Answer: 15,625 ft³
Step-by-step explanation:
You need to use the formula for calculate the volume of a cylinder:
[tex]V=r^2h\pi[/tex]
Where r is the radius and h is the height.
You know the radius and the volume of the old tank, therefore you can find the height as following:
[tex]10,000=(12)^2h\pi\\\\h=\frac{10,000}{(144)\pi}ft[/tex]
You know that the radius of the new tank is 15 feet and it has the same height as the old tank. Therefore, you can substitute h into the first equation for calculate the volume of a cylinder, to find the maximum number of cubic feet of water that the new storage tank will hold:
[tex]V=(15ft)^2(\frac{10,000}{(144)\pi}ft)\pi=15,625ft^3[/tex]
Answer:
15625 cubic feet
Step-by-step explanation:
If two sides of one triangle are proportional to two sides of another and included angles are equal, then the triangles are similar. True False
Answer:
True
Step-by-step explanation:
It was correct on my quiz
f(x)= x^2 -16x+63 find the x-intercepts of this function
Answer:
The x-intercepts will be, x= 7 or x =9
Step-by-step explanation:
f(x)= x^2 -16x+63
At the x-intercept, f(x) is zero.
Therefore;
x² - 16x + 63 = 0
solving it quadratically;
product = 63
Sum = -16
x² - 9x - 7x + 63 = 0
x(x-9) - 7( x-9) = 0
(x-7) (x-9) = 0
x = 7 or x = 9
Therefore;
The x-intercepts will be, x= 7 or x =9
Answer:
(7, 0) and (9, 0)
Step-by-step explanation:
The x-intercepts refers to the points where the graph of the function crosses the x-axis, or simply the zeroes of the function. In this case, we can determine these points analytically or graphically. We simply graph the function;
y = x^2 -16x +63 then determine where the function crosses the x-axis; see the attachment below;
The x-intercepts of this function are;
(7, 0) and (9, 0)
How many times does 3 go into 100??
Final answer:
In mathematics, to find out how many times 3 goes into 100, we divide 100 by 3, resulting in 33 times with a remainder of 1.
Explanation:
The question posed is concerned with division, which falls under the subject area of mathematics. When we consider how many times 3 goes into 100, we are calculating the number of times the number 3 can be subtracted from 100 until we reach zero or a number less than 3. To solve this problem, we use division.
To divide 100 by 3, you would start by seeing how many groups of 3 are in 100. Performing the division gives us 33 with a remainder of 1, which means that 3 goes into 100 a total of 33 times with 1 left over. Therefore the quotient (the result of division) is 33 and the remainder is 1.
The concept being described in the reference material, which mentions exponents and their use to indicate repeated multiplication of a base number, is not directly related to this question, hence it will not be incorporated in the calculation of the division of 3 into 100.
A system of equations is shown. 2x + 2y = 17 4x - y = 25 what is the x-value of the solution to the system of equations
Answer:
x=6.7
Step-by-step explanation:
What you have to do is you have to eliminate y. So you need to make y cancel each other out.
2x+2y=17. I can multiply 2 to the second equation to cancel the y's out.
8x-2y=50.
10x=67.
x=67/10 or 6.7.
The value of x for the system of equations will be x=6.7.
What is a system of equations?A set of simultaneous equations is a finite set of equations for which common solutions are sought in mathematics. It is also known as a system of equations or an equation system.
Given that the two equations are 2x + 2y = 17 and 4x - y = 25. The value of x will be calculated by eliminating the variable y from the equation.
Multiply the second equation by 2 and subtract from the first equation,
2x+2y=17.
8x-2y=50.
10x=67.
x= 67/10
x = 6.7.
Therefore, the value of x for the system of equations will be x=6.7.
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If Tina cuts a lawn by herself, she can finish in 5 hours. If bill cuts the same lawn by himself it takes him two hours longer than Tina. How long will it take them both working together?
Final answer:
Tina and Bill will take approximately 2 hours and 55 minutes to finish cutting the lawn when they work together, combining their individual rates of work.
Explanation:
If Tina cuts a lawn by herself, she can finish in 5 hours. If Bill cuts the same lawn by himself it takes him two hours longer than Tina, which means it takes Bill 7 hours. To determine how long it will take both of them working together, we can use the rates at which they work. Tina's rate of work is 1/5 of the lawn per hour, and Bill's rate is 1/7 of the lawn per hour. Working together, their combined rate is the sum of their individual rates, which is (1/5 + 1/7) of the lawn per hour.
To find the combined rate, we calculate:
(1/5) + (1/7) = (7/35) + (5/35) = 12/35 of the lawn per hour. To find out how long it will take them to finish the lawn together, we take the reciprocal of this combined rate. Therefore, 35/12 hours, or 2 hours and 55 minutes, is the amount of time they will need to finish cutting the lawn when working together.
15 A store manager receives a delivery
of 2 boxes of lightbulbs. Each box
contains 25 lightbulbs. The store
manager tests all the lightbulbs and
finds that 2 of them are defective.
Based on these results, what can
the store manager predict about the
next delivery of lightbulbs?
A A delivery of 3 boxes will contain
3 more defective lightbulbs than
a delivery of 2 boxes.
B A delivery of 4 boxes will contain
2 more defective lightbulbs than
a delivery of 2 boxes.
C A delivery of 5 boxes will contain
10 more defective lightbulbs than
a delivery of 2 boxes.
D
A delivery of 6 boxes will contain
3 more defective lightbulbs than
a delivery of 2 boxes.
Answer:
B
Step-by-step explanation:
For each box, there is 1 defective lightbulb. Therefore, a delivery of 4 boxes will have 4 defective lightbulbs. A delivery of 2 boxes has 2 defective lightbulbs. 4 defective lightbulbs subtracted by 2 defective lightbulbs equals 2 more defective lightbulbs in 4 boxes than 2. Therefore, it is B.
Which value is equivalent to x-7/7-x
Answer:
[tex]\large\boxed{\dfrac{7-x}{x-7}=-1}[/tex]
Step-by-step explanation:
[tex]\dfrac{7-x}{x-7}=\dfrac{-(x-7)}{x-7}\\\\\text{cancel}\ (x-t)\\\\\dfrac{7-x}{x-7}=\dfrac{-1}{1}\\\\\dfrac{7-x}{x-7}=-1[/tex]
Answer:
-1
Step-By Step:
The Answer on Ed
What is the result when you convert 7/8 to a percent?
Answer:
87.5%
Step-by-step explanation:
Wyatt ate 1/12 of a banana. Shane ate 7/12 of a banana. How much more did Shane eat than Wyatt?
Answer:
7/12 - 1/12 = 6/12
Step-by-step explanation:
Answer:
The answer should be 6/12 or 1/2
factor please help 30z^2-53z+12
Answer:
(2z - 3)(15z - 4)
Step-by-step explanation:
To factor the quadratic
Consider the factors of the product of the coefficient of the z² term and the constant term which sum to give the coefficient of the z- term
product = 30 × 12 = 360 and sum = - 53
The factors are - 45 and - 8
Use these factors to split the z- term
30z² - 45z - 8z + 12 ( factor the first/second and third/fourth terms )
= 15z(2z - 3) - 4(2z - 3) ← factor out (2z - 3)
= (2z - 3)(15z - 4) ← in factored form
If x= 19 and both are adjacent can you find the angle relation ship?
Answer:
8
Step-by-step explanation:
EASY QUESTION 20 POINTS& BRAINLIEST
Graph the system of equations. {3x+y=6 −3x−4y=12
please add a pic of the graph or give me the correct coordinates and explain.Thanks :)
Answer:
See explanation below, and see attached photo for graphs
Step-by-step explanation:
To graph 3x + y = 6, find the x and y intercepts.
We get the x intercept when y = 0, so plug in 0 for y and solve...
3x + 0 = 6
3x = 6
x = 2, so the x intercept is at (2, 0)
We get the y intercept when x = 0, so plug in 0 for x and solve...
3(0) + y = 6
y = 6, so the y intercept is at (0, 6)
Plot those two points and draw a line through them
To graph -3x - 4y = 12, find the x and y intercepts.
We get the x intercept when y = 0, so plug in 0 for y and solve...
-3x - 4(0) = 12
-3x = 12
x = -4, so the x intercept is at (-4, 0)
We get the y intercept when x = 0, so plug in 0 for x and solve...
-3(0) - 4y = 12
-4y = 12
y = -3, so the y intercept is at (0, -3)
Plot those two points and draw a line through them
The system of equations 3x + y = 6 and -3x - 4y = 12 is graphed by converting each to slope-intercept form, plotting points, and drawing lines. Intersection is found by solving the equations simultaneously, resulting in the intersecting point (4, -6).
Explanation:To graph the system of equations consisting of 3x + y = 6 and -3x - 4y = 12, we first need to solve each equation for y to get them into slope-intercept form (y = mx + b). Here are the steps:
For the first equation, 3x + y = 6, subtract 3x from both sides to get y = -3x + 6.For the second equation, -3x - 4y = 12, start by adding 3x to both sides to get -4y = 3x + 12, then divide everything by -4 to get y = -3/4x - 3.Next, we plot the lines on a coordinate plane by finding at least two points for each line based on the equations we've just derived:
For y = -3x + 6, we could use x = 0 (which gives us y = 6) and x = 2 (which gives us y = 0).For y = -3/4x - 3, we could use x = 0 (which gives us y = -3) and x = 4 (which gives us y = -6).After plotting these points for each line, draw straight lines through the points to complete the graph. The coordinates of the intersection of the two lines can be found by setting the two equations for y equal to each other and solving for x:
-3x + 6 = -3/4x - 3Multiplying every term by 4 to clear fractions: -12x + 24 = -3x - 12Add 12x to both sides: 24 = 9x - 12Add 12 to both sides and divide by 9: x = 4Substitute x = 4 into y = -3x + 6 to find y: y = -3(4) + 6 = -12 + 6 = -6Therefore, the intersection point is at (4, -6).
Determine the translation.
A translation by___ units to the (right/left) and ___ units (up/down)
it went to the right 4 units and up 2 units
Which equation is graphed here?
Answer:
y+4=-3/2(x-2) is the answer
Step-by-step explanation:
Again over here just use the y=mx+c
m which is the slope is change in y over change in x which in this case is [tex]\frac{-3}{2}[/tex] so which just that we can cross out the first option for the answer secondly to be able to find C just take literally any point from the graphed line, for instance we take (-2,2), just add it in the equation and solve for C
[tex]2=-\frac{3}{2}(-2)+c\\2=3+c\\0=3-2+c\\c=-1[/tex]
y=-3/2-1
Now all you have to see is which of the three equations is equivalent to the one we just found
y+4=-3/2(x-2) is the answer :)
7(c - 12)= -21 what is c?
Answer:
c=9
Step-by-step explanation:
7(c - 12)= -21
Divide each side by 7
7/7(c - 12)= -21/7
c-12=-3
Add 12 to each side
c-12+12 = -3+12
c = 9
Answer: c = 9
Step-by-step explanation:
7(c - 12)= -21
Divide each side by 7
7/7(c - 12)= -21/7
c-12=-3
Add 12 to each side
c-12+12 = -3+12
c = 9 ← Answer
* Hopefully this helps:) Mark me the brainliest:)!!
What is the maximum height, in feet, the ball will attain?
Answer:
[tex]h = 227\ ft[/tex]
Step-by-step explanation:
We know that the equation that models the height of a projectile as a function of time is:
[tex]h(t) = -16t ^ 2 +v_0t +h_0[/tex]
Where:
[tex]v_0[/tex] is the initial velocity
[tex]h_0[/tex] is the initial height of the projectile.
In our case, the height of the machine is 2 ft.
Then [tex]h_0 = 2\ ft[/tex]
The initial speed is 120 ft/s.
So the equation of the height for this case is:
[tex]h(t) = -16t ^ 2 + 120t + 2[/tex]
This is a quadratic equation whose main coefficient is negative.
The maximum value of the function is at its vertex.
For a quadratic function of the form:
[tex]at ^ 2 + bt + c[/tex]
the vertex of the equation is given by the expression:
[tex]x =\frac{-b}{2a}[/tex]
[tex]y = f(\frac{-b}{2a})[/tex]
In this case:
[tex]a = -16\\b = 120\\c = 2[/tex]
Then the maximum point occurs instantly:
[tex]t = -\frac{120}{2(-16)}\\\\t = 3.75\ s[/tex]
Finally the maximum atura is:
[tex]h(3.75) = -16(3.75) ^ 2 +120(3.75) + 2[/tex]
[tex]h = 227\ ft[/tex]
complete the square to solve the equation below. x^2+2x-9=15
Answer:
Step-by-step explanation:
x^2+2x-9=15
x^2+2x=24
x^2+2x+1=24+1
(because what you do to one side you do to the other) ^
(x+1)^2=25
(x+1)^2 -25=0
(25 is a perfect square)
(x+1-5)(x+1+5)
(x-4)(x+6)
x=4,-6
Answer: x=-6; x=4
Step-by-step explanation:
If the greatest value of n is 8, which inequality best shows all the possible values of n? (5 points) n < 8 n ≤ 8 n > 8 n ≥ 8
WRITE AND SOLVE A DIVISON EQUATION TO FIND THE NUMBER OF 1/3 POUND HAMBURGER PATTIES THAT CAN BE MADE 4 POUNDS OF GROUND BEEF.
Answer:
12 patties
Step-by-step explanation:
4 ÷ 1/3 = 12
To the nearest hundredth, what is the length of line segment AB ? The length of line segment AB is approximately ______ units.
A. 2.45
B. 2.16
C. 7.75
D. 8.25
Answer:
D. 8.25Step-by-step explanation:
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
From the graph we have the points A(2, 2) and B(-6, 4). Substitute:
[tex]AB=\sqrt{(-6-2)^2+(4-2)^2}=\sqrt{(-8)^2+2^2}=\sqrt{64+4}=\sqrt{68}[/tex]
[tex]AB\approx8.25[/tex]
Twenty-five percent of 200 is what number?
Answer:
12.5
Step-by-step explanation:
25/200
Answer:
50
Step-by-step explanation:
0.25 x 200 = 50
What is a-2÷5a+a+2÷5a
Answer:
=2a
Step-by-step explanation:
a-2/5a and a+2/5a cancel each other out and your left with a+a aka 2a
Evaluate 5x2−9 when x=−2
answer: 11
explanation: just plug in -2 for x. the new problem becomes 5(-2)^2 - 9. Negative two squared is 4. 5 times 4 is 20. 20 minus 9 is 11.
Final answer:
When evaluating the expression 5x^2 - 9 for x = -2, we substitute -2 into the expression and find that the value is 11.
Explanation:
To evaluate the expression 5x2 − 9 when x = −2, we first substitute the value of x into the expression and then perform the calculation:
5(−2)2 − 9
→ 5(4) − 9
→ 20 − 9
→ 11
Therefore, when x = −2, the value of the expression 5x2 − 9 is 11.
What is the product ?
(4y-3)(2y^2+3y-5)
Answer:
8y^3 + 6y^2 - 29y + 15
Step-by-step explanation:
8y^3 + 12y^2 - 20y - 6y^2 - 9y + 15
then
8y^3 + 6y^2 - 29y + 15 is the product
Best regards
Answer:
=8y^3+6y^2−29y+15
Step-by-step explanation:
(4y−3)(2y^2+3y−5)
=(4y+−3)(2y^2+3y+−5)
=(4y)(2y^2)+(4y)(3y)+(4y)(−5)+(−3)(2y^2)+(−3)(3y)+(−3)(−5)
=8y^3+12y^2−20^y−6y^2−9y+15
=8y^3+6y^2−29y+15
What are the solutions to the equation 3x-4y-8=12
Answer:
y= 3
--- X +1
4
Step-by-step explanation:
-4y=-3x-12+8
-4y=-3x+4
--- --- -
4 4 4
y= 3
--- X +1
4
What is the least common multiple of 14 and 4
Answer:
28
Step-by-step explanation:
It is often convenient to compute the Least Common Multiple (LCM) as the product of the numbers divided by their greatest common factor. In this case, that would be ...
LCM = (14 × 4)/2 = 28
___
As a check, you can do it by looking at the prime factors of these numbers. The LCM will be the product of the unique factors to their highest powers.
14 = 2·7
4 = 2^2
Unique factors are 2 and 7. The highest power of 2 is 2; the highest power of 7 is 1.
LCM = 2^2·7 = 28
Start by setting up a factor tree for 4 and 14.
4 factors as 2 · 2 and 14 factors as 7 · 2.
When finding the least common multiple, we're looking for factors that match up and here we have a pair of 2's that matches up.
So our least common multiple is 2 from the 2's that match up × the the 2 that doesn't match up x the 7 from the 7 that doesn't match up.
So we have 2 × 2 × 7 or 4 × 7 which is 28.
On my whiteboard, I have attached my factor tree.
A new record will be set if the temperature is less than –15°F. Which inequality shows the temperatures when a new record will be set?
A. t < –15
B. t > –15
C. t < 15
D. t > 15
Answer:
A. t < –15
Step-by-step explanation:
The temperature has to be less than -15
t < -15
HELP ASSAP WILL MARK BRAINIEST!!!!!!
Answer:
m= -5/4
Step-by-step explanation:
Slope can be translated to "rise over run". You go down 5 spaces and then move over 4 spaces.
Which of the following illustrate the commutative property? Select all that apply
The expressions that illustrate the commutative property are: A, D, E, and F (see attachment below).
What is the Commutative Property?The commutative property states that the addition or multiplication of numbers will give the same product or sum even if the the order of arrangement is changed.Thus, for addition, the property applies thus: a + b = b + a.Thus, for multiplication, the property applies thus: ab = ba.The commutative property does not apply to division and subtraction.Therefore, the expressions that illustrate the commutative property are: A, D, E, and F (see attachment below).
Learn more about commutative property on:
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if f(x) is a linear function, which statement must be true ?
a) f(x) has no constant term
b) f(x) has no x^2 term
c) f(x) has no terms with a coefficient other than 1
d) f(x) has no x term
Answer:
b) f(x) has no x^2 term
Step-by-step explanation:
The general form of a linear function is:
f(x) = ax + b
Where a and b are constant terms and x is the variable.
Option a:
This statement may or may not be true. We can have a linear function with no constant term for example f(x) = 5x is a linear function with no constant and f(x) = 5x + 5 is a linear function with a constant term. So option a cannot be the answer
Option b:
This statement is true for a linear function. x^2 term can be found in quadratic and higher degree polynomials. In linear function the power of variable must be 1.
Option c:
The function can have terms with coefficients other than 1 e.g f(x) = 5x + 5. So this is not true either
Option d:
f(x) must have x term. So this option is also not correct.
Therefore, the correct answer is option b.
Answer:
The correct statement is (b) which is f(x) has no [tex]x^2[/tex] term
Explanation:
The graph of a linear equation is a straight line. The general form of a linear equation is
ax + by + c = 0
Here, the coefficients a and b can't be zero simultaneously.
The term 'c' is a constant and can be zero.
We can see that the exponent on each variable x and y is 1. So, if the exponent in any variable is not 1 then that will not be a linear equation.
Other than this, the coefficients a and b can be zero at a time.
If a = 0 , then the x term will be zero.If b = 0, then the y term will be zero.Therefore, on the basis of these facts, we can conclude that the necessary condition for an equation is to be a linear equation is " it should not have any [tex]x^2[/tex] term"
If we have [tex]x^2[/tex] in our equation then it will be a quadratic equation.
Therefore, option b is correct.
Further Explanation:
Any function which is in the form ax+by+c=0 is called a linear function.
Linear function always represents a straight line.
The slope intercept form of a line is [tex]y=mx+b[/tex]. Here, m is the slope and b is the y-intercept.
The formula for slope of a straight is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Learn more:
https://brainly.com/question/6108704 (Answered by SociometricStar)
https://brainly.com/question/7876025 (Answered by Calculista)
Keywords:
Linear equationStraight lineGeneral form of linear equationSlope intercept form of a line