Long division gives the answer of 24 when 72 is divided by 3.
What is long division calculator?Long division in mathematics is a strategy for breaking down complicated division problems into a series of simpler steps. It is the approach that division-based issues are typically solved using. The dividend, the quotient, the remainder, and the divisor can all be seen in the following long division.
So as we know:
Start by arranging it so that the dividend 72 is on the right side and the divisor 3 is on the left:
3 ⟌ 7 2
Start by arranging it so that the dividend 72 is on the right side and the divisor 3 is on the left:
2
3 ⟌ 7 2
Write the result (3 x 2 = 6) underneath the dividend after multiplying the divisor by the outcome from the previous step.
2
3 ⟌ 7 2
6
Write the solution below after subtracting the result from the previous step from the dividend's first digit (7 - 6 = 1).
Reduce the dividend's second digit (2) as follows:
2
3 ⟌ 7 2
- 6
1 2
The bottom number (12) is multiplied by the divisor (3) four times (s). Put 4 thus on top
Subtract the result of the previous step (3 x 4) from the divisor to get the solution (12), which you should write at the bottom:
2 4
3 ⟌ 7 2
- 6
1 2
1 2
Take the number above it and deduct the outcome from the preceding calculation. Write the response at the bottom after calculating (12 - 12 = 0).
The top number is the solution, and the remaining value is the bottom one.
Therefore, the result of 72 divided by 3 using long division is 24.
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What is the result if x3 - 5x² + x + 15 will be divided by x -3?
The quotient for p(x) = x³ -5x² + x + 15 is x² – 2x – 5.
What is a polynomial?A polynomial is a mathematical expression made up of coefficients multiplied by the product of powers in one or more variables. The formula for a univariate polynomial in one variable with constant coefficients is.
What is a polynomial equation?An equation with a polynomial set to zero is referred to as a polynomial equation. It is an equation made up of coefficients, non-negative integer exponents, variables, and operations. It also contains the equal sign. Different exponents exist for it. The degree of the equation is revealed by the highest one.
Given that,
The p(x) = x³ - 5x² + x + 15
Divided by x -3
Therefore, the quotient for p(x) = x³ -5x² + x + 15 is x² – 2x – 5.
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Evaluate the following expression
28-(-2/3)x 9.6
Answer:
34.4
Step-by-step explanation:
given h(x)=-[tex]\sqrt{x}[/tex]x-6+8 witch is the correct transformation from the parent function
The correct transformation include
Horizontal translation to the right by 6 units: Vertical translation up by 8 units: How to determine the transformation of the graph?The equation of the graph is given as
y = √(x -6) + 8
The above equation is a square root
The parent equation of the square root is
y = √x
The sequence of transformations from y = √x to y = √(x - 6) + 8 is as follows:
Shift to the right by 6 unitsShift up by 8 unitsThe transformation rule of the above transformations are as follows:
Shift to the right by 6 units: (x - 6, y)Shift up by 8 units: (x, y + 8)When the above transformations are applied on the equation, we have:
Shift to the right by 6 units: (x - 6, y)Shift up by 8 units: (x - 6, y + 8)This means that the function y = √(x -6) + 8 can be gotten by applying the above sequence of transformation on y = √x
See attachment for the graphs of the transformations where the blue line represents y = √x while the other line represents y = √(x -6) + 8
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Please help me solve this problem 20 points
Answer:
56
Step-by-step explanation:
[tex]\binom{8}{3}=\frac{8!}{5!3!}=56[/tex]
Pleasee helpp
Identify where T goes if X is the midpoint of BT
The location of T is 3 units from the midpoint X or 6 units from the endpoint B
Midpoint of a Line
In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.
Since one of the endpoints is BX and the endpoint is XT and the midpoint is X.
The distance between B and X is 3 units.
Since X is the midpoint, the distance between X and T is equal to 3 units.
Therefore, the distance between B and T is 6 units and the location of T is 3 units from X or 6 units from T.
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Write a system that would produce the graph below
Answer:
2x -y ≥ -53x +y < 10x +2y > 0Step-by-step explanation:
You want a system of inequalities that will define the area within the triangle with vertices (-2, 1), (1, 7), and (4, -2), including only the left side.
Linear equationsAn equation through points (x1, y1) and (x2, y2) can be written as ...
(y2 -y1)x -(x2 -x1)y = x1·y2 -x2·y1
Removing any common factor from the coefficients, and making sure the leading coefficient is positive will put this in standard form.
For points (-2, 1) and (1, 7), the equation of the line can be ...
(7 -1)x -(1 -(-2))y = (-2)(7) -(1)(1)
6x -3y = -15 . . . simplify
2x -y = -5 . . . . . divide by 3 (shading is right of the solid line)
For points (1, 7) and (4, -2), the equation of the line can be ...
(-2 -7)x -(4 -1)y = (1)(-2) -(7)(4)
-9x -3y = -30 . . . simplify
3x +y = 10 . . . . . . divide by -3 (shading is left of the dashed line)
For points (4, -2) and (-2, 1), the equation of the line can be ...
(1 -(-2))x -(-2 -4)y = (4)(1) -(-2)(-2)
3x +6y = 0 . . . simplify
x +2y = 0 . . . . divide by 3 (shading is right of the dashed line)
InequalitiesIn each of the above equations, the x-coefficient is positive. This means the equal sign can be replaced with > when shading is right of the line, and with < when shading is left of the line.
There will be an "or equal to" symbol when the line is solid.
This means our inequalities are ...
2x -y ≥ -53x +y < 10x +2y > 0dean is going to deliver some goods. he charges £7.00 an hour and 40p per mile for delivery.
he writes down his mileage before and after he has made his journey. this journey takes 2h and 45minutes.
how much does he charge to deliver these goods?
Answer:
See below
Step-by-step explanation:
Time charge = 2.75 hr * £7.00/hr = £ 1`9.25
Mileage charge = ( 25423 - 25263) mi * 40p / mile = 6400 p
(edited: forgot to multiply by 40p)
Now add the two charges together : 19 + (.25 * 240) + 6400/240 =
£ 45.92
( I think <===if I correctly did the monetary conversion between pence and pounds! <=== I used 240 p = 1£ )
Step-by-step explanation:
what we were not told is, if he charges a full hour for a fraction of an hour, or only a corresponding fraction of his hourly rate.
I assume the first : charging a full hour for any fraction of an hour spent.
it took him 2h and 45 minutes, so that is 3 hours charged.
and he was driving
25423 - 25263 miles = 160 miles
so, he charges
3×7 + 160×0.40 = 21 + 64 = £85
if he charges also fractions of his hourly rate, then his hourly charge would be
2 3/4 × 7 = (2×4 + 3)/4 × 7 = 11×7/4 = 77/4 = £19.25
in total that would be
19.25 + 64 = £83.25
Translate the sentence into an equation.
Twice the difference of a number and 8 equals 6.
Use thr variable v for the unknown number
Answer:
2(v-8)=6
Step-by-step explanation:
you have to follow the instructions written and then plug the values
A can of cola has 41 grams of sugar in each
12-ounce can. If you drink nine cans over the span
of a week, how many pounds of sugar have you
consumed during that week from the soda?
The amount in pounds of sugar consumed during that week from the soda is 0. 0677 pounds
What is proportion?A proportion can be defined as an equation in which two elements, or numbers are being set equal to each other.
It is known as a mathematical comparison between two elements or things.
It is also defined as a comparative relation on the basis of size or magnitude of elements, quantity and numbers.
From the information given, we have that;
41 grams of sugar is in each 12-ounce can
To determine the ounces in 9 cans, we have;
If 41 grams = 12 cans
Then, x = 9 cans
cross multiply
x = 41(9)/12
expand the bracket
x = 30. 75 grams
Let's convert grams to pounds
1 gram = 0. 0022 pounds
30. 75 grams = x
x = 30. 75(0. 0022)/1
x = 0. 0677 pounds
Hence, the value is 0. 0677 pounds
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Can you explain the steps for the y intercept and slope. x-10 = 4y
I came up with (10, 0)
Use numerals instead of words.
Explain how to compare the products of two expressions without multiplying the numbers.
Since 40 x (951-686) can be rewritten as * 5x (951-686), the value of 40 x (951-686) is
of 5 x (951-685).
Since 40 x (951-686) can be rewritten as 5x (951-686), the value of 40 x (951-686) is 8 times as value of 5 x (951-685).
In what ways does multiplication compare?A multiplicative comparison compares two expressions so that they are produced when one is multiplied by a certain number.
You must be able to distinguish between the given expressions in order to do that.
So the expression 40 x (951-686) can be rewritten as 5 x (951-686), the value of 40 x (951-686) is 8 times of the expression 5 x (951-685) as we can notice here.
Without engaging in a complicated multiplication process we have to comprehend the two expressions to find the difference between the respective products.
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Find the equation of the exponential function that goes through the points (0,3) and (3,375).
The equation of the exponential function that goes through the points (0,3) and (3,375) is y = 5(3)^x
Exponential equationThe standard form of an exponential equation is given as y = ab^x
Using the coordinate points on the graph (0,3) and (3,375).
The equivalent equations are;
375 = ab^3
3 = ab^0
From equation2;
a= 3
Substitute into equation 1;
375 = 3b^3
b^3 = 375/3
b^3 = 125
b = 5
Determine the equation
y = 3ab^x
y = 3(5)^x
This gives the required exponential equation
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group 1 bought 9 tickets and received a 120 discount, group 2 bougt 3 tickets and recived a 30 dollar discount both groups spentthe total amount of money on tickets
the price of each ticket was the same
what was the cost of each ticket?
The cost of each ticket bought by each of the group is $15.
What is the cost of each ticket?The linear equation that represents the total cost spent by group 1 on the tickets is:
Amount spent = total amount spent on the tickets - discount
9x - 120
The linear equation that represents the total cost spent by group 2 on the tickets is:
3x - 30
Where:
x = is the cost of the tickets
If both groups spend the same amount, the above two linear equations would be equal to each other
3x - 30 = 9x - 120
In order to determine the value of x, take the following steps:
Combine similar terms together: 120 - 30 = 9x - 3x
Add similar terms: 90 = 6x
Divide both sides by 6
x = 90 / 6
x = 15
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What is the slope of a line that passes through the points: (3, 1) and (-2, 2)? Please no links, and get to the point quickly.
Answer:
-1/5 is the slope
Step-by-step explanation:
the equation
y2-y1 over x2-x1
Let -3 -5 be a point on the terminal
We have a terminal point (-3,-5).
We have to find cos(θ), csc (θ and tan)(θ.)
We can locate the terminal point and the angle as:
The cosine of this angle will be negative, as ( is located in the third quadrant)
The hypotenuse of this right triangle will be called R and we can calculate it using the Pythagorean theorem:
[tex]\begin{gathered} R^2=x^2+y^2 \\ R=\sqrt[]{x^2+y^2} \end{gathered}[/tex]We can estimate the cosine as:
[tex]\begin{gathered} \cos (\theta)=\frac{x}{R} \\ \cos (\theta)=\frac{-3}{\sqrt[]{(-3)^2+(-5)^2}} \\ \cos (\theta)=\frac{-3}{\sqrt[]{9+25}} \\ \cos (\theta)=\frac{-3}{\sqrt[]{34}} \\ \cos (\theta)=\frac{-3\sqrt[]{34}}{34} \end{gathered}[/tex]We can now relate this to the csc(θ) as:
[tex]\begin{gathered} \csc (\theta)=\frac{1}{\sin (\theta)} \\ \csc (\theta)=\frac{1}{\frac{y}{R}} \\ \csc (\theta)=\frac{R}{y} \\ \csc (\theta)=\frac{\sqrt[]{34}}{-5} \\ \csc (\theta)=-\frac{\sqrt[]{34}}{5} \end{gathered}[/tex]Finally, we can calculate the tangent as:
[tex]\begin{gathered} \tan (\theta)=\frac{y}{x} \\ \tan (\theta)=\frac{-5}{-3} \\ \tan (\theta)=\frac{5}{3} \end{gathered}[/tex]Answer:
cos(θ) = -3√34/34
csc(θ) = -√34/5
tan(θ) = 5/3
Ryan received a box of jelly beans for his birthday. The jelly beans in the box have fivedifferent flavors. The table below shows how many jelly beans of each flavor are in the box.JELLY BEANSFlavorGrapelucoriceNumber1610CherryhomonThe jelly beans are all the same shape and size. Ryan does not like licorice or lime. What is theprobability that he will pick a jelly bean from the full box that has a flavor he does like? Showand exolain vour work
The probability of Ryan choosing a flavor that he does not like is 3/10.
What is probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. The probability is calculated by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.So, the formula for probability:
P = favourable events/Total eventsFavorable events: (Picking flavor that Ryan does not like) = 10 + 8Total events: (sum of all the jelly) = 60Now, insert the values in the probability formula as follows:
P = favourable events/Total eventsP = 18/60 ⇒ 9/30 ⇒ 3/10Therefore, the probability of Ryan choosing a flavor that he does not like is 3/10.
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Tickets for the monster truck rally cost $12 for children and $20 for adults. Last
night 400 total tickets were sold for a total of $6000. Use c for the child tickets and
a for adult tickets. If one of the equations for this system is a + c = 400, write
the second equation for this system below.
Answer:
500
Step-by-step explanition
12-children
20-adults
400 sold for 6000
c-children were
500
Find the growth factor of the function y = 750(1.825)4.0.8251.8254750
Solution:
The growth formula is expressed as
[tex]\begin{gathered} A=P(1+r)^t----\text{ equation 1} \\ where \\ (1+r)\Rightarrow growth\text{ factor} \end{gathered}[/tex]Given the function:
[tex]y=750(1.825)^4---\text{ equation 2}[/tex]By comparison, we have
[tex]\begin{gathered} P=750 \\ t=4 \\ (1+r)=1.825 \end{gathered}[/tex]Hence, the growth factor of the function is
[tex]1.825[/tex]Write expressions to replace A and B so that the list below shows three
consecutive integers, written from smallest to largest, for all integer values
of n. A,n,B
Answer:
A = n-1
B = n+1
Step-by-step explanation:
You want values of A and B that make the sequence {A, n, B} be a sequence of consecutive integers for any integer n.
Consecutive integersIntegers are consecutive when each is one more than the previous:
A +1 = n ⇒ A = n -1
n +1 = B
A house has increased in value by 24% since it was purchased. If the current value is 465,000, what was the value when it was purchased?
In the diagram below ∠1≅∠2 and m∠CFB=124°. Find each of the following.m∠1=___m∠2=___ m∠3=___m∠4=___m∠CFB= 124°
Angles and lines
We are given the following information
Angle 1 is congruent with angle 2. They have equal measures
Angle CFB measures 124°
Note that angles 4 and F are linear because they are formed by the intersection of two lines.
Linear angles add up to 180°
This means that the measure of angle 4 is:
m angle 4 = 180° - m CFB
m angle 4 = 180° - 124°
m angle 4 = 56°
now note angle 4, 1, and 2 form a straight angle of 180°. This means that
m angle 4 + m angle 1 + m angle 2 = 180°
Since angles 1 and 2 are congruent:
m angle 4 + 2* m angle 1 = 180°
Knowing that m angle 4 = 56°:
56° + 2* m angle 1 = 180°
Subtracting 56°:
2* m angle 1 = 124°
Solving:
m angle 1 = 124° / 2 = 62°
Thus, both angles 1 and 2 measure 62°
Finally, being angles 3 and 4 vertical angles (opposed by a vertex), they are congruent, thus
m angle 3 = m angle 4 = 56°
The solution is given below:
PLEASE HELPP ME
Solve the absolute value equation, making sure to show all steps of your work.
-1/3|2x - 4|=-6
The required solution of the given absolute value equation is 11 and -7.
Given that,
An absolute value equation is given, -1/3|2x - 4|=-6.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Given expression.
-1/3|2x - 4| = -6
|2x - 4| = -6 (-3)
|2x -4| = 18
(2x - 4) = ±18
Now.
Taking (+)
2x - 4 = 18
x = 11
Similarly,
Taking (-)
2x - 4 = -18
x = -7
Thus, the required solution of the given absolute value equation is 11 and -7.
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The graph of f(x) is shown. Sketch the graphs of the following functions.1/2f (x)
1/2f(x) where f = 1 is plotted and sketched on the graph.
(Refer the graph attached below)
What are graphs of functions?The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph.We could also say that the graph of f is the graph of y = f. (x). As a result, the graph of an equation is a particular instance of the graph of a function. To determine if a graph represents a function, use the vertical line test. The graph is a function if a vertical line drawn across it is moved and only ever touches it at one point. The graph is not a function if the vertical line touches it at more than one location.So, let locate function 1/2f(x) on the graph:
Where f = 1(Refer to the graph attached below)Sketch the region as follows.Therefore, 1/2f(x) is plotted and sketched on the graph.
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URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100
POINTS!!!!!
Answer:
289 and 324
Step-by-step explanation:
first find the root of 300 then the number you get is 17.3205.... then look in the line and look at the points in between 17 and 18 then find the square root of 17 and you'll get your answer
What percent of 240 is 132? pls I need it now
Answer:
55%
Step-by-step explanation:
Answer:
55%
132 is 55% of 240
Step-by-step explanation:
What is the answer to 5x+10=-15?
Answer:
-5
Step-by-step explanation:
5x + 10 = -15
a) Subtract 10 from both sides.
5x + 10 - 10 = -15 - 10
5x = -25
b) Divide both sides by 5.
5x/5 = -25/5
-25/5 = -5
Your answer would be -5
Miguel reads that the average low temperature today is −8.5°F and that the average high temperature is 10.2º F.
Miguel plots the points on the number line to determine the temperature change between these two readings.
What is the temperature change?
Answer:
18.7 °F
Step-by-step explanation:
You want the temperature change between a low of -8.5 °F and a high of 10.2 °F.
ChangeThe change between the two readings is found by subtracting the smaller from the larger:
10.2 -(-8.5) = 10.2 +8.5 = 18.7
The temperature change is 18.7 °F.
Suppose
f
(
x
)
f
(
x
)
is an nth order polynomial, with a leading coefficient of 1. Find the compact expression
f
(
n
)
(
x
)
f
(
n
)
(
x
)
. That is, what is the solution (in terms of n) if you take the derivative to respect of
x
x
some n times?
Answer:
Hi
Step-by-step explanation: how are you doing
Write the equation of a line that is parallel to the line 2x - 3y = 5 and passes through the point (3, -1)
Answer:
The equation of the line is 2x - 3y = 9
Step-by-step explanation:
Given:
Write the equation of a line that is parallel to the line 2x - 3y = 5 and passes through the point (3, -1)
Solve:
- The line is parallel to the line 2x - 3y = 5
⇒ the slope of the line = the slope of the line 2x - 3y = 5
- Rearrange the terms of the equation to be in the form
⇒ y = mx + c to find the slope of it
2x - 3y = 5 → subtract 2x from both sides
-3y = 5 - 2x ⇒ divide two sides by -3
y = 5/-3 - 2x/-3 ⇒ y = 2/3 x - 5/3
The slope of the line is 2/3
Given that: The line passes through point (3, -1)
Lets use the rule to find the equation of the line:
y - (-1)/x - 3 = 2/3
y + 1/x - 3 = 2/3 ⇒ by using cross multiplication
3(y + 1) = 2(x - 3) ⇒ open the brackets
3y + 3 = 2x -6 ⇒ put x and y on one side
2x - 3y = 3 + 6
2x - 3y = 9
The equation of the line is 2x - 3y = 9
~Kavinsky
check whether x=1 is a solution of 3x-8
Answer: its 3
Step-by-step explanation: i looked it up and i found a quiz with the same question it was correct