Julian has partially filled the prism below with 16 unit cubes.

A rectangular prism with a length of 4, height of 3, and width of 3.

How many more unit cubes will he need to completely fill the prism?
11
20
25
36

Answer:

C. (6, 3)

Step-by-step explanation:

Use the midpoint formula!

Midpoint Formula

[tex]\text{midpoint} = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})[/tex]

x₁, x₂ ... x-coordinates of the endpoints

y₁, y₂ ... y-coordinates of the endpoints

Given endpoints:

(8, 0)

(4, 6)

Points are in form (x, y).

Now let's substitute the variables in the formula with our values.

[tex](\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})[/tex]

[tex](\frac{8 + 4}{2}, \frac{0+ 6}{2})[/tex]

[tex](\frac{12}{2}, \frac{6}{2})[/tex]

[tex](6, 3)[/tex]

(6, 3) is our midpoint!

Answer:

2/9

Step-by-step explanation:

8/12 you pick an office worker

4/12 chance you pick a manager

8/12 multiplied by 4/12 is 32/144

We can simplify this to 16/72

We can simplify this to 8/36

We can simplify this to 4/18

We can simplify this to 2/9

Using a dot plot, it is found that the number of dots of each point are given as follows:

The dot plot shows the number of times each measure appears in the data-set.

In this problem, one measure has a value of 1/8, hence:

The value [tex]\frac{1}{8}[/tex] will have one dot above it.

Two measures have a value of 1/4, hence:

The value [tex]\frac{1}{4}[/tex] will have two dots above it.

Three measures have a value of 3/8, hence:

The value [tex]\frac{3}{8}[/tex] will have three dots above it.

Five measures have a value of 1/2, hence:

The value [tex]\frac{1}{2}[/tex] will have five dots above it.

Two measures have a value of 5/8, hence:

The value [tex]\frac{5}{8}[/tex] will have two dots above it.

Three measures have a value of 3/4, hence:

The value [tex]\frac{3}{4}[/tex] will have three dots above it.

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Answer:

1 2 3 5 2 3

Step-by-step explanation:

Answer: The value of x is 3.5

Explanation:

Equation:

y = 2x - 7

When the equation's Line intersects the x-axis, the value of y shall be always 0

Insert y = 0, to find x intercept

⇒ 0 = 2x - 7

⇒ 2x - 7 = 0

⇒ 2x = 7

⇒ x = 3.5

So coordinates: (x, y) → (3.5, 0)

The system of equations is consistent and independent and the solutions are x = 4, y = 5, and z = -1 option third is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have three linear equations in three variables:

x - y - z = 0 ..(1)

2x - y + 2z = 1 ..(2)

x - y + z = -2 ..(3)

From the equation (1):

[tex]\rm x=y+z[/tex]

Plug this value in the equation (2) and (3):

[tex]\rm 2\left(y+z\right)-y+2z=1\\\\ y+z-y+z=-2[/tex]

After solving we get:

z = -1

y = 5

Plug the above two values in equation (1) we get:

x = 4

Thus, the system of equations is consistent and independent and the solutions are x = 4, y = 5, and z = -1 option third is correct.

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610

Step-by-step explanation:

Step-by-step explanation:

remember a few things :

a × -1 = -a

-a × -1 = a

-1 × -1 = 1

1 × a = a

therefore,

-1 × -1 × a = 1 × a = a

and finally

c × (a + b) = c×a + c×b

so, we can say

(1 - 5) = -1 × -1 × (1 - 5) =

= -1 × (-1×1 + -1×-5) = -1 × (-1 + 5) =

= -1 × (5 - 1) = -(5 - 1)

Answer: 8

Step-by-step explanation:

The discriminant is [tex]b^2-4ac[/tex]

in the equation:

[tex]-x^2+4x-2[/tex]

A = -1, B = 4, C = -2

plug into equation

[tex]4^2-4(-1)(-2)[/tex]

[tex]16-8[/tex]

⇒ [tex]8[/tex]

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The angle sum theorem tells you the sum of angles of a triangle is 180°. Angles of a linear pair are supplementary, so total 180°. These facts can be used to write a relation that can be solved for x.

__

The interior angle at the right end of the line is the supplement of 4x:

  180° -4x

The interior angle at the left end of the line is the supplement of 2x:

  180° -2x

  86° +(180° -4x) +(180° -2x) = 180°

Then the solution to the triangle is ...

  266° = 6x . . . . . . . . . add 6x-180°

  x = 266°/6 = 44 1/3° . . . . . divide by 6

Answer:

tanD =4/7

Step-by-step explanation:

tanD = P/B

Where P=4 and B=7

So;

tanD=4/7

The probability of coin landing with heads is an independent event.

The probability of winning 1st and 2nd prize is a dependent event.

Independents events are events whose occurrence do not depend on each other. They are random events. The probability of a coin landing on heads is a random event.

Dependent events are events that are not random. The outcome of one event depends on the outcome of another event.

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Answer:

Step-by-step explanation:

V=14h﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4aBase sidebBase sidecBase sidehHeight

Answer: y - 17 = -2(x-7)

Step-by-step explanation:

point-slope form: y - y1 = m(x - x1)

m = y2-y1/x2-x1

   = 9+17/-6-7

   = 26/-13

   = -2

y1 = -17

x1 = 7

y - 17 = -2(x-7)

The equation represents a line that is parallel to the line that passes through the points (−6,9) and (7,−17) is y =  -2x - 3

The general equation of a straight line is-

y = mx + c

where, m is the gradient and is given by y₂ - y₁/x₂ - x₁

and, c is the value where the line cuts y-axis.

Now it is given that the line passes through points (−6,9) and (7,−17)

Therefore we have,

x₁ = -6, y₁ = 9, x₂ = 7, y₂ = -17

So, the slope m of the line is given as,

m = (y₂ - y₁)/(x₂ - x₁)

Put the values,

m = (-17 - 9)/(7 - (-6))

m = -26/7+6

m = -26/13

m = -2

Thus, the equation parallel to the line will be given as:

y - y₁ =  m(x - x₁)

y - 9 =  -2{x - (-6)}

y - 9 =  -2(x + 6)

y =  -2x - 12 + 9

y =  -2x - 3

Thus, the equation represents a line that is parallel to the line that passes through the points (−6,9) and (7,−17) is y =  -2x - 3

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Step-by-step explanation:

To answer this, we need to plug in 3 as x in the equation f(x) = 5 + 4x².

That would look like this: f(3) = 5 + 4(3)²

f(3) = 5 + 4(3)²

f(3) = 5 + 36

f(5)=41

Therefore, the answer is 41.

I hope this helps!! :)

Answer:

Step-by-step explanation:

2/3 - 5/4 + 7/3

=8/12 - 15/12 + 28/12 (LCM=12)

(8 - 15 + 28)/12

=21/12

=7/4

im not sure I'd need to see the figure

Answer:

its the Pentagon, the other shaps have 2 lines if symmetry

Deductive Reasoning is the practice of arriving at a mathematical conclusion by simply analyzing the facts using the knowledge of the related concepts.

Looing at ΔOAB and ΔOEF

It is clear that

OB = OF (O is the midpoint)

∠OBA = ∠OFE = 90°

Therefore

∠AOB = ∠EOF (Vertically Opposite Angles)

⇒ ΔOAB ≅ ΔOEF and

∠ A ≅ ∠E.

QED

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Answer:

Area of Circle  = 346.5 cm².

Area of square = 272.25 cm ² .

Step-by-step explanation:

So , 2πR = 66

2 × 22 / 7 × R = 66

R comes out is 21/2 cm .

Area of Circle = 22/7 × 21/2 × 21/2 = 33×21/2

= 693 / 2 = 346.5 cm².

If bent into the shape of a square ;

4 a = 66

a = 33/2 . ( Side of a square )

Area of square = a ² = 33×33/4 = 1089/4

= 272.25 cm ² .

Answer:

28 students

Step-by-step explanation:

7 times 4 = 28

there are are seven students in 4 teams, so that means there are 4 groups of seven, and you multiply them together to get how many students in the class

Answer:

28

Keyword(s):

divided, four, 7, per team, how many

Step-by-step explanation:

7 × 4 = 28

Subtraction is a mathematical operation that reflects the removal of things from a collection. The temperature change from -4.2 to 9.1 is 13.3.

Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.

The temperature change from -4.2 to 9.1 is,

ΔT = 9.1 - (-4.2) = 9.1 + 4.2 = 13.3

Hence, the temperature change from -4.2 to 9.1 is 13.3.

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Step-by-step explanation:

1) x+6 =4

x. =4-6

x. =-2

2) x-(-4) =-6

x+ 4. =-6

x. =-6-4

x. =-10

3)2(x-1)=-200

2x-2 =-200

2x. = -200+2

2x. = -198

x. = -198/2

x. = -99

4)2x+(-3) =-23

2x-3. =-23

2x. =-23+3

2x. =-20

x. =-20/2

x. = -10

Considering the given quadratic equation, the correct statement is given by:

The airplane reaches its maximum height of 81 feet in 12 seconds.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

In this problem, the equation is given by:

h(t) = -(t - 12)² - 81.

The vertex is (12,81), with a negative leading coefficient, hence it is a maximum point and the correct statement is given by:

The airplane reaches its maximum height of 81 feet in 12 seconds.

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(x+8/3)²+y²=1

(x+8/3)²+y²+0²+2×0y=1

(x+8/3)²+(y+0)²=(V1)²

->center: C(8/3,0)

-> radius: V1

Problem 1

Any pair of equilateral triangles are always similar triangles. We can use the SSS (side side side) similarity theorem to prove this. One triangle is an enlarged copy of the other, or a shrunken reduced copy.

The rectangle is NOT similar to the square. They are different shapes. Similar figures are figures that are the same shape, but different sizes.

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

Problem 2

horizontal/vertical = horizontal/vertical

24/x = 6/5

24*5 = 6x

120 = 6x

x = 120/6

x = 20

Answer: The flagpole is 20 ft high (about 2 stories tall)

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

Problem 3

The formula to use is [tex]z = \sqrt{x*y}[/tex]

z = geometric mean of x and y

We multiply the numbers and take the square root. This only works for two values at a time. The geometric mean of three numbers will involve the cube root. Four numbers involves the 4th root, and so on.

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

Problem 4

For each figure, the y is the altitude and can be determined using the geometric mean formula.

The decimal values are approximate.

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

Problem 5

For 45-45-90 triangles, we divide the hypotenuse over sqrt(2) to find the leg length.

For the first triangle in the first row, we have y = 18/sqrt(2) = 9*sqrt(2) after rationalizing the denominator. Multiply top and bottom by sqrt(2).

Take this process in reverse to determine the hypotenuse if you know the leg length. This explains why the hypotenuse is 3.2*sqrt(2) for the second triangle in the first row.

-------------------

For 30-60-90 triangles, we go from the short leg x to the hypotenuse 2x.

Double the short leg to get the hypotenuse.

2x = 36

x = 36/2

x = 18

This is for the first triangle in the bottom row.

For the other triangle in this bottom row, we have a long leg of 4*sqrt(3). This must mean the short leg is exactly 4 units long. Therefore, the hypotenuse is 2*4 = 8 units long.

-------------------

The function on the table is decreasing on the interval [-2, 0).

A function is decreasing if, as x increases, f(x) decreases.

We can see that at x = -2, f(-2) = 12.

Then at x = 0, f(0) = 0.

And for the value after that:

x = 1, f(1) = 3

So now the function increases. Then we conclude that the function is decreasing on the interval [-2, 0), and after that the function increases.

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Answer:

1/3

Step-by-step explanation:

[tex]|\Omega|=30\\|A|=10\\\\P(A)=\dfrac{10}{30}=\dfrac{1}{3}[/tex]

Answer:

x ≈ 8.7

Step-by-step explanation:

given 2 secants from an external point to the circle, then

the product of the external part of one secant and the entire secant is equal to the product of the external part of the other secant and the entire secant , that is

6(6 + x) = 4(4 + 18) ← distribute parenthesis on both sides

36 + 6x = 4 × 22 = 88 ( subtract 36 from both sides )

6x = 52 (divide both sides by 6 )

x ≈ 8.7 ( to the nearest tenth )