Answer:
24 gallons per hour
Step-by-step explanation:
Connor filled his 150-gallon pool with water in 6.25, to find out how many gallons per hour he used, we have to divide the amount of gallons into every hour. Therefore:
150/6.25
24 gallons per hour.
The smith family wants to fence their yard. the yard is 96 meters and 52 meters wide. how much fencing will they need?
To solve the system of linear equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 by using the linear combination method, Henry decided that he should first multiply the first equation by –3 and then add the two equations together to eliminate the x-terms. When he did so, he also eliminated the y-terms and got the equation 0 = 0, so he thought that the system of equations must have an infinite number of solutions. To check his answer, he graphed the equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 with his graphing calculator, but he could only see one line. Why is this?
Answer:
Step-by-step explanation:
Both lines have same slope so the graph of both equation will be same and hence it will overlap each other that is why the Henry could only see one line.
Step-by-step explanation:
Given : A system of linear equation 3x - 2y = 4 and 9x - 6y = 12
We have to show whey when Henry graphed the equations 3x-2y=4 and 9x-6y=12 he could only see one line.
Consider the given system of linear equation
3x - 2y = 4 ................(1)
9x - 6y = 12 ..................(2)
Since,
Equation (2) is multiple of equation (1),
3 × ( 3x - 2y = 4) = 9x - 6y = 12
Also the slope of given equations are same
For equation (1),
Differentiate with respect to x, we get,
3-2dy/dx = 0
dy/dx = 3/2
Also for equation (2),
Differentiate with respect to x, we get,
9 - 6dy/dx = 0
dy/dx = 9/6 = 3/2
Since, both lines have same slope so the graph of both equation will be same and hence it will overlap each other.
That is why the Henry could only see one line.
Can someone help me understand how to solve 4 please. Would really appreciate it.
The length of RT from the figure is 8 units
Pythagoras theorem applicationIn order to find the measure of RT, we will use the pythagoras theorem. According to the theorem;
hypotenuse² = adjacent² + opposite²
From the given figure;
ST = hyp = 10
RS = adj = 6
Find RT
RT = √10² - 6²
RT = √100 - 36
RT = √64
RT = 8 units
Hence the length of RT from the figure is 8 units
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Oscar's spinner has scores from 1 to 4. The table shows the probabilities of scores 1, 2 and 3
1=0.1
2=0.5
3.0.1
4=?
Work out 4
Santa seated his guests so that X number of people sat at each of Y number of tables. Mrs. Claus placed Y number of people at each table, but she had X number of tables. Compare the number of guests Santa and Mrs. Claus were able to seat.
Answer:
they are the same
Step-by-step explanation:
The number of guests seated were, in each case, ...
(guests per table) × (number of tables)
__
For Santa, this product is ...
X × Y
For Mrs. Claus, this product is ...
Y × X
The commutative property of multiplication tells you that ...
XY = YX
The numbers of guests were the same.
A camera lens magnifies an object 10 exponent 3 times. The length of an object is
10 exponent -4 centimeter. What is its magnified length?
Answer:
10^3/10^-4
Step-by-step explanation:
FROM MATH MULLIGAN
What is Lens Focal Length
Focal length, usually represented in millimeters (mm), is the basic description of a photographic lens. It is not a measurement of the actual length of a lens, but a calculation of an optical distance from the point where light rays converge to form a sharp image of an object to the digital sensor or 35mm film at the focal plane in the camera. The focal length of a lens is determined when the lens is focused at infinity.
Lens focal length tells us the angle of view—how much of the scene will be captured—and the magnification—how large individual elements will be. The longer the focal length, the narrower the angle of view and the higher the magnification. The shorter the focal length, the wider the angle of view and the lower the magnification.
The magnified length of the object is 10⁻¹ m
What is magnified length?An image is said to be magnified when its size is greater than that of the object, and it is said to be diminished when its size is smaller than that of the object.
Given that,
A microscope magnifies an object 10³ times. The length of an object is 10⁻⁴ meters. The magnified length is:
10³ × 10⁻⁴ m
We can solve this by applying the Product of Powers Property. This property states that to multiply powers having the same base, we have to add the exponents.
10³ × 10⁻⁴ m
= 10³⁺⁽⁻⁴⁾ m
= 10³⁻⁴ m
= 10⁻¹ m
Hence, the magnified length is 10⁻¹ m.
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Which of the following is a linear function?
A. y=1 over x
B. y=x²
C. y=x
D. y=√x
Answer:
C
Step-by-step explanation:
Line A is perpendicular to Line B.
If the slope of Line A is 3
what is the slope of Line B?
Answer:
- 1/3
Step-by-step explanation:
m = slope of a line
Perpindicular slope = - 1/m
= - 1/3
Let slope of that line be m
We know product of slopes of two perpendicular line=-1
3m=-1m=-1/3Consider the line 3x+8y= 1.
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
Answer:
slope of a line parallel to this line= -3/8
slope of a line perpendicular to this line= 8/3
Step-by-step explanation:
The general equation of a line in terms of a and b is:
y=ax+b where a=slope
in order to get the slope of the line we have to write its equation as the form shown above:
3x+8y=1
8y= -3x+1
y= (-3/8)x+(1/8)
so slope= -3/8
Parallel lines have equal slopes
⇒ slope of parallel line= -3/8
The slope of the line perpendicular to another line is the opposite reciprocal of the original line's slope. This means that we have to exchange the numerater by the denomenator and multiply the obtained number by a negative sign:
⇒ slope of perpendicular line= -(-8/3) = 8/3
please explain thourougly thanks!
Answer:
There are 2 x-intercepts
Step-by-step explanation:
The equation has 2 x variables, so the graph would have 2 x -intercepts.
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's use the discriminant method, we have to find discriminant of the given quadratic function, if discriminant is greater than 0, then it has two intercepts, if it is equal to 0, then it has 1 intercepts and if it is smaller than 0, then it has no x intercepts.
[tex]\qquad \sf \dashrightarrow \:D = {b}^{2} - 4ac[/tex]
where, a, b and c are coefficients of x², x and constant term. D = discriminant
[tex]\qquad \sf \dashrightarrow \:D = {( - 30)}^{2} - 4(22 \times 1)[/tex]
[tex]\qquad \sf \dashrightarrow \:D = 900 - 4(22 )[/tex]
[tex]\qquad \sf \dashrightarrow \:D = 900 - 88[/tex]
[tex]\qquad \sf \dashrightarrow \:D = 812[/tex]
Discriminant is greater than 0, hence it has two x - intercepts.
Select all the true statements about the following parallelogram
Answer:
it is D. and A.
Step-by-step explanation:
um because
pls help me i have a 0 for math
Answer:3p
Step-by-step explanation:
405 0p x 7
Jeffrey is looking at a map of his town to help him get from his school to the library. If 1 inch is equal to 9 miles, and the distance on the map is 1/4
inch, how far is it to the library?
Answer:
2.25 miles
Step-by-step explanation:
1/4 of 9 is 2.25
Answer:
2.25 miles away
Step-by-step explanation:
first make 1/4 a percent
second set up a proportion
then solve the proportion and then you get 2.25 and add a label
If a trapezoid has bases with lengths of 10 cm and 20 cm, and the height is 12 cm, what is the area
of the trapezoid?
Answer:
180
((10 + 20/2) * 12 = 180
Step-by-step explanation:
Step-by-step explanation:
Given;
b = 10cm
a = 20cm
h = 12cm
Area of trapezoid = 1/2 *h*(a+b)
= 1/2 *12* ( 20+10)
= 180cm^2
A right circular cylinder has a height of 2214 ft and a diameter 225 times its height.
What is the volume of the cylinder?
Enter your answer as a decimal in the box. Use 3.14 for pi and round only your final answer to the nearest hundredth.
Answer:
v = 3,463,118,874
Step-by-step explanation:
2214 * 225 = 498,510
diameter = 498,510
v = pi(d) * h
v = 3.14(498,510) * 2214
v = 1,564,191 * 2214
v = 3,463,118,874
arrange in ascending order : 39, 31, 50, 18, 51, 63, 10, 34, 42, 89, 73, 11, 33, 31, 41, 25, 76, 13, 26, 23, 29, 30, 51, 91, 37, 64, 19, 86, 9, 20
Step-by-step explanation:
9, 10,11, 13,18,19,20,23,25,26,29,30,31,31,33,34,37,39,41,42,50,51,51,63,64,73,76,86,89,91
Answer:
9, 10, 11, 13, 18, 19, 20, 23, 25, 26, 29, 30, 31, 31, 33, 34, 37, 39, 41, 42, 50, 51, 51, 63, 64, 73, 76, 86, 89, 91
Find the length indicated. Round answer to the nearest tenth.
Please and thank you so very much!!!!! See picture for the full problem.
Answer:
18.1
Step-by-step explanation:
All radii of a circle are congruent (same length), which means if we draw in a radius from the center to the end of the 16.3, it would be the same length of x.
Now we can use sa very simple theorem.... the pythagorean therom!
[tex]7.9^{2} + 16.3^{2} = x^{2} \\62.41 + 265.69 = x^{2} \\328.1 = x^{2} \\18.1 = x[/tex](rounded)
I hope this helps you.
please help me if you can tysm! :))))
Answer:
9.9
Is the answer to the question
given the room below describe how you would find the perimeter and area?
Perform the following
mathematical operation, and
report the answer to the
correct number of significant
figures.
45.2 x 0.035 =
Answer:
4
Step-by-step explanation:
45.2 x 0.035=1.582
"Significant figures are the number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value. We start counting significant figures at the first non-zero digit." -Khan Academy. org > significant figures
Answer: 1.6 is the answer
Step-by-step explanation:
45.2 x 0.035 = 1.582
After you do that step Then you'll need to round 1.582 up in the tenths, and it should be 1.6!
Hope this helps
what are the magnitude and direction of u+v+w ?
The magnitude and the direction of the resultant are approximately 57.871 and 198.676°.
How to determine the magnitude and the direction of a resultantVectors are elements with two given characteristics: Magnitude and direction. A resultant is derived from the sum of vectors, the magnitude is the norm of a vector and the direction is the orientation of a vector. The resultant and its characteristics are described below:
Resultant[tex]\vec r = \left(\sum\limits_{i=1}^{n}x_{i}, \sum\limits_{i=1}^{n}y_{i}\right)[/tex] (1)
Magnitude[tex]\|\vec r\| = \sqrt{\left(\sum\limits_{i=1}^{n} x_{i}\right)^{2}+\left(\sum\limits_{i=1}^{n} y_{i}\right)^{2}}[/tex] (2)
Direction[tex]\theta = \tan^{-1}\frac{\sum\limits_{i=1}^{n}y_{i}}{\sum\limits_{i=1}^{n}x_{i}}[/tex] (3)
Where [tex]\theta[/tex] is resultant angle, measured in degrees.
If we know that [tex]\|\vec u\| = 90[/tex], [tex]\theta_{u} = 40^{\circ}[/tex], [tex]\|\vec v\| = 60[/tex], [tex]\theta_{v} = 20^{\circ}[/tex], [tex]\|\vec w\| = 40[/tex] and [tex]\theta_{w} = 30^{\circ}[/tex], then the resultant, its magnitude and its direction:
Resultant[tex]\vec r = (-90\cdot \cos 40^{\circ}-60\cdot \sin 20^{\circ}+40\cdot \cos 30^{\circ}, 40\cdot \sin 30^{\circ}+60\cdot \cos 20^{\circ}-90\cdot \sin 40^{\circ})[/tex]
[tex]\vec r = (-54.824, 18.531)[/tex]
Magnitude[tex]\|\vec r\| = \sqrt{(-54.824)^{2}+18.531^{2}}[/tex]
[tex]\|\vec r\| \approx 57.871[/tex]
Direction[tex]\theta = \tan^{-1} \left(\frac{18.531}{-54.824}\right)[/tex]
[tex]\theta \approx 198.676^{\circ}[/tex]
The magnitude and the direction of the resultant are approximately 57.871 and 198.676°. [tex]\blacksquare[/tex]
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Please help me with this!
What is the distance between ( − 2 , − 4 ) and ( 5 , 7 ) ? Use the distance formula, d = √ ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 .
4.24
6.32
10.25
13.03
Answer:
13.03
Step-by-step explanation:
Suppose ( x₁ , y₁ ) = ( − 2 , − 4 ) and (x₂ , y₂ ) = (5 , 7)
In the formula : d = √ [( x₂− x₁ )² + ( y₂ − y₁ )²]
Just replace x₁ by -2
replace y₁ by -4
replace x₂ by 5
replace y₂ by 7
We get ,
d = √ [( 5− (-2) )² + ( 7 − (-4) )²]
Then
d = √ [(7 )² + ( 11 )²]
d = √ [49 + 121]
d = √ [170]
≈ 13.03
Shaquil needs to borrow $400. the loan company charges him $80 in fees for the loan. shaquil calculates that the annual percentage rate (apr) on his loan is 250%. approximately what is the term of shaquil’s loan? a. 7 days b. 29 days c. 46 days d. 73 days please select the best answer from the choices provided a b c d
The term of shaquil's loan will be 29 days approximatly.
We have given that,
Principle amount (p) = $400
Rate (r)= 250% = 2.5
Interest = $80
t = time (in days) = t/365
What is the formula simple interest?
[tex]I=prt[/tex]
[tex]r=\frac{I}{rt}[/tex]
[tex]2.5 = \frac{80\times 365}{400\times t}[/tex]
[tex]t= \frac{80\times 365}{400\times 2.5}[/tex]
[tex]t=\frac{73}{2.5}\\ \\t=29.2[/tex]
t = 29.2
t = 29 days
Therefore option (B) is correct.
Therefore the term of shaquil's loan will be 29 days approximatly.
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Answer:
B.29 days
Step-by-step explanation:
The solution set of the system of inequalities below forms a triangle on the coordinate plane. What are the vertices of the triangle?
a.
(0,10), (3,4), (8,14)
c.
(-20,0),(1,0),(8/14)
b.
(0,0), (8,0), (8,14)
d.
(0,10),(3,4),(6,10)
i think its a but i may be rong if i am just know i tryed my vary best and that i am super sorry
Betty's bedroom is 18ft
long and 25 ft wide. She
wants to install the
hardwood flooring. The
cost is $6.00 per square
foot. How much is the
total cost for room
flooring?
Answer:
You'll need to find the area first.
18ft x 25ft= 450ft
Area is 450ft.
Area divided by $6.00 = 75
The total cost is $75 dollar for the whole room flooring.
A small movie theater sells children's tickets for $4 each and adult tickets for $10 each for an animated
movie. The theater sells a total of $388 in ticket sales.
(a) If c represents the number of children's (b) Show that c= 52 and a =18 is a solution to
tickets sold and a represents the number of
this equation (not system).
adult tickets sold, write an equation that
models the information shown above.
C) Show that after multiplying both sides of the
equation in (a) by 2, c=52 and a=18 is
still a solution to this equation.
(d) How can you interpret multiplying both sides
of the equation by 2 in letter (a) in terms of
ticket prices and total ticket sales?
Answer:
b) Show that c= 52 and a =18 is a solution to
tickets sold and a represents the number of
this equation (not system).
Linear equation that models the given equation is 4c + 10a = 388 where c is the number of children ticket sold and a is the number of adult ticket sold. c = 52 and a = 18 is a solution to the linear equation. Multiplying a constant on both sides of the equation won't affect its solutions.
What is linear equation?A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line. This is the reason why it is named as a 'linear equation'.
Let number of children ticket sold be c.
Let number of adult ticket sold be a.
Cost of one children ticket = $4.
Cost of one adult ticket = $10.
Total sales = $388
Linear equation that models the above equation: 4c + 10a = 388
Checking if a = 18 and c = 52 is a solution of the equation. It can be done by substituting the values.
LHS: 4c + 10a = 4*52 + 10*18 = 388
RHS: 388
Hence, c = 52 and a = 18 is a solution to the linear equation.
Multiplying 2 to both sides of the equation:
2(4c + 10a) = 2(388)
8c + 20a = 776
Substituting c = 52 and a = 18.
8(52) + 20(18) = 776
c = 52 and a = 18 is still a solution to the linear equation.
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I NEED HELP ASAP !!!!!!!
Answer:
$42,782.40
Step-by-step explanation:
You want to know how much more Glados paid than Shaq on a 30-year mortgage if their monthly payments were $755.99 and $637.15, respectively.
Added amountEach month, Glados paid this amount more:
$755.99 -637.15 = $118.84
Over the 360-month life of the 30-year loan, this excess amount adds up to ...
360 × $118.84 = $42,782.40
Glados pays $42,782.40 more than Shaq for the same loan amount.
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The problem is on the screenshot
Answer:
x=1 y=4
x=2 y=7
x=3 y=10
Step-by-step explanation:
To find the answer, you have to plug in the x-value for the equation to find y.
You will then find out that every time x increases by 1, y increases by 3.
Find the volume of the cylinder. Explain or show your reasoning. All measurements are in centimeters
Answer:
200π cm³ (in term of π)
628 cm³ (when define π = 3.14)
Step-by-step explanation:
Given:
radius of circular base = 5height = 8Volume of Cylinder:
[tex]\displaystyle \large{V=\pi r^2h}[/tex]
If you notice, the volume of cylinder is area of circular base * height.
Input given information in the formula:
[tex]\displaystyle \large{V=\pi \cdot 5^2 \cdot 8}[/tex]
Evaluate:
[tex]\displaystyle \large{V=\pi \cdot 25 \cdot 8}\\\displaystyle \large{V=200 \pi}[/tex]
Since all measurements are in centimeters. Therefore, our unit is cm³ since we are finding volume which is three-dimensional.
Fact
cm is used for one-dimensional measurement such as line.cm² is used for two-dimensional measurement such as area.cm³ is used for three-dimensional measurement such as volume.However, you didn’t specific which π value/digit should we use so I’ll only put both solutions in where first being in term of π and second being 3.14.
Therefore, the volume is:
200π cm³628 cm³Prove: An even times an even is
an even.
Answer: 4
Step-by-step explanation:
i just guessed and it was right, sorry i don't have a better explanation than that
