Find the value of a
Answer is 3

The value of c as per the law of cosines, to the nearest tenth, is 5.1 units.

Given information:

a = 8, b = 9 C = 34°.

To find the value of C:

According to the Law of Cosines, for any triangle ABC:

c² = a² + b² - 2ab cos(C)

Substituting the given values:

c² = 8² + 9² - 2(8)(9) cos(34°)

c² = 64 + 81 - 144 cos(34°)

c² = 145 - 144 cos(34°)

Taking the square root of both sides:

c = √(145 - 144 cos(34°))

Using a calculator:

c ≈ 5.1 units (rounded to the nearest tenth)

Therefore, the value of c is approximately 5.1 units.

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The lines are neither parallel nor perpendicular to line p

From the question, we have the following parameters that can be used in our computation:

y = -3x + 10

As a general rule

Using the above as a guide, we have the following:

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The missing values from ratio table are 17 and 28.

We have table as

3      1

48    16

51      x

78    26

84     y

So, the ratio are in proportion then

48 / 16 = 51 /x

3 = 51/x

x= 51/3

x = 17

and, 3/1 = 84/y

y= 84/3

y= 28

Thus, the values are 17 and 28.

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The solution is,  $ 12833 .59 will he have in the account after 5 years.

Compound interest is a type of interest that is calculated not only on the principal amount of a loan or investment, but also on any interest that has previously accrued. In other words, it is interest that is earned on both the initial principal and any interest that has been added to it over time.

by the question.

We can use the formula for compound interest to solve the problem:

A = P

where:

A = final amount (x in this case)

P = principal or initial amount ($10,000.00)

r = annual interest rate (5% in this case)

n = number of times the interest is compounded per year (12, since it's compounded monthly)

t = time in years (5, since Tyrone opened the account 5 years ago)

Substituting the values given, we get:

A = $ 12833 .59

The solution is,  $ 12833 .59 will he have in the account after 5 years.

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0,0,0,0,0,

Lenght of Tsing Ma Bridge in Hong Kong is, 1,377 meters

Given that;

The Mackinac Bridge in Michigan is 1158 meters long.

And,  The Tsing Ma Bridge in Hong Kong is 97 meters longer than the Golden Gate Bridge in California.

Let the length of Golden Gate Bridge = x

Then, Lenght of Tsing Ma Bridge in Hong Kong = x + 97

Since, Together, all three bridges have a length of 3815 meters.

Hence, We get;

1158 + x + (x + 97) = 3815

1255 + 2x = 3815

2x = 2,560

x = 1,280 meters

Thus, Lenght of Tsing Ma Bridge in Hong Kong = x + 97

                                                                         = 1280 + 97

                                                                        = 1,377 meters

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Answer:

only child

Step-by-step explanation:

Answer:

you got them all right except graph 4 is a function! The trick is to use the vertical line test. Put your pencil vertically on your paper and move it across the graph. If your pencil passes through the same point twice, it's not a function. :)

Step-by-step explanation:

The equation of line perpendicular to "y = (1/2)x - 1" and passing through point (5,6) is y = -2x + 16,

The equation of the line is y = (1/2)x - 1, is in slope-intercept form "y = mx + b", where m is slope,

To find the slope of the given line, we see that it is in the form y = mx + b, where m = 1/2.

We know that, slope of a line perpendicular to this line will be the "negative-reciprocal" of this slope.

So, the slope of the perpendicular line will be -2.

Now we use the point-slope form of the equation of a line to find the equation of the perpendicular line passing through the point (5, 6). The point-slope form is : y - y₁ = m(x - x₁),

where (x₁, y₁) is given point and "m" is slope of the line;

Substituting the values, we get:

⇒ y - 6 = -2(x - 5),

⇒ y = -2x + 16,

Therefore, the equation of perpendicular line is y = -2x + 16.

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The expression to represent the given situation is M =30t.

Let's use the variable M to represent Susan's overall piano practice time over the course of t days.

Given that Susan practices the piano for 30 minutes every day, the sum of her practice time over the course of t days is:

M = 30t

As a result, M = 30t is the equation that describes the total amount of time Susan spends practicing the piano over the course of t days.

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The surface area of the cylindrical pottery is S = 163 inches²

Given data ,

Let the surface area of the cylindrical pottery be S

Now , the radius of the pottery r = d/2

r = 4.3 / 2

r = 2.15 inches

And , the height of the cylindrical vase = 11 inches

where S = B + Ph

On simplifying , we get

S = πr² + 2πr ( h )

S = ( 3.14 ) ( 2.15 )² + 2 ( 3.14 ) ( 2.15 ) ( 11 )

S = 14.51465 + 2 ( 74.261 )

S = 163.03665 inches²

Hence , the surface area is S = 163 inches²

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The derivative of the function cos(xº) in radians is y' = -sin(xπ/180)

From the question, we have the following function definition that can be used in our computation:

cos(xº)

Changing the degree into radian, we have

cos(xπ/180)

Express as a function

So, we have

y = cos(xπ/180)

When the cosine function is differentiated, we have

y' = -sin(xπ/180)

Hence, the differentiated function is y' = -sin(xπ/180)

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The number of chickens and pigs the farmer saw on the field are 37 and 16 respectively.

Let

Number of chickens = x

Number of pigs = y

x + y = 53

2x + 4y = 138

From (1)

x = 53 - y

Substitute x = 53 - y into (2)

2x + 4y = 138

2(53 - y) + 4y = 138

106 - 2y + 4y = 138

- 2y + 4y = 138 - 106

2y = 32

divide both sides by 2

y = 32/2

y = 16

Substitute y = 16 into

x + y = 53

x + 16 = 53

x = 53 - 16

x = 37

Therefore, there are 37 chickens and 16 pigs respectively.

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Answer: 550.320 to the nearest whole number is 550.

Step-by-step explanation: If the number if five or more, it rounds up, but if it is four or less, it stays the same. Therefore, because 3 is less than four, the answer is 550. Hope this helps! :)

Answer:

550

Step-by-step explanation:

If we look at the number we see .320, as we can see the number in the front is 3 and behind that is 2, when we are rounding the key thing to always remember is if its greater than 5 we round up if not go down so sense 3 doesn't go over 5 we don't change the number in front of it 0 and the same thing with 2 but we wouldn't change the 3 instead. so sense .320 doesn't qualify as a whole number we do not need it so we get the answer,

550.

PPPLLSSS GIVE BRAINLIST MEAN THE WORLD TY

HAVE A NICE DAY :)

The measure of the angle is A. 125^o

A measure of an angle which lies between 90^o and 180^0 is said to be obtuse. This implies that the measure of the angle is greater than a right angle but less than the sum of angles on a straight line.

In the given expression, the halfway between 120 and 130 degrees is given as;

(120 + 130)/ 2 = 125

Thus given that the angle has one ray pointing towards zero, then the other ray is pointing towards 125 degrees.

Then it can be concluded that the measure of the angle is A. 125^o.

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Answer:

the answer is 80

Step-by-step explanation:

1pound=16ounces

The calculated measure of m∠DEF is 45 degrees

From the question, we have the following parameters that can be used in our computation:

The image of the protractor

The reading from the protactor is

Angle = 0 degrees + 45 degrees

Evaluate the sum

So, we have

Angle = 45 degrees

This reading represents the angle DEF

Hence, the measure of m∠DEF is 45 degrees

The required difference cannot be calculaed from the given parameter

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Answer:

Step-by-step explanation: A. ΔJKL and ΔLMN have only one pair of angles that are congruent

C. ΔJKL has angles that measure

step 1

Find the value of x

we know that

----> by vertical angles

substitute the given values

solve for x

step 2

Find the measure of the interior angles of triangle JKL

we have

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

so

therefore

Triangle JKL has angles that measure

step 3

Find the measure of the interior angles of triangle LMN

we have

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

so

Triangle LMN has angles that measure

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

The corresponding angles of triangle JKL and LMN are not congruent

therefore

The triangles are not similar

Verify each statement

Part a) ΔJKL and ΔLMN have only one pair of angles that are congruent

The statement is true (see the explanation)

Part b) ΔJKL and ΔLMN have two pairs of angles that are congruent

The statement is false

Because have only one pair of angles that are congruent

Part c) ΔJKL has angles that measure

The statement is true  (see the explanation)

Part d) ΔLMN has angles that measure

The statement is false

Because, Triangle LMN has angles that measure

Part e) ΔJKL and ΔLMN are similar

The statement is false

Because, the corresponding angles are not congruent

The difference between the median math test score in the morning and the afternoon is 9.5

The median can simply be described as the middle number in a given set of data when the values are arranged in an order from least to the greatest values.

From the information given, we have that;

The math scores for the afternoon test were;

55, 70, 76, 85, 95

The math scores for the morning test were;

70, 80.5, 85.5, 90.5 and 95.5

Hence,

The median for the afternoon test = 76

The median for the morning test =85.5

The difference between the values would be = 85.5 - 76 = 9. 5

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The required fraction of the number of trees in a full row that is the number of trees in the extra row is 6/10.

Number of full rows = 8450 trees / 125 trees/row = 67.6 rows

Since Emiliano cannot plant a fraction of a row, the number of full rows he plants is 67.

To find the number of trees in the extra row, we need to subtract the number of trees in the full rows from the total number of trees:

Number of trees in the extra row = 8450 trees - (125 trees/row × 67 rows) = 75 trees

Therefore, Emiliano plants 67 full rows and an extra row with 75 trees.

To find the fraction of the number of trees in a full row that is the number of trees in the extra row, we need to divide the number of trees in the extra row by the number of trees in a full row:

Fraction of the number of trees in a full row that is the number of trees in the extra row = 55 trees / 125 trees/row = 0.6 or 60/100 or 6/10

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The linear equations of the lines are y = 1/3x and y = 4x + 17, respectively

The parallel line

The equation is given a

x - 3y = 9

So, we have

3y = x - 9

y = x/3 - 3

Slope = 1/3

The slopes of parallel lines are equal

So, the slope of the required line is 1/3

The equation is then calculated as

y = mx + c

So, we have

y = 1/3x + c

Using the points, we have

2 = 1/3 * 6 + c

c = 0

So, we have

y = 1/3x

The perpendicular line

The equation is given a

y + 1/4x - 5 = 0

So, we have

y = -1/4x + 5

Slope = -1/4

The slopes of parallel lines are opposite reciprocals

So, the slope of the required line is 4

The equation is then calculated as

y = mx + c

So, we have

y = 4x + c

Using the points, we have

5 = 4(-3) + c

c = 17

So, we have

y = 4x + 17

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The requried, intersection points are (√5, 5), (-√5, 5), (√2, 2), and (-√2, 2).

To find the intersection points of the parabola y = x² and the circle with radius √6 and center at (0,4), we need to solve the system of equations:

x² + (y - 4)² = 6 (equation of circle)

y = x² (equation of parabola)

We can substitute y = x² into the equation of the circle and obtain a quadratic equation in x:

x² + (x² - 4)² = 6

x⁴ - 7x² + 10 = 0

This equation can be factored as:

(x² - 5)(x² - 2) = 0

Therefore, the solutions for x are x = ±√5 and x = ±√2. To find the corresponding values of y, we can substitute these values of x into the equation of the parabola:

y = x²

For x = √5, we have y = (√5)² = 5, and for x = -√5, we have y = (-√5)² = 5.

For x = √2, we have y = (√2)² = 2, and for x = -√2, we have y = (-√2)² = 2.

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Lee's TV costs $4.05 to operate for a month of 30 days.

To calculate the cost of operating Lee's TV for a month, we need to find out the total number of kilowatt-hours (kWh) of electricity consumed by the TV during that time.

First, let's find out how many watts Lee's TV consumes in a day:

250 watts/hour x 3 hours/day = 750 watts/day

To convert this to kilowatts, we divide by 1000:

750 watts/day ÷ 1000 = 0.75 kilowatts/day

Now, we can calculate the total number of kilowatt-hours consumed by the TV in a month:

0.75 kilowatts/day x 30 days = 22.5 kilowatt-hours

Finally, we can calculate the cost of operating the TV for a month:

22.5 kilowatt-hours x 18 cents/kilowatt-hour = $4.05

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Answer:

  30.0 ft

Step-by-step explanation:

You want the length of a pole whose shadow is 20 ft long when the angle of elevation of the sun is 62° and the pole is tilted 8° away from the sun.

Referring to the attached diagram, we see that the interior angle at B of triangle ABC is 90° -8° = 82°. This makes the interior angle at A ...

  A = 180° -82° -62° = 36°

The law of sines tells us side lengths are proportional to the sines of the opposite angles:

  c/sin(C) = a/sin(A)

  c = a×sin(C)/sin(A) = 20×sin(62°)/sin(36°) ≈ 30.043 . . . feet

The length of the pole is about 30.0 feet.

Answer:

May is 52 inches tall

Step-by-step explanation:

stephan=46in

sister=6+stephan(in inches)=6+46=52

The height attained is 1290 feet

The time taken to reach the ground is 9s

The velocity on reaching the ground is  288 m/s.

We know that we can be able to handle the problems that we have here by the use of the equations of motion and that is what we shall do in the problems that follow.

h = ut - 1/2gt^2

h = height

u = initial velocity

g = acceleration due to gravity

t = time

Thus;

h = (18 * 5) - 1/2 * (-32) * 5^2

h =90 + 400

h = 490 feet

Thus the height after five seconds is 490 feet + 800 feet = 1290 feet

Using h = ut + 1/2gt^2

h = 1290 feet

u = 0 m/s when dropped

1290=  + 1/2 * (32) *t^2

1290 = 16t^2

Thus

t = 9s

The velocity when it hits the ground is;

v = u + gt

u = 0 m/s when dropped

v = 32 * 9

v = 288 m/s

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Answer:

x = 15

Step-by-step explanation:

3x+1+4x-3 = 103

7x = 105

x = 15

The solution is the number in polar form 4 - 4i is

4 Root(2) (cos(-45) + i sin(-45)).

We know that,

Polar form of a complex number is r( cos(theta) + i sin(theta) )

r is equal to the total distance created by the rectangular coordinates of the complex number

r = Root(4^2 + (-4)^2) = Root(32) = 4 Root(2)

To find theta, if a > 0, use arctan(b/a), where:

a = the first number

b = the second number

arctan (-4/4) = -45 degrees (-0.7854 radians)

The answer is 4 Root(2) (cos(-45) + i sin(-45))

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complete question;

Express the number in polar form 4 - 4i

Work Shown:

r = 2 = radius

h = 3 = height

SA = surface area of the cylinder

SA = 2*pi*r^2 + 2*pi*r*h

SA = 2*pi*2^2 + 2*pi*2*3

SA = 8pi + 12pi

SA = 20pi   ....... exact surface area

SA = 20*3.1415926535898

SA = 62.831853071796

SA = 62.832 ....... approximate surface area

Using an equation, the number of children, parents, and grandparents in attendance were:

An equation is an algebraic statement showing the equality or equivalence of two or more mathematical expressions.

Mathematical expressions combine variables, numbers, values, and constants using mathematical operands.

The total number of people in attendance at the family reunion = 400

Let the number of grandparents = x

Let the number of parents = 2x

Let the number of children = 2x + 50

x + 2x + 2x + 50 = 400

5x = 350

x = 70

Grandparents = 70

Parents = 140 (2 x 70)

Children = 190 (2 x 70 + 50)

Total = 400 (70 + 140 + 190)

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