The derivative ds/dt at of the function s = (tan^2 t – sec^2 t)^5 is O-1 O 5(sect - tan t)(tan^2 t – sec^2t)^6 O -5 O 0
O None of the other answers

Answer:

(x + 3) × (2x - 7)

Step-by-step explanation:

2x² - x - 21

Write as a difference

2x² + 6x - 7x - 21

Factor the expressions

2x × (x + 3) - 7 (x + 3)

Factor the expression

(x +3) × (2x - 7)

Step-by-step explanation:

Since it's a right triangle, you can use Pythagoras

a^2 + b^2 = c^2

We have b and c, we just need a, so let's plug it in

\( {x}^{2} + {24}^{2} = {25}^{2} \)

\( {x}^{2} + 576 = 625\)

\( {x}^{2} = 49\)

\(x = 7\)

Answer: 7ft

Step-by-step explanation:

hypotenuse (h) = 25

perpendicular (p) = 24

base (b) = ?

We know by using Pythagoras theorem

b = √h² - p²

= √ 25² - 24²

= √ 49

= 7 ft

The value of the expression (3x^5 + y^2)^2 is 9x^10 + 6x^5y^2 + y^4

The expression is given as:

(3x^5 + y^2)^2

Expand the expression

So, we have

(3x^5 + y^2)^2 = (3x^5 + y^2)(3x^5 + y^2)

Expand the bracket

(3x^5 + y^2)^2 = 9x^10 + 3x^5y^2 + 3x^5y^2 + y^4

Evaluate the sum

(3x^5 + y^2)^2 = 9x^10 + 6x^5y^2 + y^4

Hence, the value of the expression (3x^5 + y^2)^2 is 9x^10 + 6x^5y^2 + y^4

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Answer: 15

Step-by-step explanation: we have 140 buns if a bakery bought 80 that means we don't have the 80 buns so we remove 80 from 140 so 140-80= 60. and so The remaining buns were put into 4 buns each. so we divide cause they are in 4 and so 60 divided by 4 is 15.

HOPE THIS HELPS!

Answer:

The percentage change in volume from cylinder A to cylinder B is 50% volume increased by 50% option (C) is correct.

What is a cylinder?

In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.

We know the formula for the volume of the cylinder is given by:

We have r = 10 inches and h = 5 inches

V = 500π cubic inches

Percent change in volume from cylinder A to cylinder B:

= 50%

Thus, the percentage change in volume from cylinder A to cylinder B is 50% volume increased by 50% option (C) is correct.

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Step-by-step explanation:

The parts of the triangles Ebony needs to compare so as to make sure both triangles are congruent by SAS are;

Two triangles are said to be congruent when the three sides and three interior angles of one triangle have the same measure as the three sides and the three interior angles of the other triangle.

The given triangles are ∆MON and ∆GEF

The segments and angles that Ebony has ensured are congruent are;

\( \overline{EF} \cong \overline{ON}\)

\( \angle{ MON} \cong \angle{ GEF}\)

The method by which Ebony intends to use to make sure that the two triangles are congruent, SAS, Side–Angle–Side congruency postulate.

The Side–Angle–Side congruency postulate states that two triangles are congruent if two sides and an included angle in one triangle are congruent to the corresponding two sides and included angle in the other triangle.

Given that the sides that form included angles with \( \angle{ MON} \) are \( \overline{ON}\) and \( \overline{OM}\) and the sides that form an included angle with \( \angle{ GEF}\) are \( \overline{EF} \) and \( \overline{EG} \), the other segments Ebony needs to compare are therefore the segments;

\( \overline{EG} \) and \( \overline{OM}\)

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Answer:

14.29% decrease (actual : 14.2979%)

From the given information provided, Emmett will earn $9.36 in interest after two years.

To calculate the interest Emmett will earn after two years, we can use the formula for compound interest:

A = \(P(1 + r/n)^(nt)\)

Where:

A = the final amount

P = the initial principal

r = interest rate (as decimal)

n = number of times the interest is compounded per year

t = the time (in years)

We want to find the interest earned after two years, so we need to subtract the initial principal from the final amount:

Interest = A - P

P = $90 (the initial principal)

r = 4% = 0.04 (the interest rate)

n = 1 (compounded annually)

t = 2 (two years)

A = 90(1 + 0.04/1)⁽¹ˣ²⁾⁾ = 99.36

So, the final amount after two years is $99.36.

Now we can calculate the interest earned:

Interest = A - P = 99.36 - 90 = 9.36

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Step-by-step explanation:

1: Variable term

2: constant term

3: Variable term

Answer:

20

Step-by-step explanation:

that is right...........

Answer

Step-by-step explanation:

Answer:

solution given;

length [l]=9cm

breadth [b]=7cm

height[h]=3cm

we have

the surface area of this rectangular prism =2[lb×bh×lh]=2[9×7+7×3+9×3]=222cm²

is your answer

Answer: For 1 it is A - f(x)=(x-2)(x+4) and for 2 it is C - y = 0.5x^2 + 1.5x − 5

Step-by-step explanation:

Just use Desmos

Answer:

1

Step-by-step explanation:

Because log 5 is equivalent to 0.6990

And log 2 is equivalent to 0.301

Now all that's left is whip out our calculators which gives us the answer 1

Hope this helps :)

Mark brainliest pls :)

Answer:

log5+log2=1

Step-by-step explanation:

because log 5 is equivalent to 0.6990, and log 2 is equivalent to 0.301

I hope I solved it for you

AnswerBABY BAYBY OOOOH

Step-by-step explanation:

Answer:

top

Step-by-step explanation:

divide both sides by (x-h)

Roy's younger brother's age is 11 years.

According to the question,

We have the following information:

If Roy is 4 years older than his brother and the product of their ages is 165.

Now, let's take the age of Roy's younger brother to be x years.

Age of Roy = 4+x

So, we have the following expression:

x(4+x) = 165

\(x^{2} +4x-165=0\)

Now, we will factorize this equation by splitting the middle term:

\(x^{2}\)+15x-11x-165 = 0

Now, taking x as a common factor from the first two terms and -11 as a common factor from the last two terms:

x(x+15)-11(x+15) = 0

Taking (x+15) as a common factor:

(x+15) (x-11) = 0

x+15 = 0 and x-11 = 0

x = -15 and x = 11

Now, we know that age can not be negative.

Hence, Roy's younger brother is 11 years old.  

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7.5cm2

5x3cm=15cm2 because of base x height/2 you would do

15cm2 divided by 2 since it is a triangle (a half of a square) which is 7.5cm2

Answer:

D.

Step-by-step explanation:

Area of a triangle is bh/2

So your base is 5 and your height is 3.

So you do 5*3 which is 15.

And lastly you do 15/2, which is 7.5. 7*2 is 14, and 8*2 is 16

So 7.5 times 2 is 15

Answer:

\(p=3\) and \(q=4\) the mistake was in calculating \(3q-4q-10=6\) let's solve first.

Step-by-step explanation:

if \(p= 2q-5\), substitute the \(p\) in the equation\(3q-2p=6\) as

\(3q-2(2q-5)=6\)

solve the equation in parentheses :

\(3q-2(2q-5)\\\)

multiply  \(-2 \\\) by \((2q-5)\\\) it will equal to:  \(3q-4q+10\)

now we want to let all unknown digits alone, so we will take \(10\) to the other side with a different sign it will be as:

\(3q-4q=6-10\)

now we will solve it:

\(3q-4q=6-10\\q=-4\) at this part, the given equation was wrong in the paper.

we don't want the digit to be negative so we will do it like this:

\(\frac{-q}{-1} =\frac{-4}{-1 } = q=4\)

now that we found \(q\) we will substitute it to find \(p\\\):

\(p=2q-5\\q=4\\p=2(4)-5\\p=8-5\\p=3\)

overall the mistake was in calculating \(q\) instead of putting \(3q-4q=6-10\)  

he/she put a different sign in front of the digit like :\(3q-4q-10=6\)

so when he/she flipped  \(-10\) it became positive and instead of subtracting he/she added it.  

Answer:

We have the problem:

|3r−15| if r<5

First we see the equality, if r = 5 we have:

I3r - 15I = I3*5 - 15I = I0I = 0.

Then the only restriction that we have is:

I3r - 15I > 0.

now, we could simplify it a bit further:

if r < 5, then the thing inside the absolute value will always be negative:

Then we can write:

I3*r - 15I = -(3*r -15) > 0

multiplying by -1 in both sides

(3r - 15) < 0.

if we keep simplifying this, we will get our initial restriction:

3r - 15 < 0

3r < 15

r < 15/3 = 5

r < 5

Func1(x, y) returns the sum of the original values of x and y. func2(x, y) returns the average of the final values of x and y after swapping. func3(a, b, c) returns the average of the final values of b and c after swapping and averaging.

Break down the meaning of the value returned by each of the three functions:

1. func1(x, y): This function swaps the values of x and y by assigning x the value of y and y the value of x. Finally, it returns the sum of x and y. Therefore, the value returned by func1(x, y) can be described as the sum of the original values of x and y.

2. func2(x, y): This function calls func1(x, y) and assigns the returned value to y. It then calls func1(y, x) and assigns the returned value to x. Next, it calculates z as the difference between x and y. Finally, it returns the average of x and y, which is (x + y) / 2.

The value returned by func2(x, y) can be described as the average of the final values of x and y after the swapping operations.

3. func3(a, b, c): This function calls func2(a, b) and assigns the returned value to c. It then calls func1(a, c) and assigns the returned value to b. Finally, it returns the average of b and c, which is (b + c) / 3. The value returned by func3(a, b, c) can be described as the average of the final values of b and c after the swapping and averaging operations.

In summary, func1(x, y) returns the sum of the original values of x and y. func2(x, y) returns the average of the final values of x and y after swapping. func3(a, b, c) returns the average of the final values of b and c after swapping and averaging.

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The complete question goes thus:

Consider the following confusing functions: def func1(x,y): x=y y=x y=y return (x+y) def func2(x,y): y=func1(x,y) x=func1(y,x) z=x-y return (x+y)/2 def func3(a,b,c): c=func2(a,b) b=func1(a,c) return (b+c)/3 Explain the meaning of the value returned by each of the three functions, assuming that all of the parameters are integers. (For example, you can write something like "func1(x,y) returns x2 - y2". This specific answer will not give you points because it is wrong. But a similar style answer is correct.)

The given fraction and decimals have been plotted on a number line as shown in the image attached below.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which is composed of both positive and negative numbers that are placed at equal intervals along its length.

Additionally, a number line typically decreases in numerical value towards the left from zero (0) and increases in numerical value towards the right from zero (0).

In order to place the given numbers on a number line, we would convert the fraction into a decimal number as follows:

1/3 = 0.3

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The point e. x = 5, y = 0 satisfies the two linear constraints simultaneously. We have two linear constraints which are given as;

2x + 5y ≤ 10 (Equation 1)

10x + 6y ≤ 42 (Equation 2)

We need to find the point which satisfies both equations. Let us plug in the values one by one to check which one satisfies the two equations simultaneously.

a. x= 6, y = 2

In Equation 1:2x + 5y = 2(6) + 5(2) = 17

In Equation 2:10x + 6y = 10(6) + 6(2) = 66

Thus, this point does not satisfy equations 1 and 2 simultaneously.

b. x=6, y=4

In Equation 1:2x + 5y = 2(6) + 5(4) = 28

In Equation 2:10x + 6y = 10(6) + 6(4) = 72

Thus, this point does not satisfy equations 1 and 2 simultaneously.

c. x=2, y = 1

In Equation 1:2x + 5y = 2(2) + 5(1) = 9

In Equation 2:10x + 6y = 10(2) + 6(1) = 26

Thus, this point does not satisfy equations 1 and 2 simultaneously.

d. x=2, y = 6

In Equation 1:2x + 5y = 2(2) + 5(6) = 32

In Equation 2:10x + 6y = 10(2) + 6(6) = 52

Thus, this point does not satisfy equations 1 and 2 simultaneously.

e. x = 5, y = 0

In Equation 1:2x + 5y = 2(5) + 5(0) = 10

In Equation 2:10x + 6y = 10(5) + 6(0) = 50

Thus, this point satisfies both equations simultaneously.

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The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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The following is the expected value of a number of books a student buys at the next book fair is 2.404 books.

The random variable b's expected value is then calculated as follows:

E(X) = 1 x 0.285 + 2 x 0.333 + 3 x 0.168 + 4 x 0.136 + 5 x 0.063 + 6 x 0.015 E(X)  = 2.404 books.

Thus, the expected value of discrete probability distribution is 2.404 books.

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The graph for the question is attached.

C. True, because to use the Law of Sines, at least two sides must be known.

The Law of Sines is a trigonometric rule that relates the sides and angles of any triangle. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.

To use the Law of Sines, at least two sides and the angle opposite one of them (or two angles and one side) must be known.

Therefore, the statement "The Law of Sines can be used to solve triangles where three sides are known" is false, as it is not necessary to use the Law of Sines to solve a triangle where all three sides are known.

In summary, the correct answer is C. True, because to use the Law of Sines, at least two sides must be known.

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In the next 10 years there will be 398 racoons in the state park

The annual increase in the population size is defined as a sum of differences: the difference between births less deaths and the difference between immigrants less emigrants, in a given country, territory or geographic area at a given year.

Using the formula

p(t) = p(o) e^ kt

k = 3.5/100 = 0.035

t = 10 years

p(t) = 280 e^ 0.035 ×10

p(t) = 280e^0.35

p(t) = 280 × 1.42

p(t) = 398( nearest whole number)

therefore be after 10 years there will be 398 racoons in the state park.

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1. Observe problem

1-(1/8+1/12+1/2)

Make all common denominator

The Least common multiple of 8,12, and 2 is 24

1-((3+2+12)/24)=

1-17/24=

7/24

Therefore, 28 years make up 7/24 of his life.

Simplifying, he grows 4 years for every 1/24 of his life

4 times 24 is 96, so

Fred is 96 currently(that's pretty old)

\(\bold{\huge{\pink{\underline{ Solution }}}}\)

\(\bold{\underline{ Given :- }}\)

\(\bold{\underline{ To \: Find :- }}\)

\(\bold{\underline{ Let's \: Begin :- }}\)

Let the present age of Fred be x

Therefore,

According to the question,

\(\sf{ 1/8x + 1/12x + 1/2x + 28 = x }\)

\(\sf{ (3x + 2x + 12x )/24 + 28 = x }\)

\(\sf{ 17x/24 + 28 = x }\)

\(\sf{ 28 = x - (17/24)x}\)

\(\sf{ 28 = 24x - 17x/24 }\)

\(\sf{28 = 7x/24 }\)

\(\sf{ 28 = 7x/24}\)

\(\sf{ 7x = 28 × 24}\)

\(\sf{ x = 672/7}\)

\(\sf{ x = 96\: years}\)

\(\sf{\red{ Hence,\: The\: total\: age\: of\: Fred \:is \: 96\: years }}\)