Find the unit vectors that are parallel to the tangent line to the curve y = 2 sin(x) at the point 6 , 1 .

35 degrees Celsius is equal to 95 degrees Fahrenheit.

What is the formula for Celsius to Fahrenheit?

Without a calculator, how do you convert from Celsius to Fahrenheit?

F = 9 / 5 * 35 + 32

F = 63 + 32

F = 95

35 degrees Celsius is equal to 95 degrees Fahrenheit.

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The value of the sales tax on the computer is 62 dollars and 93 cents.

Any number or a ratio which is expressed in terms of a fraction of 100 is known as a percentage.

Here, we are given that the price of a computer is 899 dollars.

The sales tax on the computer is 7%.

Thus, the value of the sales tax on the computer will be,

7% of 899

= 7/100 * 899

= 62.93

Thus, the sales tax on the computer comes out to be 62.93 dollars.

In 62.93 dollars, we can see that we have 62 complete dollars, plus 0.93 more dollars left.

0.93 dollars = 93 cents

Therefore, the sales tax on the computer is 62 dollars and 93 cents.

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Answer:

Step-by-step explanation:

Answer: domain is x and range is y

Step-by-step explanation:

Answer:

Domain: {2, 8, 30, 46}
Range: {-1, 9, 16}

Step-by-step explanation:

The domain of a function y = f(x)  is the set of all values that the input values (x) that the function can accept. The range of a function is the set of all output values that the function can produce from the domain values ie the set of all  values

Looking at the figure, the set of all x values that the function y can take are
{2, 8, 30, 46} and this is the domain

The output values produced from this domain are {-1, 9, 16} and that is the range

Answer:

9

Step-by-step explanation:

→ Substitute in the values

2³ +√64 ÷ 8

→ Simplify

8 + 8 ÷ 8

→ Calculate

8 + 1 = 9

Answer:

9

Step-by-step explanation:

2 to the power of 3 is 8

8 + 64 = 72

72 ÷ 8 = 9

Answer:

56

Step-by-step explanation:

The mode of a data set is the number that appears the most, which in this situation would be 56

:D

Answer:

48

Step-by-step explanation:

set up a proportion of 1/3 and x/144 and then divide 144 by 3 which is 48

[tex]\stackrel{\textit{ratio of 1~:~3}}{\cfrac{males}{females}~~ = ~~\cfrac{1}{3}}\implies \cfrac{males}{144}~~ = ~~\cfrac{1}{3}\implies 3males=144 \\\\\\ males=\cfrac{144}{3}\implies males=48[/tex]

Answer:

2

Step-by-step explanation:

To get the slope you must subtract the second y-coordinate and the first y-coordinate (of the 2 given points) and divide that by the difference of second x-coordinate and first x-coordinate (of the 2 given points).

y-coordinate 2 - y-coordinate 1

--------------------------------------------- <----- fraction bar/ divide

x-coordinate 2 - x-coordinate 1

3 - 1 2

------ = ---- = 2

1 - 0 1

Slope = 2

Answer:

195

Step-by-step explanation:

Since this figure is a quadrilateral you would be subtracting the inner angles from 360

360-87-40-38=195

Answer:

Sally is 12 years old.

Step-by-step explanation:

[tex]2x+3=27\\2x+3-3=27-3\\2x=24\\\frac{2x}{2}=\frac{24}{2}\\x=12[/tex]

Answer: f(-1)=-8

Step-by-step explanation:

f(x) = -x² + 7x

f(-1)=-(-1)²+7(-1)

f(-1)=-1-7

f(-1)=-8

The probability that the next two offspring will both be girls is 1/3.

To find P both children are girls

A: Event that both children are girls

A: {MM} and B: {MF, FM, MM} →→ P (A ∩∩ B) = {MM}

Probability that both are males, if we know one is a female =P(A/B)=P(A∩B)/P(B)

(P(A∩B)P(B))

Given S = {MM, MF, FM, FF}, we can see that: P (A) = 1414; P (B) = 3434; P (A ∩∩ B) = 1414

Therefore,

P(B/A)=P(A∩B)/P(A) = (1/4)/(3/4)=1/3.

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Answer: Sym. Prop. of ≅

Step-by-step explanation:

no explanation

The other angle opposite the given 72° angle is also 72°. This is because vertical angles are congruent.

The other two opposite angles are 180-72 = 108° each

See the diagram below. Notice how all four angles add to 360 degrees. Any adjacent pair of angles add to a straight line of 180 degrees.

Answer:

9222.23333 is the value good sir :)

Step-by-step explanation:

Answer:

30 meters.

Step-by-step explanation:

Meters are larger then yards.

Time taken by car to pass the truck in the same direction from the time the car enters the highway is approximately12.54 minutes with a truck speed 60mph and a car 67mph.

As given in the question,

Speed of a truck=60mph

⇒60 minutes = 60miles

⇒14 minutes = (60/60)×14

                     = 14 miles

Car speed =67mph

67 miles=60minutes

⇒1miles = (60/67) minutes

⇒14miles = (60/67)×14

                ≈12.54 minutes (approximately)

Therefore, time taken by car to pass the truck in the same direction from the time the car enters the highway is approximately12.54 minutes with a truck speed 60mph and a car 67mph.

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Answer:

36=3×2×2×3

48=2×2×2×2×3

Explanation:

Step 1: Divide the given number by the smallest prime number.

36/3=12. (1)

48/2=24. (2)

Step 2: Again, divide the quotient by the smallest prime number.

12/2=6. (1)

24/2=12. (2)

Step 3: Repeat the process, until the quotient becomes 1.

6/2= 3. (1)

12/2=6 (2)

3/3=1 (1)

6/2=3 (2)

3/3=1. (2)

Step 4: Finally, multiply all the prime factors.

36=3×2×2×3

48=2×2×2×2×3

Answer:

36 = 2 × 2× 3 ×3

48 = 2 × 2× 2 × 2 ×3

Step-by-step explanation:

Answer:

y-20=0.75(x-4)

Step-by-step explanation:

First, use slope formula to find the slope.

The points I will use are (4, 20) and (8, 23).

Formula:

y2-y1/x2-x1

23-20/8-4=

=3/4

The slope in decimal form is 0.75.

Now you put the linear equation in point-slope form.

m=0.75

Use the point (4, 20).

y-y1=m(x-x1)

y-20=0.75(x-4)

The linear equation is point-slope form is y-20=0.75(x-4).

Hope this helps!

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Answer:

cos = 4/5

Step-by-step explanation:

having sides 3 and 5, means that this is a right triangle with sides 3,4, and 5

cos = adjacent side/ hypotenuse

sin= opposite side/ hypotenuse

since 5 is the biggest number it will be the hypotenuse since that is the longest side, so it will stay on the bottom.

hope this helps! if you have any more questions just ask

The solution set of the equation is: x = -3, x = 3.

Given the equation, x² + 12 = 21, the solution set is the possible value of x that will make the equation true. To find the values of x, do the following as shown below:

x² + 12 = 21

Subtract 21 from both sides of the equation

x² + 12 - 21 = 21 - 21

x² + 12 - 21 = 0

x² - 9 = 0

Find the difference of the two squares

(x + 3)(x - 3) = 0

x = -3

x = 3

Therefore, the solution set of the equation is: x = -3, x = 3.

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Using the segment addition postulate and the bisection concept, the segment EF bisecting RS is given at the end of the answer.

The segment addition postulate is a geometry axiom that states that a line segment, divided into a number of smaller segments, has the length given by the sum of the lengths of the segments.

From this, the bisection concept is derived, which is when a line crosses a segment exactly at the segment's midpoint, meaning that point A is the midpoint of RS.

The illustration of this situation is given at the end of the answer.

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Answer:

It is everything that's bigger then (0,-3),

Picture under ↓

It's a bad drawing.

The solution region for the given pair of inequalities is found to be the common shaded region in the graph attached.

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

here, we have,

For drawing the graph of any inequality, we first have to assume the inequality as an equation and draw the graph of the resulting equation. Hence, finding the points for the inequality , we let the inequality as:

Putting y=0, we get:

The point will be: (-2,0)

Now, putting x=0, we get:

The point will be: (0,4)

Now as the sign of inequality is >, the line of graph will be dotted.

Taking a test point (0,0) to find the shaded region, substituting this in the inequality,

So, the shaded region will be away from the test point.

Similarly, finding the points for the inequality , we let the inequality as:

Putting y=0, we get:

The point will be: (6,0)

Now, putting x=0, we get:

The point will be: (0,6)

Now, as the sign of inequality is of , the line of graph will be solid.

Taking a test point (0,0) to find the shaded region, substituting this in the inequality,

So, the shaded region will be towards the test point.

The resulting graph is attached after the solution.

The solution to the pair of given inequalities will be the shaded region that is common between both the individual inequality's shaded regions.

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Answer:

The answer is 10 for your math equation

Step-by-step explanation:

The values of each variable are x = 15° and y = 7°.

Given are two lines, intersecting each other at a point to make angles,

2(5x − 5)°, 20y°, (5y + 5)° and (3x - 5)°.

We need to find the values of the variables.

The lines are intersected in such a way that the angles 2(5x − 5)°, (3x - 5)°and (5y + 5)°, 20y° are making linear pairs.

We know that the linear pair angles sum up to make 180°.

So,

2(5x − 5)° + (3x - 5)° = 180°

10x - 10 + 3x - 5 = 180°

13x - 15 = 180°

13x = 195°

x = 15°

Similarly,

(5y + 5)° + 20y° = 180°

5y + 5 + 20y = 180°

25y = 175°

y = 7°

Hence the values of each variable are x = 15° and y = 7°.

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So you know that a pound of rice crackers cost $42.88. You also know that Jacob bought 1/4 or 25% or 0.25 of a pound. This means that by multiplying 0.25 by $42.88, you can determine the cost.

0.25 x 42.88 = 10.72

Therefore, Jacob paid 10.72 cents or $10.72 for 1/4 pound of rice crackers

y = \frac{-x}{2 } + \frac{1}{4}  + ce^-{2x} is  the general solution to the differential equation put the problem in standard form.

What is meant by integrating factor?

x² + 2xy + x . dy/dx = 0

x dy/dx  + 2xy = [tex]- x^{v}[/tex]

[tex]\frac{dy}{dx} =+ 2y = -x[/tex]

[tex]left u(x) = e^{\int\limits^_ {} } 2dx = e^{2x}[/tex]

integration  factor p(x) = u(x) = [tex]e^{2x}[/tex]

Now ,multiply  [tex]e^{2x}[/tex] both sides

[tex]e^{2x} ( \frac{dy}{dx} + 2y ) = -x . e^{2x}[/tex]

[tex]e^{2x} \frac{dy}{dx} + 2e^{2x} . y = -x e^{2x}[/tex]

[tex]\frac{d}{dx} (e^{2x} .y) = -x e^{2x}[/tex]

integrate both sides

∫ [tex]d .( e^{2x} .y )[/tex]     = ∫[tex]-xe^{2x} .dx[/tex]

[tex]e^{2x} .y = -\frac{e^{2x}}{2} . x + \frac{e^{2x}}{4} + c[/tex]

[tex]y = \frac{-x}{2 } + \frac{1}{4} + ce^-{2x}[/tex]

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The complete question is -

Find the general solution to the differential equation 2 dy X+ + 2xy + x dx = 0 Put the problem in standard form. Find the integrating factor, p(x) = 2x - Find y(x) Use C as the unknown constant.

Answer:

soln ,given,

midpoint of CD=M(-2,5)

let,

C(4,7)=(x1,y1)

D(x1,y2)=?

now by using midpoint formula =(x1+x2)/2+(y1+y2)/2

M(-2,5)=( 4+x2)/2+(7+y2)/2

comparing both sides

-2=(4+x2)/2

-4=4+x2

-4-4=x2

threfore,x2= -8

again

5=(7+y2)/2

10=7+y2

therefore,y2=3

thus , the coordinate of D is D(-8,3)

The Interquartile Range (IQR) is the appropriate measure of variation for the given data points. Q1 and Q3 are 2 and 5 respectively.

The IQR is a method that gives the value of data at the 25th and 75th percentile. Alternatively, it gives the average of the two values which are nearest to these two percentiles, in case a single value does not exist. These values are called Q1 and Q3.

Because these values are less impacted by outliers than the standard deviation, it is best to use them with skewed data.

For the given data points,  Q1 and Q3 are 2 and 5 respectively. Q1 is the average of 5th and 6th values. Q3 is the average of 15th and 16th values.

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The Interquartile Range (IQR) is the appropriate measure of variation for the given data points. Q1 and Q3 are 2 and 5 respectively.

The IQR is a method that gives the value of data at the 25th and 75th percentile. Alternatively, it gives the average of the two values which are nearest to these two percentiles, in case a single value does not exist. These values are called Q1 and Q3.

Because these values are less impacted by outliers than the standard deviation, it is best to use them with skewed data.

For the given data points,  Q1 and Q3 are 2 and 5 respectively. Q1 is the average of 5th and 6th values. Q3 is the average of 15th and 16th values.

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