Very much appreciated!!!

Answer: 16 girls and 22 boys

Step-by-step explanation:

This can be solved with simple algebra.

Let's say that the number of girls is x.

Since there are 10 less than twice as many boys as girls, the number of boys would be 2x-10. (2x for twice as many, and -10 for ten less.)

The total number of students is 38. Adding the girls, the equation is now 3x-10=38.

3x=48

x=16.

2x-10=the number of boys, as said earlier. SO, 32-10=22=the number of boys.

To check our work, add 16+22. This equals 38.

The formula for x in terms of w is x = 3w² and the formula for y in terms of x is y = (1/112)x³

x = k × w²

w = 4, x = 48

48 = k × 4²

48 = k × 16

48 = 16k

k = 48/16

k = 3

So,

x = k × w²

x = 3 × w²

x = 3w²

y = k/x³

x = 2, y = 14

14 = k / 2³

14 × 2³ = k

14 × 8 = k

112 = k

So,

y = k/x³

y = 112/x³

y = (1/112)x³

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answer:

+16

steps:

number without the x should be 9

number without the x should be 9c to be 9 needs +16

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divide the number next to the x by 2

-6 divided by 2 is -3

find the square

-3 squared is 9

number without the x should be 9

x²-6x=7

make the equation = 0

x²-6x-7=0

a is the number next x²

b is the number next to x

c is the number without the x

c has to be 9

c is -7

c to be 9 needs +16

x²-6x+9 =0

x²-6x+(-3)² =0

(x-3)²

Answer:

9

Step-by-step explanation:

Completing the square  is a method used to solve the quadratic equation.

        Coefficient of x is '6'. 6 ÷ 2 = 3

       3² = 9

            x² - 6x + 9 = 7 + 9

Answer: To make into a perfect square, 9 must be added.

Answer:

100

Step-by-step explanation:

Lets first find the area of the greater square:

[tex]8*14=112[/tex]

And now the area of the cut inside of the square:

[tex]3*4=12[/tex]

Now subtract the area cut from the area of the greater square:

[tex]112-12=100[/tex]

Answer:

No

Step-by-step explanation:

Lets simplify both expressions:

We will start with Gloria's first expression:

[tex]1/4 (12x + 24) -9x[/tex]

Apply distributive property:

[tex](3x + 6) -9x[/tex]

Combine like terms, we are then left with:

[tex]6-6x[/tex]

Now lets simplify the second expression

[tex]-6(x+1)[/tex]

Apply distributive property

[tex]-6x-6[/tex]

Rearrange:

[tex]-6-6x[/tex]

Now we can see that the two equations are not equal, as the first is 12 greater than the second. Another way we could have tested this was plugging in a value for x and then solving.

The dimension of the box should be 1.7×1.7×3.58 in inches, applying minimization of surface area.

Dimensions to Minimize the Surface Area of the Box

It is given that the box is square based with an open top.

⇒ The box has one square and 4 rectangles

Thus, the total surface area of the box is given as,

S= a²+ab+ab+ab+ab  

S= a²+4ab ______________ (1)

Here, a is the side of the squared base and length of the rectangular sides of the box, b is the breath of the rectangular sides of the box.

This equation is later used for minimization of the surface area.

Also, the volume, V = a²b

It is also given that volume of the box is 184 in³.

⇒ 184 = a²b _____________ (2)

Forming a One-Variable Equation

From equation (2), b=184/a²

Now, substitute this value of b in equation (1) to get,

S = a² + 4a(184/a²)

S = a² + 4(184/a)

S = a² + 736/a

Minimization of Surface Area to find the Dimension

We require a dimension that will minimize the surface area of the box. Hence, applying minimization surface area, dS/da = 0

dS/da = 2a -736/a²

0 = 2a -736/a²

⇒ 0 = 2a³- 736

2a³ = 736

a³ = 736/2

a³ = 368

a = ∛368

a= 7.17 in

∵V = a²b

184 = (7.17)²b

b = 184/7.17²

b = 184/51.4089

b = 3.58 in

Therefore, 1.7×1.7×3.58 in inches is the required dimension for the box, using minimization of surface area..

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Answer:

-3

Step-by-step explanation:

So just like the picture provides, the slope can be defined as: [tex]\frac{\text{change in y}}{\text{change in x}}[/tex]. So this means we can take any two points and find the change in x and y to define the slope, since the slope is constant throughout the entire line, since it's a linear line, meaning it's straight.

So you can use the points (0, 15) and (2, 9). So let's look at the x-values, and you want to make sure, you maintain the order at which you look at the  "change in x", for example I can define the change in x through the two points as 0 to 2, or 2 to 0, one case is 2, and the other is -2, but if I look at the change from 0 to 2, then I looked at the first point first then the second, this means when looking at the y-values I have to find the change from 15 to 9, and not 9 to 15, since I did 0 to 2 in the first case. I could look at the change from 9 to 15, but only if I looked at the changed from 2 to 0.

Anyways let's find the change from 0 to 2, it's 2. Now let's look at the change from 15 to 9, it's -6 (since the value went down). So this gives us equation: -6 / 2 = -3

The slope is -3

Considering the volume of a rectangular prism, since the new volume is greater than the filled volume, the new dimensions would work, and 90.29% of the infuser would be filled.

The volume of a rectangular prism of length l, width w and height h is given by:

V = lwh.

The original dimensions are:

h = 7.9 cm, l = 3 cm, w = 1.5.

Hence the volume in cm³ was:

V = 7.9 x 3 x 1.5 = 35.55 cm³.

The infuser was filled to 80% capacity, hence:

Vf = 0.8 x 35.55 = 28.44 cm³.

For the new dimensions, we have that h = 7 cm, hence the volume is:

Vn = 7 x 3 x 1.5 = 31.5 cm³.

28.44/31.5 x 100% = 90.29%.

Since the new volume is greater than the filled volume, the new dimensions would work, and 90.29% of the infuser would be filled.

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Answer:

yes

no

yes

Step-by-step explanation:

sin C = opp/hyp = 9/15 yes

tan B = opp/adj = 12/9 no

tan B = 12/9; B = tan^-1 12/9 = 53.13°

The area of the triangle LMN is 4 units squared.

The area of a triangle can be described as follows:

The area of the triangle by using the base and height of the triangle.

area of a triangle = 1 / 2 bh

where

Therefore,

base = NL = 4 units

height = PM = 2 units

Therefore,

area of the triangle = 1 / 2 × 4 × 2

area of the triangle = 8 / 2

area of the triangle = 4 units²

Therefore, the area of the triangle LMN is 4 unit squared.

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Answer: B. 4 Square Units

Step-by-step explanation:

16 tiles will fit end to end on a 4 foot wall.

In unitary method we will learn how to find the value of a unit from the value of a multiple and the value of a multiple from the value of a unit.

When we go to the market to buy any article, we ask the shopkeeper to tell the price of the article. This is called unit price. We calculate the price of number of articles, we want to buy, with the help of this unit price. Sometimes, we calculate unit price when the price of a multiple is given.

1 tile in 1/4 foot

So in 4 foot wall the number of tiles = 4/(1/4) = 16 tiles.

Thus 16 tiles will fit end to end on a 4 foot wall.

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The expression (quotient) which is modelled by the given diagram as in the task content is; (x²+x-2)/(x-1) = x +2.

It follows from the task content that the diagram model in discuss by observation involves a quotient in which case, the division is; (x-1).

Additionally, the dividend in the quotient by observation is the sum of terms as follows;

x² + x +x -x -1 -1 = x²+x -2.

Ultimately, the result of the division according to the model is; (x +2).

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Answer:

  A.  The volumes are the same, based on Cavalieri's principle.

Step-by-step explanation:

Cavalieri's principle tells us the volumes of solids will be identical if their cross sectional areas are identical at every height.

A right cylinder and an oblique cylinder of the same height and radius will both have circular cross sections of the given radius at any height. Since the radius is the same, the area of the circle is the same. Hence the requirements of Cavalieri's principle are met, and the cylinders have the same volume.

Answer:

7.62

Step-by-step explanation:

length* width* height = 3/2*1/2*4=7.62 cm

The correct option is A. (4, 11) and (0, 7).

The solution of the equations y = x + 7 and y = x² – 3x + 7, the solutions are located at points: (4, 11) and (0, 7).

Estimate the y-intercept, slope, and express the equation in the form of the y-intercept (y = mx + b) to find the graphed equation. The slope is the difference between the y- and x-axis values.

A graph equation is an equation in graph theory where the unknown is a graph. Isomorphic ideas are one of the key issues in graph theory.

The equations are; y = x + 7 and y = x² - 3x + 7

At the solution, the u-values are equal, which gives;

y = y

x + 7 = x² - 3·x + 7

x² - 3·x + 7 - (x + 7) = 0

x² - 4·x = 0

x·(x - 4) = 0

x = 4, or x = 0

When x = 4, y = 4 + 7 = 11

When x = 0,

         y = 0 + 7 = 7

Therefore, the solution for the equations  y = x + 7 and y = x² - 3x + 7 are are located at points: (4, 11) and (0, 7).

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The complete question is-

Based on the graphs of the equations y = x + 7 and y = x² – 3x + 7, the solutions are located at points:

A. (4, 11) and (0, 7)

B. (4, 11) and (–7, 0)

C. (–7, 0) and (1.5, 4.75)

D. (1.5, 4.75) and (0, 7)

The point (12, 190) means that the temperature after 12 hours is 190 degrees Celsius

To do this, we make use of the following points

(12, 190), (14, 201), (15, 301), (16, 305), (18, 350), (20, 40), (25, 450)

Where x represents the number of hours and y represents temperature

See attachment for the scatter plot.

To do this, we make use of the point (12, 190)

This means that the temperature after 12 hours is 190 degrees Celsius

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The amount invested in the account that has a rate of 14% is $1767

The amount invested in the account that has a rate of 6% is $1425.

0.06a + 0.14b = 342 equation 1

b - a = $950 equation 2

Where:

a = amount invested in the account that has a rate of 6%

b =  = amount invested in the account that has a rate of 14%

Multiply equation 2 by 0.06

0.06b - 0.06a = 57 equation 3

Subtract equation 3 from equation 2

285 = 0.2a

a = 285 / 0.2

a = 1425

Substitute for a in equation 2

b - 1425 = 342

b = 1425 + 342

b = $1767

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Answer:

8.8

Step-by-step explanation:

If DEF///ABC

AB=4.4

Answer:

  A  (see attached)

Step-by-step explanation:

There are a couple of things you can look for to see if a table represents a quadratic function:

In the first of the given tables, the f(x) values start out decreasing, and end up increasing. This is a good indication the table represents a quadratic function.

In the remaining tables, the f(x) values are always increasing.

The f(x) values in table 1 have differences of ...

  -3, -1, 1, 3

These values have differences of ...

  2, 2, 2

The constant "second differences" mean that the function can be represented by a 2nd-degree polynomial, a quadratic. In fact, the equation for this table is ...

  f(x) = x² +2

In the above question, (image attached) The option that shows the segments that are parallel, if any, if ∠EDA≅∠HCB is option A: None of these.

Note that by examining the the image if ∠EDA≅∠HCB, the two lines can never intersect even if they go a longer distance.

The reason why is that there are no parallel lines on it and as such, they cannot intercept.

Hence, In the above question, (image attached) The option that shows the segments that are parallel, if any, if ∠EDA≅∠HCB is option A: None of these.

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The commutative property of multiplication addition is illustrated below.

The commutative property implies that the changing of orders of the numbers doesn't have a effect on the value.

In this case, 5 × 4 = 20. Also, changing them to 4 × 5 is still 20.

Likewise 2 + 5 as 5 + 2 gives 7.

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The values that complete the conversions are

a = 10000

b = 100

c = 1000000

From the question, we are to complete the given conversions

i)

1 m² = a cm²

NOTE: 1 m² =  10000 cm²

∴ a = 10000

ii)

1 cm² = b mm²

NOTE: 1 cm² = 100 mm²

∴ b = 100

iii)

1 km² = c m²

NOTE: 1 km² = 1000000 m²

∴ c = 1000000

Hence, the values that complete the conversions are

a = 10000

b = 100

c = 1000000

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The sine, cosine, cosecant, and secant functions have period 2π; the tangent and cotangent functions have period π.

Definition for Period of a Trigonometric Function :

The pause between any function's repetitions is known as the function's period. The duration of one complete cycle is the period of a trigonometric function. Trigonometric functions include three basic types: sin, cos, and tan, which have periods of -2π, 2π, and π respectively.

If a function repeats itself repeatedly at a predetermined frequency, it is said to be periodic. The formula for t is f(x) = f(x + p), where p is a real number that denotes the period of the function. Period is the interval between two occurrences of the wave.

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The area of the logo is 136. 14 cm²

First, let's find the area of the semicircle

Area of semicircle = 1/2(πr²)

radius = 8/2 = 4cm

Substitute into the formula

Area of semicircle = [tex]\frac{1}{2} * 3. 142 * 4 * 4[/tex] = 25. 135 cm²

Now, let's find area of trapezium

Area of trapezium = [tex]\frac{a + b}{2} * h[/tex]

Area =  [tex]\frac{12 + 10. 2}{2} * 10[/tex]

Area = [tex]11. 1 * 10[/tex]

Area = 111 cm²

Area of logo = Area of trapezium + area of semicircle

Area of logo = 111 +  25. 135

Area of logo = 136. 14 cm²

Thus, the area of the logo is 136. 14 cm²

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A)f(x)=3/5 and -1.

B)f(x)=(3/5, 0) and (-1, 0).

C)f(x)=(-0.2, -3.2)

D)f(x)= = -0.2.

Function: f(x) = 5x² + 2x-3.

a) Completely factor f(x)

  f(x) = 5x² + 2x-3.

        = 5x² + 5x-3x − 3

         = 5x(x+1)-3(x+1)

         =(5x-3)(x+1)

f(x)=3/5 and -1.

b)The x-intercepts of the graph of f(x):

    f(x) = 5x² + 2x-3.

At f(x) = 0, the x-intercepts are present.

Therefore, x-intercepts are (3/5, 0) and (-1, 0).

c) The end behavior of the graph of f(x):

      f(x) = 5x² + 2x-3.

The middle of the zeros is the vertex's x-coordinate.

           =-0.2

Find the y-coordinate of the vertex, and substitute the found value of x into the given equation:

   f(-0.2)= 5(-0.2)² + 2(-0.2) − 3

           =-3.2

d)The steps you would use to graph f(x):

The axis of symmetry is the x value of the vertex.

Therefore, the graph is symmetrical at about x = -0.2.

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If the speed of boat in still water iss 9 mph and takes 1.5 miles to go and come 4 miles uptream and downward then the current of the river is 9.24 mph.

Given that the speed in still water be 9 mph, time to travel 4 miles upstream and downward is 1.5 hours.

We are required to find the speed of current of the river.

let the speed of current be c mph.

Effective speed in downstream=9+c

Effective speed in upstream=9-c

Total time=1.5 hours.

Total distance=4 miles.

Time for upstream stream+ time for downward stream=1.5 hours

2/(9+c)+2/(9-c)=1.5

18-2c+18+2c=1.5(9+c)(9-c)

36=1.5(81-[tex]c^{2}[/tex])

36=121.5-1.5[tex]c^{2}[/tex]

1.5[tex]c^{2}[/tex]=121.5-36

[tex]c^{2}[/tex]=85.5

c=9.24 mph.

Hence the speed of the current of the river is 9.24 mph.

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The mass of brick is 2478 gram.

A rectangular prism has a total of 6 faces, 12 sides, and eight vertices. Like a cuboid, it has three dimensions- the base width, the height, and the length. The top and base of the rectangular prism are rectangular in shape. The pairs of opposite faces of a rectangular prism are identical or congruent.

A brick is in the shape of a rectangular prism with a length of 8 inches, a width of 3.5 inches, and a height of 2 inches.

The volume of rectangular prism = length×width×height

                                                        = 8×3.5×2

                                                        = 56

Thus volume of brick is 56 cubic inches.

Convert inches to centimeter

1 inch = 2.54 centimeter

Therefore,

56 cubic inches = 56 x 2.54 x 2.54 x 2.54 cubic centimeter

56 cubic inches = 917.676 cubic centimeter

Thus, we get,

volume of a rectangular prism = 917.676 cubic centimeter

The brick has a density of 2.7 grams per cubic centimeter

Density = 2.7 grams

The mass of brick is given by formula = density × volume

[tex]\Rightarrow[/tex]                                                            = 2.7 × 917.676

[tex]\Rightarrow[/tex]                                                            = 2477.72

[tex]\Rightarrow[/tex]                                                            ≅ 2478  

Thus mass of brick is 2478 gram.

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Answer:

B. [tex]2^{-14}*5^{10}[/tex].

Step-by-step explanation:

Use the power of a power property.

[tex](2^{-7}*5^{5} )^{2}[/tex]

Multiply all the exponents in the parenthesis by 2.

[tex](2^{-7}*5^{5} )^{2}=(2^{-14}*5^{10} )[/tex]

The answer is B. [tex]2^{-14}*5^{10}[/tex].

Hope this helps!

The length of diagonal is 9.5 ft

What is Pythagoras theorem?

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

We will find the length of diagonal as shown below:

l= 7 ft

h= 5 ft

w= 4 ft

Let diagonal be d.

Let v be the diagonal of the base.

Using Pythagoras theorem

[tex]v=\sqrt{7^2+4^2}[/tex]

[tex]=\sqrt{49+16}[/tex]

[tex]v=\sqrt{65}[/tex]

For finding the value of d again using Pythagoras theorem

[tex]d=\sqrt{v^2+h^2}[/tex]

[tex]=\sqrt{(\sqrt{65})^2+5^2 }[/tex]

[tex]=\sqrt{65+25}[/tex]

[tex]=\sqrt{90}[/tex]

=9.4868

Rounding to nearest tenth

=9.5

Hence, the length of diagonal is 9.5 ft

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