what is the initial value for g(x) = 3(1/4)^(x-2) - 3

Answer:

(C) x² - 5x - 14

Step-by-step explanation:

The roots of any quadratic equation will always make the equation equal to 0. So, we can test each equation with the values -2 and 7 to test if both values make the equation 0.

Let's start with A. x² + 5x - 14.

(-2²) + (5 × -2) - 14

4 - 10 - 14 = -20, so we already know that A doesn't work as it doesn't equal 0.

Let's try B. (x+2)² + 7.

(-2+2)² + 7

0² + 7

0+7 = 7, so B doesn't work either.

Let's try C. x² - 5x - 14.

(-2²) - (5×-2) -14

4 + 10 - 14 = 0, ooh we're on to something here! However, for this equation to work, both -2 AND 7 have to work with it. Let's try 7.

(7²) - (5×7) - 14

49 - 35 - 14 = 0, so yes! Both -2 and 7 work for this equation.  Therefore, the roots -2 and 7 work for the quadratic function of x² - 5x - 14, C.

Hope this helped!

Answer:

Step-by-step explanation:

[tex]Opposite = r\\Hypotenuse = 13\\\alpha = 34\\Using SOHCAHTOA\\Sin \alpha = \frac{opp}{hyp} \\Sin 34 = \frac{r}{13} \\0.559 = \frac{r}{13} \\Cross \: Multiply\\r = 0.559\times 13\\r = 7.267\\r = 7.27[/tex]

Answer:

104

Step-by-step explanation:

:D

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

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°

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:

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:

0.09

Step-by-step explanation:

11.52 / 128

First, divide both numerator and denominator by 2:

2.88 / 32

Divide both numerator and denominator by 4:

0.72 / 8

Divide 0.72 by 8, you get 0.09.

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:

$ 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:

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:

74°.

Step-by-step explanation:

From the question given above,

Cos A = 0.2785

To get the value of angle A, we simply find the inverse of Cos as shown below:

Cos A = 0.2785

Take the inverse of Cos.

A = Cos¯¹ 0.2785

A = 73.8° ≈ 74°

Therefore, the value of angle A is approximately 74°

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:

x = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Given function;

y = 5 + x - x²

To find the maximum value, follow these steps

(i) Find the first derivative (which is the slope) of the given function with respect to x. i.e;

[tex]y^{'}[/tex] = [tex]\frac{dy}{dx}[/tex] = [tex]\frac{d(5 + x - x^2)}{dx}[/tex]

[tex]y^{'}[/tex] = [tex]1 - 2x[/tex]

(ii) From the result in (i) determine the value of x for which the slope is zero. i.e.

x for which

1 - 2x = 0

=> 1 = 2x

=> x = [tex]\frac{1}{2}[/tex]

Therefore, the value of x for which the function is maximum is [tex]\frac{1}{2}[/tex]

Answer:

x = 1/2

Step-by-step explanation:

The standard equation of a quadratic function is given by:

y = ax² + bx + c, If a > 0 then the graph has a minimum but if a < 0, then the graph has a maximum. To find the maximum or minimum, we differentiate the function with respect to x and equate to zero that is y'(x) = 0.

For the function y = 5 + x - x², a = -1 < 0, therefore it has a maximum.

Differentiating with respect to x:

y'(x) = 1 - 2x

Equating to zero

-2x + 1 = 0

-2x = -1

x = -1/ -2

x = 1/2

The function has a maximum at x = 1/2

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:

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:

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:

13/90

Step-by-step explanation:

The decimal that you wrote is mixed non terminal decimal. Which means all the number don't repeat themselves.

The denominator of a non terminating decimal is always 9 even though it depends on the type of the decimal, whether it is simple or mixed

The denominator of the given decimal is 90. The denominator is 2 digit number since the given decimal is also 2 digit decimal even though it is under repeating bars.

And the numerator is 10, 13-3.

We subtract 3 since it is the one repeating itself.

Hope it helps ;) ❤❤❤

Answer:

The inclination of the through the points (5, 14) and (9, 18) is 45°

Step-by-step explanation:

The given point has coordinates (5, 14) and (9, 18)

To find the inclination, θ, of the line passing the two points, with point 1 having coordinates (x₁, y₁) and point 2,  having coordinates (x₂, y₂), we have to look for the slope as follows;

The slope, m = Change in the y-coordinate ÷ Change in the x-coordinate

[tex]m = \dfrac{y_2 - y_1}{x_2-x_1}[/tex]

Where:

y₁ = The y-coordinate of point 1 = 14

x₁ = The x-coordinate of point 1 = 5

y₂ = The y-coordinate of point 2 = 18

x₂ = The x-coordinate of point 2 = 9

Substituting, we have;

[tex]m = \dfrac{18 - 14}{9-5} = \dfrac{4}{4} = 1[/tex]

The inclination of the line is the angle the line makes with x-axis

Since the slope gives the ratio of the opposite and adjacent segment to the angle of inclination, the arc-tangent of the slope will give the angle in degrees as follows;

[tex]tan^{-1}m = tan^{-1} \left (\dfrac{y_2 - y_1}{x_2-x_1} \right) = \theta[/tex]

given that m = 1, we have;

tan⁻¹(m) = θ = tan⁻¹(1) =  45°.

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:

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:

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

Answer: y = 2/5 --> y = 0.4

Step-by-step explanation:

5y = 2 is a horizontal line at y = 2/5

so the y-value is 2/5 = 0.4 at EVERY x-value.

Answer: B

Step-by-step explanation:

4,8 and 6 all go into 24

Answer:

C

Step-by-step explanation:

trust

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:

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!!

Answer:

See Below.

Step-by-step explanation:

We have the expression:

[tex]3pf^2-21p^2f+6pf-42p^2[/tex]

Part A:

Find the GCF. Notice that we have a three in every term and a p in every term. Thus, the GCF will be 3p. Factor:

[tex]3p(f^2-7pf+2f-14p)[/tex]

This is the most we can do.

Part B:

Continuing from where we left off, we can factor the entire expression by grouping:

[tex]\displaystyle \begin{aligned} &= 3p(f^2-7pf+2f-14p) \\ \\ &= 3p(f(f-7p)+2(f-7p)) \\ \\ &=3p((f+2)(f-7p))\end{aligned}[/tex]

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:

dimensional figure are