Answer:
w = y - x is the equation to find w
Where,
w = Weight of the liquid
x = Weight of the empty can
y = Weight of the can with liquid
Step-by-step explanation:
Let
Weight of the empty can = x
Weight of the liquid = w
Weight of the can with liquid = x + w = y
x= 30 grams
w = ?
y= 47.3 grams
y = x + w
w = y - x
= 47.3 - 30
= 17.3
w= 17.3 grams
Therefore, the weight of the liquid is 17 .3 grams
1. One number is 11 more than 3 times another number. Their sum is 71. Find the smaller number. 2. Two angles are complementary. One angle measures 22 degrees more than the other angle. Find the measure of the larger angle. 3. Two angles are supplementary. One angle measures 40 degrees more than the other angle. Find the measure of the larger angle. 4. The sum of three consecutive even integers is -36. Determine the largest integer of the three.
Answer:
1. The two numbers are 56 and 15
2. The two angles are 56 and 34 degrees
3. The two angles are 110 and 70 degrees
4.The largest number is -10
Step-by-step explanation:
Solving (1):
Represent both numbers with x and y
[tex]x = 11 + 3y[/tex]
[tex]x + y = 71[/tex]
Solving for x and y
Substitute [tex]11 + 3y[/tex] for x in the second equation
[tex]11 + 3y + y = 71[/tex]
Collect Like Terms
[tex]3y + y =71 - 11[/tex]
[tex]4y = 60[/tex]
Divide both sides by 4
[tex]y = 15[/tex]
Recall that
[tex]x = 11 + 3y[/tex]
[tex]x = 11 + 3 * 15[/tex]
[tex]x = 56[/tex]
Hence, the two numbers are 56 and 15
Solving (2)
Represent the two angles with x and y
[tex]x = 22 + y[/tex]
Since they are complementary;
[tex]x + y = 90[/tex]
Substitute 22 + y for x in [tex]x + y = 90[/tex]
[tex]22 + y +y= 90[/tex]
[tex]22 + 2y =9 0[/tex]
Collect Like Terms
[tex]2y = 90 - 22[/tex]
[tex]2y = 68[/tex]
Divide both sides by 2
[tex]y = 34[/tex]
Recall that [tex]x = 22 + y[/tex]
[tex]x = 22 + 34[/tex]
[tex]x = 56[/tex]
Solving (3):
Represent the two angles with x and y
[tex]x = 40 + y[/tex]
Since they are supplementary;
[tex]x + y = 180[/tex]
Substitute 40 + y for x in [tex]x + y = 180[/tex]
[tex]40 + y + y = 180[/tex]
[tex]40 + 2y = 180[/tex]
Collect Like Terms
[tex]2y = 180 - 40[/tex]
[tex]2y = 140[/tex]
Divide both sides by 2
[tex]y = 70[/tex]
Recall that [tex]x = 40 + y[/tex]
[tex]x = 40 + 70[/tex]
[tex]x = 110[/tex]
Solving (4):
Let the smallest number be x
[tex]x + x + 2 + x + 4 = -36[/tex]
Collect Like Terms
[tex]x + x + x = -36 - 2 - 4[/tex]
[tex]3x =-42[/tex]
Divide through by 3
[tex]x = -14[/tex]
The largest number; x + 4 is
[tex]x + 4 = -14 + 4[/tex]
[tex]x + 4 = -10[/tex]
Hence, the largest number is -10
Three equal-sized cardboard boxes are stacked on top of each other. Each box is 56.4 cm in height. What is the combined height of the 3 stacked boxes?
Answer:
169.2 cm
Step-by-step explanation:
Because the boxes are identical, the height of the combined boxes = 56.4 cm x 3 = 169.2 cm
(-2)(3-4-(-1)+6 pls help
Answer:
6
Step-by-step explanation:
(-2)(3-4-(-1)+6
(-2)(-1-(-1)+6
(Since a negative and a negative make a positive that becomes -1+1.)
(-2)(0)+6
0+6
6
Answer:
Hello! :) I hope I am correct!
Step-by-step explanation:
The answer would be -12
(Look below for steps!!)
-2(-1-(-1)+6)
⇒-2(0+6)
⇒(-2)(6)
(Do the calculations above to find the answer)
=-12
Hope this helps!
By; BrainlyAnime
(Also I attached a picture of other ways to solve this problem!)
x + 1 > -5( 7-2x) I need help please.
Answer:
x<4
Step-by-step explanation:
[tex]x + 1 > -5( 7-2x) \\\\\mathrm{Expand\:}-5\left(7-2x\right):\quad -35+10x\\x+1>-35+10x\\\\\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}\\x+1-1>-35+10x-1\\\\Simplify\\x>10x-36\\\\\mathrm{Subtract\:}10x\mathrm{\:from\:both\:sides}\\x-10x>10x-36-10x\\Simplify\\-9x>-36\\\\\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}\\\left(-9x\right)\left(-1\right)<\left(-36\right)\left(-1\right)\\\\Simplify\\9x<36[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}9\\\frac{9x}{9}<\frac{36}{9}\\\\x<4[/tex]
Kim started a savings account that can be modeled with A = 500*(1.035) what is the yearly percent
increase according to the model?
A. 3.5%
B. 35%
C. 5%
D. 103.5%
Please help
Answer:
3.5% because 1.035 * 100 = 3.5
Answer:
3.5
if you take 100 times 1.035 you get 103.5
Simplify: (6x-4) (9x-2)
Step-by-step explanation:
Hey, there!!
While simplifying the algebraic expression, you must be very careful about the signs.
Here,
(6x-4) (9x-2)
Multiply 2nd expression by 1st expression,
= 6x ( 9x - 2) -4 ( 9x - 2)
[tex] = (54 {x}^{2} - 12x) - (36x - 8)[/tex]
Opening brackets,
[tex] = 54 {x}^{2} - 12x - 36x + 8[/tex]
Simplifying them we get,
[tex] = 54 {x}^{2} - 48x + 8[/tex]
Therefore, the answer is 54x^2 - 48x +8.
Hope it helps..
Solve for x:
9x - 3 - 8x = 7 - x
x= -7
x=-2
x = 4
x = 5
Answer:
x = 5
Step-by-step explanation:
Given
9x - 3 - 8x = 7 - x , that is
x - 3 = 7 - x ( add x to both sides )
2x - 3 = 7 ( add 3 to both sides )
2x = 10 ( divide both sides by 2 )
x = 5
Answer:
Step-by-step explanation:
Which formula defines the sequence f(1) = 2, f(2) = 6, f(3) = 10,f(4) = 14.
f(5) = 18?
Answer:
2 + 4(n-1).
Step-by-step explanation:
As x increases from 1, f(x) increases by 4.
Arithmetic sequence.
So the formula is a1 + d(n - 1)
= 2 + 4(n-1).
The function which defines the series will be 2 + 4(n-1).
What is a number series?
A series of numbers is called a number series. We must identify the laws that lead to the production of a number series in order to answer the questions about number series. The questions that might arise from these topics are as varied as these series themselves.
Given functions are f(1) = 2, f(2) = 6, f(3) = 10,f(4) = 14 f(5) = 18. The sequence will be represented by the function:-
As x increases from 1, f(x) increases by 4. Arithmetic sequence.
F = a₁+ d(n - 1)
F = 2 + 4(n-1).
Therefore, the function which defines the series will be 2 + 4(n-1).
To know more about the number series follow
https://brainly.com/question/6561461
#SPJ2
A line with a slope of -2/5 that passes through the point (-10,8)
Step-by-step explanation:
[tex]m = - \frac{2}{3} \\ ( - 10 ,\: 8) = (x_1,y_1)[/tex]
[tex]y-y_1=m(x-x_1)[/tex]
Plug in the values into the equation
[tex]y - 8 = - \frac{2}{3} (x - ( - 10)) \\ y - 8 = - \frac{2}{3}( x + 10) \\ [/tex]
[tex]y - 8 = - \frac{2}{3} x - \frac{20}{ 3 } \\ y = - \frac{2}{3} x - \frac{20}{3} + 8 \\ [/tex]
[tex]y = - \frac{2}{3} x + \frac{4}{3} [/tex]
To solve for x-intercept , Arrange the values in
[tex]ax + by + c = 0[/tex]
=
[tex] - \frac{2}{3} x - y + \frac{4}{3} = 0[/tex]
To find x-intercept .let y = 0 in the above equation
[tex] - \frac{2}{3} x - y + \frac{4}{3} = 0 \\ - \frac{2}{3} x - 0 + \frac{4}{3} = 0 \\ [/tex]
[tex] - \frac{2}{3} x + \frac{4}{3} = 0 \\ - \frac{2}{3} x = - \frac{4}{3} [/tex]
Solve for x ;
[tex]x = 2[/tex]
To find y intercept , let x = 0
and solve for y .
I hope it helps <3
y = mx + b
m = -²/₃ and line pases through (-10, 8) so:
8 = -²/₃(-10) + b
8 = ²⁰/₃ + b
b = 8 - ²⁰/₃
b = 8 - 6²/₃
b = 1¹/₃
b = ⁴/₃
Slope Intercept Form:
y = -²/₃x + ⁴/₃x-intercept:
-²/₃x + ⁴/₃ = 0
-²/₃x =- ⁴/₃
x = - ⁴/₃ ÷(-²/₃)
x = 2
(2, 0)y-intercept:
y = -²/₃•0+ ⁴/₃ = ⁴/₃
(0, ⁴/₃)Eric has a jar of quarters and dimes. He had 48 coins in the jar. The total value of the coins is $7.35. How many quarters are.in the jar?
Answer:
17
Step-by-step explanation:
$4.25 - 17 quarters
$3.10 - 31 dimes
Answer:
17 quarters and 31 dimes are in the jar
Step-by-step explanation:
First, you need to set up two equations based on the information given.
First is an equation for the total number of coins:
48 = d + q
d = dimes
q = quarters
Second is an equation for the total amount in the jar and the respective amount per variable (d = .1 , q = .25).
7.35 = .1d + .25q
Using the first equation, you need to solve for one variable. In this case well solve for d, so we can later plug it in to solve for q.
48 = d + q
d = 48 - q
Next, we can plug our formula for d into our second equation, so we only have one variable to solve for, q.
.1(48-q) +.25q = 7.35
4.8 - .1q + .25q = 7.36
4.8 + .15q = 7.35
.15q = 2.55
q = 17
Finally, to solve for d with a number, we can plug q = 17 back into our first formula : 48 = d + q
48 = 17 + d
d = 31
I hope this helps!
-TheBusinessMan
3x + y = 6
4x + 2y = 8
Answer:
x=2 y = 0
Step-by-step explanation:
good luck
How many (5in. by 5in. by 5in) cubes will occupy a classroom 9ft by 8ft by 7ft in dimension?
Answer:
Step-by-step explanation:
first convert feet to inches because the measure of cubes is in inches
( 12 inches=1 foot)
9 ft = 12*9=108 inches
8 ft=12*8=96 inches
7 ft= 12*7=84
the volume of the one cube= 5*5*5=125
volume of the classroom: 108*96*84=870912
divide : 870912/125=6967 cubes
A 2.5 ft wide circular track for a camera dolly is set up for a movie scene. The two rails of the track form concentric circles. The radius of the inner circle is ft. How much farther does a wheel on the outer rail travel than a wheel on the inner rail of the track in one turn?
Answer:
15.71 ft
Step-by-step explanation:
Given that:
width of the circular track = 2.5ft
Suppose the radius of the inner circle is 57 ft since it is not given
Then the radius of the outer circle = (2.5 + 57) ft = 59.5 ft
The circumference of a circle = 2πr
For inner circle now, the circumference = 2 × π × 57 ft
For inner circle now, the circumference = 358.14 ft
For the outer circle, the circumference = 2 × π × 59.5 ft
For the outer circle, the circumference = 373.85 ft
The difference between the circumference of the outer wheel from the inner wheel shows how farther does a wheel on the outer rail travel than a wheel on the inner rail of the track in one turn
∴
= ( 373.85 - 358.14 ) ft
= 15.71 ft
A teacher and a doctor each have 45 books. If 4/5 f the teacher's books and 2/3 of the doctor's books are novels, how many more novels does the teacher have than the doctor? Explain the process that was used to find your answer.
Answer:
3/5
Step-by-step explanation:
The teacher has six novels more than the doctor.
What is the fraction?A fraction is defined as a numerical representation of a part of a whole that represents a rational number.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
We have been given that 4/5 of the teacher's books and 2/3 of the doctor's books are novels.
Since a teacher and a doctor each have 45 books.
As per the fractions of the book,
The number of teacher's books = 4/5(45) = 36
The number of doctor's books = 2/3(45) = 30
Therefore the required difference would be 36- 30 = 6 books
Hence, the teacher has six novels more than the doctor.
Learn more about the fraction here:
brainly.com/question/10354322
#SPJ2
earth completes its 584-million-mile orbit of the sun in about 365 days. how fast is earth moving through its orbit in miles per hour?
Answer:
66666.67 miles/hr
Step-by-step explanation:
Given that:
Earth complete its orbit of the Sun which is 584 million miles
Time taken to complete the orbit = 365 days
To find:
Speed of earth in miles per hour = ?
Solution:
First of all, we need to convert the distance in miles and time in hours to get our answer.
Let us have a look at the conversion units:
1 day = 24 hours
So, 365 days = 24 [tex]\times[/tex] 365 hours = 8760 hours
Distance traveled = 584 million miles
1 million miles = 1000000 miles
584 million miles = 584000000 miles
Formula for speed is given as:
[tex]Speed = \dfrac{Distance}{Time}[/tex]
Let us put the values of Distance and time given in miles and hours to get the speed in miles/hr.
[tex]Speed = \dfrac{584000000}{8760}\\\Rightarrow \bold{Speed = 66666.67\ miles/hr}[/tex]
So, the answer is: 66666.67 miles/hr
A skyscraper elevator can move one-teeth of a mile in half a minute. What is this speed expressed in miles per minute?
Answer:
.2 miles per minute or .2x
Step-by-step explanation:
it move one tenth in half a minute so it moves 2 tenths in a minute.
Solve for b in the literal equation y = 11x + 11b
Answer:
b = y/11 -xStep-by-step explanation:
[tex]y = 11x + 11b\\Move \: 11x\:to\:the \:left\:and\:change\:its\:sign\\\\y -11x =11b\\\\Divide\:both\:sides\:of\:the\:equation\:by\: 11\\\frac{y}{11} -\frac{11x}{11} = \frac{11b}{11} \\y/11 -x =b\\\\b = \frac{y}{11} - x[/tex]
Answer: b = y/11 - x
Step-by-step explanation: You have to isolate your variable by dividing each side of the equation by your factors that DO NOT contain any variable.
I hope this helps you out.
.837537537 as a fraction
Answer:
.837537537 =
837537537
1000000000
Step-by-step explanation:
Answer:
0
-
1000000000
i think it will help you
Simplify 4^2 • 4^8
Multiple Choice Answers:
4^16
4^10
16^16
16^10
I would really appreciate if someone could answer this really quickly. If you could also answer a couple of other ones too that would be absolutely amazing!!!
Answer:
[tex]4^{10}[/tex]
Step-by-step explanation:
Using the rule of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex] , thus
4² × [tex]4^{8}[/tex] = [tex]4^{(2+8)}[/tex] = [tex]4^{10}[/tex]
Given the number Line, what ray does not contain CB?
Answer:
[tex]\large \boxed{\mathrm{C }}[/tex]
Step-by-step explanation:
The ray CF does not contain the ray CB.
The number line, does not contain CB is CF. Therefore, option C is the correct answer.
What is line segment?A line segment is a path between two points that can be measured. Since line segments have a defined length, they can form the sides of any polygon.
In the given number, there are six divisions A, B, C, D, E, F.
Ray CB is in the line segment AD, AE, FA, BE, BF.
The number line, does not contain CB is CF. Therefore, option C is the correct answer.
Learn more about the line segment here:
https://brainly.com/question/25727583.
#SPJ2
Write an algebraic expression that models the word phrase.
the sum of the product of a number x and 15, and 13
Choose the correct
Answer:
15x + 13
Step-by-step explanation:
Product of a number 'x' & 15 : x *15 = 15x
Sum of 15x & 13:
15x + 13
jessica's mother gave her 70 chocolates to give to her friends. She gave 3 chocolates to each of her friends at the party and had 4 chocolates left over for herself. How many friends did she have at her graduation party?
Answer:
She had 22 friends at her graduation party.
Step-by-step explanation:
70 chocolates total minus 3 chocolates times the number of friends she had at the party = 4
70-3x=4
Subtract 70 from both sides of the equation
-3x=4-70
Simplify
-3x=-66
Divide both sides of the equation by -3
-3x/-3=-66/-3
Simplify
x=22
If an arrow is shot upward on Mars with a speed of 56 m/s, its height in meters t seconds later is given by y = 56t − 1.86t^2. Find the average speed over the given time intervals. [1, 2]
Answer:
50.42m/sStep-by-step explanation:
Average speed is the change in distance of a body with respect to time. This is expressed as:
[tex]v = \delta y/\delta t\\v = \dfrac{y(t_2)-y(t_1)}{t_2-t_1}[/tex]
Given the function of the height in metres expressed as y = 56t − 1.86t² and time interval [1,2]
t₁ = 1sec and t₂ = 2 secs
y(t₂) = 56t₂ − 1.86t₂²
y(2) = 56(2) − 1.86(2)²
y(2) = 112-7.44
y(2) = 104.56
y(t₁ ) = 56t₁ − 1.86t₁ ²
y(1) = 56(1) − 1.86(1)²
y(1) = 56-1.86
y(1) = 54.14
Substituting the derived value into the formula for finding the average speed:
[tex]v = \dfrac{y(t_2)-y(t_1)}{t_2-t_1}\\\\v = \dfrac{104.56-54.14}{2-1}\\\\v = \dfrac{50.42}{1}\\\\v = 50.42m/s[/tex]
Hence, the average speed over the given time intervals. [1, 2] is 50.42m/s
q+ad=m solve for d, i need help now please!
Answer:
d =(m-q)/a
Step-by-step explanation:
[tex]q+ad=m\\ad = m-q\\\frac{ad}{a} = \frac{m-q}{a} \\\\d = \frac{m-q}{a}[/tex]
Answer:
d = ( m-q)/a
Step-by-step explanation:
q+ad=m
Subtract q from each side
q-q+ad=m-q
ad = m-q
Divide each side by a
ad/a = ( m-q)/a
d = ( m-q)/a
which statement is true? all whole numbers are rational numbers all integer's are whole numbers are rational numbers are integer's or none of the above
Answer:
a
Step-by-step explanation:
hope this helps
P=vrt slove get the r alone
Show work
Answer:
r = P / vt
Step-by-step explanation:
P = vrt
P / vt = r
r = P / vt
The digit at ones place of a two digit number is three times the digit at tens place.When 54 is added to the number its digit are reversed.Find the number
Answer:
The number is 39
Step-by-step explanation:
Let the number at the tens place be x and the number at ones place be y.
Hence, The number is 10x + y.
From the question, the digit at ones place (y) is three times the digit at tens place (x). That is, y is three times x. This means
y = 3x ...... (1)
Also, When 54 is added to the number, its digits are reversed (That is, the resulting number would be 10y + x). This means
10x + y + 54 = 10y + x ...... (2)
Put the value of y = 3x from equation (1) into equation (2) to solve for x
Then,
10x + y + 54 = 10y + x
10x + 3x + 54 = 10(3x) + x
13x + 54 = 30x + x
13x + 54 = 31x
31x - 13x = 54
18x = 54
x = 54/18
x = 3.
Now, Put the value of x = 3 into equation (1) to solve for y
y = 3x
y = 3(3)
y = 9.
Hence, x = 3 and y = 9.
Since the number is 10x + y
Substitute the values of x and y.
Then,
10x + y = 10(3) + 9
=30 + 9
= 39
Hence, the number is 39.
Which phrase is equivalent to the expression (17×4)−35?
Answer:
-2380
Step-by-step explanation:
you first multiply 17 by 4
next multiply 68 by 35
you get 2380
finally add a negative sign in front of it
A national survey of middle-school students asks which subject is most challenging. Which of these samples is a representative sample?
Answer:
The correct option is D.
Hoped I helped
Answer:D
Step-by-step explanation:
Estimate the solution to the system of equations.
You can use the interactive graph below to find the solution
-32 + 3y = 9
22 – 7y = -14
Choose 1 answer:
Answer:
see below
Step-by-step explanation:
If your equations are the ones shown in the second attachment, then their solution is the one shown in the first attachment.
_____
Apparently, your "interactive graph" needs two points to draw a line through. For these equations, the x- and y-intercepts are found easily enough.
-3x +3y = 9
To find the x-intercept, set y=0 and divide by the coefficient of x: 9/-3 = -3
To find the y-intercept, set x=0 and divide by the coefficient of y: 9/3 = 3.
2x -7y = -14
Same procedure: x-intercept = -14/2 = -7; y-intercept = -14/-7 = 2.
All of these intercepts are shown in the third attachment. Using them, you can use your tool to plot the lines and estimate their point of intersection.