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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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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

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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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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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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The answer that I got is 7 500

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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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:

[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:

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

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

500 represents the initial amount of medication, since when t=0, a=500.

Answer:

There are eight sides so it's an octagon

Step-by-step explanation:

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]

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!

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: [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]

Answer:

√33

Step-by-step explanation:

it is a right triangle and we use Pythagoras

x² = 7² - 4²

x² = 49 - 16

x² = 33

x = √33

Answer:

x=1

y=−2

z=5

(heres how i got the answer)

Step-by-step explanation:

x+2y+3z=12

x−3y+4z=27

−x+y+2z=7

Solve x+2y+3z=12 for x.

x=−2y−3z+12

Substitute −2y−3z+12 for x in the second and third equation.

−2y−3z+12−3y+4z=27

−(−2y−3z+12)+y+2z=7

Solve equations for y and z respectively.

y=−3+

5

1

​

z

z=

5

19

​

−

5

3

​

y

Substitute −3+

5

1

​

z for y in the equation z=

5

19

​

−

5

3

​

y.

z=

5

19

​

−

5

3

​

(−3+

5

1

​

z)

Solve z=

5

19

​

−

5

3

​

(−3+

5

1

​

z) for z.

z=5

Substitute 5 for z in the equation y=−3+

5

1

​

z.

y=−3+

5

1

​

×5

Calculate y from y=−3+

5

1

​

×5.

y=−2

Substitute −2 for y and 5 for z in the equation x=−2y−3z+12.

x=−2(−2)−3×5+12

Calculate x from x=−2(−2)−3×5+12.

x=1

The system is now solved.

x=1

y=−2

z=5

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

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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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 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:

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

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:

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:

Y = - 24

Step-by-step explanation:

Y/-6 +5=9 /*6 (Multiply the whole equation by the number 6 to eliminate the fraction. That is, you multiply each member of the equation by 6 because 6 is in the denominator of the fraction.
[tex]\frac{Y}{-6} *6=-Y[/tex],     [tex]5*6=30[/tex],    [tex]9*6=54[/tex]

-Y + 30 = 54
-Y = 54-30
-Y=24 /*(-1)
Y= -24

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!