Answer:
width = 4.16 meter
length = 6.49 meter
Step-by-step explanation:
Area of the rectangle =27 m²
Let the width of the rectangle be x meter
So, Length = 3 * width - 6
= 3*x - 6
= 3x-6 meter
Area of the rectangle = length * width
27 = (3x-6)*x
Flipping the sides of the equation, we have
(3x-6)*x =27
Distributing the left side, we get
(3x)*(x) - (6)*(x) = 27
=> 3x² - 6x = 27
Subtract 27 from both sides,
3x² - 6x -27 = 27 - 27
=> 3x² - 6x -27 = 0
Factoring out 3 from all the terms on the left side, we have
3(x² - 2x -9) = 0
Dividing both sides by 3, we have
[tex]\frac{3(x^{2}-2x-9) }{3}[/tex] = [tex]\frac{0}{3}[/tex]
Cancelling out the 3's on the left, we get
x² - 2x -9 = 0
We'll use the quadratic formula to solve for the x,
x = [tex]\frac{-b\pm\sqrt{b^{2}-4ac } }{2a}[/tex]
Comparing the quadratic equation x² - 2x -9 = 0 with ax² + bx + c = 0, we get
a = 1 (as x² has no coefficient)
b = -2
c = -9
Plugging in the values of a, b, and c into the quadratic formula, we get
x = [tex]\frac{-(-2)\pm\sqrt{(-2)^{2}-4(1)(-9) } }{2(1)}[/tex]
=> x = [tex]\frac{2\pm\sqrt{4+36 } }{2}[/tex]
=> x = [tex]\frac{2\pm\sqrt{40}}{2}[/tex]
=> x = [tex]\frac{2\pm2\sqrt{10}}{2}[/tex]
Factoring out 2 from the top, we get
x = [tex]\frac{2(1\pm\sqrt{10})}{2}[/tex]
Canceling out the 2's from the top and bottom, we have
x = [tex]1\pm\sqrt{10}[/tex]
Either x = [tex]1+\sqrt10[/tex] or x= [tex]1-\sqrt10[/tex]
=> x = 1 + 3.162 or x = 1 - 3.162
=> x = 4.162 (possible) or x = -2.162 (not possible as width can't be negative)
So, width = 4.16 meter (rounded off to the nearest hundredth)
Now,
Area of the rectangle = length * width
27 = length * 4.16
Flipping the sides of the equation,
length * 4.16 = 27
Dividing both sides by 4.16, we get
[tex]\frac{length * 4.16}{4.16} = \frac{27}{4.16}[/tex]
Cancelling out 4.16 from the top and bottom of the left side, we get
length = 6.490
=> length = 6.49 meter (rounded off to the nearest hundredth)
You are in charge of decorating your gym for a home coming dance. You bought 6 bags of balloons and 5 bags of sparkling balloons for 19.20$. But you realize this is not enough. Than you buy 8 bags of balloons and 2 bags of sparkling stars for 15.80$. What was the price for each item
.
Answer:
I believe your answer would be 8 dollars and 75 cents. I don't know for sure.
Step-by-step explanation:
Using the provided systems of linear equations method, one bag of regular balloons costs $1.45, and one bag of sparkling balloons costs $2.10.
Explanation:The subject of this question is a typical example of a system of linear equations. Here, we are given two different purchases which give us two equations. We have:
1) 6B + 5S = 19.20 ---> Eq (1) (where B stands for one bag of balloons and S stands for one bag of sparkling balloons)
2) 8B + 2S = 15.80 ---> Eq (2)
Now, to find the prices of B and S (the number of bags of balloons and bags of sparkling balloons, respectively), we can solve this system of equations in two steps: multiplying Eq (2) by 2.5 and then subtracting Eq (1) from the result. This gives:
20B + 5S = 39.5
Then subtract Eq (1) from this new equation, which yields 14B = 20.3. So, one bag of balloons (B) costs $1.45. Substituting B = 1.45 into Eq (1), we get 6(1.45) + 5S = 19.2, which simplifies to 5S = 10.5. Thus, one bag of sparkling balloons (S) costs $2.10. So, the cost per bag of regular balloons is $1.45, and the cost per bag of sparkling balloons is $2.10, and this is how you go about decorating your gym on a budget.
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solve for c if the product of c and 7 is less than 49
Answer:
c< 7
Step-by-step explanation:
the product of c and 7 is less than 49
Product means multiply
7c< 49
Divide each side by 7
7c/7 < 49/7
c< 7
Answer:
C = 7
Step-by-step explanation:
Equation:
C * 7 = 49
The opposite of multiplication is division, so we can find the solution through division:
49 / 7
= 7
C equals 7
We can check our work through multiplication:
7 * 7 = 49
Good Luck,
- I.A. -
shade the model to show 0.5*0.3
As, we have to find
0.5 * 0.3
→ 0.5 is equivalent to [tex]\frac{5}{10}[/tex]
→ 0.3 is equivalent to [tex]\frac{3}{10}[/tex]
To, show by modelling the value of , 0.5 *0.3 , just draw 100 rectangles or 100 squares and color 15 of them.
Because , [tex]0.5\times0.3=\frac{5\times3}{10\times10}=\frac{15}{100}[/tex]
Given the equations f(x)= 4x+3 and g(x)=2x-1 find f-g
Answer: 2x+4
Subtract the equations like so
f - g = (4x+3) - (2x-1)
f - g = 4x+3 - 2x + 1 ... distribute the negative to all terms inside parenthesis
f - g = (4x-2x) + (3+1)
f - g= 2x + 4
Which graphs show continuous data?
Select each correct answer.
50 points
Answer:
Option 1 and 3 are continuous graph.
Step-by-step explanation:
We have been given the four graphs we need to tell which one among these given graphs is continuous
Option 1 is continuous since, there is no break in the graph and points are joint that is a straight line.
Option 2 is discrete graph it is not continuous because these are points which are not joint.
Option 3 is continuous since, there is no break in the graph and points are joint that is a straight line.
Option 4 Option 2 is discrete graph it is not continuous because these are points which are not joint.
Answer:
The answer is B and C
Step-by-step explanation:
I KNOW
what is the distance between the points -3, 5 and -3,-9?
Answer:
the distance is 14
Step-by-step explanation:
To find the distance between 2 points, we can use the distance formula
d = sqrt( (x2-x1)^2 + (y2-y1) ^2 )
d = sqrt( (-3--3)^2 +(-9-5) ^2 )
= sqrt( (-3+3)^2 + (-14)^ 2)
= sqrt(0^2 +14^2)
= sqrt( 14^2)
= 14
Hi there! :)
Answer:
14
*The answer must have a positive sign.*
Step-by-step explanation:
[tex]x=\sqrt{(X_2-X_1)^2+(Y_2-Y_1)^2}[/tex]
[tex]x=\sqrt{(-3--3)^2+(-9-5)^2}[/tex]
[tex]x=\sqrt{(-3+3)^2+(-14)^2}[/tex]
[tex]x=\sqrt{(0^2+14^2)}[/tex]
[tex]x=\sqrt{14^2=14}[/tex]
Final answer is 14.
Hope this helps!
Thanks!
-Charlie
Have a nice day! :)
:D
what is the equation in plot slope form of the line that passes through the point (-1, -3) and has a slope of 4
Answer:
y+3 = 4(x+1)
Step-by-step explanation:
Point slope form of a line is
y-y1 = m(x-x1) where m is the slope and (x1,y1) is the point
y--3 = 4 (x--1)
y+3 = 4(x+1)
Answer: plot slope form is y+3= 4(x+1)
or
y = 4x+1
Step-by-step explanation:
Slope point form of equation is given by
y-y1 = m (x-x1)
where m is slope and (x1,y1) is the point
here (point) is (-1,-3) and slope = 4
so equation is
(y - (-3) )= 4 ( x -(-1))
y+3 = 4(x+1)
y+3 = 4x+4
y = 4x +1
What is the value of the expression? 3(68−12)+0.25 Enter your answer, in simplest form, in the box
Answer:168.25
Step-by-step explanation:
3(68−12)+0.25
=(3)(56)+0.25
=168+0.25
=168.25
Answer: 168.25 is the correct answer! :)
Step-by-step explanation: I took the test because of the first person!
Hope it helps for you too! Good luck
GEOMETRY
which statements are true based on the diagram? check all that apply.
All of the five statements are true expect for the second one (Points P and M are on plane B and plane S) and the fifth one (line d intersects plane A at point N).
The second statement is false point M does not lie on plane s, making the statement false. Also, line d intersects plane A at L, not n.
Answer:
Step-by-step explanation:
its a,b,d,e
Consider circle Y with radius 3m and central angle XYZ measuring 70degrees. What is the approximate length of minor arc XZ?
Answer:
XZ ≈ 3.7 cm (to 1 dec. place )
Step-by-step explanation:
arc length = circumference × fraction of circle
= 2πr × [tex]\frac{70}{360}[/tex]
= 2π × 3 × [tex]\frac{70}{360}[/tex] ≈ 3.7 cm
Brad make 3 cups of pancake batter. If he needs 3/4 cup of batter to make 4 pancakes, how many pancakes can Brad make
Answer:
(3/4) cup/4 pancakes = 3 cups/x pancakes
(3/4)x = 12
x = 16
Brad can make 16 pancakes.
Brad can make 16 pancakes with 3 cups of batter, based on the ratio of 3/4 cup batter for every 4 pancakes.
To determine how many pancakes Brad can make with 3 cups of batter, when 4 pancakes require 3/4 cup of batter, we can set up a straightforward ratio and proportion calculation.
First, we divide the total batter amount by the batter requirement for a single group of pancakes: 3 cups / (3/4 cups) = 3 / 0.75 = 4 groups of pancakes.Because each group consists of 4 pancakes, we then multiply the number of groups by the number of pancakes in each group: 4 groups \\times 4 pancakes/group = 16 pancakes.Therefore, Brad can make 16 pancakes with 3 cups of batter.
Question: Find the ratio of the width to the length of the rectangular swimming pool sketched below. Width=5.5 yards | Length=7.5 yards | Answers are: A) 11/24 yards B) 2.75/15 yards C) 15/11 yards D) 11/15 yards. Which one is it?
Answer:
D) 11/15
Step-by-step explanation:
11/15 is the doble amount of 5.5/7.5, but is the same number if you divide it.
The ratio of the width to the length of the swimming pool with a width of 5.5 yards and a length of 7.5 yards is 11/15 yards, which corresponds to answer D) 11/15 yards.
The student has asked to find the ratio of the width to the length of a rectangular swimming pool where the width is 5.5 yards and the length is 7.5 yards. To find this ratio, we divide the width by the length:
Ratio = Width / Length = 5.5 yards / 7.5 yards. Simplifying this we get:
Ratio = 11/15 yards.
Therefore, the correct answer is D) 11/15 yards.
how do you evaluate the function f(x)=x+6 when x = -2,0 & 5? (step by step please!)
Answer:
f(-2) = 4
f(0) = 6
f(5) = 11
Step-by-step explanation:
f(x)=x+6 when x = -2
Substitute x=-2
f(-2) = -2+6
f(-2) = 4
f(x)=x+6 when x = 0
Substitute x=0
f(0) = 0+6
f(0) = 6
f(x)=x+6 when x = 5
Substitute x=5
f(5) = 5+6
f(5) = 11
What is the sale of the original price?
The percent of discount is 25 percent.
The sale price is 40 dollars.
Please help I’ll give Brainliest!!
Answer:
50 dollars
Step-by-step explanation:
40*25%=10
40+10= 50 dollars
Add it to find the original sales price which would end up being 50 dollars! Hope this helps, have a good day. c;
HELP PLEASE find the rate of change
Answer:
Rise over run
Step-by-step explanation:
so I believe the answer is 6
Three hens can lay 3 eggs in 3 days.
How many hens would lay 3 eggs in 9 days?
What is (3x^4+2x^2-6) subtracted from (4x^4+2x^2-6)
Answer:
The answer is -x^4, Good Luck!
Step-by-step explanation:
(3x^4+2x^2-6) - (4x^4+2x^2-6) = -x^4
To subtract (3x^4+2x^2-6) from (4x^4+2x^2-6), subtract the corresponding terms and keep the same variable raised to the same power. For example, subtracting 3x^4 from 4x^4 gives us x^4. Therefore, the result is x^4.
Explanation:To subtract (3x^4+2x^2-6) from (4x^4+2x^2-6), we need to subtract the corresponding terms. So, subtract the coefficients of like terms. For the terms with variable x raised to a power, subtract the coefficients and keep the same variable raised to the same power. For the constant term, subtract the constants.
For example, subtracting 3x^4 from 4x^4 gives us (4x^4 - 3x^4) = x^4. Subtracting 2x^2 from 2x^2 gives us (2x^2 - 2x^2) = 0. Subtracting 6 from 6 gives us (6 - 6) = 0.
Therefore, the subtraction of (3x^4+2x^2-6) from (4x^4+2x^2-6) results in x^4 + 0 + 0 or simply x^4.
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Donata bought 4 lemons and 4 plums at the local supermarket for a total of $ 21.60. Dan bought 11 lemons and 6 plums at the same store for a total of $40.90 how much does one lemon cost. .... helppppp. How Much does 1 plum cost?
Answer:
Each lemon costs $1.70. Each plum costs $3.70.
Step-by-step explanation:
You have two unknowns and two statements about costs. First, define a variable for each unknown. Then, translate the statements about the costs into two equations. Then, solve the system of equations.
Let L = price of 1 lemon
Let P = price of 1 plum
Donata:
4 lemons and 4 plums for $21.60
4L + 4P = 21.6 Equation 1
Dan:
11 lemons and 6 plums for $40.90
11L + 6P = 40.9 Equation 2
Here is the system of equations.
4L + 4P = 21.6 Equation 1
11L + 6P = 40.9 Equation 2
Divide both sides of Eq. 1 by 4.
L + P = 5.4
Multiply both sides by -6.
-6L - 6P = -32.4
Add the equation above to the Eq. 2.
5L = 8.5
L = 8.5/5
L = 1.7 <------- price of a lemon
L + P = 5.4
1.7 + P = 5.4
P = 3.7 <------ price of a plum
Each lemon costs $1.70. Each plum costs $3.70.
A rescue helicopter is used to help victims who fell in a ditch. The helicopter begins at sea level, which is an elevation of 0 feet. It then travels down for 100 seconds at a speed of 10.5 feet per second. It then travels directly up for 150 seconds at a speed of 5.2 feet per second. After this 250 second period, how much time, in seconds, will it take for the rescue helicopter to travel back to sea level at the helicopter's maximum speed of 15.8 feet per second?
Answer:
The helicopter still needs to fly up sec 17.0886 at maximum speed.
Step-by-step explanation:
If f(x) = 4x2 – 6 and g(x) = x2 – 4x – 8, find (f – g)(x).
Answer: Use the given functions to set up and simplify (f - g)(x). You should get 3x^2 +4x+2
What is the length of RQ?
Answer:
D
Step-by-step explanation:
RQ = YZ
8 = 8
I hope I helped you.
Answer:
RQ is mm long
Step-by-step explanation:
21 is a factor of 79275. Which of the following will also be a factor of 79275
a. 7 b. 10 c. 13 d. 42
Show working. One line reasoning
Answer:a. 7 is also the factor.
Step-by-step explanation: 21 is factor of 79275, so check the factors of 21 from options.
7 is factor of 21 so 7 is also factor of 79275.
21 is a factor of 79275 then 7 is also a factor of number 79275
What is Number system?A number system is defined as a system of writing to express numbers.
To determine if a number is a factor of 79275, we need to check if it divides evenly into 79275 without leaving a remainder.
Since 21 is a factor of 79275
we can write 79275 as 21 multiplied by some other number
79275 = 21 × (some number).
If a number is a factor of both 21 and (some number), it will also be a factor of their product, which is 79275.
The only number that is a factor of 21 is 7.
Therefore, 21 is a factor of 79275 then 7 is also a factor 79275
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What percent is equivalent to 840 ? 8% 20% 25% 40%
Answer:
8/10 are none of these. 8/10 is 80% unless your talking how much percent more to get to 10/10
The correct answer is option (b).20% is equivalent to the fraction [tex]$\frac{8}{40}$[/tex]
To find the percent equivalent to the fraction [tex]$\frac{8}{40}$[/tex], we first simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4 in this case.
[tex]$$\frac{8}{40} = \frac{8 \div 4}{40 \div 4} = \frac{2}{10}$$[/tex]
Now, we convert the simplified fraction to a percentage by multiplying it by 100.
[tex]$$\frac{2}{10} \times 100 = 20\%$$[/tex]
Therefore, 20% is equivalent to the fraction [tex]$\frac{8}{40}$[/tex].
The complete question is:
What percent is equivalent to [tex]$\frac{8}{40}$[/tex]. ?
(a)8%
(b)20%
(c)25%
(d)40%
A store is having a sale on liquid soap and sponges. The cost of 6 bottles of soap is $9.12. The cost of 4 sponges is $5.00 what is the total cost of buying 2 bottles of liquid soap and 3 sponges
Answer:
$6.79
Step-by-step explanation:
We need to find the cost of a bottle of soap. We divide the cost by the number of bottles
$9.12/6 = $1.52 per bottle
We also need to find the cost for a sponge
$5.00/4 = $1.25 per sponge
We want to find the total cost of 2 bottles of soap and 3 sponges
cost = 2 * 1.52 + 3 * 1.25
= 3.04 + 3.75
= 6.79
Final answer:
The total cost comes to $6.79.
Explanation:
To calculate the total cost of buying 2 bottles of liquid soap and 3 sponges, we need to first find the cost of a single bottle of soap and a single sponge. We can do this by dividing the total cost of multiple items by the number of items to get the price per item.
The cost of 6 bottles of soap is $9.12. To find the cost of 1 bottle of soap, we divide: $9.12 / 6 = $1.52 per bottle.
The cost of 4 sponges is $5.00. To find the cost of 1 sponge, we divide: $5.00 / 4 = $1.25 per sponge.
Now, we can calculate the cost of 2 bottles of soap: 2 x $1.52 = $3.04.
And the cost of 3 sponges: 3 x $1.25 = $3.75.
Finally, we add the two amounts to find the total cost: $3.04 (soap) + $3.75 (sponges) = $6.79
So, the total cost of buying 2 bottles of soap and 3 sponges is $6.79.
Sarah feeds her fish every 2 days and her snake every 6 days. In 30 days, how many times will Sarah feed her fish and snake on the same day?
Answer:
So if sarah feeds her fish every two days, youd divide each number by 30. So the fish would be fed 15 times and the snake 5 times. Hope you get it correct! Good Luck!
Answer: hello mate!
Sara feeds her fish every 2 days: this means that if we took the 0 in a day that she feed both animals; then the fish gets food on the day 2, on the day 4, on the day 6, etc
And the snake gets food on days 6, 12, 18, etc.
now we want to count the number of days where both animals get food on the same day. Because 6 is a multiple of 2, we can see that every day that the snake is feed, the fish also feed, this is because the minimal common multiple between 2 and 6 is 6.
then we can see that each 6 days Sarah feeds her fish and snake on the same day. Now we need to see the number of times that this event happens in 30 days; we can see this dividing 30 days by 6 days:
30/6 = 5
Then in the span of 30 days, there are 5 times where both animals get food on the same day.
75.9 divided by 22 with remainders
Answer:
3.45
Step-by-step explanation:
When you divide them you will get 3. And reminders are basically decimals. So basically .45 is the reminder
Plzzz give brainlest im almost expert just need one more and plzz thank me
please help solve 6x < 42
6x<42
Divide 6 by both sides
x<7
there are 14 girls trying out for volleyball.each team will have 6 players.how many full teams will be made?how many girls will not make a team?
Answer:12 players.
Step-by-step explanation:
Since, only 6 girls can be on a team you have to find out how many teams can there be in total
14 - 6 = 8
since we can subtract another six
8 - 6 = 2
we know now there are 2 full teams and now
which we have left we also know 2 people can not make the team
I really need help with these two above.
8 more questions!
Please help, thanks
Problem 7 is choice B, which is the entire number line shaded in but the value -4 has a hole at this location to mean "exclude this point from the solution set". So basically x can be any number but -4.
Problem 8 is choice C. You have a closed circle (or filled in hole) at -1.5 on the number line. Then you shade to the left of the closed circle to indicate the set of values that are smaller than this endpoint. So n can be -1.5 or it can be smaller than -1.5 (something like -2 or -3, etc).