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Answer:

[tex]\textsf{1)} \quad t=\dfrac{48}{r}[/tex]

[tex]\textsf{2)} \quad \sf 2.4\:hours=2\:hours\:24\:minutes[/tex]

Step-by-step explanation:

[tex]\boxed{\sf Time=\dfrac{Distance}{Speed}}[/tex]

Given:

Substitute the given values into the formula:

[tex]\implies t=\dfrac{48}{r}[/tex]

Substitute r = 20 km/h into the derived equation from part 1 and solve for t:

[tex]\implies t=\dfrac{48}{20}=2.4\: \sf hours[/tex]

Note: 2.4 hours = 2 hours 24 minutes

Answer: 2.4 hours

Step-by-step explanation: t=time

         r=rate        so question one is equal to t=48/r

then question 2 is 48/20=2.4

The length of the field with area 119 square feet is 17 feet and the width of the feet is 7 feet.

The area is the total region or space in two dimension that is covered by a figure , surface or object. Area of a rectangle is calculated by the product of its length and width.

A rectangle has 4 sides where each pair of  opposite side is equal .The length of a rectangle is normally the longer side and the width defines the shorter side.

Given the area of the barn is 119 square feet.

Let us consider the width of the barn to be x feet. As the length is 10 feet longer than the width then we will find the length to be ( x +10 ) feet.

Area = length × width

or, 119 = x × (x+10)

or, 119 = x² +10x

or, x² +10x - 119=0

Now we will solve the quadratic equation thus formed by middle term-factorization method:

or, x² +17x - 7x - 119 = 0

or, x ( x + 17 ) - 7 ( x + 17) = 0

or, ( x + 17 ) ( x - 7 ) = 0

Now either x + 17 = 0 or x - 7 =0

Therefore either x = 7  

or, x = -17 (The width cannot be a negative value)

∴Width = 7 feet and length = 7 + 10 = 17 feet.

Therefore the length of the field is 17 feet and the width of the feet is 7 feet.

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A line has no endpoints (line FG), a line segment has two endpoints (line segment AB), and a ray has one endpoint (ray CD).

A line segment can be described as a line having two definite endpoints.

A ray is a part of a line that has just one fixed endpoint and extends in the opposite direction of the endpoint to infinity.

A line has no endpoint. It extends in opposite directions to infinity.

1. The figure that is a line segment is the green figure. (line segment AB).

2. The blue figure is a ray (ray CD)

3. The red figure is a line (line FG).

In summary, a line has no endpoints (line FG), a line segment has two endpoints (line segment AB), and a ray has one endpoint (ray CD).

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Answer:

y = - 8x + 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 8x - 2 ← is in slope- intercept form

with slope m = - 8

• Parallel lines have equal slopes , then

y = - 8x + c ← is the partial equation of the parallel line

to find c substitute (- 0.5, 7 ) into the partial equation

7 = 4 + c ⇒ c = 7 - 4 = 3

y = - 8x + 3 ← equation of parallel line

The measure of  angle m∠PZQ is 63degrees.

A point where two or more line segments meet is called a vertex.

The vertex point also forms an angle.

Therefore,

point P is in the interior of ∠OZQ,

Hence,

<OZQ = <OZP +  m∠PZQ

The following angles are given:

m∠OZQ = 125°

m∠OZP = 62°

Substitute the given values into the expression above:

125 = 62 +  m∠PZQ

m∠PZQ = 125 - 62

m∠PZQ = 63°

Therefore, the measure of  the angle m∠PZQ is 63degrees

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Answer:

1.2 × 10⁻⁵

Step-by-step explanation:

The exponent is negative, so the decimal was moved -5 places back, making the number a decimal.

Answer:

1.2 x 10^5

Step-by-step explanation:

All work is shown in the attached screenshot! :)

infinitely many solutions 

Example

Simplify left side using distributive property to 6x+16. Combine like terms (2x and 4x) on the right side to 6x+16. Both sides simplify to the same expression (left side = right side) so there are infinitely many solutions. You can plug in any real number for x and the left side will always equal the right side.

Answer:

[tex]f^{-1}(x)= \dfrac{1}{2}\ln \left(-\dfrac{x^2}{x^2-1}\right), \quad \textsf{for}\:\{x:0 < x < 1\}[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=\dfrac{e^x}{\sqrt{e^{2x}+1}}[/tex]

The domain of the given function is unrestricted:  {x : x ∈ R}

The range of the given function is restricted:  {f(x) : 0 < f(x) < 1}

To find the inverse of a function, swap x and y:

[tex]\implies x=\dfrac{e^y}{\sqrt{e^{2y}+1}}[/tex]

Rearrange the equation to make y the subject:

[tex]\implies x\sqrt{e^{2y}+1}=e^y[/tex]

[tex]\implies x^2(e^{2y}+1)=e^{2y}[/tex]

[tex]\implies x^2e^{2y}+x^2=e^{2y}[/tex]

[tex]\implies x^2e^{2y}-e^{2y}=-x^2[/tex]

[tex]\implies e^{2y}(x^2-1)=-x^2[/tex]

[tex]\implies e^{2y}=-\dfrac{x^2}{x^2-1}[/tex]

[tex]\implies \ln e^{2y}= \ln \left(-\dfrac{x^2}{x^2-1}\right)[/tex]

[tex]\implies 2y \ln e= \ln \left(-\dfrac{x^2}{x^2-1}\right)[/tex]

[tex]\implies 2y(1)= \ln \left(-\dfrac{x^2}{x^2-1}\right)[/tex]

[tex]\implies 2y= \ln \left(-\dfrac{x^2}{x^2-1}\right)[/tex]

[tex]\implies y= \dfrac{1}{2}\ln \left(-\dfrac{x^2}{x^2-1}\right)[/tex]

Replace y with f⁻¹(x):

[tex]\implies f^{-1}(x)= \dfrac{1}{2}\ln \left(-\dfrac{x^2}{x^2-1}\right)[/tex]

The domain of the inverse of a function is the same as the range of the original function.  Therefore, the domain of the inverse function is restricted to {x : 0 < x < 1}.

Therefore, the inverse of the given function is:

[tex]f^{-1}(x)= \dfrac{1}{2}\ln \left(-\dfrac{x^2}{x^2-1}\right), \quad \textsf{for}\:\{x:0 < x < 1\}[/tex]

Answer:

- 1

Step-by-step explanation:

2x + 2y = 1

=> 2y = - 2x + 1

=> y = - x + 1

=> Slope = - 1

Answer:

x =20°

because m and n is parallel

Answer:

x ≥ 3

Step-by-step explanation:

2(x - 3) ≥ -3(-3 + x)

2x - 6 ≥ 9 - 3x

5x - 6 ≥ 9

5x ≥ 15

x ≥ 3

Answer:

x ≥ 3

Step-by-step explanation:

write, calculate, divide both sides

Answer: c

Step-by-step explanation:

same here 2383882828x7767=?

Answer:

x > 4

Step-by-step explanation:

2x + 2 > 10

2x > 10 - 2

2x > 8

x > 8/2

x > 4

The range of scores on the fourth test to give David a B grade for the semester is at least 73 but less than or equal to 89.

A range refers to the difference between the lowest and the highest score.

A range of scores gives two values, the lowest and the highest scores.

Scores secured by David = 81, 92, and 74

Total scores in three exams = 247

The average score for a B grade is:

80  ≤  B grade  < 90      ["at least" means ≤]

Therefore,

80 ≤ (81 + 92 + 74 + x) / 4  < 89  [assume equal weights for exams]

80 ≤ (247 + x) / 4 ≤ 89  [add values]

320 ≤ (247 + x) ≤ 356   [multiply by 4, retains a sense of inequality]

73 ≤ x < 109                   [subtracting 247 retains a sense of inequality]

Since exams are graded on 100 points, David cannot score 109, so the upper limit is put at 89.

Thus, the exam grade in the fourth test must be at least 73 but less than or equal to 89 to get a B average.

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Answer:

A graphing calculator can help you.

Here is the graph, it is in the photo.

Step-by-step explanation:

wot. that's not even a qn bro

Step-by-step explanation:

the difference between the numbers are 5

so this is an arthimetic sequence with D=5

5n-7 is the formula

Answer:

(x/8)(19 - x)

Step-by-step explanation:

The quotient is the answer to a division problem.

The difference is the answer to a subtraction problem.

"Times" indicates multiplication, which you could look at it as a link between the two functions, or quantities (them being the constants and variables sectioned off into parenthesis).

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

Domain : All possible values of x for which a function is defined.

According to given graph, the curve extends to infinity on both sides on x - axis, so it is defined for all real values.

i.e : Domain : All real

Range : All possible values of y for x, as per the given function

As per the given graph, the graph extends to infinity on lower end, but has maximum value of 0.

i.e Range : [tex]\boxed{ \sf y < 0} [/tex]

The amount that would be in the account kept with BPI bank in 3 years is P3,011.2640

It would 6.9422 years for the deposit to double if interest rate is 10,5%

What is future value of immediate amount?

The future value of deposit today in 3 years means its future equivalent when the amount has earned interest over the 3 years period

FV=PV*(1+r)^N

FV=future value after 3 years=unknown

PV=immediate deposit=3,000

r=annual interest rate=0.125%

N=number of years that the deposit lasted=3

FV=3000*(1+0.125%)^3

FV=P3,011.2640

Time taken to double:

FV=future value=3000*2=6000

PV=3000

r=annual interest rate=10.5%

N=number of years that it takes initial deposit to double=unknown

6000=3000*(1+10.5%)^N

6000/3000=(1.105)^N

2=(1.105)^N

take log of both sides

ln(2)=N*ln(1.105)

N=ln(2)/ln(1.105)

N=6.9422 years

Annuity:

FV=PMT*(1+r)^N-1/r

FV=future value of annuity=unknown

PMT=annual payment=20000

r=interest rate=3%

N=number of annual payments=7

FV=20000*(1+3%)^7-1/7%

FV= 153,249.2436

FV=PMT*(1+r)^N-1/r*(1+r)

FV=20000*(1+3%)^7-1/7%*(1+7%)

FV= 157,846.7209

20,000,000=1,250,000*(1+r)^20

20,000,000/1,250,000=(1+r)^20

16=(1+r)^20

(16)^1=(1+r)^20

divide indexes on both sides by 20

(16)^(1/20)=1+r

r=(16)^(1/20)-1

r=14.8698%

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Answer:

The answer is yes. Since there is no x^2

Answer:

X= -7

X = 3

Step-by-step explanation:

| x + 2| = 5

|-7 + 2| = 5

|-5| = 5

5 = 5

|x + 2| = 5

|3 + 2| = 5

|5| = 5

5 = 5

X= -7

X = 3

Answer:

Reflected function is y = - x³ + 3

Step-by-step explanation:

When a function f(x) is reflected about the y-axis, the reflected function becomes g(x) = f(-x)

f(x) = x³ + 3

f(-x) = (-x)³ + 3 =-x³ + 3

Answer:

$700

Step-by-step explanation:

Since the deal is 30% off, that means that the price is now 70% of the original price.

70% of x = 490

0.7x = 490

x = 490/0.7

x = 700

Answer: $700

Answer:

10.75

Step-by-step explanation:

$118.25 / 11

We're finding the cost of each pizza. So, If a Coach bought 11 Pizza's for $118.25, We need to find how much x is. x = amount of cost per pizza.  Divide $118.25 by 11 to get $10.75.

Each Pizza Costs $10.75.

Using Venn sets, the cardinalities are given as follows:

a) n(A U B) = 15.

b) n(A' U C) = 16.

c) n(A ∩ B)' = 10.

Venn amounts relates the cardinality of sets that intersect with each other.

For this problem, the sets are the ones given in this problem, A, B and C, while U is the universal set.

For this problem, the cardinalities are given as follows:

Hence:

Hence:

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