Simplify: [tex]\frac{32a^2bc^3}{20abc}[/tex]

Answer:

x = 9

Step-by-step explanation:

The equation is y = mx + b

m = The slope

b = y-intercept

The slope here is undefined, and there is no y-intercept, so the equation is

x = 9

When Jim's model car ownership is compared to Terrence's model car ownership, the ratio is 8:6, Jim possesses 48 model vehicles.

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, according to the definition given by the term in its most basic form.  When two terms are placed on each side of an equal sign, a simple equation is used to show their relationship. The four mathematical operations of addition, subtraction, multiplication, and division may be used singly or in combination in simple equations.

given

You are aware that Jim and Terrence both own four model automobiles in comparison to three owned by Jim.

Let's assume that Jim owns Jim has the following number of model cars, then you can answer the task as follows:

4/3 = x/36

x = (4* 36)/ 3

x = 48

Therefore, Jims owns 48 model cars.

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Answer:

y = 4

Step-by-step explanation:

The triangles are congruent.

8y = 6y + 8

2y = 8

y = 4

Answer:

-4.3

Step-by-step explanation:

It is asking for the temperature at midnight so to find out what it is. We simply subtract the starting temperature of 11.4f from 15.7 degrees

( 11.4 - 15.7 ). That would leave us with -4.3f at night.

The vertex for the given equation [tex]y=x^2+5x-7 is (-2.5,-4.25)[/tex] and the solution  to the equation is x = -5,7/1. Similarly , the vertex for the given equation  [tex]y=-x^2+3x+8\ is\ (-3/2,1/4)[/tex] and the solution to the equation is [tex]x = -2,4[/tex].

The graph of a quadratic function is a symmetrical, U-shaped geometric form known as a parabola. It is the collection of all points that are equally spaced apart from a fixed point (referred to as the focus) and a fixed straight line (called the directrix).

A parabola's vertex is the location where its symmetry line and parabola intersect.

The vertex of a parabola is the highest or lowest point on the graph of the parabola. In the case of a parabola in the form of [tex]y = ax^2 + bx + c[/tex], the vertex is the point (h, k), where:

[tex]h = -b / 2a\\k = f(h) = a(h^2) + bh + c[/tex]

For the first equation: [tex]y = x^2 + 5x - 7[/tex]

The vertex would be:

[tex]h = -b/2a = -5/2 = -2.5\\k = f(h) = a(h^2) + bh + c = (1)((-2.5)^2) + (5)(-2.5) - 7 = 6.25 - 12.5 - 7 = -4.25[/tex]

So the vertex is [tex](-2.5,-4.25)[/tex]

For the second equation:[tex]y = -x^2 + 3x + 8[/tex]

The vertex would be:

[tex]h = -b/2a = -3/2(1) = -3/2\\k = f(h) = a(h^2) + bh + c = (-1)((-3/2)^2) + (3)(-3/2) + 8 = -9/4 + -9/2 + 8 = 1/4[/tex]

So the vertex is [tex](-3/2,1/4)[/tex]

To find the solutions or roots of the equation, you can set the equation equal to zero and solve for x.

[tex]y = x^2 + 5x - 7 = 0\\x^2 + 5x - 7 = 0\\x^2 + 5x - 7 + 7 = 0 + 7\\x^2 + 5x = 7\\x(x+5) = 7\\x = -5,7/1\\y = -x^2 + 3x + 8 = 0\\x^2 - 3x - 8 = 0\\(x-4)(x+2) = 0\\x = -2,4[/tex]

Solutions for first equation are x = -5 and x = 7/1 and for the second equation are x = -2 and x = 4

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Answer:

Step-by-step explanation:

12/3=24/6

then, 24/6+17/6=41/6

Therefore , As a result, the intersection of these two lines will be a necessary point in order to solve the specified scatter plot problem (-0.5,2).

Several dots are placed on a vertical and horizontal axis to form a scatter plot. In statistics, scatter plots are crucial because they can demonstrate the amount of correlation, if any, between both the quantities of observed quantities or occurrences (called variables).

Here,

Maria You've erred, you know that. You don't understand the points at all. The attachment can be used to your advantage.

The property of rational numbers, according to which there are an endless number of terminating decimals between any two terminating decimals, must be used in order to plot any terminating decimal on the coordinate plane.

On the X axis, indicate -0.5 between 0 and -1.

Mark integer 2 on the Y axis in a similar manner.

Draw a line perpendicular to the Y axis, passing through (-0.5,0), and a line perpendicular to the X axis, passing through (0,2).

These two lines must cross at the specified position (-0.5,2).

As a result, the intersection of these two lines will be a necessary point in order to solve the specified scatter plot problem (-0.5,2).

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Answer:

1

Step-by-step explanation:

To start, we will substitute 8 in for w. So, we get:

[tex]5 - \frac{32}{8}[/tex]

Then, we simplify our fraction, giving us:

5 - 4

Then, 5 - 4 = 1. So our answer is 1.

Hope this helped!

Answer:

5 - (32/w) = 1

Step-by-step explanation:

Given expression,

→ 5 - (32/w)

Now we have to use,

→ w = 8

Let's solve the expression,

→ 5 - (32/w)

→ 5 - (32/8)

→ 5 - (4)

→ 5 - 4

→ 1 => final value

Therefore, the answer is 1.

The correct statements are It is a trapezoid, It has only one right angle, It has two sides that are parallel.

A quadrilateral with at least one pair of parallel sides is called a trapezoid.

Given that, Samara placed the congruent sides of these two triangles together to form a quadrilateral.

2 triangles are connected at one side. One triangle has angles 25 degrees, 125 degrees, 30 degrees. The other triangle has angles 30 degrees, 60 degrees, and 90 degrees.

If we construct such quadrilateral, we will get a trapezoid with one angle a right angle.

Hence, the correct statements are It is a trapezoid, It has only one right angle, It has two sides that are parallel.

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Answers:

1. B its a trapezoid

2. D it has two right angles

3. E it has 2 sides that are parallel

Step-by-step explanation:

Answer:

11√12

Step-by-step explanation:

√12 = 2√3

2√12

= 2 * 2√3

= 4√3

√48 = 4√3

3√48

= 3 * 4√12

= 12√12

√75 = 5√3

2√12 + 3√48 - √75

= 4√3 + 12√12 - 5√12

= 16√12 - 5√12

= 11√12

Answer: My answer is 11√3

Step-by-step explanation:

Pull terms out from under the radical, assuming positive real numbers.

Exact Form:

11√3

Decimal Form:

19.05255888…

well, our origin amount will be 80, so 80 is the 100% or all papers, now, she has graded 60, so what's leftover is 20, what's 20 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 80 & 100\\ 20& x \end{array} \implies \cfrac{80}{20}~~=~~\cfrac{100}{x} \\\\\\ 4 ~~=~~ \cfrac{ 100 }{ x }\implies x=\cfrac{100}{4}\implies x=25[/tex]

Answer:

I would say 6 sets

Step-by-step explanation:

Mystery = 5  |  Romance = 8

0                        5

1                         4

2                        3

3                        2

4                        1

5                        0

each time she picks out 5 novels. There is only 5 mystery novels so you cant go past that

....but that's just me personally

Answer:

Step-by-step explanation:

560

Viewing the given triangle, the information given helped to determine side UY to be 90

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions

Examining the figure shows that pair of equivalent sides are

WX and WY, XV and YU

The solution is worked out using sides WX and XV, WY and YU

WX / WY = XV / YU

WX / WY = 1/2 since it is a mid segment

1 / 2 = (20p - 95) / (13p - 1)

13p - 1 = 2 * (20p - 95)

13p - 1 = 40p - 190

190 - 1 = 40p - 13p

189 = 27p

p = 7

solving for UY

= 13p - 1

= 13 * 7 - 1

= 90

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Answer:

PF

Step-by-step explanation:

Since the triangles are congruent, meaning they are the same shape, we can just match the lines between the two triangles. In triangle ABC, the line AC is the hypotenuse of the triangle. So, we need to find the hypotenuse of the triangle PDF. Looking, we can see the hypotenuse of the triangle PDF is the line, or side, PF.

Hope this helped!

The probability to draw a green bead is 1/3 and the probability to draw a green or yellow bead is 2/3

It is given that the bag contains 1 red bead, 2 yellow beads, 2 green beads, and 1 blue bead.

Hence the total no. of beads in the bag = no. of red + yellow + green + blue beads

= 1 + 2 + 2 + 1 beads

= 6 beads.

Let the event to draw a green bead be A

Let the event to draw a yellow bead be B

Probability of any event = no. of outcomes favorable to that event/ total number of outcomes

Hence P(A) = no. of green beads/ total no. of beads

= 2/6

= 1/3

Hence the probability that a green bead is drawn is 1/3

P(B) = no. of yellow beads/ total no. of beads

2/6 = 1/3

We need to find P(A or B)

= P(A U B) = P(A) + P(B) - P(A ∩ B)

P(A ∩ B) = P(A and B)

Since no bead is of 2 colors, P(A ∩ B) = 0

Hence we get

P(A U B) = 1/3 + 1/3

= 2/3

Hence the probability to draw a green or yellow bead is 2/3

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Answer:

66

Step-by-step explanation:

a^5

Answer:

16 929

Step-by-step explanation:

a1 = 22      d = 11     a 54  = 605

Sum = 54 ( 22 + 605) /2 = 16 929  

The real world situation that can be modelled with the given  expression can be modelled as shown below.

Given is the expression as -

D/3

A real world situation that can be modelled with this expression can be written as follows -

Amanda has a total of {D} bananas. She divides the bananas into 3 of her childrens equally. Write an expression that would represent the amount of bananas recieved by each of her child.

Therefore, the real world situation that can be modelled with the given  expression can be modelled as shown above.

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Answer:

x + 18

Step-by-step explanation:

The variable is going to be the amount of money Jason has before his grandmother gives him money.

That variable is x.

Then, his grandmother gives him $18. The $18 would be added to the amount of money that Jason already has.

The expressions would be x + 18.

Answer:

standard form

= x⁶ + 53x⁵ + 2x⁴ -2

Step-by-step explanation:

the degree is 6.

leading coefficient is 1

this is called a polynomial.

it has 4 terms

Curved surface area of frustum is 1000.82 cm² and

Volume of frustum is 2756.754 cm³.

Frustum of cone is the part of cone when it is cut by a plane into two parts. The upper part of cone remains same in shape but the bottom part makes a frustum.

Frustum is a Latin word which means ‘piece cut off’. When a solid (generally a cone or a pyramid) is cut in such a manner that base of the solid and the plane cutting the solid are parallel to each other, part of solid which remains between the parallel cutting plane and the base is known as frustum of that solid.

Height of frustum = h = 30 cm

Diameter of top of frustum = 6 cm

Radius of top = R = 6/2 = 3cm

Diameter of bottom of frustum = 15 cm

Radius of bottom = r = 15/2 = 7.5 cm

Slant Height = l = √h²+ (r - R)²

                       ⇒ l = √30² + (7.5 - 3)²

                       ⇒ l = √900 + 20.25 = √920.25 = 30.34 cm

A) Curved surface area of frustum = π(r + R)l

                                                         = 3.1416 × (7.5+3) × 30.34

                                                         = 3.1416 × (10.5) × 30.34

Curved surface area of frustum = 1000.82 cm²

B) Volume of frustum = (πh/3)(r²+R²+r.R)

                                   = (3.1416 × 30/3)(7.5² + 3² + 7.5×3)

                                   = (31.416) × (56.25 + 9 + 22.5)

                                   = 31.416 × 87.75

Volume of frustum = 2756.754 cm³

Hence, the curved surface area and volume of given conical frustum are 1000.82 cm² and  2756.754 cm³ respectively.

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Option D. is an obtuse scalene triangle in the given lists of diagrams.

In terms of geometry, an obtuse scalene triangle is one in which one of the angles is less than 90 degrees and the other two are less than 180 degrees, with the one angle measuring greater than 90 degrees but less than 180 degrees. Measurement differences exist for each of the three sides and angles.

Both the obtuse triangle and the scalene triangle's characteristics are present in an obtuse scalene triangle. A scalene triangle has all three sides and angles that are of a different size, whereas an obtuse triangle only has one obtuse angle. The following are the characteristics of an obtuse scalene triangle:

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To calculate undefined FG, subtract the original gravity (OG) from the final gravity (FG) of the beer. This will give you the amount of sugar that has been fermented and, therefore, the amount of alcohol produced. The formula is:

Undefined FG = OG – FG

In order to calculate the undefined FG of a beer, the original gravity (OG) and the final gravity (FG) of the beer must first be determined. The OG is a measure of the sugar content of the wort before fermentation, while the FG is a measure of the sugar content of the beer after fermentation. To calculate the undefined FG, the OG is then subtracted from the FG. This calculation provides the amount of sugar that has been fermented by the yeast, and therefore the amount of alcohol produced. This calculation is important for brewers, as it provides a quick and easy way to determine the ABV of a beer. In addition, the undefined FG can be used as a measure of the fermentation efficiency of the yeast, as a higher undefined FG indicates that more sugar has been fermented than a lower undefined FG. Understanding the undefined FG of a beer can help brewers make informed decisions about their brewing process and the quality of their beers.

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The Two steps equation in mathematics can be solved within exactly two steps by performing operation on both sides of the equation .

What is a Two Step Equation ?

The Two Step Equation can be defined as the equations that can be solved exactly within two steps.

When solving the  two step equation, we have to perform the operation on both sides of equals to sign.

To solve the equation we need to perform same operation on both sides of equation.

For Example ⇒ Solve [tex]3x+3=12[/tex] ;

Step1 : we Subtract 3 from both sides to isolate the variable x.

⇒ [tex]3x + 3 - 3 = 12 - 3[/tex]

⇒ [tex]3x = 9[/tex]

Step2 : We Divide both the sides of equation by 3 and solve for x.

⇒ [tex]\frac{3x}{3} =\frac{9}{3}[/tex]

⇒ [tex]x = 3[/tex] ;

Therefore , the given equation is solved in two steps .

The given question is incomplete , the complete question is

How do you solve a 2 step equation ?

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The amount of money more that Key Club still need to earn in order to have reached their target is  $ 382. 50

To find the amount of money needed  by Kay Club to get to their target, first, find the amount of money earned from the bake sale :

= 2 / 5 x Target amount

= 2 / 5 x 1, 700

= $ 680

Then, they did a good sale and earned 3 / 8 of the amount :

= 3 / 8 x 1, 700

= $ 637. 50

The amount of money that Key Club still needs is:

= Total amount - amount raised

= 1, 700 - 680 - 637. 50

= $ 382. 50

In conclusion. Key Club would still need to engage in other activities to be able to reach their goal of $ 1, 700 as they have to raise $ 382. 50.

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FG is an abbreviation for "Femtogram," which is a unit of mass equal to one quadrillionth of a gram (10^-15 g).

An exclamation is an emphatic expression of emotion or emphasis. It is often used to express strong feelings such as surprise, joy, excitement, anger, or disbelief. Exclamations are also used to emphasize a point or give an opinion. Exclamations are most commonly used in spoken language, particularly in informal conversations. They can also be used in written language, but they should be used sparingly. Exclamations are often followed by an exclamation point, although they can also be followed by a question mark or an ellipsis. Exclamations can be used to add emphasis or emotion to a statement, making it more powerful and memorable.

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The difference between the two given temperature values is 24 °F

We have got an equation that can relate these three units of measurement of temperature, as given below:

c/5 = (F - 32)/9= (K - 273)/5

where C represents the measurement of a fixed temperature in celsius, F represents the measurement of that same intensity temperature in fahrenheit, and K represents the measurement of equally intense temperature in kelvin.

The given parameter the lowest temperature = -3 °F

the highest temperature = 21 °F

To determine the difference between the two given temperature values.

The range or difference between the two given temperature values is calculated as follows;

Range = highest - lowest

Range = 21 °F -(-3 °F)

Range = 24 °F

Thus, the difference between the two given temperature values will be 24 °F

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Therefore, By using the formula actual distance = (Map distance) x (Scale ratio) the actual distance of 20 cm on the map of 1:32000 is 0.000625 km or 625 meters.

A ratio scale is a numerical scale with a genuine zero and uniform distances between adjacent points. The Kelvin scale is an illustration of a ratio scale. The actual zero point exists on a Kelvin scale.

Two locations that are close to one another are said to be adjacent points.

A scale of 1:32000 means that one unit of measurement on the map represents 32000 units of the same measurement in the real world.

To calculate the actual distance of 20 cm on the map,

We know,

Actual distance = (Map distance) x (Scale ratio)

Actual distance = (20 cm) x (1/32000)

Actual distance= 20/32000

Actual distance = 0.000625 km or 625 meters.

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