Use the Law of Sines to find the missing angle of the triangle.

Find m < C to the nearest tenth if the c= 102, a = 71 and m < A=40

Answer:

31

Step-by-step explanation:

We want to estimate 6207 / 214

Round 6207 to 6200

and 214 to 200

6200/200

62/2 = 31

We know that our estimate will be a little high since we are rounding the denominator down

Answer:

4 I guess

Step-by-step explanation:

Because

3-1=2

2^2=2*2=4

Answer:

A

Step-by-step explanation:

Find the vertex form of the quadratic function below.

y = x^2 - 4x + 3

This quadratic equation is in the form y = a{x^2} + bx + cy=ax  

2

+bx+c. However, I need to rewrite it using some algebraic steps in order to make it look like this…

y = a(x - h)^2 + k

This is the vertex form of the quadratic function where \left( {h,k} \right)(h,k) is the vertex or the “center” of the quadratic function or the parabola.

Before I start, I realize that a = 1a=1. Therefore, I can immediately apply the “completing the square” steps.

STEP 1: Identify the coefficient of the linear term of the quadratic function. That is the number attached to the xx-term.

STEP 2: I will take that number, divide it by 22 and square it (or raise to the power 22).

STEP 3: The output in step #2 will be added and subtracted on the same side of the equation to keep it balanced.

Think About It: If I add 44 on the right side of the equation, then I am technically changing the original meaning of the equation. So to keep it unchanged, I must subtract the same value that I added on the same side of the equation.

STEP 4: Now, express the trinomial inside the parenthesis as a square of a binomial, and simplify the outside constants.

After simplifying, it is now in the vertex form y = a{\left( {x - h} \right)^2} + ky=a(x−h)  

2

+k where the vertex \left( {h,k} \right)(h,k) is \left( {2, - 1} \right)(2,−1).

Visually, the graph of this quadratic function is a parabola with a minimum at the point \left( {2, - 1} \right)(2,−1). Since the value of “aa” is positive, a = 1a=1, then the parabola opens in upward direction.

Example 2: Find the vertex form of the quadratic function below.

The approach to this problem is slightly different because the value of “aa” does not equal to 11, a \ne 1a  



​  

=1. The first step is to factor out the coefficient 22 between the terms with xx-variables only.

STEP 1: Factor out 22 only to the terms with variable xx.

STEP 2: Identify the coefficient of the xx-term or linear term.

STEP 3: Take that number, divide it by 22, and square.

STEP 4: Now, I will take the output {9 \over 4}  

4

9

​  

 and add it inside the parenthesis.

By adding {9 \over 4}  

4

9

​  

 inside the parenthesis, I am actually adding 2\left( {{9 \over 4}} \right) = {9 \over 2}2(  

4

9

​  

)=  

2

9

​  

 to the entire equation.

Why multiply by 22 to get the “true” value added to the entire equation? Remember, I factored out 22 in the beginning. So for us to find the real value added to the entire equation, we need to multiply the number added inside the parenthesis by the number that was factored out.

STEP 5: Since I added {9 \over 2}  

2

9

​  

 to the equation, then I should subtract the entire equation by {9 \over 2}  

2

9

​  

 also to compensate for it.

STEP 6: Finally, express the trinomial inside the parenthesis as the square of binomial and then simplify the outside constants. Be careful combining the fractions.

It is now in the vertex form y = a{\left( {x - h} \right)^2} + ky=a(x−h)  

2

+k where the vertex \left( {h,k} \right)(h,k) is \left( {{{ - \,3} \over 2},{{ - 11} \over 2}} \right)(  

2

−3

​  

,  

2

−11

​  

).

Example 3: Find the vertex form of the quadratic function below.

Solution:

Factor out - \,3−3 among the xx-terms.

The coefficient of the linear term inside the parenthesis is - \,1−1. Divide it by 22 and square it. Add that value inside the parenthesis. Now, figure out how to make the original equation the same. Since we added {1 \over 4}  

4

1

​  

 inside the parenthesis and we factored out - \,3−3 in the beginning, that means - \,3\left( {{1 \over 4}} \right) = {{ - \,3} \over 4}−3(  

4

1

​  

)=  

4

−3

​  

 is the value that we subtracted from the entire equation. To compensate, we must add {3 \over 4}  

4

3

​  

 outside the parenthesis.

Therefore, the vertex \left( {h,k} \right)(h,k) is \left( {{1 \over 2},{{11} \over 4}} \right)(  

2

1

​  

,  

4

11

​  

).

Example 4: Find the vertex form of the quadratic function below.

y = 5x^2 + 15x - 5  

Solution:

Factor out 55 among the xx-terms. Identify the coefficient of the linear term inside the parenthesis which is 33. Divide it by 22 and square to get {9 \over 4}  

4

9

​  

.

Add {9 \over 4}  

4

9

​  

 inside the parenthesis. Since we factored out 55 in the first step, that means 5\left( {{9 \over 4}} \right) = {{45} \over 4}5(  

4

9

​  

)=  

4

45

​  

 is the number that we need to subtract to keep the equation unchanged.

Express the trinomial as a square of binomial, and combine the constants to get the final answer.

Therefore, the vertex \left( {h,k} \right)(h,k) is {{ - \,3} \over 2},{{ - \,65} \over 4}  

2

−3

​  

,  

4

−65

​  

.

Answer:

(x - 1 )^2 - 3

Step-by-step explanation:

( x - 1 )^2 + ( -3)

x^2 - 2x + 1 - 3

x^2 - 2x - 2

Answer:

Domain: 0 ≤ x < 9

Range: 0 < y ≤ 3

Step-by-step explanation:

The domain is the set of all values used for x-coordinates of all points on the curve.

The range is the set of all values used for y-coordinates of all points on the curve.

Look at the graph. The leftmost point is (0, 3). That point is included in the graph since there is no open circle there.

So far we know this:

Domain goes from 0 to ...

Range goes from 3 to ...

Now we look at the rightmost point. It is (9, 0), but there is an open circle on it, so that point itself is not included in the domain or range.

Now we know this:

Domain goes from 0 to just less than 9.

Range goes from 3 to to just more than 0.

Domain: 0 ≤ x < 9

Range: 0 < y ≤ 3

Problem 2

Josh forgot to apply the square root to 16 when he went from [tex](x-3)^2 = 16[/tex] to [tex]x-3 = 16[/tex]

Also, he forgot about the plus/minus.

This is what his steps should look like

[tex]x^2 - 6x - 7 = 0\\\\x^2 - 6x = 7\\\\x^2 - 6x +9= 7+9\\\\(x-3)^2= 16\\\\x-3= \pm\sqrt{16}\\\\x-3= 4 \text{ or } x-3= -4\\\\x= 7 \text{ or } x= -1\\\\[/tex]

There are two solutions and they are x = 7 or x = -1. To check each solution, you plug it back into the original equation

Let's try out x = 7

x^2 - 6x - 7 = 0

7^2 - 6(7) - 7 = 0

49 - 42 - 7 = 0

0 = 0 ... solution x = 7 is confirmed. I'll let you check x = -1

====================================================

Problem 3

We will have

a = 1, b = -4, c = 3

plugged into the quadratic formula below to get...

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-4)\pm\sqrt{(-4)^2-4(1)(3)}}{2(1)}\\\\x = \frac{4\pm\sqrt{4}}{2}\\\\x = \frac{4\pm2}{2}\\\\x = \frac{4+2}{2} \ \text{ or } \ x = \frac{4-2}{2}\\\\x = \frac{6}{2} \ \text{ or } \ x = \frac{2}{2}\\\\x = 3 \ \text{ or } \ x = 1\\\\[/tex]

The two solutions are x = 3 or x = 1. You would check this by plugging x = 3 back into the original expression x^2 - 4x + 3. The result should be zero. The same applies to x = 1 as well.

Answer:

49 unit²

Step-by-step explanation:

Right triangle with equal legs given, let the leg be x.

Hypotenuse of isosceles right triangle is

Area of triangle:

Since we have hypotenuse = 14 units:

Then area:

Answer:

48 in.

Step-by-step explanation:

square

P = 4s

4s = 48 in.

s = 12 in.

triangle

s = 12 in. + 4 in.

s = 16 in.

P = 3s = 3(16 in.)

P = 48 in.

Answer: The required ratio is PT:TR  = 1:2.

Step-by-step explanation:

Given: In triangle PQR, ST || QR, PT = 4cm, TR = 8cm, area of PQR = 90 cm².

To find : PT:TR

.i.e. Ratio of PT to TR.

Here, PT:TR[tex]=\dfrac{PT}{TR}[/tex]

[tex]=\dfrac{4\ cm}{8\ cm}[/tex]

Divide numerator and denominator by 4 , we get

[tex]\dfrac{1}{2}[/tex]

Therefore, the required ratio is PT:TR  = 1:2.

Answer:

The correct option is;

3 + (-9) = -6, because -6 is 9 units to the left of 3

Step-by-step explanation:

The given information are;

Kelvin's score after the first round is shown at point K on the number line

The range of numbers on the number line = -10 to +10

The position of point K after the first round = +3

The number of points Kevin lost in the second round = 9 points

Therefore, Kevin's cumulative score = +3 - 9 = -6

Therefore, the expression that shows how many total points he has at the end is of round 2 = 3 + (-9) = -6, because -6 is 9 units to the left of 3.

Answer:

19

Step-by-step explanation:

[tex]f(x) =4x^3-8x^2+ax+b[/tex] has a factor [tex]2x-1[/tex] and

when divided by [tex]x+2[/tex], remainder is 20.

To find:Remainder when divided by (x-1)  ?

Solution:

[tex]2x-1[/tex] is a factor

[tex]2x - 1 = 0 \Rightarrow x = \frac{1}{2}[/tex] when we put this value of x to the function, it will become 0.

i.e.

[tex]\Rightarrow f(\dfrac{1}{2}) =0 =4\times (\dfrac{1}2)^3-8(\dfrac{1}2)^2+\dfrac{a}{2}+b=0\\\Rightarrow \dfrac{1}{2}-2+\dfrac{a}{2}+b=0\\\Rightarrow 1-4+a+2b=0\\\Rightarrow a +2b=3 ......(1)[/tex]

Remainder is 20 when f(x) is divided by [tex]x+2[/tex]

i.e.

[tex]f(-2) =20[/tex]

[tex]\Rightarrow f(-2) =20 =4\times (-2)^3-8(-2)^2-2a+b=20\\\Rightarrow -32-32-2a+b=20\\\Rightarrow -2a+b=84 ...... (2)[/tex]

Solving (1) and (2), Multiply equation (1) by 2 and adding to (2):

[tex]5b=6+84\\\Rightarrow b = \dfrac{90}{5} = \bold{18}[/tex]

By equation (1):

[tex]a+2(18) = 3\\\Rightarrow a = -33[/tex]

So, the equation becomes:

[tex]f(x) =4x^3-8x^2-33x+18[/tex]

[tex]\Rightarrow f(1) = 4(1) -8 (1) -33(1) +18 = \bold{19}[/tex]

So, when divided by (x-1), remainder will be 19.

Answer:

x = - 2, y = - 8

Step-by-step explanation:

Given the 2 equations

13x - 6y = 22 → (1)

x = y + 6 → (2)

Substitute x = y + 6 into (1)

13(y + 6) - 6y = 22 ← distribute and simplify left side

13y + 78 - 6y = 22

7y + 78 = 22 ( subtract 78 from both sides )

7y = - 56 ( divide both sides by 7 )

y = - 8

Substitute y = - 8 into (2) and evaluate for x

x = - 8 + 6 = - 2

Thus x = - 2, y = - 8

Answer:

Below

Step-by-step explanation:

For a given shape to be a rhombus, it should satisfy these conditions:

● The diagonals should intercept each others in the midpoint.

● The diagonals should be perpendicular.

● The sides should have the same length.

We will prove the conditions one by one.

■■■■■■■■■■■■■■■■■■■■■■■■■■

Let's prove that the diagonals are perpendicular:

To do that we will write express them as vectors

The two vectors are EG and DF.

The coordinates of the four points are:

● E(0,2c)

● G (0,0)

● F (a+b, c)

● D (-a-b, c)

Now the coordinates of the vectors:

● EG (0-0,0-2c) => EG(0,-2c)

● DF ( a+b-(-a-b),c-c) => DF (2a+2b,0)

For the diagonals to be perpendicular the scalar product of EG and DF should be null.

● EG.DF = 0*(2a+2b)+(-2c)*0 = 0

So the diagonals are perpendicular.

■■■■■■■■■■■■■■■■■■■■■■■■■■

Let's prove that the diagonals intercept each others at the midpoints.

The diagonals EG and DF should have the same midpoint.

● The midpoint of EG:

We can figure it out without calculations. Since G is located at (0,0) and E at (0,2c) then the distance between E and G is 2c.

Then the midpoint is located at (0,c)

● The midpoint of DF:

We will use the midpoint formula.

The coordinates of the two points are:

● F (a+b,c)

● D(-a-b,c)

Let M be the midpoint of DF

●M( (a+b-a-b,c+c)

● M (0,2c)

So EG and DF have the same midpoint.

■■■■■■■■■■■■■■■■■■■■■■■■■■

There is no need to prove the last condition, since the two above guarante it.

But we can prove it using the pythagorian theorem.

Answer:

as ratio of two type of fabric is different .

hence, the relationship between the number of square yards and the cost

is not proportional between the two types of fabric

Step-by-step explanation:

For a relation to be proportional

a:b = c:d

in other form

a/b = c/d

______________________________________________

Ratio for first type of fabric

cost of fabric/ area of fabric = 31.25/5 = 6.25

Ratio for other type of fabric

cost of fabric/ area of fabric = 71.50/11 = 6.5

as ratio of two type of fabric is different .

hence, the relationship between the number of square yards and the cost

is not proportional between the two types of fabric

Answer:

[tex]\huge \boxed{4}[/tex]

Step-by-step explanation:

2 raised to 2 is also the base 2 with an exponent of 2.

[tex]2^2[/tex]

2 is squared or multiplied by itself.

[tex]2^2 =2 \times 2 = 4[/tex]

Answer:

[tex]SU=18[/tex]

Step-by-step explanation:

The segments ST and TU make up the line segment SU. Add the values to find SU:

[tex]ST+TU=SU\\\\13+5=18[/tex]

The length of SU is 18.

The length of SU is 18 units.

We have a point T is between S and U.

We have to determine the length SU.

According to the question -

ST = 13 units

TU = 5 units

Now -

SU = ST + TU = 13 + 5 = 18 units

Hence, the length of SU is 18 units.

To solve more questions on Line Segments, visit the link below-

brainly.com/question/19569734

#SPJ2

Answer:

60 tiles are used

Step-by-step explanation:

1m equals 100 cm.

5m equals 500

3m equals 300

the whole thing is 500 by 300 which when you multiply gives you

150,000. When you multiple 50 by 50 it gives you 2,500. So when you divide 150,000 by 2,500 it gives you a total of 60 tiles. HOPE THIS HELPS

Answer:

60 tiles

Step-by-step explanation:

First, I would convert cm to m to make it easier

50 cm is .5 m

Now we can find how many tiles across it takes to make one row (5m)

.5 goes into 5, 10 times

That means we need 10 tiles across to fill one row

Now we need to find how many tiles it takes to fill up a column (3m)

.5 goes into 3, 6 times

It takes 6 tiles to fill up a column

Now we know it takes 10 tiles across and 6 vertically

10x6=60

60 tiles

Answer:

9

Step-by-step explanation:

Add nine to both sides:

[tex]6x = 54[/tex]

Divide by six:

[tex] \frac{6x = 54}{6} [/tex]

[tex]x = 9[/tex]

Answer:

x = 9

Step-by-step explanation:

I hope this helps!

Answer:

45 minutes faster

Step-by-step explanation:

Distance:

40 x 3.75 = 150

If travel 50 miles/h:

150/50 = 3

3.75 - 3 = 0.75 of hour

45 minutes

Hope that helped!!! k

Answer:

54 km/h

Step-by-step explanation:

From H to G:

Let the distance be x km.

Average speed = distance/time

60 = x/ 3

60*3 = x

x = 180 km

From G to F:

Let the distance be y km.

Average speed = distance/time

45 = y/2

45*2 = y

y = 90 km

From H to F:

Total distance = x + y = 180 + 90 = 270 km

Total time = 3 + 2 = 5 hours

Average speed from H to F

= Total distance/ total time

= 270/ 5

= 54 km/h

Step-by-step explanation:

If a line segment AB of length 6.6cm is drawn, bisecting it perpendicularly at N, we have two lines AN and NB of length 3.3cm each.

Because the line is bisected perpendicularly, the angles formed at the point of bisection are 90 degrees.

Answer:

$11.76

Step-by-step explanation:

Given:

Baggage having its weight greater than 40 pounds is charged at rate of 1% of the one-way fare .

Here, as per statement  One way fare of a trip = $98  

Weight of bag on that trip = 52 pounds

To find:

Charge for bag for this trip = ?

Solution:

Weight greater than that of 40 pounds = Given total Weight of baggage - 40 pounds

As per the given statement:

Weight greater than that of 40 pounds = 52 - 40 pounds = 12 pounds

Charges on extra baggage =  weight in pounds more than 40 multiplied by  1% of one-way fare.

Given that this trip has one way fare = $98.

The charge for a bag weighing 52 pounds = 1% of 98 \times 12

[tex]\Rightarrow \dfrac{1}{100}\times 98 \times 12\\\Rightarrow 98 \times 0.12\\\Rightarrow \bold{\$11.76}[/tex]

So, the answer is $11.76.

Answer:

11, 71, 19, 67, 43.

Step-by-step explanation:

Answer:

f exponent − 1  ( x )  =  -X/4  +  1/ 6

Plz mark brainlyest

Step-by-step explanation:

Answer:

331

Step-by-step explanation:

A number with 3 digits: using only

3, 1, 3

then:

3>1

the biggest possible number is:

331

Answer:

331

Step-by-step explanation:

Possible Combinations:

133

313

331

Out of these combinations, using process of elimination, we can determine that 331 is the greatest value out of the three numbers provided.

Answer:

See below.

Step-by-step explanation:

p: Atlanta is the capital of Georgia.

q: There are 4 feet in a yard.

p is true; q is false

11. p V q:

Atlanta is the capital of Georgia, or there are 4 feet in a yard.

Truth value: true since one of the statements is true.

12. p ▲ q:

Atlanta is the capital of Georgia, and there are 4 feet in a yard.

Truth value: false since not both statements are true.

13. p ▲ ~q:

Atlanta is the capital of Georgia, and there are not 4 feet in a yard.

Truth value: true since both of the statements are true.

11. ~p V q:

Atlanta is not the capital of Georgia, or there are 4 feet in a yard.

Truth value: false since both statements are false.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

  We already establish an understand  that, for Brooke to graduate she needs nothing less than 132 credit hours.

Now a semester has 15 credit hours, she has 4 semester completed already.

Hence 15*4= 60 credit hours done and dusted

This means that she has 132-60 = 72 credit hours to go

Since "c" is the number of credit hours that Brooke needs to complete in order to graduate college.

The inequality can be modeled as,

60 + c > 132

c= 132-60

c= 72

Answer:

What we need to do is simply multiply the values in both columns e.g 4 * 3/36 = 12/36

Please check explanation for complete answer

Step-by-step explanation:

Here, we are concerned about filling the empty columns of the table.

What we want to do here is simply straightforward. All we need to do is to

multiply the values of x by the values of P(x) in each of the individual rows.

Also recall, we do not need to reduce the fractions.

So we have;

2. 3 * 2/36 = 6/36

3. 4 * 3/36 = 12/36

4. 5 * 4/36 = 20/36

5. 6 * 5/36 = 30/36

6. 7 * 6/36 = 42/36

7. 8 * 5/36 = 40/36

8. 9 * 4/36 = 36/36

9. 10 * 3/36 = 30/36

10. 11 * 2/36 = 22/36

11. 12 * 1/36 = 12/36

Answer:

box 1 and box2 are correct.

Answer:

1.) 3 shovels/7 buckets

2.)7 buckets/3shovels

Answer: The number of sets contain any 4 numbers = 210

Step-by-step explanation:

Given: Universal set = {0,1,2,3,4,5,6,7,8,9}.

i.e. Total choices = Numbers in set = 10

By combinations, the number of sets contain any 4 numbers =[tex]^{10}C_4[/tex]

[tex]=\dfrac{10!}{4!6!}\ \ \ \ \ [^nC_r=\dfrac{n!}{r!(n-r)!}]\\\\=\dfrac{10\times9\times8\times7\times6!}{4\times3\times2\times1 \times6!}\\\\=210[/tex]

Hence, the number of sets contain any 4 numbers = 210