Answer:
x = 22.66
Step-by-step explanation:
Raymond built a “rocket" made from a cylinder and a cone. He filled the rocket
completely with water. What is the maximum number of gallons of water the rocket can
hold?
(231 in 3 = 1 gallon)
14in
16in
4in
Answer:
Rocket can hold maximum 4.5 gallons of water.
Step-by-step explanation:
Volume of the rocket = Volume of the cone on the top + Volume of the cylinder at the bottom
Volume of the cone = [tex]\frac{1}{3}\pi r^{2}h[/tex]
Here r = radius of the circular base
h = height of the cone
Volume = [tex]\frac{1}{3}\pi (4)^{2}(14)[/tex]
= [tex]\frac{224\pi }{3}[/tex] cubic inch
Volume of the cylinder = [tex]\pi r^{2}h[/tex]
Here r = radius of the base
h = height of the cylinder
Volume = [tex]\pi (4)^{2}(16)[/tex]
= 256π cubic inches
Volume of the rocket = [tex]\frac{224\pi }{3}+256\pi[/tex]
= [tex]\frac{992\pi }{3}[/tex]
= 1038.82 cubic inches
Since 231 cubic inches volume of a rocket can hold water = 1 gallon
Therefore, 1038.82 cubic inches space can hold water
= [tex]\frac{1038.82}{231}[/tex]
= 4.497
≈ 4.5 gallons
Rocket can hold 4.5 gallons of water.
Andre and Morgan are both headed to Florida for vacation. Andre will drive 70 miles per hour. Morgan will drive 55 miles per hour but will leave 3 hours earlier than Andre. How many hours will Morgan have been driving before Andre catches up with her?
Answer:
The number of hours Moran wold have driven before Andre catches up with him is 14 hours
Step-by-step explanation:
The given information are;
The speed with which Andre will drive = 70 miles per hour
The speed with which Morgan will drive = 55 miles per hour
The time of departure of Morgan = 3 hours before Andre departs
Let the time at which Andre catches up with Morgan be, t
We have, from the definition of distance traveled;
Distance traveled =Speed × Time
The distance Morgan would have driven in t hours = 55 × t
Given that to catch up with Morgan, Andre has to travel the same distance, and that Andre starts 3 hours late, we have;
The distance Andre would drive when Morgan has driven for t hours = 70 × (t - 3)
Therefore, since the distance at the point they meet is the same distance for them both, we have;
55 × t = 70 × (t - 3)
55 × t = 70 × t - 210
210 = 70 × t - 55 × t = 15 × t
t = 210/15 = 14 hours
Therefore, Morgan would have driven for 14 hours before Andre catches uo with him.
Answer:
Morgan walks 2 miles per hour.
Step-by-step explanation:
took the test. ;)
Please help if you can. Mandy used the input and output in this table to write ratios. She concluded that because they are not all equivalent, this is not a proportional relationship. Is she correct? Explain.
Answer:
he last ratio is written incorrectly.
Mandy reversed the input and output in the numerator and denominator.
The correct ratio is 50/10.
The relationship is proportional.
A page in Johanie’s workbook is torn, and one of the questions is cut off. She can read only the first part of the question: “In which quadrant would you find point P if the coordinates of P are (–5, ...” Assuming that P is not on an axis, what are the possible answers to this question?
Answer:
Quadrant 3 and Quadrant 4
Step-by-step explanation:
If the point is negative, then it will definetely be on the left side of the graph. The two quadrants on the left side are 3 and 4. Hope this helps!
How to find midpoint
Answer:
Midpoint of a Line Segment
Step-by-step explanation:
Add both "x" coordinates, divide by 2.
Add both "y" coordinates, divide by 2.
What is the answer. What is the unknown length
Answer:
9 cm
Step-by-step explanation:
Continue each pattern with the next two numbers.
1.7,14,8,16,10,20,14,
Answer:
7, 14, 8, 16, 10, 20, 14, 28, 22...
7 times 2 is 14, 8 times 2 is 16, 10 times 2 is 20, and so on.
hope this helps
a cab company charge s a flat rate of $2 plus and additional $0.50 for every mile traveled when Sara arrived at her destination her cab fare $7.50 write and solve and equation to determine how many miles sara traveled
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What would c need to be for this equation to be no solutions? l x+8 l = c
Answer:
Basically , anything negative number.
The absolute value can not be less than 0
Step-by-step explanation:
Example
[tex]\left|x+8\right|=-8\\\\\mathrm{Absolute\:value\:cannot\:be\:less\:than\:0}\\\mathrm{No\:Solution\:for}\:x\in \mathbb{R}\\[/tex]
Sebastian compra una bicicleta en $8562; una pantalla de tv. Que cuesta el doble de la bicicleta y un refrigerador que cuesta $ 1500 más que el doble de la tv. ¿Cuánto gastó en total.?
Answer:
$61.434
Step-by-step explanation:
Teniendo en cuenta que el enunciado señala que la pantalla de tv cuesta el doble de la bicicleta, debes multiplicar el valor de la bicicleta por 2 para encontrar su precio:
Precio pantalla de tv=$8.562*2=$17.124
Además, el enunciado señala que el refrigerador cuesta $1.500 más que el doble de la tv, por lo cual para encontrar su precio debes multiplicar el valor de la tv por 2 y sumarle $1500:
Precio del refrigerador=($17.124*2)+$1.500
Precio del refrigerador=$34.248+$1.500
Precio del refrigerador=$35.748
Finalmente, el gasto total es igual a la suma de los precios de la bicicleta, la tv y el refrigerador:
$8.562+$17.124+$35.748=$61.434
De acuerdo a esto, la respuesta es que Sebastian gastó $61.434.
Math problem giving brainlist and points!
Answer:
2c + 15 = 25
Step-by-step explanation:
The total he wants to earn is $25, so we know the equation must be an expression that equals 25.
____ = 25
He earns a fixed $15. He also earns $2 per customer.
The total he earns is the sum of the fixed amount ($15) and the amount he earns per customer. Let the number of customers be c. The amount he earns from the number of customers is 2c.
fixed amount + amount per customer = 25
15 + 2c = 25
2c + 15 = 25
Answer: 2c + 15 = 25
The Johnson family is going to build a new home. They need to have working drawings of their house plans created by a design firm. They will choose between Rock the House Digital Designs and Elegant Home Architects. Rock the House Digital Designs charges $500.00 for the initial consultation with the Johnson family, plus $50.00 for every additional hour of work for the house plans. Elegant Home Architects charge $75.00 per hour for the house plans. Let ℎ represent the number of hours for which the Johnson family hires the design firm. Which of the following statements are true? Select all that apply.
Answer:
Statements B, D, E are TRUE
Step-by-step explanation:
A. The expression 50ℎ represents the total charge for Rock the House Digital Designs.
NOT TRUE
The expression 500 + 50h represent total charge for Rock the house digital design
B. The expression 75ℎ represents the total charge for Elegance Home Architects.
TRUE
Elegance Home Architects
75h
C. The cost for using Rock the House Digital Designs for an initial consultation only is $550.
NOT TRUE
The cost for using Rock the House Digital Designs for an initial consultation only is $500
D. If the Johnson family hires the design firm for 15 hours, then Elegance Home Architects will be cheaper.
TRUE
Rock the house digital designs
$500 + $50h
= 500 + 50(15)
= 500 + 750
=$1,250
Elegant home architect
$75h
= 75(15)
= $1,125
Elegant home architect is cheaper
E. If the Johnson family hires the design firm for 40 hours, then Rock the House Digital Designs will be cheaper.
TRUE
Rock the house digital designs
$500 + $50h
= 500 + 50(40)
= 500 + 2,000
= $2,500
Elegant home architect
$75h
= 75(40)
= $3,000
Rock the House Digital Designs will be cheaper.
You own a fish store with 478 fishes. You put the same number of fish into 17 tanks, but there are 2 fishes left over. How many fishes are in each tank?
Answer:
10
Step-by-step explanation:
478-2=476
476÷17= 10
therefore you put 10 fish in each tank.
Let me know if this helps:)
Answer:
10
Step-by-step explanation:
Ray KN is the angle bisector of angle JKL.
Explain how you could find m angle JKN
if you know m angle JKL.
Answer:
See Explanation
Step-by-step explanation:
Given
Angle: JKL
Bisector: KN
Required
How to determine JKN if JKN is known
When a line bisects an angle into two, the angle are divided into two equal parts.
In this case, JKL is bisected by KN;
The resulting angles are JKN and NKL
So:
[tex]JKL = JKN + NKL[/tex] --------- (1)
From the explanation, we can understand that JKN and NKL hold the same value.
i.e. [tex]JKN = NKL[/tex]
So, (1) becomes
[tex]JKL = JKN + JKN[/tex]
[tex]JKL = 2JKN[/tex]
Divide by 2
[tex]JKN = \frac{JKL}{2}[/tex]
Take for instance; JKL =8
[tex]JKN = \frac{8}{2} = 4[/tex]
Identify the real number that corresponds to the point plotted on the real number line.
Please help is due in 15mins
Answer:
40. neither
41. Perpendicular
42. Parallel
43. y= -4x+1
44. 2x-y=5
45. y=-3/2x-2
46. -1/4x+y=5
Step-by-step explanation:
If x2 + ax + b = (x – 9)(x + 9), what is the value of
ab?
A) -81
B)
0
C)
81
D) 1458
Step-by-step explanation:
X2+ax+b=(x-9)(x+9)
X2+ax+b=x2-9x+9x-81
X2+ax+b=x2-81
therefore,a=0,b=(-81)
Then , ab = 0×-81 = 0
Answer:
B) 0Step-by-step explanation:
x² + ax + b = (x – 9)(x + 9)
x² + ax + b = x² – 9x + 9x – 81
x² + ax + b = x² + 0x – 81
x²=x² +ax = +0x +b = -81
a = 0 b = -81
ab = 0(-81) = 0
The complement of an angle is 10 less than 4 times the angle itself. What is the measure of the angle and its complement?
Answer:
Below.
Step-by-step explanation:
If the angle is x degrees then its complement is 90-x degrees.
So 90-x = 4x - 10
90 + 10 = 4x + x
5x = 100
x = 20.
and the complement is 90-20 = 70.
what quadrant is -2 (radians) in?
Answer:
From unit Symbol Equals Result To unit Symbol
1 quadrant quad. = 1.57 radians rad
Step-by-step explanation:
Enter the decimal 0.56 as a fraction in simplest form. The simplest form of the decimal 0.56 as a fraction is
Answer:
7/25
Step-by-step explanation:
0.56 move two times to get rid of the point that will give you 56/100 divide by an digit that can go equally in both of them to the lowest form start from 2
Which statement is true Every real number is an integer Every integer is a counting number Every integer is a rational number Every terminating decimal number is an irrational number
Answer:
C. Every integer is a rational number
Step-by-step explanation:
Integers are whole numbers which could be positive or negative and zero. Examples of integers are 330, 21, 10,052, 0, -425, -879, etc. Fractions are not integers. Rational numbers are numbers that are expressed as the ratio of two integers. So numbers that have integers as their numerators and denominators can be rightly said to be rational numbers. Examples are, 5/7, 10,111/880, -365/15.
Since both the numerators and denominators are whole numbers, the entire figures can be said to be rational numbers. So, fractions are rational numbers.
An experienced carpenter can frame a house twice as fast as an apprentice. Working together, it takes the carpenters 2 days. How long would it take the apprentice working alone?
Answer:
6 days
Step-by-step explanation:
Let the time taken by Carpenter working alone = [tex]C[/tex] days
Then time taken by apprentice alone = Twice as that of taken by Carpenter = 2[tex]C[/tex] days
Time taken working together = 2 days
Work done in one day working together = [tex]\frac{1}{2}[/tex]
Work done in one day by Carpenter working alone = [tex]\frac{1}{C}[/tex]
Work done in one day by apprentice working alone = [tex]\frac{1}{2C}[/tex]
Work done in one day by Carpenter working alone + Work done in one day by Carpenter working alone = [tex]\frac{1}{C}[/tex]+[tex]\frac{1}{2C}[/tex] = Work done in one day working together = [tex]\frac{1}{2}[/tex]
[tex]\dfrac{1}{C}+\dfrac{1}{2C}=\dfrac{1}{2}\\\Rightarrow \dfrac{2+1}{2C}=\dfrac{1}{2}\\\Rightarrow C = 3\ days[/tex]
Time taken by Carpenter alone to complete the work = 3 days
Time taken by Apprentice alone to complete the work = 3 [tex]\times[/tex] 2= 6 days
We are required to calculate the number of days it would take the apprentice working alone
The number of days it takes the apprentice working alone is 6 days
let
Number of days taken for the carpenter to work alone = x
Number of days taken by the apprentice to work alone = 2x
Number of days taken to work together = 2 days
Work done per day Carpenter = 1/x
work done per day apprentice = 1/2x
work done per day together = 1/2
So,
work done per day together = Work done per day Carpenter + work done per day apprentice
1/2 = 1/x + 1/2x
1/2 = (2 + 1) / 2x
1/2 = 3/2x
cross product
1(2x) = 2(3)
2x = 6
x = 6/2
x = 3 days
Therefore,
Number of days taken by the apprentice to work alone = 2x
= 2(3)
= 6 days
Read more:
https://brainly.com/question/11965590
Please show all work and not just the answers.
Answer:
(-1, 6)
Step-by-step explanation:
Midpoint formula:
xm = (x1 +x2)/2ym = (y1+y2)/2For G(-7, 3) and H(5, 9) the midpoint:
((-7+5)/2, (3+9)/2) = (-1, 6)Answer:
(-1,6)
Step-by-step explanation
use the midpoint formula:
(x 1 + x2 /2 , y1 + y2/2)
(-7+ 5 /2, 3+ 9 /2)
after simplfying
(-1,6)
The square of a number minus twice the number is 48. What is the number? (An explanation would be appreciated)
Step-by-step explanation:
The square of a number minus TWICE the number is 48
let the number be" X "
X^2-2X-48 = 0
(X - 8)(X + 6) = 0
x = 8 ᴏʀ X = -6
mark brainliest
One root of f(x)=x^3-4x^2-20x+48 is x = 6. What are all the factors of the function? Use the Remainder Theorem.
A. (x + 6)(x + 8)
B. (x – 6)(x – 8)
C. (x – 2)(x + 4)(x – 6)
D. (x + 2)(x – 4)(x + 6)
Answer:
(x - 6)(x + 4)(x - 2)
Step-by-step explanation:
since x = 6 is a root then (x - 6) is a factor
x³ - 4x² - 20x + 48 ÷ (x - 6)
= (x - 6)(x² + 2x - 8)
= (x - 6)(x + 4)(x - 2) ← factors of f(x)
By using the Remainder Theorem, all the factors of the function are,
⇒ (x - 6) (x + 2) (x - 4)
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
One root of function f (x) = x³ -4x² -20x + 48 is, x = 6.
Hence, (x - 6) is divide the function f (x) = x³ -4x² -20x + 48 as;
(x - 6) ) x³ -4x² -20x + 48 ( x² + 2x - 8
x³ - 6x²
--------------
2x² - 20x
2x² - 12x
-----------------
- 8x + 48
- 8x + 48
----------------
0
Hence, We get;
f (x) = x³ -4x² -20x + 48
f (x) = (x - 6) (x² + 2x - 8)
⇒ f (x) = (x - 6) (x² - 4x + 2x - 8)
⇒ f (x) = (x - 6) (x(x - 4) + 2(x - 4))
⇒ f (x) = (x - 6) (x + 2) (x - 4)
Thus., By using the Remainder Theorem, all the factors of the function are,
⇒ (x - 6) (x + 2) (x - 4)
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why is the quotient -100/(-5) the same as the quotient 100/5
Answer:The quotient of -100 and -5 is the same as the quotient of 100/5 because if you divide a negative number by a negative number, you will get a positive number and the same way if you divide a positive number by a positive number you will get a positive number.
Step-by-step explanation:
-100/-5 = 20
100/5 = 20
URGENT! find the smallest whole number when divided by 4 gives a remainder of 3, when divided by 3 gives remainder of 2, when divided by 2 gives a remainder of 1
Answer:
11 is the smallest whole number when divided by 4 gives a remainder of 3, when divided by 3 gives remainder of 2, when divided by 2 gives a remainder of 1
. Answer:1.when divide by 4 and gives a remainder of 3 = 12
2 .when divided by 3 gives a remainder of 2 = 6
3. when divided by 2 and gives a remainder of 1 = 2
Step-by-step explanation:
1. 12 ÷ 4 = 3
2. 6 ÷ 3 = 2
3.2 ÷ 2 = 1
Simplify (-2V7)(3V28)
Answer:
v^2 -4v-21
Step-by-step explanation:
I can explain in 2 - 3 sentences why the interger -2 has a greater value than the integer -5. In order to solve 2 - 3 you __________________. The reason -2 has a greater value than -5 is because ________________________________________________.
Answer:
I can explain in 2 - 3 sentences why the interge,r -2, has a greater value than the integer, -5. In order to solve, 2 - 3, you SUBTRACT. The reason, -2, has a greater value than, -5, is because, -2, is a negative so, -2 is bigger number than -5.