distance
Jason took 40 min to drive from East Mall to West Mall. He drove at an average
speed of 60 km/h for the first 25 min. He then increased his speed by 12 km/h for
the remaining journey. What was the distance between the two malls?​

Answer:

2 /√3 or  2√3 / 3.

Step-by-step explanation:

Referring to the 30-60-90 triangle: hypotenuse = 2 , smaller leg = 1 and longer leg = √3 and the shorter side is opposite the 30 degree angle.

So cos 30 = √3/2

Sec 30 = 1 / cos 30

= 2 /√3

or  2√3 / 3.

The exact value of sec(30º) using trigonometric identity for secant is 2.

To find the exact value of sec(30º), use the trigonometric identity for secant:

sec(θ) = 1/cos(θ)

Using the special right triangle with angles 30º, 60º, and 90º, it is known that the side lengths are in the ratio 1:√3:2.

The cosine is defined as the adjacent side divided by the hypotenuse.

For a 30º angle, the adjacent side = 1 and the hypotenuse = 2.

So, cos(30º) = 1/2

Substituting this into the formula for secant:

sec(30º) = 1/cos(30º)

               = 1/(1/2)

               = 2

Therefore, the exact value of sec(30º) is 2.

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Let's solve for g.

gx=x4−3x2+4x−5

Step 1: Divide both sides by x.

gx

x

=

x4−3x2+4x−5

x

g=

x4−3x2+4x−5

x

Answer:

g=

x4−3x2+4x−5

x

[tex](f-g)(x)=2x-6-(3x+9)=2x-6-3x-9=-x-15[/tex]

Answer:

The correct option is C.

Step-by-step explanation:

The correct option is C.

We have given:

f(x) = 2x - 6 and g(x) = 3x + 9

Now we have to find (f-g)(x)

(f-g)(x) = f(x)- g(x)

Now subtract g(x) from f(x)

(2x - 6) - (3x + 9)

Open the parenthesis. When we open the parenthesis the signs of second bracket will become negative because there is a negative sign outside the bracket.

(f-g)(x)= 2x-6-3x-9

Now solve the like terms:

(f-g)(x)= -x-15

Thus the correct option is C....

Answer:

The graph of g(x) is a translation of f(x) 3 units down.

Step-by-step explanation:

The given function is

[tex]g(x) = f(x) - 3[/tex]

The parent function now is f(x).

The -3 tells us that there is a vertical translation of the parent function 3 units down.

Therefore the graph of g(x) is obtained by translating the graph of f(x) down by 3 units.

Answer:

[tex]\arge\boxed{B.\ (3x^2+4x-7)(x)+(3x^2+4x-7)(-3)}[/tex]

Step-by-step explanation:

[tex]\text{The distributive property:}\ a(b+c)=ab+ac.\\\\(3x^2+4x-7)(x-3)=(3x^2+4x-7)(x)+(3x^2+4x-7)(-3)[/tex]

Answer:

The first term of the sequence is 1/5

Step-by-step explanation:

The first term is 1/5.

The reason is that there is a common ratio between each term. In this case multiplying the previous term in the sequence by 5 would give the next term.

So in this case 1/5 is the first term.

If we multiply 1/5 by 5, it will give the next term which is 1.

1/5*5=1

Thus the first term in the sequence = 1/5....

Answer:

The left end goes up and the right end goes down.

Step-by-step explanation:

Lets solve the function first and then find out the end behavior of the polynomial:

The given function is  f(x)=-x^3+x^2-4x+2

First step is: Identify the degree of the polynomial. For this we have to  find out the variable with the largest exponent.

The variable with the largest exponent in the given function is -x³

The degree of the polynomial is the largest exponent on the variable.

3 is the degree of the polynomial.

Since the degree is Odd, the ends of the function will point in the opposite direction.

Now find out the leading coefficient of the polynomial which is -1.

Since the leading coefficient is negative the graph falls to the right.

To find the behavior we have to use the degree of the polynomial as well as the sign of leading coefficient.

If it is ODD and NEGATIVE then the the left end goes up and the right end goes down.

Therefore the end behavior of the given function will be described as "the the left end goes up and the right end goes down"....

Answer:

-4z-6y-9

Step-by-step explanation:

7z-[(2z+y)-(-5y+3z)+9]-12z

=7z-[2z+y+5y-3z+9]-12z

=7z-2z-y-5y+3z-9-12z

=7z-2z-12z+3z-y-5y-9

=-4z-6y-9

Answer:

f(8) = 8.25(1.1)^7 ; f(8) = 16.077 ⇒ answer B

Step-by-step explanation:

* Lets explain how to solve the problem

∵ The x-coordinate is the number of the obstacle

∵ The y-coordinate is the average time to complete the obstacle

∵ The order pairs of function are (1 , 8.25) , (2 , 9.075) , (3 , 9.9825) ,

  (4 , 10.98075)

- From these order pairs

# The time to finish the 1st obstacle is 8.25 minutes

# The time to finish the 2nd obstacle is 9.075 minutes

# The time to finish the 3rd obstacle is 9.9825 minutes

# The time to finish the 4th obstacle is 10.98075 minutes

∵ 2nd ÷ 1st = 9.075/8.25 = 1.1

∵ 3rd ÷ 2nd = 9.9825/9.075 = 1.1

∵ 4th ÷ 3rd = 10.98075/9.9825 = 1.1

∴ There is a constant ratio 1.1 between each 2 consecutive terms

∴ The order pairs formed a geometric series

- Any term in the geometric series Un = a r^(n - 1) , where a is the 1st

 term in the series , r is the constant ratio and n is the position of the

 term in the series

∵ a = 8.25 ⇒ the time of the first obstacle

∵ r = 1.1

- Sheila wants to find the average time she will need for the 8th

 obstacle

∴ n = 8

∵ The explicit formula is f(x) = a r^(n - 1)

∴ f(8) = 8.25 (1.1)^(8 - 1)

∴ f(8) = 8.25(1.1)^7

∴ f(8) = 16.076916 ≅ 16.077

* f(8) = 8.25(1.1)^7 ; f(8) = 16.077

Answer:

Option) BEE is the correct answer!

Step-by-step explanation:

Answer:

C. 4, 7, 11, 11, 16, 17

Step-by-step explanation:

The mean is the average of the numbers'

The median is the middle number

The mode is the number that occurs most often.

Let's look at each data set I turn.

A. 10, 10, 12, 12, 13, 13

Mean = 11. 7; Median: = 12; Modes: 10, 12, 13

All three measures are different.

B. 2, 3, 4, 4, 5, 7

Mean = 4.2; median = 4; mode = 4

Median and mode are the same, but the mean is different.

C. 4, 7, 11, 11, 16, 17

Mean = 11; median = 11; mode = 11

All three measures are the same.

D. 1, 2, 3, 3, 5, 6

Mean = 3.3; median = 3; mode = 3

Median and mode are the same, but the mean is different.

Answer:[tex]\large\boxed{C.\ (x-5)^2}[/tex]Step-by-step explanation:

[tex]f(x)=x-5,\ g(x)=x^2\\\\g\bigg(f(x)\bigg)-\text{put}\ x-5\ \text{expression instead of}\ x\ \text{in}\ g(x):\\\\g\bigg(f(x)\bigg)=(x-5)^2[/tex]

Answer:

C. 86°

Step-by-step explanation:

I just did it on A p 3 x

Answer:

Part A) The system of inequalities is

[tex]x\geq2[/tex]  and  [tex]y\geq2[/tex]

Part B) In the procedure

Part C) The schools that Natalie is allowed to attend are A,B and D

Step-by-step explanation:

Part A: Using the graph above, create a system of inequalities that only contain points C and F in the overlapping shaded regions

we have

Points C(2,2), F(3,4)

The system of inequalities could be

[tex]x\geq2[/tex] -----> inequality A

The solution of the inequality A is the shaded area at the right of the solid line x=2

[tex]y\geq2[/tex] -----> inequality B

The solution of the inequality B is the shaded area above of the solid line y=2

see the attached figure N 1

Part B: Explain how to verify that the points C and F are solutions to the system of inequalities created in Part A

we know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities

Verify point C

C(2,2)    

Inequality A

[tex]x\geq2[/tex] -----> [tex]2\geq2[/tex] ----> is true

Inequality B

[tex]y\geq2[/tex] ------> [tex]2\geq2[/tex] ----> is true

therefore

Point C is a solution of the system of inequalities

Verify point D

F(3,4)    

Inequality A

[tex]x\geq2[/tex] -----> [tex]3\geq2[/tex] ----> is true

Inequality B

[tex]y\geq2[/tex] ------> [tex]4\geq2[/tex] ----> is true

therefore

Point D is a solution of the system of inequalities

Part C: Natalie can only attend a school in her designated zone. Natalie's zone is defined by y < −2x + 2. Explain how you can identify the schools that Natalie is allowed to attend.

we have

[tex]y < -2x+2[/tex]

The solution of the inequality is the shaded area below the dotted line [tex]y=-2x+2[/tex]

The y-intercept of the dotted line is the point (0,2)

The x-intercept of the dotted line is the point (1,0)

To graph the inequality, plot the intercepts and shade the area below the dotted line

see the attached figure N 2

therefore

The schools that Natalie is allowed to attend are A,B and D

Answer:

Distance between points  (5, -3) and (0, 2) is √50 or 7.07

Step-by-step explanation:

We need to find distance between two points (5,-3) and (0,2)

The distance formula used is:

[tex]d= \sqrt {\left( { x_2-x_1 } \right)^2 + \left( {y_2-y_1} \right)^2 }[/tex]

here

x₁= 5, y₁=-3, x₂=0 and y₂=2

Putting values in the formula:

[tex]d= \sqrt {\left( {x_2-x_1} \right)^2 + \left( {y_2-y_1} \right)^2 }\\d= \sqrt {\left( {0-5} \right)^2 + \left( {2-(-3)} \right)^2 }\\d= \sqrt {\left( {-5} \right)^2 + \left( {2+3} \right)^2 }\\d= \sqrt {25+25}\\d= \sqrt {50}\\d= 7.07[/tex]

So, distance between points  (5, -3) and (0, 2) is √50 or 7.07

Answer:

here you go

Step-by-step explanation:

W = (0.6) L

       P = 2  (  L + W  )

       P = 2  [  L + (0.6) L  ]

       P = 2  ( 1.6 L  )

       P = (3.2) L  

       P = (3.2) x

The perimeter of the soccer field with the length of [tex]x[/tex] feet is equal to

[tex]3.2x[/tex] feet.

" Perimeter is defined as the total length around the given geometrical shape."

Formula used

Perimeter of the soccer field [tex]= 2 ( L + W)[/tex]

[tex]L=[/tex] length of the soccer field

[tex]W =[/tex] width of the soccer field

According to the question,

Given,

[tex]'x'[/tex] represents the length of the soccer field

As per the given condition,

Width = [tex]60\%[/tex] of length

          [tex]= \frac{60}{100} \times x\\\\= 0.6x[/tex]

Substitute the value in the formula to get the perimeter,

Perimeter of the soccer field [tex]= 2 ( x+ 0.6x)[/tex]

                                                 [tex]= 2(1.6x)\\\\= (3.2x) feet[/tex]

Hence, the perimeter of the soccer field with the length of [tex]x[/tex] feet is equal to [tex]3.2x[/tex] feet.

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Answer:

362

Step-by-step explanation:

-1,3,18,47,93,159,248

First difference (just do term minus previous term):

4, 15, 29, 46, 66 ,89

The first differences are not common.

Second difference (doing term minus previous term)

11,  14,  17, 20, 23

Third difference:

3 ,3 ,3, 3

So it is a cubic because the third differences are the same.

Anyways we don't have to find the explicit form of this sequence.  We just have to find the next term.

Let's go back through starting with second difference:

11 , 14, 17, 20, 23 , (25)

(25) would be next term here.

Let's go back to first difference:

4, 15, 29, 46, 66 ,89 , (89+25)

4, 15 ,29, 46, 66, 89 , (114)

Now let's go back to original sequence:

We want 114+248 to be the next term.

That equals 362.

Answer:

(x+1+i)(x+1-i) goes with x^2+2x+2

(x+2i)(x-2i) goes with x^2+4

(x-2+2i)(x-2-2i) goes with x^2-4x+8

Step-by-step explanation:

(x+1+i)(x+1-i)

(x+[1+i])(x+[1-i])

Use foil.

First: x(x)=x^2

Outer: x(1+i)=x+ix

Inner: x(1-i)=x-ix

Last: (1+i)(1-i)=1-i^2 since 1+i and 1-i are conjugates

__Add together to get: x^2+2x+1-i^2

We can actually simplify this because i^2=-1

So x^2+2x+1-i^2=x^2+2x+1-(-1)=x^2+2x+2

(x+2i)(x-2i)

These are conjugates so just do first and last of foil.

First: x(x)=x^2

Last: 2i(-2i)=-4i^2=-4(-1)=4

==Adding together gives x^2+4

(x-2+2i)(x-2-2i)

(x+[-2+2i])(x+[-2-2i])

This is similar to first.

Foil time!

First: x(x)=x^2

Outer: x(-2-2i)=-2x-2ix

Inner: x(-2+2i)=-2x+2ix

Last: (-2-2i)(-2+2i)=4-4i^2 (multiplying conjugates again)

==Add together giving us x^2-4x+4-4i^2

This can be simplified since i^2=-1.

So applying this gives us x^2-4x+4-4(-1)

=x^2-4x+4+4

=x^2-4x+8

Answer:

1. The first expression is equivalent to [tex]x^2+2x+2[/tex].

2. The second expression is equivalent to [tex]x^2+4[/tex].

3. The third expression is equivalent to  [tex]x^2-4x+8[/tex].

Step-by-step explanation:

(1).

The given expression is

[tex](x+1+i)(x+1-i)[/tex]

[tex][(x+1)+i][(x+1)-i][/tex]

Using the algebraic properties, we get

[tex](x+1)^2-(i)^2[/tex]                 [tex][\because a^2-b^2=(a-b)(a+b)][/tex]

[tex]x^2+2x+1-(i)^2[/tex]               [tex][\because (a+b)^2=a^2+2ab+b^2][/tex]

[tex]x^2+2x+1-(-1)[/tex]             [tex][\because i^2=-1][/tex]

[tex]x^2+2x+2[/tex]

Therefore the first expression is equivalent to [tex]x^2+2x+2[/tex].

(2).

The given expression is

[tex](x+2i)(x-2i)[/tex]

Using the algebraic properties, we get

[tex](x)^2-(2i)^2[/tex]                [tex][\because a^2-b^2=(a-b)(a+b)][/tex]

[tex]x^2-4i^2[/tex]

[tex]x^2-4(-1)[/tex]            [tex][\because i^2=-1][/tex

[tex]x^2+4[/tex]

Therefore the second expression is equivalent to  

[tex]x^2+4[/tex].

(3)

The given expression is

[tex](x-2+2i)(x-2-2i)[/tex]

[tex][(x-2)+2i][(x-2)-2i][/tex]

Using the algebraic properties, we get

[tex](x-2)^2-(2i)^2[/tex]           [tex][\because a^2-b^2=(a-b)(a+b)][/tex]

[tex]x^2-4x+4-4i^2[/tex]               [tex][\because (a-b)^2=a^2-2ab+b^2][/tex]

[tex]x^2-4x+4-4(-1)[/tex]             [tex][\because i^2=-1][/tex]

[tex]x^2-4x+4+4[/tex]

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

Therefore the third expression is equivalent to  [tex]x^2-4x+8[/tex].

For this case we must find the roots of the following equation:

[tex]x ^ 2-7x-4 = 0[/tex]

We have to:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]

Where:

[tex]a = 1\\b = -7\\c = -4[/tex]

Substituting the values:

[tex]x = \frac {- (- 7) \pm \sqrt {(- 7) ^ 2-4 (1) (- 4)}} {2 (1)}\\x = \frac {7 \pm \sqrt {49 + 16}} {2}\\x = \frac {7\pm\sqrt {65}} {2}[/tex]

We have two roots:

[tex]x_ {1} = \frac {7+ \sqrt {65}} {2} = 7.53\\x_ {2} = \frac {7- \sqrt {65}} {2} = - 0.53[/tex]

Answer:

[tex]x_ {1} = \frac {7+ \sqrt {65}} {2} = 7.53\\x_ {2} = \frac {7- \sqrt {65}} {2} = - 0.53[/tex]

Answer:

(C)

Step-by-step explanation:

♥☺

Answer:

(E) (20k - 150)/(k - 10)

Step-by-step explanation:

Sum of all scores = average × number of scores = 20 × k = 20k

                   Sum of 10 scores = 15 × 10 =150

      Sum of remaining scores = 20k - 150

Number of remaining scores = k -10

Average of remaining scores = sum of remaining/no. remaining

= (20 k -150)/(k-10)

Step-by-step explanation:

hi I have answered ur question

To make n the subject of the formula t = square root of n+3/n, we can isolate the square root term by squaring both sides of the equation and rearranging the equation to make n the subject.

To make n the subject of the formula t = √(n+3)/n, we can start by isolating the square root term. To do this, we square both sides of the equation:

t2 = √(n+3)/n2

Next, we can multiply both sides by n2 to get rid of the denominator:

t2n2 = n + 3

Finally, we can rearrange the equation to make n the subject:

n = (t2n2 - 3)/t2

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can you please add the answers to choose from? I'd like to help

Answer:

B. The second graph displayed.

Step-by-step explanation:

Recieved an 100% on my test with this question!!

Hope I could help! (´⊙◞⊱​◟⊙｀)

First of all, recall that 1.5m is the same as 150cm.

Now, we simply build a proportion where we consider 48 to be 100, and wonder what 150 will be:

[tex]48\div 100 = 150 \div x[/tex]

Solving for x, we have

[tex]x = \dfrac{150\cdot 100}{48}=\dfrac{15000}{48} = 312.5[/tex]

Which actually makes sense, because we're stating that 1.5m is about 300% of 48cm, which means three times as much. Which is true, because three times 48cm means 144cm, which is about 1.5m

Answer:

Step-by-step explanation:

To solve this problem, you must first have the numbers in the same units, that is, convert the meters to centimeters and operate with them or transform to meters and work with them, therefore, I decide to work with centimeters, like this:

Then, you can make a simple rule of three, where 150 centimeters corresponds to 100% and you look for the percentage of 48 centimeters:

So:

Therefore, the percentage of 48 centimeters is equal to 32%.

Answer:

35.3

Step-by-step explanation:

Actually, there are none but 35.3.   Here you have already defined x as 35.3.  35.3 satisfies the given equation.

The solution to the given equation x = 35.3 is simply x equals 35.3. There are no further calculations required for this straightforward linear equation.

The equation given, x = 35.3, is a simple linear equation where the variable x is already isolated on one side of the equation. The solution to this equation is straightforward: x equals 35.3. There is no need for further calculation or iterative numerical methods, as this is not a quadratic equation nor does it require techniques such as least squares to find a solution. The equation simply states that x is equal to the real number 35.3.

However, if you are given a quadratic equation or more complex equations, there can be different methods to solve for x. For example, the quadratic formula, iterative methods, or writing computer programs for finding least squares solutions in systems of equations with multiple variables.

Answer:

Horizontal shift of 1 unit to the right, a vertical shift upward of 6 units, and a vertical stretch by a factor of 3 ..

Step-by-step explanation:

Given function is:

3[|x-1|+2]

Can also be written as:

3|x-1|+6

As we can see that the -1 is grouped with x which means it is a horizontal shift of 1 unit to the right.

Now, 6 is added to the function and it is not grouped with x which means that there is a vertical shift of 6 units upward.

Lastly, 3 is multiplied with the term containing x which means that there is a vertical stretch of 3 units.

Hence, the correct option is:

Horizontal shift of 1 unit to the right, a vertical shift upward of 6 units, and a vertical stretch by a factor of 3 ..

Answer:

Horizontal shift of [tex]1[/tex] unit to the right, a vertical shift upward of [tex]6[/tex] units, and a vertical stretch by a factor of [tex]3[/tex].

Step-by-step explanation:

First we re write the equation by multiplying the number [tex]3[/tex] in this way we will see much better the solution

[tex]g(x)=3[|x-1|+2]=3|x-1|+6[/tex]

we will start from the inside to the outside

[tex]|x-1|[/tex] this [tex]-1[/tex]is grouped with the x and this means there is a horizontal shift of [tex]1[/tex] unit to the right (because of the sign)

[tex]3|x-1|[/tex] this [tex]3[/tex] is multiplying the x which means the function will be stretching by a factor of [tex]3[/tex] ([tex]g(x)[/tex] will be [tex]3[/tex] times bigger)

[tex]3|x-1|+6[/tex] this [tex]6[/tex] is not goruped with x and moves the entire function 6 units upwards.

We can see it more clearly in the graph attached.

Explanation:

Using the rule that x = x^1, we can rewrite the p as p^1

So 11m^3n^2p is the same as 11m^3n^2p^1

The exponents are: 3, 2, 1

Those exponents add up to 3+2+1 = 6

The degree of a monomial like this is simply equal to the sum of the exponents.

Answer:

6

Step-by-step explanation:

Answer: 72

Step-by-step explanation:

There are 9 students to choose from to go the library. After that person is chosen there are 8 students remaining.

First student  and   Second student

           9           x               8                 = 72

There are 36 ways for a teacher to choose 2 students out of 9 to go to the library, using combinations where the order of selection is not important.

The student is asking how many ways there are to choose 2 students out of 9 to go to the library, with the order of selection being irrelevant. This is a classic combinatorics problem that involves calculating combinations. Combinations are used in mathematics to count selections where order does not matter.

To find the number of combinations, denoted as C(n, k), where n is the total number of available options and k is the number of selections made, you can use the formula C(n, k) = n! / (k! * (n - k)!), where ! denotes a factorial. For this specific problem, the formula becomes C(9, 2) = 9! / (2! * (9 - 2)!), which simplifies to C(9, 2) = 9 * 8 / (2 * 1) = 36 ways to choose 2 students out of 9.

[tex]10x^2-7x-12=\\10x^2-15x+8x-12=\\5x(2x-3)+4(2x-3)=\\(5x+4)(2x-3)[/tex]

Answer:

(2x - 3)(5x + 4)

Step-by-step explanation:

Given

10x² - 7x - 12

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 10 × - 12 = - 120 and sum = - 7

The factors are - 15 and + 8

Use these factors to split the x- term

10x² - 15x + 8x - 12 ( factor the first/second and third/fourth terms )

= 5x(2x - 3) + 4(2x - 3) ← factor out (2x - 3) from each term

= (2x - 3)(5x + 4) ← in factored form

Answer:

Step-by-step explanation:

Distance of yellow to white = 8 inches which is given

The green ball is at the midpoint of red to white.

Since the green ball is 10 inches to the red ball, the green ball is also 10 inches from the white ball. That's what a midpoint is.

The yellow ball is closer.

Answer:

the cost of each notebook is $4.8

Step-by-step explanation:

Cost of each notebook= ?

Cost of a poster = $6

Total amount she spent = $20.40

If we subtract the cost of poster from total amount we get the cost of 3 notebooks.

$20.40-$6

=$ 14.4

It means the cost of 3 notebooks = $14.4

To find the cost of each notebook divide the cost of 3 notebooks by the number of books.

=14.4/3

=$4.8

Thus the cost of each notebook is $4.8....