Find from the first principle the derivative of y=sinsquare (3x-5).
​

Answer:

5(2t+3)

=5×(2×2+3)

=5×7

=35

5t+25

=5×7+25

=35+32

=67

Therefore,LHS≠RHS

SO,the statement is false

Answer:

3n² + 5n - 2

Step-by-step explanation:

Given sequence:

6, 20, 40, 66, 98, 136, ...

Calculate the first differences between the terms:

[tex]6 \underset{+14}{\longrightarrow} 20 \underset{+20}{\longrightarrow} 40 \underset{+26}{\longrightarrow} 66 \underset{+32}{\longrightarrow} 98 \underset{+38}{\longrightarrow} 136[/tex]

As the first differences are not the same, calculate the second differences:

[tex]14 \underset{+6}{\longrightarrow} 20 \underset{+6}{\longrightarrow} 26 \underset{+6}{\longrightarrow} 32 \underset{+6}{\longrightarrow} 38[/tex]

As the second differences are the same, the sequence is quadratic and will contain an n² term.

The coefficient of the n² term is half of the second difference.

Therefore, the n² term is:  3n²

Compare 3n² with the given sequence:

[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 & 3 & 12 & 27 & 48 \\\cline{1-5} \sf operation & +3&+8 & +13 & +18 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}[/tex]

The second operations are different, therefore calculate the differences between the second operations:

[tex]3 \underset{+5}{\longrightarrow} 8 \underset{+5}{\longrightarrow} 13\underset{+5}{\longrightarrow} 18[/tex]

As the differences are the same, we need to add 5n as the second operation:

[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 +5n & 8&22 & 42 & 68\\\cline{1-5}\sf operation & -2 &-2 &-2 & -2 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}[/tex]

Finally, we can clearly see that the operation to get from 3n² + 5n to the given sequence is to subtract 2.

Therefore, the nth term of the quadratic sequence is:

3n² + 5n - 2

Sally to get to the next town in 2/3 hour.

According to the statement

The distance covered by sally to get next town is 20 miles

Speed at which sally drive is 30 miles per hour

We know that the

TIME = DISTANCE / SPEED

Substitute the values in it and

TIME = 20 / 30

TIME = 2/3 hour

So, Sally to get to the next town in 2/3 hour.

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Answer:

x = -2

Step-by-step explanation:

you can fist distribute -5 into the parenthesis

25x - 15 - 5x + 5 = -50

then combine like terms

20x - 10 = -50

add 10 to both sides

20x = -40

lastly divide both sides by 20

x = -2

that is your answer

Step-by-step explanation:

here the answers is it helpful

The expansion of the expression is [tex]\frac{4x - 6}{20}[/tex]

Given the expression;

-2/20 (1 - 2x + 2)

= [tex]\frac{-2}{20}[/tex] × (1 -2x +2 )

Open up the bracket by multiply with -2, we have

= [tex]\frac{-2 + 4x -4}{20}[/tex]

Collect like terms in the numerator

= [tex]\frac{4x - 6}{20}[/tex]

Thus, the expression of the expression is [tex]\frac{4x - 6}{20}[/tex]

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The total area available for cars to park will be 858m².

The area of the parking lot will be:

= 78 × 19

= 1482m²

The area of aisle will be:

= 8 × 78

= 624m²

The available area will be:

= 1482m² - 624m²

= 858m².

The compact parking spaces that will fit in the lot will be:

N × 12.5 = 858

N = 858/12.5

N = 68

The non compact parking spaces that will fit in the lot will be:

N × 16.5 = 858

N = 858/16.5

N = 52

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The coordinates of the circumcenter of triangle ABC with the given vertices are (-2.5, -4.5).

In order to determine the coordinates of the circumcenter of triangle ABC with the given vertices, let its circumcenter be P(x, y). Thus, PA = PB = PC.

By squaring all sides of triangle ABC, we have:

PA² = PB² = PC²

From PA² = PB², we have:

(x - 3)² + (y - (-1))² = (x - (-3))² + (y - (-11))²

(x - 3)² + (y + 1)² = (x + 3)² + (y + 11)²

x² - 6x + 9 + y² + 2y + 1 = x² + 6x + 9 + y² + 22y + 121

-12x - 20y = 120

-3x - 5y = 30    ..........equation 1.

From PB² = PC², we have:

(x - (-3))² + (y - (-11))² = (x - 3)² + (y - (-8))²

(x + 3)² + (y + 11)² = (x - 3)² + (y + 8)²

x² + 6x + 9 + y² + 22y + 121 = x² - 6x + 9 + y² + 16y + 64

12x + 6y = -57     ..........equation 2.

Solving eqn. 1 and eqn. 2 simultaneously, we have:

x = -2.5 and y = -4.5.

Therefore, the coordinates of the circumcenter of triangle ABC with the given vertices are (-2.5, -4.5).

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To find x = [tex]\frac{1}{2} (AB+CD)[/tex]

[tex]x=\frac{1}{2} (46+25)\\\ x=\frac{1}{2} (71)\\ x =35.5[/tex]

Hope it helps!

Answer:

-3*4^2/3.

Step-by-step explanation:

[4 -⅓ ( 64 ⅓ - 64 ⅔) ]​

= 1/4^1/3 ( 4 - 4^2)

= 1 / 4^1/3 * -12

= -12/ 4^1/3

= -12 * 4^2/3 / 4

= -3*4^2/3

ΔXYZ was reflected to form ΔLMN, hence ΔXYZ ≅ ΔLMN, ∠X ≅ ∠L and XZ ≅ LN

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

Reflection is a rigid transformation, hence it produces congruent figures with congruent angles.

∠Y + ∠X + ∠Z = 180 (angle in a triangle)

86 + 38 + ∠Z = 180

∠Z = 56°

Also:

∠N + ∠M + ∠L = 180 (angle in a triangle)

86 + 56 + ∠L = 180

∠L = 38°

ΔXYZ was reflected to form ΔLMN, hence ΔXYZ ≅ ΔLMN, ∠X ≅ ∠L and XZ ≅ LN

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Answer:

17 sq. cm

Step-by-step explanation:

1st you split into 2 smaller shapes

Smaller shape:

A = lw

= 1(2)

= 2

Bigger Shape:

A = lw

= 3(5)

= 15

Add them together

15 + 2 = 17

The amount Cindy should increase for each dimension of the scaled model will be 12 meters.

The scale factor is defined as the proportion of the new image's size to that of the previous image. decision-making.

Given that:-

The scale model will be solved as follows:-

Present volume = 2 x 4 x 6 = 48 cubic meters

Let the lengths be increased by x meters now the new volume will be:-

( 2 + x ) ( 4 + x ) ( 6 + x ) = 48 x 84

( x² + 6x + 8 ) ( 6 + x ) = 48 x 84

( x³ + 44x + 12x² - 3984 ) = 0

By solving the cubic equation we will get the value of x = 12 meters.

Therefore the amount Cindy should increase for each dimension of the scaled model will be 12 meters.

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Answer:

40 km on the highway

30 km on the city roads

Step-by-step explanation:

Let x = highway

Let y = city road

The time formula: time = distance / speed.

1) Since we do not know the distance travelled on the highway and city roads but we do know the total time taken, we can say x + y = 70. Set the distances x and y and all equated to 2 hours, since we do not know them, nor do we know the time. This is called a system of equations.

x + y = 70

x/80 + y/20 = 2

2) Solve the system of equations using substitution.

x = 70 - y

---------------

70 - y/80 + y/20 = 2

70 + 3y/80 = 2

y = 30

---------------------------------

x + 30 = 70

x = 70 - 30

x = 40

Therefore, the delivery truck travelled 40 km on the highway and 30 km on the city roads.

The number of feet per second Tyrone traveled on his way to work is 45.36 ft/s

An equation is an expression that shows the relationship between two or more variables and numbers.

1 mile = 5280 ft, 1 min = 60 sec

30 mile = 30 mile * 5280 ft per mile = 158400 ft

58.2 min = 58.2 min * 60 sec per min = 3492 sec

Speed = distance / time = 158400 ft / 3492 sec = 45.36 ft/s

The number of feet per second Tyrone traveled on his way to work is 45.36 ft/s

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The confidence interval comes out to be (0.685,0.735).

Calculating the Confidence Level and Other Terms

The confidence level can be calculated as follows,

z = [tex]\frac{36}{40} * 100%[/tex]%  

z = 90 %

The margin error is given as, E= 0.025

The p value in this case is 0.71

Calculating the Confidence Interval

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test.

Confidence interval can be obtained by using the following formula,

(p-E, p+E) = (0.71-0.025, 0.71+0.025).

Therefore, the confidence interval is (0.685, 0.735).

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Answer:30

Step-by-step explanation:

To solve the problem, I will have to solve the equation for the first shape.

5^2 + 4^2 = 25 + 16 = 41

The second shape seems to be 2.5 times bigger than the first shape.

7x - 5 + 24 = 102.5

    +5               +5
   7x + 24 = 107.5
          -24      -24
           7x = 83.5
            7       7
x = 11.9285714286
          x = 11.9^2

11.9^2 = 141.61

Looking at the angles we know, there's a 4 and a 24 so the second shape is 6 times larger than the first shape. There's also a 5 which means the solution to the problem, 7x - 5, should be 30.

7x - 5 = 30

     +5   +5
    7x = 35
     7      7
      x = 5

The discount percent for the given transaction is calculated as; 6.11%

We are given;

Mark Price; M.P = 4500

Now, formula for discount amount is;

Discount amount = %Discount * M.P

Discount amount = x% * 4500 = 45x

Also;

Selling price is;

S.P = M.P - Discount Amount

S.P = 4500 - 45x

VAT = Vat% * S.P

VAT = (10%*4500) - 45x

VAT = 450 - 45x

S.P with VAT = S.P + VAT Amount = 4500 - 45x + 450 - 45x = 4950 - 90x

Thus;

4950 - 90x = 4400

Solving for x gives;

x = 6.11%

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Answer:

98

Step-by-step explanation:

From the statement of similarity, we can write this proportion.

TV/MV = UV/LV

28/x = 16/56

16x = 28 × 56

x = 7 × 14

x = 98

280 adults were there in the train.

What is linear equation definition and example?

Given,

      Total children are in the train = 40

     1/8  are children in train and no of children in train ,

      ∴ 1/8 × x = 40

     x = 40 × 8 ⇒ 320

The no of  passenger in train  = 320

in total passenger, 40 are children .

So, rest adults passengers are = 320 - 40 ⇒ 280

There fore, 280 adults were there in the train.

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Answer:

h(-3)=-1

Step-by-step explanation:

h(x)=-3x - 10

Let x = -3

h(-3)=-3(-3) - 10

      = 9-10

       =-1

Answer:

GIVEN THAT THE TRIANGLES ARE SIMILAR THEREFORE we can use similarity theorem.

Step-by-step explanation:

Hello!

The numbers should be written as :

1,750,064

one million, seven hundred fifty thousand, sixty-four

218,502

two hundred eighteen thousand, five hundred two

384,057

three hundred eighty-four thousand, fifty-seven

4,012,923

four million, twelve thousand, nine hundred twenty-three

Answer:

2

Step-by-step explanation:

Let the missing length be " x ".

( 3 + 1 ) / 6 = x / 3

4 / 6 = x / 3

Cross multiply,

x * 6 = 4 * 3

6 = 2 * 3

4 = 2 * 2

x * 2 * 3 = 2 * 2 * 3

Divide 2 * 3 on both sides,

x = 2

Answer:

12

Step-by-step explanation:

B x H x 1/2 = area of a triangle

we can break this figure into 4 different triangles and since we have the length of the chords (dotted lines) in the diamond we can easily solve it.

half of QS is 2 and half of PR is 3

2 x 3 = 6

6 / 2 = 3

since there are four triangles multiply 3 by 4 (3 x 4)

and you get 12.

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

Area of shaded region = 34 cm²

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

Area of shaded region = Area of bigger rectangle - Area of smaller rectangle.

Area (big) :

[tex] \qquad❖ \: \sf \:13 \times 6[/tex]

[tex] \qquad❖ \: \sf \:78 \: \:c m {}^{2} [/tex]

Area (small) :

[tex] \qquad❖ \: \sf \:11 \times 4[/tex]

[tex] \qquad❖ \: \sf \:44 \: \: cm {}^{2} [/tex]

Area of shaded region :

[tex] \qquad❖ \: \sf \:78 - 44[/tex]

[tex] \qquad❖ \: \sf \:34 \: \: cm {}^{2} [/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

Area of shaded region = 34 cm²

Answer: 4.77

Step-by-step explanation:

40.68-2.52=38.16/8=4.77

This is what I do :

40.68 - 2.52 = 38.16

38.16 ÷ 8 = 4.77

Each bag of oranges costs $4.77

Okay, so let's call B = the number of sandwiches Bill sells

and P = the number of sandwiches Pete sells

Since Bill sells 7 times as many sandwiches as Pete, then

B = 7P

And the difference between their sales is 414 sandwiches. Since we know that Bill sells more than Pete, then

B - P = 434

So, now we can substitute for B from the equation above B = 7P

x = bill's

y = pete's

x = 8y

B - P = 434

7P - P = 434

6P = 434

P = 72.33

Therefore, Pete sells 72.33 sandwiches

Bill sells 7 x 72.33 = 506 sandwiches.

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The exponent is greater than 1 so it is exponential growth, 500 in the equation represents the initial value, and the growth rate in the second equation is 6%.

During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.

We have an exponential function:

[tex]\rm b_1(t) = 500(1.6)^t[/tex]

a) As the base of the exponent is greater than 1 so it is exponential growth.

b) 500 in the equation represents the initial value.

c) We have another exponential equation:

[tex]\rm b_2(t) = 800(1.6)^t[/tex]

For exponentikal gropwth:

1 + r = 1.6

r = 0.6 or

r = 6%

In the equation:

[tex]\rm b_1(t) = 500(1.6)^t[/tex]

The number of bacteria initially was 500 and from the second the number of bacteria initially was 800.

Thus, the exponent is greater than 1 so it is exponential growth, 500 in the equation represents the initial value, and the growth rate in the second equation is 6%.

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