Answer:
100pi in^2, or 314.16 in^2 to nearest hundredth.
Step-by-step explanation:
The areas of the surface of water for full basin and area for the surface when the depth is 10 inches are in the ratio 25^2 : 10^2 = 6.25 : 1. (because the depth of the water = radius of the water when the basin is full).
The area for a full basin = pi r^2 = 625pi in^2.
So the area when depth is 10 inches = 625pi / 6.25 = 100pi in^2.
The slope of the line whose equation is 3y + 2x = 1 is: A.)-2/3 B.)-3/2 C.)1/3
Answer:
A
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange 3y + 2x = 1 into this form
Subtract 2x from both sides
3y = - 2x + 1 ( divide all terms by 3 )
y = - [tex]\frac{2}{3}[/tex] x + [tex]\frac{1}{3}[/tex] ← in slope- intercept form
with slope m = - [tex]\frac{2}{3}[/tex] → A
By rearranging the equation 3y + 2x = 1 into slope-intercept form, y = mx + b, we find that the slope of the line is -2/3. The correct answer is A.) -2/3.
The slope of the line whose equation is 3y + 2x = 1 is found by solving for y to get the line into slope-intercept form, which is y = mx + b, where m represents the slope.
First, subtract 2x from both sides of the equation: 3y = -2x + 1.Next, divide each term by 3 to solve for y: y = (-2/3)x + 1/3.Now that the equation is in slope-intercept form, we can see that the slope m is -2/3. Therefore, the correct answer is A.) -2/3.
PLZZZZZ HELP!!!
The graph shows two lines, A and B.
Part A: How many solutions does the pair of equations for lines A and B have? Explain your answer. (5 points)
Part B: What is the solution to the equations of lines A and B? Explain your answer. (5 points)
Answer:
Part A: 1 solution
Part B: x = 3, y = 4
Step-by-step explanation:
Lines A & B intersect one time, meaning there is only one pair of x and y values that will make the two equations equalThey intersect at x = 3, and y = 4A bank offers a home improvement loan with simple interest at an annual rate of 12%. J.T. borrows an amount of $14,000 to pay back over 3 years. How much will he pay back altogether? Explain how you found the total amount.
12%*14000*3
Which is 5040
Therefore, it will have to pay back $4050
J.T. will pay back a total of $18,480 altogether.
To calculate the total amount J.T. will pay back, we can use the formula for simple interest:
[tex]\[I = P \times r \times t\][/tex]
Where:
- (I) = Interest
- (P\) = Principal amount (the initial loan amount)
- (r) = Annual interest rate (in decimal form)
- (t) = Time (in years)
Given that J.T. borrows $14,000 at an annual interest rate of 12% for 3 years, we can plug these values into the formula:
[tex][I = 14000 \times 0.12 \times 3\][/tex]
[I = 5040]
So, the total interest J.T. will pay is $5,040.
To find the total amount J.T. will pay back, we add the interest to the principal:
[Total amount = Principal + Interest]
[Total amount = 14000 + 5040]
[Total amount = 18440]
Therefore, J.T. will pay back a total of $18,480 altogether.
In summary, by using the formula for simple interest, we determined the interest amount J.T. will pay over the 3-year period, and then added it to the principal amount to find the total repayment amount.
Complete question:
A bank offers a home improvement loan with simple interest at an annual rate of 12%. J.T. borrows an amount of $14,000 to pay back over 3 years. How much will he pay back altogether? Explain how you found the total amount.
What is the solution to the equation 1 / 4 x = 5?
x = 4 / 5
x = 5 / 4
x = 20
x = 1
Answer:
The solution to the equation 1/4 x = 5 is '' x = 20''
Step-by-step explanation:
you take ''1/4'' and multiply it by ''20'' and the answer you'll get is ''5''
The solution to the equation 1 / 4 x = 5 is found by isolating x. After multiplying both sides of the equation by 4, you find that x = 20.
Explanation:The solution to your equation, 1 / 4 x = 5, can be found using the principles of algebra. This equation is asking us 'What value of x can I multiply by 1/4 to equal 5?'
The best way to find the solution is to isolate x on one side of the equation. In this case, you'll start by multiplying both sides of the equation by 4. Now your equation looks like this:
1/4 x * 4 = 5 * 4
Simplifying the equation, you'll get:
x = 20
Therefore, you can see that the solution to the equation 1/4 x = 5 is x = 20.
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Tina raised the number 3 to a power and then added 19 to the result .She obtained the sum 100. To what power did she raise 3 ?
Answer:
3^4, she raised it to the 4th power
Step-by-step explanation:
3^x+19=100
-19
3^x=81
We can make a table now to find what power of three = 81
Powers of three table
3^1=3 3^2=9 3^3=27 3^4=81
The power she raised the number to is 4.
What is equationThis is a mathematic expression or statement often used to represent word problems.
To solve this question, we need to write an equation to represent this problem.
[tex]3^x + 19 = 100\\ [/tex]
The equation above represents the problem.
Let's solve for x
[tex]3^x + 19 = 100\\ [/tex]
collect like terms
[tex]3^x = 100 - 19\\ 3^x = 81\\ [/tex]
[tex]3^x = 81\\ x = 4[/tex]
What we did above is that how many power are we going to raise 3 to give us 81 and the answer is 4 times.
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Miryam Williams earns a 3.5% commission on all sales. She also receives a $500 bonus if her commission exceeds $5,000. Her total sales were $92,500. What was her total pay?
Final answer:
Miryam Williams' total pay is $3,237.50.
Explanation:
To calculate Miryam Williams' total pay, we first need to calculate her commission.
Her commission is 3.5% of her total sales, which is $92,500.
Commission = 3.5% × $92,500 = $3,237.50.
Next, we need to determine if Miryam's commission exceeds $5,000.
Since her commission is $3,237.50, it does not exceed $5,000. Therefore, she does not receive the $500 bonus.
Finally, to calculate her total pay, we sum her commission and the bonus (which is $0 in this case).
Total Pay = Commission + Bonus = $3,237.50 + $0 = $3,237.50.
And event organizer is reserving rooms for two companywide events. For the quarterly meeting this month she reserved 2 conference rooms and 5 ballrooms which can seat a total of 238 attendees. for safety training next month she reserved 4 conference rooms and 5 ball rooms which can seat 286 attendees. How many attendees can each room accommodate?
Final answer:
The conference rooms can accommodate approximately 34 attendees each, and the ballrooms can accommodate approximately 31 attendees each.
Explanation:
To find out how many attendees each room can accommodate, we need to divide the total number of attendees by the total number of rooms.
For the quarterly meeting, there are 2 conference rooms and 5 ballrooms, which can seat a total of 238 attendees. To find out how many attendees each room can accommodate, we divide 238 by 7 (2 + 5), which gives us approximately 34 attendees per room.
For the safety training event, there are 4 conference rooms and 5 ballrooms, which can seat a total of 286 attendees. Dividing 286 by 9 (4 + 5) gives us approximately 31 attendees per room.
Seiki is planning her workout at her gym. She wants to spend more than 40 minutes exercising. Her workout plan includes 20 minutes lifting weights and the rest of the time on three different cardio machines. She wants to spend the same amount of time on each cardio machine. How many minutes should Seiki spend on each cardio machine?
Answer:
Assuming that Seiki wants to be as close to 40 minutes are possible (to the nearest minute), She would want to spend 7 minutes on each of the 3 cardio machines
Step-by-step explanation:
With Seiki wanting to spend at least 40 minutes exercising and spending 20 minutes lifting weights, she needs to spend at least 20 more minutes on her cardio. If we are looking for a number that is divisible by 3, that would mean that she would spend 21 minutes exercising.
Seiki should spend at least 10 minutes on each cardio machine after her 20-minute weightlifting session to meet continuous exercise and weekly cumulative goals, therefore surpassing her minimum of 40 minutes of exercise and aligning with health recommendations.
Time Allocation For Cardio Machines
Seiki wants to spend more than 40 minutes exercising, with 20 minutes devoted to lifting weights and the rest on three different cardio machines. To calculate the time she should spend on each cardio machine, we first deduct the weightlifting time from the total minimum exercise time.
This leaves us with more than 20 minutes for cardio (40 minutes total - 20 minutes of weights = 20+ minutes for cardio).
Since she wants to spend the same amount of time on each machine, we divide the remaining time by three. Let's assume Seiki decides on the minimum of 21 minutes for cardio to exceed the 40 minutes total.
So, 21 minutes divided by three cardio machines equals seven minutes per machine.
However, to align with the recommendations for sessions to be continuous for 10 minutes or more and the goal of a cumulative total of 150-300 minutes from at least three days a week, Seiki should aim for at least 10 minutes on each machine.
This would translate to at least a total of 30 minutes on cardio machines, bringing her workout to a minimum of 50 minutes (20 minutes of weights + 30 minutes of cardio).
Remember, these calculations are based on the minimum requirements, and Seiki can adjust her workout duration on the cardio machines to suit her fitness goals and available time.
PLEASE HELP!!!!
Which statement about the function below is true? f(x) = x3 + 3x2 - 9x- 27 = (x-3)(x + 3)(x + 3)?
The root -3 has a multiplicity of 1.
The root -3 has a multiplicity of 2.
The root 3 has a multiplicity of 2.
The root 3 has a multiplicity of 3.
Answer:
x = - 3 with multiplicity 2
Step-by-step explanation:
f(x) = (x - 3)(x + 3)(x + 3) = (x - 3)(x + 3)²
Equating each factor to zero and solving for x
x - 3 = 0 ⇒ x = 3 with multiplicity 1
x + 3 = 0 ⇒ x = - 3
x + 3 = 0 ⇒ x = -3
Thus x = - 3 has multiplicity of 2
The fact that the factor is squared gives the multiplicity
(x + 3)³ has root - 3 of multiplicity 3
If a football player passes a football from 4 feet off the ground with an initial velocity of 36 feet per second, how long will it take the football to hit the ground? Use the equation h = -16t^2 + 6t +4. Round your answer to the nearest hundredth.
Answer:
t = 0.722 seconds
Step-by-step explanation:
Given in the question that an equation
h = -16t² + 6t + 4
here h is the height
t is the time
To solve this question we need to substitute height with zero because at ground level height is zero
h = 00 = -16t² + 6t + 4
a = -16
b = 6
c = 4
Formula to use
t = -b±√(b²-4ac) / 2a
Plug values in the formula
t = -6 ± √36-4(-16)(4) / 2(-16)
t = 6±2√73 / 32
t = 6+2√73 / 32 or t = 6-2√73 / 32
t = 0.722 or t = -0.347
since time can't be in negative so we reject t = -0.347
for the equation -4y=8x, what is the constant of variation?
Answer:
Step-by-step explanation:
In a normal equation, y=mx+b, the constant of variation is the thing that "constantly" "varies" and in other words changes the same. This is the slope. In the equation, the slope is m.
-4y=8x
y=-2x
The constant of variation, aka slope, is -2
Which model best fits the set of data shown on this graph?
A. quadratic model
B. quartic model
C. linear model
D. cubic model
Answer:
C
Step-by-step explanation:
Quadratic model is shaped like a "U", or a parabola
Quartic model is shaped like a "W", highest degree is 4 (x^4).
Linear model is a line.
Cubic model is x^3, shaped like a curvy snake.
Looking at the graph, it clearly shows a line. So, linear model is the answer.
C is the correct answer.
What is the value of x in the equation? 7 1 2 x + 3 2 3 = −13 A) −1 5 6 B) −2 1 6 C) −2 2 9 D) −2 5 9
Answer:
C - 2 2/9
Step-by-step explanation:
7 1 /2 x + 3 2/ 3 = −13
Subtract 3 2/3 from each side
7 1 /2 x + 3 2/ 3 - 3 2/3 = −13 - 3 2/3
7 1/2x = -16 2/3
Change each mixed number to an improper fraction
7 1/2 = (2*7 +1)/2 = 15/2
16 2/3 = (3*16+2)/3 = 50/3
15/2 x = -50/3
Multiply each side by 2/15 to isolate x
2/15 * 15/2 x = -50/3 * 2/15
x = -100/45
Simplify
x = -20/9
Change back to a mixed number
9 goes into 20 2 times with 2 left over
x = -2 2/9
WORTH 40 POINTSSS WILL MARK BRAINLIEST PLZ HURRY AND PLZ ANSWER CORRECTLY
4x + 1 over 3y2 What is the value of the expression above when x = 2 and y = 3? You must show all work and calculations to receive full credit.
Answer:
The Correct answer is: 1/3
Step-by-step explanation:
x = 2, y = 3
(4x + 1) / 3y²
(4*2 + 1) / 3*3²
(8 + 1) / (3*9)
9 / 27
= 1/3
The probability that Ashley drives faster than the speed limit (event A) is 0.34, and the probability that he gets a speeding ticket (event B) is 0.22. The probability that he drives faster than the speed limit, given that he has gotten a speeding ticket, is 1. Are events A and B dependent or independent? A. dependent B. independent C. insufficient data D. depends on the other events in the sample space
The correct answer between all
the choices given is the first choice or letter A. I am hoping that this answer
Answer: Option 'A' is correct
Step-by-step explanation:
Since we have given that
A be the event that Ashley drives faster than the speed limit.
P(A)=0.34
B be the event that he gets a speeding ticket.
P(B)=0.22
Probability that he drives faster than the speed limit, given that he has gotten a speeding ticket i.e.
P(A|B)=1
but for A and B to be independent ,
P(A).P(B)= P(A and B)
0.34×0.22=0.0748
but,
[tex]P(A\mid B)=\dfrac{P(A\cap B)}{P(B)}\\\\1=\dfrac{P(A\cap B)}{0.22}\\\\0.22=P(A\cap B)[/tex]
So, P(A∩B) does not satisfy the condition.
Hence, A and B are not independent events.
Option 'A' is correct as they are dependent events.
What is the effect on the graph of the function f(x) = 2x when f(x) is replaced with f(−5x)?
A) vertical stretching and reflection across the x-axis
B) vertical compression and reflection across the x-axis
C) horizontal compression and reflection across the y-axis
D) horizontal stretching and reflection across the y-axis
Answer:
C) horizontal compression and reflection across the y-axis
Step-by-step explanation:
To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.
Please see the attached image below, to find more information about the graph
The original equation is:
f(x) = 2x
The new equation is:
f(-5x) = 2(-5x)
f(-5x) = -10*x
The answer is
C) horizontal compression and reflection across the y-axis
wally has 84$. he used two seventh of his money to buy a new pair of running shoes. how much did wally spend on his new shoes?
Answer:
$24
Step-by-step explanation:
What you do is you just times 84 x 2/7 to get your answer.
84 x 2/7=$24 is your answer.
Answer:
$24
Step-by-step explanation:
To find out how much he spent on the shoes, take the amount of money he has and multiply by the fraction he spent on shoes
84 * 2/7
168/7
24
He spent 24 dollars on new shoes
Convert the function into standard form. Show your work. y-2=-3(x+4)^2
Answer:
y = -3x² - 24 x + 50
Step-by-step explanation:
y - 2 = - 3(x+4)²
y - 2 = -3(x²+8x+16)
y - 2 = -3x² -24x +48
y = -3x² - 24 x + 50
ANSWER
The standard form is
.
[tex]y = - 3 {x}^{2} - 24x - 46[/tex]
EXPLANATION
The given function is
[tex]y - 2 = - 3(x + 4)^{2} [/tex]
The standard form is given by
[tex]y =a {x}^{2} + bx + c[/tex]
We expand to obtain:
[tex]y - 2 = - 3( {x}^{2} + 8x + 16)[/tex]
We expand the parenthesis to obtain:
[tex]y - 2 = - 3 {x}^{2} - 24x - 48[/tex]
Group the similar terms to obtain:
[tex]y = - 3 {x}^{2} - 24x - 48 + 2[/tex]
[tex]y = - 3 {x}^{2} - 24x - 46[/tex]
The standard form is
[tex]y = - 3 {x}^{2} - 24x - 46[/tex]
doug decided to guess on the last three multiple choice questions on his science test. if each question had four choices, how many ways can he answer the question
There are 64 possible
Answer:
12
Step-by-step explanation:
3 questions times 4 answers equals 12 possible choices,
(4+4+4)
PLEASE HELP: The mass of a ball is 128 g. It has a density of 0.5 g/cm³. What is the volume of the ball? Show your work and place a box around your answer. Optional Bonus point: what is the radius of the ball?
Answer:
Part 1) The volume of the ball is 256 cm³
Part 2) The radius of the ball is 3.94 cm
Step-by-step explanation:
Part 1) we know that
The density is equal to divide the mass by the volume
D=m/V
Solve for the volume
The volume is equal to divide the mass by the density
V=m/D
In this problem we have
m=128 g
D=0.5 g/cm³
substitute
V=128/0.5=256 cm³
Part 2) what is the radius of the ball?
we know that
The volume of the sphere (ball) is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]V=256\ cm^{3}[/tex]
assume
[tex]\pi =3.14[/tex]
substitute and solve for r
[tex]256=\frac{4}{3}(3.14)r^{3}[/tex]
[tex]768=(12.56)r^{3}[/tex]
[tex]r^{3}=768/(12.56)[/tex]
[tex]r=3.94\ cm[/tex]
All regular polygon:
A. Have four sides
B.Have an even number of sides
C.are symmetrical
D.are the same size
C. Are simmetrical
ExplanationA. is false because only quadrilaterals have 4 sides
B. is false because polygons like equilateral triangle and regular pentagon have an odd number of sides
D. A polygon doesn't have an unique size. It changes every time, cause we can decide its size
Answer: The answer is C. are symmetrical.
Step-by-step explanation: There is a line of symmetry, which is a line where one half of the polygon is a mirror image of the other side. This means that even if a polygon has 5 sides, for example, then it would still be symmetrical.
Help on angles plzzzzzz
Answer:
85°
Step-by-step explanation:
Since you know that the overall angle measure for the whole shape is 540°, you can subtract the known angles measures to find the right one.
540-90
450-90
360-115
245-160
85
Math question,, ^-^ will give brainiest answer!
Answer:
I think its C im not sure but thats what i got
Sorry If its wrong
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
The inscribed angle ∠CAD is half the central angle ∠CBD. Therefore:
35° = 1/2 ∠CBD
∠CBD = 70°
The area of a sector is:
A = (θ/360) πr²
Since r = 10:
A = (70/360) π(10)²
A = 7000π/360
A = 175π/9
Answer is B.
Please help and explain please!
Answer: 48
Step-by-step explanation: All you are doing is substituting x and y with the numbers it gives u then u just solve. 2 to the 4th power is 16. 4 to the 3rd power is 64 and then times .5 gives u 32. then u add and get 16+32=48
The perimeter of an equilateral triangle is 51 feet.what is the length of one of its side?explain your work
Hello!
The answer is: 17 ft.
Explanation:
To find this out, just divide the perimeter, and the amount of sides in a triangle, which is 3. This will only work with equilateral triangles because an equilateral triangle has all three sides the same length. Anyway, divide 51 and 3. (51 / 3 = 17) Just to make sure, you can add three 17's together, 17 + 17 + 17 = 51, the perimeter.
I hope this helped! ~Q
The length of one of side of Equilateral Triangle is 17 feet, whose perimeter is 51 feet.
What is perimeter of equilateral triangle?
An equilateral triangle's perimeter is the sum of its three sides. P = 3a.
'a' is the side of equilateral triangle.
Given that:
Perimeter of Equilateral Triangle = 51 feet
where 'a' is the side of equilateral Triangle.
As we know that all side of equilateral triangle are equal.
So, its all sides measure 'a'.
Perimeter = a +a +a
51= 3a
a= 51/3
a=17 feet.
Hence, the side of equilateral triangle measures 17 feet.
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Which line is a graph of the equation: -2x + 5y=10
Answer:
Step-by-step explanation: first, find y by itself by adding 2x to the other side then diving by the 5y to get y=2/5x +2! Rise 2, run 5 from your start at positive 2 on the graph and you should get line a!!!
The graph of the equation -2x + 5y = 10 has a positive slope of 2/5 and a y-intercept of 2. None of the provided options accurately describe the graph of the equation, as they indicate incorrect y-intercept values and describe the slope incorrectly.
Explanation:To find which line is a graph of the equation -2x + 5y = 10, we need to identify the slope and the y-intercept of the line. To do this, we should rearrange the equation into slope-intercept form, which is y = mx + b where m is the slope and b is the y-intercept.
Rearranging the equation, we get:
5y = 2x + 10
y = (2/5)x + 2
The slope is the coefficient of x, which is 2/5, and the y-intercept is the constant term, which is 2. The line has a positive slope, and based on the slope-intercept form, it rises on the graph as the x-value increases. Therefore, option d with a positive slope and a y-intercept of 50 must have a typo since our y-intercept is 2. The correct interpretation would be that the line gradually moves upward on the graph as the x-value increases, thanks to its positive slope.
Hence, none of the provided options describe the graph of the equation -2x + 5y = 10 accurately because the y-intercept should be 2, not 50, and the slope is positive. Keep in mind that a positive slope results in an upward, not a downward, trend as x increases.
Given x varies inversely with y and xy = 2, what is the value of x when y = 1?
Answer: [tex]x=2[/tex]
Step-by-step explanation:
The equation for inverse variation is:
[tex]x=\frac{k}{y}[/tex]
Where "k" is the constant of variation.
If you solve for for the constant "k", you get the form:
[tex]k=xy[/tex]
So, if [tex]xy=2[/tex] then [tex]k=2[/tex]
Knowing the value of "k", you can find the value of "x" when [tex]y=1[/tex], by substituting these values into the equation [tex]x=\frac{k}{y}[/tex].
Therefore, you get that the value of "x" when [tex]y=1[/tex] is:
[tex]x=\frac{2}{1}\\\\x=2[/tex]
Answer:
x=2
Step-by-step explanation:
Which transformation(s) can be used to map one triangle onto the other? reflection only translation only dilation, then translation rotation, then translation rotation then dilation
Answer:
reflection only
rotation, then translation
Step-by-step explanation:reflection only rotation, then translation
Answer:
Transformation which can be used for mapping of one triangle to another are;
Only translationRotation then dilation.Step-by-step explanation:
Given information:
We need to map one triangle to another ;
Hence, for mapping of one triangle to another,
The transformation which can be used from the given options are;
Only translationRotation then dilation.For more information visit;
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Solve x2 + 2x + 5 = 4 by completing the square
There will be a second image that will be showing the answer
Answer:
x = -1
Step-by-step explanation:
[tex] x^2 + 2x + 5 = 4 [/tex]
Subtract the constant term.
[tex] x^2 + 2x = -1 [/tex]
Add half of the coefficient of the x-term to complete the square.
[tex] x^2 + 2x + 1 = -1 + 1 [/tex]
[tex] (x + 1)^2 = 0 [/tex]
[tex] x + 1 = 0 [/tex]
[tex] x = -1 [/tex]
Solve 6 over x minus 3 equals 3 over x for x and determine if the solution is extraneous or not
Answer:
Here, the given expression is,
( By the cross multiplication ),
Since, an extraneous solution is a solution, which is emerged by solving the equation but it does not satisfying the equation,
But for x = -3, the equation follows,
⇒ x = -3 is the non-extraneous,
⇒ The given equation has only one solution x = -3 which is non-extraneous.
Step-by-step explanation:
Answer:
x = -3 is not extraneous solution.
Step-by-step explanation:
[tex]\frac{6}{x-3} =\frac{3}{x}\\Cross\,\, Multiply\\6x =3(x-3)\\6x = 3x-9\\6x-3x=-9\\3x= -9\\x=-9/3\\x=-3[/tex]
An extraneous solution is the solution that is obtained by solving the question given but does not satisfy the original equation.
In our case x = -3
Putting value back to the original equation
[tex]\frac{6}{x-3} =\frac{3}{x}\\\frac{6}{-3-3} =\frac{3}{-3}\\\frac{6}{-6} =-1\\-1=-1[/tex]
Since our original equation is satisfied so,
x = -3 is not extraneous solution.