By solving the system of equations, we can see that the solutions are:
(A, B) = (4, 9)
(C, D) = (1, -6).
How to solve the system of equations?Here we have the following system of equations:
x^2 - y = 7
y - 5x = -11
If we isolate the variable y in both equations, we get:
y = x^2 - 7
y = -11 + 5x
Now we can equate these two to get:
x^2 - 7 = -11 + 5x
now we have a quadratic equation, this can be rewritten as:
x^2 - 7 + 11 - 5x = 0
x^2 - 5x + 4 = 0
Using the quadratic formula, we will see that the solutions are:
[tex]x = \frac{5 \pm \sqrt{(-5)^2 - 4*1*(4)} }{2*1}[/tex]
Solving that we get:
[tex]x = \frac{5 \pm \sqrt{(9} }{2} \\\\x = \frac{5 \pm 3}{2}[/tex]
So the two solutions for x are:
x = (5 + 3)/2 = 4
x = (5 - 3)/2 = 1
Evaluating the second equation in these x-values we get:
y = -11 + 5*4 = -11 + 20 = 9
y = -11 + 5*1 = -6
Then we have the coordinate pairs: (4, 9) (on the first quadrant) and (1, -6) on the fourth quadrant.
Learn more about systems of equations:
https://brainly.com/question/13729904
#SPJ1
If f(x) = kx^3+ x^2 − kx + 2, find a number k such that the graph of f contains the point (2, 12).
Answer:
k = 1
Step-by-step explanation:
since the graph contains the point (2, 12 ) then the coordinates of the point make the equation true.
substitute x = 2 and f(x) = 12 into the equation and solve for k
12 = k(2)³ + 2² - k(2) + 2 , that is
12 = 8k + 4 - 2k + 2
12 = 6k + 6 ( subtract 6 from both sides )
6 = 6k ( divide both sides by 6 )
1 = k
The population of a city increases by 3.1% per year. If this year's population is
290,000, what will next year's population be, to the nearest individual?
Answer:
the next year population is 122,689
Step-by-step explanation:
The computation of the next year population is as follows:
= This year population × increase percentage
= 119,000 × (1 + 0.031)
= 119,000 × 1.031
= 122,689
Hence, the next year population is 122,689
The above formula is applied so that the correct value of the population could come
and the same is relevant
F(x)=3x^2-4x+8G(x)=2x-5 use the functions above to find the value of g(f(-2)) I don’t understand how to do this
Given,
[tex]f(x)=3x^2-4x+8,\text{g(x)=2x-5}[/tex]To find g(f(-2)). we first find the value of f(-2).
The value of f(-2) is,
[tex]\begin{gathered} f(-2)=3(-2)^2-4(-2)+8 \\ \text{ =3(4)+8+8} \\ \text{ =12+8+8} \\ \text{ =28} \end{gathered}[/tex]So now to find the value of g(f(-2)),
[tex]g(f(-2))=g(28)[/tex]So the value of g(28) is,
[tex]\begin{gathered} g(28)=2(28)-5 \\ \text{ =56-5} \\ \text{ =51} \end{gathered}[/tex]So the value of g(f(-2)) is 51.
Given mn, find the value of x.
Answer:
(2x+5)° (8x+5)°
Submit Answer
m
00
Step-by-step explanation:
2x+(-8x) +5-5
-5=0. u Wii collect like terms and if u do that that's the answer if am wrong let me know
Determine which answer in the solution set will make the equation true.
2p + 9 = 4p − 13
S: {−11, 0, 11, 22}
Answer:
11
Step-by-step explanation:
If you input the number and then solve, you should get that #=#
2(11)+9=4(11)-13
22+9=44-13
31=31
Answer: 11
Step-by-step explanation: 2(11)+9=4(11)-13, 22+9=44-13, 31=31
Given A-
2 2
1 3
what is A-¹?
The inverse of matrix A = [tex]\left[\begin{array}{cc}2&2&1&3\\\end{array}\right][/tex] is [tex]A^{-1} = \frac{1}{4}[/tex] [tex]\left|\begin{array}{cc}3&-2&-1&2\\\end{array}\right|[/tex]
The given matrix is A = [tex]\left[\begin{array}{cc}2&2&1&3\\\end{array}\right][/tex]
The inverse of a matrix is given by
[tex]A^{-1} = \frac{1}{|A|} adjA[/tex] ...(1)
Now, determinant of matrix A is
|A| = [tex]\left|\begin{array}{cc}2&2&1&3\\\end{array}\right|[/tex]
= (3)(2) - (2)(1)
= 6 - 2
= 4
Now, adjoint A will be
[tex]A_{11}[/tex] = 3
[tex]A_{12}[/tex] = -1
[tex]A_{21}[/tex] = -2
[tex]A_{22}[/tex] = 2
AdjA = [tex]\left|\begin{array}{cc}3&-2&-1&2\\\end{array}\right|[/tex]
Now, substituting the values of |A| and AdjA in equation (1), we get
[tex]A^{-1} = \frac{1}{4}[/tex] [tex]\left|\begin{array}{cc}3&-2&-1&2\\\end{array}\right|[/tex]
Therefore, [tex]A^{-1} = \frac{1}{4}[/tex] [tex]\left|\begin{array}{cc}3&-2&-1&2\\\end{array}\right|[/tex]
Know more about Inverse of Matrix: -https://brainly.com/question/12442362
#SPJ9
PLEASE HURRYYYY
The segment contains points S(a, b) and T(c, d). Which formula should be used to find the midpoint of the segment?
A car journey is m
miles long.
One kilometre is equivalent to x
miles.
The car uses one litre of fuel to travel a distance of f
kilometres.
Fuel for the car costs p
pence per litre.
Which of the following expressions gives the cost of fuel for this journey, in pounds?
The expression gives the cost of fuel for this journey is option H mp / 100 fx
Given,
The total distance of a car journey = m miles
One kilometer = x miles
The amount of petrol needed to travel a distance of f kilometers = 1 liter
Cost of the fuel = p pence/ liter
Now we have to find the expression which gives the cost of fuel for this journey in pounds.
1 pound = 100 pence
So,
The distance in miles we can travel with 1 liter of petrol = fx
Total liter of petrol needed for the journey = m/fx
Total cost of petrol for the journey = mp / fx100
That is,
The expression gives the cost of fuel for this journey is option H mp / 100 fx
Learn more about cost of fuel here:
https://brainly.com/question/22104149
#SPJ1
The question is incomplete. Completed question is given below:
A car journey is m miles long.
One kilometre is equivalent to x miles.
The car uses one litre of fuel to travel a distance of f kilometres.
Fuel for the car costs p pence per litre.
Which of the following expressions gives the cost of fuel for this journey, in pounds?
(There are 100 pence in one pound.)
A. 100fmpx
B. 100fmp/x
C. 100mpx/f
D. 100mp/fx
E. fmpx/100
F. fmp/100x
G. mpx/100f
H. mp/100fx
The mean birth weights of infants born at an area hospital in the month of Aprill is 128 oz. with a standard deviation of 10.2 oz. Given an interpretation of
this situation.
The distance between each infant's weight when they were bonded in April is the proper interpretation of the standard deviation in this situation. And the average weight was 10.20 pounds.
What is standard deviation ?The variance's positive square root is the standard deviation. One of the foundational strategies in statistical analysis is standard deviation. The term "standard deviation," often shortened as "SD," tells us how far a value deviates from the mean value. It is represented by the symbol "."
Given that : The mean birth weights of infants born at an area hospital in the month of April is 128 oz. with a standard deviation of 10.2 oz.
So let's look at this and see what the correct interpretation of a standard deviation is, which is the distance between each person's actual way of being born and a braille and the main way it was, which is typically about 10 points two oh. From this, we can deduce what the question Act is. The distance between each infant's weight when they were bonded in April is the proper interpretation of the standard deviation in this situation. And the average weight was 10.20 pounds.
To learn more about standard deviation visit :
brainly.com/question/13905583
#SPJ13
John's commute to work is 20kmhr while Sheri's commute is 500mmin.
Who has the fastest commute to work in mihrif 1.61km=1mi?
By 6.2 miles per hour, Sheri commutes more quickly.
We are given that,
John travels to work = 20km/hr
Sheri travels to work = 500m/min converting this into km/hr we get ,
1.61km/hr or 1 mile
John travels to work at the following rate:
[tex]\frac{20 km}{1 hr} * \frac{1 mile}{1.61km} = 12.42 miles/hr[/tex]
Sheri travels work at the following rate:
[tex]\frac{500m}{1min} *\frac{1km}{1000 m}*\frac{1mile}{1.61km}*\frac{60min}{1hr}=18.63 miles/hr[/tex]
Computing the difference between the two,
18.63 miles/hr - 12.42 miles/hr = 6.21 miles/ hr ≈ 6.2 miles/ hr
thus, by 6.2 miles per hour, Sheri commutes more quickly.
What are conversions in maths?
An amount that is multiplied or divided between one set of units and another is known as a conversion factor. In the event that a conversion is necessary, it must be carried out with the proper conversion factor to produce an equivalent value. For instance, when translating between inches and feet, 12 inches equals one foot.
to learn more about conversions visit:
https://brainly.com/question/24376098
#SPJ9
find the measure of each angle only need numbers 22, 24, and 26
22) 68
24) 90
26) 158
Jesse recorded a temperature of 75 degrees Fahrenheit this morning for science class. The temperature increased by 4 1/2 degrees Fahrenheit in the afternoon, before decreasing 2.6 degrees Fahrenheit in the evening. What was the temperature in the evening?
The temperature in the evening is 79.5 degrees Fahrenheit.
What is basic algebra?The area of mathematics known as algebra aids in the representation of issues or circumstances into mathematical statements. Creating a meaningful mathematical expression, it requires variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in all areas of mathematics, including coordinate geometry, calculus, and trigonometry. 2x + 4 = 8 is a basic algebraic expression.When operations like addition, subtraction, multiplication, division, etc. are performed on variables and constants, we obtain algebraic expressions as the mathematical statement.
Jesse recorded a temperature in the morning of 75 degrees Fahrenheit
The temperature increased by [tex]4\frac{1}{2}[/tex] degrees Fahrenheit in the afternoon
75 + [tex]4\frac{1}{2}[/tex] =[tex]\frac{159}{2}[/tex]
=79.5 degrees Fahrenheit
Before decreasing by 2.6 degrees Fahrenheit in the evening. The temperature in the evening is 79.5 degrees Fahrenheit.
To learn more about basic algebra visit:
brainly.com/question/15167098
#SPJ10
(X) 1.10.PS-7
Simplify the expression. Write the answer in scientific notation.
(7×10¯²) (9×10¯²)
(7×10¯²) (9×10¯²) = ¯
(Simplify your answer. Use scientific notation. Use the multiplication symbol in the r
Enter you
The scientific notation is 6.3 × [tex]10^{-3}[/tex]
The expression is ( 7 ×[tex]10^{-2}[/tex] )( 9 × [tex]10^{-2}[/tex])
Calculate the product or quotient
=63 × ([tex]10^{-2}[/tex] ×[tex]10^{-2}[/tex])
Simplify using the exponent rule with the same base [tex]a^{n} . a^{m}[/tex] = [tex]a^{n + m}[/tex]
=63 × [tex]10^{-2-2}[/tex]
=63 ×[tex]10^{-4}[/tex]
= 6.3 × [tex]10^{-3}[/tex]
Therefore the scientific notation is 6.3 ×[tex]10^{-3}[/tex].
To know more about the expression refer to the link given below:
https://brainly.com/question/13961297
#SPJ1
If f(x) = (x-4)(x+3), determine the x-intercepts of each function.
a) y=f(x)
b) y=-2f(x)
c) y=f(-1/2x)
d) y=f(-(x+1))
a) The x-intercepts of y=f(x) is (-3,0) (4,0)
b) The x-intercepts of y=-2f(x) is (-3,0) (4,0)
c) The x-intercepts of y=f(-1/2x) is (-1/8,0) (1/6,0)
d) The x-intercepts of y=f(-(x+1)) is (-5,0) (2,0)
What is x-intercept?A line's x-intercept is the distance in x coordinates from the line's intersection with the x-axis at its origin. A location on the graph where y is 0 is known as the x-intercept. The x-intercept of a line that is perpendicular to the y-axis is undefined.
Here to determine the x-intercept put y=0,
Given f(x)=(x-4) (x+3)
a) y=(x-4) (x+3)
Replacing y by 0 we get,
(x-4) (x+3) =0
x=-3, 4
Therefore, x-intercepts of y=f(x) is (-3,0) (4,0)
b) y = -2(x-4) (x+3)
Replacing y by 0 we get,
-2(x-4) (x+3) =0
x=-3, 4
Therefore, x-intercepts of y=-2f(x) is (-3,0) (4,0)
c) y= (-[tex]\frac{1}{2x}[/tex]-4) (-[tex]\frac{1}{2x}[/tex]+3)
Replacing y by 0 we get,
(-[tex]\frac{1}{2x}[/tex]-4) (-[tex]\frac{1}{2x}[/tex]+3) =0
By solving the above equation
(-[tex]\frac{1}{2x}[/tex]-4) =0 and (-[tex]\frac{1}{2x}[/tex]+3) =0
-1/2x=4 and -1/2x=-3
x=-1/8 and x=1/6
Therefore, x-intercepts of y=f(-1/2x) is (-1/8,0) (1/6,0)
d) y=(-(x+1)-4) (-(x+1) +3)
Replacing y by 0 we get,
(-(x+1)-4) (-(x+1) +3) =0
By solving the above equation
(-(x+1)-4) =0 and (-(x+1) +3) =0
-(x+1) =4 and -(x+1) =-3
x=-5, 2
Therefore, x-intercepts of y=f(-(x+1)) is (-5,0) (2,0)
To know more about x-intercepts, visit:
https://brainly.com/question/14180189
#SPJ13
Would the image be categorized as a function or as a relation? Use at least one sentence to explain your answer.
Answer:
This is a relation, not function.Step-by-step explanation:
The attached graph is NOT a function, since it doesn't pass the vertical line test.
If a vertical line cuts the graph more than once, then this relation is not a function.
all the students in an algebra class took a 100-point test. five students scored 100, each student scored at least 60, and the mean score was 76. what is the smallest possible number of students in the class?
The smallest possible number of students in the algebra class is 13.
What is meant by the word inequality?Inequalities define the connection between two non-equal values. Inequality means being unequal. If two values really aren't equal, we use the "not equal symbol (≠)".Let n≥5 be the number of students.
The sum of their scores must be at least 5×100 + (n - 5).
Simultaneously, we must achieve the mean 76, which is equivalent to achieving the mean sum 76n.
As a result, we have a sufficient precondition on n: we should have 5×100 + (n - 5) ≤ 76n.
This can be reduced to 200 ≤ 16n. This is true for the smallest integer n = 13.
To complete our solution, we must now determine how 13 students might have scored just on test.
We have 13×76 = 988 points to distribute to them. Because five 100s equal 500, we must distribute the remaining 488 points as among remaining eight students.
This can be accomplished, for example, by awarding each of them 61 points.
Thus, the smallest possible number of students in the class is 13.
To know more about the inequality, here
https://brainly.com/question/25799000
#SPJ4
Evaluate the quantity of x cubed minus 2x squared plus 3x minus 7 end quantity divided by the quantity of x minus 1 end quantity period. x squared minus x plus 2 minus 5 divided by the quantity x minus 1 end quantity x squared minus 2x plus 2 minus 9 divided by the quantity x minus 1 end quantity x squared minus x plus 4 minus 9 divided by the quantity x minus 1 end quantity x cubed minus 2x plus 2 minus 5 divided by the quantity x minus 1 end quantity
Answer:
(x^3 + 3x^2 - 2x + 7)/x- 2
Expand the numerator in the above expression
(x^3 + 5x^2 - 2x^2 + 8x - 10x - 16 + 23)/(x - 2)
Rearrange the terms of the numerator in the above expression
(x^3 + 5x^2 + 8x - 2x^2 - 10x - 16 + 23)/(x- 2)
Factorize the numerator in the above expression
[x(x^2 + 5x + 8) - 2(x^2 + 5x + 8) + 23]/(x - 2)
Factor out x^2 + 5x + 8
[(x -2)(x^2 + 5x + 8) + 23]/(x - 2)
Split the fractions
(x -2)(x^2 + 5x + 8)/(x - 2) + 23/(x - 2)
Divide the common factors
(x^2 + 5x + 8) + 23/(x - 2) hope this help btw your welcome
Answer:
The answer is really option A. x^2 - x +2-5/x-1
Step-by-step explanation:
I just took the test and got it right :)
If the height of a cone is three
times of the radius of the base and its volume is
343 cm³, then find the radius of the base of the cone
As a result, the cone's volume is equal to three times its radius √343/π .
How to understand the concept of mensuration?The word "mensuration" literally means "to measure." It is typically employed when dealing with geometric shapes when it is necessary to calculate different physical values like perimeter, area, volume, or length. Mensuration is the term for measuring these amounts.
According to the given data:So with respect to the information provided to us :
Height of a cone =3* radius of the base
let height be h and radius be r
h=3r
The Formula for volume of cone is:
V=1/3hπr²
Putting the value we get:
343=1/3*π*r²*3r:
r= √343/π
Therefore ,
the volume of the cone whose height is three times its radius is:
√343/π
To Learn more about Geometric click here:
brainly.com/question/1126612
#SPJ13
24. mrs. piatt, the math teacher, has six black, nine yellow and two blue calculators. what is the probability that she will hand out a blue calculator to the first student, then hand out a yellow calculator second?
The likelihood or probability that she will give the first student a blue calculator and the second student a yellow calculator is 6.6%.
The math teacher Mrs. Piatt has six black, nine yellow, and two blue calculators.
Therefore, the total number of calculators is 17.
The probability that she hands out a blue calculator to the first student is:
P₁ = Number of blue calculators/ Total number of calculator
P₁ = 2/17
Now, as a calculator is handed out to a student. Then the remaining number of calculators is 16.
Therefore, the probability that the second student gets a yellow calculator will:
P₂ = Number of yellow calculators/ Total number of calculators.
P₂ = 9/16
Therefore, the probability that she will hand out a blue calculator to the first student, then hand out a yellow calculator second will be:
P = P₁ × P₂
P = 2/17 × 9/16
P = 18/272
P = 0.06617647058
P = 6.6%
Learn more about probability here:
brainly.com/question/13604758
#SPJ4
Jamie is 5 years older than her sister amy. If the sum of their ages is 19. how old is Jamie?
Considering the age of Amy and sum of their ages, Jamie is 12 years old.
Let the age of Amy be x years. Thus, the age of Jamie be (x + 5) years. Forming equation as per the age -
x + x + 5 = 19
Performing addition on Left Hand Side of the equation
2x + 5 = 19
Shifting 5 to Right Hand Side of the equation
2x = 19 - 5
Performing subtraction on Right Hand Side of the equation
2x = 14
Shifting 2 to Right Hand Side of the equation
x = 14 ÷ 2
Performing division to Right Hand Side of the equation
x = 7
The age of Amy = 7 years
The age of Jamie = 7 + 5
Performing addition
The age of Jamie = 12 years
Thus, the age of Jamie is 12 years old.
Learn more about expression -
https://brainly.com/question/723406
#SPJ1
a binomial experiment with probability of success and trials is conducted. what is the probability that the experiment results in exactly successes? do not round your intermediate computations, and round your answer to three decimal places. (if necessary, consult a list of formulas.)
The probability that the experiment results in exactly successes is; [tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
How to find that a given condition can be modeled by binomial distribution?Binomial distributions consist of n independent Bernoulli trials.
Bernoulli trials are those trials that end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
Consider that we have random variable X about binomial distribution with parameters n and p, then it can be written as;
[tex]X \sim B(n,p)[/tex]
The probability that out of n trials, there be x successes is given as;
[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
The expected value and variance of X are given as:
[tex]E(X) = np\\Var(X) = np(1-p)[/tex]
Hence, the probability that the experiment results in exact success are;
[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
Learn more about binomial distribution here:
https://brainly.com/question/13609688
#SPJ1
PLEASE HELP ASAP!! THANK YOU
The mathematical procedure for splitting big numbers into more manageable groups or sections is known as long division. A difficulty can be solved by breaking it down into manageable parts. Dividends, divisors, quotients, and remainders all exist in long divisions.
First 585 - 50% = ?Then, add or subtract 50% from the first total and then, I believe, add (or it might be the other way around) to get your actual total. We would want it because it shouldn't affect the cost of the first machine. I'm sorry, but I haven't done any math in a long. use a calculator if necessary
The selling price determinedCalculate the total cost of all the items you bought. To calculate the cost price, divide the total cost by the quantity of units purchased. To determine the ultimate price, use the selling price formula: Cost price + profit margin = selling price.
How is a 20% profit margin determined?Use the decimal representation of 20%, which is 0.2.To get 0.8, subtract 0.2 from 1.Your product's original cost should be divided by 0.8.You should charge this amount in order to make a 20% profit margin.To Learn more About long division, Refer:
https://brainly.com/question/25289437
#SPJ13
Please look at the image below. This is my homework by the way.The figure shown are congruent. Find a sequence of transformations for the indicated mapping. Give coordinate notation for the transformations you use.
Coordinates of PQRSTU
P = (-2, -6)
Q = (-4, -6)
R = ((-4, -2)
S = (2, -4)
T = (2, -8)
U = (0, -10)
They changed to ABCDEF
A = (4, 4)
B = (2, 4)
C = (2, 8)
D = (8, 6)
E = (8, 2)
F = (6, 0)
Transformations used = (x + 6, y + 10)
If g(x) = -x, for what value of x does
g(x) = -9?
Answer:
x = 9
Step-by-step explanation:
given g(x) = - x and g(x) = - 9 , the equate right sides
- x = - 9 ( multiply both sides by - 1 )
x = 9
What is the equation in slope-intercept form of a line that passes through the point (−2, −6) and has a slope of 12?
Answer:
y = 12x + 18
Step-by-step explanation:
Equation of line in slope-intercept form: y =mx +b
Here, m is the slope and b is the y-intercept.
m = 12
Substitute m =12 in the above equation,
y = 12x + b
This line passes through (-2,-6). So, plugin the point in the above equation.
-6 = 12*(-2) + b
-6 = -24 + b
-6 + 24 = b
b = 18
Equation of the line:
[tex]\sf \boxed{\bf y = 12x + 18}[/tex]
Look at question 23 please help! I'm giving out the brainliest!!!!!!
The expressions 8x²+3(x²+y) and 7x²+7y+4x²-4y are equivalent .
In the question ,
two expressions are given as
8x²+3(x²+y) and 7x²+7y+4x²-4y .
Simplifying the first expression
we get ,
= 8x²+3(x²+y)
= 8x² + 3x² + 3y
adding the like terms , we get
= 11x² + 3y
Simplifying the second expression
we get ,
= 7x²+7y+4x²-4y
adding and subtracting the like terms ,
we get
= 11x² + 3y
We can see that both the expressions are giving the final answer as 11x² + 3y .
hence , both the expressions are equivalent .
Therefore , the expressions 8x²+3(x²+y) and 7x²+7y+4x²-4y are equivalent .
The given question is incomplete , the complete question is
Are the expressions 8x²+3(x²+y) and 7x²+7y+4x²-4y equivalent ? Explain your reasoning .
Learn more about Algebraic Expression here
https://brainly.com/question/12722684
#SPJ1
The Smith twins, Joe and John, have a car collection.
The number of cars is represented by x.
The number of cars in Joe's collection is 2 times the number in John's collection.
The total number in both is 78. What is x, the number in John's collection?
A. 26 Cars
B. 54 Cars
C. 39 Cars
D. 78 Cars
Answer:
Step-by-step explanation:
x = 39
C. 39 Cars
A straight road makes an angle of 15 degrees with the horizontal. When the angle of elevation of the sun is 57 degrees, a vertical pole at the side of the road casts a shadow 75 feet long directly down the road, as shown in the figure. Approximate the length of the pole. Round to the nearest hundredth.
The length of the pole is 19.15 feet.
What is the angle of elevation?The angle of elevation is the angle created when an observer looks at an object placed above its height in relation to the eye level or the horizontal line. An angle of elevation is, for example, the angle created between the line of sight and the horizontal line when a man on Earth observes the Sun.
Given:
Angle made by straight road = 15°
Angle of elevation of the sun = 57°
Length of the shadow = 75 feet
∠ACB = 90° - 57° = 33°
∠CAB = 57° - 15° = 42°
Using Sine Law to find BC i.e.length of the pole.
[tex]\frac{BC}{sin A} = \frac{AB}{sin C}[/tex]
[tex]\frac{BC}{sin 42} = \frac{75}{sin 33}[/tex]
[tex]BC= \frac{75sin 42}{sin 33}[/tex]
BC ≅ 19.15 feet (to the nearest hundredth.)
Hence, the approximate length of the pole is 19.15 feet.
To know more about angle of elevation visit:
https://brainly.com/question/16716174
#SPJ10
3.if the m∠1 is 57° , find the measure of ∠6.
Show your work
123°
180°-57°=<6=123°
A robot can complete 5 tasks in 3/4 hour. each task is the same. how long does it take the robot to complete one task
The robot will take 0.15 hours to complete one task.
What is the unitary method of problem solving?
A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique. The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. In the unitary method, the value of a unit quantity is determined before the values of other units are determined. Direct variation and inverse variation are its two different forms of variations. When there is a direct variation, an increase or decrease in one quantity will result in an equivalent rise or fall in the other. If we increase one quantity in inverse variation, the value of another quantity will drop.
Given, time taken by robot to complete five tasks = 0.75 hours
Thus, time taken by robot to complete one task = (0.75/5) = 0.15 hours
Therefore, the robot will take 0.15 hours to complete one task.
To learn more about this, tap on the link below:
https://brainly.com/question/24587372
#SPJ9