Why did I get different answers to find x?
The first one I used Soh Cah Toa and the second one I used laws of sines

Answer:

c=13.2 units

Step-by-step explanation:

step 1

Find the measure of angle C

Remember that the sum of the internal angles of a triangle must be equal to 180 degrees

so

A+B+C=180°

substitute the given values

16°+49°+C=180°

65°+C=180°

C=180°-65°=115°

step 2

Find the measure of c

Applying the law of sines

c/sin(C)=a/sin(A)

substitute the given values and solve for c

c/sin(115°)=4/sin(16°)

c=4(sin(115°))/sin(16°)

c=13.2 units

Answer:

B. 62.5 m

Step-by-step explanation:

∠EDF and ∠ADC are vertical angles, and therefore equal.

EF and AC are parallel, so ∠DEF and ∠DAC are alternate interior angles, as well as ∠DFE and ∠DCA.  Therefore, each pair is equal.

From this, we can say ΔDEF and ΔDAC are similar triangles.  So we can write a proportion:

10 / 20 = DB / 125

DB = 62.5

Answer:

The correct option is B.

Step-by-step explanation:

Given information: In ΔEDF, FE=20 m and height = 10 m. In ΔADC, AC=125 m.

From the given information, we conclude that AC║EF.

In ΔEDF and ΔADC,

[tex]\angle E=\angle A[/tex]          (Alternate interior angles)

[tex]\angle EDF=\angle ADC[/tex]          (Vertically opposite angle)

By AA rule of similarity,

[tex]\triangle EDF\sim \triangle ADC[/tex]

The corresponding sides of two similar triangles are similar. So in ΔEDF and ΔADC,

[tex]\frac{base}{height}=\frac{FE}{h}=\frac{AC}{DB}[/tex]

[tex]\frac{20}{10}=\frac{125}{DB}[/tex]

[tex]2=\frac{125}{DB}[/tex]

On cross multiplication, we get

[tex]2DB=125[/tex]

Divide both sides by 2.

[tex]\frac{2DB}{2}=\frac{125}{2}[/tex]

[tex]DB=62.5[/tex]

Therefore the correct option is B.

AB= 20 and AB is the full line.

We will have to divide the length of the segment by 2 to find AC.

20/2= 10

AC is 10 units. Hope this helps!

Answer: the answer is: AC= 10

Step-by-step explanation:

you can imagine a line that represents AB with 20cm of large and the midline is located in the middle of this line; this means that AC is the half of AB

So in number=

[tex]AC= AB/2[/tex]

replacin [tex]AB[/tex]

[tex]AC= 20/2[/tex]

[tex]AC=10[/tex]

Answer:

The graph in the attached figure

Step-by-step explanation:

we know that

The equation of the line into slope intercept form is equal to

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-intercept

In this problem we have

[tex]m=-\frac{1}{3}[/tex]

[tex]b=-3[/tex]

substitute

[tex]y=-\frac{1}{3}x-3[/tex]

To graph the line find out the intercepts

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

[tex]y=-\frac{1}{3}(0)-3=-3[/tex]

The y-intercept is the point (0,-3) -----> is a given value

Find the x-intercept

The x-intercept is the value of x when the value of y is equal to zero

so

For y=0

[tex]0=-\frac{1}{3}x-3[/tex]

[tex]x=-9[/tex]

The x-intercept is the point (-9,0)

Plot the intercepts and join the points to graph the line

see the attached figure

To graph the line with a slope of -1/3 and a y-intercept of -3, plot the y-intercept at (0, -3) and use the slope to find additional points. Connect the points to graph the line.

To graph the line with a slope of -1/3 and a y-intercept of -3, we can start by plotting the y-intercept at the point (0, -3). Then, using the slope, we can find additional points on the line. Given that the slope is -1/3, we can move down 1 unit and to the right 3 units from the y-intercept to find the next point. We can continue this process to find more points and then connect them to graph the line.

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Answer:

If you choose any value for k other than 6, that will be give you the one solution.

If k=6, you have no solutions because the lines will be parallel.

Step-by-step explanation:

We are going to put each of this in y=mx+b where m is the slope and b is the y-intercept.

kx+2y=5

Subtract kx on both sides:

    2y=-kx+5

Divide both sides by 2:

     y=(-k/2)x+(5/2)

The slope is -k/2 and the y-intercept is 5/2

3x+y=1

Subtract 3x on both sides:

     y=-3x+1

The slope is -3 and the y-intercept is 1.

We want the system to have one solution so we want the slopes to be difference.

So we don't want (-k/2)=(-3).

Multiply both sides by -2: k=6.

We won't want k to be 6.

Answer:

6 is constant of the function .

Step-by-step explanation:

Given : f(x)=8x²−7x+6.

To find :  What is the constant of the function?

Solution : We have given that  f(x)=8x²−7x+6.

Standard quadratic equation : ax² +bx +c = 0.

Here,

a is the coefficient  of x² and b is the coefficient of x .

c = constant.

Hence on comparing with it standard quadratic equation

Here, 6 is constant.

Therefore, 6 is constant of the function .

Answer:

[tex]\large\boxed{A.\ \left\{\begin{array}{ccc}-3x+y=12\\-2x+4y=18\end{array}\right}[/tex]

Step-by-step explanation:

[tex]\underline{+\left\{\begin{array}{ccc}-3x+y=12\\x+3y=6\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-2x+4y=18\\\\\text{therefore}\\\\\left\{\begin{array}{ccc}-3x+y=12\\-2x+4y=18\end{array}\right[/tex]

Using the equation of the sum of the system of equations and the first equation of the system, the equivalent system of equations is:

-3x + y = 12

-2x + 4y = 18

(Option A)

Given the system of equations:

Add Eqn. 1 and Eqn. 2 together:

-3x + y = 12

x + 3y = 6 (ADD)

-2x + 4y = 18

Therefore, using the equation of the sum of the system of equations and the first equation of the system, the equivalent system of equations is:

-3x + y = 12

-2x + 4y = 18

(Option A)

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Answer:

volume

Step-by-step explanation:

volume is measured in cubic

Answer:

A. Volume

Step-by-step explanation:

IN two-dimension space we use to calculate area, perimeter but not volume.

In three-dimensional space we also find Volume, Surface area and lateral surface area only.

In volume we find what amount of substance kept inside that container/solid.

Perimeter is the length of total boundary.

Surface area is total area of each face.

And, In Lateral surface area we find the area of each face except bottom and top face.

Thus, "the amount of three-dimensional space  inside a solid" is described by VOLUME.

Answer:

Option C is correct.

Step-by-step explanation:

We are given

1452 divided by 44 = (1452 divided by 4) divided by 11

We know that 44 = 4*11

So, 4 and 11 are factors of 44.

This division problem uses the method of Factors.

Option C is correct.

Answer:

[tex]\large\boxed{(6r-1)(-8r^3)=-48r^4+8r^3}[/tex]

Step-by-step explanation:

[tex](6r-1)(-8r^3)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=(6r)(-8r^3)+(-1)(-8r^3)\qquad\text{use}\ (a^n)(a^m)=a^{n+m}\\\\=-48r^{1+3}+8r^3\\\\=-48r^4+8r^3[/tex]

The product of the binomials (6r-1) and (-8r-3) is obtained using the FOIL method, and the final product is -48r² - 10r + 3.

To find the product of the binomials (6r-1) and (-8r-3), we use the distributive property (also known as the FOIL method). The FOIL method stands for First, Outer, Inner, Last, which refers to the multiplication of the respective terms in each binomial.

Applying the FOIL method:

First: Multiply the first terms in each binomial: 6r * -8r = -48r²

Outer: Multiply the outer terms in each binomial: 6r * -3 = -18r

Inner: Multiply the inner terms in each binomial: -1 * -8r = 8r

Last: Multiply the last terms in each binomial: -1 * -3 = 3

Now, combine the like terms (-18r + 8r = -10r) and write the final product: -48r² - 10r + 3

Answer:

The total length of the molding is 21 feet and 6 inches

Step-by-step explanation:

* Lets explain how to solve the problem

- The length of the two pieces are 8 feet 7 inches and 12 feet 11 inches

- Each foot has 12 inches

- Lets change the lengths of the two pieces to inch

# First piece 8 feet 7 inches

∵ 1 foot = 12 inches

∴ 8 feet 7 inches = 8 × 12 + 7

∴ 8 feet 7 inches = 96 + 7

∴ 8 feet 7 inches = 103 inches

# Second piece 12 feet 11 inches

∵ 1 foot = 12 inches

∴ 8 feet 7 inches = 12 × 12 + 11

∴ 8 feet 7 inches = 144 + 11

∴ 8 feet 7 inches = 155 inches

- To find the total length add the two answers

∴ The total length of the molding = 103 + 155 = 258 inches

- Divide the answer by 12 to change it to feet

∵ 258 ÷ 12 = 21.5 feet

- To change it to feet and inch multiply 0.5 feet by 12

∵ 0.5 × 12 = 6 inches

∴ The total length of the molding is 21 feet and 6 inches

Answer:

yes

Step-by-step explanation:

7 * 6 = 42

Answer:

True

Step-by-step explanation:

Take 4/11 and you get 0.363636363636, which is the same if you take 12/33.  So the proportion of the two is the same.

Answer:

True

Step-by-step explanation:

To find out if the proportion is true you have to find out what multiplied by 4 equals 12.

To find that out you have to divide 12 by 4 which equals 3.

Now you have to do the same for the denominators. So, 33/11 equals 3.

The proportion is true because the numerator and denominator are both multiplied by 3 to get 12 to 33.

Answer:

The correct option is C.

Step-by-step explanation:

From the given information it is clear that the total number of divers in a group is 9.

The number of selected divers is 4.

The total ways to select r items from total n item is

[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

Using this combination formula, the number of different teams of four divers that can be selected from a group of nine divers is

[tex]^9C_4=\frac{9!}{4!(9-4)!}[/tex]

[tex]^9C_4=\frac{9!}{4!5!}[/tex]

[tex]^9C_4=\frac{9\times 8\times 7\times 6\times 5!}{4\times 3\times 2\times 1\times 5!}[/tex]

Cancel out common factors.

[tex]^9C_4=126[/tex]

Therefore the correct option is C.

The correct answer is c. 126 different teams of four divers can be selected from a group of nine divers.

To solve this problem, we use the concept of combinations from combinatorics. A combination is a way of selecting items from a collection, such that the order of selection does not matter. In this case, we want to find out how many different ways we can select 4 divers out of 9 to form a team, and the order in which we select the divers does not matter.

The formula for calculating combinations is given by:

[tex]\[ C(n, k) = \frac{n!}{k!(n-k)!} \][/tex]

For our problem:

[tex]- \( n = 9 \) (the total number of divers)\\ - \( k = 4 \) (the number of divers we want to select for a team)[/tex]

Plugging these values into the formula, we get:

[tex]\[ C(9, 4) = \frac{9!}{4!(9-4)!} \] \[ C(9, 4) = \frac{9!}{4!5!} \] \[ C(9, 4) = \frac{9 \times 8 \times 7 \times 6 \times 5!}{4 \times 3 \times 2 \times 1 \times 5!} \] \[ C(9, 4) = \frac{9 \times 8 \times 7 \times 6}{4 \times 3 \times 2 \times 1} \] \[ C(9, 4) = \frac{3024}{24} \] \[ C(9, 4) = 126 \][/tex]

Therefore, there are 126 different ways to select a team of four divers from a group of nine divers.

I doubt it says "or". It's probably an and.

[tex]\dfrac{-2}{3}x > 8\wedge\dfrac{-2}{3x} < 4[/tex]

[tex]-2x > 24\wedge3x < \dfrac{4}{-2}[/tex]

[tex]x > -12\wedge x < -\dfrac{2}{3}[/tex]

[tex]\Rightarrow\boxed{-12 < x < -\dfrac{2}{3}}[/tex]

[tex]\Rightarrow\boxed{x\in(-12,-\dfrac{2}{3})}

[/tex]

Hope this helps.

r3t40

Answer:

{x | x < -12 or x > -6}

Answer:

30

Step-by-step explanation:

Step-by-step explanation:

cost of adult ticket, AT = $22

Cost of child ticket, CT = $15

Difference in price, D = AT-CT = 22-15 =$7

Difference in price for 3 tickets = 3D = $21

Answer:

Three Adult Tickets will be $22 more than Three Children's Ticket

Step-by-step explanation:

One Adult= $22

One Child =$15

Three adults= $22 x 3= $66

Three Children= $15 x 3= $45

$66 - $45= $21

Check the picture below.

Answer:

Step-by-step explanation:

If the circle inscribed in a quadrilateral, then the sums of the opposite sides of the quadrilateral are the same.

Therefore we have the equation:

AB + CD = BC + AD

Therefore the perimeter of polygon ABCD is equal to

P = 2(AB + CD)

Substitute AB = 10.5cm, CD = 12.5cm:

P = 2(10.5cm + 12.5cm) = 2(23cm) = 46cm

Answer:

1,2, 1,203, 12,03, 12,3, 12,301

Step-by-step explanation:

1,2 → 1,200

1,203

12,3 → 12,300

12,301

I am joyous to assist you anytime.

Ordered from least to greatest:

Answer:

√3 - 2.

Step-by-step explanation:

Let A = 330 degrees so  A/2 = 165 degrees.

tan A/2 = (1 - cos A) /  sin A

tan 165 = (1 - cos 330) / sin 330

= (1 - √3/2) / (-1/2)

=  -2(1 - √3/2)

= -2 + 2 * √3/2

=  √3 - 2.

Answer:

[tex]\sqrt{3}[/tex] - 2

Step-by-step explanation:

Using the half- angle identity

tan( [tex]\frac{x}{2}[/tex] ) = [tex]\frac{sinx}{1+cosx}[/tex]

[tex]\frac{x}{2}[/tex] = 165° ⇒ x = 330°

sin330° = - sin30° = - [tex]\frac{1}{2}[/tex]

cos330° = cos30° = [tex]\frac{\sqrt{3} }{2}[/tex]

tan165° = [tex]\frac{sin330}{1+cos330}[/tex]

            = [tex]\frac{-\frac{1}{2} }{1+\frac{\sqrt{3} }{2} }[/tex]

            = - [tex]\frac{1}{2}[/tex] × [tex]\frac{2}{2+\sqrt{3} }[/tex]

            = - [tex]\frac{1}{2+\sqrt{3} }[/tex]

Rationalise by multiplying numerator/ denominator by the conjugate of the denominator

The conjugate of 2 + [tex]\sqrt{3}[/tex] is 2 - [tex]\sqrt{3}[/tex], hence

tan 165°

= - [tex]\frac{2-\sqrt{3} }{(2+\sqrt{3})(2-\sqrt{3})  }[/tex]

= - [tex]\frac{2-\sqrt{3} }{4-3}[/tex]

= - (2 - [tex]\sqrt{3}[/tex] )

= - 2 + [tex]\sqrt{3}[/tex] = [tex]\sqrt{3}[/tex] - 2

Answer:

C

Step-by-step explanation:

Substitute t = - 3 into h(t), then substitute value obtained into g(t)

h(- 3) = (- 3)² - 2 = 9 - 2 = 7, then

g(7) = (2 × 7) + 2 = 14 + 2 = 16 → C

1. 12 mph, 24 miles

2. m=4, y=22

3.15/1, $1500

4. x=30 y=60, k cheaper, j cheaper

Answer:

I just got done doing this. Full answers to all 4 problems are down below. All correct answers are bolded.  

Step-by-step explanation:

First problem: x2 + -8 x = 9

Add 16 to each side x2 – 8x = 9 to complete the square.

Now that you have x² - 8x + 16 = 9 + 16, apply the square root property to the equation. Answer: (x – 4)² = 25

Choose the solutions to the quadratic equation x2 – 8x – 9 = 0. Answer: -1, 9  

The equation x² - 8x - 9 = 0 can be written as x² +(-8x) = 9 which is of the form  x² + bx = c  where,

b = -8

c = 9

An equation is a mathematical statement which equate two algebraic expressions. An equation has an equal to (=) sign in between the expression.

The given equation is

x² - 8x - 9 = 0.

⇒ x² - 8x = 9

⇒ x² +(-8x) = 9

So the given equation is written of the form x² + bx = c, where,

b = -8

c = 9

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Answer:

B: 12.2cm

Step-by-step explanation:

Got it right on edge 2021✅

Answer:

49

Step-by-step explanation:

I think I have read this right!

You let me know if you did not mean to write the following:

[tex]\sum_{k=1}^{7}(1+(k-1)(2)[/tex]

Alright so the lower limit is 1 and the upper limit is 7.

All this means is we are going to use the expression 1+(k-1)(2) and evaluate it for each natural number between k=1 and k=7 and at both k=1 and k=7.

The sigma thing means we add those results.

So let's start.

Evaluating the expression at k=1: 1+(1-1)(2)=1+(0)(2)=1+0=1.

Evaluating the expression at k=2: 1+(2-1)(2)=1+(1)(2)=1+2=3.

Evaluating the expression at k=3: 1+(3-1)(2)=1+(2)(2)=1+4=5.

Evaluating the expression at k=4: 1+(4-1)(2)=1+(3)(2)=1+6=7.

Evaluating the expression at k=5: 1+(5-1)(2)=1+(4)(2)=1+8=9.

Evaluating the expression at k=6: 1+(6-1)(2)=1+(5)(2)=1+10=11.

Evaluating the expression at k=7: 1+(7-1)(2)=1+(6)(2)=1+12=13.

Now for the adding!

1+3+5+7+9+11+13

  4+  12+    20+13

        16+     33

           49

Answer: Y = -3x-2

Step-by-step explanation:

if there are two co-ordinates (x1,y1) and (x2,y2).

If the line is passing through these co-ordinates

Then Slopw of the line  = (y2-y1)/(x2-x1)

We have one co-ordinate (-0,-2) let it be (X1,Y1)

Let second co-ordinate be (X,Y)

Slope = -3 = (Y-(-2)) / (X-0)

-7  = (Y+2)/(X)

Y+2 = -3 (X)

Y+2 = -3X

ADDING -2 ON BOTH SIDES OF THE EQUATION

Y+2-2 = -3X-2

Y = -3x-2

Answer:

{x,y} = {3,1}

Step-by-step explanation:

// Solve equation [1] for the variable  x  

 [1]    x = -2y + 5

// Plug this in for variable  x  in equation [2]

  [2]    3•(-2y+5) + 5y = 14

  [2]     - y = -1

// Solve equation [2] for the variable  y  

  [2]    y = 1

// By now we know this much :

   x = -2y+5

   y = 1

// Use the  y  value to solve for  x  

   x = -2(1)+5 = 3

Solution :

{x,y} = {3,1}

For this case we have the following system of equations:

[tex]x + 2y = 5\\3x + 5y = 14[/tex]

To solve, we multiply the first equation by -3:

[tex]-3x-6y = -15[/tex]

We add the equations:

[tex]-3x + 3x-6y + 5y = 14-15\\-y = -1\\y = 1[/tex]

We look for the value of the variable "x":

[tex]x + 2 (1) = 5\\x + 2 = 5\\x = 5-2\\x = 3[/tex]

Thus, the solution of the system is (3,1)

Answer:

(3,1)

Answer:

8

Step-by-step explanation:

To find Y, find X first. Multiply 2 by W (3) which is 6, and divide by 3, which gives us X=2. The inequality W+Z=X+Y substituted is 10=2+Y. Subtract 2 from 10 and you get Y=8

Answer:

13) 8

14) 2X  or 4W/3 (depending on what the choices are)

Step-by-step explanation:

So I'm using the box given:

If                                 then

W  X                            W+Z=X+Y and 2W=3X

Y    Z

13)

3   X                           3+7=X+Y and 2*3=3*X

Y   7

To get W,X,Y, and Z I compared it to the first lay out and then replace the other W's,X's,Y's, and Z's.

So we have 3+7=X+Y which means 10=X+Y.

We also have 2*3=3*X which means 2=X (I divided both sides by 3).

If X=2 then 10=X+Y gives us 10=2+Y.

10=2+Y can be solved by subtracting 2 on both sides:

8=Y

Y=8

14)

W  X                                  W+W=X+Y and 2W=3X

Y   W

So W+W=X+Y means 2W=X+Y

We are also given 2W=3X which means by substitution into the first equation we get 3X=X+Y.

3X=X+Y can be solved by subtracting X on both sides:

2X=Y

We can also write Y in terms of W.

We have 2W=3X so that means X=2W/3 (I divided both sides by 3)

Now I'm going to replace X in 2X=Y with (2W/3) giving me:

2(2W/3)=Y

4W/3=Y

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=6x-27&(1)\\y=4x-17&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\6x-27=4x-17\qquad\text{add 27 to both sides}\\6x=4x+10\qquad\text{subtract}\ 4x\ \text{From both sides}\\2x=10\qquad\text{divide both sides by 2}\\x=5\\\\\text{Put it to (2):}\\\\y=4(5)-17\\y=20-17\\y=3[/tex]

Answer:

See below.

Step-by-step explanation:

You didn't need to.

The angle adjacent to angle x = 45 degrees (alternate interior  angle to the angle marked 45).

So x = 180 - 45 = 135 degrees.

Answer:

C. 135

Step-by-step explanation:

In the figure above, line M is parallel to line N. The value of x is 135.

x = 180 - 45 = 135