The function f is defined by f(x) = x^2 +
3x – 10. If f(x - 2) = x^2 + bx + c, what
are the values of b and c?

(Please explain too, I want to know how to do this)

a. The equation we get is 10(1.5 + x) = 80, where x is the number of hours Sheila can afford to hire the babysitter.

b. Sheila can afford the babysitter for 6 hours and 30 minutes.

c. The equation we get is 15(1 + x) = 80, where x is the number of hours Sheila can afford to hire the new babysitter.

d. Sheila can afford to hire the new babysitter for 4 hours and 20 minutes, while the first babysitter was hired for 6 hours and 30 minutes.

Thus, Sheila can't afford the same amount of babysitting from the second sitter as she could from the first sitter.

a. We assume the hours affordable to Sheila be x hours.

Per hour charge of the babysitter = $10.

Time taken by the babysitter traveling = 1.5 hours.

Therefore, total chargeable time = 1.5 + x.

Therefore, the total charge by the babysitter = $10(1.5 + x).

This needs to be equal to the amount Sheila is willing to spend, that is, $80.

Thus, the equation we get is: 10(1.5 + x) = 80.

b. We are asked to determine the hours Sheila can afford to hire the babysitter.

We have got the equation 10(1.5 + x) = 80, where x is the hours Sheila can afford to hire the babysitter.

Thus, by solving this equation, we can determine the hours Sheila can afford to hire the babysitter.

10(1.5 + x) = 80,

or, 1.5 + x = 8,

or, x = 8 - 1.5 = 6.5 = 6 hours and 30 minutes.

Thus, Sheila can afford the babysitter for 6 hours and 30 minutes.

c. Per hour charge of the new babysitter = $15.

Time taken by the new babysitter traveling = 1 hour.

Therefore, total chargeable time = 1 + x.

Therefore, the total charge by the new babysitter = $15(1 + x).

This needs to be equal to the amount Sheila is willing to spend, that is, $80.

Thus, the equation we get is: 15(1 + x) = 80.

d. We are asked whether Sheila affords the same amount of babysitting from the second sitter as she could from the first sitter.

To determine this, we need to find the hours she affords from the second babysitter, for which, we solve the equation 15(1 + x) = 80 as  follows:

15(1 + x) = 80,

or, 1 + x = 80/15,

or, x = 80/15 - 1 = 65/15 = 13/3 = 4 hours and 20 minutes.

Sheila can afford to hire the new babysitter for 4 hours and 20 minutes, while the first babysitter was hired for 6 hours and 30 minutes.

Thus, Sheila can't afford the same amount of babysitting from the second sitter as she could from the first sitter.

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The value of x from the given expression is 23

Given the following equation

√3x+12 = 9

Square both sides

√3x+12)² = 9²

3x + 12. = 81

Subtract 12 from both sides

3x + 12 - 12 = 81- 12

3x = 69

x = 23

Hence the value of x from the given expression is 23

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Answer: [tex]42x^3 y^2[/tex]

Step-by-step explanation:

[tex]A=(3xy)(14x^2 y)=42x^3 y^2[/tex]

Answer:

These lines are perpendicular.

Step-by-step explanation:

Put both equations in the slope intercept form of a line.

y = -6x - 8  This is already in the slope intercept form for a line

-x + 6y = 12  Add x to both sides of the equation

6y = x + 12  Divide through the whole equation by 6

y = 1/6x +2  

Now we compare the two slopes of -6 and 1/6.  They are negative reciprocals of each other.  That means that the line are perpendicular.

If the sample of bacteria is growing at an hourly rate of 15% continuously and the  bacteria began with 11 bacteria then there will be 244.178 samples bacteria after 21 hours.

Given growth of bacteria 15% ,bacteria at beginning 11.

We have to find the number of sample of bacteria after 21 hours.

We have to first form exponential function which shows the growth of bacteria in variable t.

Exponential function which shows the sum is y=P[tex]e^{rt}[/tex]

where P is initial amount ,

r is rate and

y is the sum

So in our problem P=11 and r=0.15

y=11*[tex]e^{0.15t}[/tex]

To find the  samples after 21 hours we have to put t=21.

y=11[tex]e^{0.15*21}[/tex]

y=11*[tex]e^{3.1}[/tex]

y=11*22.198  ([tex]e^{3.1}[/tex]=22.198 from e table)

y=244.178

Hence the samples after 21 hours will be 244 approximately.

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Answer:

2/3x

Step-by-step explanation

Answer:

(x³-3x²-3x-1) / (27x³)

Step-by-step explanation:

((x-1) / (3x))³

= (x-1)³ / /3x)³

(x-1)³ = (x-1)(x-1)(x-1) = x³ - 3x² - 3x - 1

then:

(x-1)³ / (3x³) = (x³-3x²-3x-1) / (27x³)

Answer: B

Step-by-step explanation:

There is a hole at x=2, so the numerator and denominator should both have a factor of x-2.

This eliminates everything except for B.

Since the geometric series has 6 terms, increases by a factor of 4, and has a sum of 1365, the value of the first term is 1.

The sum of a geometric series is given by

Sₙ = a(rⁿ - 1)/(r - 1) with r > 1 where

Now, since our Geometric Series has 6 terms, n = 6. Also, it increases by a factor of 4, so, r = 4 and has a sum of 1365, so Sₙ = 1356. So,we have that

Since we require the first term, a , making a subject of the formula, we have

a = Sₙ(r - 1)/(rⁿ - 1)

Substituting the values of the variables into the equation, we have

a = Sₙ(r - 1)/(rⁿ - 1)

a = S₆(r - 1)/(r⁶ - 1)

a = 1365(4 - 1)/(4⁶ - 1)

a = 1365(3)/(4096 - 1)

a = 4095/4095

a = 1

So, the value of the first term is 1.

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Answer:

can you give the question?

Step-by-step explanation:

didnt ask a question

The computation of the equation shows.that x is -4 and y is 0.6.

4x + 5y = -1

-5x - 8y = 10

The value of x and y will be calculated thus:

-5 × (4x + 5y = -1)

4 × -(5x - 8y = 10)

-20x - 25y = 5

-20x -32y = 40

Add the equation

57y = 45

y = 45/75 = 0.6

Since 4x + 5y = -1

4x + 5(0.6) = -1

4x + 3 = -1

x = -1 - 3

x = -4

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According to the order of operations, brackets are solved first which contains the division operation. Hence, 12 is divided by -6 first.  

Order of Operations

Given expression is,

(12 ÷ (-6))(3) + (-2)

According to the BODMAS rule of operations, the precedence order of operations is as follows,

Brackets > Of > Division > Multiplication > Addition > Subtraction

Hence, we will start by solving the brackets first, then solve the division and then the addition.

Evaluation

Solving the given expression as per the order of operations,

Brackets are solved first, then division followed by multiplication and then addition. Division is always of the highest precedence among all operations after brackets and of.

12 ÷ (-6)(3) + (-2)

= 12 ÷ (-6)(3) - 2   [∵ +(-n) = -n]

= (-2)(3) -2

= -6 - 2

= -8

Thus, solving the +(-2) and then division of 12 by (-6) are the first operations to be performed in order to evaluate the given expression.

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Answer:

396 gold bars

Step-by-step explanation:

first of all we will find numbers of gold bar 7*99

which is 693 and

we will find number of silver bars 11*99

which is 1089

then 1089-693=

396

C) graph of a quadratic function with a minimum at 2.5, negative 2.25 and x intercepts at 1 and 4

Standard Form of a Quadratic Function: ax² + bx + c = 0, where a ≠ 0

Given function: x² - 5x + 4

⇒ a = 1, b = -5, c = 4

The minimum of a function is the lowest point of its parabola. We can use the following formula to find the vertex or the minimum of the function: [tex]x=\dfrac{-b}{2a}[/tex] . This will give us the x-value of the vertex, and we will need to solve for the y-value.

The vertex or minimum.

Step 1: Find the x-value of the vertex.

[tex]\\\implies x=\dfrac{-(-5)}{2(1)}\\\\\implies x=\dfrac{5}{2}=2.5[/tex]

Step 2: Find the y-value of the vertex by substituting 2.5 as the value of x in the given function.

[tex]\\\implies x^2 - 5x + 4\\\\\implies 2.5^2-5(2.5)+4\\\\\implies 6.25-12.5+4\\\\\implies -2.25[/tex]

Vertex: (2.5, -2.25)

The x-intercepts (roots).

We can use the Quadratic Formula to find the roots of this function.

Quadratic Formula: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex] when [tex]ax^2+bx+c=0[/tex]

Equation: x² - 5x + 4 = 0

⇒ a = 1, b = -5, c = 4

Step 1: Substitute the values of a, b, and c into the formula. 

[tex]\\\implies x=\dfrac{\bold{-(-5)}\pm\sqrt{\bold{(-5)^2}\bold{-4(1)(4)}}}{\bold{2(1)}}\\\\\implies x=\dfrac{5\pm\sqrt{\bold{25-16}}}{2}\\\\\implies x=\dfrac{5\pm\sqrt{\bold{9}}}{2}\\\\\implies x=\dfrac{5\pm3}{2}[/tex]

Step 2: Separate into two possible cases.

[tex]x_1=\dfrac{5-3}{2}\implies \dfrac{2}{2}\implies \boxed{1}\\\\x_2=\dfrac{5+3}{2}\implies \dfrac{8}{2}\implies \boxed{4}[/tex]

The x-intercepts of the given function are 1 and 4.

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Using the z-distribution, the confidence interval is given by: (11.95, 12.65).

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.

The other parameters are given as follows:

[tex]\overline{x} = 12.3, \sigma = 1.5, n = 50[/tex]

Hence the bounds of the interval are:

[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 12.3 - 1.645\frac{1.5}{\sqrt{50}} = 11.95[/tex]

[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 12.3 + 1.645\frac{1.5}{\sqrt{50}} = 12.65[/tex]

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The amplitude, Period, Horizontal Shift and Vertical Shift of both graphs are as detailed below.

3)a. Amplitude is the distance between the center line and the positive or negative peak of the graph. Thus, the amplitude is 0.5.

b. The period is the time it takes for the graph to repeat or complete one cycle and in this graph, it is 3.

c. Looking at the graph, ideally the coordinate (3, -1.5) should have been on the y-axis which is at (0, -1.5). This means it was shifted by 3 units to the right side.

d. The positive peak should be equal to the negative peak but in this case, it is not so and as such the center should be on the x-axis which means that the graph was shifted down vertically by 2 units.

4) a. Amplitude is the distance between the center line and the positive or negative peak of the graph. Thus, the amplitude is 3 - 1 = 2

b. The period is the time it takes for the graph to repeat or complete one cycle and in this graph, it is 6.

c. Looking at the graph, ideally the coordinate (4, -1) should have been on the y-axis which is at (0, -1). This means it was shifted by 4 units to the right side.

d. The positive peak should be equal to the negative peak but in this case, it is not so and as such the center should be on the x-axis which means that the graph was shifted up vertically by 1 unit.

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Answer:

n = 100

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

given A = 40π , then

πr² × [tex]\frac{n}{360}[/tex] = 40π

π × 12² × [tex]\frac{n}{360}[/tex] = 40π

144π × [tex]\frac{n}{360}[/tex] = 40π ( divide both sides by π )

144 × [tex]\frac{n}{360}[/tex] = 40 ( multiply both sides by 360 to clear the fraction )

144n = 14400 ( divide both sides by 144 )

n = 100

Answer:

B

Step-by-step explanation:

Let t and d be their ages now.

2 years ago, their ages were t - 2 and d  2.

Now, Tyler is 3 years older than David: t = d + 3

2 years ago, Tyler was 4 times as old as David: t - 2 = 4(d - 2)

The system of equations is:

t = d + 3

t - 2 = 4(d - 2)

Answer: B

Answer:

D

Step-by-step explanation:

Yes

See

3 contractors took 8hours

4 contractors took 6hours

We observe

So it's inverse variation

Answer:

[tex]\fbox {Yes}[/tex]

Step-by-step explanation:

An inverse variation can be seen when two factors are compared, if one factor is seen to be increasing, then naturally the factor should be decreasing.

Here, as the number of contractors increase, the time taken to complete the work decreases.

∴ Hence, this represents an inverse variation.

Answer:

14.5 hours to the nearest tenth.

Step-by-step explanation:

4.9% = 0.049.

If the original number is 50 it will double to 100 so

100 = 50(1.049)^t

1.049^t = 2

t * log 1.049 = log 2

t = log 2 / log 1.049

 = 14.49 hours,

Triangle ABC is dilated by a scale factor of 5 to get A'(-15, -5), B'(10, -10) and C'(-5, -20)

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.

Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.

Triangle ABC has vertices at A(-3, -1), B(2, -2) and C(-1, -4). It is then dilated by a scale factor of 5 to get A'(-15, -5), B'(10, -10) and C'(-5, -20)

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The commutative property of multiplication addition is illustrated below.

The commutative property implies that the changing of orders of the numbers doesn't have a effect on the value.

In this case, 5 × 4 = 20. Also, changing them to 4 × 5 is still 20.

Likewise 2 + 5 as 5 + 2 gives 7.

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Answer:

Step-by-step explanation:

Solution

The length of all the rectangles is 7

You need the width to be               4

Area rectangle = L*w

Area rectangle = 7*4

Area rectangle = 28

Answer: B

Answer:

Step-by-step explanation:

To check this, we need to know whether

2

1

​

=

3

2

​

We have,  

2

1

​

=

2×3

1×3

​

=

6

3

​

and  

3

2

​

=

3×2

2×2

​

=

6

4

​

We find that

6

3

​

<

6

4

​

, which means that  

2

1

​

<

3

2

​

.

Therefore, The ratio 1:2 is not equivalent to the ratio 2:3

Answer:

No, they aren't equal.

Step-by-step explanation:

Answer:

[tex]x=-3[/tex]

Step-by-step explanation:

Given equation:

[tex]\dfrac{2x}{x+1}+\dfrac{3(x+1)}{x}=5[/tex]

Make the denominators the same:

[tex]\implies \dfrac{2x}{x+1} \cdot\dfrac{x}{x}+\dfrac{3(x+1)}{x} \cdot \dfrac{x+1}{x+1}=5[/tex]

[tex]\implies \dfrac{2x^2}{x(x+1)}+\dfrac{3(x+1)^2}{x(x+1)} =5[/tex]

Combine the fractions:

[tex]\implies \dfrac{2x^2+3(x+1)^2}{x(x+1)} =5[/tex]

Multiply both sides by x(x+1):

[tex]\implies 2x^2+3(x+1)^2 =5x(x+1)[/tex]

Expand the brackets:

[tex]\implies 2x^2+3(x^2+2x+1) =5x^2+5x[/tex]

[tex]\implies 2x^2+3x^2+6x+3 =5x^2+5x[/tex]

Combine like terms:

[tex]\implies 5x^2+6x+3=5x^2+5x[/tex]

Subtract 5x² from both sides:

[tex]\implies 6x+3=5x[/tex]

Subtract 5x from both sides:

[tex]\implies x+3=0[/tex]

Subtract 3 from both sides:

[tex]\implies x=-3[/tex]

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Rule 1:

1, 3, 7, 15, 31, 63, 127, 255, 511, 1023 etc

Rule 2:

40, 24, 16, 12, 10, 9, 8.5, 8.25, 8.125, 8.0625 etc

Hope this helps!

The radius of the cone's base in the unit is 9*7x².

Given:

To find:

Solution:

As we know, the volume of the cone formula is

V = πr²h/3

So, lets us compare the above formula with the given expression;

πr²h/3 = 3*7x³

Here, h is represented as x, we get;

πr²x/3 = 3*7x³

πr²/3 = 3*7x²

r²= 9*7x²

Hence, the radius of the cone's base, in units, is 9*7x².

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Answer: D

Step-by-step explanation:

If the original price was p, a price reduction would be p- the amount. Per the given answers, $275 is used for the reduction amount.

Based on Cody Ray's credit card details and the unpaid-balance method, Cody Ray's unpaid balance is $144.44 and his previous balance is $144.44. His new balance is $147.04

His unpaid balance is:

= Purchases + Finance charge - (Payments + Credit)

= 376.90 + 17.54 - 250

= $144.44

Previous balance is the $17.54 finance charges.

New balance:

= Unpaid balance + Finance charge + New Purchases

= 144.44 + (144.44 x 1.8%)

= $147.04

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Answer:

<1 =73

Step-by-step explanation:

The sum of the angles of a triangle add to 180 degrees

72+ 35 + <1 = 180

Add like terms

107 + <1 = 180

Subtract 107 from each side

<1 = 180-107

<1 =73

Using the binomial distribution, the probabilities are given as follows:

a) 0.4159 = 41.59%.

b) 0.5610 = 56.10%.

c) 0.8549 = 85.49%.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

For this problem, the values of the parameters are:

n = 3, p = 0.76.

Item a:

The probability is P(X = 2), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{3,2}.(0.76)^{2}.(0.24)^{1} = 0.4159[/tex]

Item b:

The probability is P(X < 3), hence:

P(X < 3) = 1 - P(X = 3)

In which:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{3,3}.(0.76)^{3}.(0.24)^{0} = 0.4390[/tex]

Then:

P(X < 3) = 1 - P(X = 3) = 1 - 0.4390 = 0.5610 = 56.10%.

Item c:

The probability is:

[tex]P(X \geq 2) = P(X = 2) + P(X = 3) = 0.4159 + 0.4390 = 0.8549[/tex]

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