[tex]~~~~~~~~~~~~\textit{angle between two vectors } \\\\ cos(\theta)=\cfrac{\stackrel{\textit{dot product}}{u \cdot v}}{\underset{\textit{magnitude product}}{||u||~||v||}} \implies \measuredangle \theta = cos^{-1}\left(\cfrac{u \cdot v}{||u||~||v||}\right) \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} 6i-4j\\ 2i-6j \end{cases}\implies \stackrel{\qquad a~\hfill b\qquad }{\begin{array}{llll} < 6~~,~~-4 > \\ < 2~~,~~-6 > \end{array}}[/tex]
[tex]\stackrel{\textit{\Large dot product}}{ < 6~~,~~-4 > \cdot < 2~~,~~-6 > \implies (6\cdot 2)+(-4\cdot -6)}\implies 12+24\implies 36 \\\\\\ \stackrel{\textit{\Large magnitudes}}{|| < 6~~,~~-4 > ||\implies \sqrt{6^2+(-4)^2}\implies \sqrt{52}} \\\\\\ || < 2~~,~~-6 > ||\implies \sqrt{2^2+(-6)^2}\implies \sqrt{40} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\measuredangle \theta =cos^{-1}\left( \cfrac{36}{\sqrt{52}\cdot \sqrt{40}} \right)\implies \measuredangle \theta =cos^{-1}\left( \cfrac{36}{\sqrt{52}\cdot \sqrt{40}} \right) \\\\\\ \measuredangle \theta =cos^{-1}\left( \cfrac{36}{\sqrt{2080}} \right)\implies \measuredangle \theta \approx 37.9^o[/tex]
Who ran at a faster constant rate and which equation represents the relationship between Paul's distance and his time
A = Paul ran at a slower constant speed than Melinda, y=1x x being time in hours y being the distance in miles Paul ran
B = Paul ran at a slower constant speed than Melinda, y =3x x being time in hours, y being distance in miles Paul ran
C = Paul ran at a faster constant speed than melinda, y =5x where x is the time in hours and y is the distance in miles Paul ran
D = Paul ran at a faster constant speed than melinda, y =7x x being time in hours and y is the distance in miles Paul ran
Given the proportional relationship representing the speed, Paul ran faster. The equation for Paul is, y = 7x (Option D).
What is the Equation of a Proportional Relationship?Proportional relationship between two variables that has a constant rate or unit rate of m, is given as y = mx.
In a graph, the steeper the slope, the larger the constant rate or unit rate.
The graph for Paul is steeper than that of Melinda. Since Melinda's constant speed is 5, therefore, Paul's constant speed cannot be less than 5. It should be more than 5, i.e. 7.
This means that Paul ran at a faster constant speed than Melinda did.
Paul's equation for distance covered over time can be expressed as, y = 7x. (Option D).
Learn more about proprotional relationship on:
https://brainly.com/question/15618632
Write two equivalent expressions to represent the sum of the angles of this triangle.
please help I can't remember how find the sums of a triangles angles
100 points
Answer:
Step-by-step explanation:
The 3 angles add up to 180 degrees
2y + 2y + 5y = 180
9y = 180
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
As we know, Sum of all three Angles of Triangle is equal to 180° [ by Angle sum property of triangle ]
So, the required expression is :
[tex]\qquad \tt \dashrightarrow \:5y + 2y + 2y = 180[/tex]
or
[tex]\qquad \tt \dashrightarrow \:9y = 180[/tex]
if you solve for y, you will get y = 20°
And the angles as 100°, 40° and 40°
Find the value of csc 0 if cos 0 = -3/5 and 0 is in the second quadrant.
we know that the cos(θ) is -(3/5), however θ is in the II Quadrant, where the cosine is negative whilst the sine is positive, meaning the fraction is really (-3)/5, so
[tex]cos(\theta )=\cfrac{\stackrel{adjacent}{-3}}{\underset{hypotenuse}{5}}\qquad \qquad \textit{let's find the \underline{opposite side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]
[tex]\pm\sqrt{5^2-(-3)^2}=b\implies \pm\sqrt{25-9}=b\implies \pm 4=b\implies \stackrel{II~Quadrant}{+4=b} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill csc(\theta )=\cfrac{\stackrel{hypotenuse}{5}}{\underset{opposite}{4}}~\hfill[/tex]
Determine the surface area of each triangular prism. Round to the nearest tenth if necessary.
Answer:
108 cm^2211.2 cm^2308.8 mm^2560 yd^2Step-by-step explanation:
In each case, you can use the given formula to find the surface area. The area of the triangular base (B) is ...
A = 1/2bh
where b is the base of the triangle, and h is the height of the triangle perpendicular to that base.
You will notice that B is multiplied by 2 in the area formula, because there is a triangular base at either end of the prism. That means we can save some work by not multiplying by 1/2, and then by 2.
__
For figures 1, 3, 4, the triangle is a right triangle, so the base and height make up two of the three sides of it. The perimeter is finished by adding the length of the hypotenuse. That sum is then multiplied by the "height" of the prism (distance between bases) to find the lateral area as part of the area formula (Ph).
In figure 3, the triangle is equilateral, so the perimeter is not the sum of the base and height and a third side. In the attached spreadsheet, we have used a value "rest of perimeter" to make the sum be the right value for use in computing the value of Ph. For figure 3, that is 6+6-5.2=6.8. Then the sum 6 +5.2 +6.8 is 18, the proper perimeter for that figure.
__
The idea here is to let a spreadsheet do the tedious work of applying the same formula to different sets of numbers. The areas are ...
108 cm^2211.2 cm^2308.8 mm^2560 yd^2__
By way of example, we can "show work" for problem 1:
1. S = Ph +2B
S = (4 +3 +5)(8) +2(1/2)(4)(3) = 12(8) +12 = 96 +12 = 108 . . . cm^2
Please help 10 points
Answer:
your answer to this question is option c
please consider as brainlest if i helped you
PLS HELP GIVING 11 POINTS
Answer:
3. 40 4. 132
Step-by-step explanation:
you multiply the length and the width
Answer:
3. 40. 4. 132
Step-by-step explanation:
You find the area by doing base x height so 10 x 4 is 40 and 12 x 11 is 132.
Rose is 60 inches tall. How many feet tall is Rose?
Enter the correct answer in the box.
Answer: 5 feet
Step-by-step explanation:
Answer: 5 feet
Step-by-step explanation:
Please help with this easy math problem. Due soon.
Answer:
Step-by-step explanation:
Exponential equation:
[tex]\boxed{y=a*b^{x}}[/tex]
Choose the point whose x-coordiante is 0, so that we can find the value of a. (0,2)
[tex]2 = a*b^0\\\\2 = a*1 \ [\text{\bf any \ variable raised to 0 is 1}][/tex]
[tex]\sf \boxed{a = 2}[/tex]
Now, choose (1 , 1) and find the value of b
[tex]1 = 2*b^{1}\\\\1 = 2*b\\\\\dfrac{1}{2}=b[/tex]
Exponential equation:
[tex]\bf \boxed{y =2* \left(\dfrac{1}{2}\right)^{x}}[/tex]
Please help fast. PLEASE PLEASE PLEASE
Answer:
D
Step-by-step explanation:
By subtracting the second part of the equation, you are doing the same as adding a negative.
What are the coordinates of point B' after
AABC is reflected across the y-axis?
5 y
А
В'
?
?
с
B (3,2
-5
0
-5
Answer:
B'(-3, 2)
Step-by-step explanation:
The rule for a reflection over the y-axis is (x, y) → (-x, y)
This means that the x-values change while the y-values stay the same.
B(x, y) → (-x, y)
B(3, 2) → (-3, 2)
B'(-3, 2)
Hope this helps!
Do number 7 please thanks
Answer:
120%
Step-by-step explanation:
1998/1665 = 1.2
1.2x100 = 120%
PLS HELP
No links pls and Ty <33!!!
Answer:
C = 2πr = 2·π·20 ≈ 40π ft (125.6)
How can I save the earth
Answer:
Recycling etc.
Step-by-step explanation:
Eliminate Waste from Lunches.
Stop Littering.
Reduce Paper Consumption.
Save Electricity.
Save Water.
Swap Regular School Supplies.
Bring Reusable Bags to the Grocery Store.
Walk to School or Take a Bike, Avoid Taking Cars or Carpool When Possible.
The school auditorium has 448 seats arranges in 32 equal rows. How many seats are in each row?
Where is the removable discontinuity of f (x) = startfraction x 5 over x squared 3 x minus 10 endfraction located? x = –5 x = –2 x = 2 x = 5
The removable discontinuity of the function f(x) = (x+5)/(x^2 +3x-10) is at x = -5 (given by Option A).
What are discontinuities?Holes in the graph of function, where its undefined, or non-continuous, is called discontinuity.
The points in the domain of the function over which its not continuous, is called point of discontinuity for that function.
What is removable discontinuity?A discontinuity is removable if the limit of the function at the point of discontinuity exists but this limiting value is not the value of the function at that point.
We can remove that discontinuity by making the value of the function equate to the limiting value of the function at that point.
The given function is:
[tex]f(x) = \dfrac{(x+5)}{(x^2 +3x-10)}[/tex]
Factoring the denominator, we get:
[tex]x^2 + 3x -10 = x^2 + 5x - 2x - 10 =x(x+5) - 2(x+5) = (x+5)(x-2)[/tex]
Therefore, we get:
[tex]f(x) = \dfrac{(x+5)}{(x+5)(x-2)}[/tex]
The function is not defined if x = -5, or x = 2 since at those places, the denominator would become 0. (we cannot cancel out (x+5) from numerator and denominator for all x, as it isn't defined for x = -5
Also, we have:
[tex]\lim_{x\rightarrow 2}f(x)= \infty\\\lim_{x\rightarrow -5}f(x) = \lim_{x\rightarrow -5}\dfrac{(x+5)}{(x+5)(x-2)} = \lim_{x\rightarrow -5}\dfrac{1}{(x-2)} = -\dfrac{1}{7}[/tex]
We cancelled out (x+5) from numerator and denominator because x is limiting to -5 but isn't equal to -5.
For discontinuity of x = -5, the limit of f(x) exist (left and right limit both will come as 1/3). But f(-5) is not defined. So we can remove this discontinuity by defining f(-5) = 1/3 and for rest of the values of x, it is same as before.
Thus, the removable discontinuity of the function f(x) = (x+5)/(x^2 +3x-10) is at x = -5 (given by Option A).
Learn more about discontinuities here:
https://brainly.com/question/7327714
Answer: Option A -5
Step-by-step explanation: Just took the test
PLEASE CHOSE THE RIGHT ANSWER AND EXPLAIN WHY YOU CHOSE IT PLEASE
Answer:
D
Step-by-step explanation:
See attached image.
What is the measure of the missing angle:
1150
75°
?
750
40°
40°
35°
Answer: The measure of the missing angle is 115∘.
Step-by-step explanation: To find missing interior angles, you have to add the two angles that are known and see how much they add up. The work is done below:
40∘ + 75∘ = 115∘.
In order to find out the missing interior angle, we have to subtract 115∘ from 180∘ to find that angle:
180∘ - 115∘ = 65∘, which is the missing angle that is inside the triangle.
Now, you're probably wondering how any of this has to do with finding the angle that has a ? on it. Well, us finding the missing interior angle inside of the triangle is what's going to help us find that angle with a ? on it. To find that angle, you need to subtract 65∘ from 180∘ to find the angle that you need:
180∘ - 65∘ = 115∘.
Therefore, 115∘ is your answer.
Let me know if this is right! :)
can someone help me with this I don't get it and I need help?
Answer:
Its a graph. Each of those black dots represent a person answering the survey. For example: 2 people only chose 3 letters, 1 person only chose 4 letters, 2 people chose 5 letters, and so on. So the answer is 10. Hope this helps!
Step-by-step explanation:
Lin goal is to drink 8 cups of water every day she drags 37 oz of for lunch today how much more water does Linda need to drink today to reach her goal
Answer: 27
Step-by-step explanation:
8 cups of water is 64 Ounce. If she had 37, She needs 64 - 37 To balance up
What is the total price of a boat with an original price of 12916$, if it is sold at a 15% discount? The sales tax rate is 3 3/4 %
Answer:
$11390.30
Step-by-step explanation:
Discount
12916 x 0.15 = 1937.4
Discounted price
12916 - 1937.4 = 10978.6
Tax of 3 and 3/4 percent which I think is 0.0375
10978.6 x 0.0375 = 411.6975
Total
10978.6 + 411.6975 = $11390.2975
Daniel used 4 strawberries and 12 blueberries to make a parfait. What was the ratio of the number of strawberries to the number of blueberries in the parfait?
A- 1:2
B- 1:3
C- 1:4
D- 1:6
Answer:
C- 1:3
Step-by-step explanation:
You have to simply 4 and 12, which becomes 1 and 3 (by dividing both numbers by 4). Then I guess you just keep a colon symbol in between 1 and 3.
Help me why is it this answer? How do i solve that type of math problem green is the answer
Answer:
To increase a price, add the percentage you wish to increase it by to 100%, convert the percentage into a decimal by dividing by 100, then multiply this by the original price.
To decrease a price, subtract the percentage you wish to decrease it by from 100%, convert the percentage into a decimal by dividing by 100, then multiply this by the original price.
-------------------------------------------------------------------------------------------------
100% represents the original price.
Therefore, 100% = $599.99
A 20% discount means that the price is now 80% of the original price,
as 100% - 20% = 80%
To find 80% of the original price, convert 80% to a decimal and multiply it by the original price:
80% = 80/100 = 0.8
Therefore, 80% of $599.99 = 0.8 x $599.99
= $479.992
Finally, we need to apply a sales tax of 6%. We can do this in 2 ways:
Way 1
Work out 6% of the discounted price, then add this to the discounted price to find the final price:
Sales tax = 6% of $479.992
= 0.06 x $479.992
= $28.79952
Final price = discounted price + sales tax
= $479.992 + $28.79952
= $508.79 (nearest cent)
Way 2
We need to increase the discounted price of $479.992 by 6%. Therefore, the final price will be 106% of the discounted price as
100% + 6% = 106%
Final price = 106% of discounted price
= 1.06 x $479.992
= $508.79 (nearest cent)
A train traveling at 40 mph can go 15 more miles in the same amount of time that a car can traveling at 30 mph can go. How far does the train go in the same amount of time?
Answer:
60
Step-by-step explanation:
After 1.5 hour the train travel 60 mille (1.5 × 40) and the car travel 45 (1.5 × 30) which make the train travel 15 more than the car at the same amount of time.
Use the number line to plot the numbers. then arrange them in order from smallest (1) to largest (4). startroot 0.2 endroot startroot 0.4 endroot 0.2 0.4
The number line is shown below. The numbers 0.2, 0.4, √0.2, and √0.4 are in ascending order.
What is a number line?
A number line is a line on which numbers are plotted in a particular interval.
The numbers are given below.
[tex]\sqrt{0.2}, \sqrt{0.4}, 0.2, 0.4[/tex]
Arrange in ascending order, then we have
[tex]0.2, 0.4, \sqrt{0.2}, \sqrt{0.4}[/tex]
Then mark these numbers on the number line.
The number line is shown below.
More about the number line link is given below.
https://brainly.com/question/13189025
Answer:
√0.2 ✔3
√0.4 ✔4
0.2 ✔1
0.4 ✔2
Step-by-step explanation:
My image shows that I got it correct on edge! Hope this helps:D
Sasha is making custom designs using the small trapezoidal prism she wants to cover each of the eight prisms in her current design in striped cloth on all sides she has 3500 cm² of stripped cloth does Sasha have enough cloth to cover all a prisms in her current design choose from the drop-down menu to correctly complete the statement
A 26 foot ladder is set against the side of a house so that it reaches up 24 feet. If Mila grabs the ladder at its base and pulls it 12 feet farther from the house, how far up the side of the house will the ladder reach now?
Answer
12 feet high
Step-by-step explanation:
If y varies directly as x, and y is 20 when x is 4, what is the constant of variation for this relation?
1/5
4/5
5
16
Answer:
Step-by-step explanation:
y = k*x This is the formula for a direct variation.
y = 20x = 4 Substitute these values into the direct variation20 = 4 * k Divide by 4
20/4 = 4k/4
k = 5
Answer: the constant of variation is 5
how many terms are in each factor of this expression?
5(6 + 4x)
Answer:
2 terms
Explanation:
[tex]\dashrightarrow \ \ \sf 5(6 + 4x)[/tex]
[tex]\dashrightarrow \ \ \sf 5(6) + 5(4x)[/tex]
[tex]\dashrightarrow \ \ \sf 30 + 20x[/tex]
"x" is one term and "30" which is a constant is another term.→ There are total two terms in this factor.
Answer:
2 Terms
Step-by-step explanation:
There will be two terms ..
=> 5(6 + 4x)
=> 30 + 20x
Two-thirds of a number increased by 3 is 11. What is the number?
Josh has a rewards card for a movie theater.
• He receives 15 points for becoming a rewards card holder.
• He earns 3.5 points for each visit to the movie theater.
• He needs at least 55 points to earn a free movie ticket.
Which inequality can Josh use to determine x, the minimum number of visits he needs
to earn his first free movie ticket?
PLSS HELPPPP =((( plss
Answer:
55 ≤ 3.5x + 15
Step-by-step explanation:
Missing Inequality.
Given that:
Josh has a reward card for movie theater.
He receives 15 points for becoming a rewards card holder.
He earns 3.5 points for each visit to the movie theater.
He needs at least 55 points to earn a free movie ticket.
To Find:
Which inequality can Josh use to determine x, the minimum number of visits he needs to earn his first free movie ticket?
Solution:
From the given we know that:
Points Josh received for becoming a member = 15
Points Josh received for visiting the moving theater = 3.5
Total points needed for a free movie ticket = 55
Note that:
< = Less than
> = Greater than
≤ = Less than or equal to
≥ = Greater than or equal to
Thus, We know that Josh need to get less than or equal to 55.
Therefore, we use this sign ≤
Since we know that we need to get less than or equal to 55 then
we get
55 ≤ 3.5x + 15.
Hence, the inequality that Josh can use to determine x, the minimum number of visits he needs to earn his first free movie tickets is:
55 ≤ 3.5x + 15
Kavinsky