What is the value of a for the exponential function in the
graph represented in the form of f(x) = a(b)?
O -4
O -3
O 3
O 4

Answer:

they are 16 and 4

Step-by-step explanation:

We can call the numbers x and y and we can write:

x - y = 12

x + y = 20

Adding these equations gives us 2x = 32 which means x = 16 and substituting this value into the first equation gives us y = 4.

Answer:

The numbers are 16 and 4

Step-by-step explanation:

Let the two numbers be x and y

x-y = 12

x+y = 20

Add the two equations together

x-y = 12

x+y = 20

-------------------

2x = 32

Divide by 2

2x/2 =32/2

x = 16

Now find y

x+y =20

16+y =20

Subtract 16

y = 20-16

y = 4

Answer:

i believe a=105, b=29, and c=45

Answer:

Length L = 51.88 feet

Step-by-step explanation:

From the given information,

The length of the pendulum can be determined by using the Formula for the period T which  is the time of one full oscillation of a simple pendulum.

[tex]T = 2 \pi \sqrt {\dfrac{L}{g}}[/tex]

where;

T = period of the time of one full oscillation = 8 seconds

L = length in feet

g = acceleration due to gravity in  feet = 32 ft/s²

π = 22/7

[tex]8 = 2 \times \dfrac{22}{7} \times \sqrt {\dfrac{L}{32}}[/tex]

[tex]8 = 6.2857 \times \sqrt {\dfrac{L}{32}}[/tex]

[tex]\dfrac{8}{6.2857} =\sqrt {\dfrac{L}{32}}[/tex]

[tex]1.273=\sqrt {\dfrac{L}{32}}[/tex]

[tex]1.273= {\dfrac{\sqrt L}{ \sqrt {32}}}[/tex]

[tex]1.273 \times { \sqrt {32}}}= {\sqrt L}[/tex]

[tex]7.2012= {\sqrt L}[/tex]

L = 7.2012²

L = 51.88 feet

Answer:

Step-by-step explanation:

From the information given,

Mark: 6,7,8,9,10

frequency:5,4,7,10,4

a) Range = highest mark - lowest mark

Range = 10 - 6 = 4

b) The number of students in the group is the sum of the frequency. Therefore,

Number of students = 5 + 4 + 7 + 10 + 4 = 30 students

c) Mean mark = (mark × frequency)/total frequency

[(6 × 5) + (7 × 4) + (8 × 7) + (9 × 10) + 10 × 4)]/ 30

Mean mark = (30 + 28 + 56 + 90 + 40)/30 = 244/30

Mean mark = 8.1

Answer: From the information given, Mark: 6,7,8,9,10 frequency:5,4,7,10,4 a) Range = highest mark - lowest markRange = 10 - 6 = 4b) The number of students in the group is the sum of the frequency. Therefore, Number of students = 5 + 4 + 7 + 10 + 4 = 30 studentsc) Mean mark = (mark × frequency)/total frequency[(6 × 5) + (7 × 4) + (8 × 7) + (9 × 10) + 10 × 4)]/ 30Mean mark = (30 + 28 + 56 + 90 + 40)/30 = 244/30Mean mark = 8.1

Step-by-step explanation:

Answer:

363.741 feet

Step-by-step explanation:

Let the height of the cliff be represented by x. Applying the appropriate trigonometric function, we have;

Tan θ = [tex]\frac{opposite side}{adjacent side}[/tex]

Tan [tex]60^{0}[/tex] = [tex]\frac{x}{210}[/tex]

cross multiply to have;

   x = 210 × Tan [tex]60^{0}[/tex]

      = 210 × 1.7321

      = 363.741

The cliff is 363.741 feet high.

Answer:

Sacramento

Step-by-step explanation:

S 11+9+14+12+8=54

SF 11+8+8+9+12=48

The statement that is true about the information in the table is that the data is non-linear.

The easier way to study the table is by graphing it. Here we have the points:

(11, 11), (12, 9), (9, 8), (8, 8), and (14, 12).

The graph of these points can be seen below, there you can see that the data in the table is clearly non-linear, as we can't draw a line that contains the points on the table.

So the correct option is non-linear.

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Answer:

55 games

Step-by-step explanation:

What we have to figure out is the total amount of games they played the whole year. We know they won 20% of their games, which equates to 11 games won in total. In order to find the total amount of games we will need to set up the equation [tex]g = 11/20[/tex]%. We solve this accordingly: [tex]g = (11/20) *100[/tex]; [tex]g = (.55)*100[/tex]; [tex]g = 55[/tex].

Answer:

36 in²

Step-by-step explanation:

The figure that is been described is a Parallelogram.

The area of a Parallelogram is = Base × Height

From the question, the Height of the Parallelogram = 4 inches

The Base of the Parallelogram is calculated as the Length or base of the rectangle + base of the triangle

= 5 inches + 4 inches

= 9 inches

Area of the Parallelogram = 9 inches × 4 inches

= 36 square inches or 36 in²

Answer:

20 INCHES SQUARED

Step-by-step explanation:

Answer:

[tex]x\geq 3[/tex] is the inequality to find the Domain of f(x)

Step-by-step explanation:

When we have a function where the variable "x" is inside a square root, we find its Domain by looking for all those values x for which the function is defined for the root, which means all the x-values that make the expression inside the root larger than or equal to zero, avoiding the values smaller for which the square root is not defined.

Therefore, in this case , for

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

we ask for the x-values that verify:

[tex]x-3\geq 0\\x\geq 3[/tex]

where we have isolated x on one side of the equal sign.

This would be the definition of the Domain of the function.

Answer:

The answer is C

Step-by-step explanation:

Answer:

Wolfrich lived in Brazil for 5 months and 9 months in Portugal

Step-by-step explanation:

Given;

Total Months = 14

Total Words = 1920

Required

Find the time spent in Portugal and time spent in Brazil

Let P represent Portugal and B represent Brazil; This implies that

[tex]P + B = 14[/tex] ---- Equation 1

Considering that he learnt 130 words per month in Portugal and 150 per month in Brazil; This implies that

[tex]130P + 150B = 1920[/tex] --- Equation 2

Make P the subject of formula in equation 1

[tex]P = 14 - B[/tex]

Substitute 14 - B for P in equation 2

[tex]130(14 - B) + 150B = 1920[/tex]

Open Bracket

[tex]1820 - 130B + 150B = 1920[/tex]

[tex]1820 + 20B = 1920[/tex]

Subtract 1820 from both sides

[tex]1820 - 1820 + 20B = 1920 - 1820[/tex]

[tex]20B = 100[/tex]

Divide both sides by 20

[tex]\frac{20B}{20} = \frac{100}{20}[/tex]

[tex]B = 5[/tex]

Substitute 5 for B in [tex]P = 14 - B[/tex]

[tex]P = 14 - 5[/tex]

[tex]P = 9[/tex]

Wolfrich lived in Brazil for 5 months and 9 months in Portugal

Answer:

(2, 34 )

Step-by-step explanation:

Since the points vary inversely then half the x, means double the y, thus

(2, 34) or (1, 68 ) would also belong in this inverse variation

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

Work Shown:

f ''' (x) = cos(x) .... third derivative

f '' (x) = sin(x)+C ... integrate both sides to get second derivative. Don't forget the +C at the end

We are given f '' (0) = 9, so we'll make use of this to find C

f '' (x) = sin(x)+C

f '' (0) = sin(0)+C

9 = sin(0) + C

9 = 0 + C

9 = C

C = 9

Therefore, f '' (x) = sin(x)+C turns into f '' (x) = sin(x)+9

------------

Integrate both sides of the second derivative to get the first derivative function

f '' (x) = sin(x)+9

f ' (x) = -cos(x)+9x+D ... D is some constant

Make use of f ' (0) = 4 to find D

f ' (x) = -cos(x)+9x+D

f ' (0) = -cos(0)+9(0)+D

4 = -1 + 0 + D

D = 5

So we have f ' (x) = -cos(x)+9x+D turn into f ' (x) = -cos(x)+9x+5

------------

Lastly, apply another round of integrals and substitutions to find the f(x) function. We'll use f(0) = 8.

f ' (x) = -cos(x)+9x+5

f(x) = -sin(x) + (9/2)x^2 + 5x + E .... E is some constant

f(0) = -sin(0) + (9/2)(0)^2 + 5(0) + E

8 = 0 + 0 + 0 = E

E = 8

------------

We have

f(x) = -sin(x) + (9/2)x^2 + 5x + E

turn into

f(x) = -sin(x) + (9/2)x^2 + 5x + 8

Answer: x = [tex]1\frac{1}{6}[/tex]

Step-by-step explanation:

7/12 = 1/2x

Multiply by 2

14/12=x

x = 1 1/6

Hope it helps <3

Answer:  see below

Step-by-step explanation:

Multiply the coefficient by the exponent and reduce the coefficient by 1.

1) f'(x) = 10

2) f'(x) = 12x³ + 4x - 5

3) f'(x) = 6x² + 7

4) f'(x) = 20x + 20

5) f'(x) = 20x + 23

Answer:

49

Step-by-step explanation:

[tex]3x^2+5x-2 = 0[/tex]

Apply discriminant formula : [tex]D = b^2- 4ac[/tex]

[tex]D=discriminant\\b=5\\a=3\\c=-2[/tex]

[tex]D = b^2- 4ac[/tex]

Plug in the values for a, b, and c.

[tex]D = 5^2- 4(3)(-2)[/tex]

Evaluate.

[tex]D = 25- 12(-2)[/tex]

[tex]D = 25- - 24[/tex]

[tex]D=25+24[/tex]

[tex]D=49[/tex]

Answer:

49

Step-by-step explanation:

3x²+5x-2 = 0

This is in the form

ax^2 + bx + c=0

a=3  b=5  c = -2

The discriminant is

b^2 -4ac

5^2 -4(3) (-2)

25 + 24

49

The discriminant is 49

Answer: The length is 15 yards so the answer is A.

Step-by-step explanation:

If  the length is 3 more than the width  the we will represent it by the equation L = w+3    where w is the width and to find the area of a rectangle, we need to multiply the length by the width. so the length is w+3 and the width is w so

w(w+3) = 180   solve for the w

w^2 + 3w = 180     subtract 180 from both sides

w^2 + 3w -180 = 0    find two numbers that their product is -180 and add to 3.

  the number 12 and -15 works out because -12*15= -180  and -15+ 12 =3

We will now have a new quadratic equation as

w^2 - 12w + 15w - 180 = 0  factor by grouping

w(w-12) 15(w-12)= 0     factor out w-12

(w-12)(w+15) = 0    set them both equal  zero.

w -12 = 0      or  w+15= 0  

w =  12      or  w = -15

Since we know that -15 can't represent a distance, then 12 is the width .  

So if we are to find the length and it gives us the information that the length is 3 yards more that the width then we will add 3 to the width to equal the length.

L= 12 +3

L = 15

The length of the rectangular playground is 15 yards. The correct answer would be an option (A).

The area of a rectangle is defined as the product of the length and width.

The area of a rectangle = L × W

Where W is the width of the rectangle and L is the length of the rectangle

Since the length is 3 more than the width

So, we will represent it by the equation L = W+3  ...(i)

A rectangular playground has an area of 180 square yards

So, L × W = 180

Substitute the value of equation (i), and we get

W(W+3) = 180

W² + 3W = 180

W² + 3W -180 = 0  ...(i)

Solving the above quadratic equation, we get the values of W :

W = 12 and W = -15

Take positive value because dimensions can't be negative.

Substitute the value of W = 12 in equation (i), and we get

L = 12 + 3 = 15

Therefore, the length of the playground is 15 yards.

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Answer:

Height of the kite = 86.60 meter (Approx)

Step-by-step explanation:

The angle of elevation to see a kite from a stone lying to the ground is 60 degrees. If a thread is tied with a kite and a stone, then that thread is 100 meters long, find the height of the kite.

Given:

Length of thread = 100 meter

Angle of elevation = 60°

Find:

Height of the kite.

Computation:

Using trigonometry application:

Height of the kite / Length of thread = Sin 60°

Height of the kite / 100 = √3 / 2

Height of the kite = [√3 / 2]100

Height of the kite = 50√3

Height of the kite = 86.60 meter (Approx)

Answer:

Step-by-step explanation:

from cosines theorem:

t² = 11² + 14² - 2•11•14•cos87°

t² = 121 + 196 + 308•0.05236

t² = 333.12688

t = √333.12688

t = 18.2517... ≈ 18.3

Answer:

w²-30w+210=0

Step-by-step explanation:

2w + 2l = 60 , w + l = 30, l = 30 - w

wl = 210

w(30-w) -210 = 0

30w - w²-210 = 0

w²-30w+210=0

Answer:

80%

Step-by-step explanation:

The basic idea of this problem is to convert [tex]\frac{44}{55}[/tex] into a percentage.  [tex]\frac{44}{55}[/tex]  can be simplified to [tex]\frac{4}{5}[/tex] which is also 80%.

Answer:

Step-by-step explanation:

44 out of 55

divide :44/55=0.8

to convert it to decimal  you multiply by 100 and put percentage next to it

0.8*100=80

%80

Explanation:

The x intercepts here are -1, 2 and 3. This is where the graph crosses the x axis. We can determine these three values by solving f(x) = 0.

In other words, set (x-3)(x-2)(x+1) equal to zero and solve for x.

(x-3)(x-2)(x+1) = 0

x-3 = 0 or x-2 = 0 or x+1 = 0

x = 3 or x = 2 or x = -1

x = -1 or x = 2 or x = 3

When we expand out (x-3)(x-2)(x+1), there will only be one x^3 term and the coefficient for this term is positive 1. The positive leading coefficient indicates that the graph goes up forever as we move to the right. In other words, the graph grows forever after passing that dip between x = 2 and x = 3.

Another way you could phrase it is that "as x goes to infinity, y also goes to infinity". An informal way is to say "the graph rises to the right" to describe the end behavior.

Answer:

C = 1/4

Step-by-step explanation:

When solving a quadratic equation, there are steps to follow and I'll highlight them here.

Assuming we have an equation

ax² + bx + c = 0

Step 1

If a is not equal to 1, divide all through by a

x² + bx + c = 0

Take c to the other side of the equation

x² + bx = c

Step 2

Add (b/2)² to both sides of the equation

x² + bx + (b/2)² = c + (b/2)²

In our original question,

We had x² + x = 3

a = 1 , b = 1 c = 3

Using step two, we would have

(b / 2)² = (½)² = ¼ (which is the answer)

Now back to the steps

Step 3

We factor our left side of the equation so as to have a perfect square

[x + (b/2)]² = c + (b/2)²

Step 4

Take the square root of both sides of the equation and solve for x

x + b/2 = ±√[c + (b/2)²]

The answer to the question is ¼

Answer:

1/4

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

The restriction a ≠ 0 and b ≠ 0 is applied since division by zero would make

[tex]\frac{a}{b}[/tex] and its reciprocal [tex]\frac{b}{a}[/tex] undefined, thus meaningless

The homework completed by Eric will be equal to 13/21.

The fraction is defined as the division of the whole part into an equal number of parts.

To add fractions, you first have to set the denominators equal to each other. To do this, you find the LCD (least common denominator) of the two fractions until you find a shared number.

To do this, list out the multiples of each number (3x1=3,3x2=6,3x3=9, and so on. Do this also with 7) The LCD for 3 and 7 is 21. 3x7=21, and 7x3=21. You want to set each fraction’s denominator equal to 21.

You want to multiply each side of 1/3 by 7. 1/3 would become 7/21. You’d do this because 3x7=21, and if you multiply the bottom by you need to multiply the top by. 7x3=21 so you multiply both sides by 3 to get 6/21.

Now you have 7/21 and 6/21 and can add them. Now that they are equal, you can ignore the denominator and just add the numerators. 7+6=13 so Eric completed 13/21 of his homework.

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Answer:

17 cans

Step-by-step explanation:

18 cans

7 are taken away

18-7 =11

Then we put 6 back on

11+6 = 17

There are now 17 cans

Answer:

4/ 3 = 7

Step-by-step explanation:

Answer: x=3

Step-by-step explanation:

first add two to each side

Simplify  7+2 to 9

3x=9

divide both sides by 3.

x=9/3

simplify 9/3 to 3

​

Answer:

B.

Step-by-step explanation:

Well we know that

[tex]224=2^{5} *7[/tex]

so we can get the 2 outside of the radical

[tex]x^{11} =(x^{5} )^{2} *x[/tex]

and we can get the x^2 outside too.

[tex]y^8=y^5*y^3[/tex]

and we also can get y outside.

so we have:

[tex]2x^{2}y\sqrt[5]{7xy^3}[/tex]

Answer:

D. the hours of daylight in a city throughout the year

Step-by-step explanation:

The hours of daylight in a city throughout the year represent the negative linear correlation coefficient. Then the correct option is D.

Independent quantities with an inverse relationship tend to move in different directions.

In essence, any figure between 0 and -1 denotes an opposing movement of the equity stocks.

When the correlation coefficient becomes less than 0, there is a negative (opposite) correlation. This suggests that both parameters are moving in the obverse direction.

The hours of daylight in a city throughout the year represent the negative linear correlation coefficient

Then the correct option is D.

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Step-by-step explanation:

aₙ = 2 (¼)ⁿ⁻¹

a₃ = 2 (¼)³⁻¹

a₃ = 2 (¼)²

a₃ = ⅛

Answer:

1/8 inches

Step-by-step explanation:

Using the given function

d(n) = 2(1/4)^(n-1)

the initial value is 2, which is the height of the ball after the first roll.

For the third roll, n = 3

d(n) = 2 (1/4)^(3-1)

d(n) = 2 (1/4)^2

d(n) = 2/16

d(n) = 1/8

Answer:

x = 45

Step-by-step explanation:

Since ray IK║EH and IG is a transverse,

∠GIK ≅ ∠IGF [Corresponding angles]

Therefore, m∠IGF = x

Since, m∠JIF + m∠GIF = 180° [Supplementary angles]

2x + m∠GIF = 180°

m∠GIF = (180 - 2x)

Similarly, m∠IFE + m∠IFG = 180°

3x + m∠IFG = 180°

m∠IFG = (180 - 3x)

By the property of a triangle,

"Sum of all interior angles of a triangle is 180°"

m∠IGF + m∠GFI + m∠FIG = 180°

x° + (180 - 2x)° + (180 - 3x)° = 180°

(x - 2x - 3x) + 360 = 180

-4x + 360 = 180

4x = 360 - 180

4x = 180

x = 45