Answer:
[tex]\large\boxed{h=\dfrac{3V}{\pi r^2}}[/tex]
Step-by-step explanation:
[tex]\text{The formula of a volume of a cone:}\ V=\dfrac{1}{3}\pi r^2h.\\\\\text{Solve for}\ h:\\\\\dfrac{1}{3}\pi r^2h=V\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\dfrac{1}{3\!\!\!\!\diagup_1}\pi r^2h=3V\qquad\text{divide both sides by}\ \pi r^2\\\\h=\dfrac{3V}{\pi r^2}[/tex]
Solve for x: 2 over 10 equals 3 over quantity x minus 9
Answer:
24
Step-by-step explanation:
2/10=3/x-9
2(x-9)=30
2x-18=30
2x=30+18
2x=48
x=24
Answer:
The value of x in the given phrase is 24.
Step-by-step explanation:
Given phrase,
2 over 10 equals 3 over quantity x minus 9
[tex]\frac{2}{10}=\frac{3}{x-9}[/tex]
By cross multiplication,
[tex]2x-18=30[/tex]
Adding 18 on both sides,
[tex]2x=48[/tex]
Divide both sides by 2,
[tex]x=24[/tex]
Hence, the value of x is 24.
cual o cuales de los siguientes intervalos contiene el número 0? (0,1] [-1,1] [-1,0)
Answer:
[-1,1]
Step-by-step explanation:
The question in English is
which of the following intervals contains the number 0?
case A) (0,1]
All real numbers greater than zero (the number 0 is not included) and less than or equal to 1 (the number 1 is included)
case B) [-1,1]
All real numbers greater than or equal to -1 (the number -1 is included) and less than or equal to 1 (the number 1 is included)
In this interval is included the number 0
case C) [-1,0)
All real numbers greater than or equal to -1 (the number -1 is included) and less than 0 (the number 0 is not included)
Please explain how to answer this!
[tex]\huge{\boxed{66}}[/tex]
Start by substituting in the values. [tex]3(2)+6(8+2)[/tex]
Add. [tex]3(2)+6(10)[/tex]
Multiply. [tex]6+60[/tex]
Add. [tex]\boxed{66}[/tex]
Answer:
Step-by-step explanation:
3a+6(b+2)
=3(2)+6(8+2)
=6+6(10)
=6+60
=66
Solve this inequality
[tex]3b-7<32\\3b<39\\b<13[/tex]
X^2-4x+3 factorize into its factors and give me answer I will giv u anda burger
Answer:
(x - 3)(x - 1)
Step-by-step explanation:
Consider the factors of the constant term (+ 3) which sum to give the coefficient of the x- term.
The factors are - 3 and - 1, since
- 3 × - 1 = + 3 and - 3 - 1 = - 4, hence
x² - 4x + 3 = (x - 3)(x - 1) ← in factored form
Answer:
Factors are (x-1) (x-3)
Step-by-step explanation:
X^2-4x+3 = 0
x² - x - 3x + 3 =0
x(x - 1) -3(x - 1) = 0
(x-1) (x-3) =0
HELP ASAP PLS!!!
A power outage occurs 6 min after the ride started. Passengers must wait for their cage to be manually
cranked into the lowest position in order to exit the ride. Sine function model: h = 82.5 sín 30t +0.5) +97.5
where h is the height of the last passenger above the ground measured in feet and t is the time of operation of
the ride in minutes.
(a) What is the height of the last passenger at the moment of the power outage? Verity your answer by
evaluating the sine function model.
(b) Will the last passenger to board the ride need to wait in order to exit the ride? Explain.
Answer:
I will assume
h = 82.5 sin (3 pi (t+0.5) )+97.5 , (you had no equation and no h)
so when t = 6
h = 82.5 sin (3π(6.5)) + 97.5
= 82.5(-1) + 97.5 = 15
check: period = 2π/(3π) = 2/3 minutes (that is a fast ride considering how huge it is)
So 6 ÷(2/3) = 9 , at the 6 minute mark, the last passenger has just completed 9 rotations.
the min height of the basket is -82.5 + 97.5 = 15
( the min value of 82.5 sin(anything) = 82.5(-1) )
so the last passenger must be at the platform level.
how did you get 79 ???
Step-by-step explanation:
18. What is the area of a piece of garden plot 5 yards 2 feet long by 6 yards 1 foot wide? Give your answer in square feet.
O A. 270 square feet
O B. 49 square feet
O C.323 square feet
O D. 70 square feet
Answer:
C. 323 ft²Step-by-step explanation:
1 yard = 3 feet
5yd 2ft = (5)(3)ft + 2ft = 17ft
6yd 1ft = (6)(3)ft + 1ft = 19ft
The formula of an area of a rectangle:
A = wl
w - width
l - length
Substitute w = 19ft and l = 17ft:
A = (19)(17) = 323 ft²
(8 + 5r3 - 2r2) - (8r - 8 - 6r2)
Simplify expression
Answer:
5r^3 + 4r^2 - 8r + 16
Step-by-step explanation:
(8 + 5r^3 - 2r^2) - (8r - 8 - 6r^2) =
The first set of parentheses is there just to show you that what is inside is a polynomial. The second set of parentheses has a second polynomial inside. The subtraction sign just to the left of the second set of parentheses shows that you are subtracting the second polynomial from the first one.
The first set of parentheses is not needed and can be dropped.
You are subtracting the second polynomial fromt he first one, so you can think of the the subtraction sign as a -1, and you need to distribute the -1 by the second polynomial, That will result in all signs inside the second set of parentheses changing.
Below, just the first set of parentheses is removed.
= 8 + 5r^3 - 2r^2 - (8r - 8 - 6r^2)
Now, we change every sign inside the second set of parentheses by distributing -1.
= 8 + 5r^3 - 2r^2 - 8r + 8 + 6r^2
Now we need to combine like terms. Like terms have the same variable part. We can rearrange the terms grouping like terms together before combining them. Also, it is customary to list the terms in descending order of degree.
= 5r^3 - 2r^2 + 6r^2 - 8r + 8 + 8
Now we combine like terms.
= 5r^3 + 4r^2 - 8r + 16
The Chesapeake Bay tides vary between 4 feet and 6 feet. The tide is at its lowest point when time (t) is 0 and completes a full cycle in 12 hours. What is the amplitude, period, and midline of a function that would model this periodic phenomenon?
Amplitude = 1 foot; period = 12 hours; midline: y = 5
Amplitude = 2 feet; period = 6 hours; midline: y = 1
Amplitude = 2 feet; period = 12 hours; midline: y = 5
Answer:
Amplitude = 1 foot; period = 12 hours; midline: y = 5
Step-by-step explanation:
The Chesapeake Bay tides vary between 4 feet and 6 feet.
This means the range is
[tex]4 \leqslant f(t) \leqslant 6[/tex]
The period is the length of the interval on which the function completes one full cycle.The tide is at its lowest point when time (t) is 0 and completes a full cycle in 12 hours.
The interval is [0,12] and its length is 12, hence the period is 12.
The midline
[tex]y = \frac{min + max}{2} [/tex]
[tex]y = \frac{4 + 6}{2} = 5[/tex]
The amplitude is the distance from the midline to the peak.
The amplitude is |5-4|=|5-6|=1
The first choice is correct.
The amplitude of the function modeling the Chesapeake Bay tides is 1 foot, the period is 12 hours, and the midline is at y = 5 feet.
Explanation:The amplitude of a function that models a periodic phenomenon, like the tides in this case, is half of the total variation in height. Since the tides vary between 4 feet and 6 feet, the total variation is 2 feet (6 feet - 4 feet), and thus, the amplitude is 1 foot (2 feet / 2).
The period of the function is the time it takes for the tidal cycle to repeat itself. Given that the tide completes a full cycle in 12 hours, the period of the function is 12 hours.
The midline represents the average value around which the tide oscillates. It can be found by averaging the maximum and minimum tide levels. Therefore, the midline is (4 feet + 6 feet) / 2 = 5 feet.
Considering these calculations, the correct amplitude is 1 foot, the period is 12 hours, and the midline is y = 5 feet for the function that would model the periodic phenomenon of the Chesapeake Bay tides.
in the figure, ∆ABC ~ ∆DEF. solve for x
A) x = 1.5
B) x = 6
C) x = 4
D) x = 5.5
Answer:
Option B x=6 units
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In this problem
Triangles ABC and DEF are similar
therefore
∠A≅∠D
∠B≅∠E
∠C≅∠F
and
AB/DE=BC/EF=AC/DF
Find the value of x
AB/DE=BC/EF
substitute the given values
x/3=16/8
x=3*16/8
x=6 units
Which represents the solution(s) of the graphed system of equations, y = x2 + x – 2 and y = 2x – 2
Answer:
x=1 and x=0
Step-by-step explanation:
We need to find the points at which the graphs y = x^2 + x – 2 and y = 2x – 2 intercept.
We know that:
x^2 + x – 2 = 2x – 2
x^2 - x = 0
Factorizing:
x(x-1) = 0
Therefore, the solution to the system of equation is x=1 and x=0.
What is the range of rooms in Henry's histogram?
The houses surveyed had between 1 and 10 rooms.
The histogram shows a range of 5 to 6 rooms.
The houses surveyed had between 0 and 6 rooms.
The histogram shows a range of 1 to 5 rooms.
Answer:
The houses surveyed had between 1 and 10 rooms ..
Step-by-step explanation:
We can see from the histogram that the minimum number of rooms any house had was 1 and the maximum number of rooms were 10.
Range is the difference between highest and lowest value of a data set.
Hence, the range from the given histogram can be determined as:
The houses surveyed had between 1 and 10 rooms ..
Answer: The houses surveyed had between 1 and 10 rooms.
Step-by-step explanation:
The range of any data gives us a interval which contains all the data values and provides an indication of the dispersion of data its from minimum value to the maximum value.From the histogram, the minimum number of rooms = 1
The maximum number of rooms = 10
Hence, the range of rooms in Henry's histogram is between 1 and 10 rooms.
the expression with rational exponents as a radical expression.
5 times x to the one fourth power
Answer:
5[tex]\sqrt[4]{x}[/tex]
Step-by-step explanation:
Here we are given a verbal expression, we need to convert it to algebraic expression.
5 times x to the one fourth power.
Word Meaning
Times *(Multiplication)
one fourth [tex]\frac{1}{4}[/tex]
So, 5 times x to the one fourth power is = 5*[tex]x^{\frac{1}{4}}[/tex]
Now we have to write in using radical sign.
[tex]x^{\frac{1}{4} } = \sqrt[4]{x}[/tex]
Therefore, 5*[tex]x^{\frac{1}{4}}[/tex] = 5[tex]\sqrt[4]{x}[/tex]
Round 61.062 to one decimal place.
Answer: 61.1
Step-by-step explanation: The answer would be 61.1 because .062 is greater than .05, which means that it rounds up.
In converting 7.5 pounds to ounces, what unit (omit the number) would you place
in the denominator of your ratio? Use the plural form in your answer. Remember
that there are 16 ounces in 1 pound.
Final answer:
In converting 7.5 pounds to ounces, the unit placed in the denominator of the ratio is pounds. To do the conversion, multiply the number of pounds by 16, since there are 16 ounces in one pound. Therefore, 7.5 pounds is equal to 120 ounces.
Explanation:
When converting 7.5 pounds to ounces, we start by identifying the conversion factor between these two units of weight. The unit you would place in the denominator of your ratio is pounds, since the relationship is that 1 pound is equivalent to 16 ounces. So, the conversion from pounds to ounces requires multiplying the number of pounds by 16.
Here's how you would set up your conversion:
First, write down the amount of pounds you want to convert (7.5 pounds).
Multiply this amount by 16, the number of ounces in one pound (7.5 x 16).
The product will give you the amount in ounces (7.5 x 16 = 120 ounces).
The unit in the denominator for the ratio used in this conversion is pounds, as you are starting with pounds and converting to ounces.
what is the equation of a line that contains the points 5,0 and 5, -2
x=5
x=0
y=0
y=5
Check the picture below.
Answer: X=5
Step-by-step explanation: i took the FLVS test
On a piece of paper, draw a box plot to represent the data below. Then
determine which answer choice matches the box plot you drew.
22, 23, 25, 34, 36, 42, 44, 54, 57, 58, 61
Steps for the box plot are given below.
Since they are already in the order you know the 22 and the 61 are the upper and lower extremes.
To find the median you find the number that is in the middle which is 42.
We have to find the lower quartile find the middle number starting from the first number and the number to the left of the median (22 and 36 in this case). The lower quartile is 25.
What is the quartile?a quartile is a type of quantile that divides the number of data points into four parts, or quarters, of more or less equal size. The data must be ordered from smallest to largest to compute quartiles; as such, quartiles are a form of order statistic
To find the upper quartile, fine the middle number between the number to the right of the median and the last number (44 and 61 in this case.) If the upper quartile is 57 you then just plot it and graph it.
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What number is missing in the solution to the system of equations:
4x-3y=1
5x+4y = 9
(1.11
First you must solve system of equations.
Multiply the first equation by 4 and second one by 3.
You result with,
[tex]
16x-12y=4 \\
15x+12y=27
[/tex]
Add the equations so y terms cancel out.
[tex]31x=31\Longrightarrow x=1[/tex]
Insert x that was found in either one of the equations. I'll pick first one.
[tex]4\cdot1-3y=1[/tex]
Solve for y.
[tex]
-3y=-3 \\
y=1
[/tex]
The solutions to the system of equations are,
[tex]\boxed{x=1},\boxed{y=1}[/tex]
Therefore the number missing is 1.
Hope this helps.
r3t40
Answer:
(1,1)
Step-by-step explanation:
Write an equation for a rational function with:
Vertical asymptotes of x = 1 and x = -1
x intercepts of (2,0) and (-5,0)
Horizontal asymptote of y = 7
Answer:
f(x)=(7(x-2)(x+5))/((x-1)(x+1))
Step-by-step explanation:
The vertical asymptotes should be in the denominator. The x-interceps should be in the numerator. Because the horizontal asymptote is y=7, you have to put 7 in the numerator because the horizontal asymptote is the coefficient of the numerator ÷ the coefficient of the denominator, when we have the same degree of the numerator and the denominator.
what is the solution to the equation√8x=√4+2x? A. p=2/5 B. p=2/3 C.p=24 D.=40
Answer:
B
Step-by-step explanation:
you add the like terms together and find the value of x multiple by 4
The bill for Dino's lunch was $19.45. He wanted to leave 20% of the total bill as a tip. How much should the tip be?
You could multiply 19.45 by 0.2 to solve for it, but if you're not using a calculator, then 19.45/5 would be much more convenient and easier.
0.2 is 1/5 in fraction form, which is why we can do that.
19.45/5 = 3.89
Dino should leave $3.89 as a tip.
Answer:
$3.89
Step-by-step explanation:
X = 20
19.45 = 100
19.45*20=389
389/100=$3.89
Can somebody please help me
Answer:
1) Cubic
2) 2
3) -3
4) [tex]\frac{1}{9}x^{3}[/tex]
5) [tex]\frac{1}{9}[/tex]
Step-by-step explanation:
The given polynomial is:
[tex]\frac{1}{9}x^{3}-3[/tex]
The degree i.e. the highest exponent of the variable involved is 3. So the polynomial is a Cubic polynomial.
The terms in a polynomial can be distinguished by addition and subtraction symbols. So, for the given polynomial there are 2 terms.
The constant term is the term without any variable. So the constant term in given polynomial is -3.
Leading term is the term with variable having highest exponet which defines the degree of the polynomial. So leading term of the given polynomial is [tex]\frac{1}{9}x^{3}[/tex]
Leading coefficient is the coefficient of the leading term. So for given polynomial the leading coefficient would be [tex]\frac{1}{9}[/tex]
help I don’t understand this ♀️
What is the y-intercept of the graph of the function f(x) = x2 + 3x + 5?
(0,-5)
10 (0, -3)
(0,3)
(0,5)
Answer:
(0, 5)Step-by-step explanation:
The y-intercept is exist for x = 0.
We have the equation of the function: f(x) = x² + 3x + 5 → y = x² + 3x + 5.
Put x = 0:
y = 0² + 3(0) + 5 = 0 + 0 + 5 = 5
The correct option is option D: The y-intercept of the graph of the function will be (0,5).
How to determine the y-intercept of the graph of the function?The y-intercept of the function is determined by the point where the graph intercepts the y-axis.
At the point where the graph meets the y-axis, the x coordinate will be 0.
So by putting the x value =0 in the graph function, we can determine the y-intercept of the graph function. i.e. y=f(0)
Here, the function is given by f(x)=x²+3x+5
At the y-intercept point the x coordinate=0
So putting x=0, we can determine the y-intercept of the graph.
f(0)=0²+0+5=5
The y-coordinate of the y-intercept is 5.
The x-coordinate of the y-intercept is 0.
So the coordinate of the y-intercept is (0,5).
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The system of equations: 5x-4y=-3
3x+2y=7
Has the same solution as the system
1)5x-4y=-3
6x+4y=7
2)5x-4y=-3
6x+2y=14
3)5x-4y=-3
6x+4y=14
4)5x-4y=-3
9x+6y=14
Someone please help me I’m confused
Answer:
3)5x-4y=-3
6x+4y=14
Step-by-step explanation:
The system of equations is given
5x-4y=-3
3x+2y=7
Multiplying both sides of the lower equation by 2, we get
6x + 4y = 14
That means your answer 3)
The system with the same solution as the given system of equations is the one where the second equation is a multiple of the original. In this case, option 2) 5x - 4y = -3 and 6x + 2y = 14 shows the same solution set, as it is the only one that is equivalent to the original system after multiplying the second equation by 2.
Explanation:The student is trying to identify which system of equations has the same solution as the original system given by:
5x - 4y = -33x + 2y = 7When comparing this system to the provided options, we look for a system that is equivalent after applying some algebraic operations, since the solutions of equivalent systems are the same. For the second equation in each system, it must be a multiple of the original (3x + 2y = 7), or it must be alterable to be equivalent through multiplicative or additive operations.
In case of options:
6x + 4y = 7 is obtained by multiplying the second equation of the original system by 2, but this does not match the constant term (7).6x + 2y = 14 is obtained by multiplying the entire second equation of the original system by 2.6x + 4y = 14 cannot be a result of any simple algebraic operation from the original system.9x + 6y = 14 also is not a direct result of algebraic operations from the original system.The only system that is equivalent to the original one is the second option because doubling the second equation of the original system (3x + 2y = 7) gives us 6x + 4y = 14, which has the same solution set as the original system.
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The first row of a conference hall has 8 chairs and 2 additional chairs in each subsequent row. How many chairs are in the 9th row? How many chairs in total are in the first 9 rows?
Ans:
24 chairs in 9th row and 144 chairs in ist 9th rows
Step-by-step explanation:
ist row= 8
2nd = 10
3rd = 12
.
.
.
9th row = 24
and if we add all chairs = 8+10+12+14+16+18+20+22+24= 144
The requried, there are 24 chairs in the 9th row and there are 144 chairs in total in the first 9 rows.
What is arithmetic progression?Arithmetic progression is the series of numbers that have common differences between adjacent values
The first row has 8 chairs, and each subsequent row has 2 more chairs than the previous row. So the number of chairs in each row can be given by the equation:
number of chairs = 8 + 2(row - 1)
To find the number of chairs in the 9th row, we substitute row = 9 into the equation:
number of chairs = 8 + 2(9 - 1) = 8 + 2(8) = 24
So there are 24 chairs in the 9th row.
To find the total number of chairs in the first 9 rows, we need to add up the number of chairs in each row from 1 to 9. This can be done using the formula for the sum of an arithmetic series:
sum = (n/2)(first term + last term)
where "n" is the number of terms in the series.
In this case, the first term is 8, the last term is 24, and there are 9 terms (i.e. the first 9 rows). Substituting these values into the formula, we get:
sum = (9/2)(8 + 24) = 9(16) = 144
So there are 144 chairs in total in the first 9 rows.
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Solve the system using elimination. 3x – y = 28 3x + y = 14 (8, –4) (–4, 8) (–7, 7) (7, –7)
Answer:
x=7, y=-7
Step-by-step explanation:
3x – y = 28
3x + y = 14
Add the two equations together
3x – y = 28
3x + y = 14
---------------------
6x = 42
Divide by 6
6x/6 = 42/6
x = 7
3x – y = 28
3x + y = 14
Multiply the second equation by -1, then add
3x – y = 28
-3x - y = -14
-------------------
-2y=14
Divide by -2
-2y/-2 = 14/-2
y = -7
Find the measure of arc EC.
a) 50
b) 70
c) 100
d) 140
Answer:
a) 50
Step-by-step explanation:
The angle formed by two chords is the average of the arc angles.
7x = (5x + 90) / 2
14x = 5x + 90
9x = 90
x = 10
So the measure of arc EC is 5x = 50°.
The measure of arc EC is a) 50
What is the angle of a complete circle?The angle of a complete circle is 360°
The angle formed by two chords angle= arc/radius
⇒7x = (5x + 90) / 2
⇒14x = 5x + 90
⇒ 9x = 90
⇒x = 10
So the arc EC is 5x = 50°.
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What is the surface area of the rectangular prism below?
A. 260 units
B. 612 units2
C. 800 units2
D. 689 units2
Answer:
B.612 units2
Step-by-step explanation:
To solve surface area you multiply the area of each of the faces then you add the areas together. So the equation you need to solve is 13×6+13×6+12×13+12×13+12×6+12×6
After you solve that equation the answer you should get is 612.
Answer:
612
Step-by-step explanation:
What is the equation of a circle with center (2,-5) and radius 4?
Answer:
(x - 2)² + (y + 5)² = 16
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
here (h, k) = (2, - 5) and r = 4, hence
(x - 2)² + (y - (- 5))² = 4², that is
(x - 2)² + (y + 5)² = 16 ← is the equation of the circle