Aiden calculated the area of triangle QRS below by finding half the product of 1.5 and 1.1.
Answers
Aiden should have calculated
area = (1.1 * 5.4) / 2
because triangle area = half the base times the altitude.
Answer: The correct option is
(B) Aiden should have found half the product of 1.1 and 5.4 because the 1.5 line is not perpendicular to 1.1 line.
Step-by-step explanation: Given that Aiden calculated the area of triangle QRS by finding half the product of 1.5 and 1.1.
We are to select the correct option which states the error made by Aiden.
The AREA of a triangle is given by
[tex]A=\dfrac{1}{2}\times \textup{base}\times \textup{altitude},[/tex]
where the altitude is perpendicular to the base.
In ΔQRS, the length of the base is given by
b = QS = 0.9 + 4.5 = 5.4 units
and
the length of the altitude is given by
h = 1.1 units.
So, the area of the triangle QRS will be
[tex]A=\dfrac{1}{2}\times b\times h=\dfrac{1}{2}\times 5.4\times 1.1[/tex]
Therefore, the area of ΔQRS will be calculated by finding half the product of 1.1 and 5.4.
So, Aiden made the error by finding half the product of 1.5 and 1.1, because 1.5 line is not perpendicular to 1.1 line.
Thus, Aiden should have found half the product of 1.1 and 5.4 because the 1.5 line is not perpendicular to 1.1 line.
Option (B) is correct.
Related Questions
Which of these is not an example of a geometric shape or form?
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A monomial term has the form ax^n where the coefficient is a and the degree is
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I NEED HELP ASAP! PLS HELP ME!
Answers
2.11*7 = 14.77
2.11*9 = 18.99
the answer is y=2.11x
Determine the solution set of x^2-80=0.
Answers
x^2 = 80 ...take the square root of both sides, eliminating the ^2
x = (+-) sqrt 80
x = (+-) sqrt 16 * 5
x = (+-) 4 sqrt 5
so x = 4 sqrt 5 or x = -4 sqrt 5
Answer: The required solution set of the given equation is [tex]\{4\sqrt5,-4\sqrt5\}.[/tex]
Step-by-step explanation: We are given to determine the solution set of the following quadratic equation :
[tex]x^2-80=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Since the given equation does not contain the term involving x, so we will use the method of square root to solve the given equation.
The solution of equation (i) is as follows :
[tex]x^2-80=0\\\\\Rightarrow x^2=80\\\\\Rightarrow x=\pm\sqrt{80}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{taking square root on both sides}]\\\\\Rightarrow x=\pm\sqrt{16\times5}\\\\\Rightarrow x=\pm4\sqrt5.[/tex]
Thus, the required solution set of the given equation is [tex]\{4\sqrt5,-4\sqrt5\}.[/tex]
You're setting sales goals for next month. You base your goals on previous average sales. The actual sales for the same month for the last four years have been 24 units, 30 units, 23 units, and 27 units. What is the average number of units you can expect to sell next month?
A. 26
B. 28
C. 30
D. 104
Answers
24+30+23+27 = 104
104/4 = 26
A is correct
24 + 30 + 23 + 27 = 104
104/4 = 26
The ages of 3 brothers are consecutive even integers. Three times the age of the youngest brother exceeds the oldest brother's age by 48 years. What is the age of the younger brother?
A. 14
B. 18
C. 22
D. 26
Answers
3n=n+4+48
3n=n+52
2n=52
n=26
So the youngest brother is 26 years old.
kelvin to fahrenheit f= 9/5(k-273.15) +32
Answers
find the point that splits segment cd in half if point c is located at (-2,4) and point d is located at (3,7)
Answers
x1+x2/2
so
-2+3/2
=1/2
=0.5
Answer: The required co-ordinates of the point are (0.5, 5.5).
Step-by-step explanation: We are given to find the co-ordinates of the point that splits CD in half if point C is located at (-2,4) and point D is located at (3,7).
The point that splits the line segment CD in half will be the mid-point of the segment CD.
We know that
the co-ordinates of the mid-point of a line segment with endpoints (a, b) and (c, d) are given by
[tex]\left(\dfrac{a+c}{2},\dfrac{b+d}{2}\right).[/tex]
Therefore, the co-ordinates of the given point that splits CD in half are given by
[tex]\left(\dfrac{-2+3}{2},\dfrac{4+7}{2}\right)=\left(\dfrac{1}{2},\dfrac{11}{2}\right)=(0.5,5.5).[/tex]
Thus, the required co-ordinates of the point are(0.5, 5.5).
A convex polyhedron has 30 edges and 8 fewer vertices than faces. How many faces does the polyhedron have? Euler’s formula: V + F = E + 2 12 18 20 24
Answers
Answer:
C or 20
Step-by-step explanation:
Just got the answer on Edge :)
Answer:
c
Step-by-step explanation:
Part A: Amir rented a scooter at $43 for 3 hours. If he rents the same scooter for 8 hours, he has to pay a total rent of $113. Write an equation in the standard form to represent the total rent (y) that Amir has to pay for renting the scooter for x hours. (4 points)
Part B: Write the equation obtained in Part A using function notation. (2 points)
Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)
Answers
time rent
hours $
3 43
8 113
Assume a linear relation, this is r(t)= Ax + C
=> [r - 43] / [ x - 3] = [113 - 43] / 8 - 3]
=> [r - 43] / [x - 3] = 70 / 5
=> [r - 43] / [x - 3] = 14
=> r - 43 = 14 [x - 3]
=> r - 43 = 14x - 14*3
=> r - 43 = 14x - 42
=> r - 14x - 1 = 0 <----- standard form
Part B: Write the equation obtained in Part A using function notation. (2 points)
r - 14x - 1 = 0 => r(x) = 14x + 1 <------------- function notation, r(x)
Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)
1) Horizontal axis = x
2) Vertical axis = y
3) Domain x > 0 = [0, ∞)
4) Range r > 0 = [0, ∞)
5) r-intercept=> x = 0 => r = 14(0) + 1 = 1 => (0,1)
6) slope: 14
7) x-intercept => r = 0 => 0 = 14x + 1 => x = -1/14 => (-1/14, 0)
Which expression is equivalent to (a^8)^4
Answers
The expression [tex](a^8)^4[/tex] is equivalent to [tex]a^{32}[/tex].
The correct option is [tex]a^{32}[/tex].
To simplify the expression [tex](a^8)^4[/tex], we need to apply the exponent rule for raising a power to a power. According to this rule, when we have an exponent raised to another exponent, we multiply the exponents together.
In this case, [tex](a^8)^4[/tex] can be simplified as [tex](a^8)^4[/tex], which equals [tex]a^{32}[/tex]. Therefore, the expression [tex](a^8)^4[/tex] is equivalent to [tex]a^{32}[/tex].
To understand why we multiply the exponents, think of it this way: [tex](a^8)^4[/tex] means we have the base a raised to the 8th power, and that whole expression is raised to the 4th power. When we multiply the exponents, 8 x 4, we get 32. This tells us that we have a multiplied by itself 32 times, which is represented by [tex]a^{32}[/tex].
Therefore, the correct answer is [tex]a^{32}[/tex].
To learn more about the equivalent expression;
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which of the following is equal to the rational expression when x does not equal -6
x^2-36 / x+6
A.) x^2-6
B.) x+6
C.) 1/x-6
D.) x-6
Answers
x^2-36 / x+6
(x + 6)(x - 6)
= ------------------ = x - 6
x + 6
answer
D.) x - 6
The rational equation [tex]x^2 - 36 / (x+6)[/tex], when x is not -6, simplifies to x - 6. The correct answer is D.) x - 6.
Explanation:This is a Mathematics problem related to algebraic expressions and rational expressions. Given the equation [tex]x^2 - 36 / (x+6)[/tex], when x is not equal to -6, we can simplify this equation by factoring. Note that x^2 - 36 is a difference of two squares, which factors into (x-6)(x+6). So we now have [tex](x-6)(x+6) / (x+6).[/tex]
Since x is not -6, we can cancel out the (x+6)s, leaving us with x-6. Therefore, the answer is D.) x - 6. It's important to be careful with the conditions given in the problem, as they can affect the result.
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You invest $300 in an account that has an interest rate of 1.3%, compounded monthly. How much money is in the account after 20 years? Round your answer to the nearest whole number.
Answers
A=p (1+r/k)^kt
A future value?
P present value 300
R interest rate 0.013
k compounded monthly 12
T time 20 years
A=300×(1+0.013÷12)^(12×20)
A=389.02
Answer:
$389
Step-by-step explanation:
The formula for final value of compound interest is given by
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Here, we have
P = $300
r = 0.013
t = 20 years
n = 12
Substituting these values and find A
[tex]A=300(1+\frac{0.013}{12})^{12\cdot20}\\\\A\approx389[/tex]
Therefore, in 20 years, the account will have $389.
What is the slope of a line that is perpendicular to the line y= -1/2x +5?
A(-2
B(- 1/2
C( 1/2
D( 2
Answers
B. -1/2
Explanation:
The equation is in y= mx + b form, which means that m= slope and b= y-intercept. You can see that the slope is -1/2.
What is the value of X in the isosceles trapezoid below?
A. 81 B. 15 C. 11 D. 41
Answers
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9x + (4x + 37) = 180 ;
9x + 4x + 37 = 180 ;
13x + 37 = 180 ;
Subtract "37" from each side of the equation;
13x + 37 - 37 = 180 - 37 ;
to get:
13x = 143 ;
Divide each side of the equation by "13" ;
to isolate "x" on one side of the equation ; and to solve for "x" ;
______________________________________________________
13x / 13 = 143 / 13 ;
x = 11 ; which is: Answer choice: [C] .
______________________________________________________
Without additional details, this question can't be answered accurately. Typically, one uses properties of an isosceles trapezoid, such as base angles or diagonal lengths, to find unknown variables. More information would allow a more precise answer.
Explanation:Without a visual or additional information about the isosceles trapezoid, it would be challenging to accurately identify the value of X. However, typically in a problem like this, you would use the properties of an isosceles trapezoid, such as its base angles or the lengths of its diagonals, to find the value of an unknown variable. If given the measures of the other sides, it might be possible to calculate the remaining length. An example would be a problem like this: If the bases of an isosceles trapezoid are 10 and 20 units long, respectively, and the non-parallel sides (legs) are equal and represented by X, then based on specific conditions, X could potentially be calculated.
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let i be the first of four consecutive integers. what is 3 less than the sum of those integers ?
Answers
3 less than sum of the integers
= i + i +1 + i + 2 + i + 3 - 3 = 4i + 3
The cycling tour has 340 bottles of water for each week. There are ten people on the tour. How many bottles of water is that for each person per week?
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help
The coordinate grid shows the graph of four equations:
A coordinate grid is shown from negative 12 to positive 12 on the x axis and also on the y axis. Line A passes through the ordered pairs negative 3, 4 and 9, negative 2. Line B passes through the ordered pairs 2, 8 and 8, negative 8. Line C passes through the ordered pairs negative 3, negative 4 and 4, 6. Line D passes through the points 2, negative 2 and 5 and 6.
Which set of equations has (5, 0) as its solution?
A and B
C and D
B and D
A and D
Answers
for line A, we have (-3,4) and (9, -2)
y - y1 = m(x - x1)
y - 4 = (-2 - 4/9 -(-3))(x - (-3))
y - 4 = -(1/2)(x+3)
2y - 8 = -x - 3
2y = -x + 5
substitute (5,0)
2(0) = -5 + 5
0 = 0
A function is given. f(x) = 5x − 7; x = 2, x = 3 (a) determine the net change between the given values of the variable.
Answers
A video game club charges a fixed annual membership fee of $20 and $2 per video game rented. Let f(n) represent the total annual cost of renting n video games. Which of the following functions best represents the relationship between f(n) and n if the membership was increased by $15 the next year?
f(n) = 2n + 35
f(n) = 20n + 2
f(n) = 10n + 35
f(n) = 2n + 10
Answers
$2 per video game rented.
Let f(n) represent the total annual cost of renting n video games
so
f(n) = 20 + 2n
if increased by $15 the next year
then
f(n) = 20 + 2n + 15
f(n) = 2n + 35
answer
f(n) = 2n + 35 (first choice)
Answer:
The correct answer is A, "f(n) = 2n + 35."
Step-by-step explanation:
I got it correct on the test. I hope this helps!
PLEASE HELP!! I WILL GIVE 50 POINTS AND BRAINLIEST ANSWER IF YOU PLEASE JUST HELP ME!!! ITS ONLY 8TH GRADE SO IT SHOULDNT BE THAT HARD!!! PLEASE!!!!! HELP!!!!!!!!
Task 5—Polynomial Division and the Remainder Theorem
Create a quadratic polynomial function f(x) and a linear binomial in the form (x − a).
Part 1. Show all work using long division to divide your polynomial by the binomial.
Part 2. Show all work to evaluate f(a) using the function you created.
Part 3. Use complete sentences to explain how the remainder theorem is used to determine whether your linear binomial is a factor of your polynomial function
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Part 1. In executing the long division method, you merely use the form like what were taught to in elementary:
Quotient
-------------------------
divisor| DIvidend
But in this case, we deal with polynomials instead of only numbers. The complete solution is
x + 1
-----------------------------
x+1 | x²+2x+1
-x²+x
------------------
0 + x+1
- x+1
-----------------
0
So, the answer is x+1.
Part 2. The quadratic equation is f(a) = x²+2x+1, where a is the constant in the binomial x-1. Thus, a=1. Substituting a to the x values, f(1) = (1)²+2(1)+1=0. The zero means that there is no remainder. Thus, (x+1) is a factor.
Part 3. The remainder theorem works similar to Part 2. If you substitute f(a) and the answer is a non-zero number, then that is the remainder when you divide the quadratic equation with the binomial. Only when the answer is zero that you can confirm that the linear binomial is a factor.
can someone please help
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One angle in a pair of complementary angles is 4/5th of the other . Find the measure of the two angles
Answers
complementary angles equal 90 degrees
angle 1 = x
angle 2 = 4/5x
x + 4/5x = 90
9/5x = 90
x = 90 / 9/5 = 50
angle 1 = 50 degrees
angle 2 = 4/5 x 50 = 40 degrees
Answer both please !
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36) the equation would be: 44 x 0.63 =
37) 6.1% = 0.061
59150 x 0.061 = 3608.15 increase
what are the domain and range for each of the following functions? write your answer using inequality symbols of possible PLEASE HELP :) ( on both graphs)
Answers
The Domain is the set of all first coordinates, the x'es.
The Range is the set of all the second coordinates, the y's.
1.
We can see the points (-2, 0), (-1, 1) and (2, -1)
Domain={-2, -1, 2} Range={-1, 0, 1}
2.
We see that x can be any value such that -1<x≤1
and y can be any value such that -1≤y<2
so
Domain: x, such that -1<x≤1
Range: y, such that -1≤y<2
What are the vertical and horizontal asymptotes for the function f(x)= x^2+x-6/x^3-1?
Answers
The easy way to see this is to divide all terms by the highest order variable...
(x^2/x^3 +x/x^3-6/x^3)/(x^3/x^3-1/x^3) and all of that mess boils down to
0/1 or just 0 as x approaches ±oo
So the horizontal asymptote is the horizontal line y=0
The vertical asymptote will occur when there is division by zero, which is undefined because it is not a real value.
x^3-1=0
(x-1)(x^2+x+1)=0
So this only occurs as x approaches -1, so the vertical asymptote is the vertical line x=-1.
Answer:
Hence, x=1 is the vertical asymptote
Hence, y=0 is the horizontal asymptote
Step-by-step explanation:
We have been given an expression
[tex]\frac{x^2+x-6}{x^3-1}[/tex]
For vertical asymptote we equate the denominator to zero that means
[tex]x^3-1=0[/tex]
[tex]\Rightarrow x^3=1[/tex]
[tex]\Rightarrow x=1[/tex]
Hence, x=1 is the vertical asymptote.
Now, for horizontal asymptote we compare the degree of numerator and denominator
Here degree of numerator is 2 and degree of denominator is 3
When degree of denominator is greater than degree of numerator y=0 is the horizontal asymptote
Hence, y=0 is the horizontal asymptote.
Find the measurement of arc AB
45°
60°
90°
180°
Answers
the triangle shown in the middle is a 45-90-45 degree triangle ( the orange lines on the legs mean legs are equal)
so if you were to mirror it there would be 90 degrees between A & B
answer is 90 degrees
Find the length and width of the rectangle if the length is 12 units more then the width and the perimeter is 7 times the width
Answers
P = 7W = 2L + 2W
7W = 2W + 24 + 2W
3W = 24
W = 8
L = 20
HELP If f(x)=2x-12, then f^-1(x)=?
Answers
Remember that angle measures in degrees and radians are based on the proportion of the angle to a complete circle, meaning a fraction of either 360° or 2π. Given that 360° = 2π, we can convert between degrees and radians. With this information in mind, set up a proportion and use it to convert an angle of 225° into radians.
Answers
And you want to compute 225 degrees in to radians, let's assume the final answer is x
Then, 360 / 2pi = 225 / x
Solve for it, you will get x= 5pi/4