Partial quotients can be used to find 832 ÷ 26 by the explanation that follows. C. Subtract 30 × 26 from 832 to get 52. Then subtract 2 × 26 from 52 to get 0. Then add the partial quotients 30 + 2 to get 32. The quotient is 32
How to do division using partial quotientsPartial quotient is the method that is sued to solve the big division problems in mathematics. It is one that is done through the use of logic in order to get the solution
For instance
832 ÷ 26 ⇒ 30
30 * 26 = 780
832 - 780 = 52
52 ÷ 26 ⇒ 2
2 * 25 = 52
52 - 52 = 0
The quotient is gotten by adding up the values gotten during the division
= 30 + 2
= 32
32 is the quotient and option C is the correct option
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The graph of an arithmetic sequence is shown.What is the value of the 7 th term?Round your answer to the nearest tenth. Add a decimal point and a zero if youranswer is a whole number (for example, 10 would be entered as 10.0)
10.0
Explanation
an arithmetic sequence is given by the expression
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ \text{where} \\ a_{_1}\text{ is the first term} \\ \text{and d is the common diference} \end{gathered}[/tex]in the graph , to know the value of the 7 th terms, we need to take the value that y takes, when x= 7
so
therefore, the answer is
10.0
I hope this helps you
. Ross has a spinner that is split into eight equal sections numbered 1 through 8. He spun the spinner 1120 times. Which of the following would be a good estimate of the number of times the spinner landed on number 6?
The probability of the spinner landing on number 6 is calculated as follows:
[tex]\begin{gathered} p=\frac{\text{ number of favorable outcomes}}{\text{ total possible outcomes}} \\ p=\frac{1}{8} \end{gathered}[/tex]Given that he spun the spinner 1120 times
7. An internet service provider charges $20 per month plus an initial set-up fee. One customer paid a total of $92 after 2 months of service. Write an equation in point-slope-form modeling this situation. Then, write the equation in slope-intercept form. What does the 52 represent in your slope-intercept form equation?
The internet service provider charges $20 per month plus an initial set-up fee.
Let "x" represent the number of months that are charged, then the monthly fee can be expressed as 20x
Let "y" represent the cost of the internet service after x months.
If the customer paid y=$92 after x=2 months of service, this information represents a point of the relationship that can be expressed as (2,92)
The point-slope form has the following formula:
[tex]y-y_1=m(x-x_1)[/tex]Where
m is the slope
(x₁,y₁) are the coordinates of one point of the line.
The slope of the line corresponds to the monthly fee for the internet service, so m=$20
The coordinates of the point you have to use is (2,92)
So the equation in point-slope form is
[tex]y-92=20(x-2)[/tex]To write the equation in slope-intercept form, the first step is to distribute the multiplication on the parentheses term:
[tex]\begin{gathered} y-92=20\cdot x-20\cdot2 \\ y-92=20x-40 \end{gathered}[/tex]Then pass "-92" to the right side of the equation by adding it to both sides of the equal sign:
[tex]\begin{gathered} y-92+92=20x-40+92 \\ y=20x+52 \end{gathered}[/tex]The equation in point-slope form is y-92=20(x-2)
The equation in slope-intercept form is y=20x+52
$20 is the slope of the equation and represents the monthly fee for internet service.
$52 is the y-intercept of the equation, it represents the initial set-up fee for the internet service.
Write an equation in the form y suggested by the pattern in the table. т
I'll pick uo two points from the table.
P1 = (5, 11)
P2 = (7, 13)
1.- Find the slope
slope = (y2 - y1) / (x2 - x1)
Substitution
slope = (13 - 11) / (7 - 5)
Simplification
slope = 2/2
Result
slope = 1
2.- Find the equation of the line
y - y1 = m(x - x1)
Substitution
y - 11 = 1(x - 5)
Simplification
y = x - 5 + 11
Result
y = x + 6
This is the answer to your question
Assume that a triangle ABC has standard labeling. Determine wether SAA, ASA, SSA, SAS or SSS is given. Then decide wether the law of sines or the law of cosines should be used to begin solving the triangle.a, c and B
Answer:
Explanation:
What is the length of AB? round your answer to the nearest hundred.
In order to calculate the length of the line AB, you use the following formula for the distance between points in the coordinate plane:
d = √((x2-x1)²-(y2-y1)²)
That is, it is only necessary to have a pair of points with coordinates (x1,y1) and (x2,y2). In this case you have two points A=(-5,-4)=(x1,y1) and B=(-3,3)=(x2,y2), then, by replacing these values into the formula for the distance you have:
d = √((3-(-3))²-(-5-4)²)
d = √((3+3)²+(-9)²)
d = √(36+81) = √(117) = 10.8166 ≈ 10.82
Hence, the length of the line AB is 10.82
Factorise2rs-4rt-6t+3s
Given expression:
[tex]2rs\text{ - 4rt - 6t + 3s}[/tex]Collect like terms:
[tex]=\text{ 2rs - 4rt - 6t + 3s}[/tex]Next, we bring the common terms:
[tex]=\text{ 2r(s - 2t) -3(2t - s)}[/tex]Re-writing the expression:
[tex]=\text{ -2r(2t - s) -3(2t -s)}[/tex]Since we have a common term on either side of the negative sign, we can write:
[tex]=\text{ (-2r -3)(2t-s)}[/tex]Answer:
[tex]=\text{ (-2r-3)(2t -s)}[/tex]Let us verify the answer:
[tex]\begin{gathered} (-2r\text{ -3)(2t-s)} \\ =-2r(2t\text{ -s) -3(2t -s)} \\ =\text{ -4rt + 2rs -6t + 3s} \end{gathered}[/tex]100 POINTS PLEASE HELP
Lisa is saving for college. The account is modeled by the function: F (x) = 250(1.25)^x , when x represents how many years she has saved.
Xavier is also saving for college. His account is modeled by this table:
x 0 1 2 3
g(x) 200 270 364.5 492.08
Answer the following questions:
A. After 5 years, how much does Lisa's account have in it?
B. After 5 years, how much does Xaviers account have in it?
C. What is the positive difference in their accounts after 5 years?
Show your work. (this does not have to be done by hand, but just show what you would enter into the calculator)
Answer:
A. $762.94
B. $896.81
C. $133.87
Step-by-step explanation:
Given function modelling Lisa's saving account:
[tex]\boxed{f(x)=250(1.25)^x}[/tex]
where x is the number of years.
Given table modelling Xavier's savings account:
[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5} x & 0 & 1 & 2 & 3\\\cline{1-5} g(x) & 200 & 270 & 364.5 & 492.08\\\cline{1-5}\end{array}[/tex]
Part ATo find the amount in Lisa's savings account after 5 years, substitute x=5 into the function:
[tex]\begin{aligned}\implies f(5)&=250(1.25)^5\\&=250(3.051757...)\\&=762.939453...\end{aligned}[/tex]
Therefore, the amount in Lisa's savings account after 5 years is $762.94 (nearest cent).
Part BFirst, create an exponential function to model Xavier's savings account.
General form of an exponential function:
[tex]y=ab^x[/tex]
where:
a is the initial value (y-intercept).b is the base (growth/decay factor) in decimal form.From inspection of the given table, the initial value (a) is 200.
[tex]\implies g(x)=200b^x[/tex]
To find the value of b, substitute point (1, 270) into the function:
[tex]\begin{aligned}\implies g(1)=200b&=270\\b&=\dfrac{270}{200}\\b&=1.35\end{aligned}[/tex]
Therefore. the function that models Xavier's savings account is:
[tex]\boxed{g(x)=200(1.35)^x}[/tex]
To find the amount in Xavier's savings account after 5 years, substitute x=5 into the found function:
[tex]\begin{aligned}\implies g(5)&=200(1.35)^5\\&=200(4.4840334...)\\&=896.806687...\end{aligned}[/tex]
Therefore, the amount in Xavier's savings account after 5 years is $896.81 (nearest cent).
Part CTo find the positive difference in their accounts after 5 years, subtract Lisa's balance from Xavier's balance:
[tex]\implies 896.81-762.94 =133.87[/tex]
The equation P=4s represents the perimeter P of a square with side length s. What is the perimeter of a square with side length 6 mi?
The perimeter is mi.
Answer:
24mi
Step-by-step explanation:
p=4s=4(6mi)
=24mi
Find the are of the circle below.
To find the area of the circle with diameter = 18 cm
We will use the formula:
[tex]\text{Area of a cirlce = }\pi r^2[/tex]where r= radius of the circle
From the quesion diameter = 18 cm
radius = diameter/2
radius = 18cm/2 = 9 cm
substituting r = 9cm into the formula
[tex]Area\text{ of a circle = }\pi(9)^2[/tex][tex]A\text{rea of the circle }=\text{ 81}\pi cm^2[/tex]The above answer is when we are to leave the answer in terms of π
Otherwise if π is given to be 3.14 or 22/7 , we will simply substitute into the formula
That is given that π= 3.14
[tex]\text{Area of the circle = 81 }\times3.14=254.34cm^2[/tex]
5 ft12 ftWhat is the length of the hypotenuse?
I think these are the lengths of the legs
hypotenuse^2 = 5^2 + 12^2
hypotenuse^2 = 25 + 144
hypotenuse^2 = 169
hypotenuse = 13
Shelby is searching online for airline tickets. Two weeks ago, the cost to fly from to was $210. Now the cost is $305. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?
The percentage increase of the airline ticket is 45.24%
Percentage IncreaseThe concept of percent increase is basically the amount of increase from the original number to the final number in terms of 100 parts of the original. An increase of 5 percent would indicate that, if you split the original value into 100 parts, that value has increased by an additional 5 parts.
Mathematically, the percentage increase of a quantity can be written as
[tex]\% increase =\frac{change in quantity}{original quantity} * 100[/tex]
Let's substitute the values given into the equation and find the percentage increase.
[tex]\% increase =\frac{change in quantity}{original quantity} * 100\\\% increase = \frac{305 - 210}{210} *100\\\% increase = 45.24\%[/tex]
The increase in percentage of the ticket price is 45.24%
If the airline charges an additional $50 with the new ticket price, the percentage increase will remain the same because assuming the baggage fees is also applicable to the old price, there won't be an change in the percentage increase.
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Snow is accumulating at a rate of 0.5 inches per hour. Calculate the amount, in inches of snow that will accumulate in 24 minutes.
Given:
Accumulation rate = 0.5 inches per hour
time = 24 minutes
First, convert minutes into hours:
1 hour = 60 minutes
24 / 60 = 0.4 hours (divide by 60)
Now, simly multiply the rate by the number of hours
0.5 in/h x 0.4 h = 0.2 in
Answer: 0.2 inches
Solve for X with intersecting chords
We apply the secant-angle theorem,
[tex]\frac{156+54}{2}=105^0[/tex]Then,
[tex]\begin{gathered} x+105^0=180^0\text{ (angle in a straight line)} \\ x=180^0-105^0 \\ x=7^{}5^o \end{gathered}[/tex]Therefore, x=75 degr
This year Apple has launched iPhone 14. There are 4 different colors (Silver, gold, space
black, purple) of iPhone 14 Pro Max and iPhone 14 Pro. Also, there are 5 different colors
(Midnight, blue, starlight, purple, red) available for iPhone 14 plus and iPhone 14. How many different types of phones are available this year?
There are 18 different types of phones are available this year.
What is Addition?The process or skill of calculating the total of two or more numbers or amounts.
There are 4 different colors (Silver, gold, space black, purple) for,
iPhone 14 Pro Max → 4
iPhone 14 Pro → 4
There are 5 different colors (Midnight, blue, starlight, purple, red) for,
iPhone 14 plus → 5
iPhone 14 → 5
Add all of them = 4 + 4 + 5 + 5
we get, = 18
Hence, There are 18 different types of phones are available this year.
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Find the y-intercept of the line on the graph.
Answer:
-2
Step-by-step explanation:
The y intercept is where the line crosses the y axis. It crosses at the point (0,-2)
can someone help me with this please, I need this by tomorrow pleaseeee
In the given figure,
There are non-parallel lines,
Hence these angles are formed by the non-parallel lines.
This means they do not have any relation, i.e., they are not necessarily congruent to each other.
What are Intersecting lines?They are referred to be intersecting lines when two or more lines in a plane cross each other. The point of intersection, which can be found on all intersecting lines, is the common point shared by the intersecting lines. The intersecting lines (two or more) always meet at a single location. Any angle can be used to intersect the intersecting lines. This angle is always larger than zero and less than 180 degrees. Vertical angles are created by two lines intersecting. With a common vertex, the vertical angles are opposite angles (which is the point of intersection). Curved lines, not straight ones, are what intersect at several points.To learn more about Intersecting Lines, refer to:
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8 This graph shows how fast Heidi ran on a track. Heidi says she was
running 1.5 laps per minute because 3/2= 1.5. What mistake did
she make? How fast was Heidi running?
Hi there I need help what is 39 dollars plus two rolls of pennies equals
Answer:
41
Step-by-step explanation:
According to the Rational Root Theorem, which of the following could be a root of p(x)=3x3−5x2+4? Select all that apply.
SOLUTION
The rational root theorem, also called rational root test theorem state that for a polynomial equation in one variable with integer coefficients to have a solution (root) that is a rational number, the leading coefficient (the coefficient of the highest power) must be divisible by the denominator of the fraction and the constant term (the one without a variable) must be divisible by the numerator.
Given the polynomial
[tex]p(x)=3x^3-5x^2+4[/tex][tex]\begin{gathered} \text{Leading co}eficient\text{ =3} \\ \text{Constant term =4} \end{gathered}[/tex]The factor of the constant term is
[tex]\pm1,\pm2,\pm4_{}[/tex]The factors of the Leading coefficient are
[tex]\pm1,\pm3[/tex]The root of the p(x) are
[tex]\begin{gathered} \frac{p}{q} \\ \text{where p=factors of the constant term } \\ q=\text{factor of leading coefficient } \end{gathered}[/tex]hence , the possible root of p(x) are
[tex]\pm1,\pm\frac{1}{3},\pm2,\pm\frac{2}{3},\pm4,\pm\frac{4}{3}[/tex]Hence
root of p(x) are 2/3, -2, and 1
Find the inverse of the function below. When typing your answer use the "^" key (shift+6) to indicate an exponent. For example, if we have x squared (x times x) we would type x^2. f(x)= \frac{5x+1}{2-5x}The numerator of f^{-1}(x) is Answer - AnswerThe denominator of f^{-1}(x) is Answer(Answer + Answer)
Answer:
[tex]\begin{gathered} \text{ The numerator of f}^{-1}(x)\text{ is 1-2x} \\ \text{ The denominator of f}^{-1}(x)\text{ is -5(x}+1) \end{gathered}[/tex]Step-by-step explanation:
To find the inverse of a function, replace f(x) by ''y'', then replace ''y'' with and x, and every x with a ''y''. Solve for y.
[tex]\begin{gathered} f(x)=\frac{5x+1}{2-5x} \\ Replace\colon\text{ f(x)}\rightarrow y \\ y=\frac{5x+1}{2-5x} \\ Replace\colon\text{ y}\rightarrow x\text{ x}\rightarrow y \\ x=\frac{5y+1}{2-5y} \\ \text{ Solve for y.} \\ x(2-5y)=5y+1 \\ 2x-5yx=5y+1 \\ -5yx=5y+1-2x \\ -5yx-5y=1-2x \\ y(-5x-5)=1-2x \\ y=-\frac{1-2x}{5x+5} \\ y=-\frac{1-2x}{5(x+1)} \end{gathered}[/tex][tex]\begin{gathered} Replacey\colon f^{-1}(x) \\ f^{-1}(x)=-\frac{1-2x}{5(x+1)} \end{gathered}[/tex]Can you guys please help me on this question ?
Solution
Therefore, the correct option is D.
in susan graduating class the ration of girls to boys is 3:2 and the total number of students is 250. what is the total number of girls and boys iin susan's graduating class?
Explanation:
The ratio of girls to boys = 3:2
Total number of students = 250
Sum of ratio = 3 + 2 = 5
The total number of girls = 3/5 * 250
In ΔCDE, m∠C = 86° and m∠D = 58°. Which statement about the sides of ΔCDE must be true?
ANSWER
DE > EC > CD
EXPLANATION
Let us make a sketch of triangle CDE:
Let us first find the measure of angle E.
The sum of angles in a triangle is 180 degrees. This means that:
58 + 86 + 144 + =>
The sine of the angle of a triangle and side opposite that triangle is proportional for every angle and side of a triangle.
That is, the ratio of the sine of an angle and the side opposite that angle is constant for a triangle. This is known as the Sine Law.
This law implies that the bigger an angle of a triangle is, the larger the side opposite it and vice versa.
Therefore, since DE > EC > CD
That is the answer.
Select the equation of a circle with a center at the origin and a radius 7.
The Solution.
The circle with a center at the origin implies that (a,b) = (0,0).
The equation of a circle is given by;
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ \text{Where a=0, b=0 and r=7 units.} \end{gathered}[/tex]Substituting the values above into the formula, we get
[tex]\begin{gathered} (x-0)^2+(y-0)^2=7^2 \\ x^2+y^2=49 \end{gathered}[/tex]Step 3:
Presentation of the Answer.
Thus, the correct answer is option C / third option.
[tex]x^2+y^2=49[/tex]An airplane flying against the wind travels 280 miles in the same amount of time it would take the same plane to travel
420 miles with the wind. If the wind speed is a constant 70 miles per hour, how fast would the plane travel in still air?
The speed of plane in still air is 150 miles per hour.
What is speed?
Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.
speed = distance/time
Let s = speed in still air
then(s-70) = ground speed against the wind
and
(s+70) = ground speed with the wind
Write a time equation; time = distance/speed
time against = time with still air
280/(s-30) = 420/(s+30)
Cross multiply
420(s-70) = 280(s+70)
420s - 29400 = 280s + 19600
420s-280s = 19600+29400
140s=49000
s = 49000/140
s = 350 mph
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Muffins $1.75
Cookies $1.25
Cakes
$1.00
For the bake sale, your principal would like to sell each baked good for $4.00. He also mentions that each baked good that is sold needs
at least a 60% profit. Based on this information, which of the baked goods could be sold at the bake sale? Explain how you know whether
each baked good meets or does not meet the criteria for being sold at the bake sale.
Answer:
rat
Step-by-step explanation:
I need help on a problem
Triangle BOX = Triangle DEA by Angle Side Angle
Would just like to make sure that my answer is correct.
Answer:
[tex]\text{ -2sin(}\frac{11\pi}{24})\cos (\frac{\pi}{24})[/tex]Explanation:
Here, we want to simplify the given expression
The basic rule we will be using here is:
[tex]\sin (A\text{ + B})\text{ = SinACosB + CosASinB}[/tex]Thus, we have it that:
[tex]\begin{gathered} \text{ sin(}\frac{\pi}{6}+\frac{\pi}{4})\text{ + sin(}\frac{\pi}{8}+\frac{3\pi}{8}) \\ \\ \sin (\frac{5\pi}{12})\text{ + sin(}\frac{\pi}{2}) \end{gathered}[/tex]We use the sine addition formula as follows:
[tex]\sin \text{ A + sin B = 2sin(}\frac{A+B}{2})\cos (\frac{A-B}{2})[/tex]Now, we substitute the last expression into the given addition formula above:
[tex]\begin{gathered} \text{ sin(}\frac{5\pi}{12})\text{ + sin(}\frac{\pi}{2})\text{ =2sin(}\frac{\frac{5\pi}{12}+\frac{\pi}{2}}{2})\cos (\frac{\frac{5\pi}{12}-\frac{\pi}{2}}{2}) \\ \\ =\text{ 2sin(}\frac{11\pi}{24})\cos (\frac{-\pi}{24})\text{ = -2sin(}\frac{11\pi}{24})\cos (\frac{\pi}{24}) \end{gathered}[/tex]3.Ronald loves to compete in triathlons. At a race a few months ago, hefinished in 290 minutes. At a race yesterday, he took 10% more time tofinish. What was his time at yesterday's race?
Explanation:
First we have to get 10% of 290 minutes:
[tex]290\times\frac{10}{100}=290\times0.1=29[/tex]If yesterday took him 10% MORE time to finish the race, it means that it took him 290min as a few months ago plus another 29 minutes
Answer:
Ronald's time at yesterday's race was 319 minutes
