If f(x) = x² + 3x - 5, find the value of f(3).

The situation can be described by the equation x - 3 = 13 = x = 13 + 3 = x = 16.

A mathematical phrase with two equal sides and an equal sign is called an equation. An example of an equation is 4 + 6 = 10. 4 + 6 can be seen on the equal sign's left side, and 10 can be seen on the equal sign's right side. A relationship between two terms on either side of an equal sign is represented by a simple equation. The four mathematical operations of addition, subtraction, multiplication, and division are also used in simple equations, either singly or in combination.

no of egg is decreased e= x - 3

equation to represent the situation

x - 3 = 13

x = 13 + 3

x = 16

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The range of the side of the square is 24 to 31. The interval notation is (24,31).

What is interval notation?

An interval on a number line can be represented using interval notation. It is a method of representing subsets of the real number line, in other words.

Given that, the perimeter of a square must be greater than 96 inches but less than 124 inches.

Inequality form is

96 < P < 124

Where P is the perimeter.

The perimeter of a square is P = 4s, where s is the length of the side.

Putting P = 4s in 96 < P < 124

96 < 4s < 124

Divide by 4:

24 < s < 31

The interval notation is (24,31).

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Step-by-step explanation:

geometric mean theorem for right-angled triangles :

height = sqrt(pq)

where p and q are the parts of side as split by the height of that side.

19.

x = sqrt(4×16) = sqrt(64) = 8

20.

y = sqrt(5×8) = sqrt(40) = 6.32455532...

21.

18 = sqrt(12y)

18² = 12y

324 = 12y

y = 27

22.

10 = sqrt(25x)

10² = 25x

100 = 25x

x = 4

23.

Pythagoras

x² = 5² + height² = 25 + 4×5 = 25 + 20 = 45

x = sqrt(45) = 6.708203932...

24.

Pythagoras

b² = 16² + height² = 256 + 6×16 = 256 + 96 = 352

b = sqrt(352) = 18.76166304...

25.

Pythagoras

27² = 16² + height² = 256 + 16(z - 16) =

= 256 + 16z - 256 = 16z

729 = 16z

z = 729/16 = 45.5625

26.

Pythagoras

x² = (8 - 2)² + height² = 6² + (8 - 2)×2 =

= 36 + 12 = 48

x = sqrt(48) = 6.92820323...

The value of x are:

2) x = 18.87

3) x = 26.68

5) x = 35.52

6) x = 13.75

9) x = 3.69

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

2)

Tan 48 = x / 17

1.11 = x / 17

x = 17 x 1.11

x = 18.87

3)

Sin 67 = x / 29

0.92 = x / 29

x = 0.92 x 29

x = 26.68

5)

Cos 16 = x / 37

0.96 = x / 37

x = 0.96 x 37

x = 35.52

6)

Tan 58 = 22/x

1.6 = 22 / x

x = 22/1.6

x = 13.75

9)

Sin 24 = x / 9

0.41 = x / 9

x = 0.41 x 9

x = 3.69

Thus,

The value of x is given above.

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Answer: 5.49 × 10-4

Step-by-step explanation:

When you move the decimal over move it over to the right by 4 units.

When you move right it is (-) negative. So you get 5.49 x 10-4.

Answer:

1. The unit price for a doll is three dollars. The unit price for a purse is six dollars.

2. One doll costs three. One purse costs six.

3. Polly spends $24 on the 2 dolls and 3 purses.

Step-by-step explanation:

Doing some calculations, 1 doll costs three dollars and 1 purse costs six dollars.

5 x 3 + 6 = 21

7 x 3 + 1  = 27

If Polly buys 2 dolls and 3 purses, that means she spends six dollars on the dolls and eighteen dollars on the purses.

(2 x 3) + (3 x 6) = $24

Polly spends $24 on 2 dolls and 3 purses.

a) The leash is 12.2 ft long.

b) The diagonal is 7.1m

c) The altitude is 6.1 in

We can see a right triangle here, where the leash is the hypotenuse of that triangle.

Using the Pythagorean's theorem we can write:

leash = √( (10ft)² + (7ft)²)

leash = 12,2 ft

8) Remember that for a square of side length S, we have:

perimeter = 4*S

diagonal = √2*S

We know that the perimeter is 20 meters, then:

20m = 4*S

S = 20m/4 = 5m

Then the diagonal is:

D = √2*5m = 7.1m

9) For an equilateral triangle of sidelength S, the altitude is:

A = √( S² - (S/2)²)

In this case the side length is 7 inches, then:

A = √( (7in)² - (7in/2)²)

A = 6.1 in

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Answer:-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0  1  2  3  4  5  6  7  8  9 10

-5 -4 -3 -2 -1 0  1  2  3  4  5  6  7  8  9 10

Step-by-step explanation:

The area of the triangle in terms of 'x' will be (x² + 13x + 28) / 2.

Assume 'h' is the height of the triangle and 'b' be the base of the triangle. Then the area of the triangle is given as,

A = (1/2) × h·b

The area of the triangle is given as,

A = 1/2 [(x + 4)(x + 7)]

Simplify the equation, then we have

A = [(x + 4)(x + 7)] / 2

A = (x² + 7x + 4x + 28) / 2

A = (x² + 13x + 28) / 2

The area of the triangle in terms of 'x' will be (x² + 13x + 28) / 2.

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The measure of the largest exterior angle is 96°.

Heptagon is a two-dimensional shape with seven angles, seven vertices, and seven edges. This seven-sided polygon “heptagon” is made up of two words ‘Hepta’ and ‘Gonia’, which means seven angles. Another name given to it is septagon or 7-gon.

In heptagon, the sum of the interior angles is equal to 900 degrees. The sum of exterior angles of a heptagon is 360 degrees.

Here, x°+2x°+3x°+4x°+5x°+7x°+8x°=360°

30x°=360°

x°=12°

So, 8x°= 96°

Therefore, the measure of the largest exterior angle is 96°.

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The total cost of a meal costing $32 with 7% sales tax and 18% automatic tip is $40

An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.

The sales tax is 7% and the automatic tip is 18%. If the meal costs $32, hence:

Sales tax = 7% of $32 = 0.07 * 32 = $2.24

Automatic tip = 18% of $32 = 0.18 * 32 = $5.76

The total cost = cost of meal + sales tax + automatic tip

Substituting:

Total cost = $32 + $2.24 + $5.76 = $40

The total cost is $40

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Answer:

2483 in 8yrs means you multiply the two first

2483

× 8

_____

19864

so 8% of 19864

you have to divide the number by the percentage

o. 8÷ 19864= 2483

Answer: 90%

Step-by-step explanation:

Step 1: Calculate the total number of marbles in the bag.

3 red + 3 green + 15 yellow + 9 purple = 30 marbles

Step 2: Calculate the number of marbles that are not red.

3 green + 15 yellow + 9 purple = 27 marbles

Step 3: Calculate P(not red).

27/30 = 0.9

Answer: 90%

Answer:

the answer is answer c

Step-by-step explanation:

The solution graph is given in the attached image.

The solution is x = 2 and y = 70.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

Robert and Tony love to read.

Robert reads 30 pages the first day and 20 pages each day after that.

Tony reads 40 pages the first day and 15 pages each day after that.

We have a system of equations,

y = 20x + 30

y = 15x + 40

Subtracting the equations, we get,

5x = 10

x = 2

And y = 70.

And the graph is given in the attached image.

Therefore, the solution is x = 2 and y = 70.

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The absolute inequality 3/4 * |(1/3)x + 2| < 6 has a solution of (d) x > -30 and x < 18

To solve the inequality, we'll start by isolating the absolute value expression on one side of the inequality.

3/4 * |(1/3)x + 2| < 6

We'll first distribute the 3/4 across the absolute value:

|(1/3)x + 2| < 8

To simplify this, we'll split the inequality into two cases:

(1/3)x + 2 < 8

(1/3)x + 2 > -8

First, let's consider the case where (1/3)x + 2 < 8

(1/3)x < 6

x < 18

Now let's consider the case where (1/3)x + 2 > -8

(1/3)x > -10

x > -30

So, the solution set is x > -30 and x < 18

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Complete question

Solve the inequality three-fourths times the absolute value of the quantity one third times x plus 2 end quantity is less than 6. x > −8 and x < −4 x > −30 and x < 2 x < −30 and x < 18 x > −30 and x < 18

The circle graph for the given table is as mentioned.

In graph theory, a circle graph is the intersection graph of a chord diagram. That is, it is an undirected graph whose vertices can be associated with a finite system of chords of a circle such that two vertices are adjacent if and only if the corresponding chords cross each other.

Given is a data as shown in the table.

The circle graph for the given table is attached with the answer.

Therefore, the circle graph for the given table is as mentioned.

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Worker B has the higher variance and standard deviation than Worker A.

Standard deviation in statistics, typically denoted by σ, is a measure of variation or dispersion (refers to a distribution's extent of stretching or squeezing) between values in a set of data. The lower the standard deviation, the closer the data points tend to be to the mean (or expected value), μ.

Given,

The number of parts produced per hour by the workers are as follows:

Worker A: 5, 4, 4, 6, 7, 5, 6, 3

Worker B: 4, 8, 1, 9, 2, 9, 4, 3

Average μ = 5

Variance = σ² = Σ(xi - μ)²/N

Variance for first worker

= [(5 - 5)² + (4 - 5)² + (4 - 5)² + (6 - 5)² + (7 - 5)² + (5 - 5)² + (6 - 5)² + (3 - 5)²]/8

= [0² + -1² + -1² + 1² + 2² + 0² + 1² + -2²]/8

= [1 + 1 + 1 + 4 + 1 + 4]/8

= 12/8

= 1.5

Standard deviation σ = √1.5

 = 1.2247448713916

Variance for second worker

= [(4 - 5)² + (8 - 5)² + (1 - 5)² + (9 - 5)² + (2 - 5)² + (9 - 5)² + (4 - 5)² + (3 - 5)²]/8

= [-1² + 3² + -4² + 4² + -3² + 4² + -1² + -2²]/8

= [1 + 9 + 16 + 16 + 9 + 16 + 1 + 4]/8

= 72/8

= 9

Standard deviation σ = √9

= 3

Hence, Variance and Standard deviation of worker B are higher than worker A.

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Answer: 588π = 1846.32

Step-by-step explanation:

Volume of cylinder = πr²h

Volume = (7)²*12*π = 588π = 1846.32

The solution is Option A.

The sum of the infinite geometric progression is S = -( 9/5 )

A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.

The nth term of a GP is aₙ = arⁿ⁻¹

The general form of a GP is a, ar, ar2, ar3 and so on

Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )

Given data ,

Let the sum of the geometric progression be represented as S

Now , the equation will be

∑ n = 1 to ∝ ( -3 ( 3/8 )ⁿ )   be equation (1)

The sum of the infinite GP is S = a / ( 1 - r ) , where r is the common ratio

Substituting the values in the equation , we get

when n = 1

a₁ = -3 ( 3/8 )

a₁ = -9/8

when n = 2

a₂ = -3 ( 3/8 )²

a₂ = -27/64

So , the common ratio r = a₂ / a₁

The common ratio r = 3/8

Substituting the values in the equation , we get

The sum of the infinite GP is S = a / ( 1 - r )

The sum of the infinite GP is S = ( -9/8 ) / ( 1 - 3/8 )

The sum of the infinite GP is S = ( -9/8 ) / ( 5/8 )

The sum of the infinite GP is S = - ( 9/5 )

Hence , the sum of GP is - ( 9/5 )

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The vertices of triangle J'K'L' after a reflection of the triangle JKL over the x-axis is given as follows:

The original vertices of the figure are given as follows:

J(-5,5), K(5,7) and L(2,3).

For a reflection over the x-axis, the reflection rule is defined as follows:

(x,y) -> (x,-y).

Meaning that the x-coordinate remains constant while the y-coordinate has the sign exchanged.

Then the vertices of the reflected figure are given as follows:

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Answe

Step-by-step explanation:

answer is 9

Answer:

The possible formula for the linear function h(x) is h(x) = -7x + 190. This can be determined by using the information from numerade.com, which states that the formula for a linear function is y = mx + b. Applying this formula to the given values of h(-30) = 90 and h(20) = -160 gives a formula of h(x) = -7x + 190.

Step-by-step explanation:

Answer:If the radius of the cone is equal to one half the height, we can write the radius as r = h/2. Substituting this expression into the formula for the volume of a cone, we get:

V = 1/3 * (h/2)^2 * h = 1/3 * h^3 / 4

So, the volume of a cone in terms of the height, if the radius is equal to one half the height, is V = 1/3 * h^3 / 4.

Step-by-step explanation:

If the radius of the cone is equal to one half the height, we can write the radius as r = h/2. Substituting this expression into the formula for the volume of a cone, we get:

V = 1/3 * (h/2)^2 * h = 1/3 * h^3 / 4

So, the volume of a cone in terms of the height, if the radius is equal to one half the height, is V = 1/3 * h^3 / 4.

Counting of numbers by 5's end with 0, 5, 0, 5, 0, .....

Counting in mathematics is defined as the process of finding the number of objects in a set which is finite.

Counting numbers are the natural numbers.

The question is how to count by 5's.

In order to count by 5's, we have to add 5 to each of the preceding number  to get the next number.

So the pattern will be,

5, 10, 15, 20, 25, 30, 35, ........

So the numbers end either in 0 or 5.

Hence the pattern of counting by 5's are the numbers which ends in either 0 or 5.

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The acceleration of the object when the force on the object changes to 16 N is 4 m/s²

The second law of motion by Newton says that the force is equal to the change in momentum per change in the time. For a constant mass, force equals the mass times acceleration, i.e. F = m x a.

Given here: A force acting on an object.

We know, The formula for force states that the force is equal to mass that is multiplied by the acceleration.

Thus we have the equation as F=m.a

Now in case 1 we have  

20=m×5

m=4 kg

Again in case 2 we have

16 = 4×a

a=4 ms⁻²

Hence, The acceleration of the object when the force on the object changes to 16 N is 4 m/s²

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The expression 48s represents the number of scarves (s) and its per unit  (48).

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given that, Emiko makes shibori scarves and sells them for $48 each on a website for handmade goods.

Here, the expression 48s represents the total price of buying s scarves

We need to tell what 48s mean,

So,

48s here is the total cost for buying s scarves,

That mean, if we buy s scarves we will have to pay $48s

Similarly, if we will buy 4 scarves, we will pay = 48 × 4 = $192

For 10 scarves, we will pay = 48 × 10 = $480

Therefore, we can say $48 is the unit price of the scarf.

Hence, the expression 48s represents the number of scarves (s) and its per unit  (48).

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The question was incomplete, so I answered for the question :-

Emiko makes shibori scarves and sells them for 48 each on a website for handmade goods the expression 48s represents the total price of buying scarves what do the parts of the expression 48s represents.

Answer:

Step-by-step explanation:

number of scarves

Price of scarves

The exact value of sinθ = 15.5/23

And, The exact value of cosθ = 17/23

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

The terminal side of angle θ intersects the unit circle in the first quadrant at x=17/23.

We know that;

The given parameters are represented as;

⇒ (x, y) = ( cos θ , sin θ )

Here, x = 17/23

Hence, We get;

⇒ cos θ = 17/23

Now, Using the following trigonometry identity;

⇒ cos²θ + sin²θ = 1

⇒ (17/23)² + sin²θ = 1

⇒ 289/529 + sin²θ = 1

⇒ sin²θ = 1 - 289/529

⇒ sin²θ = 529 - 289 / 529

⇒ sin²θ = 240/529

⇒ sin θ = √240/529

⇒ sinθ = 15.5 / 23

Thus, The exact value of sinθ = 15.5/23

And, The exact value of cosθ = 17/23

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The salary of each of specialist, manager and director are $62,000, $75,000 and $90,000.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Linear equations may include one or more variables.

Let x, y and z be the salary of specialist, manager and director respectively.

From the given information, we have three linear equations.

5x + 2y + z = 550,000

6x + 3y + 2z = 777,000

8x + 0y + 2z = 676,000

From the third equation,

2z = 676,000 - 8x

z = 338,000 - 4x

Substituting the value of z in the first equation,

5x + 2y + 338,000 - 4x = 550,000

x + 2y = 212,000

2y = 212,000 - x

y = 106,000 - (1/2) x

Substituting z = 338,000 - 4x and y = 106,000 - (1/2) x in the second equation 6x + 3y + 2z = 777,000,

6x + 3(106,000 - (1/2) x) + 2(338,000 - 4x) = 777,000

6x + 318,000 - (3/2)x + 676,000 - 8x = 777,000

(6x - 3/2 x - 8x) + (318,000 + 676,000) = 777,000

-(7/2) x = -217,000

x = 62,000

y = 106,000 - (1/2) x = 75,000

z = 338,000 - 4x = 90,000

Hence the salary of each specialist is $62,000, each manager is  $75,000 and each director is $90,000.

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