[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{-7}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-7}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{-5}-\underset{x_1}{1}}} \implies \cfrac{ -13 }{ -6 } \implies \cfrac{13 }{ 6 }[/tex]
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Divide the following polynomials using synthetic division, then place the answer in the proper location on the grid. Write answer in descending powers of x.
(x4 + 81) / (x + 3)
The division of the given polynomial would be (x^4) + 81.
What is the synthetic division?
Synthetic division is a method for dividing polynomials that allows you to divide a polynomial by a linear factor (a factor in the form of (x-c) where c is a constant) without actually performing the long division process. It is a short cut method that simplifies the process of dividing polynomials.
To divide the polynomials using synthetic division, we will use the following steps:
Write the polynomials in descending order of exponents. In this case, the given polynomials are already in descending order:
(x^4+ 81) / (x + 3)
Create a grid with the dividend on the left and the divisor on the right.
x^4 81
x 3
Bring down the leading coefficient of the dividend, which is x^4 in this case. Write it in the next row of the grid.
x^4 81
x^4 x 3
Multiply the divisor (x + 3) by the leading coefficient (x^4) and write the result in the next row.
x^4 81
x^4 x 3
x^5 x^5 3x^4
Subtract the second row from the third row and write the result in the next row.
x^4 81
x^4 x 3
x^5 x^5 3x^4
0 81-3x^4
Bring down the next coefficient of the dividend (81) and write it in the next row of the grid.
x^4 81
x^4 x 3
x^5 x^5 3x^4
0 81-3x^4
81
Now we repeat the steps 4-6 for the rest of the coefficients of the dividend, but there is no more coefficients in this example.
The quotient is x^4 and the remainder is 81
So the final answer is:
(x^4)+(81)
Hence, the division of the given polynomial would be (x^4) + 81.
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8 = 1/3(a + 5) pls answer fast
Answer:
19
Step-by-step explanation:
8 = 1/3 (a+5)
24 = a + 5
=> a = 19
Answer:
[tex]a=19[/tex]
Step-by-step explanation:
[tex]8=\frac{1}{3} (a+5)[/tex]
To find the answer we have to find the value of the variable. In order to find the value of the variable we need to isolate it from the equation.
[tex]8=\frac{1}{3} (a+5)[/tex]
[tex]\frac{1}{3} (a+5)=8[/tex]
Multiply 3 on both sides:
[tex]8\times3=24[/tex]
[tex](a+5)=24[/tex]
Subtract both sides by 5:
[tex]24-5=19[/tex]
[tex]a=19[/tex]
Therefore your answer is "a = 19."
Hope this helps.
determine the equation of the line, in slope intercept form, that is perpendicular to 4x+2y+18=0 and has a y-intercept of the line 3x-y+8=0
The slope intercept equation of the line that is perpendicular to 4x+2y+18=0 and has a y-intercept of the line 3x-y+8=0 is x-2y+16=0.
What is equation?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10.
Here,
4x+2y+18=0
y=-2x-9
m=-2
m1=1/2
3x-y+8=0
y=3x+8
y-intercept=(0,8)
y=mx+c
y=1/2x+8
2y=x+16
x-2y+16=0
The equation of the line, in slope intercept form, that is perpendicular to 4x+2y+18=0 and has a y-intercept of the line 3x-y+8=0 is x-2y+16=0.
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The probability distribution for a random variable x is given in the table. -5 -3 -2 0 2 3 Probability .17 .13 33 16 11 10 Find the probability that -2< x <2
The probability that -2 < x < 2 is given as follows:
P(-2 < x < 2) = 0.16.
How to obtain the probabilities?From the table given in this problem, the probability distribution is defined as follows:
P(X = -5) = 0.17.P(X = -3) = 0.13.P(X = -2) = 0.33.P(X = 0) = 0.16.P(X = 2) = 0.11.P(X = 3) = 0.10.The desired interval in this problem is given as follows:
-2< x <2.
It is an open interval, meaning that the only outcome that satisfies this interval is X = 0, and thus the probability is given as follows:
P(-2 < x < 2) = 0.16.
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Using logarithmic properties, what is the solution to log3(y + 5) + log36 = log366? Show steps. all have log of base 3
log3 (y + 5)+ log3 6 = log3 66
[tex]\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log_{3}(y+5)+\log_3(6)~~ = ~~\log_3(66) \\\\[-0.35em] ~\dotfill\\\\ \log_3[(y+5)\cdot 6]=\log_3(66)\implies (y+5)6=66 \\\\\\ y+5=\cfrac{66}{6}\implies y+5=11\implies \boxed{y=6}[/tex]
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Make and test a conjecture about the given quantity. Test at least three sets of numbers. (NOT MULTIPLE CHOICE)
a. product of any two odd integers
b. the sum of two negative integers
Answer:
a) The product of any two odd integers is an odd integer.
b) The sum of two negative integers is always smaller than the smallest negative integer.
Step-by-step explanation:
Part aGiven:
The product of any two odd integers.Carry out a few examples to find a pattern:
1 × 3 = 33 × 5 = 155 × 7 = 35Pattern:
The solution is always odd.Write the conjecture based on the found pattern.
Conjecture:
The product of any two odd integers is an odd integer.Test the conjecture for accuracy using at least three sets of numbers.
Test:
277 × 109 = 3019315 × 23 = 3459 × 61 = 549-------------------------------------------------------------------------------------
Part bGiven:
The sum of two negative integers.Carry out a few examples to find a pattern:
-1 + -2 = -3-10 + -3 = -13-20 + -1 = -21Pattern:
The solution is always smaller than the smallest number.Write the conjecture based on the found pattern.
Conjecture:
The sum of two negative integers is always smaller than the smallest negative integer.Test the conjecture for accuracy using at least three sets of numbers.
Test:
-5 + -5 = -10-40 + -52 = -92-13 + -14 = -27A hiker walks at a speed of 3 2 5 kilometers per hour. How many kilometers will the hiker walk in 5 hours
Answer:
17 km----------------------------------------
The distance is the product of the speed and time.
Given:
Speed = 3 2/5 km/h,Time = 5 hours.Find the distance:
3 2/5 × 5 = 3 × 5 + 2/5 × 5 =15 + 2 = 17 kmanswer asap for reward
If z = 2 [ cos ( - π 4 ) + i sin ( - π 4 ) ] = a + b i in rectangular form, then a = and b = .
The complex number in rectangular form is z = √2 - i√2
What is rectangular form of complex numbers?The rectangular form of of a complex number is given by z = a + ib where
a = rcosФ and b = rsinФwhere
r = magnitude of complex number and Ф = argument of complex numberHow to find the given complex number in rectangular form?Given the complex number
z = 2[cos(- π/4) + isin(- π/4)] , we desire to find the rectangular form of the complex number. We proceed as follows.
z = 2[cos(- π/4) + isin(- π/4)]
z = 2cos(- π/4) + i2sin(- π/4)]
z = 2cos(π/4) - i2sin(-π/4)]
Since cos(π/4) = sin(π/4) = 1/√2, we have that
z = 2cos(π/4) - i2sin(-π/4)]
z = 2 × 1/√2 - i2 × 1/√2
z = 2/√2 - i2/√2
Rationalizing the denominators, we have that
z = 2/√2 × √2/√2 - i2/√2 × √2/√2
z = 2√2/2 - i2√2/√2
z = √2 - i√2
So, we have the number in rectangular form as z = √2 - i√2
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Which function represents the data in the table?
Answer:
First choice
y = 3ˣ
Step-by-step explanation:
It is easier if you examine the obviously wrong choices
Choice 2, y = 9x is incorrect because at x = 0, y = 9x should be 0, instead it is 1
Choice 3 , y = 3x is incorrect for the same reason
Choice 4 y = x³ is incorrect because at x = 0, x³ should be 0, instead it is 1
Correct choice is the first one: y = 3ˣ
Let's check:
x = 0, y = 3⁰ = 1 because any number raised to the power 0 is 1
x = 1, y = 3¹ = 3; because any number raised to the power 1 is 1itself
x = 2; y = 3² = 9 ; so fts
You can test out the rest of the entries yourself
graph f (x) = x and h (x) = x - 4 describe the transformation from the graph of f to the graph of h
The transformation of graph f (x) = x and h (x) = x - 4 is a translation 4 units to the left
What is translation in math?The term transformation is used in mathematics to refer to the movements made by objects.
Translation refers to a type of transformation that involve a linear movement.
Movements as seen in translation includes
up
down
left
right
The y coordinate governs movements in the vertical direction that are up and down.
While the x coordinate controls the horizontal movement in the left and right directions.
The movement as described in the graphs f(x) and h(x) is translation 4 units to the left
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In the University belt, the traffic lights at three different road crossings
change after every 36 seconds, 64 seconds and 110 seconds, respectively. If
they change simultaneously at 11 a.m., at what time will they change
simultaneously again?
Answer:
7:48 p.m.
Step-by-step explanation:
You want to know when lights with periods 36 s, 64 s, and 110 s will change simultaneously again if they do so at 11 a.m..
LCMThe lights will change simultaneously after a time that is the least common multiple (LCM) of the periods of the lights.
The least common multiple is the product of the unique factors in each of the numbers:
36 = 2² · 3²
64 = 2⁶
110 = 2 · 5 · 11
The unique factors are 2⁶, 3², 5, and 11. Their product is 31680. The lights will change simultaneously again after 31680 seconds.
Time conversionWe can convert this to hours, minutes, and seconds by repeated division by 60:
31680 / 60 = 528 r 0
528 / 60 = 8 r 48
31680 seconds is 8 hours, 48 minutes, and no seconds.
Clock timeAdding that time to 11 a.m. gives a clock time of ...
11:00 +8:48 = 19:48 = 7:48 p.m.
The lights will change simultaneously again at 7:48 p.m..
__
Additional comment
The lights will change simultaneously at 11 a.m. again after 11 days.
NO is dilated by a scale factor of to form N'O'. NO measures 40. What is the
measure of N'O'?
N'O' is a transformation of NO. The measurement of N'O' is 30.
What is a line segment?
A line segment is a section of a straight line that is bounded by two distinct end points and contains every point on the line between them. The Euclidean distance between the endpoints of a line segment determines its length.
A scale factor is defined as the ratio of the scale of a given original object to the scale of a new object that is its representation but of a different size (bigger or smaller). For example, we can enlarge a rectangle with sides of 2 cm and 4 cm by multiplying each side by a number, say 2.
Given that NO is dilated by a scale factor of 3/4 to form N'O'.
The length of NO is 40.
To find the length of N'O', multiply the scale factor by the length of NO.
Thus the length of N'O is 3/4 ×40 =30
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N'O' is a transformation of NO. The measurement of N'O' is 30.
What is a line segment?
A line segment is a section of a straight line that is bounded by two distinct end points and contains every point on the line between them. The Euclidean distance between the endpoints of a line segment determines its length.A scale factor is defined as the ratio of the scale of a given original object to the scale of a new object that is its representation but of a different size (bigger or smaller). For example, we can enlarge a rectangle with sides of 2 cm and 4 cm by multiplying each side by a number, say 2.Given that NO is dilated by a scale factor of 3/4 to form N'O'.The length of NO is 40.To find the length of N'O', multiply the scale factor by the length of NO.Thus the length of N'O is 3/4 ×40 =30
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Explore all similar answers
ANSWER FAST HELPP!! GIVING BRANLIEST!
Answer:
152
Step-by-step explanation:
8*10+12*6 =80+72 =152
Please help!!! Will give brainlest easy 6th grade math.
A ball is dropped from different heights. The table shows the height of the first bounce after the ball is dropped.
Bouncing Ball Experiment.
Height of Drop (in inches)
10
20
30
Height of Bounce (in inches)
5
10
15
Part A
Using the data from the table, which equation can be used to find y, the height of the first bounce, in inches, when the
ball is dropped from a height of x inches?
A. y=2x
B. y=x/2
C. y=5x
D. y=x/5
Answer:
The equation that can be used to find y, the height of the first bounce, in inches, when the ball is dropped from a height of x inches is y=x/2. This can be determined by analyzing the data in the table:
-When the ball is dropped from a height of 10 inches, the height of the first bounce is 5 inches (y=5).
-When the ball is dropped from a height of 20 inches, the height of the first bounce is 10 inches (y=10).
-When the ball is dropped from a height of 30 inches, the height of the first bounce is 15 inches (y=15).
In all these cases, the height of the first bounce is half the height of the drop, meaning that the equation y=x/2 is the correct one
Answer:
B) y = x/2
Step-by-step explanation:
When the ball is dropped 10 inches, the ball bounces 5 inches
5 = 10/2
When the ball is dropped 20 inches, the ball bounces 10 inches.
10 = 20/2
When the ball is dropped 30 inches, the ball bounces 15 inches.
15 = 30/2
Part A If x is the number of miles Gavin bikes on the first day, write an expression for the distance he should bike on each of the following three days
Let x be the first day's ride.The second ride will then be equal to 1.5 times.The third day's journey will cost 1.5 (1.5x)The ride on the fourth day will cost 1.5*1.5. (1.5x)
Write an expression for the distance ?The length of the line that connects two places serves as the unit of measurement for distance.
By subtracting the different coordinates from the pair if the two points are on the same horizontal or vertical line, the distance can be calculated.
Let x be the first day's ride.
The second ride will then be equal to 1.5 times.
The third day's journey will cost 1.5 (1.5x)
The ride on the fourth day will cost 1.5*1.5. (1.5x)
Consequently, the distance traveled over the four days is
65=x+1.5x+1.5*1.5x+1.5*1.5*1.5x
65=x+1.5x+2.25x+3.375x
65=8.125x
by multiplying both sides by 8.125, we get
x=65/8.125
x=8mile
the initial ride be x miles long.
The second day's ride will be 12 miles long (=1.5 x =1.5*8).
The third day's ride will be 18 miles (1.5 x 1.5).
The fourth day's ride will be 27 miles, or 1.5*1.5(1.5x).
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In 25 years, a bond that paid 7.75% simple interest earned $3,875 interest. What was the principal of the bond in dollars?
the interest the bond paid off is $7507.8125.
What is simple interest?
A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,
The formula for simple interest is:
S = p*t*r/100
where P is the principal amount of money, R is the interest rate as a decimal, T is the time.
a bond that paid 7.75% simple interest earned $3,875 interest.
S = (3875*7.75*25)/100 = $7507.8125
Hence the interest the bond paid off is $7507.8125.
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What the means of lathi charges
Answer:
the police tactic of charging a crowd with lathis or batons in order to disperse it
Washington, DC is on Eastern standard time, Minneapolis is on Central standard time (1 hr earlier than Eastern standard time), and Las Vegas is on Pacific standard time (3 hrs earlier than Eastern standard time).
A flight leaves Washington, DC at 9:45 A.M. Eastern standard time, stops for 2 hours and 20 minutes in Minneapolis, then arrives in Las Vegas at 4:30 P.M. Pacific standard time.
How long is the plane actually flying?
Answer:
Step-by-step explanation:
When the plane landed in Las Vegas it was 4:30PM Pacific time - this converts to 730 PM Eastern time.
The entire trip lasted from 9:45 am to 7:30 pm. This is a total of 9 hours and 45 minutes.
Subtract 2 hours and 20 minutes for the layover and the plane was flying
for 7 hours and 25 minutes.
9 - 2 = 7 hours and 45 minutes - 20 = 25 minutes
Evaluate and simplify the
expression when a=2 and b=4.
4a - 2(a + b) + 1 = [?]
Answer:
Step-by-step explanation:
Your first step should be to use the Distributive property to simplify the part where it says: -2(a+b). Then you need to put in the numbers given to you for a=2 and b=4
Suppose that the following exponential function gives the dollar value of a certain house that is years old.
A decaying exponential function is modeled as follows:
y = a(1 - r)^t.
In which the parameters are given as follows:
a represents the initial value.r represents the decay rate, as a decimal.For this problem, the function is defined as follows:
y = 476000(0.81)^t.
Hence the values of the parameters are given as follows:
a = 476000, r = 0.19, meaning that the percent decay is of 19%.
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help pls help please help elhep elpelplp
Answer:
130°
Step-by-step explanation:
Since QS bisects ∠PQR, the measures of angles PQS and SQR must be the same
m ∠PQS = 3x + 5
m ∠SQR= 2x + 25
Setting these expressions equal to each other:
3x + 5 = 2x + 25
Subtract 2x from both sides
3x - 2x + 5 = 25
x + 5 = 25
Subtract 5 from both sides
x = 20
Therefore m ∠PQS which is 3x + 5:
m ∠PQS = 3(20) + 5 = 65°
m ∠SQR = ∠PQS =65° also
Adding the two together we get
m ∠PQR = 65 + 65 = 130°
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For questions 1-3, decide whether each transformation will result in congruent or similar figures.
1. Quadrilateral ABCD is translated 5 units and 4 units down, then reflected in the y-axis.
2. ΔJKL is dilated by a scale factor of 2 and then rotated 180° about the origin.
3. Line segment XY is rotated 90° about the origin , dilated by a scale factor of -1/2, and then reflected in the line x = 5.
Answer:
1) Quadrilateral ABCD is translated 5 units and 4 units down, then reflected in the y-axis. This will result in congruent figures. Translation only moves the figure without changing the size or shape, and reflection in the y-axis will mirror the figure across the y-axis without altering its size or shape. Since both operations preserve the size and shape of the figure, the resulting figure will be congruent to the original.
2) ΔJKL is dilated by a scale factor of 2 and then rotated 180° about the origin. This will result in congruent figures. Dilation by a scale factor of 2 will double the size of the triangle while maintaining its shape, and rotation by 180° about the origin will flip the triangle over the origin while maintaining its shape. Since both operations preserve the size and shape of the figure, the resulting figure will be congruent to the original.
3) Line segment XY is rotated 90° about the origin, dilated by a scale factor of -1/2, and then reflected in the line x = 5. This will result in similar figures. Rotation by 90° about the origin will rotate the line segment by 90 degrees, dilated by a scale factor of -1/2 will shrink the size by half but with a change in direction and reflection in the line x = 5 will mirror the figure across the x=5 line without altering its size or shape. Since all the operations maintain the shape of the figure but the size changes, the resulting figure will be similar to the original one.
Translation and reflection doesn't change the shape or size of the figure, therefore the resulting figure is congruent to the initial one.
Question 2Rotation doesn't change the shape of the figure, but dilation changes the size, therefore the resulting figure is similar to the initial one.
Question 3Rotation and reflection don't change, but dilation changes the size, therefore the resulting segment is similar to the initial one.
Tina and zuri are reading the same copy of the same book for a summer reading assignment tiana has already read 16 pages tiana reads 22 pages per day until the book is finished zuri has already read 24 pages zuri reads 18 pages per day until the book is finished one day the two students notice that they are on the same page what page number are they on when they have read the same amount of the book?
Answer: Tina has read 16 pages and reads 22 pages per day until the book is finished.
Zuri has read 24 pages and reads 18 pages per day until the book is finished.
We can use this information to set up an equation to represent the number of pages read by each student over a certain number of days.
Let's call the page number they are on when they read the same amount of the book "p"
We can set up the equation as follows:
16 + 22d = 24 + 18d = p
Now we can solve for p by combining like terms:
16 + 22d = 24 + 18d
4d = 8
d = 2
Now we know that it takes 2 days for Tina and Zuri to read the same amount of the book.
Now we can use this value of d to find out what page they are on when they read the same amount of the book.
p = 16 + 22*2 = 16 + 44 = 60
So Tina and Zuri are on page 60 when they have read the same amount of the book.
Step-by-step explanation:
The equation of a circle in general form is x2+y2−4x+5y−3=0.
What are the coordinates of the center of the circle and the radius of the circle?
center: (−2,52); radius = 53√2
center: (2,−52); radius = 53√2
center: (2,−52); radius = 3
center: (−2,52); radius = 3
The equation of a circle in general form is (x-a)^2 + (y-b)^2 = r^2, where (a,b) is the center of the circle and r is the radius.
To put the equation of circle in standard form x2+y2−4x+5y−3=0 you need to complete the square and
bring the equation to the form (x-a)^2 + (y-b)^2 = r^2
so the center of the circle is (-2,2) and the radius is 3
please answer a b and c! I really need help tysm
Step-by-step explanation: angle on a straight line equals=180
(a) x+2x+3x =180
(b) 6x=180 (divide both sides by the coefficient of x i.e 6)x
x=180divide by 60
x =30
(c) now we know the value of x substitute it to get the largest value
x+2x+3x =180
30+2(30)+3(30)=180
30+60+90=180
therefore the largest angle is 90 degrees
What’s the equation of the line shown above? A) y=1/3x+2 B) y=3x +2 C) y=2x +3 D) y=2x + 1/3
Please hurry
The linear function graphed is defined as follows:
B. y = 3x + 2.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change of the linear function.b is the intercept, representing the value of y at which the graph of the linear function crosses the y-axis.The line in this problem crosses the y-axis at y = 2, hence the intercept b is given as follows:
b = 2.
When x increases by one, y increases by three, hence the slope m of the function is given as follows:
m = 3.
This means that the function is defined as follows:
y = 3x + 2.
Meaning that the correct option is given by option B.
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(Slope LC) What is the slope of the linear relationship?]
The slope of the given linear relationship is; 4/5
How to find the slope of a linear relationship?Slope tells us that a unit change in x, which is the independent variable will result in a change in y by the amount of b. Thus;
slope = change in y/change in x
Slope = rise/run.
In terms of two coordinates, the slope can be expressed as;
slope = (y₂ - y₁)/(x₂ - x₁)
From the graph attached, we are given the two coordinates as;
(-3, -2) and (2,2)
Thus;
Slope = (2 - (-2))/(2 - (-3))
Slope = 4/5
This is the slope of the linear relationship.
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If 692 = 4,761, then 4,761 / 69 =
Answer: 69
Step-by-step explanation:
In the equation 692 = 4,761, we can see that 692 is being multiplied by some number to get 4,761. To find that number, we can divide 4,761 by 692:
4,761 / 692 = 69.
So, 4,761 / 69 = 69
In this case, 692 is being multiplied by 69 to get 4,761, so 69 is the value we get when we divide 4,761 by 69.
HELP PLEASEE!!
The average mass of a certain type of microorganism is 2.4 x 10^-6 grams. What is the approximate total mass of 5,000 of these microorganisms?
a. 0.12g
b. 0.0012g
c. 0.012g
d. 0.00012g
Which graph represents the inequality -2x + 3y > 12?
Answer:
y>\frac{2}{3} x+4
Step-by-step explanation:
Graph the inequality by finding the boundary line, then shading the appropriate area.
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