Answer:
400 m^3
Step-by-step explanation:
volume of cylinder = area of the base * height
volume of cylinder = 100 m^2 * 12 m
volume of cylinder = 1200 m^3
The cylinder is 1/3 filled with water, so the volume of the water is 1/3 the volume of the cylinder.
volume of water = 1/3 * 1200 m^3
volume of water = 400 m^3
Write two point-slope equations for the line passing through the points (6, 5) and (3, 1)
Answer:
Point-slope equations:
y - 5 = 4/3 (x - 6)
or
y - 1 = 4/3 (x - 3)
Step-by-step explanation:
Given two coordinate points (6, 5) and (3, 1)
Slope = (5 - 1)/(6 - 3) = 4/3
Point-slope equations:
y - 5 = 4/3 (x - 6)
or
y - 1 = 4/3 (x - 3)
Two point-slope equations for the line passing through the points
(6, 5) and (3, 1) are,
[tex]y-5=\frac{4}{3}(x-6)[/tex][tex]y-1=\frac{4}{3}(x-3)[/tex]Point-slope equationsPoint-slope exists in the general form y-y₁=m(x-x₁) for linear equations. It underlines the slope of the line and a point on the line (that exists not the y-intercept).The slope formula exists utilized to calculate the inclination or steepness of a line. It discovers application in choosing the slope of any line by finding the ratio of the change in the y-axis to the change in the x-axis. The slope of a line exists defined as the change in the "y" coordinate concerning the change in the "x" coordinate of that line.Here, the line passes through the points (6,5) and (3,1).
Let,
[tex]$$(6,5)=\left(x_{1}, y_{1}\right)$$[/tex]
[tex]$(3,1)=\left(x_{2}, y_{2}\right)$[/tex]
Substitute
Slope(m) = [tex]\frac{1-5}{3-6}=\frac{-4}{-3}[/tex]
Slope(m) =[tex]\frac{4}{3}[/tex]
Point-slope equations of the line passing through [tex]$(6,5 \6})$[/tex] and [tex](3}, 1)$[/tex]
Substitute[tex]$m=4 / 3$[/tex], and [tex]$(a, b)=(6,5)$[/tex]into [tex]$y-b=m(x-a)$[/tex]
[tex]y-5=\frac{4}{3}(x-6)[/tex] (point-slope equation)
Substitute[tex]$m=4 / 3$[/tex], and [tex]$(a, b)=(3,1)$[/tex] into [tex]$y-b=m(x-a)$[/tex]
[tex]$y-1=\frac{4}{3}(x-3)$[/tex] (point-slope equation)
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As the number of pages in a photo book increases, the price of the book also increases. There is an additional shipping charge of 15%. The price of a book can be modeled by the equation below, where P = the price of the book, 20 is the printing charge, 0.5 is the charge per page, and x = the number of pages: (2 points)
P = (20 + 0.5x) + 0.15(20 + 0.5x)
Jennifer wants to purchase a book but only has $62.10 to spend. What is the maximum number of pages she can have in her book?
Answer:
22
Step-by-step explanation:
Solve the inequality (20 + 0.5x) + 0.15(20 + 0.5x) ≤ $62.10 for x:
20 + .5x + 3 + 0.75x ≤ 62.10
Combining the x terms, we get:
20 + 3 + 1.25x ≤ 62.10.
Combining the constants on the left:
23 + 1.75x ≤ 62.10
Combining the constants:
1.75x = 39.10
Solving for x: 39.10/1.75 = 22.34
Thus, the max number of whole pages she can have in her book is 22.
Answer:
22
Step-by-step explanation:
what is the simplified form of the following expression? assume x doesn’t = 0
For this case we must simplify the following expression:
[tex]\sqrt [5] {\frac {10x} {3x ^ 3}}[/tex]
We rewrite the expression as:
[tex]\sqrt [5] {\frac {10x} {x * 3x ^ 2}} =[/tex]
We eliminate common factors:
[tex]\sqrt [5] {\frac {10} {3x ^ 2}} =\\\frac {\sqrt [5] {10}} {\sqrt [5] {3x ^ 2}}[/tex]
We multiply the numerator and denominator:
[tex](\sqrt [5] {3x ^ 2}) ^ 4:\\\frac {\sqrt [5] {10}} {\sqrt [5] {3x ^ 2}} * \frac {(\sqrt [5] {3x ^ 2}) ^ 4} {(\sqrt [5] {3x ^ 2}) ^ 4} =[/tex]
\frac {\ sqrt [5] {10} * (\sqrt [5] {3x ^ 2}) ^ 4} {\sqrt [5] {3x ^ 2} * (\sqrt [5] {3x ^ 2} ) ^ 4} =
[tex]\frac {\sqrt [5] {10} * (\sqrt [5] {3x ^ 2}) ^ 4} {(\sqrt [5] {3x ^ 2}) ^ 5} =\\\frac {\sqrt [5] {10} * (\sqrt [5] {3x ^ 2}) ^ 4} {3x ^ 2} =[/tex]
[tex]\frac {\sqrt [5] {10} * \sqrt [5] {(3x ^ 2) ^ 4}} {3x ^ 2} =\\\frac {\sqrt [5] {10} * \sqrt [5] {81x ^ 8}} {3x ^ 2} =\\\frac {\sqrt [5] {10} * \sqrt [5] {81x ^ 5 * x ^ 3}} {3x ^ 2} =[/tex]
[tex]\frac {\sqrt [5] {10} * x \sqrt [5] {81x ^ 3}} {3x ^ 2} =\\\frac {x \sqrt [5] {810x ^ 3}} {3x ^ 2}[/tex]
Answer:
[tex]\frac {x \sqrt [5] {810x ^ 3}} {3x ^ 2}[/tex]
[tex]\frac {\sqrt [5] {810x ^ 3}} {3x}[/tex]
Answer:
The simplified form is [tex]\frac{\sqrt[5]{810 x^{3}}}{3x}[/tex]
Step-by-step explanation:
we need to simplify the value of x in given expression:
[tex]\sqrt[5]{\frac{10x}{3x^{3}}}[/tex]
Re- write the above as,
[tex]\sqrt[5]{\frac{10}{3x^{2}}}[/tex]
[tex]\frac{\sqrt[5]{{10}}}{\sqrt[5]{3x^{2}}}[/tex]
Multiply numerator and denominator by [tex](\sqrt[5]{3x^{2}})^{4}[/tex]
[tex]\frac{\sqrt[5]{{10}}}{\sqrt[5]{3x^{2}}} \times \frac{(\sqrt[5]{3x^{2}})^{4}}{(\sqrt[5]{3x^{2}})^{4}}[/tex]
[tex]\frac{\sqrt[5]{{10}}{\sqrt[5]{(3x^{2}}})^4}{{3x^{2}}}[/tex]
[tex]\frac{\sqrt[5]{{10}}{\sqrt[5]{81x^{8}}}}{{3x^{2}}}[/tex]
[tex]\frac{x \sqrt[5]{810 x^{3}}}{3x^{2}}[/tex]
[tex]\frac{\sqrt[5]{810 x^{3}}}{3x}[/tex]
Hence, the simplified form is
[tex]\frac{\sqrt[5]{810 x^{3}}}{3x}[/tex]
Write the point slope form of the equation of the line passing through the points (-5, 6) and (0.1).
For this case we have by definition, that the equation of a line in the point-slope form is given by:
[tex](y-y_ {0}) = m (x-x_ {0})[/tex]
Where:
m: It's the slope
[tex](x_ {0}, y_ {0}):[/tex] It is a point through which the line passes.
[tex]m = \frac {y2-y1} {x2-x1}[/tex]
We have as data two points, replacing:
[tex]m = \frac {1-6} {0 - (- 5)}\\m = \frac {1-6} {0 + 5}\\m = \frac {-5} {5}\\m = -1[/tex]
We substitute a point, then the equation is:
[tex](y-1) = - 1 (x-0)\\(y-1) = - x[/tex]
Answer:
[tex](y-1) = - x[/tex]
Answer: [tex]y-6=-(x+5)[/tex]
Step-by-step explanation:
The Point-slope form of the equation of the line is:
[tex]y-y_1=m(x-x_1)[/tex]
Where "m" is the slope of the line and [tex](x_1,y_1)[/tex] is a point on the line.
We know that this line passing through the points (-5,6) and (0,1), then we can find the slope with this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substituting, we get:
[tex]m=\frac{1-6}{0-(-5)}=-1[/tex]
Finally, we can substitute the point (-5,6) and the slope into [tex]y-y_1=m(x-x_1)[/tex], then:
[tex]y-6=-(x-(-5))[/tex]
[tex]y-6=-(x+5)[/tex]
Suppose f(x)=x^2.What is the graph of g(x)=f(5x)?
Answer:
D
Step-by-step explanation:
g(x)=f(5x)
this means plugging in 5x for x in f(x):
g(x)=f(5x)=(5x)^2
which can be further simplified:
5^2x^2=25x^2
Since the coefficient of x being larger means a vertical stretch, the answer is D
example:
g(2)=f(5*2)=f(10)=f(10^2)=100
so for g(x), it has the coordinates (2,100), which is most definitely not C
The graph of g(x) = f(5x) is a parabola that is narrower than the graph of f(x) by a factor of 1/5, with the vertex remaining the same.
Explanation:The graph of g(x) = f(5x) can be obtained by substituting 5x for x in the function f(x) = x^2. So, g(x) = f(5x) = (5x)^2 = 25x^2. This means that the graph of g(x) is a parabola that is narrower than the graph of f(x) by a factor of 1/5. The vertex of the parabola remains the same, but the x-values and the y-values are scaled.
write 7.26451 correct to 3 decimal places
giving 50 points if you can answer this. PLEASE HELP ME ATTACHMENT BELOW
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the absolute value functions with their vertices.
Answer:
Q1: 2nd row 2nd tile
Q2: 1st row 1st tile
Q3: 1st row 3rd tile
Q4: 2nd row 3rd tile
Step-by-step explanation:
When
[tex]y = a {(x + p)}^{2} + q[/tex]
Vertex is (-p, q)
Answer:
[tex](-1,-\frac{3}{7} )-->f(x)=\frac{1}{2}|x+1|-\frac{3}{7}\\(5,\frac{2}{3} )-->f(x)=\frac{3}{5}|x-5|+\frac{2}{3}\\(0,-\frac{4}{5} )-->f(x)=\frac{1}{2}|x|-\frac{4}{5}\\(\frac{2}{5},\frac{5}{3} )-->f(x)=\frac{3}{2}|x-\frac{2}{y5}|+\frac{5}{3}[/tex]
Step-by-step explanation:
We can solve all of them by writing the equations in a general form
[tex]f(x)=a|x+b|+c[/tex]
This is a function transformation of
[tex]f(x)=|x|[/tex]
where:
a=Factor of vertical stretch
b=Horizontal shift (- shifts right, + shifts left)
c=Vertical shift (+ shifts right, - shifts left)
The original function has its vertex in [tex](0,0)[/tex] so the horizontal shift will be the new x coordinate in the new vertex and the vertical shift will be the new y in the new vertex like this:
[tex]f(x)=\frac{1}{2}|x+1|-\frac{3}{7}\\b=1=HorizontalShiftof-1\\c=-\frac{3}{7}=VerticalShiftof-\frac{3}{7}\\(-1,-\frac{3}{7})\\f(x)=-\frac{3}{5}|x-5|+\frac{2}{3}\\b=-5=HorizontalShiftof5\\c=\frac{2}{3}=VerticalShiftof\frac{2}{3}\\(5,\frac{2}{3})\\f(x)=\frac{1}{2}|x|-\frac{4}{5}\\b=0=HorizontalShiftof0\\c=-\frac{4}{5}=VerticalShiftof\frac{4}{5}\\(0,-\frac{4}{5})\\f(x)=-\frac{3}{2}|x-\frac{2}{5}|+\frac{5}{3}\\b=-\frac{2}{5}=HorizontalShiftof\frac{2}{5}\\c=\frac{5}{3}=VerticalShiftof\frac{5}{3}\\(\frac{2}{5},\frac{5}{3})[/tex]
Please someone help me thank you
Answer:
D. 9/4 ÷ 3/4
Step-by-step explanation:
In the question, the number line represents 9/4 divided into 3 equal units.
The size of each unit is 3/4 as shown.
Showing that 3/4 divides 9/4 into 3 divisions:
9/4 ÷ 3/4
= 9/4 x 4/3
= 9/3 x 4/4
= 9/3 x 1
= 3 x 1
= 3
Hence, the number line represents three divisions given by 9/4 ÷ 3/4.
What is the measure of DG?
Enter your answer in the box.
Need help finding the length of Ac
Answer:
We need to know angle C which is (180 -123 -34) = 23°
We'll use the Law of Sines
Sine (A) / side a = Sine (B) / side b
Sine (34) / 10 = Sine (123) / side b
0.55919 / 10 = 0.83867 / side b
10 * .83867 / .55919 = side b
side b (or line AC) = 14.998
Step-by-step explanation:
A local public library decides to track the number of hours that a certain computer is being used. The table represents the number of hours, y, which is dependent on the number of days, x.
What is the linear equation that represents this situation?
Answer:
Second option: y = 8x-3
Step-by-step explanation:
The equation tha satisfies the given values will be the required linear equation
So,
y = 8x + 45
For x=3 and y=21
21 = 8(3) +45
21 = 24+45
21≠69
As this equation is not satisfied by the values, it is not the correct option..
For y = 8x-3
x=3,y=21
21 = 8(3)-3
21 = 24-3
21=21
x=5, y=37
37 = 8(5)-3
37=40-3
37=37
x=7, y=53
53 = 8(7)-3
53 = 56-3
53 = 53
As the equation is true for all values of x and y. This is this correct option..
Julie needs to cut 4 pieces of yarn, each with the same length and a piece of yarn 7.75 inches long. Let x represent the length of each of the equal pieces of yarn that Julie decides to cut what is the equation that can be used to determine the total length of all of the yarn that she ends up, cutting,y? Is the graph of the equation continuous or discrete
Answer:
Total length of the x inches long pieces = 4x inches
She has to cut another piece = 7.75 inches
Total length = 4x + 7.75
This is what y represent, so
y = 4x + 7.75
The graph of the equation is continuous
Answer:
The required equation is [tex]y=4x+7.75[/tex] and the graph of the equation is continuous.
Step-by-step explanation:
Consider the provided information.
Julie needs to cut 4 pieces of yarn,
Let x represent the length of each yarn.
Then the length of 4 pieces will be: 4x
y represents the total length of all of the yarn that Julie decides to cut
Therefore the required equation that can be used to determine the total length of all of the yarn is:
[tex]y=4x+7.75[/tex]
Here, the graph is continuous, because the length of yarn can be any number.
What is the y-intercept of the function f(x)=2/9x+1/3
Answer:
1/3
Step-by-step explanation:
Slope intercept form: y=mx+b
m=rise/run (slope)
b= y-intercept
b=1/3
What is the distance between A (5, 8), and B(-3, 4)
Answer:
Step-by-step explanation:
4 square root 5
3 pipes take 60 minutes to water the field. How much time will it take to water the field with 6 pipes? Is this direct proportion or inverse proportion and why? Full working out and equation please.
Answer:
30 minutes
Step-by-step explanation:
3 pipes takes 60 minutes, so one pipe must take 3*60 minutes as it would be 3 times slower. This equates to 180 minutes.
1 pipe takes 180 minutes so 6 pipes would take 1/6 of the time or 6 times faster.
The equation becomes 180/6
= 30 minutes.
Equation is; 3*60/6 = 30 minutes
This is inverse proportion.
The answer is 30 minutes
If it takes 3 pipes 60 minutes to water the field
The amount of time it will take one pipe can be calculated as follows
t= constant(k) × number of pipes
60= k/3
cross multiply
k = 60×3
= 180
Since it takes one pipe 180 minutes to water the field, then the amount of time it will take 6 pipes can be calculated as follows
= 180/6
= 30
Hence it will take 6 pipes 30 minutes to water the field
It is an inverse proportion because an increase in one quantity leads to a decrease in the other.
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Which equation results from taking the square root of both sides of (x - 9)2 = 81?
Ох – 9 = +9
Ox+ 9 = +9
Ox+ 3 = +9
Ох – 3 = +9
Answer:
х – 9 = +9
Step-by-step explanation:
The equation results from taking the square root of both sides of
(x- 9)² = 81 is x -9 = ±9.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
We have Equation,
(x- 9)² = 81
Now, simplifying for x we get
Take square root on both side
x-9 = √81
x -9 = ±9.
Then, the equation results from taking the square root of both sides is
x -9 = ±9.
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What is the first step needed to solve 2/5x-6=-16?
Answer:
Add 6 to both sides.
Step-by-step explanation:
You are trying to solve for x in this type of question. In this case, note that there is a equal sign, and that what you do to one side you do to the other. Also note that to isolate the x (your goal), you must do the opposite of PEMDAS. (Note that PEMDAS = Parenthesis, Exponent (& Roots), Multiplication, Division, Addition, Subtraction).
So your first step is to add 6 to both sides.
2/5x - 6 (+6) = -16 (+6)
Simplify. Solve:
2/5x + (-6 + 6) = -16 + 6
2/5x = -10
_________________________________________________________
Finish finding for x.
Multiply the recipricol of the fraction to both sides to isolate the x. Multiply 5/2 to both sides:
(5/2)(2/5)x = (-10)(5/2)
x = (-10)(5/2)
x = (-50)/2
x = -25
x = -25 is your answer.
~
Erinn wrote the equation –5x + 4y = 32 to represent her hourly wage (y) and how this wage has changed during each year that she worked at a company (x).
What is the rate of change in Erinn's hourly wage per year?
Answer:
The rate of change in Erinn's hourly wage per year is [tex]1.25\$\ hour/year[/tex]
Step-by-step explanation:
we have that
x ----> the time in years that she worked at a company
y ----> represent the hourly wage
[tex]-5x+4y=32[/tex] ----> linear equation that represent the situation
Solve for y
[tex]4y=5x+32[/tex]
[tex]y=(5/4)x+32/4[/tex]
[tex]y=1.25x+8[/tex]
The slope m of the linear equation is
[tex]m=1.25\$\ hour/year[/tex]
The rate of change in Erinn's hourly wage per year is equal to the slope of the linear equation
so
The rate of change in Erinn's hourly wage per year is [tex]1.25\$\ hour/year[/tex]
Samantha works in a bakery. The profit of cupcakes in dollars, after t weeks, is given by the function, C(t) = 0.1t3. The profit of cookies in dollars, after t weeks, is given by the function, K(t) = 5(1.07)t - 5. Which function describes the total profit, M(t), at the bakery after t weeks?
Answer:
M(t) = 0.1t3 + 5(1.07)t - 5
Step-by-step explanation:
Answer:
[tex]M(t) = 0.1t^{3}[/tex] [tex]+ 5(1.07)^{t}[/tex]- 5
Step-by-step explanation:
(on attachment with step by step explanation)
What is the equation of the line in point-slope form?
y+ 4 = 1/2(x+4)
y-4 = 1/2(x + 4)
y-0 = 2(x - 4)
y-4 = 2(8-0)
Answer: y=-2x+2/4
Step-by-step explanation:
Answer:
y + 4 =1/2 (x + 4)
Step-by-step explanation:
Your welcome uwu
What is the perimeter, P, of a rectangle that has a length of x + 8 and a width of y − 1?
P = 2x + 2y + 18
P = 2x + 2y + 14
P = x + y − 9
P = x + y + 7
Answer:
P = 2x + 2y + 14
Step-by-step explanation:
Length (L) = x + 8 units
Width (W) = y - 1 units
Perimeter (P) = 2L + 2W
P = 2(x + 8) + 2(y - 1)
P = 2x + 16 + 2y - 2
P = 2x + 2y + 16 - 2
P = 2x +2y + 14
Answer:
P = 2x + 2y + 14
Step-by-step explanation:
What is the sign of -567.45 + 567.45?
Choose 1 answer:
A
Positive
B
Negative
(C) Neither positive nor negative-the sum is zero.
Answer:
C
Step-by-step explanation:
-567.45 + 567.45 = 0
What is y-5=3(x+1) in slope intercept form
Answer:
y=3x+8, :m=3, b=8
Hope this helps!
The line y - 5 = 3(x + 1) in the form of slope intercept is y = 3x + 8 and slope of the line is 3, y-intercept is 8.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have a line:
y - 5 = 3(x + 1)
In slope intercept form:
y = 3x + 3 + 5
y = 3x + 8
Thus, the line y - 5 = 3(x + 1) in the form of slope intercept is y = 3x + 8 and slope of the line is 3, y-intercept is 8.
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The total cost for 9 bracelets, including shipping was $72. The shipping charge was $9. Define your variable and write an equation that models the cost of each bracelet.
4. Use the equation you have written above determine the cost for each bracelet. Show the algebraic steps that it takes to find the answer. Provide your conclusion.
Answer:
a) Equation: 9x+9 = 72
b) x =7
Step-by-step explanation:
The total cost of 9 bracelets = $72
Shipping charge = $9
a) Define your variable and write an equation that models the cost of each bracelet.
Let x be the cost of one bracelet, the equation will be
9x + 9 = 72
As 9 bracelets were there and the shipping cost was 9 and total cost was 72.
b) Use the equation you have written above determine the cost for each bracelet. Show the algebraic steps that it takes to find the answer.
Now solving the equation to find the value of x that represent cost of each bracelet
9x + 9 = 72
Adding -9 on both sides
9x +9 -9 = 72 -9
9x = 63
Dividing both sides by 9
9x/9 = 63/9
x = 7
The value of x=7 so, the cost of each bracelet is $7
c) Provide your conclusion.
So, each bracelet was of cost $7 and $9 was the shipping charge. so, the total cost is $72.
We would check whether our equation is satisfied.
9x+ 9 = 72
9(7) + 9 = 72
63 + 9 = 72
72 = 72
The equation is satisfied.
Answer:
The cost of each bracelet is: $7
Step-by-step explanation:
Let's call x the cost of each bracelet.
Then the cost of the 9 bracelets is:
9x
If we know that the cost of the bracelets plus the shipping was $ 72 and the cost of shipping is $ 9.
So
The total cost was:
[tex]9x + 9 = 72[/tex]
Now we solve the equation for the variable x.
[tex]9x + 9 = 72[/tex]
Subtract 9 on both sides of equality
[tex]9x + 9-9 = 72-9[/tex]
[tex]9x = 72-9[/tex]
[tex]9x = 63[/tex]
Divide by 9 on both sides of equality
[tex]\frac{9}{9}x = \frac{63}{9}[/tex]
[tex]x = \frac{63}{9}[/tex]
[tex]x = \$7[/tex]
The temperature in Fargo North Dakota was 6°F at noon. By 4 PM the temperature dropped to -10°F. What integer represents the change in temperature?
The integer that represents the change in temperature is -16°F.
How to solve for the change in temperatureTo find the change in temperature, we need to calculate the difference between the final temperature and the initial temperature.
The initial temperature was 6°F, and the final temperature was -10°F. To calculate the change, we subtract the initial temperature from the final temperature:
Change in temperature
= Final temperature - Initial temperature
= (-10°F) - (6°F)
= -10°F - 6°F
= -16°F
Therefore, the integer that represents the change in temperature is -16°F.
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Thank you so much for thisb
Answer:
Choice B
Step-by-step explanation:
Formula for slope:
[tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]y_2 = 1\\y_1 = -10\frac{2}{3} \\\\x_2 = -3\\x_1 = 4[/tex]
[tex]1 - (-10\frac{2}{3}) = 11\frac{2}{3} \\-3 - 4 = -7[/tex]
[tex]\frac{-11\frac{2}{3} }{-7} = \frac{5}{3} = 1\frac{2}{3}[/tex]
What’s the common ratio of this sequence?
3, 21, 147
Answer:
r = 7
Step-by-step explanation:
The common ratio r of a geometric sequence is
r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{a_{3} }{a_{2} }[/tex], that is
r = [tex]\frac{21}{3}[/tex] = [tex]\frac{147}{21}[/tex] = 7
The common ratio of the sequence 3, 21, 147 is 7.
Start with the first and second terms:
21 ÷ 3
= 7
Confirm with the second and third terms:
147 ÷ 21
= 7
Thus, the common ratio (r) is 7.
The quotient of 4 and 2, decreased by a number, equals that number multiplied by 3
Answer:
.5
Step-by-step explanation:
4/2 -n=3n
2 -n=3n
2 =4n
2/4 =n
.5 =n
A line intersects the point (6,9) and (7,4). What is the slope intercept equation for this line?
Answer:
y = -5x + 39
Step-by-step explanation:
Plug either ordered pair into the Point-Slope Formula FIRST, y - y₁ = m(x - x₁), then convert to Slope-Intercept Form by moving whichever term is nearest to y, over to the right side of the equivalence symbol to get the above answer.
What is the distance between the points (–4, 2) and (3, –5)?
Answer:
[tex]\sqrt{98}[/tex]
Step-by-step explanation:
Using the distance formula
with (x₁, y₁ ) = (- 4, 2) and (x₂, y₂ ) = (3, - 5)
d = [tex]\sqrt{(3+4)^2+(-5-2)^2}[/tex]
= [tex]\sqrt{7^2+(-7)^2}[/tex]
= [tex]\sqrt{49+49}[/tex]
= [tex]\sqrt{98}[/tex]
C= [tex]\sqrt{98}[/tex]
What happens when you square a square root?We could say that the square root or the square cancel each other out. They are a inverse of each other. If we have the number written with the index two ( squared) then taking the square root simply means that we leave out the two ( this only applies on the positive numbers ).
How to figure out square roots?Start by i = 1, if i * i = n, then i it is the square root of n as n is the perfect square.if i * i > n, it means square root must lie between (i-1, i), let’s call them (low, high)Apply binary search in the range (low, or high). Find mid of (low, high):Using the distance formula
with (x₁, y₁ ) = (- 4, 2) and (x₂, y₂ ) = (3, - 5)
[tex]d= \sqrt{(3+4)^{2} +(-5-2)^{2}} \\\\= \sqrt{7^{2} + (-7)^{2}} \\\\= \sqrt{49+49} \\\\=\sqrt{98}[/tex]
Learn more about square root here https://brainly.com/question/3120622
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