Answer: The tank which has 3 m side.
Step-by-step explanation: A cube is a form that has equal sides. To calculate the volume of it, multiply all three sides:
V = length*width*height
Since they are all the same, volume will be:
V = s³
One tank has a 3 m side, so its volume is:
V = 3³
V = 27 m³
The other has half of the first one side, then s = [tex]\frac{3}{2}[/tex] and volume will be:
V = [tex](\frac{3}{2})^{3}[/tex]
V = [tex]\frac{27}{8}[/tex] m³
As you can see, the volume of the second tank is [tex]\frac{1}{8}[/tex] smaller than the first one. Therefore, the tank which has 3 m side can store more water than the tank with side measuring half of the first.
13. Gayle is getting ready for her first day of school. She has 7 new dresses to choose from and 4
new pairs of shoes. How many different outcomes are possible for Gayle to wear one dress and
one pair of shoes?
Answer:
49
Step-by-step explanation:
7 times 4 equals 49.
The sum of two numbers is 26. The sum of their squares is a minimum. Find the numbers.
Answer:
The numbers at 13 and 13
Step-by-step explanation:
The two numbers in question are equal, and if their sum is 26, then they must be 13 and 13.
The two numbers are (13, 13).
Given that,
The sum of the two numbers is 26.
And the sum of their square is minimum.
We have to determine,
The two numbers are.
According to the question,
Let, the first number be x,
and the second number be y.
The sum of the two numbers is 26.
[tex]x + y = 26[/tex]
And The sum of their squares is a minimum.
[tex]x^2 + y^2 = h[/tex]
Solving both the equation,
[tex]x + y = 26\\\\x = 26-y[/tex]
Substitute the value of x in equation 2,
[tex]x^2 + y^2 = h\\\\(y-26)^2 + y^2 = h \\\\y^2 + 676 -52y + y^2 = h\\\\2y^2 -52y + (676-h) = 0[/tex]
Then, The vertex of the parabola is,
[tex]\dfrac{-b}{2a} = \dfrac{-(-52)}{2(2)} = \dfrac{52}{4} = 13[/tex]
The minimum value of the parabola is 13, which is also the sum of squares.
Therefore, The two number is x = 13 and y =13.
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Find all pairs $(x,y)$ of real numbers such that $x + y = 10$ and $x^2 + y^2 = 56$. For example, to enter the solutions $(2,4)$ and $(-3,9)$, you would enter "(2,4),(-3,9)" (without the quotation marks).
Answer:
(3.26795, 6.73205)
(6.73205, 3.26795)
Step-by-step explanation:
Easiest and fastest way to get your solutions is to graph the systems of equations and analyze the graph for where they intersect.
A dilation has center (0, 0). Find the image of each point for the given scale factor. A(3,4);D7(A)
Answer:
6,8
Step-by-step explanation:
if y varies inversely as x and y=6 when x=8 find y when x=7
Answer:
y = 5 1/4
Step-by-step explanation:
For direct or inverse variation relation
relation between two variable and y can be expresses in form of
y = kx where k is constant of proportionality .
Only thing happens in inverse relation is that when x increases then y decreases and vice versa. That is care by constant of proportionality
__________________________________
Thus, let the inverse relation be
y = kx
given
when y = 6 then x = 8
we will plug this value in y = kx
6 = k*8
=>k = 6/8 = 3/4
Thus,
relation is
y = 3/4 x
we have to find y when x = 7 ,
lets put x = 7 in y = 3/4 x
y = 3/4 *7 = 21/4 = 5 1/4
Thus, when x = 7 then y = 5 1/4
Simplify 2(x - 3) + 7(x + 2)
Answer:
9x + 8.
Step-by-step explanation:
2(x - 3) + 7(x + 2)
= 2x - 6 + 7x + 14
= 2x + 7x - 6 + 14
= 9x + 8.
Hope this helps!
I need some help on this
Answer: The answer is B
Step-by-step explanation:
Answer:
Option B is correct
Step-by-step explanation:
cos (3pi/4) = -cos(pi - 3pi/4) = -cos(pi/4) = -sqrt(2)/2
=> Option B is correct
what is the sum of the values of x that are solutions to the equation x^2 - 10x - 22 = 2 ? a. -12 b. -10 c. -2 d. 2 e. 10
Answer:
[tex]x = 2, 12[/tex]
Your correct answer is D, since I don't see a -12.
Step 1: Subtracting 2 from both sides
Since we have to find the value of x, we have to factor the equation. To do so, we first have to subtract the two from both sides of the equation so all the values are on one side of the equation.
[tex]x^2-10x-22(-2)=2(-2)\\x^2-10x-24=0[/tex]
Step 2: Factoring the equation
Part 1
After subtracting 2 from both sides of the equation, we have to factor the polynomial to be able to get it into two sets of parentheses, so in order to do that, we will ignore the equal sign and the 0 for now. We are now left with:
[tex]x^2-10x-24\\[/tex]
First, we find the multiples of the first term, [tex]x^2\\[/tex], and the last term, -24. Since there is an invisible 1 before the first term, we are basically finding the multiples of [tex]1x^2[/tex], which is [tex]1x[/tex] and [tex]1x[/tex], or x and x. Now we have to find the correct set of numbers for -24. Do do that, we have to make sure that when we multiply the first set of numbers (x, x) with the second set (?, ?) and add them together, then we would get the number in the middle (-10x). So: Two of the most obvious multiples for 24 are 6 and 4, 12 and 2, and 3 and 8. But, this is a negative 24, so we have to work ahead to find out which pair we use first. If we multiply 8 and 3 with x and x, we get 8x and 3x. When we add them together, we do not get 10x, but instead, we get 11x, so it is the wrong pair. If we do the same thing to 6 and 4, we would get 10x, but since 24 is negative, it is not correct because we would need one of the numbers to be negative. In this case, they equal to 10x, but one of the numbers would have to be negative because (if 6 was the negative):
[tex]-6 * 4=-24\\[/tex]
But:
[tex]4-6\neq 10\\[/tex]
So this is not the correct set either. Our last set is 12 and 2, and when we multiply by x (12x and 2x) and we set one of the numbers to be a negative (-12) and subtract them, we get -10x, so, therefore, this is the correct number pair.
[tex]-12*2=-24\\2-12=-10[/tex]
Part 2
With all that done, we now have to factor the numbers. We take the first numbers (x and x), and we place them in front of each of the two parentheses.
[tex](x,?)(x,?)[/tex]
Now, we place -12 and 2 in those places.
[tex](x,-12)(x,2)[/tex]
To find x, we have to plug in the equal sign and 0 from the beginning.
[tex](x,-12)(x,2)=0[/tex]
Since they both have to equal to 0, then that means there would be two different answers because, for example: 12 - 12 = 0, but 12 - 2 ≠ 0.
To find both solutions, we treat the numbers in each of the parentheses as its own equation, and we solve it from there.
x - 12 = 0
12 - 12 = 0
x - 2 = 0
2 - 2 = 0
12 and 2 are our solutions! Hope this helps :)
Answer:
12 and 2
Step-by-step explanation:
factor the euqation x^2-10x-22=2 and you get (x,-12)(x,2)=0 and when you solve that you get 12 and 2
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6.
Which is a true statement about the diagram?
m∠5 + m∠6 = m∠1
m∠3 + m∠4 + m∠5 = 180°
m∠1 + m∠2 = 180°
m∠2 + m∠3 = m∠5
Answer:
m∠1 + m∠2 = 180°
Step-by-step explanation:
An interior angle and its exterior angle are supplementary (they add up to 180°).
I would really appreciate it if you would mark me brainliest!
Have a blessed day!
Answer:
c
Step-by-step explanation:
The ratio of boys to girls in a group is 5:3. If there are 24 more boys than girls, work out how many girls there are
Answer:
36
Step-by-step explanation:
Let's call the # of boys and girls 5x and 3x respectively. We can write:
5x = 3x + 24
2x = 24
x = 12 so the # of girls = 12 * 3 = 36
Answer:
36 girlssolution,
Let the number of girls be X
Number of boys be 'x+24'
Now,
[tex] \frac{x + 24}{x} = \frac{5}{3} \\ or \: 3(x + 24) = 5x \\ or \: 3x + 72 = 5x \\ or \: 3x - 5x = - 72 \\ or \: - 2x = - 72 \\ or \: x = \frac{ - 72}{ - 2} \\ x = 36[/tex]
hope this helps..
Good luck on your assignment..
Mario writes the equation (x+y ) 2 = z 2 +4( 1 2 xy) (x+y)2=z2+4(12xy) to begin a proof of the Pythagorean theorem. Use the drop-down menus to explain why this is a true equation.
Answer:
For the drop down menu:
i) x + y
ii) z²
iii) ½ xy
The complete question related to this found on brainly (ID:16485977) is stated below:
Mario writes the equation (x+y)² = z² +4( 1/2 xy) to begin a proof of the Pythagorean theorem. Use the drop-down menus to explain why this is a true equation.
_____finds the area of the outer square by squaring its side length.
_____finds the area of the outer square by adding the area of the inner square and the four triangles.
These expressions are equal because they both give the areas of outer space.
Find attached the diagram of the question.
Step-by-step explanation:
Pythagoras theorem is a formula that shows the relationship between the sides of a right angled triangle.
Pythagoras theorem
Hypotenuse ² = opposite ² + adjacent ²
From the diagram of the question.
Hypotenuse = z
Opposite = y
Adjacent = x
z² = x² + y²
Area of outer square = area of inner square + 4(area of triangles)
area of inner square = length² = (x+y)²
Expanding area of the outer square:
(x+y)² = (x+y)(x+y) = x²+xy+xy+y²
(x+y)² = x²+y²+2xy
= z² + 2xy
Area of inner square = length² = z²
Area of triangle = ½ base × height
= ½ × x × y = ½ xy
Area of outer square = area of inner square + 4(area of triangles)
(x + y)² = z² + 4(½xy )
Therefore, it is a true equation.
( x + y )² finds the area of the outer square by squaring its side length.
z² + 4( 1/2xy ) finds the area of the outer square by adding the area of the inner square and the four triangles.
These expressions are equal because they both give the areas of outer space.
So for the drop down menu:
i) x + y
ii) z²
iii) ½ xy
The average (arithmetic mean) of a - 5 and a is x, and the average of a and a + 9 is y. What is the average of x and y?
a + 1
B) a +2
C) 2a + 1
D) 2a + 2
Answer:
The answer is "Option A"
Step-by-step explanation:
Given:
[tex]\to \frac{(a-5)+a}{2}=x.....(a)\\\\\to \frac{a+(a+9)}{2}=y.....(b)\\\\[/tex]
solve the above equation:
[tex]\to \bold{\frac{(a-5)+a}{2}=x}\\\\\to \frac{a-5+a}{2}=x\\\\\to \frac{2a-5}{2}=x\\\\\to \bold{\frac{a+(a+9)}{2}=y}\\\\\to \frac{a+a+9}{2}=y\\\\\to \frac{2a+9}{2}=y\\\\[/tex]
add both value (x and y):
[tex]\to \bold{x+y}\\\\\to \frac{2a-5}{2}+\frac{2a+9}{2}\\\\\to \frac{2a-5+2a+9}{2}\\\\\to \frac{4a+4}{2}\\\\\to \frac{2(2a+2)}{2}\\\\\to (2a+2)\\[/tex]
average of x and y:
[tex]\to \frac{x+y}{2}\\\\\therefore \bold{x+y= 2a+2}\\\\\to \frac{2(a+1)}{2}\\\\\to \boxed{(a+1)}\\[/tex]
A line passes through (2,-1) and (4,5). Which answer is the equation of the line?
Answer:
C.
Step-by-step explanation:
Slope = m = (y2 - y1)/(x2 - x1) = (5-(-1))/(4 - 2) = 6/2 = 3
Slope - point form:
y - y1 = m(x -x1)
y - 5 = 3(x - 4)
y - 5 = 3x - 12
- 3x + y = - 12 + 5
- 3x + y = - 7
Answer:
[tex] - 3x + y = - 7[/tex]Option C is the correct option.
Step-by-step explanation:
A line passes through ( 2 , -1 ) and ( 4 , 5 )
The equation of line:
[tex] \frac{y - y1}{x - x1} = \frac{y2 - y1}{x2 - x1} [/tex]
Plug the values
[tex] \frac{ y - ( - 1)}{x - 2} = \frac{5 - ( - 1)}{4 - 2} [/tex]
When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression
[tex] \frac{y + 1}{x - 2} = \frac{5 + 1}{4 - 2} [/tex]
Add the numbers
[tex] \frac{y + 1}{x - 2} = \frac{6}{4 - 2} [/tex]
Subtract the numbers
[tex] \frac{y + 1}{x - 2} = \frac{6}{2} [/tex]
Reduce the numbers with 2
[tex] \frac{y + 1}{x - 2} = 3[/tex]
Apply cross product property
[tex]3x - 6 = y + 1[/tex]
Move variable to L.H.S and change its sign
Similarly, Move constant to R.H.S and change its sign
[tex]3x - y = 1 + 6[/tex]
Add the numbers
[tex]3x - y = 7[/tex]
[tex] - 3x + y = - 7[/tex]
Hope this helps...
Best regards!
PLEASE HELP ME! can someone explain this to me pls?
need this ASAP. pls answer this question
Answer:
this is ur answer so memories
A linear function includes the ordered pairs (0, 3), (3, 9), and (9, n). What is the value of n?
Answer:
the value of n will be the range
Step-by-step explanation:
lets just give an example of (9,n) and you had to find the value its actually simple
9 is the domain
n is the range
a part of ordered pair function
got it?
To create a giant gemstone, sara first made two identical square pyramids that each had a base area of 100 square inches. Then she glued the pyramids' bases together to form the gemstone. The surface area of the gemstone is 520 square inches. What is the value of x? Explain.
Answer:
8 inches.
Step-by-step explanation:
From the statement we have that they first made two identical square pyramids, each with a base area of 100 square inches.
Ab = s ^ 2 = 100
Therefore each side would be:
s = (100) ^ (1/2)
s = 10
So, side of the square base = 10 inches
Then they tell us that they glued the bases of the pyramids together to form the precious stone. The surface area of the gemstone is 520 square inches, so for a single pyramid it would be:
Ap = 520/2 = 260
For an area of the square pyramid we have the following equation:
Ap = 2 * x * s + s ^ 2
Where x is the height of each triangular surface and s is the side of the square base
Replacing we have:
260 = 2 * x * 10 + 10 ^ 2
20 * x + 100 = 260
20 * x = 160
x = 160/20
x = 8
Therefore, the value of x is 8 inches.
Help help help please I need help fast
The answer would be x =7/5 because you would need to multiply everything by two. Then you would add 4+3 and you would end up with 5x = 7. After that, you need to divided both answers by five
Please Mark brainliest
Answer:
The answer is x=7/5
Step-by-step explanation:
because you have to multiply everything by 2 the add 4+3 and you end up with 5x=7 then divide both sides by 5
Which expression is equivalent to (–3y – x) – (5y – 8x)?
Answer:
-8y +7x
Step-by-step explanation:
(–3y – x) – (5y – 8x)Distribute
-3y -x -5y +8x
Combine like terms
-3y-5y -x+8x
-8y +7x
write a function that represents the situation: A population of 210,000 increases by 12.5% each year
Answer
y= 12.5x + 210,000
Step-by-step explanation:
This is a linear function because it is increasing constantly by 12.5 percent so it will me written as y=mx+b
The value of function that represents the situation is,
⇒ P = 210,000 (1.125)ⁿ
Where, n is number of years.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The situation is,
⇒ A population of 210,000 increases by 12.5% each year.
Now, Let number of years = n
Hence, The value of function that represents the situation is,
⇒ P = 210,000 (1 + 12.5%)ⁿ
⇒ P = 210,000 (1 + 0.125)ⁿ
⇒ P = 210,000 (1.125)ⁿ
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Can any one please help me I really need help please help me thank you
Step-by-step explanation:
Plug in -2 whenever u see x
3(-2) -7= 5(-2-1)
-6-7= -10-1
-13 = -11
Therefore, x is not equal to -2.
Rewrite the expression in the form k x z^n .
Answer:
(squareroot2^2) times 27 (1/2)
Step-by-step explanation:
Answer:3z^2/9
Step-by-step explanation:
Which of the following explains why cos 60º = sin 30° using the unit circle?
Eight years ago, twice Manuel's age was 36. What is Manuel's age now? Pls hell
Answer:
Hey there!
Eight years ago, Manuel's age was 36/2, or 18.
Now, his age is 18+8, or 26 years old.
So, he is 26 years old now.
Hope this helps :)
Please help me with this question (Will get brainlist)
Answer:
169=169
Step-by-step explanation:
The pythagoras theorem states that if
[tex] {a}^{2} + {b}^{2} = {c }^{2} [/tex]
Then the triangle is a right triangle
So
[tex]{5}^{2} + {12}^{2} = {13}^{2} [/tex]
[tex]25 + 144 = 169[/tex]
[tex]169 = 169[/tex]
Therefore A is a right triangle
Answer:
Step-by-step explanation:
The pythagorian theorem :now the longest edge is 13 cm so : 13²must be equal to 5²+12²
5²+12²= 169[tex]\sqrt{169}[/tex]= 13so this triangle must be right angled
In his pocket, Hamid has $2.95 in dimes and quarters. If there are 16 coins in total, which system represents the number of dimes and quarters that Hamid has? x + y = 16. 0.10 x + 0.25 y = 2.95. x + y = 16. 0.05 x + 0.25 y = 2.95. x + y = 2.95. 0.10 x + 0.25 y = 16. x + y = 16. 0.01 x + 0.25 y = 2.95.
Answer: x + y = 16. 0.10 x + 0.25 y = 2.95. x + y = 16.
Step-by-step explanation:
You know that there are 16 coins in all, so x + y has to equal 16 (x being dimes and y being quarters) but you also know that whatever compilation of dimes and quarters is equal to $2.95.
Hope this helped you! Feel free to ask any further questions!
The system of equations which represents the number of dimes and quarters that Hamid has are x+y=16 and 0.10x+0.25y=2.95.
What is equation?Equation is relationship between two or more variables that are expressed in equal to form. Equation of two variables look like ax+by=c. It is of many types like linear equation, quadratic equation, cubic equation, etc.
How to form equation?Suppose the number of dimes be x and the number of quarters be y.
According to question there are 16 coins, so
x+y=16-----1
1 dime=$0.10
1 quarter=$0.25
According to question Hamid has $2,95 ,so
0.10x+0.25y=2.95.
Hence the system which represents the number of dimes and quarters that Hamid has are x+y=16 and 0.10x+0.25y=2.95.
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Type the correct answer in each box, If necessary, use / for the fraction bar(s).
1
-1
The point on the number line shows the opposite of
or the opposite of the opposite of
Reset
Next
Answer: -1/1
Step-by-step explanation: The fraction, -1/1 or just -1, passes through the transactional point through the slope of the line, y=3x+5.
A cup holder in a car contains 19 quarters, 39 dimes, some number of nickels, and 58 pennies. If all the coins in the cup holder equal $10.08, then how many nickels are in the cup holder?
Answer:
17 nickels
Step-by-step explanation:
To be able to find the answer, you can say that the sum of the value of each coin multiply for its quantity is equal to 10.08, which you can express as follows:
quarters= 0.25
dimes= 0.10
nickels= 0.05
pennies= 0.01
(0.25*19)+(0.10*39)+(0.05*x)+(0.01*58)=10.08, where
x= the quantity of nickels
Now, you can solve for x:
4.75+3.9+0.05x+0.58=10.08
0.05x=10.08-4.75-3.9-0.58
0.05x=0.85
x=0.85/0.05
x=17
According to this, the answer is that there are 17 nickels in the cup holder.
Two points A (-2, 9) and B (4, 8) lie on a line l.Find the distance between points A and B.
Answer:
[tex]\sqrt{37}[/tex]
Step-by-step explanation:
Calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = A(- 2, 9) and (x₂, y₂ ) = B(4, 8)
d = [tex]\sqrt{(4+2)^2+(8-9)^1}[/tex]
= [tex]\sqrt{6^2+(-1)^2}[/tex]
= [tex]\sqrt{36+1}[/tex]
= [tex]\sqrt{37}[/tex] ≈ 6.1 ( to 1 dec. place )
Ardem has two lights one flashes every 15 seconds the other flashes every 42 seconds. They start flashing at the same time. After how many seconds will they next flash at the same time??
Answer: After 210 seconds they with next flash at the same time.
Step-by-step explanation:
Given: Ardem has two lights.
One flashes every 15 seconds the other flashes every 42 seconds.
If they started flashing at the same time, then the number of seconds after that they with next flash at the same time = LCM (15, 42) [LCM - Least common multiple]
Prime factorization of 15 = 3 x 5
Prime factorization of 42 = 2 x 3 x 7
Then, LCM (15, 42) = 2 x 3 x 5 x 7 = 210
i.e. After 210 seconds they with next flash at the same time.