Let f(x) = x + 8 and g(x) = x2 − 6x − 7. Find f(g(2))

Answer:

x=-4 or x=9

Step-by-step explanation:

Either factor can be 0 for the result to be 0.

Hence you can solve x+4=0 or x-9=0 with above answers.

Answer:

x(square) - 5x -36 = 0

sorry if its wrong

Answer: b. 51 - 3

Step-by-step explanation:

Given, Easha has 3 less than 5 times the number of quarters (I)  that Isabelle has.

Here I is the number of quarters that Isabelle has.

Then, as per given,

Number of quarters Easha has = 5 ( number of quarters that Isabelle has) -3

= 5I-3

Hence, the  expression shows the number of quarters Easha has is "5I-3"

So the correct option is b.

We have,

Finding time taken by the man,

⇛ Average speed = Total Distance/Total time

⇛ Total time = Total Distance/Average speed[tex].[/tex]

⇛ Total time = 325 km/50 km/h

⇛ Total time = 6.5 h (6 hrs 30 mins)

(a) Total Time duration,

⇛ Total Time = Reaching Time - Departing time

⇛ 6.5 h = Reaching Time - 10 : 45 hours

⇛ Reaching Time = 17 : 15 hours ( 5 : 15 pm)

(b) Finding time taken in return,

Total time duration,

⇛ Total Time = Reaching Time - Departing time

⇛ Total Time = 23 : 10 hours - 18 : 35 hours

⇛ Total Time = 22 : 70 hours - 18 : 35 hours

⇛ Total time = 4 : 35 hours

☕ Hence, solved !!

━━━━━━━━━━━━━━━━━━━━

Answer:

A ≈ 47.759 cm²

Step-by-step explanation:

A = πr²

A = (3.14)(3.9)²

A = (3.14)(15.21)

A ≈ 47.759 cm²

Answer:

15/26

Step-by-step explanation:

There are 52 cards in a deck. A deck of cards contains 4 queen cards and 26 red cards. 30/52 simplified is 15/26.

Answer:

28/52, simplified is 14/26. The latter is the answer the questionnaire is probably looking for but if a human is marking it it doesn't hurt to write both.

Step-by-step explanation:

There are 26 cards that are red in a deck, plus 4 queens, minus the 2 queens that are already red.

Answer:

Use a graphing calc.

Step-by-step explanation:

On the graph, use (0, 0) and (2, 5) to graph the function.

Answer:

Ok, first we have the relation:

Speed = Distance/Time.

Here we have:

Distance = 24m

Time = 87 mins

Speed = 24m/87mins = 0.279 m/min.

Now, in 6 minutes, the distance moved will be (remember that the movement is downwards)

D(6min) = (0.279m/min)*6min = 1.66 m.

So in 6 minutes, it moves 1.66 meters down, if the initial position is 10m above the ground, then the position after 6 minutes is:

10m - 1.66m = 8.34m above the ground.

And after 70 minutes, the distance moved is:

D(70min) =  (0.279m/min)*70min = 19.53m

Again, the initial position is 10m above the ground, so after 70 minutes the position is:

10m - 19.53m = -9.53m

So after 70 minutes, the position is 9.53 meters under the ground.

The lift will go 2.76m deep from the surface after 70 mins.

The lift moves down 24m in 87 minutes.

The speed of an object that covers 'd' distance in 't' time is d/t.

So, speed of the lift = 24/87 = 3/29m/min

Distance covered in 6 minutes = 6 * 3/29 = 18/29 m

So, if initially lift is at the surface of the earth, it will go 18/29m below the surface.

Distance covered in 70 minutes = 70* 3/29 =210/29m

So, if the initially lift is at 10 m height, it will go (10-210/29) = -80/29 or 2.76m below the surface of the earth.

Therefore, the lift will go 2.76m deep from the surface after 70 mins.

To get more about time, speed and distance visit:

https://brainly.com/question/26046491

Answer:

there must be at least two lines on any plane because a plane is defined by 3 non-collinear points.

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

As per table we can conclude the function:

So for x = 4 we get:

Correct answer choice is the last one

Answer:

16

Step-by-step explanation:

was correct.

Answer:

P(t) = A * (1 + r)^t ;

14,922 ;

Year 2013

Step-by-step explanation:

Given the following :

Continuous growth rate(r) = 5% = 0.05

Population in year 2000 = Initial population (A) = 10,100

Time(t) = period (years since year 2000)

A)

Find a function that models the population,P(t) , after (t) years since year 2000 (i.e. t= 0 for the year 2000).

P(t) = A * (1 + r)^t

Trying out our function for t = year 2000, t =0

P(0) = 10,100 * (1 + 0.05)^0

P(0) = 10,100 * 1.05^0 = 10,100

B.)

Use your function from part (a) to estimate the fox population in the year 2008.

Year 2008, t = 8

P(8) = 10,100 * (1 + 0.05)^8

P(8) = 10,100 * 1. 05^8

P(8) = 10,100 * 1.4774554437890625

= 14922.29

= 14,922

c) Use your function to estimate the year when the fox population will reach over 18,400 foxes. Round t to the nearest whole year, then state the year.

P(t) = A * (1 + r)^t

18400 = 10,100 * (1.05)^t

18400/10100 = 1.05^t

1.8217821 = 1.05^t

1.05^t = 1.8217821

In(1.05^t) = ln(1.8217821)

0.0487901 * t = 0.5998151

t = 0.5998151 / 0.0487901

t = 12.293787

Therefore eit will take 13 years

2000 + 13 = 2013

Answer: B)

Step-by-step explanation:

THEY TELL THE RELATIVE AGE OF THE ROCK IN WHICH THEY OCCUR.

Answer:

∠B = 76°

Step-by-step explanation:

Supplementary angles add up to 180 degrees, so we know that angles A and B add up to 180.

We can set up an equation and solve for x:

(x + 15) + (x - 13) = 180

Add like terms:

2x + 2 = 180

2x = 178

x = 89

Now, we can plug in 89 as x to find the measure of angle B:

x - 13

89 - 13

= 76

= 76°

Answer:

π (Pi) is a mathematical constant.

Step-by-step explanation:

The digit π is a mathematical constant. It is interpreted as the ratio of a circle's perimeter to its diameter, and it also has various equivalent definitions. It appears in many formulas in all areas of mathematics and physics. It is roughly identical to 3.14159.

Answer:

The last table with x and y values:

x       y

40    60

160   15

200   0

is the correct table

Step-by-step explanation:

Notice that the x-value 40 appears in all four tables, so let's use it according to the piece-wise function definition to decide which table can be the true one.

Notice that from the function's description, when x = 40 the function that should be used is (its domain includes 40 according to: [tex]40\leq x\leq 200[/tex] ) : [tex]f(x)=-\frac{3}{8} x+75[/tex],

which therefore gives : [tex]f(40)=-\frac{3}{8} (40)+75= -15+75=60[/tex]

therefore, we know that the only table that shows a y-value of 60 associated with x=40 is the last table. We should check that the other two pairs are also correct before deciding for it:

Is f(160) = 15 , and is f(200) = 0 according to the function's definition?

Let;s calculate f(160) (for which we need to use again the second function given which is valid for x values such that: [tex]40\leq x\leq 200[/tex]

[tex]f(160)=-\frac{3}{8} (160)+75= -60+75=15[/tex]

so, this pair is also correct.

Now the last check (for x = 200):

[tex]f(200)=-\frac{3}{8} (200)+75= -75+75=0[/tex]

which also checks with the values in the given table.

Answer:

14

Step-by-step explanation:

Simplify the following:

5 - 2×9 + 9^2/3

Hint: | Evaluate 9^2.

9^2 = 81:

5 - 2×9 + 81/3

Hint: | Reduce 81/3 to lowest terms. Start by finding the GCD of 81 and 3.

The gcd of 81 and 3 is 3, so 81/3 = (3×27)/(3×1) = 3/3×27 = 27:

5 - 2×9 + 27

Hint: | Multiply -2 and 9 together.

-2×9 = -18:

5 + -18 + 27

Hint: | Evaluate 5 + 27 using long addition.

| 1 |  

| 2 | 7

+ | | 5

| 3 | 2:

32 - 18

Hint: | Subtract 18 from 32.

| 2 | 12

| 3 | 2

- | 1 | 8

| 1 | 4:

Answer: 14

Answer:

x=1

Step-by-step explanation:

-2x+4=1-4x-3

↦-2x+4x=1-3+4

↦2x=2

↦x=2/2

↦x=1

.°. x = 1

Answer:

[tex] - 2x + 4 = 1 - 4x - 3[/tex]

Firstly take all numbers with variable to L.H.S

and Take all numbers to R.H.S

[tex] - 2x - 4x = 1 - 3 - 4[/tex]

Now solve the equation we get our answer

[tex]-6x = -6[/tex]

Take -6 to the R.H.S and divide -6 by -6

[tex]x = 1[/tex]

1 is ur answer mate

Hope it helps

Answer:

Option C is the correct option.

Step-by-step explanation:

For ABD

[tex] \sf{ = \frac{2.89 + 8.59 + 8.6}{2} }[/tex]

[tex] \sf{ = \frac{20.08}{2} }[/tex]

[tex] \sf{ = 10.04}[/tex]

∆ ABD = [tex] \sf{ = \sqrt{10.04(10.04 - 2.89)(10.04 - 8.59)(10.04 - 8.6)} }[/tex]

[tex] \sf{ = \sqrt{10.04 \times 7.15 \times 1.45 \times 1.44 }}[/tex]

[tex] \sf{ = \sqrt{149.8891} }[/tex]

[tex] \sf{ = 12.2429}[/tex]

For ∆ ACD ,

[tex] \sf{s = \frac{8.6 + 4.3 + 7.58}{2} }[/tex]

[tex] \sf{ = \frac{20.48}{2} }[/tex]

[tex] \sf{ = 10.24}[/tex]

∆ ACD = [tex] \sf{ = \sqrt{10.24(10.24 - 8.6)(10.24 - 4.3)(10.24 - 7.58} }[/tex]

[tex] \sf{ \sqrt{10.24 \times 1.64 \times 5.94 \times 2.66} }[/tex]

[tex] \sf{ = \sqrt{265.3456} }[/tex]

[tex] \sf{ = 16.2894}[/tex]

Area of quadrilateral ABCD = [tex] \sf{12.2429 + 16.2894}[/tex]

[tex] \sf{ = 28.5323}[/tex]

[tex] \sf{ = 28.53}[/tex] units ²

Hope I helped!

Best regards!

Answer:

10

Step-by-step explanation:

Let the total number of poodles = [tex]x[/tex]

Let the total number of show dogs = [tex]y[/tex]

[tex]\frac{1}{4}[/tex] of the poodles are show dogs

and

[tex]\frac{1}{7}[/tex]  of the show dogs are poodles

[tex]\therefore \dfrac{1}{4}x = \dfrac{1}{7} y[/tex]

As per the question statement, [tex]x[/tex] must be divisible by 4 and

[tex]y[/tex] must be divisible by 7.

And we have to find the least number of dogs.

So, least number divisible by 4 = 4 and

Least number divisible by 7 = 7

So, least values of [tex]x[/tex] i.e. poodles = 4 in which we have 1 show dog

Hence, 3 are not show dogs.

and least value of show dogs i.e. [tex]y[/tex] = 7 (it includes the one poodle which is also show dog).

So, least number of dogs at the fair = 7 + 3 = 10

Answer:

384 square m

Step-by-step explanation:

As per description given in the question, the field is of parallelogram shape. Diagonal divides the parallelogram in two triangles

So, area of field = area of triangle 1 + area of triangle 2

Area of field

= 1/2*32 * 10 + 1/2 * 32 * 14

= 32* 5 + 32 * 7

= 32(5 + 7)

= 32 * 12

= 384 square m

Answer:

boys: total

3          8

Step-by-step explanation:

boys:girls: total

9    :  15   :  9+15

9        15      24

Divide each by 3

3         5        8

We want the ratio of boy to total

boys: total

3          8

Answer:

[tex]a^{m-n}[/tex]

Step-by-step explanation:

If we have the expression [tex]m^a \div m^n[/tex], we can use exponent rules to simplify this.

Exponent rules say that [tex]x^a \div x^b = x^{a-b}[/tex]. In this case, x is a, a is m and b is n, so the same rule applied here.

So  [tex]a^m \div a^n[/tex] will be equal to [tex]a^{m-n}[/tex].

Hope this helped!

Answer: 1/5

Step-by-step explanation: 2/5 - 1/5 = 1/5. So 1/5 more visitors saw the panda this month.

Answer:

v = 20 m /s

Step-by-step explanation:

v = 72 km / h

72 / 3.6

20

v = 20 m /s

Answer:

m = 68 - c ; 35

Step-by-step explanation:

Given the following :

Number of blocks Tegan needs to make = 68

Number of blocks completed = c

Number of blocks left to make = m

Therefore, the number of blocks 'm' left to make is given by the equation :

(Total number of blocks needed - number of blocks completed) = number of blocks left to make

(68 - c) = m

Equation : m = 68 - c

If completed blocks 'c' = 33 ; number of blocks needed to complete the igloo :

From m = 68 - c

m = 68 - 33

m = 35

Answer:

Equation: m = 68 - c   Answer: 35

Step-by-step explanation:

Tegan needs 68 more blocks for her igloo. The number of blocks she still needs to make depends on c, the number of blocks she completes.

To find the number of blocks she still needs to make, m, we can use the equation m = 68 - c

To find the number of blocks Tegan still needs to make if she completes 33 blocks we can substitute 33 into the equation for c.

m = 68 - c

m = 68 - 33

m = 35

The equation is m = 68 - c

Tegan still needs to make 35 blocks to finish the igloo.

I hope this helps you

for cosine in a right triangle

cos Angle =adiacent/hypotenuse

cosQ=4/5

Answer:

x= -2

Step-by-step explanation:

3(2x-4)= -24

expand

6x-12= -24

6x= -24+12

6x= -12

x= -12/6

x= -2

Answer:

x=-2

Step-by-step explanation:

To solve the equation, we must get x isolated on one side of the equation.

[tex]3(2x-4) = -24[/tex]

3 is being multiplied by 2x -4. The inverse of multiplication is division. Divide both sides of the equation by 3.

[tex]\frac{3(2x-4)}{3} = -\frac{24}{3}[/tex]

[tex](2x-4)= -\frac{24}{3}[/tex]

[tex](2x-4)= -8[/tex]

4 is being subtracted from 2x. The inverse of subtraction is addition. Add 4 to both sides of the equation.

[tex]2x-4 +4 = -8+4[/tex]

[tex]2x= -8+4[/tex]

[tex]2x= -4[/tex]

x is being multiplied by 2. The inverse of multiplication is division. Divide both sides by 2.

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

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

[tex]x= -2[/tex]

Let's check our solution. Plug -2 in for x and solve.

[tex]3(2x-4)= -24[/tex]

[tex]3(2(-2)-4)= -24[/tex]

[tex]3(-4-4) = -24[/tex]

[tex]3(-8)= -24[/tex]

[tex]-24=-24[/tex]

The statement above is true, so we know our solution is correct.

The answer to the equation is x= -2.

Answer:

x = 6

Step-by-step explanation:

[tex]\frac{9+x}{3x} = \frac{5}{6}[/tex]

6(9+x) = 5(3x)

6*9 + 6*x = 5*3x

54 + 6x = 15x

54 = 15x - 6x

54 = 9x

x = 54/9

x = 6

check:

(9+6)/(3*6) = 5/6

15/18 = 5/6