Answer:
B
Step-by-step explanation:
Original volume = pi * r^2 * h
New r = 2*r
New h = 3*h
New Volume = pi * (2r)^2 *3*h
New Volume = pi * 4r^2 * 3 *h
New Volume = 4*3 * pi * r^2 + h
Conclusion
The New Volume = 12* the original volume
Which point lies on a circle with a radius of 5 units and center at P(6, 1)?
Answer:
(1,1);(11,1);(6,6);(6-4)
Step-by-step explanation:
The easiest way to do is add or subtract 5 to the x or y value.
What is 127 as a percent?
Hello!
The answer is 127,000%
5/2=d−2/4
What does d=?
Answer:
d = 3Step-by-step explanation:
[tex]\dfrac{5}{2}=d-\dfrac{2}{4}\qquad\left/\dfrac{2}{4}=\dfrac{2:2}{4:2}=\dfrac{1}{2}\right/\\\\\dfrac{5}{2}=d-\dfrac{1}{2}\qquad\text{add}\ \dfrac{1}{2}\ \text{to both sides}\\\\\dfrac{5}{2}+\dfrac{1}{2}=d-\dfrac{1}{2}+\dfrac{1}{2}\\\\\dfrac{5+1}{2}=d\\\\\dfrac{6}{2}=d\to d=3[/tex]
Determine whether the parabola y = -x2 + 15x + 8 opens up, down, left, or right.
Dwight is a construction worker who will be employed for 8 months this year on a contract job, and he needs to calculate his projected yearly earnings in order to fill out a loan application. His contract states that he will make $35 an hour and that will work 45 hours per week for the duration of the contract.
Part 1: how much will dwight make pero week
Final answer:
Dwight will make $1,575 per week by multiplying his hourly wage of $35 by the 45 hours he works each week.
Explanation:
To calculate how much Dwight will make per week, we need to multiply his hourly wage by the number of hours he works per week. According to the question, Dwight earns $35 per hour and works 45 hours per week.
The calculation is as follows: Hourly wage x Hours per week = Weekly earnings
$35/hour x 45 hours/week = $1,575/week
Therefore, Dwight will make $1,575 per week from his construction job.
Please Need Help Very Badly!!!
Answer: use a ruler and measure each side multiply by 30 then multiply all of them by each other
hope this helps and if I'm wrong hope you for give me here is some memes
Answer:
50 degrees
Step-by-step explanation:
since angle bac is bisected, bae and eac are equal measurement. therefore:
x+30 = 3x-10
now isolate the variable
x-3x=-10-30
-2x=-40
2x=40
x=20
mEAC =3x-10
=3(20)-10
60-10
=50
this can be proven because BAE is the same measurement as EAC (because of the bisector): x +30
20+30
=50
A parallelogram has an area of 144 square centimeters. If the base measures 24 centimeters, what is the height?
Answer:
The height is 6.
Step-by-step explanation:
To find the answer, identify the dimensions you have and what you to find. We have the area (144) and base (24) and we need to find the height. To find the height, you must divide area by the base (it's really simple).
Ex.
[tex]144 / 24 = ?\\144 / 24 = 6[/tex]
The quotient you found is the height. Therefore, the answer is 6.
Final answer:
To find the height of a parallelogram with an area of 144 cm² and a base of 24 cm, divide the area by the base to obtain the height of 6 cm.
Explanation:
Mathematics:
To find the height of a parallelogram, you can use the formula Area = base * height. In this case, the area is given as 144 cm² and the base is 24 cm. Substituting these values into the formula, we get 144 = 24 * height. To find the height, divide both sides of the equation by 24: height = 144/24 = 6 cm. Therefore, the height of the parallelogram is 6 centimeters.
Nine times the quantity one-fourh plus a number is six less than the number divided by three
Solve for x: three over four x + five over eight = 4x
Answer:
Step-by-step explanation:
Assuming the problem is: 3/4 x +5/8=4x
Or .75 x+5/8=4x
Subtract .75 on both sides: 5/8=3.25x
Then divide both sides by 3.25: (5/8)/3.25=x
So x=5/26
The Brown family needs to rent a truck for their upcoming move. Express Movers will charge them $25 for the first day and $0.80 for every mile. Smith & Smith Co. will charge $35 for the first day and $0.60 for every mile. Before deciding which service to use, Mrs. Brown wants to find out how many miles would make the two choices equivalent in cost. The following equations represent this situation.
Final answer:
The equations are $25 + $0.80x for Express Movers and $35 + $0.60x for Smith & Smith Co.
Solving these equations shows that at 50 miles, both options cost the same.
Explanation:
The Brown family is trying to determine the breakeven point in miles for renting a moving truck from two different companies. Express Movers charges an initial fee of $25 plus $0.80 per mile, while Smith & Smith Co. charges $35 initially and $0.60 per mile. To find when these two options cost the same, we will set up equations and solve for the number of miles.
Let's define x as the number of miles driven. The totals cost from each company can be expressed as:
Express Movers: $25 + $0.80x
Smith & Smith Co.: $35 + $0.60x
To find the breakeven point, we equate the two expressions:
$25 + $0.80x = $35 + $0.60x
Now we solve for x by subtracting $0.60x from both sides and then subtracting $25 from both sides to isolate the variable:
$0.20x = $10
Dividing both sides by $0.20 gives us:
x = 50 miles
Therefore, at 50 miles, the cost of renting a truck from Express Movers or Smith & Smith Co. would be the same.
Which of the following could be the ratio of the length of the longer leg of a 30-60-90 to the length of its hypotenuse? CHECK ALL THAT APPLY.
A. √3 : 2
B. 3 : 2√3
C. 1 : √3
D. 3√3 : 6
E. √3 : √3
F. √2 : √3
-Apex Learning, Geometry
In a 30-60-90 triangle, the longer leg is sqrt(3) times the hypotenuse. Therefore, the correct ratios provided are A. sqrt(3) : 2 and D. 3sqrt(3) : 6, with the latter simplifying to the correct ratio when reduced.
Explanation:The ratio of the length of the longer leg to the hypotenuse in a 30-60-90 triangle is determined by the properties of this special right triangle. In such a triangle, the sides are in a fixed ratio: the shorter leg is 1 times the length of the hypotenuse, the longer leg is sqrt(3) times the length of the hypotenuse, and the hypotenuse itself is 2 times the length of the shorter leg.
Using this knowledge, we can evaluate the options given:
A. sqrt(3) : 2 - This ratio correctly represents the longer leg to hypotenuse ratio in a 30-60-90 triangle.D. 3sqrt(3) : 6 - Simplifying this ratio gives us sqrt(3) : 2, which is also a correct representation of the longer leg to hypotenuse ratio.Options B, C, E, and F do not represent the correct ratio of the longer leg to the hypotenuse of a 30-60-90 triangle. Therefore, options A and D are correct.
ab and bc form a right angle at point B. if a= (-3,-1) and B= (4,4) what is the equation of BC?
Answer:
Option C [tex]-7x-5y=-48[/tex]
Step-by-step explanation:
step 1
Find the slope of AB
we have
A(-3,-1) and B(4,4)
The slope m is equal to
[tex]m=(4+1)/(4+3)[/tex]
[tex]m=5/7[/tex]
step 2
Find the slope of BC
we know that
If two lines are perpendicular, then the product of their slopes is equal to -1
so
[tex]m1*m2=-1[/tex]
we have
[tex]m1=5/7[/tex]
substitute
[tex]5/7*m2=-1[/tex]
[tex]m2=-7/5[/tex]
step 3
Find the equation of the line into slope point form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-7/5[/tex]
[tex]B(4,4)[/tex]
substitute
[tex]y-4=-(7/5)(x-4)[/tex]
Multiply by 5 both sides
[tex]5y-20=-7x+28[/tex]
[tex]7x+5y=28+20[/tex]
[tex]7x+5y=48[/tex]
Multiply by -1 both sides
[tex]-7x-5y=-48[/tex]
What is the standard form of the equation of a line for which the length of the normal segment to the origin is 8 and the normal makes an angle of 120degrees with the positive x axis
The standard form of the equation for the specified line, we use the normal form equation, substitute the given values for the angle and the length of the normal segment, and simplify to obtain the equation as [tex]x - \(\sqrt{3}\) y = -16.[/tex]
Explanation:To solve this, we'll use the concept of the normal form of the line equation, which is [tex]x cos(\(\theta\)) + y sin(\(\theta\)) = p, where \(\theta\)[/tex] is the angle the normal makes with the positive direction of the x-axis, and p is the length of the perpendicular from the origin to the line.
Given[tex]\(\theta = 120^\circ\) and \(p = 8\)[/tex], we substitute these values into the normal form to get [tex]x cos(120^\circ) + y sin(120^\circ) = 8.[/tex] Simplifying further using the values of [tex]cos(120^\circ) = -1/2 and sin(120^\circ) = \(\sqrt{3}/2\)[/tex], we obtain the standard form of the equation of the line as [tex]-1/2 x + \(\sqrt{3}/2\) y = 8[/tex], or multiplying through by -2 for a cleaner form: [tex]x - \(\sqrt{3}\) y = -16.[/tex]
Follow the steps to solve this equation:
−2x + 6x − 8 = 12
Answer:
X = 5
Step-by-step explanation
Add or subtract the like terms and take numbers in one side . Do the solution part and get your answer.
Answer:
x=5
Step-by-step explanation:
combine like terms: -2x + 6x = 4x
add eight to the other side 4x - 8 = 12 ----> 4x = 20
then divide 4x = 20 -----> x = 5
What are the coordinates of the roots of the equation x^2+ 4x + 3 = 0 ?
The coordinates of the roots of the given quadratic equation x^2 + 4x + 3 = 0 are -1 and -3.
Explanation:The given equation is a quadratic equation in the form of ax² + bx + c = 0, where a = 1, b = 4, and c = 3. To find the coordinates of the roots, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Substituting the given values, we get:
x = (-4 ± √(4² - 4(1)(3))) / (2(1))
Simplifying further, we have:
x = (-4 ± √(16 - 12)) / 2
x = (-4 ± √4) / 2
x = (-4 ± 2) / 2
Therefore, the two roots of the equation are:
x₁ = (-4 + 2) / 2 = -1
x₂ = (-4 - 2) / 2 = -3
Help pls I think it’s scale factor of 2...
Answer:
The firston one is a scale factor of two and the second one is a scale factor of three.
Step-by-step explanation:
You just look at the coordinates. (1,1):(2,2) and (4,0):(8,0) and then for the second one (-1,0):(-3,0) and (3,2):(9,6).
1x2=2
4x2=8
-1x3=-3
3x3=9
2x3=6
An annoyed teacher asked her student to do the following: (1) Start with the number 12. Go to step (2). (2) Take the negative of the number reached at the end of the previous step. Go to step (3). (3) Add 1 to the number reached at the end of the previous step. Go to step (4). (4) Go back to step (2) unless you have already gone through step (3) a hundred times; if you have gone through step (3) a hundred times already, tell the teacher the last number you reached. To the teacher's surprise, the student gave her the correct final answer within a minute. What was it?
Answer:
Step-by-step explanation:
// 12
// -12
//-11
//88
plz help I dont understand
She started with 45 and added 5 each month.
Find the table that has Y values that are increased by 5's for every 1 increase in x.
45 + 5 = 50
50+5 = 55
55 + 5 = 60
The correct table is the second one.
Which of the following lines has a slope of -1/3 and a y-intercept of 6?
x - 3y = 6
x+ 3y = 18
3y - x = 18
Answer:
the second one, x+3y=18
Step-by-step explanation:
x+3y=18
3y=18-x
y=6-[tex]\frac{1}{3}[/tex]x
y=[tex]\frac{-1}{3}[/tex]x+6
The measure of angle A is 4 degrees greater than the measure of angle B. The two angles are complementary.Find the measure of each angle. Please help answer this, Thank you!!
Answer:
A = 47° and B = 43°
Step-by-step explanation:
Express angle A in terms of angle B, that is
A = B + 4
Complementary angles sum to 90°, hence
A + B = 90, that is
B + 4 + B = 90
2B + 4 = 90 ( subtract 4 from both sides )
2B = 86 ( divide both sides by 2 )
B = 43
Hence
∠B = 43° and ∠A = B + 4 = 43 + 4 = 47°
Answer:
A= 47°
B= 43°
Explanation:
A complementary angle is a 90° angle.
If A+B= 90 and B+4= A, we can rewrite it as...
B+4+B= 90
→ 2B+4= 90
→ 2B= 86
→ B= 43
Then we go back to the equation A+B= 90 and plug in B as 43...
A+43= 90
→ A= 47
What is the answer to 14+5(x-8)=-36
Hello There!
14 + 5x - 40 = -36
5x - 26 = -36
5x = -10
x = -2
Answer:
Step-by-step explanation:
14+4(x-8)=-36
19(x-8)=-36
x-8= -36-19
-8x=-55
6.875
please solve for x will mark brainliest answer
Answer:
x ≥ - 8
Step-by-step explanation:
Given
[tex]\frac{x}{2}[/tex] ≥ - 4
Multiply both sides by 2 to eliminate the fraction
x ≥ - 8
Answer:
Step-by-step explanation:
x ≥ - 8
The point (x, square root of 3/2) is on the unit circle, what is x?
Answer:
[tex]x=\frac{1}{2}[/tex]
Step-by-step explanation:
When we have a point (a,b) on the unit circle, we can say that
[tex]a^2+b^2=1[/tex]
This is a property of the unit circle.
From the point given [tex](x,\frac{\sqrt{3} }{2})[/tex] , now we can write the equation shown below and solve for x:
[tex]x^2+(\frac{\sqrt{3} }{2})^2=1\\x^2+\frac{3}{4}=1\\x^2=1-\frac{3}{4}\\x^2=\frac{1}{4}\\x=\frac{\sqrt{1}}{\sqrt{4} } \\x=\frac{1}{2}[/tex]
So, x = 1/2
Answer: x = 1/2
Step-by-step explanation:
We have that the point (x, (√3)/2)) is on the unit circle.
we can define a circle of radius R centered in the (0,0) as:
x^2 + y^2 = R^2
This means that:
x^2 + (√(3)/2)^2 = 1
x^2 + 3/4 = 1
x^2 = 1 - 3/4 = 1/4
x = √(1/4) = 1/2
So we have that x is equal to 1/2
The slope of a line is 58, and the line passes through the point (−8,−4).
What is the slope-intercept form of the equation for this line?
The slope-intercept form of the equation for this line is y = 58x + 460.
Given:
Slope (m) = 58
Point [tex](x_1, y_1)[/tex] = (-8, -4)
Using the point-slope form of the equation, which is
[tex](y - y_1) = m(x - x_1)[/tex]
Substitute the values into the equation:
(y - (-4)) = 58(x - (-8))
(y + 4) = 58(x + 8)
To convert this equation into slope-intercept form
y + 4 = 58x + 464
y = 58x + 464 - 4
y = 58x + 460
Therefore, the slope-intercept form is y = 58x + 460.
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Solve the system of equations 4x+3y+6z=3, 5x+5y+6z=5 and 6x+3y+6z=3
The answer is:
The solutions to the system of equations are:
[tex]x=0\\y=1\\z=0[/tex]
Why?To solve the system of equations by the easiest way, we need to use the reduction method. The reduction method consist of reducing the variables applying different math operations in order to be able to isolate the variables.
So, we are given the system:
[tex]4x+3y+6z=3\\5x+5y+6z=5\\6x+3y+6z=3[/tex]
Let's work with the first and the third equation:
[tex]4x+3y+6z=3\\6x+3y+6z=3[/tex]
Then, multiplying the first equation by -1, we have:
[tex]-4x-3y-6z=-3\\6x+3y+6z=3[/tex]
[tex]-4x+6x-3y+3y-6z+6z=-3+3[/tex]
[tex]2x=0[/tex]
[tex]x=0[/tex]
Now, working with the first and the second equation, we have:
[tex]4x+3y+6z=3\\5x+5y+6z=5[/tex]
Then, multiplying the first equation by -1, we have:
[tex]-4x-3y-6z=-3\\5x+5y+6z=5[/tex]
[tex]5x-4x+5y-3y-6z+6z=-3+5[/tex]
[tex]x+2y=2[/tex]
Then, substituting "x" into the equation, we have:
[tex]0+2y=2[/tex]
[tex]y=\frac{2}{2}=1[/tex]
Finally, working with the first equation and substituting "x" and "y", we have:
[tex]4x+3y+6z=3[/tex]
[tex]4*0+3*1+6z=3[/tex]
[tex]0+3+6z=3[/tex]
[tex]6z=3-3=0[/tex]
[tex]6z=0[/tex]
[tex]z=\frac{0}{6}=0[/tex]
Hence, we have that the solutions to the system of equations are:
[tex]x=0\\y=1\\z=0[/tex]
Have a nice day!
Answer:
[tex]x=0\\y=1\\z=0[/tex]
Step-by-step explanation:
Multiply the first equation by -1:
[tex](-1)(4x+3y+6z)=3(-1)\\\\-4x-3y-6z=-3[/tex]
Add the new equation and the third equation an solve for "x":
[tex]\left \{ {{-4x-3y-6z=-3\ \atop {6x+3y+6z=3} \right.\\...........................\\2x=0\\x=0[/tex]
Substitute the value of "x" into the first equation and solve for "y":
[tex]4(0)+3y+6z=3\\\\3y=3-6z\\\\y=\frac{3-6z}{3}\\\\y=1-2z[/tex]
Substitute the value of "x" and [tex]y=1-2z[/tex] into the second equation and solve for "z":
[tex]5(0)+5(1-2z)+6z=5\\\\5-10z+6z=5\\\\-4z=0\\\\z=0[/tex]
Knowing the values of "x" and "z", you can substitute them into any original equation and solve for "y". Then:
[tex]4(0)+3y+6(0)=3\\\\3y=3\\\\y=\frac{3}{3}\\\\y=1[/tex]
the length of a rectangle is 11 yd less than three times the width and the area of the rectangle is 42 yd
The length of the given rectangle is 3 yd and the width is 3.66 yd.
What is a rectangle?A rectangle is a type of parallelogram having equal diagonals.
All the interior angles of a rectangle are equal to the right angle.
The diagonals of a rectangle do not bisect each other.
Given that,
The area of rectangle is 42 square yd.
Suppose the width of the rectangle is x yd.
Then its length is given by 3x - 11 yd.
As per the problem, the following equation can be formed,
x(3x - 11) = 42
Solve the above equation for x as,
x(3x - 11) = 42
=> 3x² - 11x = 42
=> 3x² - 11x - 42 = 0
=> x = -1, 4.66
Since, the width cannot be negative. The value of x is taken as 4.66.
Thus, the length is is given by 3 × 4.66 - 11 = 3.
Hence, the length and width of the rectangle are 3yd and 4.66yd respectively.
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Please please help!!
Answer:
[tex]\large\boxed{x=0\ and\ x=\pi}[/tex]
Step-by-step explanation:
[tex]\tan^2x\sec^2x+2\sec^2x-\tan^2x=2\\\\\text{Use}\ \tan x=\dfrac{\sin x}{\cos x},\ \sec x=\dfrac{1}{\cos x}:\\\\\left(\dfrac{\sin x}{\cos x}\right)^2\left(\dfrac{1}{\cos x}\right)^2+2\left(\dfrac{1}{\cos x}\right)^2-\left(\dfrac{\sin x}{\cos x}\right)^2=2\\\\\left(\dfrac{\sin^2x}{\cos^2x}\right)\left(\dfrac{1}{\cos^2x}\right)+\dfrac{2}{\cos^2x}-\dfrac{\sin^2x}{\cos^2x}=2[/tex]
[tex]\dfrac{\sin^2x}{(\cos^2x)^2}+\dfrac{2-\sin^2x}{\cos^2x}=2\\\\\text{Use}\ \sin^2x+\cos^2x=1\to\sin^2x=1-\cos^2x\\\\\dfrac{1-\cos^2x}{(\cos^2x)^2}+\dfrac{2-(1-\cos^2x)}{\cos^2x}=2\\\\\dfrac{1-\cos^2x}{(\cos^2x)^2}+\dfrac{2-1+\cos^2x}{\cos^2x}=2\\\\\dfrac{1-\cos^2x}{(\cos^2x)^2}+\dfrac{1+\cos^2x}{\cos^2x}=2[/tex]
[tex]\dfrac{1-\cos^2x}{(\cos^2x)^2}+\dfrac{(1+\cos^2x)(\cos^2x)}{(\cos^2x)^2}=2\qquad\text{Use the distributive property}\\\\\dfrac{1-\cos^2x+\cos^2x+\cos^4x}{\cos^4x}=2\\\\\dfrac{1+\cos^4x}{\cos^4x}=2\qquad\text{multiply both sides by}\ \cos^4x\neq0\\\\1+\cos^4x=2\cos^4x\qquad\text{subtract}\ \cos^4x\ \text{from both sides}\\\\1=\cos^4x\iff \cos x=\pm\sqrt1\to\cos x=\pm1\\\\ x=k\pi\ for\ k\in\mathbb{Z}\\\\\text{On the interval}\ 0\leq x<2\pi,\ \text{the solutions are}\ x=0\ \text{and}\ x=\pi.[/tex]
PLEASE HELP!
Which equation best represents the line?
Remember that the slope intercept formula is:
y = mx + b
m is the slope ([tex]\frac{rise}{run}[/tex])
b is the y-intercept
In this case the slope is...
[tex]\frac{1}{2}[/tex]
The y-intercept is...
(0, 3)
so...
y = [tex]\frac{1}{2}[/tex]x + 3
Hope this helped!
~Just a girl in love with Shawn Mendes
The odometer in Mr. Jackson’s car shows he has travel 62,222 miles what is the least number of additional miles that Mr. Jackson much travel before the odometer again shows four of the five digits the same as each other
Answer:
444 (gets to 62,666)
Step-by-step explanation:
The closest you can think of first is 63,333. However, as long as there doesn't have to be the four numbers in a row, the "6" in the number can be one of the four same numbers.
This means that you need to get 3 other sixes in the number. There are many ways to do this, but the one requiring the least amount of driving is changing the last three digits (222). If you add 444 to the number, the amount of miles driven is 62,666, there being 4 sixes in the number. This is the least amount of driving needed before the odometer shows four of the five digits the same as each other.
444 is the least number that shows four out of the five digits same.
What is odometer?An odometer is an instrument for measuring the distance travelled by a wheeled vehicle.
Given that,
Total distance covered by Mr. Jackson = 62,222 miles,
The four digits of number 62,222 are same and are 2,
Again, odometer will show four out of 5 digit same, when there will be at least four times 6,
So add 444 in the 62,222
The number = 62,222 + 444 = 62,666
So the least number that can be added to make 4 digit same is 444.
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HELP please:)) Geometry question
Answer:
21.99 units
164.93 units²
Step-by-step explanation:
given radius r = 15 units
angle of sector = 84°
Length of sector = [tex]\frac{84}{360}[/tex] x 2 x π x r
= [tex]\frac{84}{360}[/tex] x 2 x 3.14 x 15
= 21.99 units
Area of sector = [tex]\frac{84}{360}[/tex] x π x r²
= [tex]\frac{84}{360}[/tex] x 3.14 x 15²
= 164.93 units²