if the two trains are miles apart after hours, then the rate of the westbound train is 79 miles per hour
two trains leave the station at the same time, one heading west and the other east.
the westbound train travels miles per hour slower than the eastbound train. if the two trains are miles apart after hours,
what is the rate of the westbound train?
Allow the westbound train to be "w" and the eastbound train to be "e". We can make the following equation:
4 (e + (e - 12)) = 680
4 (2e + 12) = 680
8e - 48 = 680
8e = 728
e = 91 mph
e - 12 = w
91 - 12 = w
79 = w
Therefore, the westbound train travels at 79 miles per hour.
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The value of [tex]\tan 1^{\circ}\tan 2^{\circ}+\tan 2^{\circ}\tan 3^{\circ}+\tan 3^{\circ}\tan 4^{\circ}+\cdots+\tan 88^{\circ}\tan 89^{\circ}[/tex] can be expressed in the form [tex]\cot^2 1^{\circ}-n[/tex]. What is the value of [tex]n[/tex]?
Answer:
n = 89Step-by-step explanation:
Use of identitiestan (x - y) = (tan x - tan y)/(tan x tan y + 1) 1/tan x = cot xtan (90 - x) = cot xtan (- x) = - tan xConvert the first one above:
tan x tan y = (tan x - tan y) / tan (x - y) - 1Apply this to each term of the given expression to get:
tan1°tan2° + tan2°tan3° + ... + tan88°tan89° = (tan1° - tan2°)/(tan-1°) - 1 + (tan2° - tan3°)/(tan-1°) - 1 + ... + (tan88° - tan89°)/(tan-1°) - 1 = (tan1° - tan2° + tan2° - tan3° + ... + tan88° - tan89°)/(tan-1°) - 88 = (tan1° - tan89°)/(tan-1°) - 88 = tan1°/ (tan-1°) - tan89°/tan-1° - 88 = - 1 - cot1*(- cot1°) - 88 = cot² 1° - 89The value of n is 89.
Answer:
n = 89
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5 cm}\underline{Tan double angle identity}\\\\$\tan (A - B)=\dfrac{\tan A - \tan B}{1 + \tan A \tan B}$\\\end{minipage}}[/tex]
Rewrite the tan double angle identity to isolate tanAtanB:
[tex]\implies 1 +\tan A \tan B=\dfrac{\tan A- \tan B}{\tan (A - B)}[/tex]
[tex]\implies \tan A \tan B=\dfrac{\tan A- \tan B}{\tan (A - B)}-1[/tex]
Therefore:
[tex]\implies \tan 1^{\circ} \tan 2^{\circ}+\tan2^{\circ}\tan3^{\circ}+...+\tan88^{\circ}\tan89^{\circ}[/tex]
[tex]\implies \left(\dfrac{\tan 1^{\circ}- \tan 2^{\circ}}{\tan (1 - 2)^{\circ}}-1\right)+\left(\dfrac{\tan 2^{\circ}- \tan 3^{\circ}}{\tan (2 - 3)^{\circ}}-1\right)+...+\left(\dfrac{\tan 88^{\circ}- \tan 89^{\circ}}{\tan (88 - 89)^{\circ}}-1\right)[/tex]
[tex]\implies \dfrac{\tan 1^{\circ}- \tan 2^{\circ}}{\tan (-1)^{\circ}}-1+\dfrac{\tan 2^{\circ}- \tan 3^{\circ}}{\tan (-1)^{\circ}}-1+...+\dfrac{\tan 88^{\circ}- \tan 89^{\circ}}{\tan (-1)^{\circ}}-1[/tex]
[tex]\implies \dfrac{\tan 1^{\circ}- \tan 2^{\circ}}{\tan (-1)^{\circ}}+\dfrac{\tan 2^{\circ}- \tan 3^{\circ}}{\tan (-1)^{\circ}}+...+\dfrac{\tan 88^{\circ}- \tan 89^{\circ}}{\tan (-1)^{\circ}}-88[/tex]
[tex]\implies \dfrac{\tan 1^{\circ}- \tan 2^{\circ}+\tan 2^{\circ}- \tan 3^{\circ}+...+\tan 88^{\circ}- \tan 89^{\circ}}{\tan (-1)^{\circ}}-88[/tex]
[tex]\implies \dfrac{\tan 1^{\circ}- \tan 89^{\circ}}{\tan (-1)^{\circ}}-88[/tex]
[tex]\implies \dfrac{\tan 1^{\circ}}{\tan (-1)^{\circ}}-\dfrac{ \tan 89^{\circ}}{\tan (-1)^{\circ}}-88[/tex]
[tex]\textsf{Apply the identity}\quad \boxed{ \tan(-x)=-\tan(x)}:[/tex]
[tex]\implies \dfrac{\tan 1^{\circ}}{-\tan 1^{\circ}}+\dfrac{ \tan (90-1)^{\circ}}{\tan 1^{\circ}}-88[/tex]
[tex]\implies -1+\dfrac{ \tan (90-1)^{\circ}}{\tan 1^{\circ}}-88[/tex]
[tex]\implies \dfrac{ \tan (90-1)^{\circ}}{\tan 1^{\circ}}-89[/tex]
[tex]\textsf{Apply the identity}\quad \boxed{\tan(90-x)=\cot(x)}:[/tex]
[tex]\implies \dfrac{\cot1^{\circ}}{\tan1^{\circ}}-89[/tex]
[tex]\implies \cot 1^{\circ} \cdot \dfrac{1}{\tan1^{\circ}}-89[/tex]
[tex]\textsf{Apply the identity}\quad \boxed{\dfrac{1}{\tan(x)}=\cot(x)}:[/tex]
[tex]\implies \cot 1^{\circ} \cdot \cot 1^{\circ}-89[/tex]
[tex]\implies \cot^21^{\circ}-89[/tex]
Therefore, n = 89.
what is the answer to the absolute value equation? |5x-3|=-2
Answer:
No answer
Step-by-step explanation:
An absolute cannot equal a negative number
v=u+ at
u= 2 a=-5
Work out the value of v.
Substitution
Tynel
4
View One Minute Version
Overview
Revision for 10Y1 October
Answer:
v=-0.5
Step-by-step explanation:
v=2+(-5×0.5)
v=2-2.5
v=-0.5
jeremy sells strawberries 5 pounds for $7.50. what is the cost for 1 pound of strawberries?
this is a pre for something later on in the future please help me i will give brainliest and dont make it sound to smart or use big words becausee i dont type like that
Using the Pythagorean Theorem, it is found that:
The length of the bar is of c = 8.73 ft.The amount of netting needed is of 132.76 ft².Pythagorean TheoremThe Pythagorean Theorem is a geometry axion relates the length of the sides [tex]l_1[/tex] and [tex]l_2[/tex], which are the separated by the angle of 90º, of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
For the netting, it is found that:
The legs are of 8 ft and 3.5 ft.The hypotenuse is of c.Hence the measure c, representing the length of the bar, is calculated as follows:
c² = 8² + 3.5²
c = sqrt(8² + 3.5²)
c = 8.73 ft.
The amount of netting needed is the area of the entire goal, composed by:
A rectangle of dimensions 12 ft and 8.73 ft.Two right triangles of dimensions 8 ft and 3.5 ft.Hence:
A = 12 x 8.73 + 2 x 1/2 x 8 x 3.5 = 132.76 ft².
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what is the first quartile of this data set?
11,12,15,16,17,19,22,24,29,33,38
The first quartile of the given data set would be 15 which is The middle of the numbers from the beginning up.
What is the first quartile of the data set?When data points are organized in ascending order, the first quartile, or lower quartile, (Q1), is the value at which 25% of them are located.
The given data set is:
11,12,15,16,17,19,22,24,29,33,38
Since the number of elements in the data set is 11. As a result, the data are divided into two equal parts by the sixth term. The median of the data is 19.
The middle of the numbers from the beginning up to and including the first middle value: 11,12,15,16,17.
The middle value is 15.
Therefore, the first quartile of this data set would be 15.
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HELP PLEASEEEE
Suppose that y varies directly with x and that y=84
when x=7
. What is the value of x when y=108
?
Suppose that y varies directly with x and that y=84 when x=7. What is the value of x when y=108?
when y=84 and when x=7, x to y in proportion is 1:12. Keeping the ratio of x to y at 1 to 12, when y = 108, x = 9.
7+4x= -5 helppppppppppppp
What is an equation of the line that passes through the points (-2, 5) and (−2,−8)?
The equation of the line that passes through (-2, 5) and (−2,−8) is: x = -2.
What of the Equation of a Line?The equation of a line that passes two given points on the line, can be expressed in slope-intercept form as y = mx + b. In this form, the variable "m" represents the slope of the line, while the "b" represents the y-intercept.
Find the slope using the two points (-2, 5) and (−2,−8):
Slope (m) = change in y / change in x = (-8 - 5)/(-2 -(-2))
Slope (m) = -13/0 [cannot divide]
The slope of the line is undefined. This means the line is a vertical line that intercepts the x-axis at -2.
The equation of the vertical line would therefore be: x = -2.
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A building company employs 3 labourers 12 joiners 8 electrician 4 plumbers. For a job, the company needs one of each type of worker in how may ways can the company choose four workers
The number of ways that the company can choose four workers is 40920 ways.
How to calculate the number?From the information, the building company employs 3 laborers 12 joiners 8 electrician 4 plumbers. The total number of workers will be:
= 3 + 12 + 8 + 4
= 27 workers
It should be noted that combination will be used to choose the 4 workers. This is illustrated as
Combination formula
ⁿCr = n! / ((n – r)! r!)
n = the number of items.
r = how many items are taken at a time.
where n = 33
r = 4
ⁿCr = n! / ((n – r)! r!)
³³C₄ = 33! / (33 - 4)! 4!
= 33! / 29! 4!
= 33 × 32 × 31 × 30 / 4 × 3 × 2
= 40920 ways
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ben is making a dessert that requires 212 lb of strawberries and 112 lb of blueberries. strawberries cost $1 less per pound than blueberries. ben spent a total of $9.50 on the fruit. what is the price per pound of each type of fruit?
Answer:
Step-by-step explanation:Price per pound of strawberries is $-0.31635 and blueberries is $0.6836.
Explanation :
Given data ;
Weight of strawberries required for dessert = 212 lb
Weight of blueberries required for dessert = 112 lb
Total cost spent = $9.50
Let,
Cost of blueberries per pound =x
Cost of strawberries per pound = (x-1)
We know that,
Cost of blueberries for overall weight + Cost of strawberries for overall weight = Total cost spent on fruits.
x(112) + (x-1)212 = 9.50
112x + 212x – 212 = 9.50
324x = 221.5
X = 221.5/324
X = $0.6836
So, (x-1) = $-0.31635
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Price per pound of strawberries is $0.02476 and the price per pound of blueberries is $0.03794
Given that ;
Ben is making a dessert that requires 212 lbs of strawberries and 112 lbs of blueberries. Strawberries cost $1 less per pound than blueberries. Ben spent a total of $9.50 on the fruit.
So according to the question get the price per pound of each type of fruit;
Let ' x ' be the price per pound of strawberries and ' y ' be the price per pound of blueberries.
By assuming the following equations;
212x - 112y = 1 → ( I )
212x + 112y = 9.5 → ( II )
By solving above equations ( I ) ( II ) we get;
424x = 10.5
x = 10.5/424
x = 0.02476
224y = 8.5
y = 8.5/224
y = 0.03794
Price per pound of strawberries is $0.02476 and the price per pound of blueberries is $0.03794
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The formula C=3.14d can be used to approximate the circumference of a circle given its diameter. Company A manufactures and sells a certain washer with an outside circumference of 4 centimeters. The company has decided that a washer whose actual circumference is in the interval 3.9≤C≤4.1 centimeters is acceptable. Use a compound inequality and find the corresponding interval for diameters of these washers.
1.242 ≤ d ≤ 1.305 is the corresponding interval for the diameter of the washer.
Given that,
Company A makes and sells a washer having a 4-centimeter outer radius. The corporation has decided on a washer with an actual radius in the range of 3.9 ≤ C ≤ 4.1.
Inequality is defined as the connection of an equation having the symbol ( ≤, ≥, <, >) in place of the assignment operator.
Here,
C = 3.14d
Given inequality,
3.9 ≤ C ≤ 4.1
3.9 ≤ 3.14d ≤ 4.1
dividing both sides of the inequality by 3.14,
1.242 ≤ d ≤ 1.305
As a result, the needed matching spacing for the washer's diameter is 1.242 ≤ d ≤ 1.305.
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if l //m and m<4=5x-42 and m<5=-x+82, what is the m<5
The measure of <5 is 47
what is parallel lines?Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.
The fundamental characteristics listed below make it simple to recognise parallel lines.
Straight lines that are always the same distance away from one another are called parallel lines.No matter how far apart they are from one another, parallel lines can never intersect.Given:
m<4=5x-42
and m<5=-x+82
as, <4 and <5 are in co- interior angle
<4 + <5 = 180
5x - 42 + (-x + 82) = 180
5x -42 - x + 82= 180
4x +40 = 180
4x = 140
x= 140/4
x= 35
Hence, the measure of <5 = -x+ 82 = -35 + 82 = 47
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C(0)=0
Let c(t) be the number of customers in a restaurant t hours after 8am Explain the meaning of each statement please help
The meaning of each statement is shown below.
Step-by-step explanation:
Assume that the given statements are
(a) c(0)=0
(b) c(3)=c(8)
(c) c(n)=29
(d) c(13)<c(12)
Let c(t) be the number of customers in a restaurant t hours after 8 A.M.
We need to find the meaning of each given statement.
(a) c(0)=0 means the number of customers 0 hours after 8 A.M (i.e., 8 A.M.) is 0.
(b) c(3)=c(8) means the number of customers 3 hours after 8 A.M (i.e., 11 A.M.) is equal to the number of customers 8 hours after 8 A.M (i.e., 4 P.M.).
(c) c(n)=29 means the number of customers n hours after 8 A.M is 29.
(d) c(13)<c(12) means the number of customers 13 hours after 8 A.M (i.e., 9 P.M.) is less than the number of customers 12 hours after 8 A.M (i.e., 8 P.M.)
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An angle measures 4pi/5 radians. What is this angle's measure in degrees?
4π/ 5 radians = ?
Then if
π radians= 180°
(4/5)•π radians = 180• 4/5
. = 144
Answer is
4pi/5 radians = 144 degrees
solve for p 3w+4pw=a
I really need help on this, tyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
Answer:3
Step-by-step explanation: 105 divided by 3 is 35 there are 3 groups so 1 ten would go in each group.
ad and solve the problems.
Dan builds identical model cars and sells them
online. He records the number of models he
completes every couple of hours. The graph shows
Dan's data. Choose two pairs of points on the line
and calculate the slopes between them. Is Dan's
productivity constant? Explain.
The slope between the two pair of points is 3/2. Yes, Dan's productivity is constant.
Number of model are represented on y axis and the hours are represent on x axis.
As we can observe,
One pair of points on the graph is (4,6) and (2,3) and the other pair of points is (6,9) and (0,0)
The slope m between any two points (a,b) and (c,d) can be calculated as,
m = (d-b)/(c-a)
The two points we have are (4,6) and (2,3), so the slope M between them is,
M = (3-6)/(2-4)
M = -3/-2
M = 3/2.
And the slope M' between other two point (6,9) and (0,0) is,
M' = (9-0)/(6-0)
M' = 9/6
M' = 3/2.
As we can see, the slope is same. The slope represents the ratio of number of models and hours. We can conclude that Dan's productivity is constant.
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Given: <1 and <2 are complementary; <1=<4 prove: <3 and <4 are complementary
Statements:
1. <1 and <2 are complementary
2. m<1 + m<2= 90°
3. <1=~<4
4. m<1 = m<4
5. <2 =~<3
6. m<2 = m<3
7. m<4 + m<3 = 90°
8. <3 and <4 are complementary
Please list reasons (geometry)
Answer:
<3 and <4 are complementary
Need help with this, if you can edit it and send back,, that’ll help, thank you<3
The quotient of the triangle side lengths are same as below for different triangle ( please refer attached image for better understanding)-
For ABC - 9/4 or 2.25, 9/6 or 1.5, 6/4 or 1.5
For DEF - 18/8 or 2.25, 18/12 or 1.5, 12/8 or 1.5
For GHI - 27/12 or 2.25, 27/18 or 1.5, 18/12 or 1.5
For JKL - 4.5/2 or 2.25, 4.5/3 or 1.5, 3/2 or 1.5
Quotient in mathematics, can be defined as the result of the division of a number by any divisor.
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place the numbers in order from least to greatest…PLS HELP!
Answer:
If the numbers are arranged from the least to the greatest, then it is called ascending order. In this form, the numbers are in increasing order. The first number should be lesser than the second number. If the numbers are arranged from the greatest to the least, then it is called descending order.
Absolute Value Calculator: Heron's Calculator
Coterminal Angle Calculator: Graphing Functi...
Step-by-step explanation:
Given the function f(x)=x^2+7x+6f(x)=x
2 +7x+6, determine the average rate of change of the function over the interval −4≤x≤−1.
The average rate of change of the function f( x ) = x² + 7x + 6 at the interval of −4 ≤ x ≤ −1 is 2
What is the average rate of change the function?The average rate of change the function is simply the change in y-values of the two points divided by the change in x-values of the two points.
It is expressed as;
Given the data in the question;
f( x ) = x² + 7x + 6Interval: −4 ≤ x ≤ −1 ⇒ [-4.-1]Average rate of change = ( f(-1) - f(-4) ) / ( (-1) - (-4) )
Average rate of change = ( (-1)² + 7(-1) + 6 ) - ( (-4)² + 7(-4) + 6 ) ) / ( (-1) - (-4) )
Average rate of change = ( (1 + -7 + 6 ) - ( 16 - 28 + 6 ) ) / (-1 + 4 )
Average rate of change = ( ( 0 ) - ( -6 ) ) / (-1 + 4 )
Average rate of change = ( 0 + 6 ) / ( 3 )
Average rate of change = 6 / 3
Average rate of change = 2
Therefore, the average rate of change of the function is 2.
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The diagram shows a rhombus inside a regular pentagon.
Work out the size of angle x.
The size of the angle x in the pentagon is 36 degrees.
How to find the angles in a pentagon?A regular pentagon is a polygon with five sides. The angles of a regular polygon is equal to each other.
Therefore,
the sum of angles in a regular pentagon = 540 degrees.
Each angle in a regular pentagon is 540 / 5 = 108 degrees.
The rhombus is inside the pentagon. Opposite angles in a rhombus are equal.
Therefore, the sum of interior angles of a rhombus adds up to 360 degrees
Hence,
108 + 108 + 2y = 360
where
y is the angle of the rhombus on the x variable.
Therefore,
2y = 360 - 216
2y = 144
y = 144 / 2
y = 72°
Therefore,
x = 108 - 72
x = 36 degrees
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the null and alternative hypotheses are given. determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. what parameter is being tested? 105
The hypothesis test is a Left-tailed test and the parameter being tested is known as a Population mean.
What is a null and alternative hypotheses?
A null hypothesis predicts no effect between variables while an alternative hypothesis predict an effect or relationship between variables of the study.
What is the given hypothesis test?
In the question, the given hypothesis test includes "H0: σ=110" and "H1: σ<110"
Hence, based on the test above, the hypothesis test is a Left-tailed test and the parameter being tested is known as a Population mean.
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The average U.S. home uses about 11,000 kilowatt-hours (kWh) of electricity per year. Appliances and refrigeration account for about 17% of this total. If electricity costs $0.16 per kWh in a particular area, how much would the average U.S. homeowner pay annually to run appliances and refrigeration?
First we need to find the 17% of 11,000
Combine like terms, if possible. Write the result with descending powers. -7x^4 + 4x^4 - 6x^4
Select the correct choice below and fill in the answer box to complete your choice.
A. The polynomial can be simplified. -7x^4 + 4x^4 - 6x^4 =
B. The polynomial cannot be simplified. The polynomial written in descending powers is =
The polynomial can be reduced to -9x^4
Addition of Polynomial
To solve this, we can simply add the similar polynomials or polynomials with the same power. This will help us simplify the polynomial to the lowest possible value.
[tex]-7x^4 + 4x^4 -6x^4 = -9x^4[/tex]
The polynomial given is simplified to become -9x^4
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-|4-7|+3 whats the answer to this question?
The answer to the question -|4-7|+3 is 0 .
The Absolute Value of x denoted by |x| is the non negative value of , without regarding its sign .
For example the absolute value of -3 will be |-3| = 3 .
and absolute value of |-2| = 2 .
In the question ,
it is given that
the question is -|4-7|+3 .
and we have to find the answer of -|4-7|+3 .
let the answer be "y"
So , y = -|4-7|+3
= -|-3| + 3
On further simplification ,
we get ,
= -(3) + 3 because |-3| = 3
= -3 +3
= 0
Therefore , The answer to -|4-7|+3 is 0 .
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Find the value of x to the nearest tenth.
Milly and Lotte are knitting scarves. For every 6 cm that Milly knits, Lotte knits 11 cm. If Milly knits a scarf that is 1.2 m long, how long will Lotte's scarf be in metres?
If Milly knits a scarf that is 1.2 m long then Lotte's scarf be 2.20 in metres.
We will use unitary method to solve this problem.
We know, Milly and Lotte are knitting scarves.
For every 6 cm that Milly knits, Lotte knits 11 cm. This can also be written as,
6 cm Milly knits ----------------> 11 cm Lotte knits
1 cm Milly knits ----------------> (11/6 ) cm Lotte knits
We know, 1m = 100cm. So, we can write
120 cm Milly knits ----------------> ( 11/6 ) × 120 cm Lotte knits
120 cm Milly knits ----------------> 220 cm Lotte knits
120 cm Milly knits ----------------> 2.20 m Lotte knits
Thus, we can conclude that if Milly knits a scarf that is 1.2 m long then Lotte knits 2.20 metres scarf .
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4(a-c)+2(a-b)
x(x-y)+y(y-x)
Answer:
hi how are you . i cant find the answer youre looking for
Answer:
1) 6 ( a - b )
2) x² - 2xy + y²
Step-by-step explanation:
1) 4 ( a - c ) + 2 ( a - b )
First, solve the brackets.
4a - 4c + 2a - 2b
Combine like terms.
6a - 6b
Take the common factor out.
6 ( a - b )
2) x ( x - y ) + y ( y - x )
First, solve the brackets
x² - xy + y² - xy
Combine like terms.
x² - 2xy + y²