = [tex]\pi 9^2\frac{36}{3}[/tex] = 972[tex]\pi[/tex]
Carrie borrows $960 interest-free to pay for a car repair. She will repay $120 monthly until the loan is paid off. How many months will it take Carrie to pay off the loan? Explain.
Answer:
8 months.
Step-by-step explanation:
We have been given that Carrie borrows $960 interest-free to pay for a car repair. She will repay $120 monthly until the loan is paid off.
To find the number of months, it will take to pay off the loan, we will divide total amount of loan by monthly payment.
[tex]\text{Months to pay off the loan}=\frac{960}{120}[/tex]
[tex]\text{Months to pay off the loan}=8[/tex]
Therefore, it will take Carrie 8 months to pay off the loan.
I need help with these .help me plz
Answer:
The answer to your question would be Area = 280.13
Step-by-step explanation:
Area of the circle without the square: 380.13
Area of the square: 100
380.13 - 100 = 280.13
A family’s monthly budget is 1000.00. If only 8% is spent on transportation, how much is left for other things
$920 is left
$1,000/.08=$80
$1,000-$80=$920
A jar contains 100 marbles. There are 10 blue marbles, 79 green marbles, 6 red marbles, and 5 yellow marbles. What is the probability of randomly selecting a blue marble?
Final answer:
The probability of selecting a blue marble from a jar with 10 blue marbles among a total of 100 marbles is 0.10 or 10%.
Explanation:
The probability of randomly selecting a blue marble from a jar containing 100 marbles with 10 blue marbles, 79 green marbles, 6 red marbles, and 5 yellow marbles is calculated using the formula:
Probability (P) = Number of favorable outcomes / Total number of outcomes
Here, the favorable outcomes are the blue marbles, and the total number of outcomes is the total number of marbles in the jar.
P(blue marble) = 10 blue marbles / 100 total marbles = 0.10 or 10%
This means there is a 10% chance of selecting a blue marble. This probability calculation assumes each marble has an equal chance of being selected.
is anyone good with algebra I?
Yes. I take algebra 1 honors
An article fills 5/8 of a magizine page. A related photo takes up 1/4 of the article. how much of the page is taken up by the photo?
the photo takes up 2/8 of the page
a rectangular whiteboard in the ckassroom is twice as long as it is high. its perimeter is 24 ft. what are the dimensions of the whiteboard
Answer: The height of the whiteboard is 4 feet and the length of the white board is 8 feet long
Step-by-step explanation:
The height of the whiteboard is 4 feet and since the length on the white board is double the height it would be 8 feet long.
4+4=8
8+8=16
16+8=24
The dimensions of the whiteboard are 4 ft by 8 ft.
Explanation:To solve this problem, we can use algebra. Let's assume that the height of the whiteboard is x. Since the length is twice the height, the length is 2x. The perimeter of a rectangle is given by the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.
In this case, we are given that the perimeter is 24 ft, so we can write the equation as 24 = 2(2x) + 2x. Solving this equation, we get 24 = 6x. Dividing both sides by 6, we find that x = 4.
Therefore, the height of the whiteboard is 4 ft and the length is 2 * 4 = 8 ft.
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Solve for n: 21k − 3n + 9p > 3p + 12. (2 points) n > −4p − 7k + 4
n > 2p + 7k − 4 n < −4p − 7k + 4 n < 2p + 7k − 4
Answer: The correct option is
(D) [tex]n<2p+7k-4.[/tex]
Step-by-step explanation: We are given to solve the following inequality for the unknown variable n :
[tex]21k-3n+9p>3p+12~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To solve the given inequality for n, we must take terms involving n on the left side and other terms on the right side of the inequality.
From inequality (i), we have
[tex]21k-3n+9p>3p+12\\\\\Rightarrow -3n>3p+12-21k-9p\\\\\Rightarrow -3n>-6p-21k+12\\\\\Rightarrow 3n<6p+21k-12~~~~~~~~~~~~~~~~~[\textup{since }a>b~~\Rightarrow -a<-b]\\\\\Rightarrow n<\dfrac{6p+21k-12}{3}\\\\\Rightarrow n<2p+7k-4.[/tex]
Thus, the required solution for n is [tex]n<2p+7k-4.[/tex]
Option (D) is CORRECT.
How many times does 9 go into 260
9 goes into 260, 28.8 repeating times. hope this helps!
28.8 is your answer.
please help me i need to do this fast
Pretty sure it's c because when you want to stretch something, you multiply and divide if compressing
I need help!!!
Select the correct answer.
Sean has a rectangular painting with an area of 80 square inches. He wants to enlarge the painting to 320 square inches.
If the length and width of the original painting are 10 inches and 8 inches, what will the dimensions of the enlarged painting be?
A.
12 inches and 10 inches
B.
14 inches and 12 inches
C.
20 inches and 16 inches
D.
40 inches and 32 inches
Answer: OPTION C.
Step-by-step explanation:
1. By defintion the scale factor of the area is [tex]k^{2}[/tex] and this is:
[tex]k^{2}=\frac{A_1}{A_2}=\frac{320}{80}=4[/tex]
2. Then, the scale factor for the sides is:
[tex]k=\sqrt{4}=2[/tex]
3. Now, you must multiply the length and the width of the original rectangle by 2 to obtain the new dimensions. Thefore, you obtain:
[tex]l=10in*2=20in\\w=8in*2=16in[/tex]
Therefore, the answer is the option C.
Answer:
THE ANSWER ISSS OPTION C
Step-by-step explanation:
I GOT IT RIGHT ON EDMENTUM HOPE THIS HELPS YOU OUT ALOT ;0
SOMEONE HELPETH ME PLEASE
Bob Bluster, the KNEWS meteorologist, determined that the mathematical odds of no rain tomorrow are 11:9. What would a mathematics student determine as the percent chance there will be rain tomorrow?
(If the odds of an event happening are a:b, then the probability that it occurs is a/a + b.)
what is the answer
[tex] {5}^{ - 7} \times {5}^{12} \times {5}^{ - 2} [/tex]
Hey there!!
Simple equation :
mᵃ × mᵇ = m ᵃ⁺ᵇ
We have :
5⁻⁷ * 5¹² * 5⁻²
... 5⁻⁷⁺¹²⁻²
... 5¹²⁻⁹
... 5³
... 125
Hope my answer helps!!
The Fall Festival charges $0.75 per ticket for the rides. Kendall bought 18 tickets for rides and spent a total of $33.50 at the festival. She only spent her money on ride tickets and admission into the festival. The price of admission is the same for everyone. Use y to represent the total cost and x to represent the number of ride tickets.
(a) Define your variables.
(b) Write a linear equation to calculate the cost for anyone who only pays for festival admission and rides
(c) Explain your answer to Part B.
Answer:
a) Here x represent number of ride tickets
z represent admission fees. = $20
y represent total cost.
Step-by-step explanation:
a) Here x represent number of ride tickets
z represent admission fees.
y represent total cost.
b) Given that,
$0.75 per ticket for the rides.
Number of tickets (x) = 18
Total spent (y) = $33.50
Total cost = (number of tickets)*(price per ticket) + admission fees
y =0.75x + a
We can calculate the cost for anyone who only pays for festival admission and rides.
c)
Put y = 33.50
x = 18
33.50 = 0.75*18 + a
33.50 = 13.5 + a
Solve for a,
Subtract 13.50 both the side
33.50 - 13.50 = 13.50-13.50 + a
20 = a
So, admission cost (a) = $20
How could you how many blocks there where in 20 stories
take the number of blocks and multiply it by the stories
hope this helps :)
Solve for x. −2(x+14)+1=5 Enter your answer in the box.
-2(x+14)+1=15
distribute
-2x - 14 + 1 = 15
add 14 to each side
-2x + 1 = 29
subtract one from each side
-2x = 28
divided by -2
x = -14
-2(x+14)+1=5
First, distribute -2 into x and 14.
-2x-28+1=5
Combine like terms.
-2x-27=5
Add 27 to both sides.
-2x=32
Divide both sides by -2.
x=-16
Your answer is -16.
I hope this helps :)
Solve the following addition problems. Remember to carry as necessary. a. 995 lb. 6 oz. + 1,004 lb. 11 oz. b. 24 T. 1,507 lb. 12 oz. + 7 T. 938 lb. 6 oz. c. 6 T. 14 oz. + 11 T. 1,949 lb. + 8 oz. + 5 T. 49 lb. 15 oz.
a. 995 lb. 6 oz.
+ 1,004 lb. 11 oz.
______________
1999 lb 17 oz = 2000 lb 1 oz.
16 oz = 1 lb
Therefore,
1999 lb 17 oz = 1999 lb + 16 oz + 1 oz = 1999 lb + 1 lb + 1 oz
= 2000 lb. 1 oz._______________________________________________b. 24 T 1,507 lb 12 oz.
+ 7 T 938 lb 6 oz.
______________
31 T 2445 lb 18 oz
2000 lb = 1 T.
16 oz = 1 lb
Therefore,
31 T 2445 lb 18 oz = 31 T + 2000 lb + 445 lb + 16 oz + 2 oz
= 31 T + 1 T + 445 lb + 1 lb + 2 oz
= 32 T. 446 lb. 2 oz._______________________________________________c. 6 T. 14 oz.
+ 11 T. 1,949 lb.
+ 8 oz.
+ 5 T. 49 lb. 15 oz.
______________________
22T. 1998 lb. 37 oz.
22T. 1998 lb. 37 oz. = 22 T + 1998 lb + 16oz + 16 oz + 5 oz.
= 22 T + 1998 lb + 1 lb + 1 lb + 5 oz.
= 22 T + 2000 lb + 5oz
= 22 T + 1 T + 5 oz.
= 23T. 5oz.Answer:
A. 2000 pounds 1 ounce
B. 32T 446 pounds 2 ounces
C. 23T 5 ounces
Step-by-step explanation:
What is the factored form of the polynomial?
x2 − 12x + 27?
Answer:
(x-9)(x-3) which is the same as (x-3)(x-9)
Step-by-step explanation:
Think of ways to factor the last number 27. One way is 1*27 = 27. Another way is 3*9 = 27 and so on. Now think to yourself "which factor of 27 add to -12?". You'll need to consider negative factors. It turns out that
-3 plus -9 = -12
-3 times -9 = 27
Therefore the two values we care about are -9 and -3. So x^2-12+27 factors to (x-3)(x-9). The order of the factors does not matter. So we can write the answer as (x-9)(x-3) just fine.
An image of a book shown on a website is 1.5 inches wide and 3 inches tall on a computer monitor. The actual book is 9 inches wide.
Answer:
18 inches tall.
Step-by-step explanation:
The width of an image of a book shown on a website = 1.5 inches
and length of the book shown on the website = 3 inches
The actual width of the book = 9 inches
Scale of the book image = [tex]\frac{9}{1.5}[/tex]
1 inches = 6 inches
The actual length of the book = 3 × 6
= 18 inches.
The actual book is 9 inches wide and 18 inches tall.
The actual height of the book, given the image size can be found to be 18 inches.
How to find the actual height ?The image of the book is shown on the computer monitor at 1.5 inches wide, while the actual book is 9 inches wide.
To find the scale of the image on the computer monitor, divide the width of the image on the monitor by the actual width of the book:
= 1.5 inches / 9 inches
= 1/6
So, the scale of the image on the computer monitor is 1/6.
This means that every inch on the monitor represents 6 inches of the actual book.
Now, to find the actual height of the book, you can use the scale and the height of the image on the monitor:
= 3 inches * 6
= 18 inches
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solve the simultaneous equations
3x + 4y = 5
2x - 3y = 9
We label each equation
3x + 4y = 5 (1)
2x – 3y = 9 (2)
We now want to get rid of one of the variables (x or y). Lets get rid of x:
We need (1) and (2) to have the same number of x's so we multiple (1) by 2 and (2) by 3 so they both have 6 x's
6x + 8y = 10 (1)*2
6x - 9y = 27 (2)*3
Now to get rid of the x's we take one of the equations from the other. It is easier to do (2)*3 -(1)*2
6x - 9y = 27 (2)*3
6x + 8y = 10 (1)*2
-17y = 17
If we devide this equation by -17 we get
y = -1
We can plug this value of y into (1) to get
3x -4 = 5
add 4 to both sides of the equation
3x = 9
Divide by 3
x = 3
Now to check put x and y into (2)
6 - (-3) = 9
As this is true, we have the solution
x = 3, y = -1
A construction crew has just finished building a road. The road is 8 2/5 kilometers long. If the crew worked for 6 days, how many kilometers of road did they build each day?
HELP ME PLEASE HAVING TROUBLE!
Answer,
The top right one.
Explanation,
7 to the 2nd power = 49
The model is showing 49 cubes
In conclusion, that's how I got the answer.
Hope this helps :-)
what property does this demonstrate -1/4 = -0.25 then -0.25 = -1/4
A: Reflexive property
B: symmetric property
C: associative property
D: transitive property
Answer: B: symmetric property
Reflexive property states that for every real number x, x = x.
symmetric property states that for all real numbers x and y, if x = y then y = x.
associative property states that you can add or multiply regardless of how the numbers are grouped. =(like adding/multiplying like terms.
Transitive property states that for all real numbers x,y, and z, if x = y and y = z then x = z.
The equation -1/4 = -0.25 then -0.25 = -1/4 demonstrates the Symmetric Property of equality, which means order does not matter in an equation for it to be true.
Explanation:The equation you provided, -1/4 = -0.25 then -0.25 = -1/4, demonstrates the Symmetric Property of equality.
This property essentially says if a = b, then b = a. It shows that order does not matter in an equation; the elements can be flip-flopped, and the equality will still hold true. In your case, -1/4 = -0.25, and if you switch the order, -0.25 = -1/4, the equation still stays true. That's why we say it shows the symmetric property.
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a pair of socks is purchased at wholesale for $2.00.it is then sold for $4.00 to the customer.what is the percent increase?
200 percent i am pretty sure
Tom is making a punch that contains 80% cranberry juice and the rest ginger ale. The punch has 2 liters of ginger ale. Part A: Write an equation using one variable that can be used to find the total number of liters of cranberry juice and ginger ale in the punch. Define the variable used in the equation. Hint: 0.8x represents the number of liters of cranberry juice in the punch. (5 points) Part B: How many liters of cranberry juice are present in the punch? Show your work. (5 points)
Given that Tom is making a punch that contains 80% cranberry juice and the rest ginger ale. The punch has 2 liters of ginger ale.
Part A:
Let the number of litres of cranberry juice be x, then the total number of liters of the punch is given by x/0.8
Thus, x + 2 = x/0.8
0.8x + 1.6 = x
0.2x = 1.6
Therefore, the equation with one variable that can be used to find the total number of liters of canbelly juice and ginger ale in the punch is: 0.2x = 1.6, where x is the number of liters of canberry juice in the punch.
Part B.
Given from part A that the number of liters of canberry juice in the punch is given by 0.2x = 1.6, where x is the number of liters of canberry juice in the punch.
Therefore, the number of liters of canberry juice in the punch is x = 1.6 / 0.2 = 8 liters of canberry juice.
Answer:
Given that Tom is making a punch that contains 80% cranberry juice and the rest ginger ale. The punch has 2 liters of ginger ale.
Part A:
Let the number of liters of cranberry juice be represented by = x
Then the total number of liters of the punch is given by [tex]\frac{x}{0.8}[/tex]
Now we have [tex]x+2= \frac{x}{0.8}[/tex] (ginger ale is also added)
Solving this, we get
[tex]0.8x+1.6= x[/tex]
[tex]0.2x= 1.6[/tex]
Further solving we get x = 2
So, the required equation with one variable is : [tex]0.2x=1.6[/tex]
Part B.
From part A we have-
[tex]0.2x=1.6[/tex]
We will find x now, that is liters of cranberry added.
We have x = [tex]\frac{1.6}{0.2}[/tex] = 8
Hence, there is 8 liters of cranberry juice in the punch.
a softball team bought a box of sweatshirts for $240. E.ach sweatshirt cost $12 to print and will sell for $18. Graph a system of equations to find the number of sweatshirts the softball team needs to sell in order to break even
Answer:The number of sweatshirts to sell in order to break even is 40
Step-by-step explanation:
Let x be the number of sweatshirts. We are looking for break even, which means profit is 0 here.
And softball team purchased a box for 240$ and for printing it costs 12$ per shirt.
So total cost of sweatshirts = 240+12x
And selling price is 18$ per shirt.
Hence selling price for x shirts = 18x.
Now we need to graph y=18x and y=240+12x first and then look for intersection to find the break even.
From the graph attached, we can see that both lines are intersecting at x=40.
Hence number of sweatshirts to sell in order to break even is 40.
17 nickels to 49 dimes
factor each expression 4x +12
Hii!
__________________________________________________________
Answer:
4(x+3)
Step-by-step explanation:
In this example, both terms, 4x and 12, have something in common. In math, this is known as the greatest common factor (g.c.f.)
The g.c.f. of 4 and 12 is 4, so that's what I'm going to divide both 4x and 12 by.
Upon doing so, we obtain
x+3
Put parentheses around x+3. You'll see why soon.
(x+3)
Now we put 4 outside the parentheses.
4(x+3)
See, the parentheses indicate that we multiply 4 times both x and 3.
--
Hope that this helped! Best wishes
--
The factored expression of 4x + 12 is 4(x + 3), applying the highest common factor (HCF) method.
Explanation:To solve the expression 4x +12, we want to factor it, which means we need to find the highest common factor (HCF) of the terms 4x and 12. In this case, the HCF is 4. Once we identify the HCF, we divide each term of the expression by the HCF, which reduces the expression to simpler terms. For our expression:
4x + 12 = 4(x + 3)
This means the factored form of the expression 4x +12 is 4(x + 3).
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Adam has been asked to post a parcel for a family member. He has been told that the parcel weighs 12 lbs 8 oz. 1lb = 16 oz 1lb = 454 g How much does the parcel weigh to the nearest whole kilogram?
Answer:
The weight of the parcel is approximately 6 kilograms.
Step-by-step explanation:
The weight of the parcel is 12 lbs and 8 oz.
1 lb = 16 oz
So, 8 oz = [tex]\frac{1}{2}lb = 0.5[/tex] lb.
That means, 12 lbs and 8 oz = (12 + 0.5) lbs = 12.5 lbs
Now, 1 lb = 454 g
So, 12.5 lbs = (12.5 × 454) g = 5675 g
As, 1 kilogram = 1000 g
That means, 1 g = 0.001 kilogram
So, 5675 g [tex]= (5675 \times0.001) kilograms= 5.675 \approx 6[/tex] kilograms. (Rounded to the nearest whole kilogram)
Thus, the weight of the parcel is approximately 6 kilograms.