Answer:
The between the given vector and the positive direction of the x-axis is approximately 41.186º.
Step-by-step explanation:
Let be [tex]\vec u = 8\,i + 7\,j[/tex] and [tex]\vec v = i[/tex] (Positive direction of the x-axis), the angle between both vectors can be determined from definition of dot product:
[tex]\vec u \bullet \vec v = \|\vec u\|\cdot \|\vec v\| \cdot \cos \theta[/tex]
Angle is cleared:
[tex]\cos \theta = \frac{\vec u\bullet \vec v}{\|\vec u\|\cdot \|\vec v\|}[/tex]
[tex]\theta = \cos^{-1}\left(\frac{\vec u \bullet \vec v}{\|\vec u\|\cdot \|\vec v\|} \right)[/tex]
The norms of [tex]\vec u[/tex] and [tex]\vec v[/tex] are found by Pythagorean Theorem:
[tex]\|\vec u\| = \sqrt{8^{2}+7^{2}}[/tex]
[tex]\|\vec u\| \approx \sqrt{113}[/tex]
[tex]\|\vec v\| = 1[/tex]
The dot product between both vectors is:
[tex]\vec u \bullet \vec v = (8)\cdot (1) + (6)\cdot (0)[/tex]
[tex]\vec u \bullet \vec v = 8[/tex]
The angle is now calculated:
[tex]\theta = \cos^{-1}\left(\frac{8}{\sqrt{113}} \right)[/tex]
[tex]\theta \approx 41.186^{\circ}[/tex]
The between the given vector and the positive direction of the x-axis is approximately 41.186º.
Your favorite dog groomer charges according to your dog’s weight. If your dog is 15 pounds and under, the groomer charges $35. If your dog is between 15 and 40 pounds, she charges $40. If your dog is over 40 pounds, she charges $40, plus an additional $2 for each pound over 40 pounds.
A. Write a piecewise function for the cost of a dog grooming based on the number of pounds at this grooming salon.
B. Sasha weighs 30 pounds, Link weighs 15 pounds, and their friend Bailey weighs 85 pounds. How much will it cost them all together to get groomed?
Answer:
it would cost them $100
Answer:
it would cost them $100
Step-by-step explanation:
Write the equation of the line with slope = -3 and passes through (2,7)
Answer:
Step-by-step explanation:
y - 7 = -3(x - 2)
y - 7 = -3x + 6
y = -3x + 13
Zero equals two-thirds a number decreased by twelve?
Answer:
X= 12 or 18 (see below)
Step-by-step explanation:
This could be read two different ways.
0=2/3x-12
12=2/3x
12÷2/3=x
12*3/2=x
18=x
—-OR—-
0=2/3(x-12)
0=2/3x-8
8=2/3x
8÷2/3=x
8*3/2=x
12=x
When finding all the roots of polynomials, how do you find the possible rational zeros to know which numbers you plug back into the function to get the number you synthetically divide by?
Answer:
You would have to break the polynomial down into smaller binomials or monomials. Take x^2-6x-9 for instance. It would break down into (x+3)(x-3) through the a^2+2ab+b^2 formula. After that set the two nomials equal to zero and solve for x. After that, you would plug back in x to see whatever x works. You may more than two nomials after breaking it apart so keep that in mind.
You have been assigned the job of doubling an investment by putting it in an account that earns 8% simple interest annually. About how many years will it take for this to happen?
Answer:
12.5
Step-by-step explanation:
100 ÷ 8 = 12.5, so it'll take 12.5 years to double
Answer:
12.5
Step-by-step explanation:
Which pair of expressions have equivalent values?
Answer:
5 + y - 2 - 6 y + y; 8 y + 3
Step-by-step explanation:
A research team aboard an underwater research vessel descends 1,500 feet beneath the surface of the water. They then rise 525 feet and descend again 350 feet. Where are they currently located?
Answer:
-1,325 ft below sea level
Step-by-step explanation:
0(surface level) - 1,500 = -1,500
-1,500 + 525 = -975
-975 - 350 = -1,325
Answer:
they are currently at -1325 ft.
Step-by-step explanation:
first yo go up or in other words you subtract 525 to 1500 which gives you 973 then they descend 350 so they are going back down so you add 350 onto 975
-61 times the difference between a number and 56 is equal to the number plus – 28.
Solve the equation for z. Express your answer as an integer, a reduced fraction, or a decimal number rounded to two places.
Answer:
1722/31 or 55.55
Step-by-step explanation:
We need to write an equation.
-61( z - 56 ) = z - 28
-61z + 3416 = z - 28
-61z + 61z + 3416 = z + 61z - 28
3416 = 62z - 28
3416 + 28 = 62z - 28 + 28
3444 = 62z
3444/62 = 62z/62
3444/62 = z
Since 3444/62 isn't a whole number let's reduce
3444/2 = 1722 62/2 = 31
1722/31 is our reduced fraction
Plug it into a calculator 55.5483 but rounded to two decimal places is 55.55
The height of a helicopter above the ground is given by h=3.00t3, where h is in meters and t is in seconds. After 2.00 s, the helicopter releases a small mailbag. How long after its release does the mailbag reach the ground?S
Answer:
7.96 s
Step-by-step explanation:
Given the following :
h = 3t³
After t seconds, that is, t = 2
h = 3(2)³ = 3 × 8 = 24 m
Rate of change, Velocity = dh/dt
dh/dt = 3*3t^(3 - 1) = 3*3t² = 9t²
At t = 2 s ; initial velocity = 9(2)² = 9 × 4 = 36 m/s
From the 3rd equation of motion:
v² = u² + 2gh
Where g = acceleration due to gravity 9.8m/s
upward motion, g = - ve
Displacement = - 24
v² = 36² + 2(-9.8)(-24)
v² = 1296 + 470.4
v² = 1766.4
v = sqrt(1766.4)
= 42.03 m/s
Since final velocity is in downward direction : take it as negative.
Recall, :
Velocity = Displacement / time
Displacement = Velocity × time
Average Velocity = (Initial + final velocity) / 2
Displacement = - 24 m
-24 = [(36 + (-42.03)) /2] × t
-48 = - 6.03t
t = 48 / 6.03
t = 7.96s
-43 times the difference between a number and 74 is equal to the number plus - 64.
Answer: -43( n - 74) = n + (-64)
Step-by-step explanation:
The statement can be represented by the equation
-43( n - 74) = n + (-64) where n is the number
Answer:
[tex]\huge\boxed{-43(n-74)=n+(-64)}\\\boxed{n=\dfrac{1623}{22}=73\dfrac{17}{22}}[/tex]
Step-by-step explanation:
[tex]n-\text{a number}\\\\\text{the difference between a number and 74}:\ n-74\\\\\text{-43 times the difference between a number and 74}:\ -43(n-74)\\\\\text{the number plus - 64:}\ n+(-64)\\\\\text{The equation}:\\\\-43(n-74)=n+(-64)[/tex]
[tex]solution[/tex]
[tex]-43(n-74)=n+(-64)\qquad/\text{use the distributive property}\\\\(-43)(n)+(-43)(-74)=n-64\\\\-43n+3182=n-64\qquad/\text{subtract 3182 from both sides}\\\\-43n=n-3246\qquad/\text{subtract}\ n\ \text{from both sides}\\\\-44n=-3246\qquad/\text{divide both sides by (-44)}\\\\n=\dfrac{-3246}{-44}\\\\n=\dfrac{3246:2}{44:2}\\\\\boxed{n=\dfrac{1623}{22}=73\dfrac{17}{22}}[/tex]
Determine the scale factor for a circle with radius 9 in. to a circle with diameter 24 in. Type your answer as a fraction.
Answer:
bhhhhhhhhhhhhhhhhbhbhb
Step-by-step explanation:
3/4 is the scale factor for a circle with radius 9 in to a circle with diameter 24 in.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
The scale factor of a circle to another is the ratio of their radii
Radius of the first circle = 9 in
Diameter of the second circle = 24 in
Radius = Diameter / 2
Radius of the second circle = 24 / 2
Radius of the second circle = 12 in
Scale factor = (Radius of the first circle) / (Radius of the second circle)
Scale factor = 9/12
Scale factor = 3/4
Hence, 3/4 is the scale factor for a circle with radius 9 in to a circle with diameter 24 in.
To learn more on Circles click:
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35 out of 14 is what percentage
Answer:
40% is the answer. Hope this helped you
Answer:
The answer is 40%
Hope this answeris helpful...
Hope this answeris helpful...Make me as brainliest.....
Diego and Anya live 72 miles apart. They both meet at
their favorite restaurant, which is (16x – 3) miles from
Diego's house and (5x + 2) miles from Anya's house.
Diego argues that in a straight line distance, the restaurant
is halfway between his house and Anya's house. Is Diego
right? Justify your reasoning.
Answer:
The restaurant is not at half way
Step-by-step explanation:
Given
[tex]Total\ Distance = 72[/tex]
[tex]Diego = 16x - 3[/tex]
[tex]Anya = 5x + 2[/tex]
Required
Accept or reject Diego's claim
To do that, we need to determine the value of x by:
Diego + Anya =Total Distance
Substitute values for each parameter
[tex]16x - 3 + 5x + 2 = 72[/tex]
Collect Like Terms
[tex]16x + 5x = 72 + 3 - 2[/tex]
[tex]21x = 73[/tex]
Divide both sides by 21
[tex]x = \frac{73}{21}[/tex]
Substitute the value of x in Diego and Anya's distance
[tex]Diego = 16x - 3[/tex]
[tex]Diego = 16 * \frac{73}{21} - 3[/tex]
[tex]Diego = \frac{1168}{21} - 3[/tex]
[tex]Diego = \frac{1168 - 63}{21}[/tex]
[tex]Diego = \frac{1105}{21}[/tex]
[tex]Diego = 52\frac{13}{21}[/tex]
[tex]Anya = 5x + 2[/tex]
[tex]Anya = 5 * \frac{73}{21} + 2[/tex]
[tex]Anya = \frac{365}{21} + 2[/tex]
[tex]Anya = \frac{365 + 42}{21}[/tex]
[tex]Anya = \frac{407}{21}[/tex]
[tex]Anya = 19\frac{8}{21}[/tex]
Since, both distances are not equal,
Then Diego's claim is false and incorrect
which number line shows the solution to -3-{-1}?
Answer:
please send the picture of the number line.
Answer:me not know
Step-by-step explanation:
Hehuehuejejejje
Rewrite the following expression as a single logarithm: log7(x2+5x−14)−log7(x+7)
Answer:
log7(x-2)
Step-by-step explanation:
Use of property: log(ab) = log(a) + log(b)
log7(x²+5x−14)−log7(x+7) = log7(x+7)(x-2) - log7(x+7) =log7(x+7) + log7(x-2) - log7(x+7) = log7(x-2)how do you find the area of a partial circle
Answer:
Divide!
Step-by-step explanation:
Find the area of the whole circle then divide it by whatterver percent of the circle you are looking at....
What is the answer for 29+n=13
Answer:
n=-16
Step-by-step explanation:
Answer:
n = - 16.............
................
Solve (x + 2)(2x + 3) = 6 {-2, -3/2} {-7/2, 0} {0}
Answer:x=−3/2 or x=−2
Step-by-step explanationLet's solve your equation step-by-step.
(x+2)(2x+3)=6(−2−3/2)(−7/2(0))(0)
Step 1: Simplify both sides of the equation.
2x2+7x+6=0
Step 2: Factor left side of equation.
(2x+3)(x+2)=0
Step 3: Set factors equal to 0.
2x+3=0 or x+2=0
x=−3/2 or x=−2
The sum of five times a number, and 1, is equal to four times the number
I need help with the
translation part!
Answer:
5x + 1 = 4x
You can really put any letter for "a number":
5n + 1 = 4n
Lisa purchased a hat for $10, a purse for $20, and a book for $23. The sales tax rate was 7.2 percent. What was the total amount she paid?
Answer:
$56.82
Step-by-step explanation:
The sum of all the stuff she bought is 10+20+23, so 53.
Now you need to find the tax, so you multiply 53 x 7.2%, and to change a % to a number you move the decimal place two to the left, so you get .072
$53 x .072 = $3.816 sales tax
$53 for the stuff plus $3.816 tax = $56.816
and since money is only two decimal places and the 6 is higher than 5, you have to round up to the nearest penny, so $56.82!
Answer:
56.81$ she paid
Step-by-step explanation:
Can you help me please
Answer:
what is your question ? and where are these points that you are talking about?
Which number has an 8 that is 1/10 the value of the 8 in 78?
Step-by-step explanation:
Step one:
Firstly we need to determine the place value of 8 in the term 78
in the term, we have 7 tens and 8 units
hence the place value of 8 in 78 is the units
Step two:
Now 1/10 of 8 is given as
0.1*8= 0.8
According to the problem statement, we are expected to find a number that has an 8 that is the same as 0.8.
Say 5.8, 6.8, 9.8
we cannot say exactly, but any number that has an 8 that is one decimal away is an equivalent
Evaluate the expression when a=-7. a^2+4a-2
Plug in the value to solve the expression.
[tex](-7)^2+4(-7)-2[/tex]
[tex]49-28-2[/tex]
[tex]19[/tex]
Hope this helps.
頑張って!
Hey there!
a^2 + 4a - 2
= -7^2 + 4(-7) - 2
= -49 - 28 - 2
= -77 - 2
= -79
Therefore, your answer is: -79
Therefore, your answer is: -79
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Mark made a business trip of 259.5 miles. He averaged 59 mph for the first part of the trip and 57 mph for the second part. If the trip took 4.5 hours, how long did he
travel at each rate?
Answer: He spends 1.5 hours on the first part of trip and 3 hours on the second part of trip
Step-by-step explanation:
Let x = the number of hours for first part
Let y = the number of hours for second part
Concept: speed × time = distance
----------------------------------------------------------------
x+y=4.5
59x+57y=259.5
-----
y=4.5-x
59x+57y=259.5
-----
59x+57(4.5-x)=259.5
59x+256.5-57x=259.5
2x+256.5=259.5
2x=3
x=1.5
4.5-1.5=3 hrs
Find the 44th percentile, P44, from the following data! pls help
Answer:
[tex] P_{44} = 29.9 [/tex]
Step-by-step Explanation:
The 44th percentile, [tex] P_{44} [/tex], of the given data can be calculated using the kth formula for percentile given as:
[tex] i = \frac{k}{100}(n + 1) [/tex]
where,
i = the ranking or the position of the percentile = ?
k = the percentile = 44
n = total number of the given data values = 23
Plug in the values into the formula to find "i"
[tex] i = \frac{44}{100}(23 + 1) [/tex]
[tex] i = \frac{44}{100}(24) [/tex]
[tex] i = \frac{1,056}{100} [/tex]
[tex] i = 10.56 [/tex]
Since "I", 10.56, is not an integer, round the number down, and round it up to the nearest integer, then look for the position each occupy in the ordered data set, and find their average.
Thus,
[tex] i_{down} = 10.56 = 10 [/tex]
[tex] i_{up} = 10.56 = 11 [/tex]
The data occupying the 10th position on the data set = 28.7
11th = 31.1
[tex] P_{44} = \frac{28.7 + 31.1}{2} = \frac{59.8}{2} [/tex]
[tex] P_{44} = 29.9 [/tex]
Which two numbers does 128 lie between on a number line?
Answer:
So the answer is:
127 and 129
Natural resources that are used to make goods and services are considered _____. Equipment Money Land Labor
natural resources that are used to make goods and services are considered land
hope that helped :))
how many times greater is the value of the 3 in 4,367 than the value of the 3 in 39?
Answer: Roughly 111.97
Step-by-step explanation:
1. 39 divided by 3 is 13.
2. 4367 divided by 3 is not evenly distributed. Rounding, it would work out to be roughly 1455.66
3. 1455.66 divided by 13 is roughly 111.97 (Again, this does not distribute evenly)
4. To check your work, multiply 111.97 times 13 and you should get somewhere around 1455.66 which is (4367 divided by 3).
Hopefully this helps! Feel free to mark brainliest! :)
Perform the indicated operation. y^2 + 3y-10/3y+15 divided (10-5y)
Answer:
-1/15
Step-by-step explanation:
(y^2+3y-10)/(3(y+5)) / (5(2-y))
-----
Factor::
[(y+5)(y-2)/(3(y+5))] / (-5(y-2))
--------------
Cancel (y+5) and (y-2) to get::
= -1/15
The coordinates of the point 3/10 of the way from A to B are _
Answer:
(-1, -4.8)
Step-by-step Explanation:
Let the point be P, which is 3/10 of the way from A to B. This means, it divides P into AP and PB in the ratio, 3:10 = AP/PB = 3/10.
Apply the formula for internal division to find the coordinates which is given as:
[tex] x = \frac{mx_2 + nx_1}{m + n} [/tex]
[tex] y = \frac{my_2 + ny_1}{m + n} [/tex]
Where,
[tex] A(-4, -8) = (x_1, y_1) [/tex]
[tex] B(9, 6) = (x_2, y_2) [/tex]
[tex] m = 3, n = 10 [/tex]
Plug in the necessary values to find x and y coordinates for point P
[tex] x = \frac{mx_2 + nx_1}{m + n} [/tex]
[tex] x = \frac{3(9) + 10(-4)}{3 + 10} [/tex]
[tex] x = \frac{27 - 40}{13} [/tex]
[tex] x = \frac{-13}{13} [/tex]
[tex] x = -1 [/tex]
[tex] y = \frac{my_2 + ny_1}{m + n} [/tex]
[tex] y = \frac{3(6) + 10(-8)}{3 + 10} [/tex]
[tex] y = \frac{18 - 80}{13} [/tex]
[tex] y = \frac{-62}{13} [/tex]
[tex] y = \frac{-62}{13} [/tex]
[tex] y = -4.8 [/tex]
The coordinates of the point 3/10 of the way from A to B are (-1, -4.8)
Answer:
(0.2,-2.3)
Step-by-step explanation: