How can you use the distributive property to factor the expression 3/4x+9/4

Answer:

(x + 10)(x - 4)

Step-by-step explanation:

x² + 6x - 40

consider the factors of the constant term (- 40) which sum to give the coefficient of the x- term.

the factors are + 10 and - 4 , since

10 × - 4 = - 40 and 10 - 4 = + 6 , then

x² + 6x - 40 = (x + 10)(x - 4) ← in factored form

2.40.π is the  expression can be used to find the circumference of the skating rink.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given that a circular skating rink has a radius of 40 feet.

Radius = 40 ft.

We need to find the  expression can be used to find the circumference of the skating rink.

The formula for circumference of circle is 2πr.

Circumference=2.40.π.

Hence, 2.40.π is the  expression which can be used to find the circumference of the skating rink.

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Answer: 2 x 40 x pie

Step-by-step explanation:

3) Ascending order of numbers are, 3/100 , 1/10, 0.8, 0.91.

4) Ascending order of numbers are, 11/100, 0.21, 0.35, 0.6, 7/10, 0.9

5) Ascending order of numbers are, 8/100, 1/10, 0.2, 36/100, 0.44, 0.5

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

3) Numbers are,

⇒  0.8, 1/10, 3/100, 0.91

It can be written as;

⇒ 0.8, 0.1, 0.03, 0.91

Hence, Ascending order of numbers are,

⇒ 0.03, 0.1, 0.8, 0.91

⇒ 3/100 , 1/10, 0.8, 0.91

4) Numbers are,

⇒ 0.9, 0.35, 11/100, 7/10, 0.6, 0.21

It can be written as;

⇒ 0.9, 0.35, 0.11, 0.7, 0.6, 0.21

Hence, Ascending order of numbers are,

⇒ 0.11, 0.21, 0.35, 0.6, 0.7, 0.9

⇒ 11/100, 0.21, 0.35, 0.6, 7/10, 0.9

5) Numbers are;

⇒ 36/100, 0.2, 1/10, 8/100, 0.5, 0.44

It can be written as;

⇒ 0.36, 0.2, 0.1, 0.08, 0.5, 0.44

Hence, Ascending order of numbers are,

⇒ 0.08, 0.1, 0.2, 0.36, 0.44, 0.5

⇒ 8/100, 1/10, 0.2, 36/100, 0.44, 0.5

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The linear equation that represents this situation will be y = 4x + 3.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

To ride go-carts at Rick's Play Zone costs $4 per ride plus $3 to rent a helmet.

Let 'y' be the total cost in dollars and 'x' be the number of times you ride the go-carts. Then the equation is given as,

y = 4x + 3

The equation that represents this situation will be y = 4x + 3.

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Respuesta: $500

Explicación paso a paso:

S/2000 es el que no tiene por ciento entonces pones x sobre 2000 y haces 20/100 para el primero y 25/100 para el segundo

X

2000           20

                   100

100x=40,000/100x=$400 al final del año

tomas $400 y le agregas otro 25%

X

400          25

                100

100x=10,000/100x=$100 se agrega a su salario

En total obtendrá $500

The quantity of 68% hydrochloric acid solution must be mixed are;

94 ml of 68% Acid type I

1,535.33 ml 16.00% acid type II

The quantities and percentages given are;

Acid type I 68% ---------------- x liters

Acid type II 16% ------ 1629.33 - x liters

Mixture 19% ---------------- 1629.33

Thus, by combination of the values given we have;

68% x + 16%(1629.33 - x ) = 19% * 1629.33

Multiply through by 100 to get;

68x + 16(1629.33 - x ) = 30957.27

68x + 26069.28 - 16x = 30957.27

68x - 16 x = 30957.27 - 26069.28

52x = 4,887.99

x = 4,887.99/52

x = 94 ml of 68% Acid type I

Acid type II 16% ------ 1629.33 - 94

= 1,535.33 ml 16.00% acid type II

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So, approximately 2.28% of the observations are less than 140.

To find the percentage of observations that are less than 140, we need to find the standard score (z-score) that corresponds to 140, and then use a standard normal table to find the proportion of data that is less than that z-score.

The standard score is calculated as follows:

z = (140 - 130) / 5 = 2

Using a standard normal table, we can find the proportion of data that is less than 2 standard deviations from the mean. This proportion is approximately 0.0228 or 2.28%.

Mean is nothing but the average of data.

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Answer:

To find the distance around a hat, you need to find the circumference of a circle with a diameter of 4.7 inches.

The formula for the circumference of a circle is C = π * d, where d is the diameter.

Plugging in the values and using π = 3.14, we have:

C = 3.14 * 4.7 = 14.758

Rounding to the hundredths place, the circumference of the hat is 14.76 inches.

So, the answer is 14.76 inches.

Answer:it is correct the awnser is d 14.76

Step-by-step explanation:did the test

Answer:

[tex]\textsf{A)} \quad \cos 2 \theta=\dfrac{9}{25}[/tex]

[tex]\textsf{B)} \quad \sin\left(\dfrac{\theta}{2}\right) = \sqrt{\dfrac{5+\sqrt{17}}{10}}[/tex]

Step-by-step explanation:

Given:

[tex]\sin \theta=\dfrac{2\sqrt{2}}{5},\quad \dfrac{\pi}{2} < \theta < \pi[/tex]

[tex]\hrulefill[/tex]

To determine the exact value of cos 2θ, we can use the Cosine Double-Angle formula:

[tex]\large\boxed{\cos^2\theta = 1 - 2 \sin^2 \theta}[/tex]

Substitute the given value of sin θ into the formula:

[tex]\begin{aligned}\cos 2 \theta&=1-2\left(\dfrac{2\sqrt{2}}{5}\right)^2\\\\\cos 2 \theta&=1-2\left(\dfrac{8}{25}\right)\\\\\cos 2 \theta&=\dfrac{25}{25}-\dfrac{16}{25}\\\\\cos 2 \theta&=\dfrac{9}{25}\end{aligned}[/tex]

[tex]\hrulefill[/tex]

To determine the exact value of sin (θ/2), we can use the half-angle formula for sine:

[tex]\large\boxed{\sin\left(\dfrac{\theta}{2}\right) = \pm \sqrt{\dfrac{1-\cos \theta}{2}}}[/tex]

First, find the value of cos θ by substituting the given value of sin θ into the trigonometric identity sin²θ + cos²θ = 1:

[tex]\begin{aligned}\left(\dfrac{2\sqrt{2}}{5}\right)^2+\cos^2\theta&=1\\\\\dfrac{8}{25}+\cos^2\theta&=1\\\\\cos^2\theta&=1-\dfrac{8}{25}\\\\\cos^2\theta&=\dfrac{17}{25}\\\\\cos\theta&=\pm \sqrt{\dfrac{17}{25}}\\\\\cos\theta&=\pm \dfrac{\sqrt{17}}{5}\end{aligned}[/tex]

As cos θ is negative on the interval π/2 < θ < π, we take the negative square root. Therefore:

[tex]\cos\theta&=-\dfrac{\sqrt{17}}{5}[/tex]

Now, substitute the found value of cos θ into the half-angle formula:

[tex]\sin\left(\dfrac{\theta}{2}\right) = \pm \sqrt{\dfrac{1-\left(-\dfrac{\sqrt{17}}{5}\right)}{2}}[/tex]

Therefore:

[tex]\sin\left(\dfrac{\theta}{2}\right) = \pm \sqrt{\dfrac{\dfrac{5}{5}+\dfrac{\sqrt{17}}{5}}{2}}[/tex]

[tex]\sin\left(\dfrac{\theta}{2}\right) = \pm \sqrt{\dfrac{\dfrac{5+\sqrt{17}}{5}}{2}}[/tex]

​​

​[tex]\sin\left(\dfrac{\theta}{2}\right) = \pm \sqrt{\dfrac{5+\sqrt{17}}{10}}[/tex]

As sin θ is positive on the interval π/2 < θ < π, we take the positive square root. Therefore:

[tex]\sin\left(\dfrac{\theta}{2}\right) = \sqrt{\dfrac{5+\sqrt{17}}{10}}[/tex]

Yes, his pulse rate is in the normal range for children. His pulse rate was calculated to be 120 beats per minute, which falls within the range of 60-100 beats per minute.

The student took his resting pulse rate by counting the number of beats in 20 seconds. He then multiplied his result by three to calculate his pulse rate for a minute. To determine if his pulse rate was within the normal range for children, he compared his result to the data shown in the table. His pulse rate of 120 beats per minute was within the range of 60-100 beats per minute, so it was considered to be normal for children. To ensure accuracy, the student could have taken his pulse rate for a longer period of time, such as 30 or 60 seconds, before calculating his pulse rate for a minute. This would have given him a more accurate result.

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The volume of the preservative inside the box is 487.83 cm³.

The total volume of the box is calculated by using the following formula as shown below.

V = L x B x W

where;

V = 16 cm  x  8 cm  x  8 cm

V = 1,024 cm³

The total volume of the metal spheres inside the box is calculated as follows;

V = 16 x ( ⁴/₃πr³ )

where;

V = 16 x ( ⁴/₃π(2 cm)³ )

V = 536.17 cm³

The volume of the preservative inside the box = 1,024 cm³ -  536.17 cm³

= 487.83 cm³

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The decimal number that corresponds to the binary number 11111111 is 255.

The decimal numeral system is the most widely used system for representing both integer and non-integer values. It is the Hindu-Arabic numeral system's expansion to non-integer numbers. Decimal notation is the method of representing numbers in the decimal system. A decimal number is made up of two parts: a whole number and a fractional component separated by a decimal point. The decimal point is the dot between the whole number and the fractions. 25.5, for example, is a decimal number.

Here,

In binary, each digit represents a power of 2, starting with the rightmost digit. The rightmost digit in 11111111 represents 2^0, the second digit from the right represents 2^1, and so on. To convert a binary number to decimal, you add up the value of each digit times the corresponding power of 2.

For 11111111, the calculation would be:

=1 * 2^7 + 1 * 2^6 + 1 * 2^5 + 1 * 2^4 + 1 * 2^3 + 1 * 2^2 + 1 * 2^1 + 1 * 2^0 = 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1

=255

The decimal equivalent of the binary number 11111111 is 255.

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The inequality that represents the graph is y ≤ -x - 2.

In mathematics, inequality is a declaration of an order connection between two numbers or algebraic expressions (greater than, greater than or equal to, less than, or less than or equal to).

In the graph, we have

1. the line is going down (negative slope) so that's why u have the negative

2. it translated 2 units Downwards on the y-axis so that's why there is - 2

3. the line is Solid so it's going to have the equal sign under it, if the line was dashed it would just be a regular sign fr example (<)

4. the shading is below the line so that means it's going to be Less than or Equal to.

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The linear function that models the giraffe's height after x months is given as follows:

y = 6 + 0.5x.

The graph is given by the image presented at the end of the answer.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The parameters for this problem are given as follows:

Hence the function is defined as follows:

y = 0.5x + 6.

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The table that represents a linear relationship that is also proportional is; Table B

In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and as such it can be modeled or represented by the following mathematical expression:

y = kx

Where:

x and y represents the variables.

k represents the constant of proportionality.

For us to have a proportional relationship and equivalent ratios, the variables x and y must have the same constant of proportionality.

Next, we would determine the constant of proportionality (k) using table B as follows:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = -2/-1 = 2 or 2/1 = 2

Constant of proportionality (k) = 2

Thus, table B is correct.

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Answer:

the second one....

x −1 0 1

y −2 −1 0

Step-by-step explanation:

tricia wants to install a decorative wall paper border around the top of the wall in her master bedroom. the room measures 14ft by 17ft. then perimeter 62 feet of the border will will she need

For the installation of a decorative wall paper Tricia will need 70 ft of the border to decorate the wall of her master bedroom.

The measures of the room is 17 ft by 14 ft.

So, the length of the room (l) = 17 ft

The width of the room(w) = 14 t

As we know that, perimeter of rectangle is 2(l×w).

We will get perimeter of he room = 2l × 2w

                                                   = 2(17) × 2(14)

                                                   = 62 ft.

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The approximate distribution (give distribution name and parameters) of the total length will be =  450 minutes

The estimated distribution of the total length of Tina's simulation study is a triangular distribution with a base worth of 2 minutes, a greatest worth of 4 minutes, and a mode (most reasonable worth) of (2+4)/2 = 3 minutes.

Since the simulation time is generally consistently distributed somewhere in the range of 2 and 4 minutes, the total simulation time will be the sum of 150 free random variables each with a triangular distribution.

Hence, the total simulation time will also have a triangular distribution with a base worth of 2 minutes x 150 = 300 minutes, a greatest worth of 4 minutes x 150 = 600 minutes, and a method of (300+600)/2 = 450 minutes.

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The complete question is:

Tina is running a simulation study on her laptop. The duration of each simulation is roughly uniformly distributed between 2 and 4 minutes. She needs to run 150 simulations and she runs all her simulations back-to-back. - What is the approximate distribution (give distribution name and parameters) of the total length of Tina's simulation study? Explain your answer

The actual distance between the two cities is 288 miles.

A scale drawing is a smaller version of a larger image / city. The scale drawing is reduced by a constant ratio.  This means that the scale drawing of the two cities would be smaller than the actual cities.

The scale is used to keep the proportion of the dimensions between the scale drawing and the original diagram similar. This means that the scale drawing of the two cities would be smaller than the actual cities.

The actual distance between the two cities = (3 x 24) ÷ 1/4

= 3 x 24 x 4 = 288 miles

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As ΔABC ≅ ΔDEF, Using congruence properties the value of x= 5 and the value of y= 14.

Congruent triangles are two triangles that are the same size and shape. Two congruent triangles remain congruent even if we flip, turn, or rotate one of them. Two triangles must have the same angles and, as a result, must be congruent if their sides are the same.

Given that ΔABC ≅ ΔDEF, so that

AB ≅ DE

BC ≅ EF

AC ≅ DF

and AB = 8

BC = 19

AC = 14

EF = 4x-1

DE = y-6,

As AB ≅ DE

8 = y - 6

add 6 both sides we get

y = 8 + 6

y = 14

and BC ≅ EF

19 = 4x - 1

Add 1 both sides we get

4x = 19 + 1

4x = 20

divide both sides by 4 we get

x = 20/4

x = 5

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Answer: I think cash and checks??

Step-by-step explanation:

Sorry if I'm wrong

Luke was solving the equation √(3-x) = -16. He was about to square

each side, but then he realized he could give an answer without doing any algebra, here is explanation,

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Luke realized that squaring each side of the equation √(3-x) = -16 would lead to an extraneous solution. This happens because squaring each side of the equation changes the direction of the inequality, which may result in solutions that do not actually satisfy the original equation.

The square root of any positive number is always positive, so the left side of the equation is always non-negative. However, -16 is a negative number, so there is no real solution to the equation √(3-x) = -16.

Therefore, Luke realized that he could give an answer without doing any algebra and that the equation has no real solution.

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1 furlong, a unit used in horse racing, is equal to 40 rods and 10 chains, both units used in surveying and equal to 201.168 meters (660 feet).

A furlong is a unit of length used primarily in horse racing. It is equal to 201.168 meters (660 feet). A rod is a unit of length used in surveying and is equal to 5.5 yards (16.5 feet). A chain is also a unit of length used in surveying and is equal to 66 feet.

To calculate 1 furlong in rods, we multiply 1 furlong by the conversion factor of 40 rods per furlong:

1 furlong x 40 rods/furlong

= 40 rods

To calculate 1 furlong in chains, we multiply 1 furlong by the conversion factor of 10 chains per furlong:

1 furlong x 10 chains/furlong

= 10 chains

To convert from furlongs to rods, we multiply the number of furlongs by the conversion factor of 40 rods per furlong:

4.0 furlongs x 40 rods/furlong = 160 rods

And to convert from furlongs to chains, we multiply the number of furlongs by the conversion factor of 10 chains per furlong:

4.0 furlongs x 10 chains/furlong = 40 chains

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Here are the simplified expressions for each equation:

(x⁵) * (x⁸) * (2x³)² * (x⁻³) * (x⁵) = (x⁵) * (x⁸) * (2x⁶) * (x⁻³) * (x⁵) =

2x⁽⁵⁺⁸⁺⁶⁻³⁺⁵⁾ = 2x²¹

(y⁶) * (y⁹) = y⁽⁶⁺⁹⁾ = y¹⁵

(3x)³ = 27x³

(y⁷) * (y⁻³) = y⁽⁷⁻³⁾= y⁴

(z⁻⁸) * (z³) = z⁽⁻⁸⁺³⁾ = z⁻⁵

(x⁻²) * (x^⁻⁶) * (x⁴) = x⁽⁻²⁻⁶⁺⁴⁾ = x⁻⁴

(x¹⁵) * (x¹⁰) = x⁽¹⁵⁺¹⁰⁾ = x²⁵

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. Term is defined as a constant, a single variable, or a combination of a variable and a constant multiplied or divided. An expression in mathematics is a collection of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)

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the simplified expressions for each equation is:

a) 2x²¹            b)  y¹⁵

c) 27x³           d)  y⁴

e) z⁻⁵              f)   x⁻⁴

g)  x²⁵

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation.

Addition, subtraction, multiplication, or division are all examples of math operations. Term is defined as a constant, a single variable, or a combination of a variable and a constant multiplied or divided.

An expression in mathematics is a collection of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)

Here are the simplified expressions for each equation:

(x⁵) * (x⁸) * (2x³)² * (x⁻³) * (x⁵) = (x⁵) * (x⁸) * (2x⁶) * (x⁻³) * (x⁵) =

2x⁽⁵⁺⁸⁺⁶⁻³⁺⁵⁾ = 2x²¹

(y⁶) * (y⁹) = y⁽⁶⁺⁹⁾ = y¹⁵

(3x)³ = 27x³

(y⁷) * (y⁻³) = y⁽⁷⁻³⁾= y⁴

(z⁻⁸) * (z³) = z⁽⁻⁸⁺³⁾ = z⁻⁵

(x⁻²) * (x^⁻⁶) * (x⁴) = x⁽⁻²⁻⁶⁺⁴⁾ = x⁻⁴

(x¹⁵) * (x¹⁰) = x⁽¹⁵⁺¹⁰⁾ = x²⁵

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Answer:

Last option: Stocks which drop from 5.25 by 1.35

Step-by-step explanation:

5.25 + (- 1.35) = 5.25 - 1.35

This represents a decrease in value of stock which starts at 5.25 and drops by 1.35.

The stock value at end of day = 5.25 - 1.35 = $3,9

Answer:

2:3:7

Step-by-step explanation:

a/b = 2/3 and b/c = 3/7

a/b/c =2/3/7

Answer:

a and c

Step-by-step explanation:

The lines on the graph cross over those two points. Hope this helps.

12 ounces of cherries did Ms Winn buy.

The same attribute is expressed using a unit conversion, but in a different unit of measurement.

For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.

Given:

Ms. Winn bought = 3/5 lb of grapes

Ms Winn bought = 5/8 lb of cherries.

As, there are 16 ounces in a pound then

= 3 pounds/4 x 16 ounces/pound

= 3 x 4

= 12 ounces

Hence, She buy 12 ounce of cherries.

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Resolviendo un sistema de ecuaciones, veremos que que la piedra estuvo 7 segundos en el aire y 5 en el agua.

Sabemos que:

En el aire tuvo una velocidad promedio de 16 m/s. En el agua tuvo una velocidad promedio de 3 m/s antes de tocar el fondo del mar.

Definamos las variables:

x = tiempo que la piedra estuvo en el aire.

y = tiempo que la piedra estuvo en el agua.

Sabemos que el trayecto completo duro 12 segundos, entonces podemos escribir:

x + y = 12

Y la caida total fueron 127 metros, entonces:

x*16 + y*3 = 127

Entonces tenemos un pequeño sistema de ecuaciones:

x + y = 12

x*16 + y*3 = 127

En la primera podemos aislar x:

x = 12 - y

Reemplazar eso en la otra ecuacion:

(12 - y)*16 + y*3 = 127

192 - 13y = 127

192 - 127 = 13y

65 = 13y

65/13 = y

5 = y

Entonces la piedra esta 5 segundos en el agua y los otros 7 segundos en el aire.

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Answer:

96

Step-by-step explanation:

large rectangle area = 7* (4+3+5) =7*12 =84

top & bottom 2 little triangles:

look at the bottom one:

triangle area formula = 1/2 base * height

so it's a right angle triangle, so the height is 4, base is 3

so area = 1/2 * 3* 4 =6

you have another one on the top

so 12

total = 84+12 =96