The dimensions for the width and height of the fish tank will be 4 feet and 2 feet .
What is dimension?Dimension is the measurable extent of a particular kind, such as length, breadth, depth, or height.
According to the given problem,
let , b = is the width of the fish tank
h = is the height of the fish tank given that , hold at least 35 cubic feet of water .
so ,
4×b×h ≥ 35
⇒ h ≥ 35/4b
now , surface area of the fish tank
⇒ 4b + 2× 4h + 2× bh
now substitute the value of h
here
⇒ ≥ 4b +70/b + 35/2
⇒ ≥ 40(70)^1/2 + 35/2 (if and only if b= (70)^1/2 / 2 , the equal sign holds )
therefore ,
= (70)^1/2 / 2 b ≈ 4.18 so b is 4 . when b = 4 ,
h = 35 / 4 × 4 = 2.1875 round off h = 2
so , the minimum surface area of fish tank is
⇒ 4×4+ 2× 4×2 + 2× 4×2⇒ 48
hence , the height and the width of the fish tank is 2 and 4 .
learn more about dimension here :brainly.com/question/27022535
#SPJ2
At George Washington High School, 119 students walk to school. If this number is 35% of school enrollment, then how many students are enrolled at the school ?
Answer: 340 students
Step-by-step explanation:
The number of students walking to school is 119 and this is 35% of the total number of students.
Assume the total number is denoted by "x".
That would mean that the following formula captures the situation:
119 = 35% * x
119 = 0.35x
x = 119/ 0.35
= 340 students
If using the method of completing the square to solve the quadratic equation x^2+5x+10=0x 2 +5x+10=0, which number would have to be added to "complete the square"?
Answer:
(5/2)² must be added to the equation to complete the square.
Step-by-step explanation:
The given equation is
x^2+5x+10=0
writing it in in square form
(x)² + 2(x) (5/2) + (5/2)²-(5/2)² + 10= 0
We multiply (5/2) to the mid term because we have to make 2x equal to 5x.
As the square formula tells that square of first element plus 2 into first element multiplied by second element plus square of second element.
Making 2x equal to 5x gives (5/2) as the second element.
Therefore add square of the second element but also subtract square of second element to make it equal to the given original equation.
Now we can solve it.
(x)² + 2(x) (5/2) + (5/2)²-(5/2)² + 10= 0
(x + 5/2)²-(5/2)² + 10= 0
(x + 5/2)²- 25/4+ 10= 0
(x + 5/2)²- 25*5 +10*5/4*5= 0
(x + 5/2)²- 125+50/20= 0
(x + 5/2)²- 175/20= 0
(x + 5/2)²= 175/20
cos C(sec C - 1) = 1 - cos C
Answer:
Step-by-step explanation:
Cos(Sec - 1 ) = 1 - cosC
Cos and Sec are reciprocals which when multiplied together is 1
-1 * Cos = -Cos
SO: 1 - Cos = 1 - Cos
Hope this helps!
(trigonometry) solve for x
Answer:
Step-by-step explanation:
take 23 degree as reference angle
using tan rule
tan 23=opposite/adjacent
0.42=25/x
x=25/0.42
x=59.52
x=60
Here is a diagram and its corresponding equation. Find the solution to the equation.
4(+7)=38
Answer:
The solution to the equation is:
x = 2.5 or x = 5/2Step-by-step explanation:
To find the solution to the equation, you only must operate the equation until you clear the x variable, with the next steps:
Equation: 4(x+7) = 38And we solve:
4x + 28 = 38 (we multiply 4 by x and 7)4x = 38 - 28 (we pass the +28 to subtract to the right side of the equality and operate)x = 10 / 4 (we pass the 4 that is multiplying to divide to the right side of the equality)x = 2.5 (we divide)As you can see, the solution of the equation is x = 2.5 or x = 5/2
I need help please!!
Answer:
20
Step-by-step explanation:
6×2=12 + 8 = 20
so you answer for number 3 is twenty
(6x2 -5x + 10) - (2x2 -x +13)
Answer:
[tex](6 {x}^{2} - 5x + 10) - 2 {x}^{2} - x + 13 \\ 6 {x}^{2} - 5x + 10 - 2 {x}^{2} + x - 13 \\ = 4 {x}^{2} - 4x - 3[/tex]
The water level in an ocean bay changes at an average rate of 3 meters per hour. At this rate, how many hours would it take for the water level to change 12 meters?
please help
Answer:
4 hours
Step-by-step explanation:
You divide 12 by 3 and the answer is 4.
hope this helped
Match each expression on the left with an equivalent expression on the right.
The expression on the left matched with an equivalent expression on the right are;
3x + 0 = 3x
5/3 - x + 1/3 = -3/2x + 2 + 1/2x
2x - 3 = x - 3 + x
2x - 6 = -6 + 2x
3/5 - 13/5 = -6.9 + 4.9
How to solve equivalent expression?3x + 0 = 3x
5/3 - x + 1/3
combine like terms
= 5/3 + 1/3 - x
= (5+1)/3 - x
= 6/3 - x
= 2 - x
-3/2x + 2 + 1/2x
combine like terms
-3/2x + 1/2x + 2
= (-3+1)x / 2 + 2
= -2/2x + 2
= -x + 2
2x - 3 = x - 3 + x
2x - 6 = -6 + 2x
3/5 - 13/5
= (3-13)/5
= -10/5
= -2
-6.9 + 4.9
= -2
Ultimately, an expression is said to be equivalent when the value on the right hand side is equal to the value on the left hand side.
Read more on equivalent expression:
https://brainly.com/question/15775046
#SPJ1
Sandy mixed together 9 gallons of one brand of juice and 8 gallons of a second brand of juice, which contains 48 percent real fruit juice. Find the percent of real fruit juice in the first brand if the mixture contained 30 percent real fruit juice. Which of the following equations could be used to solve this?
Group of answer choices
a(9)+48(8)17=0.30100
a(9)+0.48(8)17=30100
a(9)+0.48(8)a+0.48=30100
a(9)+0.48(8)17=30
Answer:
14 % pure juice comes from first brand
Step-by-step explanation:
Mixture:
17 gal 30% contains: 17x 30% = 5.10 gal pure juice
Second brand:
8 gal 48% contains: 8x40% = 3.84 gal pure juice
5.10 − 3.84 = 1.26 gal
1.26 gal is coming from 9 gal of first brand
The percentage of first brand is:
(1.26/9) x100 = 14 % pure juice.
Hurry plz
In which quadrant is the point (-5, -4) in?
IV
I
III
II
Answer:
(-5,-4) quadrant is in III quadrant
If tanΘ = 6/5 and cosΘ < 0, what is sin2Θ?
An explanation on how to solve this problem would be great, thanks!!
Answer:
[tex]\displaystyle \sin2\theta=\frac{60}{61}[/tex]
Step-by-step explanation:
We are given that:
[tex]\displaystyle \tan\theta=\frac{6}{5}\text{ and } \cos\theta <0[/tex]
And we want to find the value of sin(2θ).
First, recall that tangent is the ratio of the opposite side to the adjacent side.
Therefore, the hypotenuse is:
[tex]h=\sqrt{6^2+5^2}=\sqrt{61}[/tex]
Next, note that tangent is positive and cosine is negative. Tangent is positive in QI and QIII. Cosine is negative in QII and QIII.
Hence, we can conclude that θ must be in QIII.
In QIII, sine is negative, cosine is negative, and tangent is positive.
And with respect to θ, our opposite side is 6, adjacent side is 5, and the hypotenuse is √(61).
We can rewrite our expression as:
[tex]\sin2\theta=2\sin\theta\cos\theta[/tex]
Using the above information, substitute:
[tex]\displaystyle =2\left(-\frac{6}{\sqrt{61}}\right)\left(-\frac{5}{\sqrt{61}}\right)[/tex]
Simplify. Hence:
[tex]\displaystyle \sin2\theta=\frac{60}{61}[/tex]
A computer downloads a 48 kilobyte file in 5 seconds. At this rate, how long will it take the computer to download a file that is 120 kilobytes?
Answer:
12,5
Step-by-step explanation:
First, you need to find how many kilobytes do you download every seconds.
You simply divide 48 kilobyte / 5 seconds and you get 9,6 kB/s.
Now you know that your download speed is this you can find the amount of time needed for downloading 120 kilobytes.
You simply divide [tex]\frac{120 kilobytes}{9,6 kilobytes/s} = 12.5 s[/tex].
12,5 seconds.
Select the correct image.
Answer:
Triangle 2
Step-by-step explanation:
That is Pythagorean Theorem, which is only for right triangles. The second triangle has the little square, so you know it is 90 degrees.
Find Y
A: 14.3
B: -6.3
C: 7.0
D: 11.6
Answer:
D
Step-by-step explanation:
Using the sine ratio in the right triangle
sin51° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{9}{y}[/tex] ( multiply both sides by y )
y × sin51° = 9 ( divide both sides by sin51° )
y = [tex]\frac{9}{sin51}[/tex] ≈ 11.6 ( to 1 dec. place ) → D
Janelle draws line segments AB and BC in the same plane such that AB = 8 cm and BC = 6 cm. Then Janelle draws
line segment AC.
Use this information to determine the length, in centimeters, of AC for the following two situations.
• AB, BC, and AC form a triangle. Enter a possible value of AC in the first response box.
• Points A, B, and C lie on the same line, and C lies between A and B. Enter this value of AC in the second
response box.
Answer:
Step-by-step explanation:
• AB, BC, and AC form a triangle. Enter a possible value of AC....
So it asks for only a possible value of AC as there are many possible values.
Given AB = 8 cm and BC = 6 cm, they are in the ratio of 3:4.
Line segments of 3, 4 and 5 length will form a right-angled triange.
A possible value of AC = 5*2 = 10cm
• Points A, B, and C lie on the same line, and C lies between A and B.
So AC+CB = AB
AC+6 = 8
AC = 2cm
Enter this value of AC in the second
response box.
Answer:
Step-by-step explanation:
if ABC forms a triangle, AB=8 and BC=6
a possible value of AC=10cm
if ABC is a line segment n C is between A n B
AC + BC = AB
AC = 8 - 6 = 2cm
What are the first 5 terms of the sequence Tn= 2n-3?
(Please answer quickly)
Answer:
-1, 1, 3, 5, 7
Step-by-step explanation:
At a high school the average grade for the first semester for all subjects was 79.3. Based on this mean , the principal concludes that half of the grades were 79.3. Higher is her conclusion justified? Why or why not?
Answer:
That is incorrect. It would be appropriate if the median were 79.3, since the median is the value in the middle (when placing the data in order).
Conclusion of principal about mean is not justified. Mean represents the average of the data. For such conclusion mode is the correct option.
What is mean?
" Mean is defined as the ratio of the sum of all the given numbers in the data to the total numbers of numbers in the data. It is also known as average of the data."
What is mode?" Mode represents the value which occurs maximum numbers of times in the set of data."
According to the question,
Average grade for the first semester for all subjects = 79.3
Based on this mean
Principal concludes that half of the grades scored 79.3.
For example:
There are 5 students 3students score 100 , one student score 48 and another one got 50.
Mean of the class = [tex]\frac{398}{5}[/tex]
= 79.6
Here no student score 79.6.
Principal conclusion is not justified.
Mean is not the correct option to justify maximum number of students marks it is represented by mode.
Hence, conclusion of principal about mean is not justified. Mean represents the average of the data. For such conclusion mode is the correct option.
Learn more about mean and mode here
https://brainly.com/question/6813742
#SPJ2
Triangle LMN is similar to triangle OPQ. Find the measure of side QO. Round your answer to the nearest tenth if necessary.
Answer:
90.8
Step-by-step explanation:
20/13 = x/59
13x = 1180
x=90.76
x=90.8
What is -5+56<1 please and thank you
On a coordinate plane, a parabola opens down. It has an x-intercept at (negative 5, 0), a vertex at (negative 1, 16), a y-intercept at (0, 15), and an x-intercept at (3, 0).
The function f(x) = –x2 − 2x + 15 is shown on the graph. What are the domain and range of the function?
The domain is all real numbers. The range is {y|y < 16}.
The domain is all real numbers. The range is {y|y ≤ 16}.
The domain is {x|–5 < x < 3}. The range is {y|y < 16}.
The domain is {x|–5 ≤ x ≤ 3}. The range is {y|y ≤ 16}
Answer:
the domain is xl-5<×< 3 is the range of 16
The domain is all real numbers. The range is {y|y ≤ 16}.
Domain of the functionThe domain of a function is all the of values of the input or independent variable into the function
Since the x-intercepts of the function are at (-5, 0) and (3, 0), and also, the graph opens downwards, the values of x are in the interval (-∞ ≤ x ≤ -5) ∪ (-5 ≤ x ≤ 3) ∪ (3 ≤ x ≤ ∞). This is (-∞ ≤ x ≤ ∞).
So, the domain is the set of all real numbers.
The range of a functionThe range of a function is all the output values of the function
Since the vertex of the parabola is at (-1, 16) and its y-intercept is at (0, 15), the maximum value of y is 16. So, the values of y are in the range y ≤ 16.
So, the range of the function is {y|y ≤ 16}
So, the domain is all real numbers. The range is {y|y ≤ 16}.
Learn more about domain and range of a function here:
https://brainly.com/question/10197594
Plz answerrrr due todayy
Answer:
Step-by-step explanation:
87 = x + 90
Isolate the variable by subtracting 90 on both sides
87 = x + 90
-90 -90
x=-3
-4x = 16
Isolate the variable by dividing by -4 on both sides
-4x=16
/-4 /-4
x = -4
43 = 6x - 5
The circle below is
centered at (2, 3) and has a radius of 4. What is its equation?
Answer:
Step-by-step explanation:
The standard form of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex] where h and k are the center of the circle and r is the radius. Filling in:
[tex](x-2)^2+(y-3)^2=16[/tex]
PLEASE HELP WITH STEPS SOLVE IN SCIENTIFIC NOTATION WILL GIVE BRAINLIEST
Answer:
use this <3 (helps calculate scientific notation) https://www.calculatorsoup.com/calculators/math/scientific-notation-converter.php
Step-by-step explanation:
Helloooo possess I need help as soon as possible
A report states that the mean household income last year for a certain rural county was $46,200 and the median was $54,500. If a histogram were constructed for the incomes of all households in the county, would you expect it to be skewed to the right, to the left, or approximately symmetric
Answer:
skewed to the left
Step-by-step explanation:
A histogram is used to represent data graphically. the histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class interval. the frequency is usually on the vertical axis while the class interval is usually on the horizontal axis.
If the mean is greater than the median, the histogram would be skewed to the right
If the mean is less than the median, the histogram would be skewed to the left.
The mean in this question is $46,200 while the median is $54,500. So, the histogram would be skewed to the left
Use the Law of Sines to solve for the variable. Round your answer to the
nearest whole number. Write the value only. *
Answer:
y ≈ 61
Step-by-step explanation:
Using the Sine rule in the triangle
[tex]\frac{y}{sin117}[/tex] = [tex]\frac{21}{sin18}[/tex] ( cross- multiply )
y × sin18° = 21 × sin117° ( divide both sides by sin18° )
y = [tex]\frac{21sin117}{sin18}[/tex] ≈ 61 ( to the nearest whole number )
In circle O, AE and DC are chords and intersect at B. If arc AC is 36 degrees and arc DE is 20 degrees, what is the measure of angle ABC? (Type in numbers only)
Answer: 28
You add 36 and 20 and divided it by 2
write the five rational number which can be expressed has terminating decimal
Answer:
1/3
1/7
1/11
1/13
1/17
Step-by-step explanation:
mark me brainliest!!
Find sin s, sin r , cos s , and cos r
Hi there! For this question, you need to know the ratio of sine and cosine.
sinA = opposite/hypotenusecosA = adjacent/hypotenuseDefine A = angle
opposite and adjacent side changes only if we focus on another angle.
From the picture, if we focus on angle S, the opposite would be 36. But if we focus on angle R (flip to make RT as base), see that the opposite would be 14.
Answer
sinS = 36/42 = 6/7sinR = 14/42 = 1/3cosS = 14/42 = 1/3cosR = 36/42 = 6/7The bold one is simplest form while the non-bold is non-simplest.
Questions can be asked through comment.
Hope this helps, and Happy Learning ! :)