Suppose you make $1500 at your summer job and you decide to invest this money in a savings account that
pays interest at an annual rate of 5.5% compounded continuously. How many dollars will be in the account
after 5 years?

The x-intercepts are (-2, 0) and (2, 0), the minimum is at (0, -3), and the line of symmetry is x = 0 if the equation of the parabola is y = x²—4

It is defined as the graph of a quadratic function that has something bowl-shaped.

Here the graph or equation is not given:

So we are assuming the equation for the parabola is:

y = x²—4

If we plot the graph of the parabola, we can say:

Thus, the x-intercepts are (-2, 0) and (2, 0), the minimum is at (0, -3), and the line of symmetry is x = 0 if the equation of the parabola is y = x²—4

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Answer:

  step 1

Step-by-step explanation:

The product of fractions is the quotient of the product of the numerators and the product of the denominators. When negative fractions are involved, the sign of the result will be negative if the number of minus signs among the factors is odd.

__

The product Emanuel wanted to compute was ...

  [tex]\dfrac{3}{5}\cdot\dfrac{4}{9}\cdot\left(-\dfrac{1}{2}\right)[/tex]

The first calculation step used was ...

  [tex]=\dfrac{3\cdot4\cdot(-1)}{5\cdot9\cdot(-2)}\qquad\textbf{Error}\text{ -- a minus sign added}[/tex]

The error was in the first step where a minus sign was added. This brings the total to an even number of minus signs, changing the sign of the result.

__

A more appropriate first step might have been ...

  [tex]=-\dfrac{3\cdot4\cdot1}{5\cdot9\cdot2}\qquad\text{correct first step}[/tex]

Answer: 1.5

Step-by-step explanation:

If we translate the triangle right one unit, we get it has vertices (3,4), (0[tex]\frac{1}{2}|(9)(3)-(4)(6)|=\boxed{1.5}[/tex],0), and (6,9).

So, the area is

Answer:

Slope is positive

Answer:

• positive

Step-by-step explanation:

Here is what you need to know:

slope up to the right: positive slope

slope down to the right: negative slope

horizontal line: zero slope

vertical line: undefined slope

Look at the graph. the line slopes up to the right, so it is a positive slope.

Answer:

A. $3,535.20.

To find the total amount paid, you can simply multiply the monthly payment by the number of payments:

$98.20 x 36 = $3,535.20

The area and perimeter 10.7625 sq. cm and 11.5536 cm.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

let us construct perpendicular bisector.

Using trigonometry

cos [tex]\theta[/tex]= B/H

cos 32.4 = x / 5.5

5.5 cos 32.4 =x

We will consider the third side 2x.

So, 2( 5.5 cos 32.4) is the third side

P = 5.5 + 5.5 + 2( 5.5 cos 32.4)

  = 11 + 0.5536

  = 11.5536 cm

Area= 1/2* 5*5* sin 115.2

        = 12.5 * 0.861

        = 10.7625 sq. cm

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Answer: [tex]x^{2}+14x-6y[/tex]

Step-by-step explanation:

[tex]4(3x+y)+2(x-5y)+x^{2} \\ \\ 12x+4y+2x-10y+x^{2} \\ \\ \boxed{x^{2}+14x-6y}[/tex]

The missing coefficient of the x-term after finding the product of (-x - 5)², is: C. 10.

The coefficient of a variable is the numerical value that comes before the variable and multiplies it.

Find the product of (-x - 5)²:

(-x - 5)(-x - 5)

-x(-x - 5) -5(-x - 5)

x² + 5x + 5x + 25

x² + 10x + 25

The x-term is "10x". The coefficient is: 10.

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Answer:

Step-by-step explanation:

a)

Planteamiento:

2x - 6 = 4

Procedimiento:

2x - 6 + 6 = 4 + 6

2x + 0 = 10

2x = 10

2x/2 = 10/2

1x = 5

x = 5

Comprobación:

2*5 - 6 = 4

10 - 6 = 4

Solución:

x = 5

b)

Planteamiento:

3x - 3 = 3

Procedimiento:

3x - 3 + 3 = 3 + 3

3x - 0 = 6

3x = 6

3x/3 = 6/3

1x = 2

x = 2

Comprobación:

3*2 - 3 = 3

6 -3 = 3

Solución:

x = 2

c

Planteamiento:

x + 3 = 4

x + 3 - 3 = 4 -3

x + 0 = 1

x = 1

Comprobación:

1 + 3 = 4

Solución:

x = 1

Algebraic expression of the product of a quarter of 3 more than a number a and two times a number b is equals to [tex](\frac{3}{4} +a)[/tex]×[tex](2b)[/tex]

" An algebraic expression is defined as the expression which is represents using variables, number and mathematical operation."

According to the question,

'a' represents a number

'b' represents another number

Algebraic expression  as per the given condition we get,

The product of

Quarter of 3 more than a number a = [tex]\frac{3}{4} +a[/tex]

Two times a number b = 2b

Algebraic expression = [tex](\frac{3}{4} +a)[/tex]× [tex](2b)[/tex]

Hence, algebraic expression of the product of a quarter of 3 more than a number a and two times a number b is equals to [tex](\frac{3}{4} +a)[/tex]×[tex](2b)[/tex].

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The equation that has the same solution as x² + 8x + 15 = -4x is x = -6± √21.

Step 1 - Move terms to the left

x² + 8x + 15 = -4x

x² + 8x + 15-(-4x) = 0

Step 2  - Combine the terms

x² + 8x + 15 + 4x = 0

x² + 12x + 15 = 0

Step 3 - Apply the quadratic formula

x = (-b ± √(b² - 4ac) )/ 2a

Recall that form our equation:

a = 1

b = 12

c = 15

Thus,  x = (-12 √(12² - 4 * 1 *15) )/2 *1

⇒x = -6 ± √21


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Answer: -2

Step-by-step explanation: The answer is -2 because -1 x 8 = -8, and -8 x 4 = -32. Because multiplying two negatives cancels out and becomes positive, we can apply this same principle and figure out that -32 x -2 would give us positive 64. Hope this helps!

Given the area of the house and the basement, the basement accounts for 21.67 percent of the total square footage.​

Percentage is simply number or ratio expressed as a fraction of 100.

It is expressed as;

Percentage = ( Part / Whole ) × 100%

Given that;

Percentage = ( Part / Whole ) × 100%

Percentage = ( 455ft² / 2100ft² ) × 100%

Percentage = 0.21666 × 100%

Percentage = 21.67%

Given the area of the house and the basement, the basement accounts for 21.67 percent of the total square footage.​

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When the sum of two angles measures up to 90° then these angles are known as complementary angles of each other. The correct option is C.

When the sum of two angles measures up to 90° then these angles are known as complementary angles of each other.

for example, ∠x + ∠y = 90°, therefore, the ∠x and ∠y are the complementary angles of each other.

The two angles which are complementary angles are  1° and 89° because their sum is 90°.

Hence, the correct option is C.

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The three deductions someone would see on their paystubs are:

A. Social Security Tax

C. Federal Income Tax

D. Medicare Tax

Paystubs is a paycheck and can be defined as a check that an employer issued out to the employee  for the service the employee rendered to the employer.

The three deductions someone would see on their paystubs are:

Social Security Tax

Federal Income Tax

Medicare Tax

Therefore the correct options are A, C, D.

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The sampling distribution of the mean if all possible random samples of size 50 were chosen will be 0.731.

From the information given, the mean of all the possible sample means will be:

= 5.17/✓50

= 5.17/7.071

= 0.731

It should be noted that the sample means will have the same mean as the population.

The intervals that you would expect to contain the true mean will be:

= 0.95 × 250

= 237.5 intervals

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The answer that I got is 7 500

Answer:

[tex]\dfrac{\text{d}}{\text{d}x} \tan^{-1}x=\dfrac{1}{1+x^2}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.5 cm}\underline{Trigonometric Identity}\\\\$\tan^{-1}(A)-\tan^{-1}(B) \equiv \tan^{-1}\left(\dfrac{A-B}{1+AB}\right)$\\\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{3 cm}$\displaystyle \lim_{h \to 0} \left[\dfrac{\tan^{-1} \theta}{\theta} \right]=1$\\\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Differentiating from First Principles}\\\\$\text{f}\:'(x)=\displaystyle \lim_{h \to 0} \left[\dfrac{\text{f}(x+h)-\text{f}(x)}{(x+h)-x}\right]$\\\end{minipage}}[/tex]

Given function:

[tex]\text{f}(x)=\tan^{-1}x[/tex]

[tex]\implies \text{f}(x+h)=\tan^{-1}(x+h)[/tex]

Differentiating from first principles:

[tex]\begin{aligned}\text{f}\:'(x) & =\displaystyle \lim_{h \to 0} \left[\dfrac{\text{f}(x+h)-\text{f}(x)}{(x+h)-x}\right]\\\\& =\lim_{h \to 0} \left[\dfrac{\tan^{-1}(x+h)-\tan^{-1}x}{(x+h)-x}\right]\end{aligned}[/tex]

Using the trigonometric identity to rewrite the numerator:

       [tex]\begin{aligned}& =\lim_{h \to 0} \left[\dfrac{\tan^{-1}\left(\dfrac{x+h-x}{1+x(x+h)}\right)}{(x+h)-x}\right]\\\\& =\lim_{h \to 0} \left[\dfrac{\tan^{-1}\left(\dfrac{h}{1+x^2+xh)}\right)}{h}\right]\end{aligned}[/tex]

[tex]\textsf{Multiply the denominator by }\dfrac{1+x^2+xh}{1+x^2+xh}:[/tex]

       [tex]= \displaystyle \lim_{h \to 0} \left[\dfrac{\tan^{-1}\left(\dfrac{h}{1+x^2+xh)}\right)}{\dfrac{h(1+x^2+xh)}{(1+x^2+xh)}}\right][/tex]

Separate:

       [tex]= \displaystyle \lim_{h \to 0} \left[\dfrac{\tan^{-1}\left(\dfrac{h}{1+x^2+xh)}\right)}{\dfrac{h}{(1+x^2+xh)}} \right] \cdot \displaystyle \lim_{h \to 0} \left[\dfrac{1}{1+x^2+xh}\right][/tex]

[tex]\textsf{Use }\displaystyle \lim_{h \to 0} \left[\dfrac{\tan^{-1} \theta}{\theta} \right]=1:[/tex]

       [tex]= 1 \cdot \displaystyle \lim_{h \to 0} \left[\dfrac{1}{1+x^2+xh}\right][/tex]

As h gets close to zero:

       [tex]= 1 \cdot \left[\dfrac{1}{1+x^2}\right][/tex]

Simplify:

       [tex]=\dfrac{1}{1+x^2}[/tex]

Answer:

To find the derivative of [tex]\tan^{-1} x[/tex] using the first principle of derivative, we need to use the definition of the derivative:

f'(x) = lim(h->0) [(f(x + h) - f(x)) / h]

where f(x) = [tex]\tan^{-1} x[/tex].

Substituting f(x) into the definition of the derivative, we get:

f'(x) = lim(h->0) [([tex]\tan^{-1}[/tex](x + h) - [tex]\tan^{-1}/tex) / h]

To simplify this expression, we can use the formula for the inverse tangent of a sum:

[tex]\tan^{-1}[/tex](a + b) = [tex]\tan^{-1}[/tex]a + [tex]\tan^{-1}[/tex]b - [tex]\pi[/tex]/2

Using this formula, we can rewrite the numerator of the expression above as:

([tex]\tan^{-1}[/tex](x + h) - [tex]\tan^{-1}/tex) = [tex]\tan^{-1}[/tex]((x + h) / (1 + (x + h)^2)) - [tex]\tan^{-1}[/tex](x / (1 + x^2))

Now, substituting this expression back into the definition of the derivative, we get:

f'(x) = lim(h->0) [[tex]\tan^{-1}[/tex]((x + h) / (1 + (x + h)^2)) - [tex]\tan^{-1}[/tex](x / (1 + x^2))] / h

We can simplify this expression using algebra and trigonometry, and we get:

f'(x) = lim(h->0) [h / (1 + x^2 + hx + h^2 + x^2h + xh^2)] / h

f'(x) = lim(h->0) 1 / (1 + x^2 + hx + h^2 + x^2h + xh^2)

Now we can simplify this expression by dropping the terms that contain h^2 or higher powers of h, since they will approach zero faster than h as h approaches zero. We also drop the term containing x^2h, since it is a second-order term and will also approach zero faster than h. This leaves us with:

f'(x) = lim(h->0) 1 / (1 + x^2 + hx)

Now we can evaluate the limit as h approaches zero:

f'(x) = 1 / (1 + x^2)

Therefore, the derivative of [tex]\tan^{-1} x[/tex] by first principle of derivative is:

[tex]\frac{d}{dx}[/tex][tex]\tan^{-1} x[/tex] = 1 / (1 + x^2)

Answer:

18 cm

Step-by-step explanation:

To find the distance, take the larger number and subtract the smaller number

26 cm - 8 cm

18 cm

Answer:

Area of a rectangle = l × b

11. 35 = 5 × b

b = 35/5

b = 7 m

12. 48 = 6 × h

h = 48/6

h = 8 ft

13. 24 = b × 3

b = 24/3

b = 8 in

Hope it helps!

Answer:

4.75 or round up to 5.

Step-by-step explanation:

if each pie has 8 slices, then you must do 8+8+8... and so on until u reach 38. However you wont get exactly 38 because 8 doesn't add up evenly into 38. You can find the exact number by divding the amount of people, 38, by the number of slices per pie, 8. The answer will be 4.75 but you can not buy a fraction of a pie so you must round up to 5 whole pies. There will be extra left over in the end, but you cant round down because 4 pies would not be enough, so you must buy 5.

Answer:

The remainder is 9

Step-by-step explanation:

x-7=0

x=7

Plug x=7 into the given fxn

-2(7)²+15(7)

-2(49)+105

-96+105

9

Answer:

£23490

Step-by-step explanation:

10/100×£234900=23490

The equation of the transformed function is y = 5cos(x/4 + 60) - 3

The equation of the graph is given as:

y = cos(x)

The rule of downward shift is:

(x, y) ⇒ (x, y - h)

So, the function when shifted downwards by 3 units is

y = cos(x) - 3

The rule of horizontal shrink is:

(x, y) ⇒ (x/k, y)

So, the function when shrink horizontally by a fourth unit is:

y = cos(x/4) - 3

The rule of left shift is:

(x, y) ⇒ (x +h, y)

So, the function when shifted left by 60 units is

y = cos(x/4 + 60) - 3

The amplitude is given as:

A= 5

So, we have:

y = 5cos(x/4 + 60) - 3

Hence, the equation of the transformed function is y = 5cos(x/4 + 60) - 3

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Answer:

  12 gallons

Step-by-step explanation:

The amount of juice in the mix is the sum of the amounts of juice contributed by each of the constituents of the mix. Those amounts will be the product of the quantity of constituent and the fraction that is juice.

__

Let x represent the amount of 80% juice drink that must be added to the mix. The total amount of orange juice in the mix is ...

  20% × 12 gallons + 80% × x gallons = 50% × (12 +x) gallons

__

Dividing by gallons, eliminating parentheses, and using decimals for percentages, we have ...

  2.4 +0.80x = 6.0 +0.50x

  0.30x = 3.6 . . . . . . . . subtract 0.50x+2.4

  x = 12 . . . . . . . . . . . divide by 0.30

12 gallons of 80% juice drink must be added to obtain the desired mix.

_____

Additional comment

We notice that 50% is the average of 20% and 80%, so each must be half of the mix. If there are 12 gallons of 20%, then there must be 12 gallons of 80%.

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Answer:

The pencil cost $0.05 and the pen cost $1.05.

Step-by-step explanation:

Let, the price of the pencil is $ .

Given that the pen costs a dollar more than the pencil,

So, the price of the pen=$+1.

Therefore, ++1=1.10

, 2+1=1.10

, 2=1.10–1

, 2=0.10

, =0.10/2

, =0.05

The pencil cost $0.05 and the pen cost $1.05.

Answer:

23/28   (82.1%)

Step-by-step explanation:

See attached Venn Diagram

23 out of 28  play basketball or baseball

Step-by-step explanation:

[tex]5 = {a}^{x} [/tex]

[tex] \frac{5}{a} = \frac{a {}^{x} }{a} [/tex]

[tex] \frac{5}{a} = {a}^{x - 1} [/tex]