The amount by which the length and width of a shed can be increased to
more than double the area, depends on the initial dimensions.
The amount that can be added to both the length and the width to increase the floor area by more than double the original area is more than 3 meters.Reasons:
The given parameters of the shed are;
The length of the shed = 12 m
Width of the shed = 5 m
The amount by which the length and the width are increased = The same amount
The new area after the increase in the length and width of the shed = More than double the initial area
Required:
The amount of increase in the length.
Solution:
Let the amount by which the length and width are increased = x
We have;
Initial area of the shed = 12 m × 5 m = 60 m²
The new area = (12 + x) × (5 + x) > 2 × 60
By multiplication, we get;
(12 + x) × (5 + x) = x² + 17·x + 60 > 2 × 60 = 120
x² + 17·x + 60 - 120 > 120 - 120 = 0
x² + 17·x - 60 > 0
By factorization, we get;
(x + 20)·(x - 3) > 0
x > -20, or x > 3
The increase (positive) amount of the solution is x > 3
Therefore, the amount by which both the length and the width can be increased to more than double the area is x > 3 meters
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After the math contest, Basil noticed that there were four extra-large pizzas that were left untouched. In addition, another three slices of pizza were uneaten. If there were a total of 51 slices of pizza left, how many slices does an extra-large pizza have
s = number of slices for a large pizza
so if "s" is the number of slices in 1 large pizza, the total for 1 pizza will just be 1s, for two pizzas will be 2s and so on, so for 4 pizzas the total will just be 4s.
we also know there were an extra 3 slices, and we also know that whatever 4s is plus 3 will give us the total of 51 slices of pizza.
[tex]4s + 3 = 51\implies 4s = 48\implies s = \cfrac{48}{4}\implies \boxed{s = 12}[/tex]
10. If 0 = tan-'1, find angle 0. Angle 0 is an acute angle.
Answer:
45°
Step-by-step explanation:
θ = arctan(1) = 45°
__
Make sure your calculator is in degrees mode.
_____
Additional comment
The tan⁻¹( ) function is the inverse tangent function. It can be read as "arctangent of ..." or "the angle whose tangent is ...". In spreadsheets and some calculators, it comes in two flavors: ATAN(x) and ATAN2(x, y). The latter is useful for finding the angle associated with a vector whose components are known, and that can be in any of the four quadrants.
Calculators will give an angle in degrees or radians according to the mode that is set. Spreadsheets always give the angle in radians. The range of a calculator tan⁻¹( ) or ATAN( ) function is -π/2 to π/2 radians, or -90° to 90°.
Single choice question
The expression 24(1−x) gives the discounted price of a pair of shorts, where x is the percent of the discount written in decimal form.
What does 1−x represent in the expression?
A. Discount price of the shorts.
B. Original price of shorts.
C. Percent of discount.
D. Percent of original price being paid.
Answer:
D
Step-by-step explanation:
Because the discount price is the whole equation 24(1-x),
the original price is 24 technically, and the percent of discount has been given as x...
Write the equation for the axis of symmetry for the
follow absolute value graph:
Answer:
The equation for the axis of symmetry is x=3
Step-by-step explanation:
Because the vertex is (-2,3) then the axis of symmetry must pass that point.
Sabriana hiked along a trail that was 9.66 miles long she hated 4.2 miles every hour how many hours did it take Sabriana to finish hiking the trail
Answer:
3 hours
Step-by-step explanation:
please help me on this, thank you
45 - 4 =41 and x is 20.5 or 20 1/2
Ahmad gives his friend Juana a lottery ticket for her birthday. The ticket cost Ahmad $1, and the back of the
ticket says, "The overall odds of winning a prize with this ticket are 1 : 50, and the expected return for this
ticket is $0.50.6000000
Ahmad says, "lf 1,000 people each bought one of these tickets, they'd have spent $1,000 in total and get back
about $5,000."
Juana says, "The probability that one of these tickets wins a prize is 0.50, on average."
Whose statement is correct based on the expected value?
Choose 1 answer:
Only Ahmad's
Only Juana's
Both statements are correct.
Neither statement is correct.
According to the information provided the statement of both people is incorrect (option D)
Ahmad's statement is false because he claims that in the situation where 1000 people spend $ 1000 on lottery tickets they would get back $ 5000. However, the recovery would be $ 500 This statement can be verified by doing the following operation:
0.50 x 1000 = 500
On the other hand, Juana's statement is false because she says that people who buy a lottery ticket have a probability of winning of 0.50 on average. However, the true probability is 0.02. This statement can be checked by doing the following operation:
1 ÷ 50 = 0.02
According to the above, none of the statements of the characters is true.
Learn more about mathematics in: https://brainly.com/question/19003099
Answer:
Neither statement is correct
Step-by-step explanation:
Got it right on Khan Academy
If 3 basketball game tickets and 4 football game tickets were purchased for $50.25, and if 5 basketball game tickets and 5 football game tickets were purchased for $71.25, what are the costs of basketball game tickets and football game tickets?
Answer:
Basketball: $6.75
Football: $7.50
Step-by-step explanation:
lmk if you want an explanation
The costs of basketball game tickets and football game tickets are $7.5 and $6.75 respectively.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
If 3 basketball game tickets and 4 football game tickets were purchased for $50.25, and if 5 basketball game tickets and 5 football game tickets were purchased for $71.25.
The linear equation can be framed:
3x + 4y = 50.25
5x + 5y = 71.25
Here x is the cost of basketball game tickets and y is the football game ticket.
After solving the above linear equation by substitution method,
5([50.25 - 4y]/3) + 5y = 71.25
y = $6.75
x = $7.5
Thus, the costs of basketball game tickets and football game tickets are $7.5 and $6.75 respectively.
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#SPJ5
What is the measure of angle A in the triangle below? 30° 45° 60° 90°
Use distribution property to this expression
6( 5 —q) what is the answer plzzzzzz helpppppp meeeee
Step-by-step explanation:
All the steps are in the pictures. If you have any questions let me know and I'll explain in simple terms :)
answer this pleaseEeeeeeee
Answer:
no solution ?
Step-by-step explanation:
Answer:
Infinitely many solutions because the system of equations are the exact same.
Help with algebra class please
Answer:
t=6.8
Step-by-step explanation:
t=2.01[squareroot(L)]
L=11.56
t=2.01[squareroot(11.56)]
t=2.01(3.4)
t=6.834
(round to nearest tenth)
t=6.8
Help I will give brainliest
the inequality is 8 (w+18) ≤ 19
Answer: -15.625
Step-by-step explanation:
Let w represent the number:
8 (w + 18) ≤ 19
[tex]\frac{8\left(w+18\right)}{8}\le \frac{19}{8}[/tex]
[tex]w+18\le \frac{19}{8}[/tex]
[tex]w+18-18\le \frac{19}{8}-18[/tex]
[tex]w\le \:-\frac{125}{8}[/tex]
-125/8 or -15.625
Check:
[tex]8\left(-15.625+18\right)\le \:19[/tex]
[tex]8\cdot \:2.375 \leq 19[/tex]
[tex]19 \leq 19[/tex]
Therefore, the number is -15.625
2.3+0.02(x+20)-4.8=-9
Solve for x
Answer:
[tex]x=-345[/tex]
Step-by-step explanation:
[tex]2.3+0.02\left(x+20\right)-4.8=-9[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:}100[/tex]
[tex]2.3\cdot \:100+0.02\left(x+20\right)\cdot \:100-4.8\cdot \:100=-9\cdot \:100[/tex]
[tex]230+2\left(x+20\right)-480=-900[/tex]
[tex]\mathrm{Subtract\:}230-480\mathrm{\:from\:both\:sides}[/tex]
[tex]230+2\left(x+20\right)-480-\left(230-480\right)=-900-\left(230-480\right)[/tex]
[tex]2\left(x+20\right)=-650[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}2[/tex]
[tex]\frac{2\left(x+20\right)}{2}=\frac{-650}{2}[/tex]
[tex]x+20=-325[/tex]
[tex]\mathrm{Subtract\:}20\mathrm{\:from\:both\:sides}[/tex]
[tex]x+20-20=-325-20[/tex]
[tex]\bold{x=-345}[/tex]
can someone please help me solve these 4
Answer:
find the area and then multiply
Step-by-step explanation:
Help help help math math help
Answer:
63°
Step-by-step explanation:
Angle 2 is congruent in angle that has 63°
Refer to the attached pic
Stacy started a banking account with $150 and is spending $7 per day on lunch. This situation models which type of function?
ОООО
linear function
quadratic function
exponential function
None of these choices are correct.
Answer:
Linear
Step-by-step explanation:
She is spending the same amount per day, so it is linear
Question is in image
Which best explains if qudrillateral WXYZ can be a parallelogram?
Answer:
A
Step-by-step explanation:
If the figure is to be a parallelogram, opposite sides must be the same length. This requires ...
15 = x +8 ⇒ x = 7 . . . . long sides equal length
and ...
x +2 = 2x -5 . . . . . short sides equal length
7 = x . . . . . . . . . . add 5-x
The value x=7 will make opposite long sides have lengths 15 mm and opposite short sides have lengths 9 mm.
Figure WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 9 mm.
Put the numbers in order from least to greatest: -2.15,-9/4,2,-2,-15/7
Read the below scenario and then answer the questions that follow. The Ancestry Society of North Carolina is compiling records so they can learn about the history of African Americans in North Carolina from 1820 to 1980. They have complied records of all 15,125 gravestones in cemeteries across all 15 counties. They want to choose a sample of 600 records to check their accuracy by visiting the actual gravestones.
a) Using the hat method explain how they could gather a simple random sample of 600 gravestones to visit.
b) Explain why it would be better to take a sample 40 gravestones from all 15 counties.
c) For what population could they make inference about after gathering and examining the sample?
Using the hat method they can randomly choose the tombstones they are going to visit in each county, the best option is to visit 40 tombstones in each county so that it is the same number of tombstones analyzed in each county. This study will benefit the residents of these counties because the information is specific to them.
When conducting research, it is sometimes necessary to take samples to analyze and study and obtain a result. In the situation presented there are a large number of tombstones to study, however it is difficult for researchers to visit each of the tombstones.
Therefore, the best option is to take a sample, that is, to study a small proportional part of the tombstones to obtain an estimated result of the study. The best way to do this is by taking the same number of samples in each county.
Additionally, the information resulting from this study will directly impact the residents of these counties because they are issues related to their past and their evolution through the years, especially the African American population.
Learn more about research in: https://brainly.com/question/1596108
The movement of the progress bar may be uneven because questions can be worth more or less (ir
Add: (– 15xz + 4xy) + (20xy - 9yz + 16xz)
O 24x2 y2 – 9yz + x² zº
0 16xyz
0 5xy – 5 yz + 16xz
024xy - 9yz + xz
Your Answer Is : - 31xz + 16xy - 9yz
Solve each absolute value equation
1. [n - 3]= 5
Answer:
n=8
n=-2
Step-by-step explanation:
or,n-3=5
or,n=5+3
or,n=8
Now consider,
or,n-3=-5
or,n=3-5
or,n=-2
A cube has a volume of 1000cm^3. Work out the surface area Of the cube.
Answer:
600
Step-by-step explanation:
V = s×s×s = s³
V = 10×10×10 =1,000
Surface area
6a² = 6(10²) =600
Lola is in the process of forecasting the sales growth rate for an early-stage venture specilizing in the production of durable running shoes. Lola predicts a 0.15 probability of an 85% growth in sales, a 0.2 probability of a 20% growth in sales, a 0.45 probability of a 10% growth in sales, nd a 0.20 probability of a 20% decrease in sales. What is the expected sales growth rate of the venture?
Answer:
Step-by-step explanation:
Expected growth = 0.15*85 + 0.20 *20 + 0.45*10+0.20 * -20
= 17.25%.
Erin spent half of her weekly allowance at the movies. To earn more money her parents let her wash the car for
$7. What is her weekly allowance if she ended with $12?
Write an equation to represent this situation
59) Two times a number added to another number is 25. Three times the first number minus the other number is 20.
Find the two numbers.
[tex]\huge \bf༆ Answer ༄[/tex]
Let the first number be x and second one be y !
Here's the Expressions representing the above scenario ~
[tex] \sf2x + y = 25[/tex][tex] \sf3x - y = 20[/tex]If we add these two equations we will get ~
[tex] \sf2x + y + 3x - y = 25 + 20[/tex][tex] \sf5x = 45[/tex][tex] \sf x= 45 \div 5[/tex][tex] \sf x = 9[/tex]Now, plug the value of x in first equation ~
[tex] \sf2x + y = 25[/tex][tex] \sf(2 \times 9) + y = 25[/tex][tex] \sf18 + y = 25[/tex][tex] \sf y = 25 - 18[/tex][tex] \sf y = 7[/tex]Therefore, the first number is x = 9 and the second number is y = 7
NEED HELP PLS
Use point-slope form to write the equation of a line that passes through the point (-14, -17) with slope 1.
Answer:
point-slope form: y-y1=m(x-x1) -> m=slope, (x1, y1) = coordinates of a point
point = (-14,-17) -> x1=-14, y1=-17
slope = 1 -> m=1
y-(-17)=1*(x-(-14)
y+17=1(x+14)
you don't need the *1 but some teachers are picky about that
Answer:
y + 17 = 1 ⋅ ( x + 14 )
Step-by-step explanation:
i think... trust someone else because i'm not 100% sure..
Simplify the expression 16+(−5)−6/7j−2/7j+6
Convert 27 inches to feet in dimensional analysis .
Answer:
2.25 feet.
Step-by-step explanation:
Formula: divide the value in inches by 12 because 1 foot equals 12 inches.
So, 27 inches = 27 /12 = 2.25 feet.
75° b Arrange the three side lengths in increasing order. 350 c [?]
Answer:
a < b < c
Step-by-step explanation:
The side opposite the larger angle measure is the longer side.
The side opposite the smallest angle measure is the shortest side.
The sum of the three angles = 180° ; (75° + 35° + ? = 180°). The missing angle is 70°
The angles in order from the smallest to the largest:
35° < 70° < 75°
The side for the shortest to the largest
side opposite 35° is a
side opposite 70° is b
side opposite 75° is c
Answer a < b < c