[tex]\rm \int_{-\infty}^0\sqrt{1+2^2}e^{2\theta}d\theta=\phi-\frac12\\[/tex]​

Using the substitution method, if sum of two numbers is 96 and difference of the two numbers is 42, then the two numbers are 69 and 27

Consider the largest number as x and the smallest number as y

The sum of two numbers is 96

The equation will be

x+y = 96

x = 96-y

The difference of the two numbers 42

x-y = 42

Use the substitution method here

Substitute the value of x in the second equation

x-y =42

(96-y)-y =42

96-2y = 42

-2y = 42-96

-2y = -54

y = 27

Substitute the value of y in the first equation

x+y = 96

x+27 = 96

x = 96-27

x = 69

Hence, using the substitution method, if sum of two numbers is 96 and difference of the two numbers is 42, then the two numbers are 69 and 27

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x − 8 =  − 10

Explanation: 9x −13 = − 31 Add 13 to each side.

Answer:

-1

Step-by-step explanation:

3x = 21

Divide both sides by the co efficient of x

3x = 21

3      3

x = 21/3

x = 7

Find x - 8

x = 7

7 - 8

= -1

Equation: h(t) = 96t - 16t²

h(t) = 96t - 16[tex]t^{2}[/tex]

Find the zeros of the given equation:

Factor out the greatest common factor (GCF)

h(t) = 8t (12 - 2t)

The two factors are:

0 = 8t

0 = 12 - 2t

For both factors, solve for t

8t = 0

8t/8 = 0/8

t = 0

12 - 2t = 0

-2t = -12

t = 6

Now we have the x-values (t) of our zeros:

t = 0

(0, 0)

t = 6

(6, 0)

The ball will land on the ground at 6 seconds

Recall that the maximum point of the graph is halfway between the two zeros:

6 + 0 = 6

6 ÷ 2 = 3

The ball will reach its maximum height in 3 seconds

To find this height, substitute t for 3 in the given equation, and solve for h:

t = 3

h(3) = 96(3) - 16(3)²

       = 288 - 16(9)

       = 288 - 144

       = 144

The maximum height the ball will reach is 144 feet

***Refer to the graph below to check your answer:

=======================================================

Explanation:

I'll use x in place of t

And use y in place of h(t)

The equation we have is y = 96x - 16x^2

This rearranges to y = -16x^2 + 96x

Compare this to y = ax^2+bx+c to find that

The x coordinate of the vertex is

h = -b/(2a)

h = -96/(2*(-16))

h = 3

Then plug this into the equation to find the value of y

y = -16x^2 + 96x

y = -16(3)^2 + 96(3)

y = 144

The y coordinate of the vertex is k = 144

The vertex is located at (h,k) = (3, 144) to represent the highest point of the parabola.

The max height of 144 feet occurs when the ball is in the air for 3 seconds.

It is to be noted that at the equilibrium level, the Equilibrium price/output combination is $4 and 300,000 units respectively. See further calculations and answer below.

Recall that the equilibrium level of the national income is defined as that point where the aggregate supply  (QS) and the aggregate demand (AQD) are the same.

To calculate the market equilibrium price/output combination (EQL:

Step I - Recall the given data

Recall that at EQL, QD = QS

Where:

Qd = 500000 – 50000P; and ....................1

Qs = -100000 + 100000P. ...........................2

Hence, at EQL,

500000 – 50000P = -100000 + 100000P

⇒ 150,000P = 600,000 [divide both sides by 150,000

⇒ P = 600,000/150,000

⇒P = $4

Step II

To get Q, substitute P into (1)

thus, we have:

500,000 – 50000 (4)

500,000 – 200,000

= 300,000 units.

Hence, at EQL, P = $4 and Q = 300,000 units.

B)i What is P = $3?

Recall Step II above,

Simply substitute $3 into  (1)

⇒ 500,000 – 50,000 (3)

= 500,000 – 150,000

= 350,000 units

ii) what is P = $6, just repeat the above steps to get

200,000 units.

C) Price Elasticity of Demand (PED) at Equilibrium Price

The PED is the percentage change in the quantity requested as a result of a 1% change in price. The PED coefficient is often negative, although economists frequently overlook the sign. If the PED coefficient is less than one, demand for an item is generally inelastic (in absolute value).

The formula for demand (PED) at P = 6 is determined using the formula:

PED = %Δ in QD / %Δ in Price..................1

%Δ in QD = (200,000-300,000)/300,000 ..............2

With 300,000 beings (Original Unit at Equilibrium)

Hence %Δ in QD = -0.333

%Δ in Price =  (6-4)/4

= 1/2j or 0.5

PED = -0.333/0.5

PED = |-0.666|

Given that the PED is < 1, we can conclude that the demand for dry cleaning is inelastic.

In a situation where it is greater than 1, then the demand is elastic.

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Answer:

The top and the bottom numbers are not in scientific notation; the other two are in scientific notation.

[tex]x \leqslant 48[/tex]

Answer:

32?

Step-by-step explanation:

????????tell me if it is correct??

Differentiation of the given function f(x)=sinx/(1+tanx)​ is equal to

(cos³x -sin³x) / (cos²x)(1 + tanx)².

As given in the question,

Given function : f(x) = sinx /(1 + tanx )

Let u = sinx , v = ( 1 + tanx)

Differentiate the given function with respect to x

du/dx = cosx

dv/dx = sec²x

         = 1/cos²x

(d/dx)(f(x)) = (d/dx)(sinx /(1 + tanx ))

                = ( d/dx) (u / v)

                = [v (du/dx) -u (dv/dx)] / (v)²

               = [(1+tanx)(cosx) -(sinx)(1/cos²x)] / (1 + tanx)²

               = [cos²x(cosx + sinx) -sinx]/ (cos²x)(1 + tanx)²

               = [cos³x +sinx(cos²x -1)] / (cos²x)(1 + tanx)²

               =  (cos³x -sin³x) / (cos²x)(1 + tanx)²

Therefore, differentiation of the given function f(x)=sinx/(1+tanx)​ is equal to

(cos³x -sin³x) / (cos²x)(1 + tanx)².

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Midpoint formula

where (x1, y1) and (x2, y2) are two points and (xm, ym) are the coordinates of the midpoint between (x1, y1) and (x2, y2).

In this case, we want to find the coordinates of the midpoint between Y(0, -4b) and Z(-2a, 0). Substituting into the above formula:

The probability that the person has either had Covid or has been vaccinated and therefore has some protection against Covid is 45%

From the question given, the following data were obtained:

The probability that the person has either had Covid or has been vaccinated and therefore has some protection against Covid can be obtained as follows:

The percentage of person that had Covid and not vaccinated

= 40% - 25%

= 15%

The percentage of person that has been vaccinated and never had Covid

= 55% - 25%

= 30%

The probability that the person has either had Covid or has been vaccinated

= 15% + 30%

= 45%

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Step-by-step explanation:

Solve for X for one equation then input that value into the other equation.

x+2y=9

x=9-2y

x-y=3

(9-2y)-y=3

9-3y=3

6=3y

y=2

x=5

The value of the y-coordinate of the system of equations is y=2.

I hope it help

So basically you do 2096 divided by 8

Answer : 262 Minutes is alr i got u bro

An equation of the quadratic function in standard form is equal to -2x² - 7x - 6 = 0.

A quadratic function can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph.

In Mathematics, the standard form of a quadratic equation is given by;

ax² + bx + c = 0

y = f(x) = ax² + bx + c

Next, we would formulate a system of equations from the data contained in the table above:

-6 = a(-3)² + b(-3) + c  ⇒ -6 = 9a - 3b + c      .......equation 1.

0 = a(-2)² + b(-2) + c  ⇒   0 = 4a - 2b + c      .......equation 2.

-2 = a(-1)² + b(-1) + c  ⇒   -2 = a - b + c          .......equation 3.

From eqn. 2, we have:

c = -4a + 2b   .....equation 4.

Substituting eqn. 4 into eqn. 1 and 3, we have:

-2 = a - b - 4a + 2b          ⇒ -2 = -3a + b

-6 = 9a - 3b - 4a + 2b     ⇒ -6 = 5a - b

By using the elimination method, we have:

-8 = 2a

a = -4

For the value of b, we have:

-2 = -3a + b

b = -2 + 3a

b = -2 + 3(-4)

b = -2 - 12

b = -14

For the value of c, we have:

c = -4a + 2b

c = -4(-4) + 2(-14)

c = 16 - 28

c = -12.

Substituting the values of a, b and c into the standard form of a quadratic equation:

ax² + bx + c = 0

-4x² - 14x - 12 = 0

-2x² - 7x - 6 = 0

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The value of the expression one fifth times the quantity 3 times x plus 10 end quantity minus 11 over 15 times x is 2 - 2/15x.

It should be noted that expressions are simply used to show the relationship that exists between the variables that are given.

In this case, one fifth times the quantity 3 times x plus 10 end quantity minus 11 over 15 times x will be illustrated as:

= 1/5(3x + 10) - (11/15x)

= 3/5x + 2 - 11/15x

= 9/15x + 2 - 11/15x

= 2 - 2/15x

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Solution:

Given:

To get the precise name of the quadrilateral PQRS, using the coordinates of the points given;

The distance between points P and Q, and points Q and R are the same.

Also the distance between points P and S, and points R and S are also the same.

This means;

Hence, the image is as shown;

By the property of a kite, which says that two pairs of consecutive sides are congruent sides.

Hence, the most precise name for the quadrilateral PQRS is a KITE.

Number 2 is not a function, because we have more that one value of x that is the same

Number 3 is also not a function, we have more than one value of x that is the same

Number 4 is also not a function

Therefore, only number 1 is a function

There are three main distinctions between AAA, ASA, and SSS:

AAA: A triangle is said to be comparable to another if any two of its three angles are equal to any two of its three angles.

ASA: According to the ASA rule, two triangles are said to be congruent if any two angles and the side located between the angles of one triangle are equal to the corresponding two angles and the side located between the angles of the second triangle.

SSS: According to the SSS rule, two triangles are considered to be congruent if all three sides of one triangle are comparable to the corresponding three sides of the other triangle.

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After evaluating the limit we have came to find that the limit of   [tex]\lim_{x\rightarrow \infty }-\frac{3x^2}{x^2\ +4}[/tex] as x approaches ∞ is -3

A limit is the value that a function, sequence, or index approaches as an input or index approaches a specified value in mathematics. Limits are required in the definitions of continuity, derivatives, and integrals, which are essential in calculus and mathematical analysis.

The notion of a limit of a sequence is further generalized to include the notion of a limit of a topological network, in addition to being closely related to the concepts of limit & direct limit in category theory.

A limit of a function is typically expressed in formulas as

[tex]{\displaystyle \lim _{x\to c}f(x)=L,}[/tex]

To find the limit we will use L'Hôpital's Rule

Find the derivative

⇒ [tex]\lim_{x\rightarrow \infty }-\frac{3x^2}{x^2\ +4}[/tex]

⇒ [tex]\lim_{x\rightarrow \infty }-\frac{6x}{2x + 0}[/tex]

⇒ [tex]\lim_{x\rightarrow -\infty }\frac{-6x}{2x }[/tex]

Evalúe ∞ as x

⇒ [tex]\frac{-6(\infty)}{2(\infty)} }[/tex]

⇒ -3

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nswer:

Explanation:

iven the below expression;

We'll follow the below steps to factor the given expression;

tep 1: L

The factors are 12 and 5. We'll go ahead and replace the middle term 17x with these factors as seen below;

tep 2: GG

tep 3: F

tep 4: FW

The base and height of the triangle are 9 cm and 14 cm respectively.

The height of the triangle is 5 centimetres greater than the base.

The area of the triangle is 63 cm².

Therefore,

area of a triangle = 1 / 2 bh

where

Therefore,

h = 5 + b

Hence,

area of a triangle = 1 / 2 × b × (5 + b)

area of a triangle =  1 / 2 × 5b + b²

63 = 5b + b² / 2

cross multiply

126 = 5b + b²

b² + 5b - 126 = 0

b² + 14b - 9b  - 126 = 0

b(b + 14) - 9(b + 14) = 0

(b + 14)(b - 9) = 0

b = -14 or b = 9

Therefore, the base can only be positive .

Hence,

Base of the triangle = 9 cm

height of the triangle = 9 + 5 = 14 cm

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Answer:

Step-by-step explanation:

Total attendance = 500 people

Parents of children in play = 65% of 500

=>0.65 * 500

=> 325

325 were the parents of children in the play.

The x and y values that makes the relation a function are x = -4, y = 0, x = 5, y = -1 and x = 2, y = 8

The ordered pairs are given as

(− 3, 7), (–2, 3), (0, 8), (1, − 1), (x,y)

For a list of ordered pairs to represent a function, the following must be true

The x values must have exactly one y value

Using the above as a guide, we can see that x = -4, y = 0, x = 5, y = -1 and x = 2, y = 8 fits the above description

Hence, the values of x and y are x = -4, y = 0, x = 5, y = -1 and x = 2, y = 8

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Answer: 50%

Step-by-step explanation:

when you divide 90 by 2 you get 45 so 45+45=90

Answer: 8% of the students in the sixth grade are girls

Step-by-step explanation:

The domain and range of the given inequality graph are; Domain: {x | -2 ≤ x ≤ 2} and Range: {x | -6 ≤ x ≤ 6}

The domain of a function is the set of all possible input values that make a function possible. Meanwhile the range of a function is the set of all possible output values that make a function possible.

Now, when dealing with an inequality graph, it is pertinent to note that a shaded dot implies less than or equal to (≤) or greater than or equal to (≥) while unshaded means less than or greater than.

Now. the range of the graph is closed from y = -6 to y = 6. Thus, the range is; {y| -6 ≤ y ≤ 6}

Meanwhile the domain of the graph is closed from x = -2 to x = 2. Thus, the domain of the graph is;

{x | -2 ≤ x ≤ 2}

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The larger number is 33 and the smaller number is 17.

Let the larger number be x

Then, the smaller number will be x-16

According to the question,

Larger number + smaller number = 50

So,

x+(x-16) = 50

2x = 50+16

2x = 66

x = 66÷2

x = 33

Hence,

Larger number = x = 33

Smaller number = x-16 = 33-16 = 17

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The (equivalent) compound annual rate at which Anders' salary has grown during the 12 years is 4.9%.

The compound annual rate is the equivalent rate of interest at which the present value of money grows to attain a future value.

At a 4.9% compound annual rate, Anders' salary has been growing by adding the growth amount to the initial salary and compounding both the principal and subsequent interest amounts until 12 years.

N (# of periods) = 12 years

PV (Present Value) = $2,800

PMT (Periodic Payment) = $0

FV = $-4,971.23

Results:

I/Y (Interest per year) = 4.9%

Total Interest = $2,171.23

Thus, using the online finance calculator, we can determine that Anders' salary has been compounded at 4.9% annually.

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the vectors are :  (i+5j) , (5i+j)

Here a vector is an object that has both a magnitude and a direction. Geometrically, able to picture a vector as a coordinated line fragment, whose length is the magnitude of the vector, and with an arrow demonstrating the direction. The direction of a vector is from its tail towards its head. Two vectors are the same on the off chance that they have the same magnitude and direction. We signify vectors utilizing boldface as in a or b. In the given graph we can see, for the vector T, it is 1 unit on the x-axis and 5 units on the y-axis, whereas for the vector S its 5 units on the x-axis and 1 unit on the y-axis. Since the unit vectors for the x-axis and y-axis are i and j,

So, the vectors will  i+5j and 5i+j

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Explanation:

Total number of students = 28

75% of 28 = 75% × 28

= 0.75 × 28 = 21

This means 21 students have met their reading goal

Fraction of 28 students that met their reading goal = 21/28

Divide numerator and denominator by 7

3/4

Attaching the label:

I omitted the first label on both lines: it should be 0 and 0% respectively

28/4 = 7

100%/4 = 25%

Each demacation represent 7 units on the first line

Each dividing line represent 25% on the second line

From the triangle given, we are required to solve for x and y.

Since they are similar triangles, let's find x and y below.

For x:

Let's find x, from the equation above.

Cross multiply:

Divide both sides by 8:

For y:

ANSWER:

x = 1.25, y = 1.75

In the metric system, centimeters per minute (cpm) represents speed or velocity. It counts the centimeters that are covered in a minute.

65 mi/hr to 174346 centimeters per minute.

$1 mi/h = 2682.2346355307 cm/ min.

65 × 2682.2346355307 cm/min = 174345.2513095 Centimeters Per Minute.

Always check the results; rounding errors may occur.

The base unit of [speed] (meters per second), 1 Miles Per Hour (mi/h) exists equivalent to

0.44704 meters-per-second,

while 1 Centimeters Per Minute (cm/min) = 0.000166667 meters-per-second.

65 Miles Per Hour to common speed units

65 mi/ h = 65 miles per hour (mi/h)

65 mi/h = 1.0833333333333 miles per minute (mi/m)

65 mi/h = 174346 centimeters per minute

Therefore, the correct answer is 174346 centimeters per minute.

The base unit for speed is meters per second (Non-SI Unit)

[Miles Per Hour] symbol/abbreviation: (mi/h)

[Centimeters Per Minute] symbol/abbreviation: (cm/min)

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