Answer:
Part A) [tex]h=V/(\pi r^{2})[/tex]
Part B) [tex]h=4\ cm[/tex]
Step-by-step explanation:
Part A)
we have the formula of the volume of a cylinder
[tex]V=\pi r^{2}h[/tex]
Solve for h
That means ----> isolate the variable h
Divide both side by πr²
[tex]V/(\pi r^{2})=\pi r^{2}h/(\pi r^{2})[/tex]
Simplify
[tex]V/(\pi r^{2})=h[/tex]
Rewrite
[tex]h=V/(\pi r^{2})[/tex]
Part B) Find the height of a cylinder with a volume of 36π cm3 and a base with a radius of 3 cm
we have
[tex]V=36\pi\ cm^3[/tex]
[tex]r=3\ cm[/tex]
substitute in the formula and solve for h
[tex]h=36\pi/(\pi 3^{2})[/tex]
[tex]h=4\ cm[/tex]
To solve for h in the formula V = πr2h, divide both sides of the equation by πr2 to isolate h. The height of a cylinder with a volume of 36π cm3 and a base radius of 3 cm is 4 cm.
Explanation:To solve the formula V = πr2h for h, we need to isolate h on one side of the equation. To do this, divide both sides of the equation by πr2. This gives us the equation h = V/(πr2). Therefore, the correct formula for solving for h is h = V/(πr2).
To find the height of a cylinder with a volume of 36π cm3 and a base radius of 3 cm, substitute the given values into the formula h = V/(πr2). This gives us h = 36π / (π * 32). Simplifying further, h = 36 / 9 = 4 cm.
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lost 6balls yesterday bought 12 balls, then lost 4 balls, how many balls did i have to begin with
Answer
2
Step-by-step explanation:
as -6+12-4
What are the zeros of f(x) = (x − 5)(x − 4)(x − 2)?
Answer:
x=5 , x=4, x=2
i got this answer by setting the x-5=0 then solve for x. same for each x-5, x-4, x-2.
Answer:
The zeros are 2,4 and 5.
Step-by-step explanation:
Consider the provided function.
[tex]f(x) = (x-5)(x-4)(x-2)[/tex]
To find the zeros equate the function equal to 0.
[tex](x-5)(x-4)(x-2)=0[/tex]
The zeros are:
[tex](x-5)=0[/tex] or [tex](x-4)=0[/tex] or [tex](x-2)=0[/tex]
[tex]=5[/tex] or [tex]x=4[/tex] or [tex]x=2[/tex]
Hence the zeros are 2,4 and 5.
16=4y-12 Solving various types of equations
Answer:7
Step-by-step explanation:
1.flip the equation 4y-12=16
2.add 12 to both sides 4y-12+12=16+12
3.divide both sides by 4
4y/4 =28/4
Y=7
13xyz + 9 + 2xyz + 3
The local meteorologist claims that the temperature is going to steadily drop over the next 4 hours. If the temperature changes by the same amount each hour, and it changes by a total of -28°F, how much will it change each hour? Explain how you got your answer in two or more complete sentences.
Answer:
-7 degrees
Step-by-step explanation:
-28 divided by 4 equals -7. -7 x 4 = -28
Answer:
[tex]-7^{\circ}F[/tex]
Step-by-step explanation:
Let x represent temperature change per hour.
We have been given that the temperature is going to steadily drop over the next 4 hours and the temperature changes by the same amount each hour.
So temperature change in 4 hours would be [tex]4x[/tex].
We are also told that the temperature changes by a total of -28°F, so we can represent this information in equation as:
[tex]4x=-28^{\circ}F[/tex]
Let us solve for x.
[tex]\frac{4x}{4}=-\frac{28^{\circ}F}{4}[/tex]
[tex]x=-7^{\circ}F[/tex]
Therefore, the temperature changes [tex]-7^{\circ}F[/tex] each hour.
2. y + 2x = 12 for D = {2,3,4}
What’s the domain and range
The domain of the function is the set of values for x, given as {2,3,4}. The range, which is the set of all output values for y that result when substituting each x value in the domain into the equation, is {8,6,4}.
Explanation:In this problem, we are given an equation y + 2x = 12 and a domain D = {2,3,4}, which means x takes the values 2, 3, and 4. The domain of a function is all the possible values that x can take. Therefore, in this case, the domain (D) is {2,3,4}.
The range, on the other hand, includes all the corresponding output values that y takes for each x in the domain. The output is determined by plugging each value of the domain (x) into the equation and solving for y:
For x=2, y=12-2(2)=8. For x=3, y=12-2(3)=6. For x=4, y=12-2(4)=4.
Hence, the range for this equation, given the domain {2,3,4}, is {8,6,4}.
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2r+8>16-2r and 7r+21
Answer:
First Equation answer: r > 2
Second Equation answer: 7 (r+3)
Step-by-step explanation:
First Equation Explanation: Move variable to the left side (2r + 2r + 8 > 16)
See the like terms (4r > 16-8)
Divide both sides by inequality of 4 (4r > 8) 4r----> r > 2
Second Equation Explanation: Factor out 7.
Complete
Complete each family of facts.
2 8 6
Answer:
all work is shown and pictured
The given family of facts can be completed as follows:
2 8 6 0 -4 -2 22 86.
by observing the given number pattern.
To complete the family of facts, observe the pattern and determine the missing numbers.
Starting with the first number, 2, observe that each subsequent number is obtained by multiplying the previous number by 4 and then subtracting 2.
So, to find the next number, multiply 6 by 4 and subtract 2, giving 22.
Similarly, to find the next number after 22, we multiply 22 by 4 and subtract 2, resulting in 86.
Therefore, the completed family of facts is 2 8 6 0 -4 -2 22 86.
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Hailey went to the market and bought 5 pounds of coffee that costs $2 a pound. She also purchased 2/3 pounds of lunch meat that cost $9 a pound . How much did Hailey spend at the market?
please help TVT
Answer:
$16
Step-by-step explanation:
$2 x 5 = $10
1 pound = $9
2/3 = $6
10+6=16
If a point is on the bisector of an angle, then it is:
Answer:
is equidistant from the sides of the angle
Step-by-step explanation:
Answer:
equidistant from the sdie of the angles
Step-by-step explanation:
8. Find the value of the variable(s) in each figure.
Explain your reasoning.
Answer:
(attached is the formulas and equations)
PLS HELP ME ASAP THIS IS DUE TMRW
Answer:
Dylan and Nadhii agree. The value of both of their ratios is equivalent, so their ratios are also equivalent.
Good luck<3
find the equation of the horizontal line that contains the point (-4,8). express the equation using either the general form of the slope intercept form of the equation of a line
Answer: [tex]y=8[/tex]
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
We know that this is a horizontal line. This means that:
[tex]m=0[/tex]
Knowing that this line contains the point (-4,8) we can substitute this coordinates and [tex]m=0[/tex] into [tex]y=mx+b[/tex], and then solve for "b":
[tex]8=0(-4)+b\\\\b=8[/tex]
Therefore, the equation of this line in Slope-intercept form is:
[tex]y=(0)x+8\\\\y=8[/tex]
Final answer:
The equation of the horizontal line that contains the point (-4,8) is y = 8 and it demonstrates that for a horizontal line, the slope is 0 and the y-coordinate remains constant along the line.
Explanation:
The equation of a horizontal line that contains a given point can be determined by looking at the y-coordinate of that point. Since a horizontal line has a slope of 0, the y-coordinate of any point on the line does not change. Therefore, the equation of the horizontal line that contains the point (-4,8) is simply y = 8. This equation indicates that the y-value will always be 8, regardless of the x-value, which is characteristic of a horizontal line. In the slope-intercept form of the equation of a line, which is y = mx + b, the slope (m) is 0, and the y-intercept (b) is 8.
Problem Set#3:
Choose a situation that could be described by the following ratios, and write a sentence to describe the ratio in the context of the situation you chose.
For example:
3: 2 When making pink paint the art teacher uses the ratio 3:2. For every 3 cups of white paint she uses in the mixture, she needs to use 2 cups of red paint.
a. 1 to 2
b. 29 to 30
c. 52:12
*Answer A-C
The ratios 1:2, 29:30, and 52:12 can be represented in different situations, such as recipe measurements, voting results, and quantities of colored marbles.
Explanation:a. 1 to 2: In a recipe for pancakes, the ratio 1:2 could be used to represent the ratio of flour to milk. For every 1 cup of flour, you would need 2 cups of milk.
b. 29 to 30: Suppose a group of students are voting for their favorite ice cream flavor, and there are 29 votes for chocolate and 30 votes for vanilla. The ratio of 29:30 represents the ratio of votes for chocolate to votes for vanilla.
c. 52:12: Let's say you have a bag of different colored marbles, and there are 52 red marbles and 12 blue marbles. The ratio 52:12 would then represent the ratio of red marbles to blue marbles in the bag.
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If 4 is added to five times a number, the result is equal to 9 more than four times the number. Find the number
Answer:
5
Step-by-step explanation:
4+5x=4x+9
-4x -4x
4+x=9
-4 -4
x=5
Janice went out to eat and bought a hamburger, a bag of chips,
and a drink. The hamburger cost $2.57, and the chips cost $1.25.
Janice gave the cashier $20.00 and received $14.39 in change.
How much did the drink cost?
Find Sn for the given arithmetic series.
a1 = 18, d = –3, n = 14
Answer:
- 21
Step-by-step explanation:
The sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ], thus
[tex]S_{14}[/tex] = [tex]\frac{14}{2}[/tex][( 2 × 18) + (13 × - 3) ]
= 7 (36 - 39) = 7 × - 3 = - 21
The sum of the arithmetic series with the first term 18, common difference -3, and 14 terms is 231.
Explanation:To find the sum, Sn, of an arithmetic series where a1 is the first term, d is the common difference, and n is the number of terms, you can use the formula:
Sn = ⅓n × (a1 + an)
First, find the nth term (an) using the formula:
an = a1 + (n - 1)d
For a1 = 18, d = –3, and n = 14:
an = 18 + (14 - 1)(-3)
an = 18 - 39 = –21
Sn = ⅓(14) × (18 + (–21))
Sn = 7 × (18 - 3) × 33
Sn = 231
So, the sum of the series is 231.
A storage locker is 15 Ft long, 2 ft wide, and 4 ft high. How many boxes that are 3 ft long, 2 ft wide, and 1 ft high can the locker fit?
Answer:
20 boxes can fit
Step-by-step explanation:
15x2×4=120 so 120 is the area of the storage locker
3×2×1=6 so 6 is the area of the boxes
120÷6=20
The fraction models below represent two fractions of the same whole. How much of the Fraction 5 over 8 is in the Fraction 1 over 2?
Two rectangles of the same size are drawn side by side touching each other. The first rectangle is divided into 8 portions of equal size. Five of these are shaded. The shaded portion alone is labeled as 5 over 8. The second rectangle is divided into 2 portions of equal size. One portion is shaded. The shaded portion alone is labeled 1 over 2.
Fraction 5 over 16
Fraction 4 over 5
Fraction 5 over 4
Fraction 16 over 5
To find how much of 5/8 is you would need to divide 1/2 by 5/8:
X = (1/2) / (5/8)
When dividing fractions, you reverse the second fraction and multiply:
X = (1/2) x (8/5)
X = 8/10
Simplify:
X = 4/5
The fractional amount of the fraction 5 over 8 in the fraction 1 over 2 is the fraction 4 over 5. Therefore, Option B is correct.
From the information given;
We are to find how much the Fraction 5 over 8 is in the Fraction 1 over 2
This implies that we need to divide the fraction 5 over 8 i.e. [tex]\mathbf{\dfrac{5}{8}}[/tex] by the fraction 1 over 2 i.e. [tex]\mathbf{\dfrac{1}{2}}[/tex]
Mathematically;
[tex]\dfrac{1}{2} \div \dfrac{5}{8}[/tex]
[tex]\mathbf{= \dfrac{1}{2} \times \dfrac{8}{5} }[/tex]
[tex]\mathbf{= \dfrac{4}{5}}[/tex]
Therefore, we can conclude that the fractional amount of the fraction 5 over 8 in the fraction 1 over 2 is the fraction 4 over 5.
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11. Isaac wrote two simplified expressions that were not equal to each other. Each equation also had
a different coefficient on the variable. If he sets the expressions equal to each other, will the
equation have one solution, no solution or infinitely many solutions? Use an example to support
your answer.
Answer:
The equation has only one solution
Step-by-step explanation:
* Lets explain how to solve the problem
- There are three types of solutions for the equations
Case (1)
# Two sides of the equation have different coefficient of the variable
and same or different numerical terms, then the equation has only
one solution
- Ex: 2x + 5 = x + 5, lets solve it
∵ 2x + 5 = x + 5
- subtract x from both sides
∴ x + 5 = 5
- Subtract 5 from both sides
∴ x = 0
- Zero is a solution
∴ The solution of the equation is x = 0
- If the numerical terms are different x will be any other value, so the
equation has only one solution
∴ The equation has one solution
Case (2)
# Two sides of the equation have same coefficient of the variable,
and different numerical terms, then the equation has no solution
- Ex: 14x - 20 = 14x + 10, lets solve it
∵ 14x - 20 = 14x + 10
- Subtract 14x from both sides
∴ - 20 = 10
- The left hand side not equal the right hand side , then there is
no value of x can make the two sides equal
∴ The equation has no solution
Case (3)
# Two sides of the equation have same coefficient of the variable,
and same numerical terms, then the equation has infinitely
many solutions
- Ex: 3x + 5 = 3x + 5, lets solve it
∵ 3x + 5 = 3x + 5
- Subtract 3x from both sides
∴ 5 = 5
- The left hand side is equal to the right hand side , then x can be
any value because the two sides is already equal without x
∴ The equation has infinitely many solutions
∵ He will write two expressions simplified , not equal , have different
coefficients on the variables and equate them, then it is like
the first case
- That means not same coefficient of the variable, and may be not
same numerical term
∴ The equation has only one solution
What is the rate of change for this problem??
same thing here, let's pick two points, any two points off the table to get the slope.
[tex]\bf \begin{array}{|cc|ll} \cline{1-2} tables&cost\\ \cline{1-2} 1&10\\ 2&18\\ 3&24\\ 4&28\\ \cline{1-2} \end{array} \begin{array}{llll} \\[1em] \leftarrow \\\\ \leftarrow \end{array}\qquad \qquad (\stackrel{x_1}{2}~,~\stackrel{y_1}{18})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{28})[/tex]
[tex]\bf \stackrel{\textit{\large average rate of change}}{\stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{28}-\stackrel{y1}{18}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{2}}}\implies \cfrac{10}{2}\implies 5}[/tex]
Ivan and Tanya share £150 in the ratio 4:1 how much more Ivan has then tanya
Hey!
--------------------------------------------------------
Solution:
Ratio is 4/1
Add.
4 + 1 = 5
Divide.
150 / 5 = 30
Multiply for Ivan.
30 x 4 = 120
30 x 1 = 30
Check.
120 + 30 = 150
Subtract.
120 - 30 = 90
--------------------------------------------------------
Answer:
Ivan has £90 more than Tanya has!
--------------------------------------------------------
Hope This Helped! Good Luck!
Answer:
90
Step-by-step explanation:
Since the ratio is 4:1 there are 5 (4+1) parts you should divide it into.
150 ÷ 5 = 30
30 = 1 part
30 × 4 = 120
Ivan has 120 while Tanya has 30. to find the difference you subtract the two.
120 - 30 = 90
What’s the answer?????
Answer:
1:0,2,4,6,8,10
2:0,5,10,15,20,25
Step-by-step explanation:
What is 14/49 in its simplest form???
Answer:2/7
Step-by-step explanation: 14 divided by 2 equals 7 and 49/7 equals 7 which means 7 is your GCF because seven going into both numbers
Answer:
2/7
Step-by-step explanation:
14÷7 / 49÷7 = 2/7
3. Find the annual salary when the monthly salary is $4,725,
Answer:
4725 * 12 = $56,700
Step-by-step explanation:
Salary for 1 month = 4725
Salary for 12 months = 56700 (4725 times 12)
Answer:
$56,700
Step-by-step explanation:
Since there are 12 months in a year, you take the Monthly salary and multiply it by 12 to get the annual salary
How many angle degrees does a minute hand travel in 1 minute? What angle does an hour hand travel in 1 min?
Answer:
Minute hand moves 6 degrees, hour hand moves .5 degrees.
Step-by-step explanation:
Doing the math we agree that in 1 minute the little hand (hours) will move .5 degrees and the big hand (minutes) will move 6 degrees.
A _____ is the difference between the greatest number and the least number . What’s the blank ?
Answer:
Lamb is the difference
Step-by-step explanation:
Answer:
range
Step-by-step explanation:
HELP ASAPPPPP 20 POINTS !!!!! Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Polygon ABCD is a parallelogram, and m2ABC = 127°. The length of BC Is 10 units, and the length of AB is 5 units.
The perimeter of the parallelogram is ————
units, and mZBCD IS ——- degrees
Answer:
The perimeter is 30 and the angle is 53.
Step-by-step explanation:
The perimeter is found by adding the length of all four sides. Two sides are 10 units and two sides are 5 units. 10+10+5+5 = 30.
The angle is found by subtracting angle ABC's value from 180.
180 - 127 = 53.
The perimeter of a parallelogram ABCD is 30 units and the measure of angle BCD is 53°.
What is parallelogram?A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent.
Given that, from given parallelogram ABCD, m∠ABC=127°.
The length of BC Is 10 units, and the length of AB is 5 units.
Here, the perimeter of of a parallelogram is AB+BC+CD+DA
= 10+5+10+5
= 30 units
Here, m∠ABC+m∠BCD=180° (Sum of co-interior angles is 180°)
127°+m∠BCD=180°
m∠BCD=180°-127°
m∠BCD=53°
Therefore, the perimeter of a parallelogram ABCD is 30 units and the measure of angle BCD is 53°.
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A bedroom is 11.4 feet long amd 12.5 feet wide. Shui wants to paint the floor. A gallon of paint will cober approximately 150 square feet. Will one gallon of paint be enough to paint the bedroom floor with 2 coats of paint? Explain your reasoning
Answer:
One gallon of paint is not enough to paint the bedroom floor
Step-by-step explanation:
step 1
Find the area of the bedroom floor
The area is in the shape of rectangle
so
[tex]A=(11.4)(12.5)=142.5\ ft^2[/tex]
Remember that the bedroom floor will be painted with two coats of paint
so
Multiply the area by two
[tex]A=(2)142.5=285\ ft^2[/tex]
A gallon of paint will cover approximately 150 square feet
[tex]285\ ft^2 > 150\ ft^2[/tex]
therefore
One gallon of paint is not enough to paint the bedroom floor
Final answer:
No, one gallon of paint will not be enough to paint the bedroom floor with 2 coats of paint.
Explanation:
To determine if one gallon of paint will be enough to paint the bedroom floor with 2 coats of paint, we need to calculate the total area of the floor and then divide it by the coverage area of a gallon of paint.
The area of the bedroom floor is calculated by multiplying the length and width together: 11.4 feet * 12.5 feet = 142.5 square feet.
Since we need to apply 2 coats of paint, we need to double the area: 142.5 square feet * 2 = 285 square feet.
Since one gallon of paint covers approximately 150 square feet, one gallon of paint will not be enough to paint the bedroom floor with 2 coats of paint.
1/4 (12x−5.6)=0.5(3x+0.7)
Answer:
7/6
Step-by-step explanation:
Firstly we have to distribute it and write in this form
1/4*12x-1/4*5.6=0.5*3x+0.5*0.7
3x-1.4=1.5x+0.35 ( now that we have multiplied and simplified it we will combine like terms remember whenever you move it to the other side of equal signs it turns the opposite of the sign value eg positive to negative.
subtract 0.35 from both sides leaving the equations as 3x-1.75=1.5x
now we move 3x on other side to combine with 1.5x and 3x becomes negative
-1.75=1.5x-3x
-1.75= -1.5x (divide -1.5 from both sides
-1.75/-1.5=1.5x/-1.5
1.166666666666667=x
or 7/6 if you left the fraction as it is and didn't simplify further.
Let me know if you don't understand or need more help .
The student's algebraic equation 1/4 (12x−5.6)=0.5(3x+0.7) simplifies to x = 1.17. This is found by distributing numbers, rearrangement of terms, and final division to solve for x.
Explanation:The question is an algebraic equation that needs to be simplified and solved. First, distribute the numbers in front of the parentheses to both the terms inside. This gives:
3x - 1.4 = 1.5x + 0.35Next, rearrange terms to bring all terms involving x to one side of the equation and constants to the other side. This gives:
3x - 1.5x = 0.35 + 1.4Simplify the equation to get:
1.5x = 1.75Finally, divide by 1.5 on both sides to solve for x:
x = 1.75 / 1.5So, x = 1.17 (rounded to two decimal places).
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