Answer:
[tex]\cos(\theta_1) = \frac{\sqrt{111}}{20}[/tex]
Step-by-step explanation:
Given
[tex]\sin(\theta_1) = \frac{17}{20}[/tex]
[tex]Quadrant = 1[/tex]
Required
[tex]\cos(\theta_1)[/tex]
We know that:
[tex]\sin^2(\theta_1) + \cos^2(\theta_1) = 1[/tex]
This implies that:
[tex](\frac{17}{20})^2 + \cos^2(\theta_1) = 1[/tex]
Collect like terms
[tex]\cos^2(\theta_1) = 1 -(\frac{17}{20})^2[/tex]
[tex]\cos^2(\theta_1) = 1 -\frac{289}{400}[/tex]
Take LCM and solve
[tex]\cos^2(\theta_1) = \frac{400 -289}{400}[/tex]
[tex]\cos^2(\theta_1) = \frac{111}{400}[/tex]
Take square roots
[tex]\cos(\theta_1) = \frac{\sqrt{111}}{\sqrt{400}}[/tex]
[tex]\cos(\theta_1) = \frac{\sqrt{111}}{20}[/tex]
The graphs below have the same shape. What is the equation of the blue
graph?
g(x) = ?
ve
-5
-5
g(x) =
O A. g(x) = (x+3)2 - 2
O B. g(x) = (x - \3)2 - 2
xx
O c. g(x) = (x + 3)2 + 2
O D. g(x) = (x – 3)2 + 2
The equation of the translated function is:
g(x) = (x + 3)^2 - 2
How to get the equation for the blue graph?
We can see that the blue graph is a translation of the red one, where the equation for the red graph is:
f(x) = x^2
Remember that the translations are:
Horizontal translation:
For a general function f(x), a horizontal translation of N units is written as:
g(x) = f(x + N).
If N is positive, the shift is to the left.If N is negative, the shift is to the right.Vertical translation:
For a general function f(x), a vertical translation of N units is written as:
g(x) = f(x) + N.
If N is positive, the shift is upwards.If N is negative, the shift is downwards.By analyzing the vertices, we can see that the vertex of the blue graph is at (-3, -2) so we have a translation of 3 units to the left and 2 units down, meaning that we have:
g(x) = f(x + 3) - 2 = (x + 3)^2 - 2
So the correct option is A.
If you want to learn more about translations, you can read:
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Your house had a value of $480,000 and increased in value by 3.5%. How much is your house worth now?
Answer:
$496,800
Step-by-step explanation:
Present cost = $480,000
%increase = 3.5%
Present price of the house = 480,000 + 3.5% of 480,000
= 480,000 + 0.035 * 480,000
= 480,000 + 16,800
= $496,800
Present price of the house = $496,800
It takes 70 pounds of seed to completely plant a 9 -acre field.
How many pounds of seed are needed per acre?
Answer:
7.8 to 1 decimal place
Step-by-step explanation:
70 pounds for 9 acre
for one acre it'll be 70/9
7.7 recurring or 7.8 to 1dp or 8 to the nearest whole number
Answer:
7/9 pounds
Step-by-step explanation:
I did 70/9 to get 7/9 pounds
FOR MATH FINAL WILL GIVE BRAINLIEST FOR CORRECT ANSWER
Answer:
180 cm³
Step-by-step explanation:
2 x 5 x 6 = 30 x 2 = 60
3 x 8 x 5 = 40 x 3 = 120
120 + 60 = 180
How many 1/4 - pound packages of cheese can the deli make with 12 - pound of cheese? Please help !!!
Answer:
48 packages
Step-by-step explanation:
recipicate 1/4 which is 4 the multiply by 12
Hope this helps!!!
Answer:
48
Step-by-step explanation:
1/4 = 0.25
12 / 0.25 = 48
You can make 48 packages.
ASAPPPPPPPPPPPPPP HELPPPPPPPPP
Answer:
1) supplementary
2) complementary
Step-by-step explanation:
1) FGH= 109 JKL=71
109+72=180
2) AED=45 BEC=45
45+45=90
Find the values of x and y. State which theorems you used
Answer:
Step-by-step explanation:
5/6.
use that alternate exterior angles are congruent
3x= 5x -64; 64 = 5x-3x; 64= 2x ; 32 =x
use that lines form 180°
y+ 5x-64= 180
y= 180 +64 -5*32; y= 84
7/8.
use that alternating exterior angles are congruent
x=86
use that same side exterior angles are supplementary
x+y = 180; y= 180 -86; y= 94
9/10.
use that vertical angles are congruent
2y=59; y= 59/2; y= 29.5
use that alternate exterior angles are congruent
3x-4= 2y; 3x = 2y+4; x= (59+4)/3; x=21
WHAT IS THE PROBABLITY OF GETTING FACE CARD?
Answer:
3/13?
Step-by-step explanation:
Pls I need help ASAP❤️
Answer: third option 60t + 24t
Step-by-step explanation:
Answer: 60[tex]x^{3}[/tex]-24[tex]x^{2}[/tex]
Step-by-step explanation:
Which of the following statements is true?
A blue star is hotter than the sun.
Both stars and planets are capable of generating their own light.
A star with a magnitude of 0.2 is brighter than a star with a magnitude of -0.2.
The Big Dipper is the largest constellation in the winter sky.
Answer:
B
Step-by-step explanation:
The figure below shows a triangular piece of cloth: What is the length of the portion BC of the cloth?
6 cos 32°, 6 sin 32°, cos32°/6, sin32°/6
Answer:
the answer is simple
Step-by-step explanation:
hope you got mu explanation
Answer:
6 sin 32°
Step-by-step explanation:
Hope this helps :)
If a=2i+4j, b=2i-5j.What is the vector equation of line AB?.
Answer:
9j
Step-by-step explanation:
vector AB means going to B from A.
= pos. final - pos. initial
= pos.B - pos.A
= (2i + 4j) - (2i - 5j)
= 2i + 4j - 2i + 5j
= 9j
1,100,300 in written in words please!
Answer:
one million one hundred thousand three hundred
The ratio of cars to vans at “Mason’s Used Cars” is 7:5. The ratio of cars to vans at “Hyland Auto” is 4:3. There are 60 vans in each used car lot.
Which lot has more cars? How many more?
“Hyland Auto” added 2 vans (add to 60). Does this make the ratio the same in both cases? Explain.
Show all of your work.
Answer:
Mason's has 4 cars more.
no, it is still not the same ratio.
Step-by-step explanation:
each lot has 60 vans.
the ratio of cars/vans at Mason's is 7:5.
this means for every group of 5 vans there are 7 cars.
how many groups of 5 vans are there ? 60/5 = 12
so, for each of the 12 groups of 5 vans there are 7 cars.
=> 12×7=84
another way to get there (and faster) :
you can also say that a ratio is actually a division.
7:5 is 7/5
so, 60 × 7/5 = 12 × 7 = 84
in any case, Mason's has therefore 60 vans and 84 cars.
Hyland also has 60 vans, but a ratio of cars to vans of 4:3.
let's do the fast route :
60 × 4/3 = 20 × 4 = 80
Hyland has therefore 60 vans and 80 cars.
so, Mason's has more cars (4 more than Hyland).
now Hyland adds 2 vans, having then 62 vans and still 80 cars.
so, the ratio cars to vans is now 80:62. or 80/62
=> 80/62 = 40/31 which cannot be further simplified, as 31 is a prime number.
40/31 is not equal to 7/5. so, it is still not the same ratio.
The length of a rectangle is five centimeters less than four times the width. If the perimeter id 50cm, find the width and length.
Answer:
W is 6
L is 19
Step-by-step explanation:
L= 4W - 5
P= 2L + 2W
P= 2(4W-5) +2W
50=8W -10 +2W
60 = 10W
W= 6
L= 19
Drag the tiles to the correct boxes to complete the pairs. Simplify the mathematical expressions to determine the product or quotient in scientific notation. Round so the first factor goes to the tenths place.
Answer:
Kindly check attached picture for detailed explanation
Step-by-step explanation:
Kindly check attached picture for detailed explanation
Answer:
the other person has it correct
A lawn fertilizer company is working on different formulas for lawn fertilizer. They want to examine the difference between their "Original Formula" and their "Improved Formula".
Answer:
From below table compare growth rates for every lawn that required and made a decision based on function family.
Step-by-step explanation:
Following attached table contains each and every lawn details as per time with original, and improvised shown their heights in mm (millimeters).
Solve for x. Round to the nearest tenth, if necessary.
Answer:
Step-by-step explanation:
take 42 degree as reference angle
using sin rule
sin 42=opposite/hypotenuse
0.66=6.4/x
x=6.4/0.66
x=9.69
What is 6 1/12 - 3 6/12? Move numbers to the boxes to show the answer. If there is no whole number put a 0 in the first box
6/12
- 1/12
= 5/12
6 - 3 = 3
= 3 5/12
which structure is found in the cytoplasm of a typical plant cell?
Answer:
Lysosomes
Step-by-step explanation:
hELP!!!!!!!!!!!!!!!!!!
Answer:
the second one
Step-by-step explanation:
Can someone please help me with this
Answer:
the last one
Step-by-step explanation:
it has nothing to do with 200 so not one or two
and then it is less than 300 that she will drive so she will not drive more than 300 miles away and that is represented by the last inequality
These are 230 calories in 4 ounce of a type of ice cream how many calories are in 6 ounces of that ice cream
Answer:
345
Step-by-step explanation:
230/4 = 57.5
57.5 times 6 = 345 calories
20 POINTS!!!!!
which phrase best describes the expression : 3x + 4y + 1/2z
a. product of three variables
b. value of three coefficients
c. the quotient of three terms
d. the sum of three terms
How many distinct triangles can be drawn by using three of the seven dots below? (Two
triangles are considered different if they don’t share the same three vertices.)
Answer:
With 3 dots, you can only draw 1 triangle.
Step-by-step explanation:
All Triangles must have 3 sides, and 3 angles.
Note:
Pls, brainliest.
Thank you!
Please solve all with explanation
Answer:
1. [tex]\frac{x^2}{y^8}[/tex]
2 a) [tex]\frac{-49}{2}[/tex]
b) 0
3. x = 10
Step-by-step explanation:
1.
[tex](\frac{x^{-3}y^4}{x^{-2}})^{-2}\\({x^{-3+2}y^4})^{-2}\\({x^{-1}y^4})^{-2}({x^{-1*-2}y^{4*-2})= \frac{x^2}{y^8}[/tex]
2. a)
[tex]2 [(\frac{-1}{4}) -12 (-1)^2] - 5[24 +2 (-12)]^2\\2[(\frac{-1}{4}) -12] - 5[24 -24]^2\\2 * [(\frac{-1}{4}) -12] -0\\\frac{-49}{2}[/tex]
b)
[tex]-a^2b^2 - 3a^3b^2\\-\frac{1}{9}*1 - 3 * \frac{-1}{27} *1\\-\frac{1}{9} + \frac{1}{9}\\0[/tex]
3.
[tex]\frac{3}{4}x + \frac{5}{6} = 5x -\frac{125}{3} \\\frac{5}{6} + \frac{125}{3} = 5x - \frac{3}{4}x\\\frac{5+250}{6} = \frac{20x -3x}{4}\\\frac{255}{6} = \frac{17x}{4}\\x = 10[/tex]
En una oficina hay 96 computadores en total. La razón entre los computadores que deben ser reparados y aquellos que se encuentran operativos es 3 : 5. ¿Cuántos computadores de la oficina deben ser reparados en total?
Answer:
36 computadores deben ser reparados.
Step-by-step explanation:
Dado que en una oficina hay 96 computadores en total, y la razón entre los computadores que deben ser reparados y aquellos que se encuentran operativos es 3:5, para determinar cuántos computadores de la oficina deben ser reparados en total se debe realizar el siguiente cálculo:
(96 / (3+5)) x 3 = computadores que deben ser reparados
(96 / 8) x 3 = computadores que deben ser reparados
12 x 3 = computadores que deben ser reparados
36 = X
Por lo tanto, 36 computadores deben ser reparados.
A = 3^5 x 5 x 7^3
B = 2^3 x 3 x 7^4
Find the Lowest Common Multiple (LCM) of A and B.
Answer: A) 416745x^2 | B) 57624x^2
How to: The least common multiple (LCM) of two or more non-zero whole numbers is the smallest whole number that is divisible by each of those numbers. In other words, the LCM is the smallest number that all of the numbers divide into evenly.
Have a great day and stay safe ! sorry if im wrong
someone help as soon as possible pls
Answer:
Check the explanation below please! :)
Step-by-step explanation:
"It is provided that the students has to select new colors for the hats and the pants of the marching band uniforms.
The color options for each item are: yellow (Y), green (G), or black (B).
The sample space for the color selection of hats and pants is:
Sample Space
Hats Pants
Y Y
Y G
Y B
G Y
G G
G B
B Y
B G
B B
There are a total of 9 possible selections."
Credit goes to: https://brainly.com/app/profile/13544493/answers
On a coordinate plane, triangles R S T and L M N are shown. Triangle R S T has points (5, 5), (2, 1), and (1, 3). Triangle L M N has points (0, negative 1), (2, negative 4), and (negative 2, negative 3). How does the area of triangle RST compare to the area of triangle LMN? The area of △RST is 2 square units less than the area of △LMN. The area of △RST is equal to the area of △LMN. The area of △RST is 2 square units greater than the area of △LMN. The area of △RST is 4 square units greater than the area of △LMN.
Answer:
The answer should be "B" (The area of △RST is equal to the area of △LMN.)
The area of ΔRST is equal to the area of ΔLMN.
How to find the area of a triangle from its vertices ?We know that, if the vertices of a triangle are [tex](x_{1},y_{1}), (x_{2} ,y_{2} ), (x_{3} ,y_{3} )[/tex],
then the area of the triangle is [tex]\frac{1}{2}[/tex] | [tex]x_{1} (y_{2} -y_{3} )+x_{2} (y_{3} -y_{1} )+x_{3} (y_{1} -y_{2} )[/tex] |
What is the result of comparing area of two given triangles ?In ΔRST, Vertices are R=(5,5), S=(2,1), T=(1,3)
In ΔLMN, Vertices are L=(0,-1), M=(2,-4), N=(-2,-3)
Area of ΔRST = [tex]\frac{1}{2}[/tex] | [tex]x_{1} (y_{2} -y_{3} )+x_{2} (y_{3} -y_{1} )+x_{3} (y_{1} -y_{2} )[/tex] |
= [tex]\frac{1}{2}[/tex] | 5(1-3)+2(3-5)+1(5-1) |
= [tex]\frac{1}{2}[/tex] | 5×(-2)+2×(-2)+4 |
= [tex]\frac{1}{2}[/tex] | -10-4+4 |
= [tex]\frac{1}{2}[/tex] | -10 |
Removing the absolute sign, we get,
Area of ΔRST = [tex]\frac{1}{2}[/tex] ×10 = 5 square unit
Again, Area of ΔLMN = [tex]\frac{1}{2}[/tex] | [tex]x_{1} (y_{2} -y_{3} )+x_{2} (y_{3} -y_{1} )+x_{3} (y_{1} -y_{2} )[/tex] |
= [tex]\frac{1}{2}[/tex] | 0(-4+3)+2(-3+1)-2(-1+4) |
= [tex]\frac{1}{2}[/tex] | 0+2(-2)-2(3) |
= [tex]\frac{1}{2}[/tex] | -4-6 |
= [tex]\frac{1}{2}[/tex] | -10 |
Removing the absolute sign, we get,
Area of ΔLMN = [tex]\frac{1}{2}[/tex] ×10 = 5 square unit
Hence, we can say that, the area of ΔRST = the area of ΔLMN
Learn more about area of a triangle from its vertices here :
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