What are the coordinates of the vertex of the function f(x) = x2 − 12x + 5?

(6, 31)
(−6, 31)
(6, −31)
(−6, −31)

Answer: Isosceles triangle

Step-by-step explanation: Two of the base sides are equal distance away. (Sides AB and AC)

The equation of the line that passes through the point (-4 , 3) with slope ₋2 is:

y = ₋2x ₋ 5

Given the points are (₋4 , ₋3) and (4 , 1)

The gradient of the line through the points' locations (x₁ , y₁) and (x₂ , y₂) is:  y₂ ₋ y₁/x₂ ₋ x₁

Substitute the given points in the above formula:

=1 ₋(₋3)/4 ₋ (₋4)

=4/8

=1/2

If the product of the slopes of two perpendicular lines is -1, then the slope of the perpendicular line is ₋1/1/2 = ₋2

Therefore the line that passes through the point (-4 , 3) with slope ₋2 has equation:

y ₋ 3 = ₋2(x ₊ 4)

y = ₋2x ₋ 8 ₊ 3

y = ₋2x ₋ 5

Hence we get the expression as y = ₋2x ₋ 5

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Answer:

Pythagoras was the Greek geometer .

Please mark me as the brainliest.

The highest common factor of [tex]x^2 y[/tex] and [tex]x[/tex] is [tex]\boxed{x}[/tex]

Answer:

52, 53, 54, pack 1.

Step-by-step explanation:

1)

1.56 = 30

10 = 1.56 / 3

10 = 52 pence

2)

2.12 = 40

10 = 2.12 / 4

10 = 53 pence

3)

3.78 = 70

10 = 3.78 / 7

10 = 54 pence

The cheapest one is the small pack

We have proven that line TU is parallel to line VW as shown below. That is, TU || VW

From the question, we are to prove that TU || VW

In the given image,

   Statements           Reasons

1. ST || UV                  Given

2. ∠T ≅ ∠U                Alternate angles

3. ∠T ≅ ∠V                Given

4. ∠U≅ ∠V                 Substitution property

5. TU || VW                 Alternate interior angles theorem

NOTE: If the alternate interior angles formed by a transversal of two lines are equal, then the lines are parallel

Hence, we have proven that line TU is parallel to line VW. That is, TU || VW

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Answer:

a c c

Step-by-step explanation:

The equation of the line in slope-intercept form is y = (1/2)x + 3 and the slope is 1/2.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}\\[/tex]

As we can see in the graph the line goes from (-6, 0) and (0, 3)

Finding the slope:

[tex]\rm m =\dfrac{3-0}{0-(-6)}\\[/tex]

m = 3/6 = 1/2

y = mx + c

y = (1/2)x + c

c is the y-intercept

c = 3

The equation:

y = (1/2)x + 3

Thus, the equation of the line in slope-intercept form is y = (1/2)x + 3 and the slope is 1/2.

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Answer:

[tex]\fbox {See below} \downarrow[/tex]

Step-by-step explanation:

Question 1

Part (a) :

⇒ 6 × 6 × 6 × 6 × 6 × 6 × 6 = 6ˣ

⇒ 6⁷ = 6ˣ

⇒ x = 7

Part (b) :

⇒ y² = 169

⇒ √y² = √169

⇒ y = ± 13

⇒ y = 13, y = -13

Question 2

Part (a) :

⇒ (√5)² × (√3)²

⇒ 5 × 3

⇒ 15

Part (b) :

⇒ (∛9)³ × (√30)²

⇒ 9 × 30

⇒ 270

The elimination method is valid for the system of equation because the y term cancels.

The system of equation can be solved using elimination methods.

Therefore,

x - 2y = 3

3x + 2y = 17

Hence,

x + 3x  = 4x

-2y + 2y = 0

3 + 17 = 20

Therefore,

4x = 20

The y term cancels. Therefore, we can solve for x and later solve for y.

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Answer:

Adding a quantity like x – 2y to one side of an equation and another quantity like 3 to the other side maintains the equality if the two quantities are equal.

Answer:

a) 270000

b) 2000000

c) 24000000

Step-by-step explanation:

For a)

346 to 1 s.f is 300

904 to 1 s.f is 900

300 × 900 = 270000

For b)

2451 to 1 s.f is 2000

988 to 1 s.f is 1000

2000 × 1000 = 2000000

For c)

3204 to 1 s.f is 3000

7756 to 1 s.f is 8000

3000 × 8000 = 24000000

Hope this helped and have a good day

Answer: D. 2

Step-by-step explanation:

The question is asking for the rate of change from x=1 to x=2. Remember that the rate of change is also the slope, which can be seen as [tex]\frac{rise}{run} or \frac{y}{x}[/tex]. The rise would be going up/down the graph and the run would go left/right of the graph. Let's look at where x=1 and x=2 on the graph.

First, look at where the line falls between x=1 and x=2. Then, on where x=1, go up, then right on the graph, until you find the point where x=2. In this case, the rise over run is [tex]\frac{2}{1}[/tex]. This can be simplified to 2.

Therefore, the answer is 2.

I hope this helps!! Pls mark brainliest :))

find the length using the Pythagorean theorem.

Length = sqrt(20^2 - 12^2)

Length = 16 feet

area = 12 x 16 = 192 square feet

Answer:

y+2= -4(x-8)

Step-by-step explanation:

Answer:

c. 0

Step-by-step explanation:

3(x+8) - 1 = 3x+4

3x+24-1 = 3x+4

3x+23 = 3x+4

There are no solutions since both equations have the same slope meaning they are parallel and they will never intersect since they have different y-intercepts.

Answer:

p = 13

Step-by-step explanation:

The mean of 5, 11, 6, 4, 7, 10, p is 8

So 8 = 5+11+6+4+7+10+p divided by 7.

So 56 = 43+p

Therefore p = 56-43

                    = 13

Hope I helped

⇒ 5 + 11 + 6 + 4 + 7 + p + 10 / 7 = 8

⇒ 43 + p = 56

⇒ p = 13

The value of p is 13.

Answer:

slope = 3

y-intercept: -4

explanation on how to graph given in step-by-step explanation

Step-by-step explanation:

y=3x-4 is given in slope-intercept form which is y=mx+b where m is the slope and b is the y-intercept (when x = 0)

So the first coordinate that is easy to graph is the y-intercept since it's just (0, b) or in this case (0, -4). So that's the first point you graph. Now from here you can use the slope to graph all the other points. The slope is 3, which essentially means every time x increases by 1, the y-value increases by 3. So from the y-intercept (0, -4) you're going to go one unit to the right and three units up which should give you the coordinates (1, -1). Then from that coordinate go one unit to the right and three units up which should get you (2, 2) then from that coordinate go one unit to the right and three units up which should get you to (3, 5). Now go back the y-intercept (0, -4) and instead of going to the right 1 and up 3 you're going to do the inverse and instead go left 1 and down 3. So from (0, -4) go to the left one unit and down 3 units which should get you to (-1, -7). And now with all these points plotted draw a line through all of them

Answer:

Kathy

Step-by-step explanation:

Answer:

Step-by-step explanation:

what is the question?

Answer:

Median = A

Mean = B

Step-by-step explanation:

Khan Academy

Answer:

See below

Step-by-step explanation:

arrange to standard form   (x-h)^2   + (y-k)^2 = r^2     h,k = center   r = radius

x^2 - 4x        +    y^2 + 2y   =   4        complete the square for 'x' and 'y'

(x-2)^2    -  4    +    (y-1)^2  -1  = 4

(x-2)^2    +  ( y-1)^2  = 4 + 4 + 1 = 9           '9' is equal to r^2  so r = 3

center = 2,1     radius = 3

Answer:

you're welcome!!!

Step-by-step explanation:

For the matrix given , the element a₂₃ is the number at 2nd row and 3 column ,which is 6 , Option B is the correct answer.

It is a table or a rectangular array of numbers or expressions arranged in rows and columns ,

For a Matrix of m x n , m is the no. of rows and n is the no. of column

For the matrix given the element a₂₃ is the number at 2nd row and 3 column ,

which is 6 ,

Therefore Option B is the correct answer.

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Answer:

D

Step-by-step explanation:

i just know i guess

Answer:

D(1,12)

Step-by-step explanation:

See attached graph.

Answer:

24 is the answer for the following

Step-by-step explanation:

please mark me as brainlest

Answer:

cost price = £ 600

discount = 5%

selling price =

5/100 * 600.

5 * 6

30 £

price = 600 - 30

= 570

The number of traders that sell oranges and mangoes only are 17.

Since there are three sets, use the formula

n (A∪O∪M) = n(A) + n(O) + n(M) - n(A∩O) -n(O∩M) - n(A∩M) + n(A∩O∩M)

A represents apple traders = 40

O represents orange traders = 46

M represents mangoes traders = 50

A∪O∪M = total traders = 100

A∩O = 14

O∩M = ?

A∩M = 15

A∩O∩M = 10

Substitute values into the formula

100 = 40 + 46 + 50 - 14 - 15 - O∩M + 10

100 = 146 - 29 - O∩M

100 = 117 - O∩M

Make O∩M subject of formula

- O∩M = 100 -117

O∩M = 17 traders

Therefore, the number of traders that sell oranges and mangoes only are 17.

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Answer:

Julie's score is 15.

Step-by-step explanation:

This can be solved in two ways:

⇒ 120 ÷ 8

⇒ Experimentation on what × 8 = 120 (adding random numbers until you get 120 as a product).

Let's use the first method.

⇒ 120 ÷ 8

         1 5

   __________

8 |  1  2 0

   -     8

        ____

        4    0

       - 4  0

      ____

       0

Therefore, Julie's score is 15.