Use the elimination method to solve the system of equations. Choose the
correct ordered pair.
X+ y = 8
x- y = 6
A. (7,1)
B. (8,2)
C. (9,3)
D. (60)

Answer:

1. Cosine

2. x = 49°

3. Sine

4. y = 41°

Step-by-step explanation:

1. The trig function that will be used to solve for x is cosine.

2. Determination of angle x

x° =..?

Adjacent = 13

Hypothenus = 20

Cos x = Adjacent /Hypothenus

Cos x = 13/20

Take the inverse of Cos

x = Cos¯¹ (13/20)

x = 49°

3. The trig function that will be used to solve for y is sine.

4. Determination of angle y.

y° =..?

Opposite = 13

Hypothenus = 20

Sine y = Opposite /Hypothenus

Sine y = 13/20

Take the inverse of Sine

y = Sine¯¹ (13/20)

y = 41°

Answer:

prime

Step-by-step explanation:

x^2 - 2x + 3

What two numbers multiply to 3 and add to -2

There are none so this cannot be factored in the real numbers

I'm assuming your teacher wants you to distribute. If so, then you multiply the outer term 8 by each term inside (3a and 5). After that you add.

8 times 3a = 24a

8 times 5 = 40

So 8(3a+5) becomes 24a+40

We do not combine 24a and 40 as they are not like terms. So we leave 24a+40 as it is.

Answer:

C

Step-by-step explanation:

trust

Answer:

[tex]\Large \boxed{\sf \ \ 6x^2-2x-6 \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

[tex](f-g)(x)=f(x)-g(x)=6x^2-4-(2x+2)\\\\=6x^2-4-2x-2=\large \boxed{6x^2-2x-6}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Step-by-step explanation:

[tex](3x)^{2}[/tex]=[tex](3(2))^{2}[/tex] =36

(OR)

3([tex]x^{2}[/tex])=3(4)=12

Its depend on your sentence structure, what u r asking!!

The value of 3x squared when x = 2 is 36.

Given expression  [tex](3x)^2[/tex].

We have to calculate the value of this at [tex]x=2[/tex].

Now putting the value of x in the expression we get,

[tex](3\times2)^{2}[/tex]

Or,[tex]6^{2}[/tex]

[tex]36[/tex]

Hence the value of [tex](3x)^2[/tex] at [tex]x=2[/tex] will be 36.

For more details follow the link:

https://brainly.com/question/14170328

Answer: P(t) = $1000*2^t

Step-by-step explanation:

Ok, we know that in the week 1 the price is: p = $1000

After one week, the price doubles, so here we have: p = 2*$1000

After another week, the price doubles again, here the price is:

p = 2*(2*$1000) = $1000*2^2

Here we already can see the relation, for each week, we multiply the previous price by two, which will increase the exponent in the two by 1 unit.

Then, for week number t, the price will be:

P(t) = $1000*2^t

Answer:

Your parameter of interest is the thing that your research is focusing on. For example, if you want to find the weight of an average goat, your parameter of interest will be the weight of an average goat.

In this case, you will have two parameters of interest: percentages of children in a school district living in two-parent homes that graduated high school, and percentages of children living in single-parent homes that graduated from high school.

Hope this helps!

Answer:

The point (1,0) is common to all log functions of the form k(x) = logb x with any base (b). Logarithmic functions share this feature because of a property of exponents that states b0 = 1 for any value of b.

In a log function of the form k(x) = logb x, k(1) = logb 1.

So, by the definition of a logarithm, bk(1) = 1.

Applying the property of exponents to bk(1) = 1 = b0, we get k(1) = 0.

So, (1,0) is a point on the graph.

Step-by-step explanation:

Answer:

Distance between Amanda and Angela (c) = 4.30 km (Approx)

Step-by-step explanation:

Given:

Amanda rides (a) = 10 km

Angela rides (b) = 12 km

Angel between them = 20°

Find:

Distance between Amanda and Angela (c)

Computation:

Using law of cosines:

c² = a² + b² - 2abCosФ

c² = 10² + 12² - 2(10)(12)Cos20°

c² = 100 + 144 - 2(10)(12)(0.9397)

c² = 244 - 225.528

c² = 18.472

c = 4.2979

Distance between Amanda and Angela (c) = 4.30 km (Approx)

Answer:

1040

Step-by-step explanation:

Answer: The number is 1040.

Step-by-step explanation:

The question says 12.5% of a number is 130 so we can represent it by the equation.

12.5% * x = 130   where x is the number.Solve for x

12.5% * x = 130   convert 12.5% to a decimal

0.125 * x = 130

0.125x = 130   Divide both sides by 0.125

x= 1040  

Check.  

1040 * 12.5% = 130

Answer:

Approximately 11.5 units.

Step-by-step explanation:

We need to find the side opposite to ∠W. We are given the two angles ∠W and ∠X. We are also given that Side X is equal to 7. Therefore, we can use the Law of Sines.

Now, like last time, use the Law of Sines:

[tex]\frac{\sin(V)}{v}=\frac{\sin(W)}{w}=\frac{\sin(X)}{x}[/tex]

We can ignore the first term. Plug in 144 for ∠W, 21 for ∠X, and 7 for x.

[tex]\frac{\sin(144)}{w}=\frac{\sin(21)}{7}[/tex]

Cross multiply:

[tex]7\sin(144)=w\sin(21)\\w=\frac{7\sin(144)}{\sin(21)} \\v\approx11.4812\approx11.5[/tex]

Answer:

Step-by-step explanation:

a² - b² = (a +b)(a - b)

a = 525  & b  = 475

525² - 475² = (525 + 475) (525 - 475)

                   =1000 * 50

                   = 50,000

The value of (525)² - (475)² using the identity (a²- b²) = (a+b) (a-b) is 50000.

The expression given is:

(525)² - (475)²

The above expression looks similar to the expression (a²- b²).

The simplified form of the expression (a²- b²) is (a+b) (a-b).

So, (525)² - (475)² can be written as:

(525)² - (475)² = (525+475) (525-475)

(525)² - (475)² = 1000 * 50

(525)² - (475)² = 50000

Therefore, the value of (525)² - (475)² using the identity (a²- b²) = (a+b) (a-b) is 50000.

To get more about algebraic identities visit:

https://brainly.com/question/1528309

Answer:

Step-by-step explanation:

If m∠CED = 30° and m∠CDE = 90° than triangle CED is half of equilateral triangle where CE is side of the equilateral triangle, DE is hight of equilateral the triangle and CD is half of side of the equilateral triangle.

[tex]\dfrac{CE\sqrt3}2=2\sqrt3\\\\CE\sqrt3=4\sqrt3\\\\CE=4=s\\\\CD=\dfrac s2=\dfrac42=2[/tex]

Step-by-step explanation:

you can use any value either in place of x or y to find the corresponding coordinate but if you want to find the x and y intercept you can desigate x as zero and find the y intercept and vice versa.

so to find x and y intercept

y=25x+3. to find x intercept designate y as zero

0=25x+3

-3=25x

x= -3/25. p( -3/25,0)

y=25x+3 to find y intercept designate x as zero

y=25(0)+3

y=3. p(0,3)

the above y and x intercept indicates the points that the line of equation pass through when drawn graphically.

Answer:

I would think it is 45° (Sorry if it turns out I'm wrong)

Step-by-step explanation:

We know that one corner is already 90 degrees so we can take 180 and subtract 90 from it which gets us 90. The other two angles are equal so we take 90 and divide it by 2. This gets us 45°.

Answer:

? = 46

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp/ hypotenuse

sin ?  = 38 / 53

Take the inverse sin of each side

sin ^-1 ( sin ?) = sin ^-1 ( 38/53)

? = sin ^-1 ( 38/53)

? =45.80579628

To the nearest degree

? = 46

Answer:

y = 12.9

Step-by-step explanation:

To find the value of the side y, simply apply the law of cosines.

y^2 = (14)^2 + (9)^2 - 2(14)(9)cos(64)

y^2 = 196 + 81 - 110.47

y^2 = 166.53

y = 12.9

Therefore, your solution should be y = 12.9

Cheers.

Answer:

Dilation factor of 3

Step-by-step explanation:

First you wil want to find out the the coordinates for each of the shapes:

Regular:

P =9,6

Q =3,6

R =6,3

S =3,3

Prime notation:

P' =3,2

Q' =1,2

R' =2,1

S' =1,1

Then using great old common sense in the picture you will see 3 units go down to 1 unit which will indicate Dilation factor of 3 as the answer!

Hope this helps!

Answer:

The Dilation of the polygon would be 3

Step-by-step explanation:

The reason the answer shall be three is because if you look at both polygons and then look at their angles you should come to notice that the angle coordinates for the polygon that has been used for dilation multiplied by 3 would be congruent to the dilated shape, so in short look at lets say... the top right angle of both polygons, look at both of them and multiply the shape that has not been dilated and multiply that top right angle by whatever equals the dilated shapes angle value, for example (3,3)x3 = (9,9), thus the answer would be that the dilation is equal to 3.

Hope this helps, have a great day, and please consider giving me a Brainliest!!! ;)

Answer:

$ 27.6.

Step-by-step explanation:

Let the cost of tea be C.

Let the mass of tea be M

From the question given, we were told that the cost of tea varies directly with the mass. This can be expressed as:

C & M

C = KM

K is called constant of proportionality.

C is the cost of the tea.

M is the mass of tea.

Next, we shall determine the constant of proportionality, K.

Cost (C) = $ 10.35

Mass (M) = 4.5 kg

Constant (K) =..?

C = KM

10.35 = K × 4.5

Divide both side by 4.5

K = 10.35/4.5

K = 2.3

Finally, we shall determine the cost of 12kg of tea as follow:

Mass (M) = 12 kg

Constant (K) = 2.3

Cost (C) =..?

C = KM

C = 2.3 × 12

C = $ 27.6

Therefore, the cost of 12 Kg of tea is $ 27.6

Answer:

$27.6

Step-by-step explanation:

10.35 divided by 4.5 = 2.3

$2.3 for 1 kg

2.3 times 12= 27.6

Answer:

2<F(x)<5

Step-by-step explanation:

We can guess that it come between 2 and 5 given the pattern that we see in the table, but there’s no reason we can’t solve it to be sure.

F(x)=3 (Times the square root of 1.5-1)+2

3(square root of .5)+2

3(0.7)+2

2.12+2

4.12

So, yes, it is between 2 and 5

2<F(x)<5

Answer: B

Step-by-step explanation:

4,8 and 6 all go into 24

Answer:

x=1.94

x = - 1.94

Step-by-step explanation:

8x² + 5 = 35

Subtract 5 from each side

8x² + 5-5 = 35-5

8x²  = 30

Divide each side by 8

8x² /8 = 30/8

x² = 15/4

Take the square root of each side

sqrt( x²) = ±sqrt(15/4)

x = ±sqrt(15/4)

x=1.93649

x = - 1.93649

To the nearest hundredth

x=1.94

x = - 1.94

Answer:

1.94

Step-by-step explanation:

[tex]8x^2+5=35\\8x^2=30 \\x^2=30/8\\x^2=3.75\\\sqrt{3.75} \\[/tex]

≈ ±1.94

Answer:

5.8 cm

Step-by-step explanation:

Area of the shaded sector of the circle = 31.2 cm²

Angle (θ) of the minor sector = 360 - 256 = 104°

Are of sector of a circle is given as, θ/360*πr²

Therefore:

[tex] \frac{104}{360}*3.142*r^2 = 31.2 [/tex]

[tex] 0.29*3.142*r^2 = 31.2 [/tex]

[tex] 0.91*r^2 = 31.2 [/tex]

Divide both sides by 0.91

[tex] \frac{0.91*r^2}{0.91} = \frac{31.2}{0.91} [/tex]

[tex] r^2 = \frac{31.2}{0.91} [/tex]

[tex] r^2 = 34.286 [/tex]

[tex] r = \sqrt{34.286} [/tex]

[tex] r = 5.8 [/tex] (nearest tenth)

Answer:

see explanation

Step-by-step explanation:

In a trapezium the lower base angle is supplementary to the upper bas angle on the same side, thus

4x + 91 - 9x + 59 = 180, that is

- 5x + 150 = 180 ( subtract 150 from both sides )

- 5x = 30 ( divide both sides by - 5 )

x = - 6

Thus

∠ N = - 9x + 59 = - 9(- 6) + 59 = 54 + 59 = 113°

∠ K = 4x + 91 = 4(- 6) + 91 = - 24 + 91 = 67°

Answer:

dimensional figure are

Answer

(a - y) (b - y)

Step-by-step explanation:

(ab - ay) (-by + y^2)

a (b - y)  -y ( b - y)

(a-y) (b - y)

.. ..

Answer:

[tex]\boxed{(a-y) (b - y)}[/tex]

Step-by-step explanation:

Rearrange the terms.

[tex](ab - ay) (-by + y^2)[/tex]

Factor out common term.

[tex]a (b - y) -y ( b - y)[/tex]

Apply rule : [tex]a(b+c)+d(b + c) = (a+d)(b+c)[/tex]

[tex]a (b +- y) +-y ( b +- y)[/tex]

[tex](a+-y) (b +- y)[/tex]

Answer:

104

Step-by-step explanation:

:D

Answer:

[tex] r = 17.5 [/tex]

Step-by-step explanation:

Given ∆TRS,

Where,

m < R = 105°

TR = s = 15

RS = t = 6

ST = r = ?

Find r using the Law of Cosines.

[tex] r^2 = s^2 + t^2 - 2*s*t*cos(R) [/tex]

Plug in the values stated above into the formula

[tex] r^2 = 15^2 + 6^2 - 2*15*6*cos(105) [/tex]

[tex] r^2 = 225 + 36 - 180*(-0.2588)[/tex]

[tex] r^2 = 261 + 46.584 [/tex]

[tex] r^2 = 307.584 [/tex]

[tex] r = \sqrt{307.584} [/tex]

[tex] r = 17.5 [/tex] (to the nearest tenth)

Answer:

Option C is the correct option.

Step-by-step explanation:

[tex]f(x) = a {x}^{2} + bx + c[/tex]

Discriminant = [tex] {b}^{2} - 4ac[/tex]

Given d = 15

When discriminant D > 0 --> roots are real and distinct. ( unequal )

So , [tex] {3}^{rd} [/tex] option has real and distinct roots.

Hope this helps..

Best regards!!

Correct question :

There is a bag with only red marbles and blue marbles. The probability of randomly choosing a red marble is 7 9 . There are 28 red marbles in the bag and each is equally likely to be chosen. Work out how many marbles in total there must be.

Answer:

Total number of marbles = 36

Step-by-step explanation:

Marbles in bag: Red and Blue only

Probability of randomly choosing a red marble = 7/9

Number of red marbles = 28

Total number of marbles in the bag =?

Probability = required outcome / Total possible outcomes

P(red marble) = required outcome (number of red marbles) / Total possible outcomes(total number of marbles

7/9 = 28 / total number of marbles

Total number of marbles * 7/9 = 28

Total number of marbles = 28 ÷ 7/9

Total number of marbles = 28 * (9/7)

= 252 / 7

Total number of marbles = 36