Answer: [tex]\dfrac{6\sqrt{2}+\sqrt{7}}{12},\ \dfrac{-3-2\sqrt{14}}{12}[/tex]
Step-by-step explanation:
Given
x and y is in the fourth quadrant
[tex]\sin x=-\dfrac{1}{3}\\\\\cos y=\dfrac{3}{4}[/tex]
we know,
[tex]\cos (x-y)=\cos x\cos y+\sin x\sin y\\\sin (x+y)=\sin x\cos y+\cos x\sin y[/tex]
using [tex]\sin ^2\theta +\cos^2 \theta =1[/tex]
[tex]\Rightarrow \cos x=\dfrac{2\sqrt{2}}{3}\\\\\Rightarrow \sin y=-\dfrac{\sqrt{7}}{4}[/tex]
[tex]\Rightarrow \cos(x-y)=(\dfrac{2\sqrt{2}}{3})\times (\dfrac{3}{4})+(-\dfrac{1}{3})\times (-\dfrac{\sqrt{7}}{4})=\dfrac{6\sqrt{2}+\sqrt{7}}{12}\\\\\\\Rightarrow \sin (x+y)=(-\dfrac{1}{3})\times \dfrac{3}{4}+\dfrac{2\sqrt{2}}{3}\times (\dfrac{-\sqrt{7}}{4})=\dfrac{-3-2\sqrt{14}}{12}[/tex]
A TV has an original price of
$499. Find the new price given a 10% increase
plz help me with the puiz
Barry carefully measured all three sides of the triangle and the dimensions were as follows: 7 meters, 8 meters, 10 meters. Was it a Right Triangle? Please help!
Answer: Not a right-angled triangle
Step-by-step explanation:
Given
The sides of a triangle are [tex]7\ m, 8\ m, \text{and}\ 10\ m[/tex]
For a right-angle triangle, it must satisfy the Pythagoras theorem
[tex]a^2+b^2=c^2[/tex]
i.e. the square of the larger side must be equal to the sum of the square of the remaining two sides
Here,
[tex]\Rightarrow 7^2+8^2\ ?\ 10^2\\\Rightarrow 49+64\ ?\ 100\\\Rightarrow 113\neq 100[/tex]
Therefore, it is not a right-angle triangle
A forest covers 58,000 acres. A survey finds that 0.7% of the forest is old-growth trees. How many acres of old-growth trees are there?
Answer:
406
Step-by-step explanation:
0.7 % / 100 = 0.007
58000 * 0.007 = 406 acres
Can a triangle be formed with the sides lengths of 8 cm, 5 cm and 13 cm?
The side lengths of 8 cm, 5 cm and 13 cm _______ form a triangle.
Drop down options:
cannot
can
The rule says that the sum of any two sides has to be smaller than the third side so, no it can't
A
Write an explicit formula for an, the nth term of
the sequence 17, 15, 13, ...
Tn=-2n+19
Step-by-step explanation:
Well in south africa we use Tn
Tn=a+(n-1)d
a=is the first term in the sequence which is 17
d=is the the difference between the terms which is - 2
Tn=17+(n-1)(-2)
Tn=17-2n+2
Tn=-2n+19
How long is side c ?
Answer:
you do pythagorean theorem
Step-by-step explanation:
the base is 8 and the side length is 6 so you do 8²+6²
8²=64 +6²=36
64+36=100 you have to square 100 which is 10
C=10
Which dilation is shown by the graph?
Answer:
D. D₂ (∆XYZ)
Step-by-step explanation:
Dₙ = (x,y) → ((n)x, (n)y)
_________________
X = (-1, 2).
Y = (2, -1).
Z = (-2, -1).
_________
Dₙ ∆XYZ:
X(-1, 2) → X'(-2, 4)
Y(2, -1) → Y'(4, -2)
Z(-2, -1) → Z'(-4, -2)
______________
-2 / -1 = 2, 4 / 2 = 2.
4 / 2 = 2, -2 / -1 = 2.
-4 / -2 = 2, -2 / -1 = 2.
_______________
D₂ = (x,y) → ((2)x, (2)y).
X(-1, 2) → ((2)(-1), (2)(2)) = X'(-2, 4)
Y(2, -1) → ((2)(2), (2)(-1)) = Y'(4, -2)
Z(-2, -1) → ((2)(-2), (2)(-1)) = Z'(-4, -2)
_________________________
Can anyone help me please ?
Write an equation of the line that passes through the points (3,8) and (2.6). Write the equation in slope-intercept form.
The equation of the line in slope-intercept form is
Answer:
2x - y + 2 = 0 is the equation
y = 2x + 2 is the equation in slope-intercept form
Step-by-step explanation:
slope = (y₂ - y₁) / (x₂ - x₁)
slope = (6 - 8) / (2 - 3)
slope = -2 / -1
slope (m) = 2
equation through the points (3,8) and (2,6):
(y - y₁) / (y₂ - y₁) = (x - x₁) / (x₂ - x₁)
(y - 8) / (6 - 8) = (x - 3) / (2 - 3)
(y - 8) / -2 = (x - 3) / -1
-y + 8 = -2x + 6
2x - y + 2 = 0
slope-intercept form,
y = mx + c
y = 2x + 2
X+3y=17 -2x+3y=-7 how do you solve it
Answer:
X+3y=17 is x=−3y+17
-2x+3y=-7 is x= 3 /2 y+ 7 /2
Step-by-step explanation:
What is the value of this expression? 44−{(6+8)÷2}×3
14
23
69
111
Answer:
23
Step-by-step explanation:
First, open the brackets.
44 - (14/2) x 3
44 - 7 x 3
44 - 21
23
UHHHH HELP ME PLEASE THANK U
Answer:
The average or mean of the two fights would be 19.5
Step-by-step explanation:
Basically all you have to do for this problem is add the total scores of the two fights and then divide by 2 to find your mean. 32 plus 7= 39/2= 19.5
find the volume of the solid figure
Answer:
Volume= Length × Width × Height
How do you do this what the answer to number 12
PLEASE ANSWER URGENT!! TWO QUESTIONS IN ONE
Which number has the least absolute value?
15
5
1
-25
Which number has the greatest absolute value?
15
5
0
-25
Answer:
1 has the least absolute value and -25 has the greatest absolute value
Step-by-step explanation:
If it is absolute value all numbers will be positive no matter the sign they have
Is it the first one the second one the third one the fourth one ??not to be rude but please hurry !!! 20 points !!!
Answer:
5/6 ÷ 1/12 = 10
Step-by-step explanation:
5/6 ÷ 1/12 = 5/6 x 12/1 = 60/6 = 10
Proof:
5/6 tank = 10/12 tank
If each trip takes 1/12 tank, then 10 ÷ 1 = 10 trips
if prism A and B have a ratio of similarity of 6:11, what is the volume of prism B if the volume of prism A is 96 cubic units
Answer:
176cubic units
Step-by-step explanation:
a:b
6:11
a=96
6/11=96/x
6x=1056(96×11)
x=176 cubic units
Determine if the two triangles are congruent. If yes, which theorem proves their congruence?
Answer:
Not congruent.
The Angle-Side-Side Postulate does not exist because an angle and two sides does not guarantee that two triangles are congruent. If two triangles have two congruent sides and a congruent non included angle, then triangles are NOT NECESSARILLY congruent.
Step-by-step explanation:
HELP ME NOW PLEASE AND THANK YOUUU !! Asap on this questions
Answer:
y ≥ -1/2x + 1
Step-by-step explanation:
Not the 1st choice since it's going down
Not the 2nd choice since it's solid line
It's the 3rd choice
Answer:
y ≥ -1/2x + 1
Step-by-step explanation:
Hope this helps
Oscar buy his lunch in the school cafeteria the cost of 15 schools lunches is $33.75
Answer:
$2.25
Step-by-step explanation:
If the answer is how much is one school lunch then...
33.75/15
=2.25
$2.25
3. Write the inverse of the function g(x) =x-3/5
Answer:(x)= 0.6
Step-by-step explanation:
The graphs below were created by an advertising agency for the computer store TechPlus to show its average price on laptops and desktops compared to another computer store's prices.
Which of the following statements best explains how the advertising agency misrepresented the data?
The graphs use different scales, making it appear that the prices at TechPlus are much lower than CompStar.
The graphs were created with different colors.
The graph for CompStar makes its prices appear much higher, but its prices are only a little higher.
The graphs do not include tablet computers, so there is not enough information to compare their prices.
The misrepresentation lies in the fact that ; The graphs use different scales, making it appear that the prices at TechPlus are much lower than CompStar.
Taking a look at both graphs, it could be observed on the y - axis that the graphs do not follow the same scale.
For CompStar, the y-axis which shows the price of laptops and desktops starts it's labeling from $0 ; while TechPlus's labeling began from $600
This representation means that comparing the two graphs would give an erroneous inference as it would make the price of TechPlus appear lower than that of Complus.
Learn more : https://brainly.com/question/1370154?referrer=searchResults
easy 25 points!!!!!!!!!
look at the picture provided, find G
Answer:
There right there u don't see it?
Carly had some markers. After she bought 16 more, she had 40 markers. How
many markers did Carly start with?
Answer:
24 markers
Step-by-step explanation:
24+16=40
40-16=24
what is the 30th term In the sequence 10,7,4,1-3,...
determine the term to term rule
Answer:
7
Step-by-step explanation:
ok so it 7 but 10 is out so is 3
What is the value of x in the equation shown below?
x3 + 1 = 9
Answer:
x = 7/3 or 2.33
Step-by-step explanation:
x3 + 1 = 8
x3 = 8 - 1
x3 = 7
x = 7/3 or 2.33
HOPE THIS HELPS YOU!! :)
Answer: x = 2
Step 1.
In order to solve this non-linear equation, we need to move all the terms to the left side.
In x³ + 1 = 9...
- term 1, will be moved to the right side.
Notice that a term changes sign when it 'moves' from one side of the equation to the other.
Rewrite the equation like this: (x³ + 1) + (-1) = 9 + (-1)
Step 2.
Add x³ + 1 + (-1)
x³ + 1 + (-1) = 8
Now, x = 8.
Step 3.
In this non-linear equation, the variable needs to be isolated.
This is accomplished when both sides are exponentiated by the reciprocal of the variable's exponent, which in our example, 1/3 is equal to
Notice that since we exponentiated a simplified fraction with an odd denominator, only one solution has been created.
Rewrite the equation: [tex](x^3)^\frac{1}{3} =8^\frac{1}{3}[/tex]
Step 4.
We need to exponentiate the power.
The following rule is applied: [tex](A^B)^C=A^B^C[/tex]
According to the formula,
A = X
B = 3
C = 1/3
Rewrite the equation: [tex]x^3^\times^\frac{1}{3} =(2^3)^\frac{1}{3}[/tex]
Step 5.
We need to reduce this fraction, the 3 in x to the lowest terms.
This can be done by dividing out those factors that appear both in the numerator and in the denominator.
In our example, 3 is the common factor.
Rewrite the equation: [tex]x=2^\frac{3}{3}[/tex]
Step 6.
Lastly, we'll need to do the same thing as we did in step 5. Reduce the fraction in [tex]x=2\frac{3}{3}[/tex]. This can be done by dividing out those factors that appear both in the numerator and in the denominator.
Hence, the common factor is 3 since it occurs both in the numerator and the denominator.
Hence, x = 2.
#1) Catherine takes AC transits to school and the bus travels 35 blocks in 7 minutes. At this rate, how long
should the ride take if Catherine's school is 50 blocks away from her house? Explain how you know.
find the solution of given expression
[tex] \sqrt{652 \times 652} [/tex]
Answer:
652
Step-by-step explanation:
[tex]\sqrt{652 \times 652}[/tex] is equal to [tex]\sqrt{652^{2} }[/tex], and the square root of a number squared is always the original number, so [tex]\sqrt{652^{2} }[/tex] is equal to [tex]652[/tex].
Answer:
√{652×652}=√652²=±652
Step-by-step explanation:
Solve the equation for x, and enter your answer in the box below.
x + (-12) = 11
Answer here
Answer:
X=23
Step-by-step explanation:
x + (-12) = 11
Open the bracket
x-12=11
Collect like terms
X=11+12
X=23