How many solutions does the system have?
8x+ 2y = 14
8x+ 2y =4
Choose 1 answer:
A. Exactly one solution
B. No solutions
C. Infinitely many solutions

If [tex]3x-4[/tex] is a factor of [tex]p(x)=-6x^3-7x^2+qx-12[/tex], then [tex]x=\frac43[/tex] is a root of [tex]p(x)[/tex] so that [tex]p\left(\frac43\right)=0[/tex]:

[tex]-6\left(\dfrac43\right)^3-7\left(\dfrac43\right)^2+q\left(\dfrac43\right)-12=0[/tex]

[tex]\dfrac{4q-116}3=0[/tex]

[tex]4q-116=0[/tex]

[tex]4(q-29)=0[/tex]

[tex]\implies\boxed{q=29}[/tex]

Answer:

All whole numbers are integers. AND All natural numbers are rational numbers.

Step-by-step explanation:

Answer:

The answer is D and E

Step-by-step explanation:

Answer:

r = 4.

Step-by-step explanation:

0.4r = 1.6

4r = 16

2r = 8

r = 4.

0.4(4) = 1.6

1.6 = 1.6

Hope this helps!

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

Work Shown:

b = 5

(2b)^2 = (2*5)^2 = 100

So we want the expression a^2+3b to be less than (2b)^2 = 100

We need to solve a^2 + 3b < 100 which turns into

a^2 + 3b < 100

a^2 + 3(5) < 100

a^2 + 15 < 100

after substituting in b = 5.

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

Let's isolate 'a'

a^2 + 15 < 100

a^2 < 100-15

a^2 < 85

a < sqrt(85)

a < 9.2195

'a' is an integer, so we round down to the nearest whole number to get [tex]a \le 9[/tex]

So the greatest integer possible for 'a' is a = 9.

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

Check:

plug in a = 9 and b = 5

a^2 + 3b < 100

9^2 + 3(5) < 100

81 + 15 < 100

96 < 100 .... true statement

now try a = 10 and b = 5

a^2 + 3b < 100

10^2 + 3(5) < 100

100 + 15 < 100 ... you can probably already see the issue

115 < 100 ... this is false, so a = 10 doesn't work

Answer:

9

Step-by-step explanation:

I just did the question on AOPS, please see the attachment down below.

Hope this helped! :)

f(3) = 13

f(x) = 2x + 7

replace x with 3

f(3) = 2×3 + 7

= 6 + 7

= 13

Answer: 30.85%.

Step-by-step explanation:

Let X denotes the score of  random student.

Given: [tex]\mu = 50[/tex] and [tex]\sigma=10[/tex]

We assume that scores are normally distributed.

Then , the probability that a a student score higher than 55:

[tex]P(X>55)=P(\dfrac{X-\mu}{\sigma}>\dfrac{55-50}{10})\\\\=P(Z>0.5) \ \ [Z=\dfrac{X-\mu}{\sigma}]\\\\=1-P(Z<0.5)\\\\=1-0.6915\ [\text{By p-value table for z}]\\\\= 0.3085[/tex]

Hence, the percent of students have a higher score than hers is 30.85%.

Answer:

Bacterial population at the time of 10 hours = 1040000

Step-by-step explanation:

Let the function that defines the bacterial population after 'x' hours is,

p(x) = a(b)ˣ

Where a = Initial population

And 'x' = Duration or time

Since bacterial population is getting doubled every hour,

2a = a(b)¹

b = 2

Therefore, function will be,

p(x) = a(2)ˣ

From the graph attached,

Point (5, 32500) lies on the graph of the function.

32500 = a(2)⁵

a = [tex]\frac{32500}{32}=1015.625[/tex]

Therefore, the function will be,

p(x) = 1015.625(2)ˣ

For x = 10 hours,

p(10) = 1015.625(2)¹⁰

        = 1040000 bacteria

Answer:

422 cm²

Step-by-step explanation:

Surface area of the composite figure = (surface area of the upper cuboid + surface area of lower cuboid) - 2(base area of the lower cuboid)

Surface area of composite figure = [tex] (2(lw + lh + hw)) + (2(lw + lh + hw)) - 2(l*w) [/tex]

Upper cuboid has the following dimensions:

[tex] l = 4, w = 3, h = 8 [/tex]

Lower cuboid has the following dimensions:

[tex] l = 10, w = 7, h = 5 [/tex]

Plug these values into the formula

Surface area of composite figure

[tex] = (2(4*3 + 4*8 + 8*3)) + (2(10*7 + 10*5 + 5*7)) - 2(4*3) [/tex]

[tex] = (2(12 + 32 + 24)) + (2(70 + 50 + 35)) - 2(12) [/tex]

[tex] = (136 + 310) - 24 [/tex]

[tex] = 446 - 24 = 422 [/tex]

Surface area of composite figure = 422 cm²

Answer:

7 + 8i

Step-by-step explanation:

Conjugate of 7 - 8i is 7 + 8i

Answer:

Step-by-step explanation:

7+8i

Rayne sell each desk at the price of $125.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given the following information;

The Number of desks sold = 3

The Amount of rent paid = $4

The Amount paid to carpenter = 1/2 of revenue

The Amount left = $185.50

If Rayee gave half of his revenue to the carpenter and then had $185.50 left.

The his revenue before paying the carpenter will be twice what he has left will be;

($185.50 * 2) = $371

Hence, the total revenue from the sale of 3 desk = ($371 + rent)

= (371 + 4)

= $375

Then each desk cost :

$375 / 3 = 125

Hence, Rayne sell each desk at the price of $125.

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The addition is one of the four fundamental mathematical operations. The selling price of each desk is $122.33.

The addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.

Revenue generated = Revenue left with Rayne + Revenue with carpenter

Since Rayne gave half of his revenue to the carpenter, therefore, both of them will have the same revenue will them

Revenue generated = Revenue left with Rayne + Revenue left with Rayne

Revenue generated = 2(Revenue left with Rayne)

Revenue generated = 2($185.50)

Revenue generated = $371

Also, Rayne paid a booth rent of $4. Therefore, the total revenue generated will be,

Total revenue generated = Revenue generated + $4

                                          = $371 + $4

                                          = $367

Since Rayne sell 3 desks, therefore, the selling price of each desk will be,

Selling price = $367 / 3

                     = $122.33

Hence, the selling price of each desk is $122.33.

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Answer:

A general way of explaining this is

Suppose that we have a given property (or a pattern if we are working with a series of numbers):

Now, if that property is true, for example, for the numbers 1, 2, 3... etc.  Then we can suppose that the property is also true for an unknown number N.

Now, if using the hypothesis that the property is true for N, we can prove that the property is also true for N + 1, then we actually proved that the property is true for all the set.

We actually can use any set, not only the natural numbers.

For example, we can use the set of the even numbers {2, 4, 6, 8....}, suppose that the property is true for a random number N, that is even, and then see if using that hypothesis we can prove that the property is also true for the next number in the set; N + 2.

Answer:

0.0208333...

Step-by-step explanation:

You would just divide 7 seconds by 3600 seconds (1 hr) and that would be ur answer so in this case it would be 0.0208333...

Answer:

1/48 or 0.02083 hours

Step-by-step explanation:

75s×1 min/60s×1 hour/60 mins so the seconds and minutes cancel out and you are left with 75/3600=1/48 hours

Answer:

712,402,207

Step-by-step explanation:

;)

Answer: 711,142,207

Step-by-step explanation:

Answer:

S = 6x² + 5x - 6

5544 sq. units

Step-by-step explanation:

Area of parallelogram is:

Given:

Then:

S = 6x² + 5x - 6

If x = 30, then plug it in the equation:

Answer:

Step-by-step explanation:

[tex] \sf{6(4 - y) = 5 + 3}[/tex]

Distribute 6 through the parentheses

[tex] \sf{24 - 6y = 5 + 3}[/tex]

Add the numbers

[tex] \sf{24 - 6y = 8}[/tex]

Move constant to right hand side and change it's sign

[tex] \sf{ - 6y = 8 - 24}[/tex]

Calculate

[tex] \sf{ - 6y = - 16}[/tex]

Divide both sides of the equation by -6

[tex] \sf{ \frac{ - 6y}{ - 6} = \frac{ - 16}{ - 6} }[/tex]

Calculate

[tex] \sf{y = 2.6}[/tex]

Hope I helped!

Best regards!!

Answer: Hi!

First, we need to distribute 6 to the terms inside of the parentheses, 4 and -y.

6 * 4 = 24

6 * (-y) = -6y

Our equation now looks like this:

24 - 6y = 5 + 3

We can now combine like terms.

24 - 6y = 5 + 3

5 + 3 = 8

Our equation now looks like this:

24 - 6y = 8

We can now use inverse operations to get rid of 24. Remember, our goal is to isolate the x. The inverse operation for addition (24 is positive) is subtraction, so we subtract 24 on both sides:

 24 - 6y = 8

- 24       - 24

Our equation now looks like this:

-6y = -16

Last step! We now use inverse operations to get rid of -6. The inverse operation for multiplication is division (-6 is being multiplied by y); so we divide -6 on both sides.

-6y/-6 = y

-16/-6 = 8/3 = 2 2/3

Our equation now looks like this:

y = 2 2/3

Therefore, your solution is 2 2/3.

Hope this helps!

Answer:

[tex]\boxed{ x = \sqrt{8.5} }[/tex]

Step-by-step explanation:

Hey there!

Irrational numbers are numbers that cannot be expressed as fractions.

[tex]\sqrt{8.5}[/tex]

=2.915475947422650235437076438772791538260699167442985977225003372433905030998356313832620163226517699278394811037677455675906936808085403142951613039412223590832527179885119634084324188271634828210865

The shown decimal goes on for 200 digits.

And it cannot be put into fraction form, meaning it is irrational.

Hope this help :)

Literally, irrational numbers are numbers that cannot be expressed as simple fractions. Some irrational numbers between 7 and 10 are 7.4833,7.9372,8.3666,8.4852,9.4868.

Given that

[tex]Min = 7[/tex]

[tex]Max = 10[/tex]

There are several ways to generate the irrational numbers between the given range.

One of the ways is as follows:

First, we list the pairs of relatively prime integers between the given range.

They are:

[tex]x = \{(7,8),(7,9),(7,10),(8,9),(9,10)\}[/tex]

Calculate the product

[tex]x = \{56,63,70,72,90\}[/tex]

Take the positive square root of the numbers to generate some irrational integers

[tex]x = \{\sqrt{56},\sqrt{63},\sqrt{70},\sqrt{72},\sqrt{90}\}[/tex]

[tex]x = \{7.4833...,7.9372....,8.3666...,8.4852....,9.4868....\}[/tex]

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Answer:

25x - 15

Step-by-step explanation:

Indian books = malay books - 15

=4x -15

Total books =

English books + chinese books + malay + indian

= 12x + 5x + 4x + 4x -15

= 25x - 15

Answer:

Step-by-step explanation:

Indian books = 4x - 15

Total books = 12x + 5x + 4x + 4x - 15  {add like terms}

                     = 25x - 15

Composite functions are multiple functions combined to form another function.

The value of the composite function (p - q)(2) is 5

To find (p - q)(2), we make use of the following composite function formula:

[tex](p - q)(x) = p(x) - q(x)[/tex]

Substitute 2 for x in the above formula

[tex](p - q)(2) = p(2) - q(2)[/tex]

From the table entries, we have:

[tex]p(2) =3[/tex]

[tex]q(2) = -2[/tex]

So, the equation becomes

[tex](p - q)(2) = 3 -- 2[/tex]

Rewrite the above equation as:

[tex](p - q)(2) = 3 + 2[/tex]

Take the sum of 3 and 2

[tex](p - q)(2) = 5[/tex]

Hence, the value of (p - q)(2) is 5

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Answer:

x = -16/5  or

x = 6/5

Step-by-step explanation:

[tex]-\left|5+5x\right|-9=-20\\\\\mathrm{Add\:}9\mathrm{\:to\:both\:sides}\\-\left|5+5x\right|-9+9=-20+9\\\\Simplify\\-\left|5+5x\right|=-11\\\\\mathrm{Divide\:both\:sides\:by\:}-1\\\\\frac{-\left|5+5x\right|}{-1}=\frac{-11}{-1}\\\\\left|5+5x\right|=11\\\\\mathrm{Apply\:absolute\:rule}:\\\\\mathrm{If}\:|u|\:=\:a,\:a>0\:\mathrm{then}\:u\:=\:a\:\quad \mathrm{or}\quad \:u\:=\:-a\\5+5x=-11\quad \mathrm{or}\quad \:5+5x=11\\\\5+5x=-11\quad :\quad x=-\frac{16}{5}\\\\5+5x=11\quad :\quad x=\frac{6}{5}\\[/tex]

[tex]x=-\frac{16}{5}\quad \mathrm{or}\quad \:x=\frac{6}{5}\\[/tex]

The value of x after solving the expression -|5 + 5x| - 9 = -20 is equal to x  = -16/5 or x = 6/5.

What do you mean by algebraic expressions ?

Algebraic expression is an equation which consists of variables and the arithmetic operations such as division , multiplication , etc.

The algebraic expression given is -|5 + 5x| - 9 = -20

We know that a modulus sign is a representation of  ran absolute value which has two values either a positive or negative value.\

After solving the expression we get :

-|5 + 5x| - 9 = -20

So , after removing the modulus sign we will get two expressions :

-(-(5 + 5x) - 9 = -20

5 + 5x = -11

or

-(5 + 5x) - 9 = -20

-(5 + 5x) = -11

Solving the two expressions we get the value of x as :

x  = -16/5

or

x = 6/5

Therefore , the value of x after solving the expression -|5 + 5x| - 9 = -20 is equal to x  = -16/5 or x = 6/5.

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Answer:

20 m

Step-by-step explanation:

The maximum height is given by the vertex form of the equation, that is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Given

h(t) = - 5t² + 20t ← factor out - 5 from each term

      = - 5(t² - 4t)

Using the method of completing the square

add/subtract ( half the coefficient of the t- term)² to t² - 4t

h(t) = - 5(t² + 2(- 2)t + 4 - 4 )

      = - 5(t - 2)² + 20 ← in vertex form

with vertex = (2, 20 )

The maximum height is at the value of k = 20

That is the maximum height is 20 m

Answer:

D. is the answer

The equation that represents a circle with a center at (–3, –5) and a radius of 6 units is given by:

[tex](x + 3)^2 + (y + 5)^2 = 36[/tex]

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

In this problem, we have that:

Hence:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

[tex](x + 3)^2 + (y + 5)^2 = 36[/tex]

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Answer:

A

Step-by-step explanation:

x      y

-5   -22

0     -2

3     10

Answer:

341.25in²

Step-by-step explanation:

Width=x

Length=x+2

X+x+x+2+x+2=74

4x+4=74

4x=70

x=17.5

width=x=17.5

length=x+2=19.5

A=LW

A=17.5*19.5

A=341.25in²

Answer:

1/6

Step-by-step explanation:

There are six factors of 12: 1, 2, 3, 4, 6, and 12.

So the probability that the chosen factor is 4 is 1/6.

s=d/t

Step-by-step explanation:

s=16.5/0.5

s=33

33 km/h since 30 min is half an hour

Answer:

Step-by-step explanation:

Distance ( d ) = 16.5 km

Time ( t ) = 30 minutes

( To convert minutes to hour , divide the minutes by 60)

Time ( t ) = [tex] \sf{ \frac{30}{60} }[/tex] = [tex] \sf{0.5}[/tex] hours

Now, let's find the speed

Speed = [tex] \sf{ \frac{distance \: travelled \: ( \: in \: km)}{time \: taken \: ( \: in \: hrs)} }[/tex]

plug the values

⇒[tex] \sf{ \frac{16.5}{0.5} }[/tex]

Calculate

⇒[tex] \sf{33 \: km/h}[/tex]

Hope I helped !

Best regards!!

Greetings from Brasil...

As said:

1° angle: X

2° angle: 2X

3° angle: 20 + 5X

"...The sum of the measures of the angles of a triangle is 180 degrees..."

(1° angle) + (2° angle) + (3° angle) = 180

X + 2X + (20 + 5X) = 180

X + 2X + 5X = 180 - 20

8X = 160

X = 160/8

X = 20

But the problem asks for the value of each angle. Thus

1° angle: X

as X = 20, so

1° angle: X = 20

2° angle: 2X

as X = 20, so

2° angle: 2.20 = 40

3° angle: 20 + 5X

as X = 20, so

3° angle: 20 + 5.20 = 20 + 100 = 120

The values of the first, second, and third angles are 20°, 40° and 120° respectively.

Let the first angle = x

Let the second angle = 2 × x = 2x

Let the third angle = 20 + (5 × x) = 20+5x

Total angles in the triangle = 180°

Based on the information above, the angles will be calculated thus:

x + 2x + 5x + 20 = 180

Collect like terms

8x = 180 - 20

8x = 160

x = 160/8

x = 20

First angle = 20°

Second angle = 2x = 2 × 20° = 40°

Third angle = 5x + 20 = (5 × 20°) + 20° = 120°

The angles are 20°, 40°, and 120°

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Answer:

  D. f(1) = 4, f(n) = –1/2f(n – 1) for n > 1

Step-by-step explanation:

We assume your sequence is supposed to be ...

  4, -2, 1, -1/2, 1/4, ...

This has no common difference, but it has a common ratio of -1/2. That is, the first term is 4, and each successive term is -1/2 times the previous one. The function is described by the recursive formula ...

  f(1) = 4;

  f(n) = -1/2·f(n-1)