Answer:
The vector direction is 83.0° relative to the positive x-axis
Step-by-step explanation:
* Lets explain how to find the direction of a vector
- A vector is a quantity which has both magnitude and direction
- The vector has two components x-component and y-component
- The x-component = v cos Ф , and the y-component = v sin Ф,
where Ф is the angle between the vector and the positive part
of the x-axis
- The magnitude of the vector = [tex]\sqrt{x^{2}+y^{2}}[/tex]
- The direction of the vector = [tex]tan^{-1}(\frac{y}{x})[/tex]
* Lets solve the problem
∵ x-component of the vector = 0.15
∵ y-component of the vector = 1.22
- Both x-component and y-component are positive
∴ Ф will be between 0° and 90°
∵ The direction of the vector = [tex]tan^{-1}(\frac{y}{x})[/tex]
∴ The direction of the vector = [tex]tan^{-1}(\frac{1.22}{0.15})[/tex]
∴ The direction of the vector = 83.0°
* The vector direction is 83.0° relative to the positive x-axis
Given the function below, select all the equalities that are true.
f(x) = x2 + 3
Answer:
a&c
Step-by-step explanation:
because you can multiply to numbers and reach 0 or 2, but no number times another equals 7 and no number times 0 equals three (multiplicative identity of 0)
Rearrange to make x the subject
P=hx/5. Pls help
Answer:
x = [tex]\frac{5P}{h}[/tex]
Step-by-step explanation:
Given
P = [tex]\frac{hx}{5}[/tex] ( multiply both sides by 5 )
5P = hx ( divide both sides by h )
x = [tex]\frac{5P}{h}[/tex]
The given equation P = hx/5 can be rearranged to x = 5P/h, by first multiplying both sides by 5, and then dividing both sides by h
Explanation:The current equation P = hx/5 can be rearranged to isolate x by employing algebraic steps. We first need to get rid of the division by 5 from the right side of the equation to leave hx isolated. We achieve this by performing the opposite operation, that is multiplication on both sides of the equation by 5:
5P = 5*(hx/5)
This simplifies to 5P = hx.
Finally, to obtain x by itself, we want to get rid of the multiplication by h in the equation. We do so by dividing both sides of the equation by h:
(5P)/h = hx/h
Which simplifies to: x = 5P/h
This is the final rearranged equation with x isolated.
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4 miles 999 feet = in feet
Answer:
approximately = 26394.72
Convert between the 2 units.
Can i plz have the brainliest answer plz!!!!!!!!!!!
Which of the following polynomials is equivalent to the expression above?
A) x² + 5
B) x² +7
C) 4x² +7
D) x² + 4x + 7
Answer:
D) x² + 4x + 7
Step-by-step explanation:
2x + 6 + x² + 2x + 1
x² + 2x + 2x + 6 + 1
x² + 4x + 7
The equivalent expression for the given polynomial is x² + 4x + 7.
Option D is the correct answer.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
(2x + 6) + (x² + 2x + 1)
Removing the parenthesis.
2x + 6 + x² + 2x + 1
Adding the like terms.
4x + 7 + x²
x² + 4x + 7
Thus,
The final expression is x² + 4x + 7.
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Roselyn wants to drive her car at a speed of 606060 miles per hour for 1.251.251, point, 25 hours. Her car has a fuel efficiency of 151515 miles per gallon.
How many gallons of fuel does Roselyn need for her journey?
Answer:
Hence, there is 5 gallons of fuel Roselyn needed for her journey.
Step-by-step explanation:
Since we have given that
Speed at which Roselyn wants to drive her car = 60 miles per hour
Time taken by her car = 1.5 hours
As we know the formula for "Distance-Speed " :
Her car has fuel efficiency = 15 miles per gallon
Number of gallons of fuel is given by
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Answer:
5 gallons.
Step-by-step explanation:
Roselyn wants to drive her car at a speed of 60 mph
Speed of car, S = 60 mph
She drives for 1.25 hours.
Time travel, t = 1.25 hours
Total distance travel = s × t
= 60 × 1.25
= 75 miles
The fuel efficiency of car is 15 miles per gallon.
[tex]\text{Number of gallon used}=\dfrac{\text{Total distance travel}}{\text{Fuel efficiency}}[/tex]
[tex]\text{Number of gallon used}=\dfrac{75}{15}[/tex]
[tex]=5\text{ gallons}[/tex]
Hence, she needs 5 gallons.
6 x 7 - 3 + 2 = __
Insert parentheses to make the expression equal 26.
A) 6 x (7 - 3 + 2)
B) 6 x (7 - 3) + 2
C) (6 x 7 - 3) + 2
D) 6 x 7 - (3 + 2)
Answer:
B is the correct answer
solve problem y+7=-9
Answer: -16
Step-by-step explanation:
y + 7 = -9
-9 - 7 = -16
-16 + 7 = -9
What is the expanded form for 6 * 532?
Answer:
(6*500)+(6*30)+(6*2)=3192
Step-by-step explanation:
532 is 500+30+2. By expanding this number to its components and multiplying each by 6, you can solve this problem significantly faster without the use of a calculator.
Square root of xy squared multiply by the square root of x cubed and y to the seventh power
Answer:
=[tex]x^{2} y^{9}\sqrt{x}[/tex]
Step-by-step explanation:
[tex]xy^{2}[/tex] multiplyed by [tex]\sqrt{x^{3} }[/tex]multiplyed by [tex]y^{7}[/tex]
=[tex]x^{2} y^{9}\sqrt{x}[/tex]
Have a nice day!!!!!!!!!!! :-)
KA
The expression with square roots simplifies to x squared times y to the 4.5th power, or x squared times y to the 4th power times the square root of y, applying the rules for multiplying exponents and expressing square roots as fractional powers.
Explanation:To solve the expression involving square roots and variables raised to different powers, we apply the rules of exponents and radical expressions. The student asks about the square root of xy2 multiplied by the square root of x3y7. First, we express the square roots as fractional powers, and then we use the rule of multiplication of exponents.
For square roots, the rule is that the square root of x can be rewritten as x raised to the 1/2 power. As in the examples provided, the rule for raising a number to a power (xp) and then multiplying it by the same base raised to another power (xq) is to add the exponents, resulting in xp+q. Finally, the cube of an exponential involves cubing the digit term and multiplying the exponent by 3.
In this case:
Square root of xy2 is x1/2ySquare root of x3y7 is x3/2y7/2When we multiply these together:
(x1/2y) * (x3/2y7/2) = x1/2+3/2y1+7/2 = x2y9/2
This expression simplifies to x2y4.5 or x2y4√y.
For f(x) = 3x +1 and g(x) = х2 - 6, find (f-g)(x).
Answer:
(f-g)(x) = -x^2 + 3x + 7
Step-by-step explanation:
Note that -g(x) = -x^2 + 6.
Thus, (f-g)(x) = f(x) + [-x^2 + 6]: Add the following:
f(x) = 3x + 1
-g(x) = -x^2 + 6
--------- ------------------
(f-g)(x) = -x^2 + 3x + 7 (answer)
Which is a possible turning point for the continuous function f(x)? (–6, 8) (-4, 2) (-2, 0) (0,-2)(2,-1)(4,0)(6,4)
The function breaks at (-2,0),(0,-2)&(4,0).So at all these points function i.e triangular curve takes the turn.
That is what kind of continuous function?
A continuous function in mathematics is one whose value does not abruptly change due to discontinuities, or breaches in the continuity of the function.
For example, the function f (x) = 2 sin (x), f (x) = 2 sin (x), and f (x) = 2sin (x) is continuous everywhere. We can sketch its outline without ever lifting our hand. Contrarily, there is a discontinuity at x = 2 x = 2 x = 2 in the function f (x) = 1 x 2 f(x) = frac 1 x 2 f(x) = x 21.
The four points given are (-2,0),(0,-2),(2,-1),(4,0).When you will plot these points on the coordinate axes and join all these points you will get the shape of a triangle. One line lies completely on x axis another two lies below x axis. These two lines intersect at (0,-2).
The meaning of continuity is that there should be no breaking points in the function.
But the function breaks at (-2,0),(0,-2)&(4,0).So at all these points function i.e triangular curve takes the turn.
So this might be also the turning point.
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The possible turning point for the continuous function f(x) from the given list is likely the point (2, -1), where the second derivative y" = 6x - 12 equals zero, indicating a point of inflection.
Explanation:To determine a possible turning point for the continuous function f(x), we need to consider the concept of a point of inflection, which is a point where the concavity of the function changes. According to the excerpts, a point of inflection occurs where the second derivative of the function changes sign or is zero. If we examine the given points, a turning point might be where we can see such a change in concavity or where the f'(x) equals zero.
From the excerpt that gives us the second derivative y" = 6x - 12, we can determine that at x = 2, the second derivative is zero, which signals a possible point of inflection. This would correspond to the point (2, -1) in the list provided. Hence, this is a possible turning point for the function f(x).
Find the value of C. m^2+7/12m+c
Use b^2 - 4ac = 0.
Let a = 1
Let b = 7/12
(7/12)^2 - 4(1)c = 0
Take it from here.
The number 21 is decreased to 15. What is the percentage by which the number was decreased, to the nearest tenth of a percent?
Answer:
Initial Number = x = 21
Number after it is decreased = y = 15
Total decrease form initial to the current number = z = x-y = 21-15 = 6
% of decrease = (z/x) * 100 = (6/21)*100 = 600/21 = 28.5714286 = 28.6 ( correcting it to 10th place)
Step-by-step explanation:
For 21 decreased to 15, the percentage decrease is 28.6%.
The percentage by which a number was decreased can be calculated by finding the difference between the original number and the decreased number, dividing that by the original number, and then multiplying by 100 to get the percentage.
Given number: 21
On reduction, number becomes: 15
To find the percentage decrease:
(21-15)/21 x 100 = 28.6%.
what is 40÷1/4?? pls hurry
Answer:
160
Step-by-step explanation:
Answer:
160 is the answer for this problem
there are 18 oranges in box A and 36 in box B, what is the ratio of box A to box B
Answer:
1 : 2
Step-by-step explanation:
Express the ratio as the number of oranges in each box, that is
box A : box B
= 18 : 36
Simplify the ratio by dividing both parts by 18, thus
ratio = 1 : 2 ← in simplest form
Find the slope of the line that passes through the points (-8,-3), (2,3)
Answer:
⅗
Step-by-step explanation:
-y₁ + y₂\-x₁ + x₂ = m
[tex] \frac{3 + 3}{8 + 2} = \frac{6}{10} = \frac{3}{5} [/tex]
I am joyous to assist you anytime.
2(2X-3)-10 <_ 6(X-2)
Answer:
x<14/5
Step-by-step explanation:
expand
4x-6-10 < -6x+12
4x-16 < -6x+12
4x < -6x+12+16
4x < -6x+28
4x+6x < 28
10x < 28
x < 28/10
hope this helps
Answer:
[tex]\large\boxed{x\geq-2\to x\in[-2,\ \infty)}[/tex]
Step-by-step explanation:
[tex]2(2x-3)-10\leq6(x-2)\qquad\text{use the distributive property}\ a(b+c)\\\\(2)(2x)+(2)(-3)-10\leq(6)(x)+(6)(-2)\\\\4x-6-10\leq6x-12\\\\4x-16\leq6x-12\qquad\text{add 16 to both sides}\\\\4x\leq6x+4\qquad\text{subtract}\ 6x\ \text{from both sides}\\\\-2x\leq4\qquad\text{change the signs}\\\\2x\geq-4\qquad\text{divide both sides by 2}\\\\x\geq-2[/tex]
Critique the reasoning of others. Oriana said that the difference between 9.298 and 3.01 was 8.997.
Was she correct? If not, what error did she make?
Answer: Oriana was not correct, because she didn't line up the decimal points of the numbers [tex]9.298[/tex] and [tex]3.01[/tex]
Step-by-step explanation:
By definition, the "Difference" is the result of a subtraction.
In order to subtract the decimal numbers [tex]9.298[/tex] and [tex]3.01.[/tex], Oriana needed to apply these steps:
1. Write one number under the other. The decimal points must be lined up:
[tex]9.298 \\3.01-\\..........[/tex]
2. Since the decimal numbers must have the same number of decimal places, she needed to add zeros to the right side:
[tex]9.298 \\3.010-\\..........[/tex]
3. Subtract the numbers and put the decimal point in the result:
[tex]9.298 \\3.010-\\..........\\6.288[/tex]
Oriana was not correct, because she didn't line up the decimal points. Her procedure was:
[tex]9.298 \\ 0\ 3.01-\\..........\\8.997[/tex]
Select the correct answer.
Anton is approved for overtime at his job. Last week, he worked a total of 45 hours. How many hours of overtime did he work?
3 hours
B. 5 hours
C. 15 hours
D.45 hours
Answer: 15 hours
Step-by-step explanation: full time is 30 hours so if he worked 45 that’s 30+15=45 so 15hrs over time
This graph displays a linear function. What is the rate of change?
Answer:
rate of change is 5!!! :)
Step-by-step explanation:
Hope this helps!!! :)
The rate of change of the linear function in the graph is: 5
How to find the rate of change of the linear graph?Rate of change problems can generally be approached using the formula R = D/T, or rate of change equals the distance traveled divided by the time it takes to do so.
However, in this case with coordinates, it is expressed as:
Rate of change = (y₂ - y₁)/(x₂ - x₁)
From the graph, we can take two coordinates which are:
(1, -1) and (2, 4).
Thus:
Rate of change = (4 - (-1))/(2 - 1)
= 5/1
= 5
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What is the real interest rate for a savings account that has a nominal interest rate of 1% when the rate of inflation is 1% ?
A.) -2%
B.) 0%
C.) 1%
D.) 2%
The real interest rate of a savings account that has a nominal interest rate of 1% when the rate of inflation is 1% is B.) 0%
How to find the real interest rate ?The real interest rate is the interest rate that is adjusted for inflation. It is calculated by subtracting the inflation rate from the nominal interest rate. In this case, the nominal interest rate is 1% and the inflation rate is also 1%.
So, the real interest rate is:
= 1% - 1%
= 0%
In other words, if you deposit $100 in a savings account with a nominal interest rate of 1%, you will earn $1 in interest after one year. However, because inflation is also 1%, the purchasing power of your $100 will decrease by $1. So, the real value of your savings will not change.
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Final answer:
The real interest rate for a savings account with a nominal interest rate of 1% and an inflation rate of 1% is 0%. This is found by subtracting the inflation rate from the nominal interest rate.
Explanation:
The real interest rate is calculated by taking the nominal interest rate and subtracting the rate of inflation. In this case, if you have a nominal interest rate of 1% and an inflation rate of 1%, the real interest rate would be calculated as follows:
Real interest rate = Nominal interest rate - Inflation rate
Real interest rate = 1% - 1% = 0%
Therefore, the real interest rate for the savings account is 0%. This means that the purchasing power of the money in the savings account is essentially staying the same. The correct answer is B.) 0%.
For the given exercises:
If the nominal interest rate is 5 percent and the inflation rate is 3 percent, the real interest rate is 2 percent.Yes, the real interest rate can be negative if inflation rate exceeds the nominal interest rate.Risks involved in investing in a foreign bank include exchange rate risk, political risk, and differing levels of financial regulationplease help me with this
Answer:
a. 10cmb. 5 cmc. 31.4 cmd. 78.5 cm²e. 100 cm²Step-by-step explanation:
Let:
s - side of the square
d - diameter of the circle
r - radius of a circle
C - circumeference of the circle
AC - area of the circle
AS - area of a square
The formula of a perimeter of a square:
P = 4s
We have P = 40cm.
Substitute:
4s = 40 divide both sides by 4
s = 10 cm
a.
The length of the diameter of the circle inscribed in the square is equal to the length of the side of the square.
Therefore d = s → d = 10 cm.
b.
The length of the circle diameter is two lengths of the circle radius.
Therefore d = 2r → r = d : 2 → r = 10 : 2 = 5 cm.
c.
The formula of a circumference of a circle:
C = dπ.
Substitute d = 10cm, and π = 3.14.
C = 10(3.14) = 31.4 cm.
d.
The formula of an area of a circle:
AC = πr²
Substitute r = 5cm and π = 3.14
AC = 3.14(5²) = 3.14(25) = 78.5 cm².
e.
The formula of an area of a square:
AS = s²
Substitute s = 10 cm
AS = 10² = 100 cm²
-9.5 as a mixed number
You know that .5 = 0.5 = 5/10 = 1/2.
Mixed number sought: -9_1/2.
cos12sin78+cos78sin12
Sin 12 x cos 78 + cos 12 x sin 78
= sin 12 x cos (90-12) + cos 12 x sin (90-12)
=sin 12 x sin 12 + cos 12 x cos 12
=sin^2 12 + sin^2 12
=1
Please help me i really need it
Answer:
B and C
Step-by-step explanation:
It can't be A because that would equal 5b.
For C, you multiply 2b by 2 and get 4b.
For B, you add b to 3b to get 4b.
If two is added to four times a certain number, the result
is 26. What is the number?
For this sort of question you have to work backwards.
.
26 - 2 = 24.
24 / 4 = 6
.
The number would be 6
x + 10 = 2x
PLEASE SHOW EXPLANATION + WORK
Answer:
X=10
Step-by-step explanation:
x+10-10=2x-10
x=2x-10
x-2x=2x-10-2x
-x= -10
-x/-1= -10/-1
x=10
3x+15=8x+25 i need x
Answer: -2 = X
Step-by-step explanation:
3x +15 = 8x +25
-3x -3x *Make sure you do it to both sides
15 = 5x + 25
-25 -25 *Your goal is to get X on one side
-10/5 = 5x/5
-2 = X
X=-2
3x+15=8x+25
-8x. -8x
-5x+15=24
-15
-5x=10
-5x/5 -10/5
X=-2
Y/-7=10 solve and check
Always write y in lower case
y/-7 = 10
y = 10(-7)
y = -70
Check:
Let y = -70
(-70)/-7 = 10
10 = 10
Done!
Please help me with this
the answer is true it is a rational number
As a fraction, 2 is 2/1
Oh no, there is always an odd exponent. So it could not have been made by squaring a rational number! This means that the value that was squared to make 2 (ie the square root of 2) cannot be a rational number. In other words, the square root of 2 is irrational.