The student that simplified the expression incorrectly is student 2
How to determine the incorrect result?The steps are given as:
[tex]\frac{\cot(\theta) + \tan(\theta)}{\cot(\theta)}[/tex]
Student 1:
Step 1: [tex]\frac{\cot(\theta)}{\cot(\theta)} + \frac{\tan(\theta)}{\cot(\theta)}[/tex]Step 2: [tex]1 + \frac{\tan(\theta)}{\cot(\theta)}[/tex]Step 3: 1 + tan²(Ф)Step 4: sec²(Ф)Student 2:
Step 1: [tex]\frac{\cot(\theta)}{\cot(\theta)} + \frac{\tan(\theta)}{\cot(\theta)}[/tex]Step 2: [tex]\frac{1 + \tan^2(\theta)}{\cot(\theta)/\tan(\theta)}[/tex]Step 3: sec²(Ф)/tan²(Ф)Step 4: csc²(Ф)As a general trigonometry rule;
[tex]\frac{\cot(\theta) + \tan(\theta)}{\cot(\theta)} = \sec^2(\theta)[/tex]
This means that student 1 is correct, while student 2 is not
The first error in student 2's workings is in step 2, where we have:
[tex]\frac{\cot(\theta)}{\cot(\theta)} + \frac{\tan(\theta)}{\cot(\theta)} = \frac{1 + \tan^2(\theta)}{\cot(\theta)/\tan(\theta)}[/tex]
The above expression is not justified and cannot be proved by any trigonometry rule
Since the step 2 is incorrect, the other steps cannot be used.
Hence, the student that simplified the expression incorrectly is student 2
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how to Solve for x. -1/2 (x + 2) + 1 1/2 x = 3
Chandler wants to buy a bike
that costs $345. He has a job that
pays an hourly wage of $6. He
needs to pay back $35 that he
borrowed from his mom. How
many hours does Chandler need to
work to have enough money to
purchase the bike?
Use the functions a(x) = 7x + 10 and b(x) = 12x - 18 to complete the function operations listed below. Part A: Find (a + b)(x). Show your work. (8 points) Part B: Find (a - b) (x). Show your work. (8 points) Part C: Find (a - b)(x). Show your work. (9 points) Part D: Find a(b(x)]. Show your work. (10 points)
a) [tex](a+b)(x)=a(x)+b(x)=7x+10+12x-18=\boxed{19x-8}\\[/tex]
b) [tex](a-b)(x)=a(x)-b(x)=(7x+10)-(12x-18)=7x+10-12x+18=\boxed{-5x+28}[/tex]
c) [tex](a-b)(x)=a(x)-b(x)=(7x+10)-(12x-18)=7x+10-12x+18=\boxed{-5x+28}[/tex]
d) [tex]a(b(x))=a(12x-18)=7(12x-18)+10=84x-126+10=\boxed{84x-116}[/tex]
Can someone pls help quickly?
From the question given above, the ratio of L : W in simplified form is given as: 6 : 5. See the explanation below.
What is a ratio?A ratio, simply, can be defined as the quantitative relationship that exists between two values which is indicative of the number of times one value can be obtained from the other.
What is the explanation for the solution above?Step 1 - Indicate your assumptionsLet X be the width of one of the rectangles and let its height be Y.
It is clear from the image that:
4X = 3Y
Hence
(4/3)X = Y
Therefore,
Lenght (L) = 3Y
= 3 (4/3)X
= 4X
Width (W) = Y + 2X
= (4/3)X + 2X
= (10/3)X
Therefore,
L : W = 4X: 10/3X
= 4:10/3
To remove the fraction, multiply both sides of the ratio by 3
= 12 : 10, furhter simplify by halving each value, and we have
= 6:5
Hence, the ratio L: W in simplified form is 6 : 5.
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what percentage of 2m is 40cm
Answer:
20%
Step-by-step explanation:
the units of measure must be the same, so
2m = 2 × 100 cm = 200 cm
then
[tex]\frac{40}{200}[/tex] × 100%
= 0.2 × 100%
= 20%
Answer:
20%
Step-by-step explanation:
2 m = 200 cm We are required to find: what percentage of 2m is 40cm.Required percentage [tex]=\frac{40}{200}\times 100[/tex]Required percentage [tex]=\frac{4000}{200}[/tex]Required percentage [tex]=20%[/tex]A rectangle measures 12 m by 14 m. If the width is decreased by 3 m and the length is increased by 4 m, how much would the area change?
Answer:
6 m²
Step-by-step explanation:
Original area :
12 × 14 = 168 m²
New area :
(12-3) × (14+4) =
9 × 18 = 162 m²
168 - 162 = 6
Area would change by 6 m²
What is the directrix of the parabola defined by `(1)/(4)(y + 3) = (x − 2)^2`?
The directrix of the parabola is [tex]y = \frac {-49}{16}[/tex]
How to determine the equation of the directrix?The parabola equation is given as:
[tex]\frac 14(y + 3) = (x -2)^2[/tex]
A parabola is represented as:
[tex]4p(y - k) =(x -h)^2[/tex]
By comparing both equations, we have:
4p = 1/4 ==> p = 1/16
-k= 3 ==> k = -3
The directrix is represented as:
y = k - p
So, we have:
[tex]y = -3 - \frac 1{16}[/tex]
Take the LCM
[tex]y = \frac {-16 * 3- 1}{16}[/tex]
Evaluate
[tex]y = \frac {-49}{16}[/tex]
Hence, the directrix of the parabola is [tex]y = \frac {-49}{16}[/tex]
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What is the solution to the equation |x − 4| = 17?
[tex]~~~~~~|x-4| = 17\\\\\implies x -4 = 17~~~~ \text{or}~~~~~ x -4 = -17\\\\\implies x = 17+4~~~~\text{or}~~~~~ x = -17+4\\\\\implies x = 21~~~~~~~~~\text{or}~~~~~x = -13[/tex]
what is the mean of 12342634
Answer:
Mean = 3.125 ≈ 3.13
Step-by-step explanation:
Mean = Sum of numbers = 1 + 2 + 3 + 4 + 2 + 6 + 3 + 4 = 25 = 3.125≈3.13
Amount of number 8 8
What’s the answer to the picture I took?
Answer:
y = - x
Step-by-step explanation:
From the given table:-
( x_1,x_2): (5,-5)
( y_1,y_2): (6,-6)
1) Let's find the slope (m):-
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{ - 6( - 5)}{6 - 5} = \frac{ - 6 + 5}{1} = \frac{ - 1}{1} = - 1[/tex]
2) Substitute x_1= 5, y_1=-5 and m=-1 into y-y_1=m(x-x_1)
[tex]y - ( - 5) = - 1(x - 5)[/tex]
[tex]y + 5 = - x + 5[/tex]
[tex]y = - x + 5 - 5[/tex]
[tex]y = - x[/tex]
What is the sum of the first 40 positive odd integers?
Answer:
1600
Step-by-step explanation:
[tex]\text{Number of terms}, ~n = 40\\\\\text{Sum of n odd integers} = n^2 = 40^2 = 1600[/tex]
Select the correct answer.
Over which interval of the domain is function h decreasing?
25?
Answer:
the function is only increasing.
Step-by-step explanation:
A total of 10,800 pharmacy technicians were hired last year in particular country. This is 3% of all pharmacy technicians employed in the country. How many pharmacy technicians are employed in the country?
well, the total amount of technicians employed is 100% and that is "x" amount, now, we also know that 3% of of that is 10800, so
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 10800& 3 \end{array} \implies \cfrac{x}{10800}~~=~~\cfrac{100}{3} \\\\\\ 3x=1080000\implies x=\cfrac{1080000}{3}\implies x=360000[/tex]
Which measure of central tendency is the most affected by outliers
Median
Mean
Midrange
Mode
(Is it the mean or midrange?)
Mean measure of central tendency is the most affected by outliers. Then the correct option is B.
What is Mean?The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean. The normal is alluded to as the number-crunching mean. It's the proportion of the number of genuine perceptions to the absolute number of perceptions.
Mean measure of central tendency is the most affected by outliers.
Then the correct option is B.
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b solve each problem . use ñ= 3.14 1. what is the volume of a regular cylinder whose base has radius of 5 cm and has height of 4 cm? 2. the diameter of sphere is 10 cm. find the volume. 3. juice is sold in aluminum cans that measure 7 inches in height and 4 inches in diameter. how many cubic inches of juice are contained in a full can? 4. the square pyramid has a volume of 297 cm³. the area of the base is 81 cm². What is the height.? 5. A glass is 10 cm deep and 8 cm wide . How much liquid the glass hold?
#1
Volume
πr²hπ(5)²(4)100π3.14(100)314cm³#2
Radius=10/2=5cm
Volume
4/3πr³4/3π(5)³125(4/3π)500π/3523.3cm³#3
Volume
π(4/2)²(7)2²(7π)28π87.92in³#4
V=1/3a²hV=1/3(81)h27h=297h=11cm#5
radius=8/2=4
Volume
π(4)²(10)160π502.4cm³502.4mLAnswer:
1) 314 cm³
2) 523.33 cm³
3) 87.92 in³
4) 11 cm
5) 502.4 cm³
Step-by-step explanation:
Part 1[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Given:
r = 5 cmh = 4 cmπ = 3.14Substitute the given values into the formula:
[tex]\begin{aligned}\implies \textsf{Volume} & =3.14 \cdot 5^2 \cdot 4\\& = 3.14 \cdot 25 \cdot 4\\& = 3.14 \cdot 100\\& = 314 \: \sf cm^3\end{aligned}[/tex]
Part 2[tex]\textsf{Volume of a sphere}=\sf \dfrac43 \pi r^3\quad\textsf{(where r is the radius)}[/tex]
Given:
d = 10 cm ⇒ r = 5 cmπ = 3.14Substitute the given values into the formula:
[tex]\begin{aligned}\implies \textsf{Volume} & =\dfrac{4}{3} \cdot 3.14 \cdot 5^3 \\& =\dfrac{4}{3} \cdot 3.14 \cdot 125 \\& =\dfrac{500}{3} \cdot 3.14 \\& = 523.33\: \sf cm^3\:(2\:dp)\end{aligned}[/tex]
Part 3[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Given:
d = 4 in ⇒ r = 2 inh = 7 inπ = 3.14Substitute the given values into the formula:
[tex]\begin{aligned}\implies \textsf{Volume} & =3.14 \cdot 2^2 \cdot 7\\& = 3.14 \cdot 4 \cdot 7\\& = 3.14 \cdot 28\\& = 87.92\: \sf in^3\end{aligned}[/tex]
Part 4[tex]\textsf{Volume of a square pyramid}=\sf \dfrac{1}{3} a^2h \quad\textsf{(where a is the base edge and h is the height)}[/tex][tex]\textsf{Area of base of square pyramid}=\sf a^2 \quad\textsf{(where a is the base edge)}[/tex]
Given:
Volume = 297 cm³Area of base = 81 cm²[tex]\implies 81=a^2[/tex]
[tex]\implies a=\sqrt{81}[/tex]
[tex]\implies a=9\: \sf cm[/tex]
Substitute the given values into the formula and solve for h:
[tex]\begin{aligned}\implies \textsf{297} & =\dfrac{1}{3} \cdot 9^2 \cdot h\\\\297 & =\dfrac{81}{3} h\\\\891 & =81 h\\\\h & = 11 \: \sf cm\end{aligned}[/tex]
Part 5[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Given:
d = 8 cm ⇒ r = 4 cmh = 10 cmπ = 3.14Substitute the given values into the formula:
[tex]\begin{aligned}\implies \textsf{Volume} & =3.14 \cdot 4^2 \cdot 10\\& = 3.14 \cdot 16 \cdot 10\\& = 3.14 \cdot 160\\& = 502.4\: \sf cm^3\end{aligned}[/tex]
How do you find the length of an unknown leg in a right triange
By using the pythagoras theorum you can find an unknown leg of right angled triangle.
Hypotenuse side is in the front of the 90 degree angle and other two sides can be taken as base and perpendicular, so formula goes as :-
(Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2
H^2 = B^2 + P^2
Step-by-step explanation:
Hope it helps you!!Is this right if not please tell me explanation
Answer:
No, right answer is = 1017.36
Answer:
1017.36
Step-by-step explanation:
All your work is correct, but the final answer is not. In the problem it says to use 3.14 as pi, but when you multiplied you did:
[tex]\pi * 6^{2}*9 = 1017.88[/tex]
instead of
[tex]3.14*6^{2}*9 = 1017.36[/tex]
like you had written above. So the final is actually supposed to be 1017.36
Polygon G H I J K has 5 sides.
Which statements are true about the regular polygon? Select three options.
The sum of the measures of the interior angles is 900°.
Each interior angle measures 108°.
All of the angles are congruent.
The polygon is a regular hexagon.
The sum of the measures of the interior angles is 180(5 – 2)°.
Answer:
Each interior angle measures 108°.All of the angles are congruent.The sum of the measures of the interior angles is 180(5 – 2)°.Step-by-step explanation:
(1) The sum of the interior angles of a polygon is [tex]180(n-2)[/tex] degrees, where n is the number of sides. In this case, n=5, so the sum is 180(5-2)=540 degrees, meaning the first statement is false.
(2) Since the angles add to 540 degrees, dividing this amongst the five equal angles, we get that each angle measures 108 degrees, so this statement is true.
(3) By definition, all angles of a regular polygon are congruent.
(4) A hexagon has 6 sides, but this polygon has only 5 sides, so this statement is false.
(5) This is true. (See statement (1)).
Answer:
Options B, C, E
Step-by-step explanation:
Which one is the right conversion?
Answer:
1, 4, 5, 6
Step-by-step explanation:
to convert a rational to an exponential it's the index (number left of radical) over the power (number on the right).
you can also double check by plugging both into a calculator and see if they equal the same number.
Leonardo, who is married but files separately, earns $80,000 of taxable income. He also has $15,000 in city of Tulsa bonds. His wife, Theresa, earns $50,000 of taxable income.
If Leonardo and his wife file married filing jointly in 2021, what would be their average tax rate?
When Leonardo and his wife file married filing jointly in 2021, the average tax rate will be 15.63 percent
What is the tax rate about?In the question above, Leonardo's taxable income = $80,000
Theresa's taxable income = $15,000
Total taxable income for both of them will be:
$ 80,000 + $ 50,000 = $ 130,000
When you make use of the Schedule Y-1,
The amount of the tax on total income shall be said as:
Tax liability = $9,086 + (($130,000 - $78,950) * 22%)
= $9,086 +($51,050 * 22%)
= $9,086 + $11,231
= $ 20,317
To get the Effective tax rate, it will be:
= tax liability / Total taxable income Effective tax rate
= [tex]\frac{20,317}{30000}[/tex] that is also written as $20,317/ $130,000
So, the average tax rate is = 15.63%
Therefore, the average tax rate will be = 15.63 percent
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What is the median of 3,4,5,5,7,8
Find the area of the circle. A circle has a diameters of 17 centimeters. Pi value is 3.142
Answer:
Area of the circle = 227.0095 cm^2
Step-by-step explanation:
Given:
Diameter (D) = 17 cmπ = 3.142To Find:
Area of the circle
Soln:
We know that,
Area of the circle: πr²
where:
π = 3.142r = radiusBut we don't know the radius,as the diameter is given.We could use the formula of diameter & plug the value of it do find the radius.
We know that,[tex] \rm \: Diameter = 2(r)[/tex]
Where
r = radiusSubstitute the value of Diameter:
Diameter = 2r
17 = 2r
17/2 = r
8.5 = r
r = 8.5
Now we got the radius, so substitute radius onto the formulae:
Area of the circle = πr²Ar(circle) = π(8.5)²Ar(circle) = 72.25π(Answer in terms of π)Ar(circle) = 72.25 * 3.142Ar(circle) = 227.0095 cm^2[tex]\text{Area of circle} = \pi\cdot \text{Radius}^2\\\\\\~~~~~~~~~~~~~~~~~~=\pi~ \left( \dfrac{\text{Diameter}}2 \right)^2\\\\\\~~~~~~~~~~~~~~~~~~=3.142 \left(\dfrac{ 17}2 \right)^2\\\\\\~~~~~~~~~~~~~~~~~~=227.0095~ \text{cm}^2[/tex]
find x
give your answer to 3 significant fingers
Answer:
1.64
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
6.6^2 + x^2 = 6.8^2
43.56+x^2=46.24
Subtract 43.56 from each side
x^2 = 46.24-43.56
x^2 =2.68
Take the square root of each side
sqrt(x^2) = sqrt(2.68)
x =1.637080554
To 3 significant digits
x = 1.64
Answer:
Step-by-step explanation:
x = 1.637 mm
Pythagorean theorem:We can use Pythagorean theorem, to find the unknown side for a right angled triangle.
The side opposite to 90 is the longest side and it is the hypotenuse.
Base² + altitude² = hypotenuse²
x² + 6.6² = 6.8²
x² + 43.56 = 46.24
x² = 46.24 - 43.56
x² = 2.68
x = √2.68
[tex]\sf \boxed{\bf x = 1.637 \ mm }[/tex]
For each of the number lines, write an absolute value equation in the form |x - c |=d,
where c and d are some numbers, to satisfy the given solution set.
The absolute value equation that satisfy the solution set of -4 and -8 is |2 - x| = -6
How to determine the absolute value equation?The solution sets on the number line are given as:
x = {-8, -4}
Calculate the average of the solutions
Mean = (-8 - 4)/2
Mean = -6
Calculate the difference of the solutions divided by 2
Difference = (-4 + 8)/2
Difference = 2
The absolute value equation is the represented as:
|Difference - x | = Mean
Substitute known values
|2 - x| = -6
Hence, the absolute value equation is |2 - x| = -6
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Answer:
|b+6|=2
Step-by-step explanation:
Which of the following functions best fits the data shown in the scatterplot below? y=100x+2y is equal to 100 x plus 2 y=20x2+10y is equal to 20 x squared plus 10 y=4x+8y is equal to 4 to the x th power plus 8 y=2x+5y is equal to 2 to the x th power plus 5
The equation of the scatter plot is (a) y = 100x + 2
How to determine the equation of the scatterplot?The line of best fit of the scatter plot passes through the points
(x,y) = (0,2) and (1,102)
Start by calculating the slope using:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{102 - 2}{1 - 0}[/tex]
m = 100
The equation is then calculated as:
y = m(x - x1) + y1
This gives
y = 100(x -0) + 2
Evaluate
y = 100x + 2
Hence, the equation of the scatter plot is (a) y = 100x + 2
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PLEASE ILL GIVE 25 POINTS ANS MARK BRAINIEST IF SOMEONE GIVES ME THE RIGHT ANSWER PLEASE PLEASE PLWASE
Answer:
Circumference: 25.12m
Area: 50.24 [tex]m^{2}[/tex]
Step-by-step explanation:
Formula for circumference of a circle: C=[tex]\pi d[/tex] or C=[tex]2\pi r[/tex] since the diameter is double the radius
C=3.14*2*4=3.14*8=25.12
Formula for area of a circle: A=[tex]\pi r^{2}[/tex]
A=3.14*[tex]4^{2}[/tex]=3.14*4*4=3.14*16=50.24
[tex]-3/z+7/4z=5/z-25[/tex]
Answer:
z = 1/4
Step-by-step explanation:
See attached image
Answer:
z = 5
Step-by-step explanation:
simplify
5/(z-25) first
turning it into
((0 - 3/z) + 7/4z) - 5/(z - 25) = 0
then simplify 7/4z
((0 - 3/z) + 7/4z) - 5/(z-25) = 0
when the fractions denominator is 0 then the numerator must be 0
turning the equation into
-25 * (z - 5) = 0
solve
-25 = 0
something that is not zero cannot equal zero.
z - 5 = 0
5 - 5 = 0
z = 5
hope this helps:)
Mr. Garcia had some blueberries. He sold 2 3/4 kilograms of the blueberries and packed the rest equally into 9 bags. Each bag contained 1/4 kilogram of blueberries. Find the mass of blueberries that mr. Garcia had at first
Answer:
Mr. Garcia had 5 kilograms of blueberries at first
Step-by-step explanation:
to make this easiest, we can imagine that we're undoing mr. garcia's actions.
So, we can start by 'unpacking' mr garcia's bags
we know that each of the nine bags had 1/4 kilograms, so we can multiply 1/4 by 9 to find the collective mass packed into bags
(remember, multiplication is repeated addition. we could also add 1/4 + 1/4 + 1/4... nine times, but this would take a while)
so,
1/4 x 9 = 9/4
(9 = 9/1 [if that is how you're used to multiplying a fraction])
Then, he also sold 2 3/4 kilograms
so, we can add 2 3/4 + 9/4 to find the total mass of the blueberries at first
2 3/4 + 9/4 = 2 + 12/4
(12/4 = 3)
2 + 3 = 5
So, Mr. Garcia had 5 kilograms of blueberries at first
A class sold tickets to their school play. Each of the 232323 students in the class sold 444 tickets. The cost of each ticket was \$7$7dollar sign, 7.
How much money did the class earn by selling tickets to the play?
\$
Answer:
the class earned $722059884
Step-by-step explanation:
because each person sold 444 tickets and there was 232323 students
=232323×444
=103151412
because 103151412 tickets were sold and a ticket cost $7
=103151412×7
=722059884
2a - (a + 3) I need Answers
Answer:
a-3
Step-by-step explanation:
[tex]2a-(a+3)\\= 2a - a - 3\\= a - 3[/tex]
Answer:
a-3
Step-by-step explanation:
2a - (a+3)
removing bracket
2a -a-3
a-3
final answer
a-3