Step-by-step explanation:
3over4 which is 75percentNEED HELP ASAP. :)))
The difference in mail handled between 195 and 1965 is -5.4 x 10
What is the difference in mail handled?The data on the pieces of mail handled by the United States Postal Service is written in scientific notation. Scientific notation is used to compress larger numbers into smaller numbers.
In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10. For example, 1 x 10² is equivalent to 100
Difference in mail handled = mail handled in 1995 - mail handled in 1965
(1.8 x [tex]10^{11}[/tex]) - (7.2 x [tex]10^{10}[/tex])
(1.8 - 7.2) x [tex]10^{11 - 10}[/tex]
-5.4 x 10
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which number best represents the scope of the graphed line? a. -5 b. -1/5 c. 1/5 d.5
write 3 ratios equivalent to 2:5. Show your work
Answer: 4/10, 6/15, 8/20
Hope this helps!
How would i kill a snake with fractions? it's on my homework question... i dont get it at all
Just me:
? I will just explain what I understand
Answer:
(Think hard) If you cut a snake in half you get 1/2 but if you cut it into 4's 1/5
I tried.
Write the first five terms of the sequence with the given nth term. an = 3n − 1 n!.
The first five terms of the sequence with the given nth term are 1, 3/2, 3/2, 9/8, 27/40.
In this question,
The nth term of the sequence is [tex]a_n=\frac{3^{(n-1)} }{n!}[/tex]
Now substitute the values of n = 1,2,3,4,5
For n = 1,
⇒ [tex]a_1=\frac{3^{(1-1)} }{1!}[/tex]
⇒ [tex]a_1=\frac{3^{0} }{1}[/tex]
⇒ a₁ = 1
For n = 2,
⇒ [tex]a_2=\frac{3^{(2-1)} }{2!}[/tex]
⇒ [tex]a_2=\frac{3^{(1)} }{(1)(2)}[/tex]
⇒ [tex]a_2=\frac{3}{2}[/tex]
For n = 3,
⇒ [tex]a_3=\frac{3^{(3-1)} }{3!}[/tex]
⇒ [tex]a_3=\frac{3^{(2)} }{(1)(2)(3)}[/tex]
⇒ [tex]a_3=\frac{9}{6}[/tex]
⇒ [tex]a_3=\frac{3}{2}[/tex]
For n = 4,
⇒ [tex]a_4=\frac{3^{(4-1)} }{4!}[/tex]
⇒ [tex]a_4=\frac{3^{(3)} }{(1)(2)(3)(4)}[/tex]
⇒ [tex]a_4=\frac{27}{24}[/tex]
⇒ [tex]a_4=\frac{9}{8}[/tex]
For n = 5,
⇒ [tex]a_5=\frac{3^{(5-1)} }{5!}[/tex]
⇒ [tex]a_5=\frac{3^{(4)} }{(1)(2)(3)(4)(5)}[/tex]
⇒ [tex]a_5=\frac{81}{120}[/tex]
⇒ [tex]a_5=\frac{27}{40}[/tex]
Hence we can conclude that the first five terms of the sequence with the given nth term are 1, 3/2, 3/2, 9/8, 27/40.
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Find the term that must be added to the equation x2 4x=1 to make it into a perfect square.
The term that must be added to the equation x2+4x=1 to make it into a perfect square is 4.
What is Quadratic equation?Any equation that can be rewritten in standard form as where x represents an unknown, a, b, and c represent known numbers, and where a 0 is true is a quadratic equation. Since there is no ax2 term, the equation is linear if a = 0, not quadratic.
Why is it called a quadratic equation?This is true because the Latin word quadratum, which means "square," plus the fact that the area of a square with side length x is equal to x2, make up what is known as the quadratic (or "square-like") definition of a polynomial equation with exponent two.
According to the given information:x²+4x=1
as, the x has coefficient 4.
so,
half the coefficient of x and add and subtract the square of the remaining.
x²+4x + 2 ² - 2² =1
Now,
make the whole square term
x²+4x + 2 ² - 4 - 1=0
( x + 2)² -5= 0
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One rectangular solid with a square base has twice the height of another rectangular solid with a square base with the same side length. which statements about the two rectangular solids are true? check all that apply.
The correct statements about the solids are:
(A) The bases are congruent.(D)The volume of the first solid is twice as much as the volume of the second solid.(E) If the dimensions of the second solid are x by x by h, the first solid has 4xh more.What are solids?Solid geometry or stereometry is the standard name for the geometry of three-dimensional Euclidean spaces in mathematics. Stereometry is concerned with the volume measurements of various solid forms, such as pyramids, prisms, and other polyhedrons; cylinders; cones; truncated cones, and balls bordered by spheres.To find which statements are correct:
Congruent base: This is used to indicate that the triangles' bases are the same and that they have the same shape.
The volume of the first triangle is: [tex]2x^{2} h[/tex]
The volume of the second triangle is: [tex]x^{2} h[/tex]
Therefore, the correct statements about the solids are:
(A) The bases are congruent.(D)The volume of the first solid is twice as much as the volume of the second solid.(E) If the dimensions of the second solid are x by x by h, the first solid has 4xh more.Know more about solids here:
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The complete question is given below:
One rectangular solid with a square base has twice the height of another rectangular solid with a square base with the same side length. Which statements about the two rectangular solids are true? Check all that apply.
A) The bases are congruent.
B) The solids are similar.
C) The ratio of the volumes of the first solid to the second solid is 8:1.
D)The volume of the first solid is twice as much as the volume of the second solid.
E) If the dimensions of the second solid are x by x by h, the first solid has 4xh more
surface area than the second solid.
The equation for least regression line to this data set is ŷ = 76. 82x 88. 56. what is the predicted value (in dollars) for maintenance expenses when a truck is 7 years old?
The predicted value (in dollars) for maintenance expenses when a truck is 7 years old is $626.3.
In this question,
The equation for least regression line to this data set is
y' = 76.82x + 88.56 ------- (1)
Number of years, x = 7
The general form of equation for least regression line is
y' = a + bx
where y is the dependent variable, x is the independent variable, a is the intercept of regression line and b is the slope of regression line.
The predicted value (in dollars) for maintenance expenses when a truck is 7 years old can be calculated as
y' = 76.82x + 88.56
Substitute the value of x in the above equation, we get
y' = 76.82(7) + 88.56
y' = 537.74 + 88.56
y' = 626.3
Hence we can conclude that the predicted value (in dollars) for maintenance expenses when a truck is 7 years old is $626.3.
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If g(x)=-2x), which graph is the graph of function g?
Answer:
The graph of g(x) has a y-intercept at (0,0) and a slope of -2.
The two lines y = 2x + 8 and y = 2x - 12 intersect the x-axis at the P and Q.
Work out the distance PQ.
Answer:
PQ = 10 units
Step-by-step explanation:
to find where the lines cross the x- axis let y = 0 and solve for x , that is
2x + 8 = 0 ( subtract 8 from both sides )
2x = - 8 ( divide both sides by 2 )
x = - 4 ← point P
and
2x - 12 = 0 ( add 12 to both sides )
2x = 12 ( divide both sides by 2 )
x = 6 ← point Q
the lines cross the x- axis at x = - 4 and x = 6
using the absolute value of the difference , then
PQ = | - 4 - 6 | = | - 10 | = 10 units
or
PQ = | 6 - (- 4) | = | 6 + 4 | = | 10 | = 10 units
Answer: [tex]\Huge\boxed{Distance=10~units}[/tex]
Step-by-step explanation:
Find the point PGiven expression
y = 2x + 8
Substitute 0 for the y value to find the x value
This is the definition of x-intercepts
(0) = 2x + 8
Subtract 8 on both sides
0 - 8 = 2x + 8 - 8
-8 = 2x
Divide 2 on both sides
-8 / 2 = 2x / 2
x = -4
[tex]\large\boxed{P~(-4,0)}[/tex]
Find the point QGiven expression
y = 2x - 12
Substitute 0 for the y value to find the x value
(0) = 2x - 12
Add 12 on both sides
0 + 12 = 2x - 12 + 12
12 = 2x
Divide 2 on both sides
12 / 2 = 2x / 2
x = 6
[tex]\large\boxed{Q~(6,0)}[/tex]
Find the distance between PQGiven information
[tex](x_1,~y_1)=(-4,~0)[/tex]
[tex](x_2,~y_2)=(6,~0)[/tex]
Substitute values into the distance formula
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]Distance=\sqrt{(6-(-4))^2+(0-0)^2}[/tex]
Simplify values in the parenthesis
[tex]Distance=\sqrt{(10)^2+(0)^2}[/tex]
Simplify values in the radical sign
[tex]Distance=\sqrt{100}[/tex]
[tex]\Huge\boxed{Distance=10~units}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
PLS HELP ASAP! Ty
Let g(x)= 2x^2+3x-9 and h(x)=x^2+2x-6
Find (h-g)(2.1)
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: (h - g)(x) [/tex]
[tex]\qquad \sf \dashrightarrow \: h(x) - g(x) [/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} + 2x - 6 - (2 {x}^{2} + 3x - 9)[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} + 2x - 6 - 2 {x}^{2} - 3x + 9[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} - 2 {x}^{2} + 2x - 3x - 6 + 9[/tex]
[tex]\qquad \sf \dashrightarrow \: - {x}^{2} - x + 3[/tex]
For, (h - g)(2.1), put x = 2.1
[tex]\qquad \sf \dashrightarrow \: - {(2.1)}^{2} - (2.1) + 3[/tex]
[tex]\qquad \sf \dashrightarrow \: - 4.41 - 2.1 + 3[/tex]
[tex]\qquad \sf \dashrightarrow \: - 6.51 + 3[/tex]
[tex]\qquad \sf \dashrightarrow \: - 3.51[/tex]
A Rental Truck Is Company Charges $25 Per Day Plus A Fee Of $0.35 For Every Mile (m) Driven. Which Equations Can Be Used To Find The Numbers Of Miles Driven For A Truck That Cost A Total Of $42.50 To Rent For One Day?
A)$25m + 0.35m = $42.50
B)$0.35 + $25m = $42.50
C)$42.50 + $0.35m = $25
D)$0.35 = $42.50
The Option A is correct. The Numbers of Miles Driven for A Truck That Cost a Total Of $42.50 To Rent for One Day $25m + 0.35m = $42.50
According to the statement
we have given that the Rental Truck Is Company Charges $25 Per Day Plus A Fee Of $0.35 For Every Mile (m) Driven. and a Truck That Cost A Total Of $42.50 To Rent For One Day.
And we have to find the equation for this.
So, for given purpose,
we know that the A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
And from the given values the equation formed that the
In the equation the charges per mile is added to the original charges is equal to the total charges per day.
So, The equation become
$25m + 0.35m = $42.50
And by this equation we represent the all given conditions related charges.
So, The Option A is correct. The Numbers of Miles Driven for A Truck That Cost a Total Of $42.50 To Rent for One Day $25m + 0.35m = $42.50
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A student weighs out 0. 0422 g of magnesium metal. The magnesium metal is reacted with excess hydrochloric acid to produce hydrogen gas. A sample of hydrogen gas is collected over water in a eudiometer at 32. 0°c. The volume of collected gas is 43. 9 ml and the atmospheric pressure is 832 mmhg. Using the experimentally collected data, calculate r and the percent error.
The value of r = 9.078.
What is ideal gas law?pv = nrt. The factor “r” in the ideal gas law equation is known as the “gas constant”. r = [tex]\frac{pv}{nt}[/tex]. The pressure times the volume of a gas divided by the number of moles and temperature of the gas is always equal to a constant number.
so the student weights out .0422 grams of the magnesium metal so from here we can calculate that more's, the magnesium that he used, that is the mass of the magnesium over the more mass, which is .024422 over 24 point. That's equal to about .001758. More so also, it says the magnesium metal is react with excessive hydrochloric acid and produce hydrogen gas. A sample of the hydrogen gas is collected over water in a meter at 22 cecr, the volume of clictic gas is 43.9 and mastic pressure. Is that so using the experimental and collected data calculated are in the percent error? So we know the magnesium react with hydrochloride. The reaction ratio is 1 to 2 and we produce 1. More is the hydrogen and 1. More is magnesium chloride. So from this equatium we know that more of the hydrogen that would be produced in this case is equal to the mass of the magnesium here, that's his .001758 more and set way. There's among hydrogen. The temperature is 32 (degree celcius) which we need to convert the unit into kelvin, so it's actually about field 5.15 kelvin and tells you. The volume of the gas is 43.9 in ml, which is .0439 liter and tells you the pressure of the gas is about 832 millimeter. Mercury, which is a 2 times 13332 plus ca, that's equal to about 110922.24 par. So in this case we know p v = n r t.
r = [tex]\frac{pv}{nt}[/tex]
So p = 110922.24. V = 0.0439 , n = 0.001758 t = 305.15. So let's just do the calculations here.
In this case you will find r=?
Here it's about 9.078.
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Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to tariqareesha2, tysm for the help!
Please help answer my questions like these I have many more quick algebra 1 questions that are all due in 2 days so it would be much appreciated if you check them out. Once again, tysm!
Answer:
its the 4th one i think
Step-by-step explanation:
Which value of y completes the proportion?
18/27 = 2/y
A. 1
B. 2
C. 3
D. 9
I picked c.) 3 am I right?
Answer:
c. 3
yes you are right, good job!!
Step-by-step explanation:
18 divided by what equals 2?
18 / 2 = 9 so 18 / 9 = 2
so 27 / 9 = y which y = 3
check: 9 x 3 = 27
Answer:
Yes, C
Step-by-step explanation:
18/2 = 9 so you need to divide 27 by 9 to get 3
Find the equation of the linear function represented by the table below in slope-intercept form.
x 0 1 2 3 4
y 7 15 23 31 39
Answer:
y = 8x+7
Step-by-step explanation:
firstly reduce the equation to an arithmetic series starting from the 0th term so:
7, 15, 23, 31, 39....
Secondly, identify the common difference: 8
we now know that the answer must contain 8x
Thirdly, form the equation 8x + c = y where y is a constant. Afterwards insert the values of any given x and y so:
8*0 + c = 7
c = 7
Thusly we now know that the series and thus equation is 8x+7 = y
Answer:
y = 8x + 7
Step-by-step explanation:
the equation of a linear function in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2-y_{1} } }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1,15) and (x₂, y₂ ) = (2, 23) ← 2 ordered pairs from the table
m = [tex]\frac{23-15}{2-1}[/tex] = [tex]\frac{8}{1}[/tex] = 8
the ordered pair (0, 7 ) indicates c = 7
y = 8x + 7 ← equation of linear function
3x +2y +4z = 11
2x -y +3z = 4
5x -3y +5z = -1
I need to know how to solve it
The solution to the system of equations is x = 1, y = 10 and z = 4
How to solve the system of equations?The system of equations is given as:
3x +2y +4z = 11
2x -y +3z = 4
5x -3y +5z = -1
Multiply the second equation by 2
So, we have
4x - 2y + 6z = 8
Add this equation to the first equation
3x + 4x + 2y - 2y + 4z + 6z = 11 + 8
Evaluate the like terms
7x + 10z = 19
Multiply the second equation by 3
So, we have
6x - 3y + 9z = 12
Subtract this equation from the third equation
6x - 5x - 3y + 3y + 9z - 5z = 12 + 1
Evaluate the like terms
x + 4z = 13
Make x the subject
x = 13 - 4z
Substitute x = 13 - 4z in 7x + 10z = 19
7(13 - 4z) + 10z = 19
Expand
91 - 28z + 10z = 19
Evaluate the like terms
-18z = -72
Divide
z = 4
Substitute z = 4 in x = 13 - 4z
x = 13 - 4 * 4
Evaluate
x = 1
We have:
2x -y +3z = 4
This gives
2(1) - y + 3 * 4 = 4
Evaluate
2 - y + 12 = 4
This gives
y = 10
Hence, the solution to the system of equations is x = 1, y = 10 and z = 4
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A central role of members at this time is to recognize and deal with the many forms of?
Answer:
Resistance
Step-by-step explanation:
PLEASE HELP its math
Answer:
y = 3x + 6
Step-by-step explanation:
We are given a line.
We know this line is parallel to the line y=3x+2, and passes through (1, 9).
We want find the equation of this line.
Parallel lines have the same slopes.
So, let's find the slope of y=3x+2.
The line is written the format y=mx+b, where m is the slope and b is the value of y at the y intercept.
As 3 is in the place of where m (the slope) is, the slope of the line is 3.
It is also the slope of the line parallel to it.
We should write the equation of the line parallel y=3x+2 in slope-intercept form as well, however, before we do that, we can write the line in point-slope form, and then convert it to slope-intercept form.
Point-slope form is given as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1,y_1)[/tex] is a point.
We can substitute 3 as m in the formula, as we know that is the slope of the line
[tex]y-y_1=3(x-x_1)[/tex]
Recall that we were given the point (1, 9), which also belongs to (it passes through) the line.
Therefore, we can use its values in the formula.
Substitute 1 as [tex]x_1[/tex] and 9 as [tex]y_1[/tex].
y - 9 = 3(x-1)
We can now convert the equation into slope intercept form.
Notice how y is by itself in slope-intercept form; this means we'll need to solve the equation for y.
Start by distributing 3 to both x and -1.
y - 9 = 3x - 3
Now add 9 to both sides.
y = 3x + 6
x² + y² if x = 7 and y = 5. What is the solution to this??
Step-by-step explanation:
x = 7
y = 5
[tex] = {x}^{2} + {y}^{2} [/tex]
[tex] = (7 {)}^{2} + (5 {)}^{2} [/tex]
= 7 × 7 + 5 × 5
[tex] = 49 + 25 [/tex]
[tex] = 74[/tex]
Hey there!
x^2 + y^2
= 7^2 + 5^2
= 7 * 7 + 5 * 5
= 49 + 25
= 74
Therefore, your answer should be: 74
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
LOTS OF POUNT PLS HELP
Answer:
Option 2
Step-by-step explanation:
Using the quadrstic formula,
[tex]\tan \theta=\frac{-2 \pm \sqrt{2^2 - 4(\sqrt{3})(-\sqrt{3})}}{2\sqrt{3}} \\ \\ =\frac{-2 \pm 4}{2\sqrt{3}} \\ \\ =\frac{-1 \pm 2}{\sqrt{3}} \\ \\ = -\sqrt{3}, \frac{1}{\sqrt{3}}[/tex]
Case 1
[tex]\tan \theta=-\sqrt{3} \implies \theta=\frac{2\pi}{3}, \frac{5\pi}{3}[/tex]
Case 2
[tex]\tan \theta=\frac{1}{\sqrt{3}} \implies \theta=\frac{\pi}{6}, \frac{7\pi}{6}[/tex]
1 of 2. Very much apprexiated
Answer:x=5
Step-by-step explanation: 73+73+6x+4=180
150+6x=180
6x=30
x=5
Here are yesterday's high temperatures (in Fahrenheit) in 12 U.S. cities. 48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80 Notice that the temperatures are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:
The median value is 63 and Lower quartile range is 48 and Interquartile range is 80.
According to the given statement
we have given data set and we have to find the five number summary.
So, For this purpose,
the given data set is:
48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80
Firstly we have to find the upper quartile means median for it.
So, Median = n /2
median = 12/2
median = 6th term.
So, Upper quartile range for this data set is 63.
And
Lower quartile for data set is the lower value of the data set.
So, That's why
Lower quartile range for this data set is 48.
And now, we have to find the Interquartile range
so, Interquartile range means maximum value of data.
So, That's why
Interquartile range of this data is 80.
So, The median value is 63 and Lower quartile range is 48 and Interquartile range is 80.
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To select the correct student's t-distribution requires knowing the degrees of freedom. How many degrees of freedom are there for a sample of size n?
The correct student's t- distribution requires knowing the degrees of freedom. The degrees of freedom are there for a sample of size n is B) n-1.
Distribution is described as the technique of having items to consumers. An instance of distribution is rice being shipped from Asia to the USA. The frequency of occurrence or quantity of lifestyles.
Distribution manner to spread the product for the duration of the market such that a big quantity of humans should purchase it. Distribution involves doing the following matters. An amazing delivery machine to take the goods into one-of-a-kind geographical regions.
Distribution is one of the four elements of the advertising and marketing mix. Distribution is the method of creating a service or product available for the consumer or enterprise user who needs it. this may be executed without delay through the manufacturer or service company or the usage of indirect channels with vendors or intermediaries.
Disclaimer: The question is incomplete. Please read below to find the missing content.
Question: To select the correct Student's t-distribution requires knowing the degrees of freedom. How many degrees of freedom are there for a sample of size n?
A) n
B) n-1
C) n+1
D) [X - μ / (s / n)]
The degrees of freedom depends on the number of parameters you are estimating.
8=
i-1
In student t distribution we estimate the population mean through sample mean and population standard deviation through sample standard deviation
So here both parameters depend on the sample mean i.e. we just calculate from a sample of size n so
Degrees of freedom for students t distribution is B) n-1
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10 points please help and marked brainlyist
Answer:
A.
Sample 1 mean: 6.375
Sample 2 mean: 6.375
Sample 3 mean: 6.625
B.
Range of sample means: 0.25
C.
The first and last boxes should be checked, as they are true.
Step-by-step explanation:
To calculate the mean you must add all of the numbers together and then divide the sum by the quantity of numbers. Ex: 3+7+8+3+7+9+6+8 = 51.
51/8 = 6.375.
Use the bisection method to find solutions accurate to within 10−2 for x 4 − 2x 3 − 4x 2 4x 4 = 0 on each interval.
(a) [−2, −1].
(b) [0, 2].
(c) [2, 3].
(d) [−1, 0].
The solution accurate to equation within [tex]10^{-2}[/tex] for [tex]x^{4}-2x^{3} -4x^{2} +4x+4=0[/tex] lies in [0,2].
Given the equation [tex]x^{4}-2x^{3} -4x^{2} +4x+4=0[/tex] and range is [tex]10^{-2}[/tex].
We are required to find the interval in which the solution lies.
The attached table shows the iterations. At each step, the interval containing the root is bisected and the function value at the mid point of the interval is found. The sign of its relative to the signs of the function values at the ends of the interval tell which half interval contains the root. The process is repeated until the interval width is less than [tex]10^{-2}[/tex].
Interval:[0,2], signs [+,-],mid point:1, sign at midpoint +.
[1,2] 3/2
[1,3/2] 5/4
The rest is in the attachment. The listed table values are the successive interval mid points.
The final midpoint is 181/128=1.411406.
This solution is within 0.0002 of the actual root.
Hence the solution accurate to equation within [tex]10^{-2}[/tex] for [tex]x^{4}-2x^{3} -4x^{2} +4x+4=0[/tex] lies in [0,2].
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Find the missing length indicated.
The missing length of given right triangle is equal to 1500.
RIGHT TRIANGLEA triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.
The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.
The Pythagorean Theorem says: [tex]hypotenuse^2=(leg_1)^2+(leg_2)^2[/tex] . And the main trigonometric ratios are: sin (x), cos (x) and tan (x) , where:
[tex]sin(x)=\frac{opposite\ side}{hypotenuse} \\ \\ cos(x)=\frac{adjacent\ side}{hypotenuse} \\ \\ tan (x)= \frac{opposite\ side}{adjacent\ side}[/tex]
There is another important property, where h²=m*n. See the attached image.
From the previous informations presented, you can solve the given question.
Thus, if h²=m*n. You can write:
h²=900*1600
[tex]h=\sqrt{1440000}\\ \\ h=1200[/tex]
If h=1200, you can find x from Pythagorean Theorem.
x²=1200²+900²
x²=1440000+810000
x²=2250000
x=[tex]\sqrt{2250000}[/tex]
x=1500
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Use the recursive formula to find the first five terms in the arithmetic sequence.
The first five terms of the given arithmetic sequence are:
54, 45, 36, 27, 18 (First option)
The arithmetic sequence is given as follows,
f(n) = f(n-1) - 9 ............ (1)
Also, f(1) = 54 .............. (2)
Now, for finding the first five term of this arithmetic sequence, we will substitute n as 1, 2, 3, 4, and 5 one by one. Using the above formula for the arithmetic sequence, we can deduce the first five terms.
f(1) is the first term of the sequence which is already provided as 54.
Now, putting n=2 in equation (1), we get,
f(2) = f(2-1) - 9
f(2) = f(1) - 9
Substitute f(1) = 54 from equation (2)
⇒ f(2) = 54 - 9
f(2) = 45
To find the third term of the arithmetic sequence, put n = 3 in equation (1)
f(3) = f(3-1) - 9
f(3) = f(2) - 9
⇒ f(3) = 45 - 9
f(3) = 36
Similarly, we can find the fourth and fifth terms of the arithmetic sequence by substituting n = 4 and n = 5 respectively.
∴ f(4) = f(3) - 9
⇒ f(4) = 36 - 9
f(4) = 27
Likewise, f(5) = f(4) - 9
⇒f(5) = 27 - 9
f(5) = 18
Thus, using the recursive formula, the first five terms of the arithmetic sequence are deduced to be:
54, 45, 36, 27, 18
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5. Find the arc length on a circle with radius of 19 feet created by
an angle of 2(pie)/3radians.
19T
O
38
38T
O 19
O None of the above
**Disclaimer** Hi there! I am not fully sure what [ T ] represents. From the answer that I got [ 38π / 3 ], it does not match any one of them, so I choose none of the above. If there's a specific meaning of [ T ] and I am incorrect, please let me know and I will modify my answer.
Answer: None of above
Step-by-step explanation:
Given formula
S = r θ
S = arc lengthr = radiusθ = angle in radiansGiven information
radius = 19 ft
Angle = 2π / 3
Substitute values into the formula
S = r θ
S = (19) (2π / 3)
Simplify by multiplication
[tex]\Large\boxed{S=\frac{38\pi}{3} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
A rental car company is running two specials. Customers can pay $50 to rent a compact car for the first day plus $6 for each additional day, or they can rent the same car for $40 the first day and $8 for every additional day beyond that. Camilla notices that, given the number of additional days she wants to rent the car for, the two specials are equivalent. How much would Camilla pay in total?
The number of additional days she wants to rent the car for the two specials are equivalent is 5 days.
EquationCompact car:
Fixed price = $50Additional price per day = $6y = 50 + 6x
Another special:
Fixed price = $40Additional price per day = $8y = 40 + 8x
let
x = number of additional days
50 + 6x = 40 + 8x
collect like terms50 - 40 = 8x - 6x
10 = 2x
Divide both sides by 2x = 10/2
x = 5 days
Therefore, the number of additional days she wants to rent the car for, the two specials are equivalent is 5 days.
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