Which is the solution of the quadratic equation (4y - 3)2 = 72?
y
3 +/Z and y
y=
3-6/2
4
3+62
y=
and y=
-3 – 6/2
4
4
0
y=
9/2
4
and y= -3/2
4
9/2
4.
y=
3/2
and y=
4​

Answer:

See explanation below for further details.

Step-by-step explanation:

A rational consist of two real numbers such that:

[tex]\frac{a}{b} =c[/tex]

If c is a polynomial with a certain grade, then, both the numerator and the denominator must be also polynomials and the grade of the numerator must be greater than denominator.

If c is linear function, that is, a first order polynomial, then a must be a (n+1)-th polynomial and b must be a n-th polynomial.

Example:

If [tex]a = x^{2}[/tex] and [tex]b = x[/tex], then:

[tex]c = \frac{x^{2}}{x}[/tex]

[tex]c = x[/tex]

If c is a quadratic function, that is, a second order polynomial, then a must be a (n+1)-th polynomial and b must be a n-th polynomial.

Example

If [tex]a = 3\cdot x^{3}[/tex] and [tex]b = x[/tex], then:

[tex]c = \frac{3\cdot x^{3}}{x}[/tex]

[tex]c = 3\cdot x^{2}[/tex]

But if c is an exponential, both the numerator and the denominator must be therefore exponential function and grade of each exponential function must different to the other.

Example

If [tex]a = 10^{2x}[/tex] and [tex]b = 3\cdot 10^x[/tex], then:

[tex]c = \frac{10^{2\cdot x}}{3\cdot 10^{x}}[/tex]

[tex]c = \frac{1}{3}\cdot 10^{2\cdot x -x}[/tex]

[tex]c = \frac{1}{3}\cdot 10^x[/tex]

Otherwise, c would be equal to a constant function, that is, a polynomial with a grade 0.

If [tex]a = 5\cdot e^{x}[/tex] and [tex]b = -3\cdot e^{x}[/tex], then:

Example

[tex]c = \frac{5\cdot e^{x}}{-3\cdot e^{x}}[/tex]

[tex]c = -\frac{5}{3}[/tex]

It is worth to add that exponential functions can be a linear combination of single exponential function, similar to polynomials.

Example

[tex]5\cdot a^2\cdot x -9[/tex]

Answer:

Solution,

Finding the value of X,

[tex]11x + 2 = 68[/tex]

( being vertically opposite angles)

[tex]11x = 68 - 2 \\ 11x = 66 \\ x = \frac{66}{11} \\ x = 6[/tex]

Value of X is 6

Now, finding the value of z

[tex]z + 68 = 180[/tex]

(sum of angle in linear pair)

[tex]z = 180 - 68 \\ z = 112[/tex]

Value of z is 112.

Hope this helps....

Good luck on your assignment...

Answer:

5/8

Step-by-step explanation:

The value of the expression is 8/15

An expression in maths is a sentence with a minimum of two numbers or variables and at least one maths operation.

Given an expression, (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/225)

The expression is in the form of (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/n²)

We know, (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/n²) = (n+1)/2n

Here, n = 15.

So, (1- 1/4) * (1- 1/9) * (1- 1/16) *...* (1- 1/225) = (15+1)/(2.15) = 16/30

= 8/15

Hence, The value of the expression is 8/15

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Answer:

19 : 25

Step-by-step explanation:

Answer:

The factors of the polynomial are 5,  ( 3x - 2y), and  (3x + 2y)

Step-by-step explanation:

The given polynomial is 45x² - 20y²

45x² - 20y² = 5 (9x² - 4y²)

45x² - 20y² = 5 [ (3x)² - (2y)² ]

Using difference of two squares,  (3x)² - (2y)² = ( 3x - 2y)(3x + 2y)

45x² - 20y² = 5 ( 3x - 2y) (3x + 2y)

The factors of the polynomial are 5,  ( 3x - 2y), and  (3x + 2y)

Answer:

5(3x - 2)(3x + 2)

Step-by-step explanation:

Please indicate exponentiation with " ^ " :  45 x^2 - 20 y^2​.

Identify the GCF and factor it out:  5(9x^2 - 4y^2)

Recognize that (9x^2 - 4y^2) is the difference of two squares, which factors into (3x - 2y)(3x + 2y)

Then   45 x^2 - 20 y^2 = 5(3x - 2)(3x + 2)

Answer:

25

Step-by-step explanation:

The Side Splitter Theorem says that if a line intersects two sides of a triangle and is parallel to the third side of the triangle, it divides those two sides proportionally. Therefore:

6/15 = 10/?

6*? = 10*15

? = 10*15/6

? = 25

Answer:

answer is (0,1)

Step-by-step explanation:

check

by substituting x=0 and y=1 in the equation above

- 2(0)+1> -4

1> -4

Thereby (0,1) is the required solution to the inequality

Answer:

Step-by-step explanation:

1+2 cos α

[tex]=1+2(2 cos^{2} \frac{\alpha }{2} -1)\\=1+4 ~cos^2\frac{\alpha }{2} -2\\=4 ~cos^2\frac{\alpha }{2} -1\\=(2cos \frac{\alpha }{2} +1)(2 cos \frac{\alpha }{2} -1)[/tex]

Answer:

$3.55

Step-by-step explanation:

You need to add 29% of $2.75 to $2.75.

That means the price will be 129% of $2.75.

129% of $2.75 =

= 1.29 * $2.75

= $3.55

Answer:

Step-by-step explanation:

Let width = w units

Length = 4w - 3

Cost for lining corners of wall = $ 18.50

Perimeter of the wall = 18.50/0.25 =  74 ft

2*(length  +width ) = 74

2*(4w - 3 + w) =74

2*(5w - 3) =74

10w - 6 = 74   {Add 6 to both sides}

10w - 6 + 6 = 74 + 6

10w = 80

Divide both sides by 10

10w/10 = 80/10

w =  8 ft

Length = 4w - 3 = 4*8 - 3 = 32 - 3

Length = 29 ft

Area of the wall = length * width

                           = 29 * 8

                           =  232 square ft

Cost of painting the wall per square feet = 20 cents = 0.20

Cost of painting 232 square feet = 232 * 0.20

                                                             = $ 46.40

Answer:

[tex]5\sqrt{3}[/tex]

Step-by-step explanation:

=> [tex]\frac{15}{\sqrt{3} }[/tex]

Multiplying and dividing by [tex]\sqrt{3}[/tex]

=> [tex]\frac{15}{\sqrt{3} } *\frac{\sqrt{3} }{\sqrt{3} }[/tex]

=> [tex]\frac{15\sqrt{3} }{(\sqrt{3})^2 }[/tex]

=> [tex]\frac{15\sqrt{3} }{3}[/tex]

=> [tex]5\sqrt{3}[/tex]  (A Rationalized denominator!)

Answer:

5√3

Step-by-step explanation:

To rationalize the denominator, all you have to do is multiply both the numerator and the denominator by whatever is in the denominator, if it is only a single term in the denominator. This means you multiply [tex]\frac{15}{\sqrt{3} }[/tex] [tex]* \frac{\sqrt{3}}{\sqrt{3}}[/tex] . Since √3 divided by itself is 1, this doesn't change the value of the expression. Now multiplying this we get (15√3)/3. Now we can divide 15√3 by 3 to get 5√3, which is the final answer.

Answer:

A. 1/8

Step-by-step explanation:

m = rise/run

m = (y2-y1)/(x2-x1)

m = (-5- - 4)/(1-9)

m = (-5+4)/(-8)

m = (-1)/(-8)

m = 1/8

Answer:

The answer is A.

Step-by-step explanation:

Given that the formula to find gradient, m, is :

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

Then, you have to substitute the coordinates into the formula :

[tex]let \: (9, - 4) \: be \: (x1,y1) \\ let \: (1, - 5) \: be \: (x2,y2)[/tex]

[tex]m = \frac{ - 5 - ( - 4)}{1 - 9} [/tex]

[tex]m = \frac{ - 5 + 4}{ - 8} [/tex]

[tex]m = \frac{ - 1}{ - 8} [/tex]

[tex]m = \frac{1}{8} [/tex]

Answer:

Table 2

Step-by-step explanation:

The question is to identify the table where the relative frequency of orders for blue pants is half the relative frequency of their orders for black shorts.

We are interested in the number of blue pants and black shorts.

If we name them as p and b respectively, then we are looking for a table where s/p=2

Let's verify relevant data in all tables:

Table 1:

Table 2:

Table 3:

Table 4:

So only one of tables- the second one from top represents the required data.

Answer:

The second table

Step-by-step explanation:

I did the test.

Answer:

36/100

Step-by-step explanation:

this is because you find the overlapping ranges of each bag which is 5 - 10 on the first bag and 5 - 10 on the second bag. both bags have 10 total numbers, so 6/10 * 6/10 because there are six numbers on each bag and 10 overall choices, so we multiply these two because its an and statement which gives us 36/100.

The probability that we get the same number is 9/25.

It is simply likeliness of happening an event. The probability of an event lies between 0 to 1.

Numbers in first bag=10

Numbers in second bag=10

Common numbers=5,6,7,8,9,10

Total common numbers=6

So the probability that we get the same numbers will be

= 6/10* 6/10

=36/100

=18/50

=9/25

Hence the probability that we will get the same numbers is 9/25.

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Hey there! :)

Answer:

C. (0, 5)

Step-by-step explanation:

Where the equation crosses the y axis is known as the y-intercept.

In the equation y = mx + b, the b  value represents the y-intercept where x = 0. Therefore:

Rearrange the equation pictured:

y = 5 - 3x --> y = -3x + 5

The b value in this equation is 5, so

The y-intercept of this equation is (0, 5).

Answer:

Option C is the correct option.

Here,

When X=0

y= 5-3*0

= 5-0

=5

x=0

y=5

Hope this helps...

Good luck on your assignment..

Answer: 3.5 pi.

Step-by-step explanation: Since we know the circumference formula of a circle is 2*pi*radius, we just have to substitute 7 in there, and divide by 4. So here ya go, 3.5 pi.

Answer:x − 3 y = − 36

Step-by-step explanation:

Answer: The initial form is called slope intercept form// and the equation in standard form is 3y=37

Step-by-step explanation:

standard form = ax+by=c so you basically just have to take that and put it into the formula

Hope this helps

Answer:

117,600 ways

Step-by-step explanation:

This problem can be solved using fundamental principle of counting , according to which , if there are m different things and n different things,

then there m*n ways to combine.

Example: if there 5 shirts and 3 ties,

then number of ways in which different combination shirt and tie can be worn is

5*3 = 15 ways.

____________________________________

In the problem,\

number of states is 50,

let those states be

A1, A2, A3, A4 ......A50

in each state there are 2 senate

Condition

3-Senator committee in which no two members are from the same state.

then

first member can be chosen from any of the 50 state,

hence first member can be chosen in 50 ways

for simplicity lets take state A1, you can choose any one you wish

second member cannot be from state A1, then number of state left = 49

second member can be chosen from  any of 49 state left

hence second member can be chosen in 49 ways

for simplicity lets take state A2,

Third member cannot be from state A1 and A2, then number of state left = 48

Third member can be chosen from  any of 48 state left

hence Third member can be chosen in 48 ways

for simplicity lets take state A3,

Hence no. of ways of choosing  3-Senator committee be formed such that no two Senators are from the same state = 50*49*48 = 117,600 ways

Answer:

see below

Step-by-step explanation:

15+2x> 31

Subtract 15 from each side

2x > 16

Divide by 2

2x/2 > 16/2

x > 8

There is an open circle at 8

The line goes to the right

Answer: 2 1/10, 3.122, 3.19, 61/10

Step-by-step explanation:

Let's first turn each number into decimal form: (1/10=.1, 2/10=.2,etc.)

2.1, 6.1, 3.122, 3.19.  Obviously, the smallest number is 2.1, because it has a 2 in the ones place.  Next, we see a tie in the ones place between 3.122 and 3.19.  Then we look at the tenths place and see another tie.  Then, at the hundredths place, we see that 3.19 is greater that 3.122.  Thus, the order of the numbers is 2.1,3.122,3.19,6.1.

Hope it helps <3

Answer: The correct answer is 94 cm.

Step-by-step explanation:

wingspan         length

60 meters        70.5 m

----------------- = ----------------

80 cm                   x

Cross multiply

(60 m)x = (70.5 m)(80 cm)

Solve for x by dividing both sides of equation by 60 m:

x = (70.5 m)(80 cm) / (60 m) = 94 cm

The length of the model is 94 cm.

Answer:

94 cm

Step-by-step explanation:

Write and solve an equation of ratios:

70.5 m       60 m

----------- = -----------

    L           80 cm

Cross multiplying, we get:

(70.5 m)(80 cm) = (60 m)L

                                                                     (70.5 m)(80 cm)

Then the model length, L, should be  L = -------------------------

                                                                              60 m

or

L = 94 cm

Corrected Question

The solution to an inequality is represented by the number line. How can this same solution be written using set-builder notation? {x | x > }

Answer:

[tex]\{x | x >3 \}[/tex]

Step-by-step explanation:

Given an inequality whose solution is represented by the number line attached below.

We observe the following from the number line

There is an open circle at 3, therefore the solution set does not include 3. (We make use of > or < in cases like that)

The arrow is pointed towards the right. All points to the right of 3 are greater than 3, therefore:

The solution in the number line can be written using set-builder notation as:

[tex]\{x | x >3 \}[/tex]

Answer:

  78π m²

Step-by-step explanation:

The lateral area of the cylinder is ...

  LA = 2πrh

  LA = 2π(3 m)(8 m) = 48π m²

The lateral area of one cone is ...

  LA = πrh . . . . where h is the slant height

  LA = π(3 m)(5 m) = 15π m²

Then the total surface area of the figure is the area of the two cones plus that of the cylinder:

  S = 2(cone area) + cylinder area

  S = 2(15π m²) +(48π m²)

  S = 78π m²

Answer: 9πcm²

Step-by-step explanation: area of the square= 36cm²

Therefore, the area of one side= √area = √36 = 6cms

Since the circle is touching the sides of the square, the side of the square = the diameter of the circle

Therefore the radius of the circle= side/2 = 3cm

The formula for the ares of the circle is πr²

π*3*3 = 9πcm²

Answer:

-3x^2-15x-30

Step-by-step explanation:

Follow order of operations

Answer:

-3x^2 -15x -30

Step-by-step explanation:

First you would square the parenthesis, and get x^2 +6x+9 inside the parenthesis, then you would multiply it by the -3 and get -3x^2 -18x-27-3+3x then you combine like terms to get the answer.

Answer:

The correct option is:

x+y = 2

Step-by-step explanation:

Street 1 is given.

If Street 2 is parallel to Street 1, then they will have the same slope.

Find slope of Street 1:

Take any 2 points on Street 1. Consider (-2,3) and (1,0)

Slope is given by:

m = (y₂ - y₁) / (x₂ - x₁)

m = 0-3 / 1-(-2)

m = -3/3

m = -1

For Street 2:

y = mx + c

y = -1x +c

As it passes through (-2,4), substitute the point in the above equation:

4 = -1(-2) + c

c = 2

So substitute m = -1 and c =2 into general form of equation:

y = mx + c

y = -x + 2

or

x+y = 2

Answer:

For the first question, there is a 39% chance for only boys and a 61% chance for only girls. For the second one it is, about 136 groups.

Step-by-step explanation:

100: 224 = 61:x → 61/100 = x/224

100x = 13664

x = 136.64 → 136 groups (You can't round up if you don't have enough people)

Hope this helped!

Answer: 39% chance for only boys and a 61% chance for only girls. For the second one it is, about 136 groups.

Step-by-step explanation:

:) The other answer is correct too! But just for clarification! :)