Answer:
0.46 m
Step-by-step explanation:
area of desks: 8 m by 12 m = 8 m * 12 m = 96 m^2
20% of this area is 20% * 96 m^2 = 19.2 m^2
The area of the border is 19.2 m^2.
Let the path around the desks have width x.
The area of desks plus path is a rectangle 2x + 8 by 2x + 12.
area of desks plus path = (2x + 8)(2x + 12)
= 4x^2 + 24x + 16x + 96 = 4x^2 + 40x + 96
The area of the border is the area of the rectangle that includes the border minus the rectangle that has just the desks.
area of border = (4x^2 + 40x + 96) - (96) =
= 4x^2 + 40x
Above, we have the area of border = 19.2, so we get this equation:
4x^2 + 40x = 19.2
4x^2 + 40x - 19.2 = 0
x^2 + 10x - 4.8 = 0
We now use the quadratic formula to solve the equation for x.
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex] x = \dfrac{-10 \pm \sqrt{10^2 - 4(1)(-4.8)}{2(1)} [/tex]
[tex] x = \dfrac{-10 \pm \sqrt{100 + 19.2 )}{2} [/tex]
[tex] x = \dfrac{-10 \pm \sqrt{119.2 )}{2} [/tex]
[tex] x = 0.46 [/tex] or [tex] x = -10.46 [/tex]
We discard the negative solution.
Answer: the border is 0.46 m wide.
One ounce of cheddar cheese contains 9 grams of fat. Six of the grams of fat are saturated fats. Find the ratio of saturated fats to total fat in an ounce of cheese.
Group of answer choices
6:9
2:3
3:2
9:6
Answer: 6:9
Just divide saturatedfats/TotalFats=6/9
Step-by-step explanation:
Are the ratios 5:15 and 1:3 equivalent
Answer:
Yes, both are one third of the other number
Step-by-step explanation:
Fractions are determined to be equivalent by multiplying the numerator and denominator of one fraction by the same number.
// have a great day //
A chocolate brownie recipe is as follows 200g chocolate ,4eggs 60g flour, 60g cocoa, 100g butter, 250g sugar trhe recipe make 24 brownies sarah is making 96 brownies for the village faire how much cocoa does she need
Answer:
240g of cocoa
Step-by-step explanation:
96/24 = 4 times as many brownies, 4 times as many ingredients needed. To find the amount of cocoa, multiply the original amount by four to get 60g × 4 = 240g.
Find the sum of (1-1/n) + (1-2/n) + (1 - 3/n)....upto n terms
Answer:
(n - 1)/2
Step-by-step explanation:
F = (1 - 1/n) + (1 - 2/n) + (1 - 3/n) + ...(1 - n/n)
= (1 + 1 ... + 1) - (1/n + 2/n + 3/n + ...n/n)
(there are n terms of 1)
= n - (1 + 2 + 3 + ... + n)/n
= n - [n x (n + 1)/2]/n
= n - [n x (n + 1)]/[2 x n]
= n - (n+1)/2
= (2n - n - 1)/2
= (n - 1)/2
Hope this helps!
Determine the smallest integer that makes -3x + 7 - 5x < 15 true.
State the smallest possible value for x in the solution set below as a number only.
Answer:
-1
Step-by-step explanation:
write it in the following manner:
-3x + 7 - 5x = 15
-8x + 7 = 15
-8x = 8
x = -1
Thus, the number has to be smaller than -1.
The smallest integer that makes the given inequality true is 0.
What is Linear Inequalities?Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.
Given inequality,
-3x + 7 - 5x < 15
We have to find the value of x.
(-3x - 5x) + 7 < 15
-8x < 8
Dividing whole sides by -1, the inequality sign changes.
x > -1
Smallest possible value is 0.
Hence the smallest posible value is 0.
Learn more about Inequalities here :
https://brainly.com/question/26855203
#SPJ2
BRAINLIEST!!!!!!BRAINLIEST!!!! BRAINLIEST!!!!!!BRAINLIEST!!!! BRAINLIEST!!!!!!BRAINLIEST!!!! BRAINLIEST!!!!!!BRAINLIEST!!!!
Answer:
B
Step-by-step explanation:
Descending order means that the exponents are in decreasing order and the polynomial ends with the constants. Therefore the answer is B.
Answer:
B.
Step-by-step explanation:
Arranged from largest to smallest
The product of Chau's height and 5 is 70.
Answer: 14
Step-by-step explanation: chau's height = x
x * 5 =70
5x = 70
x = 70/5
x = 14
A certain virus is dying off at a rate of 18% per hour. Initially there were
40,000 grams of the strain. If this continues at this rate, how much of the
strain would still be alive after 48 hours? (Round your answer to the
nearest whole number.) *
Answer:
3 strain would still alive after 48 hours
Step-by-step explanation:
Initial population of virus = 40000 grams
A certain virus is dying off at a rate of 18% per hour.
We are supposed to find how much of the strain would still be alive after 48 hours
Formula : [tex]N(t)=N_0(1-r)^t[/tex]
[tex]N_0[/tex]=Initial population
N(t)= Population after t hours
r = rate of decrease = 18% = 0.18
t = time = 48 hours
So,the strain would still be alive after 48 hours=[tex]40000(1-0.18)^{48}=2.91 \sim 3[/tex]
Hence 3 strain would still alive after 48 hours
Calculate the surface area and the volume of the cylinder.
Pls!! Show how you got the surface area and volume
Find the volume of the prism
pls!! show how you got the volume
Answer:
Step-by-step explanation:
The way you can solve this is by splitting the cube into two parts.
Split the top cube apart from the bottom cube and then find the volume of each and add them together.
The first cube on top would be 80x90x75= 540000 centimeters
The second cube would be 270x75x80=1620000 centimeters
540000+1620000=2160000 centimeters
Hope this help!
Comment if you would like a visual drawing of the math!!
(Also the answer can be written as 21600 meters)
tom gets a bonus of 30% of £96
sally gets a bonus of £31.40
work out the difference between the bonus that tom gets and the bonus that sally gets
Answer:
The difference between the bonus is £2.6
Step-by-step explanation:
First, you have to calculate the amount that Tom get for his bonus. So you have to multiply 30% to £96 :
[tex] \frac{30}{100} \times 96 = 28.8[/tex]
Next, you have to subtract Tom's amount from Sally's amount because Sally has the higher amount of bonus than Tom :
[tex]31.4 - 28.8 = 2.6[/tex]
Solve the following quadratic equation.
(x - 16)^2 = 256
A. x = -32 and x = 0
B. x = 30 and x = -4
C. x = -30 and x = 4
D. x = 32 and x = 0
The answer is D. x = 32 and x = 0
============================================================
Explanation:
Think of x-16 as y. In other words, let y = x-16
We have (x-16)^2 = 256 become y^2 = 256.
Solve for y to get y = 16 or y = -16. You apply the square root to both sides. Don't forget about the plus/minus. This is because (-16)^2 = (-16)*(-16) = 256. We square the negative as well.
--------
If y = 16, then y = x-16 solves for x to get
y = x-16
16 = x-16
x-16 = 16
x = 16+16
x = 32 is one solution
---------
Plug in y = -16 and isolate x
y = x-16
x-16 = y
x-16 = -16
x = -16+16
x = 0 is the other solution
----------
We can check each answer by plugging them back into the original equation
Let's try x = 0
(x-16)^2 = 256
(0-16)^2 = 256
(-16)^2 = 256
256 = 256 ... works
Now try x = 32
(x-16)^2 = 256
(32-16)^2 = 256
(16)^2 = 256
256 = 256 ... also works; both answers have been confirmed
Simplify (x-5)-(x-1)
Answer:
-4
Step-by-step explanation:
→Distribute the -1 to (x - 1):
(x - 5) - (x - 1)
x - 5 - x + 1
→Add like terms (x and -x, -5 and 1):
-4
Answer:
-4
Step-by-step explanation:
(x-5)-(x-1)
x-5-x+1
x-x-5+1 = -4
Kimmy walks to school each day. She uses a map that is drawn on a standard (x,y) coordinate plane to see how far she walks. On the map, one coordinate unit represents 100 feet. Her house is located at (8, 4) and the school entrance is located at (-4, -2). Each day, she walks directly from her house to the school entrance. To the nearest foot, what is the distance Kimmy walks to school each day?
Answer:
1342 feet
Step-by-step explanation:
Kimmy's house is located at (8, 4)
The school entrance is located at (-4, -2).
To find the distance Kimmy walks to school every day, we use the Distance formula:
[tex]\text{Distance =}\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Where [tex](x_1,y_1)=(8, 4),$ and (x_2,y_2)=(-4, -2).[/tex]
[tex]\text{Distance=}\sqrt{(-4-8)^2+(-2-4)^2}\\=\sqrt{(-12)^2+(-6)^2}\\=\sqrt{144+36}\\=\sqrt{180} \\=13.42$ Units\\Since 1 coordinate unit represents 100 feet.\\\\Distance walked by Kimmy to school every day\\=13.42*100 feet\\=1342 feet (to the nearest foot)[/tex]
9y + 6 + 2(5 + y) = blank y + blank
Answer:
11y+16Solution,
[tex]9y + 6 + 2(5 + y) \\ = 9y + 6 + 10 + 2y \\ combine \: like \: terms \\ = 9y + 2y + 6 + 10 \\ simplify \\ = 11y + 16[/tex]
hope this helps...
Good luck on your assignment..
Answer:
11y+16
Step-by-step explanation:
9y+6+2(5+y)=
9y+6+10+2y=
Combine like terms
11y+6+10=
11y+16
Solve 4x -1 = 3x – 5 pls answer
Answer:
[tex]\fbox{\begin{minipage}{4em}x = -4\end{minipage}}[/tex]
Step-by-step explanation:
Given:
Equation: [tex]4x - 1 = 3x - 5[/tex]
Solve for:
[tex]x[/tex]
Solution:
Step 1: Select relevant approach:
Let's move all the components containing x to the left side and other components to the right side (notice the change of sign of each one from positive to negative and negative to positive), then solve for [tex]x[/tex]
Step 2: Perform the calculation:
[tex]4x - 1 = 3x - 5[/tex]
Moving components:
<=> [tex]4x - 3x = 1 - 5[/tex]
Performing simplification to get [tex]x[/tex]
<=>[tex]x = -4[/tex]
Hope this helps!
:)
At Shimla, temperature was -1℃ on Saturday and rose by 3℃ on Sunday. What was the temperature on Sunday?
PLSS HELP ME FIND THE SURFACE AREA OF THE TRIANGULAR PRISM
THXXSSSS AND HURRY PLS
Answer:
108m^2
Step-by-step explanation:
surface area of any shape: sum of the area of its sides.
area of cross section x 2 = 4 x 3 12 m^2
area of slope: 5m x 8m = 40m^2
area of base: 8 X 3 = 24 m^2
area of back: 8m x 4m = 32m^2
sum = surface area = 108m^2
Please mark brainiest
Given right triangle ABC . To the nearest degree, find the measure of angle B. 20° 43° 47° 70°
Answer:
The answer is "70°"
Step-by-step explanation:
In the given question an attachment file is missing. so, the attachment file and its solution can be defined as follows:
Given:
ABC is the right triangle.
Find B=?
Solution:
[tex]\Rightarrow \sin \theta= \frac{p}{h}\\\\[/tex]
[tex]\Rightarrow \sin B^{\circ}=\frac{AB}{AC}= \frac{4.8}{5.1}\\\\[/tex]
[tex]\Rightarrow \sin B^{\circ}= .941[/tex]
[tex]\Rightarrow B^{\circ}= \sin^{-1} (0.941)\\\\\bold{\sin^{-1} (0.941) = 70.2^{\circ}}\\\\\therefore \ \ \ \ \bold{B^{\circ} = 70^{\circ}}[/tex]
Answer:
70
Step-by-step explanation:
If the 6th terre
an Alis 11 and the first term is 1
find the common difference
Answer:
6th term = 11
1st term = 1
d = 11 - 1/5 = 2
Anna bought a backpack for $36.
She also bought a lunch box for $15.
Which is the total amount of money Anna spent?
Answer:
Anna spent $51 in all.
Step-by-step explanation:
36+15=51
Answer:
$51
Step-by-step explanation:
Anna bought two items: a backpack and a lunch box. If we want to find the total amount of money Anna spent, we have to add the price of the backpack and the price of the lunchbox.
price of backpack+price of lunchbox
The backpack cost $36 and the lunchbox cost $15
$36+$15
Add 36 and 14
$51
Anna spent $51 in total
wegnerkolmp2741o plz help me only wegnerkolmp2741o
Answer:
1. Triangular prism
5 faces6 vertices9 edges2. Trapezoidal prism
6 faces8 vertices12 edges3. Pentagonal prism
7 faces10 vertices15 edges4. Hexagonal prism
8 faces12 vertices18 edgesCam bounces a ball 2.528 feet in front of his feet. The path of the ball from the time it hits the ground until it lands on the floor is represented by
f(x)= -(x-7)^2+20
Assuming that Cam's feet located at the origin, (0,0), what is the maximum height of the ball in (feet)?
Answer:
20 feet
Step-by-step explanation:
Since the term -(x-7)^2 is negative, the largest height that the ball can reach is when this term is 0. 0+20=20, meaning that the highest the ball can go is 20 feet. Hope this helps!
Answer: 20 feet
Step-by-step explanation:
The vertex form of a quadratic equation is: y = a(x - h)² + k
where (h, k) is the vertex
h is the axis of symmetry (time at which maximum height is reached)
k is the maximum height
Given: y = -(x - 7)² + 20
--> h = 7, k = 20
therefore, the maximum height of the ball is 20
Which phrase should be inserted on the line to correctly compare the two fractions? Use the models to help.
Answer:
is greater than
Step-by-step explanation:
The answer is C less than we got it wrong
Step-by-step explanation:
PLEASE HELPP ME FAST!!!!! solve for x. Show your work -1/2x < -12
Answer:
-1/2x<-12
Multiply through by 2
-x < -24
Multiply through by -1
x > 24
Hope this helps.
What is the best approximate of the square root of 50
Answer:7
Step-by-step explanation:
7^2 = 49 (or square root of 49 is 7)
8^2 = 64 (or square root of 64 is 8)
how do I solve: 8 – (m - 3) = 7 – 3m
Answer:
m=-2
Step-by-step explanation:
8-(m-3)=7-3m
8-1(m)-1(-3)=7-3m
8-m+3=7-3m
-m+3m+8+3=7-3m+3m
2m+8+3=7
2m+11=7
2m=-4
m=-2
Hope this helps!
Step-by-step explanation:
So, this is how you do it.
(15 POINTS AND BRAINLIEST)
A health club has a one time membership fee of $99, then charges $15 per month for members.
a) Write an equation in slope-intercept form for the cost y of joining the club
for x months.
b) How much has Muscular Marty paid if he has been a member for one year?
Answer:
a) The line will be y = 15x + 99 because the 99 is a one time purchase.
b) After 1 year, x will be 12 so Muscular Marty will pay 15 * 12 + 99 = $279.
Answer:
a) y = 99 + 15x
b) 279
Step-by-step explanation:
b) 1 yr = 12 months
thus x is 12
y = 99 + 15(12) = 99 + 180 = 279
50 pts help pls...
Combine Felix's and Tyler's data. What is the mean of the combined data? Include your calculations as part of your answer. (Hint: Use a shortcut to find the answer.)
Felix
mean = 9.4
median = 7
Tyler
mean = 54
median = 66
what is factorization of the trinomial below 4x^2-20x+24 a)4x(x-4)(x-6) b)4(x-4 )(x-6) c)4(x-2)(x-3) d)4x(x-2)(x-3)
Answer:
4(x-3)(x-2)
Step-by-step explanation:
4x^2-20x+24
4(x-3)(x-2)
