Express 2x² - 12x + 7 in the form a (x + b)² + c, where a, b and c are constants.

Answer:

x + y = 4

substitute (-A, 2B) in the equation.

-A + 2B = 4

substitute (3A-2, 3-B) in the equation

3A-2 + 3-B = 4

Use elimination method and hence multiply the first substituted equation by 3

-3A + 6B = 12

3A-2 + 3-B = 4

-2 + 3 + 5B = 16

5B = 15

B = 3

Substitute value of B in any of the equations

and hence A = 2

Using it's concept, it is found that the inequality represents the domain of the exponential piece is:

d) [tex]x \leq -2[/tex].

The domain of a function is the set that contains all possible input values.

Researching this problem on the internet, we have that the function is divided as follows:

Hence, for the domain of the exponential piece, option d is correct.

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Answer:

y ≥ 14

Step-by-step explanation:

Add 27 to both sides to get:

y ≥ 14

Therefore the answer is y ≥ 14.

The value of tan(x) is [tex]-\frac{\sqrt{91}}{3}[/tex] if cos(x) = -3/10 and the angle is in the second quadrant i.e. quadrant II

The expression is given as:

cos(x) = -3/10

Using the following trigonometry identity:

sin²(x) + cos²(x) = 1

The equation become

sin²(x) + (-3/10)² = 1

Evaluate the exponent

sin²(x) + 9/100 = 1

Subtract 9/100 from both sides

sin²(x)  = 91/100

Take the square root of both sides

[tex]\sin(x) = \frac{\sqrt{91}}{10}[/tex]

Sine is positive in quadrant II.

So, the tangent is calculated using:

[tex]\tan(x) = \sin(x) \div \cos(x)[/tex]

This gives

[tex]\tan(x) = \frac{\sqrt{91}}{10} \div -\frac{3}{10}[/tex]

Evaluate

[tex]\tan(x) = -\frac{\sqrt{91}}{3}[/tex]

Hence, the value of tan(x) is [tex]-\frac{\sqrt{91}}{3}[/tex]

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The formula is given by

Or

Where

Step-by-step explanation:

When two statements are connected with an 'and,' you have a conjunction.

For conjunctions, both statements must be true for the compound statement to be true.

When the connector between two statements is "or," you have a disjunction. In this case, only one statement in the compound statement needs to be true for the entire compound statement to be true.

Answer:

13

Step-by-step explanation:

11 * 12 * 19 * 20 * 13 = 75

75/5 = 15

Answer:

13

Step-by-step explanation:

the mean is calculated as

mean = [tex]\frac{sum}{count}[/tex]

let x be the fifth number , then

[tex]\frac{11+12+19+20+x}{5}[/tex] = 15

[tex]\frac{62+x}{5}[/tex] = 15 ( multiply both sides by 5 to clear the fraction )

62 + x = 75 ( subtract 62 from both sides )

x = 13

The height of the square-based pyramid is 3.5 in.

The volume of the square-based pyramid is the product of the base area multiplied by one-third of the height of the square-based pyramid.

Mathematically;

[tex]\mathbf{V = a \times \dfrac{1}{3}h}[/tex]

[tex]\mathbf{V = a \times \dfrac{h}{3}}[/tex]

Given that:

[tex]\mathbf{10.5 = 9 \times \dfrac{h}{3}}[/tex]

[tex]\mathbf{10.5 =3\times h}[/tex]

[tex]\mathbf{h = \dfrac{10.5}{3}}[/tex]

h = 3.5 in

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Answer:

3.5 or third option

Step-by-step explanation:

I got it right on edge

Answer:

No graph was provided but Ive attached my own

Step-by-step explanation:

f(x) = 3x + 4 → y = mx + b

y - intercept (b) is 4

slope (m) is 3 so the rise / run = 3 / 1

To Sketch a graph of each of the four angles of 30°, 150°, 210°, 330°, one can follow the example that is given in the image.

In the mathematics, a sketch is known to be a given category  that tells what a thing is all about.

Note that in sketching, one need to take not of the key points and angles and as such, To Sketch a graph of each of the four angles of 30°, 150°, 210°, 330°, one can follow the example that is given in the image.

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Answer:

3

Step-by-step explanation:

The N1, N6 and N8 national highways meet in Bloemfontein,

Hope This Helped

Answer:

3.2 and 3.92

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Factors of 40: 1 2 4 5 8 10 20 40

Factors of 56: 1 2 4 8 14 28 56

Common factors: 1 2 4 8

Greatest common factor: 8

Answer:

8

Step-by-step explanation:

Prime factorization

40  = 2 x 2 x 2 x 5

56 = 2 x 2 x 2 x 7             common factor 2 x 2 x 2 = 8

Answer:

3349.5 [tex]cm^{3}[/tex]

Step-by-step explanation:

see image

To translate something:

  ⇒ is to write out the equations

Let's examine what information this problem gives us:

            ⇒ with '2' being the number of adults tickets

                ⇒total charge from purchasing adult tickets = 2 * 62.5 = 125

            ⇒ with 'x' being the number of child tickets bought

                 ⇒total charge from purchasing child tickets = 42.5x

Since the sum of total charge from purchasing adult tickets and total charge from purchasing child tickets is equal to 400:

   ⇒ 42.5x + 125 = 400 <== translated form

Let's solve:

   [tex]42.5x+125=400\\42.5x=275\\x=6.47[/tex]

Since we can only buy whole tickets:

Mrs. Albert could have bought at most 6 child tickets

Answer: Mrs. Albert can bring 6 kids

Hope that helps!

Answer:

64 men

Step-by-step explanation:

80 men / 10 months = 8 men per month, so in 8 months, 64 men can construct the same building.

Answer:

no i cannot help you

Step-by-step explanation:

thats good

Answer:

Reflection

Explanation:

This is a reflection because A B and C and A' B' C' are at the same points in their quadrants. A' B' C' is flipped over the X-Axis

Answer:

reflection about the x -axis

Step-by-step explanation:

Mirror line is the x-axis for this translation

Answer:

 D is your answer  Outlier An extreme value in a set of data which is much higher or lower than the other numbers.

Step-by-step explanation:

Outliers affect the mean value of the data but have little effect on the median or mode of a given set of data

Answer:

84/100

Step-by-step explanation:

We know that 100% is a whole, so we can use this as our denominator. If the student only got an 84, this will be our numerator. The numerator is a part of a whole, 84 is a part of 100. Therefore the answer would be 84/100.

The value of the definite integral corresponds to the total area of two triangles (see attached plot).

[tex]\displaystyle \int_{-4}^3 \left|\frac x2\right| \, dx = \dfrac12 \times 2 \times 4 + \dfrac12 \times 3 \times \dfrac32 = \boxed{\frac{25}4}[/tex]

Yolanda is correct since the boulders have a circular shape, the best shape to model the surface area of a sphere.

A sphere is a three dimensional object that has all the set of all points equidistant from a single point in space. An example of a sphere is a ball. The boulder in this question has a spherical shape.

Surface area of a sphere = 4πr²

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Answer:

Step-by-step explanation:

Yolanda is correct since the boulders have a circular shape, the best shape to model the surface area of a sphere.

What is a sphere?

A sphere is a three dimensional object that has all the set of all points equidistant from a single point in space. An example of a sphere is a ball. The boulder in this question has a spherical shape.

Surface area of a sphere = 4πr²

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Answer:

Claro esta:

139 x 1

Pero tambien

69.5 x 2

Y

46.3 x 3

Y muchos mas

Answer:

e.  0.308.

Step-by-step explanation:

I can't draw the tree diagram but the answer is

P(red first) = 7/14 = 1/2

P( then black)  = 4/13

P(red then black) = 1/2 * 4/13 = 2/13

P(black first) = 4/14 =  2/7

P( then red)  = 7/13

P(black then red) =2/7 * 7/13 = 2/13

So Probability of red and black in any order

= 2/13 + 2/13  = 4/13

= 0.308.

Answer:

Step-by-step explanation:

Answer:

Quick answer, C. 7 units!

Answer:

x+1y=-4

Step-by-step explanation:

use ax+by=c

Answer:

13.9%

Explanation:

Rolling for 2 : (1, 1)

Rolling for 5 : (1, 4), (4, 1), (2, 3), (3, 2)

So, there are (4 + 1) = 5 possible outcomes out of 36 outcomes

Note: There are 36 outcomes when rolling a two fair cubes.

[tex]\sf Probability = \dfrac{possible \ outcomes}{Total \ outcomes}[/tex]

[tex]\rightarrow \sf \dfrac{5}{36} \ x \ 100[/tex]

[tex]\rightarrow \sf \dfrac{125}9} \%[/tex]

[tex]\rightarrow \sf 13.9 \%[/tex]