1. The direction of the vector [tex]\theta[/tex] relative to the positive x-axis satisfies
[tex]\tan\theta=\dfrac35\implies\theta\approx30^\circ[/tex]
2. A vector with magnitude [tex]\|\mathbf v\|[/tex] and direction [tex]\theta[/tex] has component form
[tex]\mathbf v=\langle\|\mathbf v\|\cos\theta,\|\mathbf v\|\sin\theta\rangle[/tex]
We have [tex]\|\mathbf v\|=5[/tex], but "angle of 60 degrees with the negative x-axis" is a bit ambiguous. I would take it to mean "60 degrees counterclockwise relative to the negative x-axis", so that the direction is [tex]\theta=240^\circ[/tex]. Then
[tex]\mathbf v=\langle5\cos240^\circ,4\sin240^\circ\rangle\approx\langle-2.5,-4.3\rangle[/tex]
But this doesn't match any of the options, so more likely it means the angle is 60 degrees clockwise relative to the negative x-axis, in which case [tex]\theta=120^\circ[/tex] and we'd get
[tex]\mathbf v=\langle5\cos120^\circ,4\sin120^\circ\rangle\approx\langle-2.5,4.3\rangle[/tex]
3. Same as question 2, but now we're using [tex]\mathbf i,\mathbf j[/tex] notation. The vector has magnitude [tex]\|\mathbf v\|=14[/tex] and its direction is [tex]\theta=-30^\circ[/tex]. So the vector is
[tex]\mathbf v=14\cos(-30^\circ)\,\mathbf i+14\sin(-30^\circ)\,\mathbf j=12.1\,\mathbf i-7\,\mathbf j[/tex]
4. The velocity of the plane relative to the air, [tex]\mathbf v_{P/A}[/tex] is 175 mph at 40 degrees above the positive x-axis. The velocity of the air relative to the ground, [tex]\mathbf v_{A/G}[/tex], is 35 mph at 60 degrees above the positive x-axis. We want to know the velocity of the plane relative to the ground, [tex]\mathbf v_{P/G}[/tex].
We use the relationship
[tex]\mathbf v_{P/G}=\mathbf v_{P/A}+\mathbf v_{A/G}[/tex]
Translating the known vectors into component form, we have
[tex]\mathbf v_{P/G}=\langle145\cos40^\circ,145\sin40^\circ\rangle+\langle35\cos60^\circ,35\sin60^\circ\rangle\approx\langle152,143\rangle[/tex]
This vector has magnitude and direction
[tex]\|\mathbf v_{P/G}\|\approx\sqrt{152^2+143^2}\approx208\,\mathrm{mph}[/tex]
[tex]\tan\theta\approx\dfrac{143}{152}\implies\theta\approx43^\circ[/tex]
(or 43 degrees NE)
Answer: #3 is v=12.1i-7j
got it right on my test
#4 is C 208 mph and 43 northeast
Step-by-step explanation:
The temperature today is 7 degrees celsius. Yesterday it was 13 degrees celsius cooler. What was the temperature yesterday?
Answer:
The temperature yesterday was -6 because 7-13 is -6.
Step-by-step explanation:
Answer:
The yesterday’s temperature is 6°C below the zero degree Celsius or (-6) degree Celsius.
Step-by-step explanation:
The temperature today is 7 degrees Celsius. Yesterday was 13 degrees Celsius cooler. That the temperature is colder means that the temperature was lower than today's temperature. This means that to obtain the temperature on the previous day, 13°C must be subtracted from today's temperature.
yesterday’s temperature=today’s temperature-13°C
It is now possible to replace today's temperature with 7 ° C
yesterday’s temperature=7°C-13°C
Remember that to subtract two integers of a different sign (one positive and the other negative), as in this case, you must subtract their absolute values (that is, subtract 13-7 = 6), and the answer will have the same sign as the number with the highest absolute value (absolute value or module of any real number is the same number but with a positive sign). As in absolute value 13 is greater than 7, the answer to the subtraction will be negative
yesterday’s temperature=7°C-13°C
So, finally, the yesterday’s temperature is 6°C below the zero degree Celsius or (-6) degree Celsius.
the price of family dinner was $48.00 . A sales tax of 5% to the final bill. The family left a $10.08 tip. If the family included the sales tax when calculating the tip, what percent tip did the family leave?
Answer:
20% tip
Step-by-step explanation:
Dinner: $48.00
Tax: 0.05($48.00) = $2.40
Total (final) bill before tip: $50.40
Tip: $10.08
Percentage tip was then $10.08 (100%) / $50.40 = 20%
The family left a 20% tip.
x-y<3
Do I need to flip the sign?
Express as a fraction or a mixed number.
0.15%
Answer:
15/100
Step-by-step explanation:
If the the number as a decimal is in the hundredths place you put the number over 100
-10-|1+4b|=-19
Y = 0
Answer:
b=2 or b=-2.5
Step-by-step explanation:
We solve absolute value equations the same as any other equation using inverse operations. However, the inverse operation for absolute value requires one special condition. Since absolute values change a number to a positive regardless if it has a negative sign, we have two possible answers. When we have the absolute value operation isolated, we will set it equal to both the negative and positive option.
[tex]-10-|1+4b|=-19\\-10+10-|1+4b|=-19+10\\-|1+4b|=-9\\\frac{-|1+4b|}{-1} =\frac{-9}{-1} \\|1+4b|=9[/tex]
We now have the absolute value isolated. We will set it equal to both 9 and -9.
[tex]1+4b=9\\1-1+4b=9-1\\4b=8\\b=2[/tex]
and
[tex]1+4b=-9\\1-1+4b=-9-1\\4b=-10\\b=\frac{-10}{4}=\frac{-5}{2}= -2.5[/tex]
When you own a pet, there are one-time costs, such as a leash, and continuing costs, such as food. Suppose the one-time costs for owning a small dog are $180, and the continuing costs are $400 per year Which function models the average annual cost of owning a small dog for x years?
Answer:
Average cost per year = 400 + 180/x
Step-by-step explanation:
Using the formula y=mx+b
We know that b is the y intercept or initial value. That would be the start up costs
m is the slope on costs each time x increases, that would be 400 per year
Costs = 400x + 180
To find the average cost per year, we need to divide by x
Average cost per year = (400x + 180)/x
= 400 + 180/x
Answer:
answer to this question is f(x) = (180 + 400x)/x
If x = 1 is a zero of the polynomial x3 – 7x + 6, find the other two zeroes.
Answer:
x = - 3, x = 2
Step-by-step explanation:
Since x = 1 is a zero then (x - 1) is a factor of the polynomial
dividing x³ - 7x + 6 ÷ (x - 1)
= (x - 1)(x² + x - 6)
= (x - 1)(x + 3)(x - 2)
equating (x + 3)(x - 2) = 0 gives the other zeros
equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
x - 2 = 0 ⇒ x = 2
HELPP plzzzzz plzzzz
Answer:
121/100
Hope it helps!
Karonlina flips a coin 60 times. how many times would you expect it's to land heads up?
Answer:
30 times
Step-by-step explanation:
There's a 50% chance that they will get heads.
60 divided by 2 is 30
50% of 60 is 30
Answer:
We expect 30 heads.
Step-by-step explanation:
There are 2 sides to a coin, heads and tails. They are equally likely. So the probably of getting a heads is 1/2
If we want to know how many times we will get heads, we multiply the number of flips by the probability of getting heads.
number of heads = 60 * 1/2
= 30
Solve. Give your answer in scientific notation. (3.4x10^2)x(2x10^3)
A.1.4x10^-1
B.6.8x10^5
C.5.4x10^5
D.6.8x10^6
Plz answer
Final answer:
The multiplication of (3.4x10²) and (2x10³) results in 6.8x10⁵ after multiplying the coefficients and adding the exponents. Therefore, the correct answer is option (B).
Explanation:
Considering, the question it has asked to solve the following arithmetic operation in scientific notation: (3.4x10²)x(2x10³).
To solve this the following steps can be used :
we multiply the coefficients (3.4 and 2) and then add the exponents (2 and 3).
Multiplication of coefficients: 3.4 * 2 = 6.8
Addition of exponents: 2 + 3 = 5
Combining both parts: 6.8 x 10^5
The correct answer in scientific notation is therefore 6.8x10⁵, which corresponds with option B.
Using the slope formula, find the slope of the line through the given points.
(-8, -5) and (9, -5)
Simplify
Answer:
0
Step-by-step explanation:
Slope = (y2-y1)/(x2-x1)
= (-5--5)/ (9--8)
= (-5+5)/(9+8)
= 0/17
=0
The slope it 0
This is a horizontal line because the y value doesn't change. If the y value doesn't change, the slope it zero.
The inverse of y = 2x + 2 is
Answer:
The inverse of given function is [tex]y=\frac{1}{2}x-1[/tex].
Step-by-step explanation:
The given function is
[tex]y=2x+2[/tex]
The step and shown below to find the inverse of the function.
Step 1: Interchange x and y.
[tex]x=2y+2[/tex]
Step 2: Isolate variable y.
[tex]x-2=2y[/tex]
[tex]\frac{1}{2}(x-2)=y[/tex]
[tex]\frac{1}{2}(x)+\frac{1}{2}(-2)=y[/tex]
[tex]\frac{1}{2}(x)-1=y[/tex]
Therefore the inverse of given function is [tex]y=\frac{1}{2}x-1[/tex].
Answer:
The inverse of y = 2x+2 is 1/2x-1.
Step-by-step explanation:
Given equation is
y = 2x+2
let y = f(x) = 2x+2
We have to find the inverse of given function.
Adding -2 to both sides of given equation,we get
y-2 = 2x+2-2
y-2 = 2x
dividing by 2 to both sides of above equation , we have
(y-2) / 2 = 2x / 2
y/2 - 1 = x
Swapping equation, we have
x = y/2-1
put x = f⁻¹(y) in above equation ,we have
f⁻¹(y) = y/2 -1
Replace y with x , we have
f⁻¹(x) = x/2-1
Hence , the inverse of given function is 1/2x-1.
Julie had $2000 in her savings account, but then she purchased a plane ticket for spring break, decreasing her savings account by 14%. How much was her plane ticket? How much money was left in the account after she bought it?
Step-by-step explanation:
find the common ratio for this geometric sequence 8, 2, 1/2, 1/8, 1/32
Answer:
Multiply 1/4 ; dividing 4
Step-by-step explanation:
Note that in each number going from left to right, it decreases by dividing 4 each time (or multiplying 1/4)
8/4 = 2 ; 2/4 = 1/2 ; (1/2)/(4) = 1/8 ; etc.
(8)(1/4) = 2 ; (2)(1/4) = 1/2 ; etc.
~
Answer: 1/4
Step-by-step explanation:
-2⁄3 a − 6 = 12
a =
Answer:
a = -27
Step-by-step explanation:
-2⁄3 a − 6 = 12
add 6 to both sides:-
-2/3 a -6 + 6 = 12 + 6
-2/3 a = 18
Now multiply each side by -3/2:-
a = 18 * -3/2 = -54/2
= -27
To solve the equation -2⁄3 a - 6 = 12 for 'a', add 6 to both sides of the equation and then multiply both sides of the equation by -3/2 to isolate the variable 'a'. The value of 'a' that satisfies the equation is a = -27.
Explanation:To solve the equation -2⁄3 a - 6 = 12 for 'a', we can start by isolating the variable on one side of the equation. First, let's add 6 to both sides of the equation:
-2⁄3 a - 6 + 6 = 12 + 6
-2⁄3 a = 18
Next, we can multiply both sides of the equation by -3/2 to get:
(-3/2)(-2/3 a) = (-3/2)(18)
a = -27
The value of 'a' that satisfies the equation -2⁄3 a - 6 = 12 is a = -27.
Simplify
[tex]\frac{(3 + i)}{(5 + 2i)} [/tex]
Answer:
17-i
--------
29
Step-by-step explanation:
To simply fractions with complex numbers, we have to multiply by the complex conjugate of the denominator.
The denominator is 5+2i, so the complex conjuate is 5-2i
3+i 5-2i
------ * ---------------
5+2i 5-2i
Simplifying the numerator
(3+i) * (5-2i) = 3*5 + 5i -3*2i -2i^2 = 15 +5i -6i -2(-1) = 15-i+2 = 17-i
Simplifying the denominator
(5+2i) (5-2i) = 25 -10i + 10i -4i^2 = 25 -4(-1) = 29
17-i
--------
29
Answer:
- [tex]\frac{1}{29}[/tex] i + [tex]\frac{17}{29}[/tex]
Step-by-step explanation:
to simplify the fraction ewe require to rationalise the denominator.
This is done by multiplying the numerator/ denominator by the conjugate of the denominator.
the conjugate of 5 + 2i is 5 - 2i, hence
= [tex]\frac{(3+i)(5-2i)}{(5+2i)(5-2i)}[/tex]
= [tex]\frac{15-i-2i^2}{25-4i^2}[/tex]
[ i² = ([tex]\sqrt{-1}[/tex])² = - 1 ]
= [tex]\frac{-i+17}{29}[/tex] = - [tex]\frac{1}{29}[/tex] i + [tex]\frac{17}{29}[/tex]
A computer is normally $550 but is discounted to $385 which precent of the original price does mark pay
Answer:
70%
Step-by-step explanation:
We assume, that the number 550 is 100% - because it's the output value of the task.
We assume, that x is the value we are looking for.
If 100% equals 550, so we can write it down as 100%=550.
We know, that x% equals 385 of the output value, so we can write it down as x%=385.
Now we have two simple equations:
1) 100%=550
2) x%=385
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
100%/x%=550/385
Now we just have to solve the simple equation, and we will get the solution we are looking for.
Solution for 385 is what percent of 550
100%/x%=550/385
(100/x)*x=(550/385)*x - we multiply both sides of the equation by x
100=1.4285714285714*x - we divide both sides of the equation by (1.4285714285714) to get x
100/1.4285714285714=x
70=x
x=70
Find the volume of a sphere
v=4/3 πr^3.
Use this formula
It could be possibly this
v=4/3 πr^3
I hope it helped AND I hope it's right,,
Rewrite in simplest radical form
Answer:
sqrt(x)
Step-by-step explanation:
1/ ( x^(-3/6))
We can simplify the fraction
1/ ( x^(-1/2))
A negative exponent means that since it is in the denominator, it goes to the numerator. It still keeps the exponent.
x^ (1/2)
sqrt(x)
Matt had a full jar of marbles. He gave Kayla 3/4 of the marbles. Then Kayla returned 1/3 of a jar's worth of marbles to the jar. how much of the jar is full of marbles?
Answer: 7/12 jar is full of marbles
Step-by-step explanation:
Matt had full Jar of Marbles = 1
After giving 3/4 to Kayla , jar has marbles = [tex]1-\frac{3}{4} \\=\frac{4}{4} -\frac{3}{4} \\=\frac{1}{4}[/tex]
Kayla returned = 1/3 of Jar
Now jar has marbles = 1/3+ 1/4
= 4/12 + 3/12 [ making denominator same]
= 7/12
All geometric figures,shapes,and solids can be named using sets of
Answer:
All geometric figures, shapes and solids can be named as a sets of surface regions and plane regions and they all lie in three dimensional spaces.
Step-by-step explanation:
Please help
Evaluate - 8×|12|
Answer:
-96 or 96
Step-by-step explanation:
this is because the distance from zero is twelve, so it could be -12 or 12, plug both into the problem and then solve.
the absolute value |x| of a real number x is the non-negative value of x without regard to its sign.
|x| = x for x ≥ 0.
|x| = -x for x < 0.
Examples:
|2| = 2
|-5| = -(-5) = 5
If is -8 × |12| = -8 × 12 = -96
If is 8 × |12| = 8 × 12 = 96
Compute the amount of interest earned in the following simple interest problem. A deposit of 1,295 at 7% for 180 days=____. (note: use 365 days in a year
The interest earned is approximately $50.06.
To calculate the amount of interest earned in a simple interest problem, we can use the formula:
[tex]\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \frac{\text{Time}}{\text{Total days in a year}} \][/tex]
Given:
- Principal (P) = $1,295
- Rate (R) = 7% or 0.07
- Time (T) = 180 days
- Total days in a year = 365 days
Plugging these values into the formula:
[tex]\[ \text{Interest} = 1295 \times 0.07 \times \frac{180}{365} \]\[ \text{Interest} = 1295 \times 0.07 \times \frac{180}{365} \]\[ \text{Interest} \approx 1295 \times 0.07 \times 0.493150685 \]\[ \text{Interest} \approx 50.05958904 \][/tex]
A function f(x) is graphed.
What is the slope of the function? M= 1,2,3,4
What is the y-intercept of the function? B= -2,-1,1,2
Which equation represents the graph of the function y=-x+2 , y=x+2 , y=2x+1 , y=-2x+1
Answer:
Point-Slope form: The equation of line is given by:
[tex]y-y_1=m(x-x_1)[/tex] ......[1]
where m is the slope and [tex](x_1,y_1)[/tex] is the point on the line.
From the given graph:
Consider two points i.e,
[tex](0, 1)[/tex] and (-0.5, 0)
Calculate slope:
Formula for slope is given by;
[tex]\text{Slope}(m) = \frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the given values we have;
[tex]m = \frac{0-1}{-0.5-0} = \frac{-1}{-0.5} = \frac{10}{5} =2[/tex]
Now, substitute the value of m = 2 and (0, 1) in equation [1] we have;
[tex]y-1 = 2(x-0)[/tex]
y-1 = 2x
Add 1 to both sides we get;
y = 2x+1
On comparing equation y = 2x+1 with the slope intercept form of a line (i.e, y = mx+b) then we have;
slope(m) = 2
y-intercept(b) = 1
therefore, the slope of the function:
m = 2
y-intercept(b) = 1
and the equation represents the graph: y = 2x+1
Answer:
2
1
y = 2x + 1
Step-by-step explanation:
Which quantity is proportional to 35⁄80? Check all that are true. 3⁄5 14⁄36 26⁄52 21⁄48 7⁄16
Hey there!
"Which quantity is proportional to [tex]\frac{35}{80}[/tex]?"
The easier way, I figured out how to solve this particular problem is simplify the fraction to decimal
[tex]\frac{35}{80}[/tex] [tex]= 0.4375[/tex]
[tex]\frac{3}{5}[/tex] [tex]= 0.60[/tex] so, this one isn't your answer[tex]\frac{14}{36}[/tex][tex]=0.288889[/tex] so this one isn't your answer [tex]\frac{26}{52}[/tex][tex]=0.50[/tex] so this one isn't your answer[tex]\frac{21}{48}[/tex][tex]=[/tex][tex]=0.4375[/tex] this one is your answer [tex]\frac{7}{16}[/tex][tex]= 0.4375[/tex] so this one is your answer[tex]\boxed{Answer: \frac{21}{48} AND \frac{7}{16}}[/tex]
Good luck on your assignment and enjoy your day!
~[tex]LoveYourselfFirst:)[/tex]
Answer:
3/5 no
14/36 no
26/52 no
21/48 yes
7/16 yes
Step-by-step explanation:
What is equal to 19.04 divided 5.6
Answer: 19.04 divided by 5.6 is 3.4
Step-by-step explanation:
Simplify 7x +42/ x2+13x +42
[tex]\dfrac{7x+42}{x^2+13x+42}=\dfrac{7(x+6)}{x^2+7x+6x+42}=\dfrac{7(x+6)}{x(x+7)+6(x+7)}\\\\=\dfrac{7(x+6)}{(x+7)(x+6)}=\boxed{\dfrac{7}{x+7}}[/tex]
Your answer should be 2(10x^3+21x^2+21) over X^2 2(10x^3+21x^2+21)/X^2 unless the / was a fraction symbol and not a division symbol then your answer would be 7 over x+7 7/x+7
If you let y = length of the foot and x = length of the forearm, this equation can be simplified to y = 0.860x + 3.302. Using this equation, how long would the foot of a person be if his forearm was 17 inches long? Be sure to show your work using the equation above.
Answer:
17.922
Step-by-step explanation:
first you plug it in
y=0.860(17) + 3.302
then u simplify
y=14.62+3.302
then add them
y=17.922
Answer:
17.922 inches long
Step-by-step explanation:
y=0.860x + 3.302
y= 0.860(17) + 3.302
y= 14.62 + 3.302
y= 17.922
Hope it helps!!
Multiply: (3x + 7)(5x2 − 3x + 6)
Answer:
15x^3+26x^2-3x+42
Step-by-step explanation:
The multiplication is 15x³ +26x² - 3x + 42.
What is multiplication?Multiplication is the process of adding a number up to a given number.
The multiplication (3x + 7)(5x²-3x+6) is as shown:
(3x + 7)(5x²-3x+6)
= 15x³ - 9x² + 18x +35x²- 21x +42
= 15x³ +26x² - 3x + 42
Hence, the multiplication is 15x³ +26x² - 3x + 42.
To learn more about multiplication, click here:
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What is the result of factoring out the GCF from the expression (24 + 36)?
A. 12 × (12 + 18)
B. 12 × (2 + 3)
C. 6 × (8 + 12)
D. 12 × (4 + 6)
24 = 2 · 2 · 2 · 3
36 = 2 · 2 · 3 · 3
GCF(24, 36) = 2 · 2 · 3 = 12
24 = 12 · 2
36 = 12 ·3
24 + 36 = 12 × 2 + 12 × 3 = 12 × (2 + 3)
Answer: B.The result of factoring out the Greatest Common Factor (GCF) from the expression (24 + 36) is 12 × (2 + 3).
Explanation:To factor out the Greatest Common Factor (GCF) from the expression (24 + 36), we first need to determine the largest number that divides evenly into both 24 and 36. The GCF of 24 and 36 is 12. We divide each term by the GCF to factor out it from the expression:
24 ÷ 12 = 2
36 ÷ 12 = 3
Thus the expression factored out by the GCF is 12 × (2 + 3).
Learn more about Factoring Out GCF here:https://brainly.com/question/29055991
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