A. The graph is translated 2units down.
B. The graph is translated 2 units left.
C. The graph is translated 2 units right.
D. The graph is translated 2 units up.

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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Answer:

a dash is 1/8 tsp.

Step-by-step explanation:

a dash is 1/8 tsp or called 0.13

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

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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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:

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

Answer:

Hi,

a=b+3

Step-by-step explanation:

[tex]\begin{array}{c||c|c|c|c}&x^3&x^2&x&1\\---&---&---&---&---\\&1&-a&b&c\\x=-1&&-1&a+1&-a-b-1\\---&---&---&---&---\\&1&-a-1&a+b+1&c-a-b-1\\\end{array}[/tex]

[tex]\begin{array}{c||c|c|c|c}&x^3&x^2&x&1\\---&---&---&---&---\\&1&-a&b&c\\x=2&&2&4-2a&2b+8-4a\\---&---&---&---&---\\&1&2-a&b+4-2a&c+2b+8-4a\\\end{array}[/tex]

Thus:

c+2b+8-4a=c-a-b-1

3b-3a=-9

a=b+3

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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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.

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Problem 4

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

The decimal values are approximate.

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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.

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

Answer:

Step-by-step explanation:

The total number of bags in the bottle = 20 + 15 = 35

Then

the probability that the first bag is blue = 20/35

If we replace the first bag :

the probability that the second (picked) bag is blue = 15/35

Conclusion:

If two bags are picked at random one after the other with replacement

Then

the probability that the first bag is blue and then red is :

(20÷35)×(15÷35)

= (4÷7)×(3÷7)

= 12÷49

= 0.244897959184

Answer:

1/3

Step-by-step explanation:

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

im not sure I'd need to see the figure

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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Answer:

Step-by-step explanation:

Answer:

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

Using translation concepts, it is found that the variables h and k affect the graph of the function as follows:

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, we consider the parent cube root function as follows:

[tex]y = \sqrt[3]{x}[/tex]

Then, these following changes happened:

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Answer:

C

Step-by-step explanation:

Evaluating the options :

Option A

⇒ 5/2x + 7/2 = 3/4x + 14

⇒ 2.5x - 0.75x = 14 - 3.5

⇒ 1.75x = 10.5

⇒ x = 6

⇒ No ×

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

Option B

⇒ 5/4x - 9 = 3/2x - 12

⇒ 1.5x - 1.25x = -9 + 12

⇒ 0.25x = 3

⇒ x = 12

⇒ No ×

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

Option C

⇒ 5/4x - 2 = 3/2x - 4

⇒ 1.5x - 1.25x = -2 + 4

⇒ 0.25x = 2

⇒ x = 8

⇒ Yes √

C is the right answer.

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

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

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:

No

Step-by-step explanation:

Since an equilateral triangle has equal sides and angles, each angle measures 60°, which is acute. Therefore, an equilateral angle can never be obtuse-angled. A triangle cannot be right-angled and obtuse angled at the same time. Since a right-angled triangle has one right angle, the other two angles are acute.

Answer:

false

Step-by-step explanation:

610

Step-by-step explanation:

(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

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

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: 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)

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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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: