Solve similar triangles (advanced)

Differentition of \(y=log_{2}x^{3}.(5x^{4}+2)\) is \(y'=log_{2}x^{3}(20x^{3} )+(5x^{4}+2)\frac{1}{x}\)

A differential equation is an equation that contains one or more functions with its derivatives.

Given,

\(y=log_{2}x^{3}.(5x^{4}+2)\)

We have to differentiate with respect to x.

y'=xy'+yx'

\(x=log_{2}x^{3}\)

\(y=5x^{4}+2\)

\(y'=log_{2}x^{3}(20x^{3} )+(5x^{4}+2)\frac{1}{x^{3}} .3x^{2}\)

\(y'=log_{2}x^{3}(20x^{3} )+(5x^{4}+2)\frac{1}{x}\)

Hence, differentiation of \(y=log_{2}x^{3}.(5x^{4}+2)\) is \(y'=log_{2}x^{3}(20x^{3} )+(5x^{4}+2)\frac{1}{x}\)

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The total amount paid during the lease period is £45,665.64.

To find the total amount paid during the lease period, we need to add the initial payment of £10,000 to the present value of the four equal payments, which can be calculated using the present value formula:

PV = FV / (1 + r)^n

Where PV is the present value, FV is the future value, r is the discount rate, and n is the number of periods. In this case, the present value of the four equal payments is £26,496, the discount rate is 8%, and the number of periods is 4. We can solve for the future value by rearranging the formula:

FV = PV × (1 + r)^n

Plugging in the given values, we get:

FV = £26,496 × (1 + 0.08)^4

FV = £26,496 × 1.34

FV = £35,664.64

This is the total future value of the four payments. To find the total amount paid during the lease period, we need to add this to the initial payment of £10,000. Therefore, the total amount paid during the lease period is:

£35,664.64 + £10,000 = £45,665.64

Therefore the total amount paid during the lease period is £45,665.64.

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Answer:

Step-by-step explanation:

This doesn't factor. Not only that, but it does not give real results. The discriminate is negative.

a = 2

b = 4

c = 10

You could divide this equation by 2

a = 1

b = 2

c = 5  

These three are smaller and easier to calculate. The answer will be the same.

x = (- b +/- sqrt(b^2 - 4*a*c ) / (2 a)

x = (-2 +/- sqrt(^2 - 4(1)*(5) ) / 2*1

x = (-2 +/- sqrt(4 - 20) ) / 2

X = (-2 +/- sqrt(-16) ) /2

x = (-2 +/- 4i ) / 2

x = ( - 1) +/- 2i

The value of side length x in diagram a) is 4.3mm and side length x in diagram b) is 309.7 m.

The figures in the image are right triangles.

A)

angle D = 17 degree

Adjacent to angle D = 14 mm

Opposite to angle D = x

To solve for the missing side length x, we use the trigonometric ratio.

Note that: tangent = opposite / adjacent

Hence:

tan( 17 ) = x/14

x = tan( 17 ) × 14

x = 4.3mm

B)

angle Z = 82 degree

Adjacent to angle Z = 43.1 m

Hypotenuse = x

Using trigonometric ratio,

cosine = adjacent / hypotenuse

cos( 82 ) = 43.1 / x

x = 43.1 / cos( 82 )

x = 309.7 m

Therefore, the measure of x is 309.7 meters.

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The equation to show the perimeter of the rectangle is P = 2(2w + 5)

From the question, we have the following parameters that can be used in our computation:

Length = 5 more than the width

Also, we have

Perimeter = 58

This means that

P = 2(w + 5 + w)

P = 2(2w + 5)

In (a), we have

P = 2(2w + 5)

This gives

2(2w + 5) = 58

So, we have

2w + 5 = 29

2w = 24

w = 12

Next, we have

l = 12 + 5

l = 17

Lastly, we have

Area = 17 * 12

Area = 204

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Answer:

The constant of proportionality is 0.3

Step-by-step explanation:

» The graph shows a direct proportiinality.

\({ \rm{y \: \alpha \: x}}\)

» Therefore, input the constant;

\({ \rm{y = kx}}\)

» When x is 5, y is 1.5:

\({ \tt{1.5 = (k \times 5)}} \\ { \rm{k = 0.3}}\)

Answer:

0.3

Step-by-step explanation:

On a graph, proportional relationships are straight lines that extend through the origin.  

Slope of a graph = constant of proportionality of the equation

Let (5, 1.5) = \((x_1,y_1)\)

Let (20, 6) = \((x_2,y_2)\)

Formula of a slope: \(m=\dfrac{y_2-y_1}{x_2-x_1}\)

\(\implies m=\dfrac{6-1.5}{20-5}=0.3\)

So as the slope = 0.3, the constant of proportionality = 0.3

Answer:

5.2236 X 10^4

Step-by-step explanation:

52,236 in standard form is 5.2236 X 10^4

Answer:

m=0

Step-by-step explanation:

the slope is calculated using two points on the line and the formula

m = (y2 - y1) ÷ (x2 - x1)

where

x1 and y1 are the coordinates of point 1

x2 and y2 are the coordinates of point 2

for example, you can take

point 1 = (x1;y1) = (-2;3)

point 2 = (x2;y2) = (-1;3)

then your slope is

m = (3 - 3) ÷ (-1 - (-2)) = 0

notice that x1 is always at the left of x2 on the x axis

and it makes sense that your slope is 0 because for each x your y is the same

Answer:

\(\text{27}\)

Step-by-step explanation:

Given that :

\(\text{Dimension of poster board} = 1 \ \text{yd} \ \text{by} \ 1 \ \text{yd}\)

\(\text{Dimension of each poster board} = \dfrac{1}{3} \ \text{yd} \ \text{by} \ \dfrac{1}{9} \ \text{yd}\)

Number of poster signs that can be cut :

\(\text{Area of poster sign} = \dfrac{1}{3} \times \dfrac{1}{9} = \dfrac{1}{27} \ \text{yard}^2\)

\(\text{Area of poster board} = 1 \ \text{yard}^2\)

Number of poster signs that can be cut :

\(\dfrac{\text{Area of poster board}}{\text{Area of poster sign}}\)

\(1 \ \text{yard}^2\div (\dfrac{1}{27} ) \ \text{yard}^2\)

\(1 \div \dfrac{1}{27}\)

\(1 \times \dfrac{27}{1}\)

\(\bold{= 27 \ poster \ signs}\)

It is better to apply the 10% off coupon first and then the $2 off coupon.

Let's assume the price of the pizza is P.

If we apply the $2 off coupon first, the price of the pizza would be reduced to $P-2$. Then, if we apply the 10% off coupon, the price would be further reduced by 0.1(P-2). Therefore, the total price paid would be:

\($$P_{total}=P-2-0.1(P-2)=0.9P-1.8$$\)

If we apply the 10% off coupon first, the price of the pizza would be reduced to 0.9P. Then, if we apply the $2 off coupon, the price would be further reduced by 2. Therefore, the total price paid would be:

\($$P_{total}=0.9P-2$$\)

Comparing the two total prices, we can see that:

\($$0.9P-1.8 < 0.9P-2$$\)

Therefore, it is better to apply the 10% off coupon first and then the $2 off coupon.

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The resulting answer is 39000 N/mm, this equation can be used to convert a given measurement from N/cm to N/mm.

39000/1 = ? N/mm

Multiply 39 by 1000 to convert centimeters to millimeters.

39000/1 = ? N/mm

Divide the measurement 39000 N/cm by 1 to convert it to N/mm.

The answer is 39000 N/mm.

To convert a measurement from N/cm to N/mm, the equation that needs to be set up is 39000/1 = ? N/mm. This equation can be broken down into two steps. First, the measurement needs to be multiplied by 1000 to convert centimeters to millimeters. Then, 39000/1 needs to be divided to convert the measurement from N/cm to N/mm. The resulting answer is 39000 N/mm. Therefore, this equation can be used to convert a given measurement from N/cm to N/mm.

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The simplified form of the given expression as required in the task content is; 8.

It follows from the task content that the simplified form of the given expression; -4 ( 2 - (³√8 × 6) ) / 5 is to be determined.

Therefore, By solving the innermost parentheses; we have;

-4 ( 2 - (2 × 6) ) / 5

= -4 ( 2 - 12 ) / 5

= -4 ( -10 ) / 5

= 40 / 5

= 8.

Therefore, the simplified form of the expression is; 8.

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Answer:

y=2x-6

Step-by-step explanation:

y+4=-2(x-1)

Since the slope intercept form is in the form of:

y=mx+c

Making above equation in this form.

y+4=-2(x-1)

opening bracket

y+4=2x-2

subtracting both side by 4.

y+4-4=2x-2-4

y=2x-6

This equation is the slope intercept form.

Answer:

5

Step-by-step explanation:

the slope is Δy/Δx

0-(-5) =5

6-5 =1

slope is 5

Answer:

149 sq. ft

Step-by-step explanation:

For the triangle:

Base = 16-9 = 7 ft

Area of Triangle = 1/2 of  b.h

= 1/2 of 7 * 6

= 21 sq. ft

Area of Rectangle = l.b

= 5 * 16

= 128 sq. ft

Total Area = 149 sq. ft

25 + 2x = 55

2x = 30

x = 15

The number is 15

Answer:

Step-by-step explanation:

If the number is 15 then twice is 30 then add 25 = 30 + 25 = 55

$22.50

45/60 = 0.75 in hours

3.75 hours in total

3.75x6=22.5

Hope this helps!

Answer:

-3/4

Step-by-step explanation:

Answer:

B. 4/3

Step-by-step explanation:

The slope is rise over run or the change in y over the change in x. To find the slope count how many units y increases by then divide that by how many units x increases. In this graph y goes up by 4 and x increases by 3, so 4/3. Another way to find slope is the slope formula which is \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\), then plug in any two points and solve them.

Answer:

12x42=504

504/2=252

252

Step-by-step explanation:

Answer:

therefore, the expression for John's age in terms of y is 4y - 16.

Step-by-step explanation:

Answer:

John's age = 4y - 16

Step-by-step explanation:

We can start by using the information given to write expressions for the ages of Libby and John in terms of Alfred's age y.

We know that Libby is 4 years younger than Alfred, so her age can be written as:

Libby's age = Alfred's age - 4

We also know that John is 4 times as old as Libby, so his age can be written as:

John's age = 4 × Libby's age

Substituting the expression for Libby's age from the first equation into the second equation, we get:

John's age = 4 × (Alfred's age - 4)

Simplifying this expression, we get:

John's age = 4 × Alfred's age - 16

Therefore, an expression in terms of y for John's age is:

John's age = 4y - 16

Answer:

x- coordinate = 5

Step-by-step explanation:

Given a parabola in standard form , f(x) = ax² + bx + c ( a ≠ 0 ) , then

The x- coordinate of the vertex is

x = - \(\frac{b}{2a}\)

f(x) = x² - 10x + 3 ← is in standard form

with a = 1 , b = - 10 , then x- coordinate of vertex is

x = - \(\frac{-10}{2}\) = 5

Answer:

y= -14

Step-by-step explanation:

First, distribute to get 9y-10y+15=1-2y

Then, combine like terms: -y+15=1-2y

Then, bring the 2y over and the 15 over: y= -14

Hope this helped!

Answer:

(1) F

(2) T

(3) F

(4) T

(5) T

Step-by-step explanation:

(1) False; The edge is not a flat surface but rather it is the point where two surfaces meet

(2) True; Rectangular prisms, also known as cuboids have the following properties.

\(Edges = 12\\ Vertices = 8\\ Faces = 6\)

(3) False; A cylinder has 3 faces (2 flat faces and 1 curved face)

(4) True; A cone has 1 flat surface

(5) True; All pyramids have triangular faces

The volume of the solid generated by rotating the part of the curve y = x^3 from x = 1 to x = 2 about the y-axis is equal to 18π cubic units.

The part of the curve y = x^3 from x = 1 to x = 2 can be thought of as the graph of a function that maps x values to y values. When this part of the graph is rotated about the y-axis, it generates a 3-dimensional solid.

To find the volume of this solid, we can use the method of cylindrical shells. The volume of the solid generated by rotating a curve from x = a to x = b about an axis perpendicular to the x-axis is given by the formula:

V = π * ∫[a,b] (f(x))^2 dx

where f(x) is the equation of the curve. In this case, f(x) = x^3.

Substituting the values, we get:

V = π * ∫[1,2] (x^3)^2 dx

V = π * ∫[1,2] x^6 dx

Evaluating the definite integral, we get:

V = π * (x^7/7) evaluated at x = 2 - (x^7/7) evaluated at x = 1

V = π * (2^7/7 - 1^7/7)

V = π * (128/7 - 1/7)

V = π * (128/7) - π * (1/7)

V = 18 * π

Therefore, the volume of the solid generated by rotating the part of the curve y = x^3 from x = 1 to x = 2 about the y-axis is equal to 18π cubic units.

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Answer:

3

Step-by-step explanation:

Select an ordered pair: (2, 7)

Select another ordered pair: (6, 19)

slope = (difference in y)/(difference in x)

slope = (19 - 7)(6 - 2)

slope = 12/4

slope = 3

Answer:

Step-by-step explanation:

Pick any two points.

(2 ,7)  & (4, 13)

x₁  = 2  ; y₁ = 7    & x₂ = 4  ; y₂ = 13

\(Slope =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

         \(=\dfrac{13-7}{4-2}\\\\\\=\dfrac{6}{2}\\\\\\= 3\)

Answer:

2.

Step-by-step explanation:

First, make sure you always solve from left to right when doing this. For this situation we need PEMDAS. This stands for: Parenthesis, Exponents, Multiplication/Division, and Addition/Subtraction. These are the steps that we need to follow to answer this question.

1.) First, we solve for the parenthesis. We can take the parenthesis down once we solve for that part. 2 + 1 = 3. Now we have: -3 ÷ 3 x 2 + 4.

2.) There are no exponents, so we move onto to multiplication from left to right. -3 ÷ 3 = -1. So, now we have -1 x 2 + 4.

3.) Now we do the right side of the problem with the multiplication. -1 x 2 = -2. Now we have -2 + 4.

4.) Because the larger number is positive, that means that the answer will be positive. So -2 + 4 (or 4 -2) = 2.

So, -3 ÷ (2 + 1) x 2 + 4 = 2.

I hope that this helps.

Answer:

is 50

Step-by-step explanation:

..

Answer:

50 mgghh*gffh CD d yuh hgcft

Answer:

D.

Step-by-step explanation:

\(x^2-10x-2=17\)

Add 2 to both sides:

\(x^2-10x-2+2=17+2\)

\(x^2-10x=19\)

Add half of the coefficient of the x, squared to both sides:

\(x^2-10x+\left(-5\right)^2=19+\left(-5\right)^2\)

Simplify:

\(x^2-10x+\left(-5\right)^2=44\)

Complete the square:

\(\left(x-5\right)^2=44\)

\(x-5=\sqrt[]{44}\) or \(x-5=-\sqrt[]{44}\)

\(x=\sqrt{44} +5\) or \(x=-\sqrt{44} +5\)

The answer is D..............

The quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

A division is a process of splitting a specific amount into equal parts.

We have to find 3x³-2x²+7x+9 divided by x²-3x

3x³-2x²+7x+9 is the dividend and x²-3x is the divisor.

The steps to solve this are given below.

Step 1: Take the first digit of the dividend from the left. Check if this digit is greater than or equal to the divisor.

Step 2: Then divide it by the divisor and write the answer on top as the quotient.

Step 3: Subtract the result from the digit and write the difference below.

Step 4: Bring down the next digit of the dividend (if present).

Step 5: Repeat the same process.

Hence, the quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

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