Recall that for two vectors x and y,
x • y = ||x|| ||y|| cos(θ)
where θ is the angle between them.
We have
i • (√3 i + j) = √3
||i|| = 1
||√3 i + j|| = √((√3)² + 1²) = √4 = 2
Solve for θ :
√3 = 2 cos(θ)
cos(θ) = √3/2
θ = arccos(√3/2) = π/6
(Note that we assume θ is the acute angle between the vectors.)
Which picture shows the inverse, f −1, of the function shown?
Domain: 8, 10, 12. Range: 6, 9, 3. 8 goes to 6; 10 goes to 9; 12 goes to 3.
CLEAR CHECK
Inverse of f. Domain: 8, 10, 12. Range: negative 6, negative 9, negative 3. 8 goes to negative 6; 10 goes to negative 9; 12 goes to negative 3.
Inverse of f. Domain: 6, 9, 3. Range: one-eighth, one-tenth, one-twelfth. 6 goes to one-eighth, 9 goes to one-tenth; 3 goes to one-twelfth.
Inverse of f. Domain: 8, 10, 12. Range: one-sixth, one-ninth, one-third. 8 goes to one-sixth; 10 goes to one-ninth; 12 goes to one-third.
Inverse of f. Domain: 6, 9, 3. Range: 8, 10, 12. 6 goes to 8; 9 goes to 10; 3 goes to 12.
Answer:
(d) Inverse of f. Domain: 6, 9, 3. Range: 8, 10, 12. 6 goes to 8; 9 goes to 10; 3 goes to 12.
Step-by-step explanation:
Apparently function f is defined by the ordered pairs (8, 6), (10, 9), (12, 3).
The inverse function will be defined by the ordered pairs with the input and output reversed:
(6, 8), (10, 9), (3, 12)
This seems to be described by the last answer choice.
Please help!! Will mark brainlyest.
Answer:
C
Step-by-step explanation:
It cannot be D and A and B are the same
Answer:
90 degrees around the origin
Step-by-step explanation:
When you rotate the first time it is 90 degrees
When you rotate two times it is 180 degrees
When you rotate three times it is 270 degrees
Hope it helps:)
At what rate per cent per annum will $400 yield an interest of $78 in 1 1/2 years?
Use language that's easy-to-understand. If there's a piece of vocabulary that you feel needs clarifying, define it! 23
Step-by-step explanation:
Our sense of smell is responsible for ___ of our overall chocolate tasting experience. Group of answer choices 10% 30% 50% 70%
Answer:
70%
Step-by-step explanation:
Our sense of smell is responsible for 70% of our overall chocolate tasting experience.
the equation of a line is shown
6x-3y=5
a dilation c entered at the origin with a scale factor of 6 is applied to this line
A: what is the slope of the line after dilation
B: what is the value of the y-intercept of the line after the dilation
Answer: See below
Step-by-step explanation:
Let us write the equation of the given line in standard form:
[tex]6 x-3 y=5 \quad \Rightarrow \quad y=2 x-\frac{5}{3}[/tex]
A. The line moves away from the origin by a scale factor of 6, but its inclination still remains the same. Therefore, after any dilation, the slope of that line never changes.
Thus, the slope of the given line after dilation will be the same as the original slope, which is m = 2.
B. The x-intercept of the line before dilation will be given by substituting x = 0 in the given equation as shown below:
[tex]y=2(0)-\frac{5}{3}=-\frac{5}{3}[/tex]
Now, the y-intercept of the line after the dilation will be given by:
[tex]6\left(-\frac{5}{3}\right)=-10[/tex]
name the 3d shape formed by each net.
Answer:
1. Rectangular Prism
2. Cylinder
3. Triangular Pyramid
4. Triangular Prism
5. Cone
6 Rectangular Pyramid
A $35 item is marked down 25%. What is the new price?
Answer:
$26.25
Step-by-step explanation:
35*.25 is 8.75
35-8.75=$26.25
Find the perimeter of the triangle .
Answer:
P = 9x + 22
Step-by-step explanation:
Perimeter = sum of all sides
P = (3x + 11) + (3x + 11) + (3x)
P = 9x + 22
I hope this helps! God bless
Dennis drew the line of best fit on the scatter plot shown below:
What is the approximate equation of this line of best fit in slope-intercept form?
y = −15x + 2/3
y = -2/3 x + 15
y = −15x + 3/2
y = -3/2 x + 15
Answer:
4th option
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, 12) and (x₂, y₂ ) = (6, 6) ← 2 points on the line
m = [tex]\frac{6-12}{6-2}[/tex] = [tex]\frac{-6}{4}[/tex] = - [tex]\frac{3}{2}[/tex]
the line crosses the y- axis at (0, 15 ) ⇒ c = 15
y = - [tex]\frac{3}{2}[/tex] x + 15 ← approximate equation of line of best fit
The graph of a function is a transformation of the graph of its parent function in which the graph is
vertically stretched by a factor of 2;
shifted left 3 units; and
shifted up 2 units.
write an equation for the function.
Answer:
f(x) = 2(x+3)+2
Step-by-step explanation:
20 points!!! please help
Do 13, 14, 15, and 16
Answer:
13. 360 14. 1080 15. x=53 16. x=135
Step-by-step explanation:
Equation: (n-2)*180
For 13. all angles in a a quadrilateral add up to 360
For 14. 8 sides-2=6. 180*6=1080 degrees
For 15. 15+155+137=307. 360-307=53. x=53 degrees
For 16. 6 sides-2=4. 4*180=720. 90*2=180. 720-180=540. 540/4=135.
x=135
8. (3x-5) mZS = 0 MZR = Р T con A (117 Bux+5)* S
Answer:
95°, 110°
Step-by-step explanation:
Since we're dealing with a cyclic quadrilateral ,
m<T + m<R 180°
7y + 11y = 180°
18y = 180°
y = 10°
Also,
m<S + m<U = 180°
3x+5+3x-5= 180°
6x = 180°
x = 30°
m<S = 3x+5 = 3(30)+5
= 95°
m<R = 11y = 11(10)
= 110°
Given -
m∠R = (11y)°m∠S = (3x + 5)°m∠T = (7y)°m∠U = (3x - 5)°To find -
m∠Rm∠S(nullifying x and y)
Explanation -
As we know this is a cyclic quadrilateral and it's either pair of the opposite angles sum up to 180°.
Therefore,
m∠S + m∠U = 180° ---(1)
m∠R + m∠T = 180° ---(2)
Solution -
Substituting the values of the measure of angles in (1)
➜ m∠S + m∠U = 180°
➜ (3x + 5)° + (3x - 5)° = 180°
➜ 6x = 180°
➜ x = 180/6
➜ x = 30
Therefore, m∠S = (3x + 5)° = {3(30)+5}° = (90+5)°
m∠S = 95°
Substituting the values of the measure of angles in (2)
➜ m∠R + m∠T = 180°
➜ (11y)° + (7y)° = 180°
➜ 18y = 180°
➜ y = 180/18
➜ y = 10
Therefore, m∠R = (11y)° = (11×10)° = 110°
Amy works and is paid by the hour. Her sister Jo helps her work. As shown in the table identify the independent and dependent ( first gets some!)
Answer:
The dependent variable is Amy's pay
The independent variable is Jo's pay
Step-by-step explanation:
Depending on how much Amy gets paid, Jo gets 20% of it.
helpppppppppppppppppppllssssssssssssssssss
Owen is going on a multi-day hike up a large mountain. He wants to know what clothes he should bring for the higher elevation as he hikes. What clothes should Owen bring?
Answer:
Owen should wear thick, layered clothing thats will keep him warm
Example:Jackets,sweaters,heavy socks, gloves, benies, Balaclavas...ect
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Heavier Clothes, Since, The higher elevation will have cooler tem
Find an ordered pair that is a solution to the equation.
Answer:
[tex](x,y) = (4,1)[/tex]
Step-by-step explanation:
[tex]-4+5\cdot 1 = 5-4 =1[/tex]
Answer:
(2, 3/5)
Step-by-step explanation:
Step 1. Rewrite as slope-intercept form, y = mx + b (OPTIONAL)
-x + 5y = 1
5y = x + 1
y = 1/5x + 1/5
Step 2. Pick an x value, then sub for y
x = 2
y = 1/5(2) + 1/5
y = 2/5 + 1/5
y = 3/5
Ordered pair: (2, 3/5)
God bless!
PLEASE HELP
Find AB,. Round to the nearest tenth.
Answer:
11.6
Step-by-step explanation:
11.64 without rounding. since the 2nd decimal is below 5, we round down to 0. 11.60, or just 11.6 :) hope this helps!
What is the solution to the system of equation?
Answer:
(0, -4)
Step-by-step explanation:
The solution to the system is the point that is on both lines. It is where the lines intersect (cross). They intersect at the point (0, -4)
Find the missing side lengths. Leave your answers as radicals in simplest form.
Answer:
B x = 3, y= 3
Step-by-step explanation:
Trigonometric ratios
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleH is the hypotenuse (the side opposite the right angle)Given:
[tex]\theta[/tex] = 45°O = [tex]x[/tex]A = [tex]y[/tex]H = [tex]3\sqrt{2}[/tex][tex]\implies \sin(45^{\circ})=\dfrac{x}{3\sqrt{2}}[/tex]
[tex]\implies x=3\sqrt{2}\sin(45^{\circ})[/tex]
[tex]\implies x=3\sqrt{2} \cdot \dfrac{\sqrt{2}}{2}[/tex]
[tex]\implies x=\dfrac{3\sqrt{2} \sqrt{2}}{2}[/tex]
[tex]\implies x=\dfrac{3 \cdot 2}{2}=3[/tex]
[tex]\implies \cos(45^{\circ})=\dfrac{y}{3\sqrt{2}}[/tex]
[tex]\implies y=3\sqrt{2}\cos(45^{\circ})[/tex]
[tex]\implies y=3\sqrt{2} \cdot \dfrac{\sqrt{2}}{2}[/tex]
[tex]\implies y=\dfrac{3\sqrt{2} \sqrt{2}}{2}[/tex]
[tex]\implies y=\dfrac{3 \cdot 2}{2}=3[/tex]
The Pyramid of Menkaure is a square pyramid located in Giza. The pyramid has a height of about 215 feet, a slant height of about 274 feet, and a base side length of about 339 feet. After a windstorm, an architect was tasked with inspecting the outer surfaces of the pyramid for damage. How many square feet does the architect need to inspect? Type the correct answer in the box. Use numerals instead of words. The architect will need to inspect square feet
Answer:
The architect will need to inspect 185,772 square feet.
Step-by-step explanation:
The square feet the architect must inspect represents the lateral surface area of the square pyramid. Since the base of the pyramid is a regular polygon, a square, then the given formula can be used. Let P be the perimeter of the base and l be the slant height of 274 feet.
Find the perimeter of the base by multiplying the length of a side, 339 feet, by the number of sides of the base, 4.
So, the architect will need to inspect 185,772 square feet of the pyram
The total of 109327.5 feet² of the square area the architect needs to inspect.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
There are many types of triangles such that right angle triangle, equilateral triangle, and much more.
A pyramid consists of 3 equal triangles given that the vertical height of a triangle is 215 feet, and the base is 339 feet.
Area of one triangle = (1/2) × base × height.
⇒ (1/2) × 339 × 215
⇒ 36442.5
Since in a pyramid, there are a total 3 triangles so
Total surface area = 3 × surface area of 1 triangle.
Total surface area = 3 × 36442.5 = 109327.5 hence correct answer will be 36442.5.
For more about triangles,
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Please help!! Will mark brainlyest.
Answer:
Answer:
47
Step-by-step explanation:
a)
a^2 + b^2 = c^2
33^2+33^2=c^2
2178=c^2
c=(nearest is 47)
b)
If you cut the square in half diagonally, it forms two right triangles with angle measures 90-45-45. You can use sin (opposite over hypotenuse) to find the length of the hypotenuse. sin (45) would be 33/(hypotenuse length). From a trig chart, you can find that sin (45) is 1/sqrt(2), meaning that 33/x = 1/sqrt(2). This means that x=33sqrt(2), which is around 47.
Step-by-step explanation:
what is the expression to (4×+3)+(-2×+4)
Answer:
4x(3-2)
Step-by-step explanation:
since in 2 groups, there are number 4 in common
Apply Distributive Law to achieve this.
Darlene picked 7 apples. Juan picked 4 times as many as Darlene. How many apples did Juan pick?
What equation represents this situation?
Group of answer choices
7*4=a
7-4=a
a-7=4
a*4=7
Good luck
Answer:
ok, i think this would be.....a.
Step-by-step explanation: so i know 7x4=28 so 7*4=a makes sense cause a = 28
have a nice day
Ming was planning a trip to western smaoa be fore she was going she did some research and learned that the exchange rate is 6 tala for 2$ how many tala would she get if she exchanged 6$
Answer:
18 tala
Step-by-step explanation:
The exchange is proportional, so the number of tala Ming receives will be proportional to the number of dollars she exchanges.
x / ($6) = 6 tala / ($2)
__
Multiplying by $6, we have ...
x = (6 tala)($6/$2) = 18 tala
Ming would get 18 tala when exchanging $6.
Pls and help me with this !!!
Answer:
#20 is -20
#21 is -3
#22 is 36
A certain circle can be represented by the following equation. x^2+y^2+16x-14y+49=0x 2 +y 2 +16x−14y+49=0x, squared, plus, y, squared, plus, 16, x, minus, 14, y, plus, 49, equals, 0 What is the center of this circle ? ((left parenthesis ,,comma ))right parenthesis What is the radius of this circle ? units
Answer:
center = (-8, 7)
radius = 8 units
Step-by-step explanation:
Equation of a circle: [tex](x-h)^2+(y-k)^2=r^2[/tex]
(where (h, k) is the center of the circle and r is the radius)
Rewrite the given equation:
[tex]x^2+y^2+16x-14y+49=0[/tex]
[tex]\implies x^2+16x+y^2-14y+49=0[/tex]
[tex]\implies (x+8)^2-64+(y-7)^2-49+49=0[/tex]
[tex]\implies (x+8)^2+(y-7)^2=64[/tex]
Therefore:
center = (-8, 7)radius: [tex]r^2=64 \implies r=\sqrt{64} =8[/tex]Answer:
The circle is centered at (8,0)
The circle has a radius of 10 units.
Step-by-step explanation:
trust
Groceries R Us is selling 8 apples for $2.80.
Food Galore is selling 6 apples for $2.16.
Shop Here is selling 4 apples for $1.42.
Find their unit rates. Which store has the best deal?
Answer:
Groceries R Us
Step-by-step explanation:
i dont know how to explain lol
A rancher wants to fence in an area of 1000000 square feet in a rectangular field and then divide it in half with a fence down the middle, parallel to one side. What is the shortest length of fence that the rancher can use
The shortest length of the fence used by the rancher in a rectangular field of 1000000 square feet is 4899 ft.
What is the area of a rectangle?The area of a rectangle is a region enclosed in four corners where two opposite sides are equal. The area of the rectangle is mathematically expressed as:
Area of a rectangle = length(x) × breath(y)
1000000 sq.ft = (x) × (y) ---- (1)
However, to determine the fencing, we have:
Length of fencing = 2x + 2y
since the rectangle has four sides and opposite sides are equalSuppose we use the x-direction to estimate the region where the fencing is located, we have:
Length of fencing = 2x + 2y + x
Length of fencing = 3x + 2y ---- (2)
From equation (1), make (y) the subject of the formula and replace the value of y with equation (2)
The Length of fencing is:
[tex]\mathbf{L = 3x - 2( \dfrac{1000000}{x})}[/tex]
[tex]\mathbf{\dfrac{dL}{dx} = 3 - \dfrac{2000000}{x^2} = 0}[/tex]
[tex]\mathbf{ x^2= \dfrac{2000000}{3} }[/tex]
[tex]\mathbf{ x= \dfrac{1000\sqrt{2}}{\sqrt{3}} }[/tex]
[tex]\mathbf{x = \dfrac{1000 \sqrt{6}}{3}}[/tex]
Now, if we replace the value with equation (1), then y will be:
[tex]\mathbf{y = \dfrac{1000000}{\dfrac{1000 \sqrt{6}}{3}} }\\ \\ \\ \\ \mathbf{y = \dfrac{3000 }{\sqrt{6}}}[/tex]
[tex]\mathbf{x =500\sqrt{6}}[/tex]
Now, the shortest length of the fencing can be computed by using the equation (2):
L = 3x + 2y
[tex]\mathbf{L = 3( \dfrac{1000 \sqrt{6}}{3}) + 2(500 \sqrt{6})}[/tex]
[tex]\mathbf{L =1000 \sqrt{6} + 1000 \sqrt{6}}[/tex]
[tex]\mathbf{L =2000 \sqrt{6} }[/tex]
[tex]\mathbf{L \simeq 4899 \ ft}[/tex]
Learn more about the area of a rectangle here:
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Kavya is surveying how seventh-grade students get to school. In her first-
period class, 10 out of 32 students ride the bus to school. There are 160
students in seventh grade. Based on her survey, how many seventh-grade
students can she predict ride the bus to school?
• A. 40
B. 138
• C. 50
• D. 512
Please help I’ll give brainlist to the first person to answer and the answer is correct please help!! Fast hurry!!!
There are 50 seventh-grade students who can she predict riding the bus to school.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
The unitary method is a method by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.
We are given that first-period class, 10 out of 32 students ride the bus to school. There are 160 students in seventh grade.
Therefore, we have;
160/32=5
10 x 5 =50
Thus, the answer is 50
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Keisha makes individual servings of nuts by dividing 4 1/2 cups of nuts into individualcup servingsHow many individual 3 8 . servings can Keisha make?Show work
Answer:
4 1/2 = 9/2
Dividing 9/2 by 3/8,
9/2 x 8/3 = 72/6 = 12
Therefore, Keisha made 12 individual servings.