Absolute value equality entered:
|x-3|+2 = 7
Another term is moved/added to the right-hand side.
|x-3| = 7 - 2
|x-3| = 5
Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.
The Absolute Value term is |x-3|
For the Negative case, we'll use -(x-3)
For the Positive case, we'll use (x-3)
-(x-3) = 5
Multiply
-x+3 = 5
Rearrange and add up
-x = 2
Multiply both sides by (-1)
x = -2
Which is the solution for the Negative Case
(x-3) = 5
Rearrange and add up
x = 8
Which is the solution for the Positive Case
x=-2
x=8
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A small cylindrical can of tuna has a radius of 4 centimeters and a height of 3.8 centimeters. A larger and similar can of tuna has a radius of 5.2 centimeters.
b. What is the volume of the larger can? Round to the nearest tenth.
The volume of the larger cylindrical can of tuna with radius 5.2 centimeters is 419.6 cubic centimeters.
Solids of the same type that have proportional corresponding linear measures are similar solids. In the case of similar cylinder:
height of A / height of B = radius of A / radius of B
Using this scale, if the larger and similar can of tuna has a radius of 5.2 centimeters, and the small cylindrical can of tuna has a radius of 4 centimeters and a height of 3.8 centimeters, then:
radius of larger cylinder / radius of smaller cylinder = 5.2 cm/4cm = 13/10
height of larger cylinder / height of smaller cylinder = 13/10
height of larger cylinder = 13/10 (3.8 cm)
height of larger cylinder = 4.94 cm
Solving for the volume of the larger can using the formula for the volume of cylinder:
V = πr^2h
V = π(5.2 cm)^2(4.94 cm)
V = 419.6464068 cubic centimeters
Rounding off to the nearest tenth.
V = 419.6 cubic centimeters
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Find the value of A if the 4-digit number 3A5A is divisible by 15.
Answer:
let 3A5A be equal to 15
3A5A=15
A=1
Answer:
a = 5
Step-by-step explanation:
3555/15 is 237 which means it is divisible
Caroline walks 9 and 1/2 inches per second. Give the rate in miles per hour. Round to the nearest tenth.
Please help.
Which value of x is the solution to this equation?
5x² 30x45
=
Find the sum of each series. Σ⁵ n=1 (3 n+1)
The sum of the given series is 50
The summation notation or sigma notation is used to simplify the writing of long summation into a single formula.
The given series in sum notation is:
[tex]\sum\limits^5_{n=1} {(3n+1)}[/tex]
Substitute n = 1 ...5 into the nth term formula inside the sum notation:
a(1) = 3 . (1) + 1 = 4
a(2) = 3. (2) +1 = 7
a(3) = 3. (3) +1 = 10
a(4) = 3. (4) +1 = 13
a(5) = 3. (5) +1 = 16
Hence, the series:
4 + 7 + 10 + 13 + 16
We can evaluate the sum directly by adding all the terms:
S(5) = 4 + 7 + 10 + 13 + 16 = 50
Or we can also use the sum formula of an arithmetic series:
S(n) = n/2 [a(1) + a(n)]
For n = 5
S(5) = 5/2 (4 + 16)
S(5) = 5/2 . 20 = 50
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The first two steps a student takes to solve the equation 2 (x-3) = 6x + 9 are shown. Step 1: Use the Distributive Property to distribute the 2. Step 2: Subtract 9 from both sides. What is most likely the next step they should take? Subtract 2x from both sides. Multiply both sides by 4. O O Add 2x to both sides. O Divide both sides by 4.
Answer:
x= negative goes on the out side of it 15 over 4
Write an equation in slope-intercept form for the line described.
passes through (-12,3), perpendicular to y=-2/3x-11
The equation in slope-intercept form for the line that passes through (-12,3), perpendicular to y = -(2/3)x-11 is y = (3/2)x + 21.
The slope intercept form of a line is:-
y = mx + b
Where:-
m represents the slope of a line
b represents the y-intercept of a line
x and y represent the ordered pairs (x,y) throughout a line
We are given the line y = - (2/3)x-11 is perpendicular to the line whose equation we have to find.
Hence,
slope of the line*(-2/3) = -1
slope of the line, m = 3/2
Also, (-12,3) passes through the line,
Hence,
3 = (3/2)*(-12) + b
3 = -18 + b
b = 21
Hence, the equation of the line in slope intercept form is y = (3/2)x + 21.
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PLSSS HURRY I REALLY NEED THIS
Answer: 1/10
Step-by-step explanation: -2/5+1/2=0.1
If we convert 0.1 into a fraction, it becomes 1/10.
Answer:
1/10 is the answer
Step-by-step explanation:if correct mark as BRAINLIESTThe hobbits Frodo, Sam, Pippin and Merry have breakfast at different times. Each one takes a quarter of the porridge in the pan, thinking that the other three have not yet eaten. What fraction of the porridge is left after all four hobbits had their breakfast?
Step-by-step explanation:
Let us start with Frodo's breakfast. He starts eating a quarter of the porridge. Let us say the porridge is 100 spoons, to make dividing easier. After Frodo we have [tex]\frac{3}{4}[/tex] left of the original bowl; we are left with 75 spoons.
100 - [tex]\frac{1}{4}[/tex] = 100 - 25 = 75
Next, comes Sam's breakfast. He eats 75 - [tex]\frac{1}{4}[/tex] = 75 - 18.75 = 56.25 spoons left.
Next, we have Pippin's breakfast. He eats 56.25 - [tex]\frac{1}{4}[/tex] = 42.1875 spoons.
Lastly, we have Merry's breakfast. He eats 42.1875 - [tex]\frac{1}{4}[/tex] = 31.640625 spoons.
Now, we know we have 31.640625 spoons left. However, we need to know what fraction this is out of the original porridge bowl. So, we do:
31.640625 * 100 = 3164.0625 * 1 = 3164.0625
3164.0625% of the bowl remaining!
What a yummy breakfast!
Solve each system by substitution.
3u + 8 = 4v , 24v = 6 - 3u
By substitution, the solution of the system of equations, 3u + 8 = 4v and 24v = 6 - 3u, is (u , v) = (-2 , 1/2).
A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
There are three methods that can be used to solve system of linear equations.
1. Elimination
2. Substitution
3. Graphing
Using substitution method, given two linear equations in u and v,
3u + 8 = 4v (equation 1)
24v = 6 - 3u (equation 2)
Using the first equation, find the value of one variable, lets say u, in terms of the other.
3u + 8 = 4v (equation 1)
3u = 4v - 8
u = (4v - 8)/3
Substitute the value of u to the second equation.
24v = 6 - 3u (equation 2)
24v = 6 - 3[(4v - 8)/3]
24v = 6 - (4v - 8)
24v = 6 - 4v + 8
Combining all terms containing the variable v on one side and the constants on the other side of the equality, and solve for v.
24v = 6 - 4v + 8
24v + 4v = 6 + 8
28v = 14
v = 1/2
Substitute the value of v in the equation for u and solve for u.
u = (4v - 8)/3
u = [4(1/2) - 8]/3
u = (2 - 8)/3
u = -6/3
u = -2
Hence, the solution of the given system of equations is (u , v) = (-2 , 1/2).
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A coin is tossed and a die is rolled. What is the probability that the coin lands heads up and the number rolled is a 6 ?
The probability that the coin lands heads up and the number rolled is a 6 is 1/12.
Given that a die is rolled and a coin is tossed.
We have to find the probability that the coin lands heads up and the number rolled is a 6.
Probability of getting heads in tossing a coin = 1/2
Probability of getting 6 in rolling a die = 1/6
The event of tossing a coin and rolling die are independent.
Hence,
Probability that the coin lands heads up and the number rolled is a 6 =
Probability of getting heads in tossing a coin * Probability of getting 6 in rolling a die = (1/2)*(1/6) = 1/12.
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Two spherical pieces of cookie dough have radii of 3 centimeters and 5 centimeters, respectively. The pieces are combined to form one large spherical piece of dough. What is the approximate radius of the new sphere of dough? Round to the nearest tenth.
The radius of the new sphere of dough is 5.3368
In the given statement is :
Two spherical pieces of cookie dough have radii of 3 centimeters and 5 centimeters, respectively. The pieces are combined to form one large spherical piece of dough.
To find the approximate radius of the new sphere of dough
V 1 = 4/2 · 3³ π = 108/3 π
V 2 = 4/3 · 5³ π = 500/3 π
The new sphere: V = V 1 + V 2 = 608/3 π
4/3 r³ π = 608/3 π / : π/3
4 r³ = 608
r³ = 608 : 4 = 152
r = ∛152
r = 5.3368 cm
Hence, The radius of the new sphere of dough is 5.3368
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Things are usually pretty uneventful during the day in the reptile building as the snakes prefer their beauty sleep, but the critters are stirring as they sense freedom. The python is the first one to leave her cage, and she begins to slowly slither towards the exit at a pace of 1 mile per hour. The anaconda decides to snooze for another 30 minutes before beginning the long trek ahead. He leaves his cage after the python has already traveled half a mile, and he slithers at a pace of 5 miles per hour. Write an equation to represent this scenario letting x represent the number of hours it would take.
The linear functions that model the positions of the Python and of the Anaconda are given as follows:
P(x) = 0.5 + x.A(x) = 5x.What is a linear function?A linear function is modeled by the following rule:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, the change in y divided by the change in x.b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.For the functions in this problem, we have that:
The initial position is the intercept.The velocity is the slope.Considering their velocities, and that when the Anaconda leaves the Python has already traveled half a mile, the functions are given as follows:
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Points A and B have coordinates A(-4,2) and B(3,-6). Find the coordinates of point P, the weighted average of points A and B, in which point A has a weight of 4 and point B has a weight of 3.
A (-7/2, -5)
B (-1,-10/7)
C (-1/2, -2)
D (0,-20/7
The coordinates of the point P is P(x, y) = (- 1, - 10 / 7). (Correct choice: B)
How to determine the coordinates of a resulting point by weighted averages approach
In this problem we find the coordinates of two points on Cartesian plane, of which we must determine the location of a third point by using a formula based on a weight average-like formula:
P(x, y) = (4 / 7) · A(x, y) + (3 / 7) · B(x, y)
P(x, y) = (4 / 7) · (- 4, 2) + (3 / 7) · (3, - 6)
P(x, y) = (- 16 / 7, 8 / 7) + (9 / 7, - 18 / 7)
P(x, y) = (- 7 / 7, - 10 / 7)
P(x, y) = (- 1, - 10 / 7)
The coordinates of the point P is P(x, y) = (- 1, - 10 / 7).
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Can someone explain this to me??
Answer:
see attached
Step-by-step explanation:
You want the height drawn on each triangle corresponding to the base shown.
HeightThe height of a triangle is the perpendicular distance from the base to the opposite vertex. The point at which the height segment meets the base may or may not lie on the triangle.
The height segments for the two given triangles are shown in the attachment.
__
Additional comment
As this problem suggests, any side of a triangle may be designated the "base."
The height segment is also called an altitude. When all three altitudes are extended until they coincide, the point at which they meet is called the "orthocenter" of the triangle.
The orthocenter of an acute triangle lies inside the triangle. For a right triangle, it lies at the right-angle vertex. For an obtuse triangle, the orthocenter is outside the triangle.
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Please help me solve the true or false math problem included in the picture!
Answer:
c=0/0
Step-by-step explanation:
Let's solve for c.
x−c
c−x
=−1
Step 1: Multiply both sides by c-x.
−c+x=−c+x
Step 2: Add c to both sides.
−c+x+c=−c+x+c
x=x
Step 3: Add -x to both sides.
x+−x=x+−x
0=0
Step 4: Divide both sides by 0.
0
0
=0/0
c= 0/0
Answer:
Step-by-step explanation:
False for all value of x, because "x" should not be equal "c"
Unit: NUMBER RELATIONSHIPS
and COMPUTATION
Objective: Estimate to determine the quotient of a decimal.
89.904 divided by 34??
The quotient of the decimal number 89.904 divided by 34 will be 2.65.
What is the quotient?In mathematics, the sum obtained by diluting two numbers is known as a quotient. In mathematics, the word "quotient" is widely used, and it is sometimes referred to as the integer part of a division, a fraction, or a ratio.
The decimal numeral system is widely used to express both integer and non-integer numbers.
Given numbers are 89.904 and 34. The quotient will be calculated as below:-
Quotient = 89.904 / 34
Quotient = 2.65
Therefore, the quotient of the decimal number 89.904 divided by 34 will be 2.65.
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On his quiz, Jim answered 1
10
of the questions incorrectly.
What percent is equal to?
10
Answer:
90%
Step-by-step explanation:
Mrs. Rushdan buys 4 bananas and 6 apples. What is the ratios for
bananas to apples?
Answer:
2;3, that is the ratio =)
Step-by-step explanation:
Answer:The answer would be 4 to 6 or 4:6
Pls pls pls pls pls pls pls pls
the correct statement is the first one.
The inverse of 6^2 is 6^(1/2), then 6^(1/2) is the square root of 6.
Which statement explains why 6^(1/2) is equal to √6?Well, this is just a notation thing.
We know the following property for exponents:
(a^n)^m = a^(n*m)
And we know that the square rooth is the inverse of the square power (exponent equal to 2) such that:
√x^2 = 2
Then if we define the square root as an exponent, let's say that is an exponent "a" we will have:
√x = x^a
Rewritting the above relation again, we can write:
√(x^2) = (x^2)^a = x^(2*a)
And we know that it must be equal to x, so we get:
x^(2*a) = x
This means that 2*a = 1
then a = 1/2
√x = x(1/2)
Then the correct statement is the first one.
The inverse of 6^2 is 6^(1/2), then 6^(1/2) is the square root of 6.
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Is 3 + (-4) the same as -4 + 3? Explain
Answer:
Yes, 3 + (-4) is the same as -4 + 3.
Step-by-step explanation:
When doing addition problems such as this, the order of the numbers does not matter, even when negative numbers are included.
For example, 1 + 2 or 2 + 1 would equal 3.
3 + (-4) = -1
-4 + 3 = -1
Hope this helped you! Let me know if you need more clarification. :)
David is going out for a pizza. The Pizza costs $10.50 plus $1.50 for each extra topping ,x. Write an equation to represent the total cost of the pizza, t.
Dependent variable:________
Independent variable:____
Equation:____ (Use your equation to determine the total cost of the pizza with 3 extra toppings).
10.50+1.50x=total cost
since they wanted 3 topings it would be x=3
10.50+(1.50*3)
simplify
10.50+4.50=15
I hope this helps
Abdoulaye is driving on a long road trip. He currently has 11 gallons of gas in his car. Each hour that he drives, his car uses up 1 gallon of gas. How much gas would be in the tank after driving for 3 hours? How much gas would be left after tt hours?
The amount of gas he would have in the tank after 3 hours is 8 gallons.
The gas left after tt hours is 11 - tt.
How much gas would be left in the tank?In order to determine the amount of gas that would be left in the tank, the amount of gas used would have to be subtracted from the initial amount of gas in the car.
Subtraction is the mathematical operation that is used to determine the difference between two or more numbers. The sign that is used to represent subtraction is -.
Amount of gas left = initial amount of gas - (gas used per hour x number of hours travelled)
11 - tt
11 - 3 = 8 gallons
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um can u guys pls help
Answer:
if I can't explain in one line, then I will include the steps in the explanation.
2x - 7 2x - 7 = x + 97Step-by-step explanation(Q3):
[tex]3^2-\left(5-3\right)^3+6\\5-3=2\\3^2-2^3+6\\3^2=9\\9-2^3+6\\2^3=8\\9-8+6\\9-8=1\\1+6\\1+6=7\\=7[/tex]
Hope it helps!
[tex]log_5 11= ?[/tex]l
Answer:
1.48
Step-by-step explanation:
Redefined the logarithm into its decimal form within the base.
Hope this helps.
Identify the segment bisector of JK
The length of JM is
PLEASE HELP! NEED THIS ASAP! PLS HELP!!
Nick mowed about 3/7 of the school lawn yesterday. he mowed another 1/4 of the lawn this morning. how much is left to mow?
Answer:
9/28 of the lawn is left
Step-by-step explanation:
Make 3/7 and 1/4 have the same denominator
3/7 becomes 12/28 and 1/4 becomes 7/28
added together is 19/28
x - (-3) = 8
what does x equal?
Answer:
x = 5
Step-by-step explanation:
Change "minus a negative" to "plus a positive"
x - (-3) = 8
x + 3 = 8
Next, subtract 3 from both sides.
x + 3 - 3 = 8 - 3
x = 5
Check it!
x - (-3) = 8
5 - (-3) = 8
5 + 3 = 8
8 = 8 Check!
I will Mark Brainlist Please Help Its A Math Problem !!! Approximate the unknown angle A, in the diagram to the nearest degree. ?
Thank you for the help !!! have good day :)
If the cost, C(x), for manufacturing x units of a certain product is given by
C(x) = x² - 19x+60
find the number of units manufactured at a cost of $8900.
The number of units manufactured at a cost of $8900 will be 104 units.
What is factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
If the cost, C(x), for manufacturing x units of a certain product is given by
C(x) = x² - 19x + 60
The number of units manufactured at a cost of $8900 will be given by factorization.
x² - 19x + 60 = 8900
x² - 19x - 8840 = 0
x² - 104x + 85x - 8840 = 0
x(x - 104) + 85(x - 104) = 0
(x - 104)(x + 85) = 0
x = 104, -85
The number of units manufactured at a cost of $8900 will be 104 units.
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