Fernando evaluated the expression below. What was Fernando’s error?
Answer:
C. Fernando incorrectly found the product of -2 and -5.
Step-by-step explanation:
We have been given an image, which represents work of Fernando's evaluation of an expression. We are asked to find the error in Fernando's work.
[tex]\frac{5(9-5)}{2}+(-2)(-5)+(-3)^2[/tex]
Let us evaluate our given expression using order of operations (PEMDAS).
[tex]\frac{5(4)}{2}+(-2*-5)+9[/tex]
[tex]\frac{20}{2}+10+9[/tex]
[tex]10+10+9[/tex]
[tex]29[/tex]
Since we know that product of two negative numbers is always positive, therefore, the product of negative 2 and negative 5 will be positive 10.
Therefore, Fernando incorrectly found the product of -2 and -5 and option C is the correct choice.
Which statement describes the translation of y = −one half (x − 2)2 − 2 from standard position?
Eight subtracted from the product of
5
and a number is at most
30
.
Use the variable
c
for the unknown number.
A tourist in ireland wants to visit seven different cities. if the route is randomly selected, what is the probability that the tourist will visit the cities in alphabetical order? round your answer to five decimal places.
The probability that the tourist will visit the cities in alphabetical order is 0.00020.
There are a total of 7! ways to visit 7 different cities, but there is only one way to visit them in alphabetical order. So, the probability that the tourist will visit the cities in alphabetical order is:
1/7! = 1/5040 = 0.0002
To five decimal places, the probability is 0.00020.
Here is a step-by-step explanation of the calculation:
We can think of the route as a permutation of 7 letters, with no of the letters being identical.
The number of permutations of 7 letters is 7!.
So, the number of ways to visit the cities in alphabetical order is 1.
The probability that the tourist will visit the cities in alphabetical order is 1/7!.
Here are some additional things to consider:
The probability that the tourist will visit the cities in alphabetical order is very small, because there are many other possible routes.
The probability would be 1 if there were only one city to visit.
The probability would be 0 if there were 7 cities and the tourist had to visit them all in alphabetical order.
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Line segment XY is tangent to circle Z at point U. If the measure of UV is 84, what is the measure of YUV. A. 42 B. 84 C. 96 D. 168
Answer:
The measure of angle YUV is equal to [tex]m<YUV=42\°[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we have that
[tex]arc\ UV=84\°[/tex] -----> given problem
so
[tex]m<UZV=84\°[/tex] ------> by central angle
we know that
The triangle UZV is an isosceles triangle
because
[tex]ZU=ZV=radius[/tex]
so
[tex]m<ZUV=m<ZVU[/tex] -----> bases angle of the isosceles triangle
Remember that
The sum of the internal angles of a triangle is equal to [tex]180\°[/tex]
so
[tex]m<ZUV+m<ZVU+m<UZV=180\°[/tex]
[tex]2m<ZUV+m<UZV=180\°[/tex]
substitute and solve for m<ZUV
[tex]2m<ZUV+84\°=180\°[/tex]
[tex]m<ZUV=(180\°-84\°)/2=48\°[/tex]
[tex]m<ZUV+m<YUV=90\°[/tex] ------> by complementary angles
solve for m<YUZ
[tex]48\°+m<YUV=90\°[/tex]
[tex]m<YUV=90\°-48\°=42\°[/tex]
Answer: A. 42
Step-by-step explanation: trust i got a 100% on the quiz
WXYZ is an isosceles trapezoid with legs WX and YZ and a base XY. If the length of WX is 6x+5, the length of XY is 10x+4 and the length of YZ is 8x-3, find the value of x.
Given f(x)=3x^2+10x−8 and g(x)=3x^2−2x .
What is (fg)(x)
Answer:
[tex]\frac{x+4}{x} \hspace{8}where\hspace{8}x\neq0,\frac{2}{3}[/tex]
Step-by-step explanation:
The division between functions is defined as:
[tex](\frac{f}{g})(x)=\frac{f(x)}{g(x)} ,\hspace{10}g(x)\neq0[/tex]
So:
[tex](\frac{f}{g} )(x)=\frac{3x^2+10x-8}{3x^2-2x}\\ \\Factor\hspace{3}x\hspace{3}out\hspace{3}the\hspace{3}denominator\\\\(\frac{f}{g} )(x)=\frac{3x^2+10x-8}{x(3x-2)}\\\\Factor\hspace{3}the\hspace{3}numerator\\\\(\frac{f}{g} )(x)=\frac{4(3x-2)+x(3x-2)}{x(3x-2)}\\\\Factor\hspace{3}3x-2\hspace{3}from\hspace{3}the\hspace{3}numerator\\\\(\frac{f}{g} )(x)=\frac{(3x-2)(x+4)}{x(3x-2)}=\frac{x+4}{x}[/tex]
Since [tex]g(x) \neq0[/tex] , let's find its roots:
[tex]3x^2-2x=0\\\\Factor\\\\x(3x-2)=0\\\\Split\hspace{3}into\hspace{3}two\hspace{3}equations:\\\\(1):x=0\\(2):3x-2=0[/tex]
For (2)
[tex]3x=2\rightarrow x=\frac{2}{3}[/tex]
Therefore the roots are:
[tex]x=0,\hspace{3}x=\frac{2}{3}[/tex]
Finally the complete answer is:
[tex](\frac{f}{g})(x)= \frac{x+4}{x} \hspace{8}where\hspace{8}x\neq0,\frac{2}{3}[/tex]
If F(x)=x-5 and G(x)=x^2, what is F(F(x))?
Answer:
(A)[tex]G(F(x))=(x-5)^2[/tex]
Step-by-step explanation:
Given: It is given that [tex]F(x)=x-5[/tex] and [tex]G(x)=x^2[/tex].
To find: [tex]G(F(x))[/tex]
Solution:
It is given that [tex]F(x)=x-5[/tex] and [tex]G(x)=x^2[/tex], then [tex]G(F(x))[/tex] is written as:
[tex]G(F(x))=G(x-5)[/tex]
⇒[tex]G(F(x))=(x-5)^2[/tex]
Thus, it matches with the option A of the given options.
Provide a possible situation that the graph shown could represent
Add the opposite number of 1 1/5 to the sum of the numbers (−8 3/4 ) and (−2 5/6 ).
The result of the sum of the three numbers is: [tex]\frac{-767}{60}[/tex]
The numbers are given as:
Number 1: 1 1/5Number 2: -8 3/4Number 3: -2 5/6Start by calculating the sum of numbers 2 and 3 as follows:
[tex]Sum = -8\frac 34 -2\frac 56[/tex]
Express the numbers as improper fraction
[tex]Sum = -\frac{35}4 -\frac{17}6[/tex]
Take LCM
[tex]Sum = \frac{-3 \times 35 - 2 \times 17}{12}[/tex]
[tex]Sum = \frac{-139}{12}[/tex]
The opposite of number 1 is: -1 1/5
So, the overall sum is:
[tex]Sum = -1\frac 15 - \frac{139}{12}[/tex]
Express as improper fraction
[tex]Sum = -\frac 65 - \frac{139}{12}[/tex]
Take LCM
[tex]Sum = \frac{-72 - 695}{60}[/tex]
[tex]Sum = \frac{-767}{60}[/tex]
Hence, the result of the sum is: [tex]\frac{-767}{60}[/tex]
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Give the domain and range a. Domain: {-3, 0, 2}, range: {3, 0, -2} b.
The domain of a function is the set of all possible input values, while the range is the set of possible output values. In the given example, the function's domain is {-3, 0, 2}, which means the input data will be either -3, 0, or 2. Similarly, the function's range is {3, 0, -2}, which means the output data will be either 3, 0, or -2.
Explanation:In mathematics, the domain of a function refers to the set of all possible input values (often represented as 'x' values) that the function can accept without producing an undefined result. Similarly, the range of a function refers to the set of all possible output values (often represented as 'y' values) that the function can produce.
To address your examples: for a function with domain {-3, 0, 2} and range {3, 0, -2}, it means all input data ('x' values) will be either -3, 0, or 2; and all output data ('y' values) will be either 3, 0, or -2.
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Phil received a prize of x dollars from a poker tournament. The tournament cost him 100 dollars to enter. What were Phil's net winnings from the tournament? Write your answer as an expression.
Answer: [tex]x-100[/tex]
Step-by-step explanation:
Given : Phil received a prize of x dollars from a poker tournament.
The tournament cost him 100 dollars to enter.
To find Phil's net winnings from the tournament, we need to subtract the tournament cost from the prize amount he had won.
Thus, the expression to show Phil's net winnings from the tournament :-
[tex]x-100[/tex]
Jim's family went on vacation and rented a car. The rental car agency charged $64.75 plus an additional $0.03 for each mile the car was driven. If Jim's family paid a total of $71.14 for the car rental, how many miles did the family drive the car? Explain how you set up an equation to solve this word problem
helppppppppppppppppppppp
What is the line of symmetry for the parabola whose equation is y = x2 + 10x + 25? x = -10 x = -5 x = 5
Answer:
[tex]y=x^2 + 10x + 25\\\\y=(x+5)^2[/tex]
Used the identity, [tex](a+b)^2=a^2+2ab+b^2[/tex]
The given parabola is of the form , [tex](x+a)^2=y[/tex], having vertex at ,which can be obtained by
x+a=0
x= -a
(-a,0).
So, vertex of the given parabola is , at (-5,0).
The Meaning of term line of symmetry,is that line which divides the parabola in two equal halves.
Drawing the parabola,and finding the line of symmetry,which can be obtained by drawing a line parallel to y axis, passing through (-5,0).
So, the equation of line is : x= -5
Antoine wants to convert millimeters into kilometers. Which operation should he choose?
I need help! Really struggling with understanding how to do this
Which algebraic expression represents the phrase “the quotient of negative eight and the sum of a number and three”?
How much will it cost to mail a first-class letter that weighs 2.8 oz?
The rate is $.22 for the first ounce and $.17 for each additional
ounce or fraction of an ounce.
a. $.56
b. $5.60
c. $.53
d. $.39
Final answer:
The total cost to mail a first-class letter that weighs 2.8 oz is $0.56, which includes $0.22 for the first ounce and $0.34 for the additional weight.
Explanation:
To calculate the cost of mailing a first-class letter that weighs 2.8 oz, you need to know the initial rate for the first ounce and the rate for each additional ounce. According to the given rates, the cost for the first ounce is $0.22, and each additional ounce (or fraction thereof) costs $0.17.
Since the letter weighs 2.8 oz, you have 1.8 oz over the first ounce. Thus, you need to pay for 2 additional ounces.
The total cost = cost for first ounce + cost for additional ounces = $0.22 + 2 x $0.17 = $0.22 + $0.34 = $0.56. Therefore, the correct answer is (a) $.56.
Write a sentence representing the equation x+56/7=11
Which algebraic expression is equivalent to the expression below?
9(8x + 10) + 9(9 - x)
A. 63x - 171
B. 81x + 171
C. 63x + 9
D. 63x + 171
Joselyn is a manager at a sign-painting company. She has two painters, Allen and Brianne. Allen can complete a large project in 16 hours. Brianne can complete the project in 18 hours. Joselyn wants to know how long it will take them to complete the project together.
Write an equation and solve for the time it takes Allen and Brianne to complete the project together. Explain each step.
The area of a rectangle is 300 square centimeters. If the sides of the rectangle are given as 5 centimeters and [tex] \sqrt{x+2600} [/tex] centimeters, then find the value of x and the other side of the rectangle.
Which describes how to calculate the range of this data set?
4, 5, 6, 8, 11, 12
A. Subtract 11- 5
B. Subtract 12- 4
C. Add 11+ 5
D. Add 12+ 4
The range of this data set will be 8. The range of the data set is simply the difference between the maximum and the minimum value.
What is a data set?A data set is a set of information that corresponds to one or more database tables in the case of tabular data,
The maximum value is 12
The minimum value is 4
The range of the data set will be;
R = M-m
R=12-4
R=8
Hence the range of this data set will be 8.
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nick is stuck at the top of a ferris wheel. his mother is standing 38 feet from the base of the wheel watching him. if the angle of elevation from nick's mom to nick is 73 degrees, how far off the ground is nick?
A. 118.2 ft
B. 120.9 ft
C. 124.3 ft
D. 126.5 ft
E. 128.1 ft
Answer:
C. 124.3 ft
Step-by-step explanation:
Let h represent Nick's distance from ground.
We have been given that Nick is stuck at the top of a ferris wheel. his mother is standing 38 feet from the base of the wheel watching him. The angle of elevation from nick's mom to nick is 73 degrees.
Nick, his mother and angle of elevation forms a right triangle with respect to ground, where, h is opposite side and 38 feet is adjacent side.
[tex]\text{tan}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]
[tex]\text{tan}(73^{\circ})=\frac{h}{38}[/tex]
[tex]\text{tan}(73^{\circ})*38=\frac{h}{38}*38[/tex]
[tex]3.270852618484*38=h[/tex]
[tex]h=3.270852618484*38[/tex]
[tex]h=124.292399502392[/tex]
[tex]h\approx 124.3[/tex]
Therefore, Nick is 124.3 feet above the ground.
What is the area of a sector with a central angle of 10π/7 radians and a radius of 18.4 m? Use 3.14 for π and round your final answer to the nearest hundredth. Enter your answer as a decimal in the box.
Area of sector= \frac{\Theta}{360}\times \Pi \times r^{2}
Area =\frac{10\Pi }{7 }\times \frac{1}{360}\times \Pi \times (18.4)^{2}
Area = \frac{1800 }{7 }\times \frac{1}{360}\times (3.14) \times (18.4)^{2}
So, Area of the given sector= 759.34 square meters.
Answer:
759.34 m²
Step-by-step explanation:
solve f(1) for f(x)=1-5x
f(1)= [?]
Ali must choose a number between 61 and 107 that is a multiple of , 2, 4 and 5 . Write all the numbers that he could choose.
The numbers between 61 and 100 are given as 80 and 100.
How to find the LCM of two numbers?The LCM or least common multiple of two numbers is such a small number that is divisible by both. It can be obtained by taking the prime factors of both the numbers and then taking the product of them having highest power.
The required numbers between 61 and 107 are given as follows,
The LCM of 2,4 and 5 is 20.
Thus, the numbers divisible by 2, 4 and 5 are multiples of 20.
Now, the multiples of 20 are 20, 40, 60, 80 and 100.
80 and 100 lies between 61 and 107.
Hence, the numbers that Ali can choose are given as 80 and 100.
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What is the volume of the cone with diameter 7in and height 9in? Round to the nearest cubic inch
Burt & ernie went to the toy store & saw a total of 51 rubber duckies. they saw twice as many yellow as orange. let y = the # of yellow duckies & r = the # of orange duckies. write a system that could be used to find the total of each color & then solve.