Answer:
[tex]\theta[/tex] must be in the third quadrant so that [tex]\sin \theta < 0[/tex] and [tex]\cos \theta < 0[/tex].
Step-by-step explanation:
We have to determine that in which quadrant the angle [tex]\theta[/tex] lies if [tex]\sin \theta < 0[/tex] and [tex]\cos \theta < 0[/tex].
The horizontal axis i.e. x-axis and the vertical axis i.e. y-axis divides the coordinate plane into four zones, the zone with x and y both positive is the first quadrant and rotating about the origin in anticlockwise we will find 2nd, 3rd and 4th quadrant one by one.
In the first quadrant all the trigonometrical functions [tex]\sin \theta[/tex], [tex]\cos \theta[/tex] and [tex]\tan \theta[/tex] are positive.
In the second quadrant only [tex]\sin \theta[/tex] is positive.
In the third quadrant only [tex]\tan \theta[/tex] is positive i.e. [tex]\sin \theta[/tex] and [tex]\cos \theta[/tex] are negative.
In the fourth quadrant only [tex]\cos \theta[/tex] is positive.
Therefore, [tex]\theta[/tex] must be in the third quadrant so that [tex]\sin \theta < 0[/tex] and [tex]\cos \theta < 0[/tex]. (Answer)
If both sin 0 and cos 0 are negative, the angle 0 lies in the third quadrant because only in this quadrant are both sine and cosine functions negative.
Explanation:The question asks in which quadrant does 0 lie given that sin 0<0 and cos 0<0. In the context of trigonometric functions in the Cartesian coordinate system, the sin of an angle is negative in the third and fourth quadrants, and the cos function is negative in the second and third quadrants. As such, if both sin 0<0 and cos 0<0, it indicates that the angle 0 must lie in the third quadrant. This is because it is the only quadrant where both the sin and cos of an angle are negative. Therefore, the angle 0 lies in the third quadrant.
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Triangle A and Triangle B have the same base. The height of Triangle B ice the height of Triangle A. How many times greater is the area of is tw Triangle B? Big Ideas Math G
Final answer:
The area of Triangle B is two times greater than the area of Triangle A, due to the height of Triangle B being twice that of Triangle A with the base remaining constant.
Explanation:
The question pertains to the comparison of the areas of two triangles that share the same base. The height of Triangle B is twice the height of Triangle A. To find the area of a triangle, we use the formula 1/2 × base × height. Given that both triangles have the same base, if we call the height of Triangle A 'h', then the height of Triangle B is '2h'.
So, the area of Triangle A is (1/2 × base × h), and the area of Triangle B is (1/2 × base × 2h). Simplifying the expression for the area of Triangle B, we find it is equal to 2 × (1/2 × base × h), which means it's exactly twice the area of Triangle A. Thus, the area of Triangle B is two times greater than the area of Triangle A.
If one triangle's height is double the other's, its area is four times greater, with same base.
let's break it down step by step.
1. Area of a Triangle Formula: The area of a triangle is calculated using the formula:
[tex]\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]
2. Given Information:
- Both Triangle A and Triangle B have the same base.
- The height of Triangle B is twice the height of Triangle A.
3. Comparing the Areas:
- Let's denote the base of both triangles as [tex]\( b \).[/tex]
- Let the height of Triangle A be [tex]\( h_A \)[/tex] and the height of Triangle B be [tex]\( h_B \).[/tex]
4. Area of Triangle A [tex](A_A)[/tex]:
- Using the area formula, the area of Triangle A is:
[tex]\[ A_A = \frac{1}{2} \times b \times h_A \][/tex]
5. Area of Triangle B [tex](A_B)[/tex]:
- Triangle B has double the height of Triangle A, so the height of Triangle B is [tex]\( 2h_A \).[/tex]
- Using the area formula, the area of Triangle B is:
[tex]\[ A_B = \frac{1}{2} \times b \times (2h_A) = b \times h_A \][/tex]
6. Comparing the Areas:
- Since both triangles have the same base [tex](\( b \)),[/tex] and the height of Triangle B [tex](\( 2h_A \))[/tex] is twice the height of Triangle A [tex](\( h_A \)),[/tex] the area of Triangle B is [tex]\( b \times h_A \)[/tex] which is exactly the same as Triangle A.
7. Conclusion:
- The area of Triangle B is not just greater, it's exactly the same as Triangle A.
So, if the base and one of the heights are doubled, the area of the triangle also doubles. This is because the area of a triangle is directly proportional to its height when the base is constant.
Solve and share these questions
There are 24 times as many non-vegetarian students as vegetarian students. If there are 1200 non-vegetarian students, how many students are vegetarian?
Answer:veg students: 50
Step-by-step explanation:
Antonia has $2,000 earning 3% simple interest in her bank account. Use the formula I = prt where I is the interest earned, p is the principal amount, r is the interest rate, and t is the amount of time the money is in the account to calculate the amount of interest that Antonia will earn after 4 years. Round to the nearest penny if necessary.
Answer:
$240
Step-by-step explanation:
i = prt
i = $2,000 x 0.03 x 4
i = $240
The amount of interest Antonia will earn in 4 years is $240.
what is the slope of the line that passes through the pair of point? (5, 7), (2, 1)
The slope of the line that passes through the pair of point (5, 7), (2, 1) is 2
Solution:
Given that line that passes through the pair of point (5, 7), (2, 1)
To find: slope of the line
The slope of line is given as:
For a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] slope is given as:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Here in this problem,
[tex]\left(x_{1}, y_{1}\right)=(5,7) \text { and }\left(x_{2}, y_{2}\right)=(2,1)[/tex]
Substituting the values in above formula,
[tex]m=\frac{1-7}{2-5}=\frac{-6}{-3}=2[/tex]
Thus the slope of given line is 2
Half of Roberts piece of wire is equal to 2/3 of Maria’s wire. The total length of their wires is 10 feet. How much longer is Roberts wire than Maria’s.
Answer: roberts wire = 5.71
Marias wire. = 4.29
Step-by-step explanation:
Robert wire : y
Marias wire: x
y/2=2/3x
3y=4x
y=4/3x
x+y=10
x+4/3x=10
3x+4x=30
7x=30
x=30/7
X=4.29 feet
Y=4.29*4/3=5.71
To find out how much longer Robert's wire is than Maria's, we need to determine their respective lengths. Let's assume that Maria's wire is x feet long. Then we can set up an equation to solve for the length of Maria's wire and the length of Robert's wire.
Explanation:To find out how much longer Robert's wire is than Maria's, we need to determine their respective lengths. It is given that half of Robert's wire is equal to 2/3 of Maria's wire, and the total length of their wires is 10 feet.
Let's assume that Maria's wire is x feet long. According to the given information, half of Robert's wire would be x/2 feet long. And since half of Robert's wire is equal to 2/3 of Maria's wire, we can set up the following equation: x/2 = (2/3) * x
We can solve this equation to find the length of Maria's wire. Once we have that, we can find the length of Robert's wire by doubling it (since it is given that half of Robert's wire is equal to x/2).
After finding the lengths of their wires, we can subtract Maria's wire length from Robert's wire length to determine how much longer Robert's wire is than Maria's.
20% tip on a bill of 13.98
Answer:
$2.80 (rounded from 2.796)
Step-by-step explanation:
13.98*0.2
Answer:
$2.80
Step-by-step explanation:
Multiply $13.98 by 0.2 (0.2 = 20%):
[tex]13.98*0.2=2.796[/tex]
Since you can't tip less than a cent, round to the nearest cent (hundredth of a dollar):
[tex]2.80[/tex]
20% tip on a bill of $13.98 is $2.80.
5x + 2 = 7 y = x + 1 what is the solution set of the given system?
Answer:
x = 1 , y = 2
Step-by-step explanation:
Solve the following system:
{5 x + 2 = 7 | (equation 1)
y = x + 1 | (equation 2)
Express the system in standard form:
{5 x+0 y = 5 | (equation 1)
-x + y = 1 | (equation 2)
Add 1/5 × (equation 1) to equation 2:
{5 x+0 y = 5 | (equation 1)
0 x+y = 2 | (equation 2)
Divide equation 1 by 5:
{x+0 y = 1 | (equation 1)
0 x+y = 2 | (equation 2)
Collect results:
Answer: {x = 1 , y = 2
Solve the equation.
-3x +.1 + 10x = x + 4
N
olu
R
X =
18
Answer:
Hence after solving the given equation we get x = 13/20.
Step-by-step explanation:
Given:
-3 x + 0.1 + 10 x = x + 4
-3 x + 10 x - x = 4 - 0.1
6 x = 3.9
x = [tex]\frac{3.9}{6}[/tex]
x = [tex]\frac{1.3}{2}[/tex]
x = [tex]\frac{13}{20}[/tex]
Two supplementary angles have measures in the ratio 5:4 what is the measure of the smaller angle
Answer:
The smaller one measures 80 degrees.
Step-by-step explanation:
We are given:
[tex]a+b=180[/tex]
[tex]\frac{a}{b}=\frac{5}{4}[/tex]
So we have a system to solve.
I'm going to solve the bottom equation for [tex]a[/tex] by multiplying [tex]b[/tex] on both sides:
[tex]a=\frac{5}{4}b[/tex].
Let's plug this into the first equation: [tex]a+b=180[/tex]:
[tex]\frac{5}{4}b+b=180[/tex]
[tex]\frac{5}{4}b+\frac{4}{4}b=180[/tex]
[tex]\frac{9}{4}b=180[/tex]
Multiply both sides by 4/9:
[tex]b=\frac{4}{9} \cdot 180[/tex]
[tex]b=\4 \cdot \frac{180}{9}[/tex]
[tex]b=4 \cdot 20[/tex]
[texb=80[/tex].
This means [tex]a=\frac{5}{4} \cdot 80=5 \cdot \frac{80}{4}=5 \cdot 20=100[/tex].
We do have [tex]100+80=180 \text{ and } \frac{100}{80}=\frac{5}{4}[/tex].
So the smallest of the two angles is the one that measures 80 degrees.
The one that is the larger of the two is the one that measures 100 degrees.
Final answer:
The measure of the smaller angle, which is part of a pair of supplementary angles in a 5:4 ratio, is 80 degrees.
Explanation:
Supplementary angles are two angles that add up to 180 degrees. When two angles are in the ratio of 5:4, we can find the measure of the smaller angle by first adding the parts of the ratio together, which gives us 5+4=9 parts. Since the total is 180 degrees, each part is equal to 180 ÷ 9 = 20 degrees. Therefore, the smaller angle, which is 4 parts of the ratio, is 4 x 20 degrees = 80 degrees.
Which best explains the relationship between lines a and b?
Planes T and X are parallel. Plane T contains line a. Plane X
contains line b.
They are skew and will never intersect.
They are parallel and will never intersect.
They are perpendicular and will intersect.
They will intersect at two points.
Answer: They are skew and will never instersect.
Step-by-step explanation: First of all, they will never instersect because they are in the parallel planes. They are also skew because in the 3 dimensional geometry, they are also not parallel because they can be different directions.
Answer:
They are skew and will never intersect.Step-by-step explanation:
WE know that lines are in different planes which are parallel, this means that those planes have the same angle of direction.
If planes are parallel, then all lines inside them are skew, that is, line a and line b will never intersect and they aren't necessarily has to be parallel.
For example, imagine you are in a apartment, parallel planes are the roof and the floor, they are parallel, that is, the will never intersect each other. So, if you have a ruler attached to the roof and another ruler on the floor, you will see that those rulers are not necessarily parallels, and they won't intersect each other because, they have the same angle of direction.
Therefore, the right answer is "They are skew and will never intersect"
During the basketball season, Shane scored 53 points. He scored 3 fewer points than two times the number Jason did. How many points did Jason score?
Answer:
23 points
Step-by-step explanation:
If he shane scored 3 fewer points, then that means double of Jason's score is 56. divide 56 by two to get Jason's real score, which is 23.
f(x)=-2x+15 from x=0 to x=3
Find the average rates of change
Answer:
see below
Step-by-step explanation:
Let
f(x)=
4
x
.
Let
g(x)=
4
x
+2
.
Which statement describes the graph of
g(x)
with respect to the graph of
f(x)
?
g(x)
is translated 2 units left from
f(x)
.
g(x)
is translated 2 units down from
f(x)
.
g(x)
is translated 2 units up from
f(x)
.
g(x)
is translated 2 units right from
f(x)
.
The right answer is: g(x) is translated 2 units up from f(x)
Step-by-step explanation:
Given functions are:
[tex]f(x) = 4x\\g(x) = 4x+2[/tex]
In order to shift the functions upward or downward, an integer is added or subtracted from the original function's output.
We can see by comparing both functions that 2 can be added to f(x) to make function g.
As 2 is added to the function, not the input, it is a vertical shifting.
As the integer is positive, the shift is upward.
So,
The right answer is: g(x) is translated 2 units up from f(x)
Keywords: Functions, shifting
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10 POINTS!!
Draw a tree diagram to show the sample space for each event.
dessert choices: a cake or a shake, each available in vanilla or strawberry flavors
Answer:
The first answer is the correct choice.
Step-by-step explanation:
For this, there are two initial options. A cake or a shake. This means that there are two different trees that need to exist. One for Cakes and one for shakes.
Each of these trees needs to have the options of having vanilla and strawberry.
The first answer is the only one that follows this criteria
Answer:
1st one is correct.
Step-by-step explanation:
Find the percent of increase from 12 to 18
Answer: 50%
Step-by-step explanation:
12x1.5=18
Answer:
50% increase
Step-by-step explanation:
Percentage change = increase/original × 100
[tex]change = \frac{(18 - 12)}{12} \times 100[/tex]
[tex]change = \frac{6}{12} \times 100[/tex]
[tex]change = 0.5 \times 100[/tex]
[tex]change = 50\%[/tex]
Name two points on the graph that show that this relation is not a function
Tickets for a children's musical cost 3.50 for adults and 2.00 for children. If 250 tickets were sold for a total of 650.00 how many tickets of each kind were sold
Number of adult tickets sold is 100 and number of children tickets sold is 150
Solution:
Let "c" be the number of childrens ticket sold
Let "a" be the number of adult tickets sold
Cost of 1 children's musical ticket = $ 2.00
Cost of 1 adult musical ticket = $ 3.50
Given that 250 tickets were sold
number of childrens ticket sold + number of adult tickets sold = 250
c + a = 250 ---- eqn 1
250 tickets were sold for a total of 650
So we can frame a equation as:
number of childrens ticket sold x Cost of 1 children's musical ticket + number of adult tickets sold x Cost of 1 adult musical ticket = 650
[tex]c \times 2.00 + a \times 3.50 = 650[/tex]
2c + 3.50a = 650 ---- eqn 2
Let us solve eqn 1 and eqn 2 to find values of "a" and "c"
From eqn 1,
c = 250 - a ----- eqn 3
Substitute eqn 3 in eqn 2
2(250 - a) + 3.50a = 650
500 - 2a + 3.50a = 650
1.5a = 150
a = 100From eqn 1,
c = 250 - 100
c = 150Thus number of adult tickets sold is 100 and number of children tickets sold is 150
Please help with 14 and 15
Answer: 14. The three consecutive numbers are 12, 14 and 16.
15. An example of equation whose solution is 5 is given below
2X — 20 = X — 15
Step-by-step explanation: please see attachment for explanation.
plz help ill rate you
Answer:
The only correct statement is the first one
because the product of a number greater than 1 and another positive number always makes the second number greater than its original value
:)
I just need help on the restrictions part
Answer:
B
Step-by-step explanation:
x² - 10x -24 = (x + 2) (x - 12) ....(1)
x² - 3x - 108 = (x + 9) ( x - 12) ....(2)
(1) / (2) formula (2) can't be 0 ∴ x ≠ -9 and x ≠ 12
(1) / (2) = (x + 2) / (x + 9)
answer is (B)
how do you solve this equation 5/2c = 8 1/3
Answer:
all work is shown and pictured
The solution of the expression is,
⇒ c = 10/3
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The expression is,
⇒ 5/2c = 8 1/3
Now,
We can simplify the expression is,
⇒ 5/2c = 8 1/3
⇒ 5/2c = 25/3
⇒ c = 25/3 × 2/5
⇒ c = 10/3
Thus, The solution of the expression is,
⇒ c = 10/3
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The Chinstrap Penguin about 68.58 centimeters tall whilethe Emperor penguin is 1.143 meters tall. How many centimeters taller is theEmperor penguin than the chinstrap pengin
Answer:
I DONT KNOW
Step-by-step explanation:
I DO NOT KNOW
x = - y - 2
0.5x + y = 1
Answer:
Step-by-step explanation:
substitute x = - y - 2 in 0.5x + y = 1
0.5(- y - 2) + y = 1
-0.5y-1+y=1
0.5y=2
y=4
x=- y - 2
x=-4-2
x=-6
Answer:
x=4; x=-6
Step-by-step explanation:
solve by substitution
-4x+y=6
-5x-y=21
Answer:
x=-3, y=-6. (-3, -6).
Step-by-step explanation:
-4x+y=6
-5x-y=21
--------------
-9x=27
x=27/-9
x=-3
-5(-3)-y=21
15-y=21
y=15-21
y=-6
find the slopes of the lines graphed below
Answer:
There is no picture
Step-by-step explanation:
solve the following system of equations graphically. After graphing, be sure to label each line with equation and state your final solution as a coordinate pair
y=1/3x+1
x+y=5
Answer:
The solution is the ordered pair (3,2)
The graph in the attached figure
Step-by-step explanation:
we have
[tex]y=\frac{1}{3}x+1[/tex] -----> equation A
[tex]x+y=5[/tex] ----> equation B
Solve by graphing
Remember that
The solution of the system of equations is the intersection point both lines
using a graphing tool
The intersection point is (3,2)
see the attached figure
therefore
The solution is the ordered pair (3,2)
A system of equation can be solved in several ways, which includes the use of graphs
The solution to the system of linear equations is (3,2)
The system of equations is given as:
[tex]y=\frac 13x+1[/tex]
[tex]x+y=5[/tex]
See attachment for the graphs of [tex]y=\frac 13x+1[/tex] and [tex]x+y=5[/tex].
From the attachment, the point of intersection of the lines of both equations is (3,2)
Hence, the solution to the system of linear equations is (3,2)
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Multiply(2.3x10^-5)(3.1x10^12)
Answer: 71300000
Step-by-step explanation:
Answer:
7.13 x 10^7.
Step-by-step explanation:
2.3x10^-5)(3.1x10^12
= 2.3x3.1 x 10^-5 x 10^12
= 7.13 x 10^(-5+12)
= 7.13 x 10^7.
8.27-52.48
7.38-6.18
Answer:
Answer to #1: -44.21
Answer to #2: 1.2
:)
8.27 - 52.48 = -44.21
7.38 - 6.18 = 1.2
During a radio contest, $50 is added to the prize money each time a caller answers the contest question incorrectly. The first
caller has a chance to win $100. Which equation represents the amount the 10th caller receives if this caller is the first to
answer the question correctly?
a10=100+(10-1)50
a10=50+(10-1)100
a11=100+(11-1)50
a11=50+(11-1)100
Answer:
The expression is [tex]a_{10}[/tex] = 100+(10 - 1)50 .
Step-by-step explanation:
Given as :
The amount of money added as prize money = $50
The amount that first caller will win = [tex]a_{1}[/tex] = $100
Let The amount that 10th caller win = $A
∴ common difference for the callers amount = $50
Now, According to question
The given statement is in arithmetic expression
So, For A.P , The nth term is written as
nth term = first term + (n - 1) × common difference
I.e [tex]a_{10}[/tex] = [tex]a_{1}[/tex] + (n - 1) × common difference
Here n = 10
Or, A = $100 + (10 - 1) × 50
So, The expression = [tex]a_{10}[/tex] = 100+(10 - 1)50
Hence, The expression is [tex]a_{10}[/tex] = 100+(10 - 1)50 . Answer
Answer:
The answer is A.
Step-by-step explanation:
a10=100+(10-1)50
Got it correct in the quiz.