The scale factor used for scaling the actual rectangular pool was 4/15 and the length of the scaled rectangle is 9.6 feet.
How to calculate the scale factor?Suppose the initial measurement of a figure was x units.
And let the figure is scaled and new measurement is of y units.
Since the scaling is done by multiplication of some constant, that constant is called scale factor. Let that constant be 's'.
Then we have:
[tex]s \times x = y\\s = \dfrac{y}{x}[/tex]
Thus, scale factor is the ratio of the new measurement to the old measurement.
For this case, we're specified that:
Dimensions of the original pool = 24 feet wide by 36 feet long
The scaled rectangle's dimension: 6.4 feet width and L feet length (we assume the length be L units).
So, in scale drawing, 24 feet was converted to 6.4 feet. Let the scale factor be 's', then:
[tex]6.4 = s \times 24\\\\s = \dfrac{6.4}{24} = \dfrac{4}{15}[/tex]
Thus, since length is also scaled by same factor(as the whole figure is scaled by constant scale factor assumingly), we get:
Scaled length = s times original length
[tex]L = \dfrac{4}{15} \times 36 = 9.6 \: \rm feet[/tex]
Thus, the scale factor used for scaling the actual rectangular pool was 4/15 and the length of the scaled rectangle is 9.6 feet.
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Ethan drove the first half of his trip's distance at an average rate of 60 miles per hour, and the second half at an average
rate of 70 miles per hour. What was Ethan's average speed for the entire trip, in miles per hour?
Answer:
Simple
65 miles per hour on average
Step-by-step explanation:
You add 60 to 70 and then you divide them by 2
Which is
60 + 70 = 130
130 ÷ 2 = 65
The average speed Ethan will be 65 miles per hour on average.
What is speed?The speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.
That Ethan drove the first half of his trip's distance at an average rate of 60 miles per hour, and the second half at an average rate of 70 miles per hour.
The average speed will be calculated as,
60 + 70 = 130
130 ÷ 2 = 65 miles per hour
Therefore, the average speed Ethan will be 65 miles per hour on average.
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Victor is working on a project and has cut a number of wooden blocks of equal size that are represented by this right rectangular prism. He now needs to cover the wooden blocks on all sides with a red fabric.
How much fabric does Victor need in order to cover 12 of these blocks?
156 cm²
24 cm²
13 cm²
2 cm²
Answer:
(a) 156 cm²
Step-by-step explanation:
The total surface area of the 12 blocks can be computed by first finding the surface area of one block. That result can then be multiplied by 12. The area of one rectangular prism is given by the formula ...
A = 2(LW +H(L +W))
A = 2(4·1 +1/2(4+1)) = 2(4 +5/2) = 13 . . . cm²
The area of 12 such prisms will be ...
12 × (13 cm²) = 156 cm²
Victor needs 156 cm² of fabric to cover 12 blocks.
_____
Additional comment
This problem offers an opportunity to exercise your number sense. The area of the largest surface of one block is (4 cm)×(1 cm) = 4 cm². 12 of these surfaces will have an area of 48 cm². This is only part of the total area, so the only reasonable choice among those offered is 156 cm².
Answer:
156 cm² for K12
¿Cuáles son los términos algebraicos que representan a una función cuadrática incompleta
con solamente término cuadrático?
Una ecuación cuadratica que solo tiene el termino cuadratico se escribe como:
y = a*x^2
¿Como escribir esta ecuación cuadratica?
La ecuación cuadratica general se escribe como:
y = a*x^2 + b*x + c
Donde el termino cuadratico es el primero, el segundo es el lineal y el tercero es el constante.
Entonces, si queremos una ecuación cuadratica que solo tenga el termino cuadratico, la ecuación sera:
y = a*x^2
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Please help me with my home work
2.334567890 x 3.04576879 =
Multiply. What is the product (3 x 10^9) * (2 * 10^17) in scientific
notation?
?
(3 * 10^9) * (2 x 10^17 = ? * 10^?
DONE
Answer:
[tex]\boxed{6}\times 10^{\boxed{26}}[/tex]
Step-by-step explanation:
[tex](3 \times {10}^{9} ) \times (2 \times {10}^{17} ) \\ \\ = (3 \times 2) \times ( {10}^{9} \times {10}^{17}) \\ \\ = 6 \times {10}^{9 + 17} \\ \\ = \huge \boxed{ 6} \times {10}^{ \boxed{26}} [/tex]
What are the coordinates?
Answer:
[tex](1,1)[/tex]
Step-by-step explanation:
If you graph it, You can see that the last point will be [tex](1,1)[/tex].
Hope This Helps!
1. Jennifer can mow the lawn in 20 min. Kristen can mow the lawn in 30 min. If they work together, how long will it take them to mow the lawn
Answer:
Sam can do the job in 20 min. So he can do the whole job at the rate of 1 job in 20 minutes.
So he does 1/20 of the job per minute.
.
Rob can do the job in 30 min. His rate is 1/30 of the job per minute.
.
Working together how does it take?
.
1/20*x + 1/30*x = 1 job done
, where x = minutes.
.
Step-by-step explanation:
What does Mean median and mode mean?
Answer:
mean-average of a data set
mode-most common number in a set
median-middle number of the set
Step-by-step explanation:
you can ask me a question for more info
Answer:
Step-by-step explanation:
Mean - Is the average taken for a set of numbers
Median - The middle value in a data set of numbers
Mode - The number that occurs the most in a given list of numbers.
PLEASE HELP AS I SAID I HAVE A F IN MATH AND I HAVE LIKE 6 OTHER SI TO DO PLEASE ANSWER ALL OF THEM
The prism below is made of cubes which measure of a foot on one side. What is the volume?
Note: Figure is not drawn to scale.
A.
B.
C.
D.
Answer: 32
Step-by-step explanation: count one row and then multiply that by 4 And then it equals 32
What is the area of the following circle?
Answer:
Step-by-step explanation: A= π r²
π=3.14
4x4 = 16
so 3.14 x 16 =50.24
Suppose you bought 20 tickets in a drawing for a color television. There were 300 tickets sold in the drawing,
a. What is the probability that you win the color television?
b. What are the odds in favor of you winning the television?
c. What are the odds against you winning the television?
yeah help me okay thanks
Answer:
4
3
Step-by-step explanation:
A husband and wife are building a tiny house for a vacation getaway, and they want to measure the height of the roof of the house to see if they will be able to have a bedroom on the second floor. One side of the house is 18 ft long and the slant height of the roof along this side is 13 ft. The point on the roof's peak is above the center of the house. What is the height of the roof of the house? Round your answer to the nearest hundredth. Question 4 options: 9.38 ft 11.28 ft 15.21 ft 9.4
By using a right triangle as a model, we will see that height of the roof is 9.38 ft.
What is the height of the roof of the house?The slant height is equivalent to the hypotenuse of a right triangle, so we know the length of the base and the hypotenuse of a right triangle. The cathetus will be half of 18ft
We need to find the other cathetus, so we can use the Pythagorean theorem, if X is the other cathetus we will get:
X^2 + (9ft)^2 = (13 ft)^2
X = √( (13 ft)^2 - (9 ft)^2) = 9.38ft
So the height of the roof is 9.38 ft.
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What is the solution to the equation startfraction m over m 4 endfraction startfraction 4 over 4 minus m endfraction = startfraction m squared over m squared minus 16 endfraction? m = –4 m = –2 m = 2 m = 4
The value of them after solving the equation will be m=-2
What will be the value of m?The given equation will be
[tex]\dfrac{m}{m+4} + \dfrac{4}{4-m} =\dfrac{m^2}{m^2-16}[/tex]
multiply both sides by [tex](m+4)(m-4)[/tex]
[tex](m+4)(m-4) (\dfrac{m}{m+4} + \dfrac{4}{4-m} )=(m+4)(m-4) \dfrac{m^2}{m^2-16}[/tex]
[tex]m(m-4)-4(m+4)=m^2[/tex]
[tex]m^2-4m-4m-16=m^2[/tex]
[tex]8m=-16[/tex]
[tex]m=-2[/tex]
Thus the value of them after solving the equation will be m=-2
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Answer:
b
Step-by-step explanation:
edge
If a 45-45-90° triangle's leg has a length of 18 units, what is the length of the hypotenuse?
Answer:
25.45584...
Step-by-step explanation:
The length of the hypotenuse can be found using the pythagorean theorem: [tex]a^{2} +b^{2} =c^{2}[/tex] So in this situation, the solution can be found by solving [tex]\sqrt{2(18)^{2} }[/tex]
The Great Pyramid at Giza is a square-based pyramid with height 146 meters and a base that measures 230 meters on each side. What is the volume of the pyramid, in cubic meters?
Round your answer to the nearest cubic meter.
Answer:
The Volume of the Great pyramid will be "2586810 m³". A further solution is provided below.
Given:
Sides of length,
[tex]s = 230m[/tex]
Height,
[tex]h = 146.7m[/tex]
According to the formula,
The Volume (V) will be:
[tex]= \frac{1}{3} s^{2} h[/tex]
By substituting the values, we get
[tex]= \frac{1}{3} (230)^{2} * 146.7[/tex]
[tex]= \frac{1}{3} *520900 *146.7[/tex]
[tex]=\frac{1}{3} * 7760430[/tex]
[tex]= \frac{7760430}{3}[/tex]
[tex]= 2586810m^{3}[/tex]
Thus the above is the correct solution.
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16 more than craigs score is 62
Step-by-step explanation:
what is the question ?
to find Craig's score ?
if that is the case :
Craig's score = 62 - 16 = 46
What would be the formula if the farm agency could only use the letters A, B, C, and blank spaces?
The formula of the farm agency illustrates a geometric progression
The formula the farm agency could use is y = 3^n
How to determine the formula?The number of characters is given as:
n(A,B,C) = 3
Represent the number of tags to create with y.
So, we have:
y = 3×3×3×3×..........×3( in n places)
Express as exponent
y = 3^n
Hence, the formula the farm agency could use is y = 3^n
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Answer: y=4^n
Step-by-step explanation: I got the question right and this was the answer, I believe its because the company uses A,B,C and blank spaces so that adds one.
What is the Greatest Common Factor for 39 and 57?
Answer:
3
Step-by-step explanation:
As you can see when you list out the factors of each number, 3 is the greatest number that 39 and 57 divides into.
An account with $300 gains 0. 5% annual interest compounded continuously. How
many years would it take to reach $600? Round to the nearest whole year and type
your answer into the box.
Formula: A=
Pert
Answer:
139
Step-by-step explanation:
A = Pe^rt
A = 600$
P = 300$
R = 0.005
T = ?
600 = 300e^(0.005)(t)
t = 138.63
After eating at the restaurant, Tom, Mary, and
Sara decided to divide the bill evenly. If each
person paid 42 dollars, what was the total of the
bill?
Answer:
$126
Step-by-step explanation:
since they divided it evenly therefore everyone paid $42 you just times that by the amount of people. there is tom, mary and sara therefore 3. 42*3=126
Answer:
total bill was $126
Step-by-step explanation:
3 people ate: Tom, Mary and Sara
if they split the bill evenly, they would all pay the same amount
if each person paid 42 dollars, you just multiply that amount by the number of people
42 x 3 = 126
A plastic alphabet cube is 7 cm on each side. What is the surface area of the cube?
Answer:
In a cube, the length and width are the same, so both sides will be 7 cm, yielding an area of 49 square centimeters.
Step-by-step explanation:
Answer:
Cube's features;
6 sides to a cubeAll side lengths are equal, so all areas are the sameGiven this information, we must find the area of one side and multiply that area by 6 since there are 6 equal sides of the same area.
Formula for area of square:-
A = a^2
or
A = a · a
Where 'a' represents the length of one side.
Plug in values;
A = a^2
A = 7^2
A = 49 centimetres is the area of one side.
Now we find the areas of all sides (6 sides in total);
49(6)
= 294 is the surface area of the cube.
A. 197 cm
B. 158 cm
C. 155 cm
D. 55 cm
Answer:
158
Step-by-step explanation:
The Formula for Area is: A = L * W
First lets start with the rechtangle:
A = L * W
A = 17 * 7 = 119
the area of the rechtangle is 119
Now the triangle the formula is a little diffrent but it is the same concept
A=hbb (Picture below, it wont let me write it out right)
2=6·13
2=39
The area of the triangle is 39
Now add the both areas
119 + 39 =
158
What is the outlier in the data set shown below?
A. 6
B. 36
C. 40
D. 46
Where do rivers usually begin?
if A = (0,0) and B = (8,2), what is the length of AB
Answer:
Hope the picture will help you
Can someone help me please and thank you! :))))
Original price = $7200
But he bought it for 65%
So it is just 65% of $7200
0.65 * $7200 = $4680
1. Find the total area. Round to the nearest hundredth.
Answer:
1052.39 cm2
Step-by-step explanation:
too lazy to type all that
1) find the radius of the half circle using pythagorus. (34-16=18, √30^2-18^2 = 24 = diameter. radius = 12)
2) find the area of the cirlcle then divide by 2 youll get the area of the half circle
3) find the area of the other thing (i forgot its name) using
1/2×24×(16+34) = 600
then add them up
The number 175 is 25% of what number?
Answer: 700
Step-by-step explanation:
175 * 4 = 700
Answer:
700
Step-by-step explanation:
To solve this problem you multiply 175 by 100 and then divide the total by 25 as follows: (175 x 100) / 25
When we put that into our calculator, we get the following answer:
700
What is the slope of the line that passes through the points (9, 2) and (9,27)? write your answer in simplest form.
[tex]\textsf{The slope of a line passing through two}[/tex]
[tex]\sf{given \: points \:(x_1,y_1) \:and \:(x_2,y_2) \: is \:given \: by - }[/tex]
[tex]\green{ \underline { \boxed{ \sf{ Slope, =\frac{y_2-y_1}{x_2-x_1}}}}} [/tex]
Here,
[tex]\sf{x_1= 9}[/tex][tex]\sf{y_1=2}[/tex][tex]\sf{x_2=9}[/tex][tex]\sf{y_2= 27}[/tex]
Putting Values:-
[tex]\begin{gathered}\begin{gathered}\\\implies\quad \bf Slope =\frac{27-2}{9-9} \\\end{gathered} \end{gathered} [/tex]
[tex]\begin{gathered}\begin{gathered}\\\implies\quad \bf \frac{25}{0}\quad(not\: defined) \\\end{gathered} \end{gathered}[/tex]
>>The slope of the line that passes through the given points is not defined.
Note- We can conclude that if x-coordinate of the points through which line passes are same , then slope is always not defined .
Solve for x: 2(x 3)2 − 4 = 0 Round your answer to the nearest hundredth. X = 4. 41, 1. 59 x = 1. 34, 5. 24 x = −1. 34, −5. 24 x = −4. 41, −1. 59.
The two values when the provided quadratic equation is solved for the x are -4.41 and -1.59 to the nearest hundredth.
What is a quadratic equation?A quadratic equation is the equation in which the unknown variable is one and the highest power of the unknown variable is two.
The standard form of the quadratic equation is,
[tex]ax^2+bx+c=0[/tex]
Here, (a,b,c) are the real numbers and x is the variable.
To find the value of x, the following formula is used,
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
The given equation is,
[tex]2(x+ 3)^2 - 4 = 0[/tex]
To solve this equation, we need to apply some mathematical operations over it. Let's start with opening the brackets.
[tex]2(x+ 3)^2 - 4 = 0\\2(x^2+6x+9)-4=0\\2x^2+12x+14-4\\2x^2+12x+12=0\\x^2+6x+7=0[/tex]
On comparing with standard equation we get,
[tex]a=1, b=6, c=7[/tex]
Put this values in the above formula,
[tex]x=\dfrac{-(6)\pm\sqrt{(6)^2-4(1)(7)}}{2(1)}\\x=\dfrac{-(6)\pm\sqrt{(6)^2-4(1)(7)}}{2(1)}\\x=-4.41,-1.59[/tex]
Hence, the two values when the provided quadratic equation is solved for the x are -4.41 and -1.59 to the nearest hundredth.
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