The angle between the two extreme vectors of Sofia bats is 74.60 degrees.
In this question,
The angle between two vectors will be deferred by a single point, which is called as the shortest angle at which we have to turn around one of the vectors to the position of co-directional with another vector.
The extreme vectors of Sofia bats are [tex]\vec u = < -8, 12 >[/tex] and [tex]\vec v = < -8, 12 >[/tex]
The angle between the vectors is
[tex]\theta = cos^{-1} \frac{\vec u.\vec v}{||\vec u|| ||\vec v||}[/tex]
The dot product is calculated as
[tex]\vec u. \vec v = (-8)(13)+(12)(15)[/tex]
⇒ [tex]-104+180[/tex]
⇒ 76
The magnitude can be calculated as
[tex]||\vec u|| = \sqrt{(-8 )^{2} +(12)^{2} }[/tex]
⇒ [tex]\sqrt{64+144}[/tex]
⇒ [tex]\sqrt{208}[/tex]
[tex]||\vec v|| = \sqrt{(13 )^{2} +(15)^{2} }[/tex]
⇒ [tex]\sqrt{169+225}[/tex]
⇒ [tex]\sqrt{394}[/tex]
Thus the angle between the vectors is
[tex]\theta = cos^{-1} \frac{76}{(\sqrt{208} )(\sqrt{394} )}[/tex]
⇒ [tex]\theta = cos^{-1} \frac{76}{\sqrt{81952} }[/tex]
⇒ [tex]\theta = cos^{-1} \frac{76}{286.27 }[/tex]
⇒ [tex]\theta = cos^{-1} (0.2654)[/tex]
⇒ [tex]\theta=74.60[/tex]
Hence we can conclude that the angle between the two extreme vectors of Sofia bats is 74.60 degrees.
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Complete the equation.
2 x 4 =
x 2
2x4=8
8x2=16
the answer is 16
Joy is training for a triathlon. she runs a distance of 2x miles, cycles a distance of (x2 7) miles, and swims a distance of (x − 2) miles. which simplified expression is equivalent to the total distance, in miles, joy covers? x2 3x 5 x2 3x 9 3x2 5 3x2 9
The simplified expression that is equivalent to the total distance, in miles, Joy covers is (A) x² + 3x + 5 miles.
What is an expression?An expression or mathematical expression is a finite combination of symbols that is well-formed according to context-dependent norms.To find the simplified expression:
Given -
Distance cycled = x² + 7 milesDistance ran = 2x milesDistance swam = x - 2 milesThus,
Total distance she covers = x² + 7 + 2x + x - 2Total distance = x² + 3x + 5 milesTherefore, the simplified expression that is equivalent to the total distance, in miles, Joy covers is (A) x² + 3x + 5 miles.
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The complete question is given below:
Joy is training for a triathlon. She runs a distance of 2x miles, cycles a distance of (x2 + 7) miles, and swims a distance of (x - 2) miles. Which simplified expression is equivalent to the total distance, in miles, Joy covers?
(A) x2 + 3x + 5
(B) x2 + 3x + 9
(C) 3x2 + 5
(D) 3x2 + 9
Answer:
The person on top is right.
ITS A
Step-by-step explanation:
Classify the expression: 5x 2. linear expression quadratic expression cubic expression quartic expression
The given expression is a (A) linear expression.
What are linear expressions?A linear expression is an algebraic expression in which each term is a constant or a variable raised to the first power. To put it another way, none of the exponents may be greater than 1. x2 is a variable raised to the second power, whereas x is a variable raised to the first power. A constant is represented by the number 5.Reduce the equation as much as feasible to the form y = mx + b. Examine your equation for exponents. It is nonlinear if it has exponents. Your equation is linear if it contains no exponents.2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, 3x - y + z = 3 are some instances of linear equations.Therefore, the given expression is a (A) linear expression.
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The correct question is given below:
Classify the expression: 5x 2.
(A) linear expression
(B) quadratic expression
(C) cubic expression
(D0 quartic expression
Tickets to the movies cost $24 for 1 adult. The price of 1 child was 2/3 of that price. How much did a family with 2 adults and 2 children have to pay?
Solve the following system using the algebraic method of substitution. Verify your solution.
x + 2y = -5
3x - y = -1
Solve the following linear system using the algebraic method of elimination. Verify your solution.
x + 2y = 2
3x + 5y = 4
I've done it on the attached pages.
I hope this helps you...
Find the general solution of the given system of odes. { dx/dt =2x 2y,dy/dt =x 3y}
The general solution of the given system of odes is
m=1 ; m=4 (real roots)
In arithmetic, a system of odes equations is a finite set of differential equations. Any such device may be either linear or non-linear. Also, such a machine can be both a machine of normal differential equations or a system of partial differential equations.
the compatibility conditions of an overdetermined system of odes equations may be succinctly stated in terms of differential forms (i.e., a shape to be specific, it needs to be closed). See integrability situations for differential systems for more.
It is an elaborately based poem praising or glorifying an event or character, describing nature intellectually as well as emotionally. A traditional ode is dependent on three essential parts: the strophe, the antistrophe, and the epode. Distinct forms together with the homostrophic ode and the abnormal ode also enter.
dx/dt = 2x+2y = x^1 = 2x+2y 1
dy/dt = x+3y = y^1 = x+ 3y 2
differentiating 1 with respect to 't'
x^11 = 2x^1+ 2y^1
y^1 = x+3y
x^11 = 2x^1= 2(x+3y)
x^11 = 2x^1+ 2x+ 6y
x^11 = 2x^1+ 2x+ 6(x^1-2x/2)
x^11 = 2x^1+ 2x+ 3x^1- 6x
x^11 = 5x^1 - 4x
x^11 -5x^1 - 4x
x^11 - 5x^1 -4x =0
Auxillary equation is m^5- 5m+4=0
m^2 - m - 4m + 4 = 0
m(m-1) -4 (m-1) =0
(m-1) (m-4) = 0
m=1 ; m=4 (real roots)
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A rectangle is 5 inches long and 2x inches wide. The value of the perimeter
(in inches) is equal to the value of the area (in square inches). Find x.
Answer:
Area=length× berngth
A=5×2x
A=10x square
30 POINTS FOR THIS QUESTION
Answer:
Perimeter is 4a - 10
Area is a^2 - 5a
Step-by-step explanation:
Two sides of the rectangle are "a" and two sides of the rectangle are "a-5" add all four sides and you get a+a+a-5+a-5 Combine the like terms and you get 4a - 10.
The area is when you multiple the two sides together
A = lw
A - a(a-5) = a^2 - 5a
What is the least positive integers which , when subtracted 7300 would make a result a perfect square?
75 is the least positive integers which , when subtracted 7300 would make a result a perfect square
What is the least positive value?So normally the least positive integer of all the numbers is the number 1 but when you talk about least positive integer, often times you are talking about the special function called the ceiling function
Least positive integer:
The smallest of the numbers in the set {1, 2, 3, …} is 1.
So, the number 1 is the smallest positive integer.
7300
If we Take Square root of 7300 we have to subtract 75 from 7300 to get a perfect square.
7300-75=7225
(85)^2=7225
75 to be subtracted
√7300 ≥ 85
Perfect Square = 85² = 7225 or (7300-7225 = 75)
75 is the least positive integers which , when subtracted 7300 would make a result a perfect square
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Find the values of x and y.
Write answers in simplest radical form.
x=______ y=_____
Using the Geometric mean theorem and the Pythagorean theorem:
x = 3√3, and y = 6.
What is the Right Triangle Altitude Theorem/Geometric Mean Theorem?The Geometric mean theorem or the right triangle altitude theorem states that the geometric mean of the the two segments equals he length of the altitude of a right triangle.
The geometric mean theorem is expressed by the equation, h = √(ab), where:
a is the length of one segmentb is the length of the other segmenth is the length of the altitude of the right triangle.Given the following:
h = x
a = 9
b = 3
x = √(9 × 3)
x = 3√3
Find y using the Pythagorean theorem
Based on the Pythagorean theorem, we would have the following:
y = √(x² + 3²)
y = √((3√3)² + 3²)
y = √(27 + 9)
y = √(36)
y = 6
Thus, in the simplest radical form, the value of x = 3√3, and y = 6.
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How many species go extinct in an average day? a. 3 b. 72 c. 1000 d. 20000 please select the best answer from the choices provided a b c d
It has been estimated that every year 20,000 species are going extinct and 72 species are going extinct on an average day.
What are species?
Species exist as organisms that contain similar characteristics and exist capable of interbreeding. A common example is human beings.
It has been observed that over the years, species have been going extinct due to human reasons such as excessive hunting, environmental factors such as natural disasters, global warming, and also due to changes in their genetic makeup or reduced reproduction.
It has been estimated that every year 20,000 species are going extinct and 72 species are going extinct on an average day.
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Answer: Edge 2022, B. 72
Find the value of the trigonometric ratio. Make sure to simplify the fraction if needed.
generally, tanA=opposite/adjacent
answer:tanC=36/15=12/5
Answer:
[tex]Tan \space\ \theta =\frac{\boxed{12}}{\boxed5}}[/tex]
Step-by-step explanation:
The tangent (Tan) of an angle is the ratio of the opposite side and the adjacent side, so that:
[tex]\boxed{Tan\space\ \theta = \frac{opposite}{adjacent}}[/tex].
In this case, with respect to angle C:
• opposite = AB = 36 units
• adjacent = CB = 15 units.
Substituting the values into the equation:
[tex]Tan \space\ C = \frac{36}{15}[/tex]
= [tex]\bf \frac{12}{5}[/tex] (simplified)
Minnie bought 6 postcards during 3 days of vacation. After 8 days of vacation, how many total postcards will Minnie have bought?
A. 12
Answer:
16
Step-by-step explanation:
6/3 = 2 postcards per day
2x8 = 16 postcards
A function is shown: f(x) = 36x² - 1.
Choose the equivalent function that best shows the x-intercepts on the graph
Based on the given function, the equivalent function that best shows the x-intercepts on the graph is f(x) = (6x - 1)(6x + 1)
What are equivalent functions?Equivalent functions are different functions that have equal values when evaluated and compared
How to determin the equivalent function that best shows the x-intercepts on the graph?
The function is given as:
f(x) = 36x^2 - 1
Express 1 as 1^2
f(x) = 36x^2 - 1^2
Express 36x^2 as (6x)^2
f(x) = (6x)^2 - 1^2
Apply the difference of two squares.
This is represented as:
(a + b)(a - b) = a^2 - b^2
So, we have the following equation
f(x) = (6x - 1)(6x + 1)
Based on the given function, the equivalent function that best shows the x-intercepts on the graph is f(x) = (6x - 1)(6x + 1)
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Rajani is making smoothies. Each smoothie uses 3/5 cup of yogurt. How much yogurt
does she need to make 13 smoothies?
Answer:
Rajani needs 7.8 (39/5) cups of yogurt to make 13 smoothies.
Step-by-step explanation:
3/5 = 0.6
The amount of cups of yogurt needed to make 13 smoothies = 13 x 0.6
This equals to 7.8 cups or 39/5 cups of yogurt to make 13 smoothies.
Hope this helps!
Which graph shows the solution to this system of inequalities y < - 1/3 x + 1
Answer:
See attached image.
Step-by-step explanation:
The image does not show the graph options. The attachment sjhhows the graph of y < - 1/3 x + 1.
A pygmy hippo and a regular hippo were recently born. The pygmy hippo had a mass of 5 1/2 kg at birth. The regular hippo had a mass of 24 1/2 kg at birth. Complete the comparison. At birth, the regular hippo massed ? times as much as the pygmy hippo.
The mass of the regular hippo at birth to that of the pygmy hippo is 49/11
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
The pygmy hippo had a mass of 5 1/2 kg at birth = 5.5 kg.
The regular hippo had a mass of 24 1/2 kg at birth = 24.5 kg
Hence:
Ratio of regular hippo to pygmy hippo = 24.5 / 5.5 = 49/11
The mass of the regular hippo at birth to that of the pygmy hippo is 49/11
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Answer:
49/11 or 4 5/11
Step-by-step explanation:
just did it on khan Academy.
help me plss its ttm
For the first representation, the equation is : y = 3x-5.
For the second representation, the equation is : y = -12x+2.
For the third representation, the equation is : y = 5/4x-5.
For the fourth representation, the equation is: y = -6x+3.
Analyze the representations given in the question, in order to find its corresponding equation.
According to the question,
For the first representation, y=1 when x=2, y=-2 when x=1 and y=4 when x=3. On substituting these values of x and y in the given equations, we get that y = 3x-5.
Similarly, for the second representation, we get, y = -12x+2.
For the third representation, we get, y = 5/4x-5.
For the fourth representation, we get, y = -6x+3.
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A spaceship is traveling at a steady rate. The table shows the distance the spaceship travels in a given period of time. Find the distance the spaceship travels in 4 minutes.
Ty.
The distance of the spaceship in discuss as in the task content given can be evaluated as; 800miles.
What is the distance the spaceship travels in 4 minutes?The distance travelled by the spaceship in discuss can be evaluated by means of the slope of the linear relationship as follows;
Hence it follows from ratios that by observation, the linear relationship has a slope of 200mi/min.
Consequently, we can evaluate the distance travelled after 4 minutes as;
Distance = 200 × 4 = 800mi.
Ultimately, the distance travelled per minute by the spaceship is; 800mi.
Remarks:
600 miles
520 miles
800 miles
1,080 miles
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At a walk-in interview, 12% of candidates can be selected, and 28% of candidates can be put on hold for the next hiring date. if 75 candidates are interviewed, about how many are expected to be rejected?
45 candidates are expected to be rejected.
What is a percentage in math?
percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part. 100 percent represents the entirety and 200 percent specifies twice the given quantity.Here, we want to calculate the number of candidates to be rejected
The number of candidates to be rejected can be calculated from;
100% - (28% + 12%) = 60%
So 60% of the 75 interviewed are to be rejected
Thus, we have
60/100 * 75
= 45
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The motion of an object was recorded by measuring the velocity of the object in meters per second at various times, as shown in the table. The scatterplot below was graphed from the data in the table, where t represents the time, and v represents the velocity. Based on the scatterplot, which equation BEST represents the relationship between velocity and time?
Based on the scatterplot, the equation that BEST represents the relationship between velocity and time is y = 2.2x + 6
How to determine the line of best fit?The line of best fit is the line that best represents the relationship between 2 variables. The equation of a line in slope-intercept form is expressed as:
y = mx + b
where
m is the slope
b is the intercept
Using the coordinate points on the plane (0, 6) and (10, 28)
Determine the slope
Slope = 28-6/10-0
Slope = 22/10
Slope = 2.2
Determine the y-intercept
6 = 2.2(0) + b
b = 6
Determine the equation of aline of best fit.
y = 2.2x + 6
Hence based on the scatterplot, the equation that BEST represents the relationship between velocity and time is y = 2.2x + 6
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Solve the proportion.
A. 12
B. 2
C. 8
D. 16
D. 16
Cross multiply, to cancel the denominator; so if you multiple by 6 on one side, to cancel the division of 6 - you must also multiply the other side by 6 & vice versa.
You get:
8(x-4) = 6x
Expand bracket to get:
8x - 32
Now solve for x :
8x - 32 = 6x
- 8x
- 32. = - 2x
÷ - 2
16 = x
Or
8x - 32 = 6x
+ 32
8x. = 6x + 32
- 6x
2x. = 32
÷2
x =16
Check:
16 - 4 = 12, then ÷ 6 is 2
16/8 = 2
Hope this helps!
x-1/x-2+x+3/x-4=2/(x-2).(4-x)
The given equation x-1/x-2+x+3/x-4=2/(x-2).(4-x) is correct. the answer is proved.
According to the statement
we have given that the equation and we have to prove that the given answer is a correct answer for those equivalent equation.
So, The given expression are:
[tex]\frac{x-1}{x-2} +\frac{x+3}{x-4} = \frac{2}{(x-2).(4-x)}[/tex]
And we have to prove the answer.
So, For this
[tex]\frac{x-1}{x-2} +\frac{x+3}{x-4}[/tex]
[tex]\frac{({x-1}) ({x-4}) +({x+3})({x-2})} {(x-2) (x-4)}[/tex]
Then the equation become
[tex]\frac{x^{2} -4x -x +4 + x^{2} -2x + 3x -6 }{(x-2) (x-4)}[/tex]
Now solve it then
[tex]2x^{2} - 4x -2 / (x-2) (x-4)[/tex]
Now take 2 common from answer then equation become
[tex]\frac{x-1}{x-2} +\frac{x+3}{x-4} = \frac{2}{(x-2).(4-x)}[/tex]
Hence proved.
So, The given equation x-1/x-2+x+3/x-4=2/(x-2).(4-x) is correct. the answer is proved.
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y = 3x + 15
3x + 3y = 9
Answer:
[tex]\Large\boxed{x=-3}[/tex][tex]\Large\boxed{y=6}[/tex]
Step-by-step explanation:
Given the system of equations
[tex]1)~y=3x+15[/tex]
[tex]2)~3x+3y=9[/tex]
Divide 3 on both sides of the 2) equation
[tex]3x+3y=9[/tex]
[tex]3x\div3+3y\div3=9\div3[/tex]
[tex]x+y=3[/tex]
Current system
[tex]1)~y=3x+15[/tex]
[tex]2)~x+y=3[/tex]
Substitute 1) equation into the 2) equation
[tex]x+(3x+15)=3[/tex]
Combine like terms
[tex]x+3x+15=3[/tex]
[tex]4x+15=3[/tex]
Subtract 15 on both sides
[tex]4x+15-15=3-15[/tex]
[tex]4x=-12[/tex]
Divide 4 on both sides
[tex]4x\div4=-12\div4[/tex]
[tex]\Large\boxed{x=-3}[/tex]
Substitute the x value into one of the equations to find the y value
[tex]y=3x+15[/tex]
[tex]y=3(-3)+15[/tex]
[tex]y=-9+15[/tex]
[tex]\Large\boxed{y=6}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Use the graph to write the explicit rule of the arithmetic sequence.
Question 19 options:
A)
ƒ(n) = 9 + 2(n – 1)
B)
ƒ(n) = 5 + 3(n – 1)
C)
ƒ(n) = –3 + 2(n – 1)
D)
ƒ(n) = 3 + 2(n – 1)
Answer: D
Step-by-step explanation:
The first term is 3 and the common difference is 2.
Substituting into the explicit formula for an arithmetic sequence gives D as the correct answer.
please help!
Amara needs 90 kilograms of meat to feed her 4 pet dragons each day. Each pet dragon eats the same amount of meat. How many kilograms of meat does Amara need to feed 2 pet dragons each day?
45 kilograms of meat is required to feed 2 pet dragons each day.
Amara needs 45 kilograms of meat to feed 2 pet dragons each day.
What is unitary method ?Unitary method is a mathematical way of deriving a single unit then obtaining the required units by multiplying it with the single unit.
According to the given question Amara needs 90 kilograms of meat to feed her 4 pet dragons each day.
Also given that each pet dragon eats the same amount of meat.
∴ 1 pet dragon eat 90/4 kilograms of meat which is
= 22.5 kilograms of meat.
So, Amara need (22.5×2) = 45 kilograms of meat to feet 2 pet dragons.
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HELP WITH THE BONUS PLEASE!!!!
Based on the stock price and its growth rate, the function that models the situation is 48 (1 + 8%) ^ n. The price of the stock 6 years from now is $76.17.
What is the best function for the stock's growth?The value of a stock in future can be calculated using several types of formulas that take into account the various characteristics of the stock.
For this stock, the value of the stock at any given year is:
= Current price of stock x ( 1 + growth rate) ^ number of years from now
Assuming the number of years is n, the function becomes:
= 48 x ( 1 + 8%) ^n
In 6 years, the price will be:
= 48 x ( 1 + 8%) ⁶
= $76.17
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Solve the system of equations.
y equals x plus 8
y equals 3 x plus 2
Answer:
The answer is (3,11) or x = 3, y = 11
Step-by-step explanation:
:)
Answer:
(3, 11 )
Step-by-step explanation:
y = x + 8 → (1)
y = 3x + 2 → (2)
substitute y = 3x + 2 into (1)
3x + 2 = x + 8 ( subtract x from both sides )
2x + 2 = 8 ( subtract 2 from both sides )
2x = 6 ( divide both sides by 2 )
x = 3
substitute x = 3 into either of the 2 equations and solve for y
substituting into (1)
y = 3 + 8 = 11
solution is (3, 11 )
Which of the graphs below shows the solution set for -36 ≤ 2x + 4(x-3)?
A.
B.
-10-9-8-7-6-5-4-3-2-1 0
-10-9-8-7-6-5-4-3-2-1 0
C. A++
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
-10-9-8-7-6-5-4-3-2-1 0
D. +++
-10-9-8-7-6-5-4-3-2-1 01
Considering the given inequality, the solution is given by graph D.
What is the solution to the inequality?The inequality is given by:
-36 ≤ 2x + 4(x-3)
Applying the operations:
-36 ≤ 2x + 4x - 12
-24 ≤ 6x
6x >= -24
x >= -24/6
x >= -4.
Hence option D is correct.
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Instructions: State what additional information is required in order
to know that the triangles in the image below are congruent for the
reason given.
Reason: AAS Postulate
∠KJI≅ZJX is the additional information.
What are the AAS congruency criteria?
⇒ AAS stands for Angle-Angle-Side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent
We have been given that
⇒ kJ=ZJ
⇒∠KJI=∠ZJX (vertically opposite angle)
And we require one more angle which can't be on the non-included side
so we have only one angle that can satisfy this
⇒∠JIK=∠JXZ
⇒ Now we can say that △KJI ≅ △ZJX is congruent with AAS congruency criteria
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