fully factor 9a2 + 24ab + 16b2

Answer:

The correct answer is first option

(2, 3)

Step-by-step explanation:

It is given that,

3y = -x + 11  and

x + 4y = 14

To find the solutions

The given equation can be written as,

x + 3y = 11 --------(1)

x + 4y = 14  -------(2)

Subtract (1)  from (2) we get

y = 3

Substitute vale of y in eq(1)

x + 3*3 = 11

x = 11 - 9 = 2

Therefore x = 2 and y = 3

The correct answer is first option

Answer:

first option

(2, 3)

Step-by-step explanation:

We have the following system of linear equations

[tex]\left \{{{3y=-x+11} \atop {x+4y=14}} \right.[/tex]

This is the same as

[tex]\left \{{{x + 3y=11} \atop {x+4y=14}} \right.[/tex]

To solve the system multiply the first equation by -1 and then add it to the second equation.

[tex]-1*(x+3y)=11*(-1)[/tex]

[tex]-x -3y=-11\\x+4y=14[/tex]

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

[tex]y = 14-11[/tex]

[tex]y = 3[/tex]

substitute [tex]y = 3[/tex] in any of the two equations and then solve for x

[tex]x+4(3)=14\\x+12=14\\x =14-12\\x = 2\\[/tex]

[tex]x =2[/tex]

The answer is the first option

(2, 3)

Answer:

2A/h = b

Step-by-step explanation:

A= (1/2)(b)(h)

Multiply each side by 2

2A = 2*1/2 *b*h

2A = bh

Divide each side by h

2A/h = bh/h

2A/h = b

Step-by-step explanation:

all work is pictured and shown

Since f(d) and g(d) represent two types of discounts that you will receive off of the price, the composite function is f(g(d)) = 0.8d - 15.

In Mathematics and Geometry, a function composition is an operation (∘) that combines two functions f(x) and g(x), in order to produce a composite function h(x) = (g∘f)(x), such that h(x) = g.

In this exercise, we would determine the corresponding output values for the composite functions by using the substitution method as follows;

f(g(d)) = 0.8d - 15

In this context, we can reasonably infer and logically deduce that the composite function is f(g(d)) = 0.8d - 15.

Complete Question:

You go to a store to buy sneakers f(d) and g(d) represent two types of discounts that you will receive off of the price of the sneakers that you want.

Find f(g(d))

f(d)=d-15

g(d)=0.8d

Answer:

[tex]\$1,598.23[/tex]  

Step-by-step explanation:

we know that

The formula to calculate continuously compounded interest is equal to

[tex]A=P(e)^{rt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

[tex]t=7\ years\\ P=\$740\\ r=0.11[/tex]  

substitute in the formula above  

[tex]A=\$740(e)^{0.11*7}[/tex]  

[tex]A=\$1,598.23[/tex]  

Answer:

9[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

Simplify each radical before summing

[tex]\sqrt{8}[/tex] = [tex]\sqrt{4(2)}[/tex] = 2[tex]\sqrt{2}[/tex]

3[tex]\sqrt{2}[/tex] is in simplified form

[tex]\sqrt{32}[/tex] = [tex]\sqrt{16(2)}[/tex] = 4[tex]\sqrt{2}[/tex]

Hence

2[tex]\sqrt{2}[/tex] + 3[tex]\sqrt{2}[/tex] + 4[tex]\sqrt{2}[/tex] = 9[tex]\sqrt{2}[/tex]

Answer:

The range is f(x) ≥ 0

Step-by-step explanation:

The range of the function is defined as the set of values of the dependent variable for which the function is defined.

Here the function f(x) = 1/2 √x is defined for all values of x which are greater than or equal to zero or we can say all non-negative real numbers.

So, the range is  f(x) ≥ 0

Final answer:

The range of the function f(x) = ½√x is all real numbers greater than or equal to 0, which is written in interval notation as [0, ∞).

Explanation:

The range of a function is the set of all possible output values it can produce. For the function f(x) = ½√x, the domain (input values) must be non-negative because we cannot take the square root of a negative number in the real number system. Since the smallest non-negative number is 0 and the value of the function at x=0 is f(0) = ½√0 = 0, the function starts at 0. The square root function increases as its input increases; thus, for any positive value of x, you get a positive value for f(x). Moreover, as x approaches infinity, the output of the function also grows without any upper bound, although it does so slower than the increase in x.

Therefore, the range of the function f(x) = ½√x is all real numbers greater than or equal to 0, which can be written in interval notation as [0, ∞).

Answer:

5 • (9x2 + 5)

 ———————

       9      

Step-by-step explanation:

Step  1  :

           25

Simplify   ——

           9  

Equation at the end of step  1  :

               25

 (5 • (x2)) +  ——

               9  

Step  2  :

Equation at the end of step  2  :

        25

 5x2 +  ——

        9  

Step  3  :

Rewriting the whole as an Equivalent Fraction :

3.1   Adding a fraction to a whole  

Rewrite the whole as a fraction using  9  as the denominator :

           5x2     5x2 • 9

    5x2 =  ———  =  ———————

            1         9  

Hope this helps! Please mark brainliest!

Answer: C) 6.0025

Step-by-step explanation:

The equation for the area of a circle requires the radius, you put in the full diameter. Just divide 4.9 by 2, which gives you 2.45. 2.45 squared is equal to 6.0025 and then slap your pi on to the end of it.

Answer:

[tex]6.0025\pi \: {m}^{2} [/tex]

Step-by-step explanation:

The formula for the area of a circle:

[tex]\pi \times {r}^{2} [/tex]

We are given the diameter of the circle, which is two times its radius. To find the radius, we divide the diameter by 2.

4.9 ÷ 2 = 2.45 m^2.

Now we need to square the radius:

[tex] {2.45}^{2} = 6.0025[/tex]

So, the area in terms of pi would be

[tex]\pi \ \times {6.0025}^{2} \: {m}^{2} [/tex]

Or

[tex]6.0025 \times \pi \: {m}^{2} [/tex]

Hope this helps!

Answer:

-2

Step-by-step explanation:

Isolate the variable y. Note the equal sign, what you do to one side, you do to the other. Divide 3 from both sides:

(3y)/3 = (15 - 6x)/3

y = (15 - 6x)/3

y = 5 - 2x

Note the equation:

y = mx + b

m = slope

b = y-intercept

x & y = the point (x , y)

Note that the slope is directly next to x. -2 is your answer.

~

For this case we have by definition, that the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

We have the following equation:

[tex]3y = 15-6x\\y = \frac {15} {3} - \frac {6x} {3}\\y = 5-2x\\y = -2x + 5[/tex]

So we have to:

[tex]m = -2[/tex]

Answer:

The slope is -2

Answer:

Theoretical  P(3) = 1/6

Experimental P(3) = 67/450

Step-by-step explanation:

A die has 6 possibilities that can come up {1,2,3,4,5,6}  They are all equally likely, so each has a probability of 1/6

a  P(getting a 3) = 1/6

We rolled a 3 67 times out of 450.  This is our experimental probability

b P (getting a 3) = 67/450

This does not simplify

As your math teacher, let's solve this problem together step by step.

a. Theoretical Probability of Rolling a 3:
A standard number cube, often referred to as a die, has six faces numbered 1 through 6. Since all faces are usually designed to be equally probable, the theoretical probability of rolling a three (or any specific number) is the ratio of the number of successful outcomes (rolling a 3) to the total number of possible outcomes (any number from 1 to 6).

So,

Theoretical Probability = Number of successful outcomes / Total number of possible outcomes
                       = 1 / 6

This is already in the simplest form since 1 and 6 have no common divisors other than 1.

b. Experimental Probability of Rolling a 3:
The experimental probability, in contrast to the theoretical probability, is determined based on actual trials or experiments. In this case, the cube was rolled 450 times, and the number 3 appeared 67 times.

So,

Experimental Probability = Number of times a 3 was rolled / Total number of rolls
                        = 67 / 450

Now, to simplify the fraction, you would find the greatest common divisor (GCD) of 67 and 450 and divide both numerator and denominator by that GCD.

Looking at the numbers, they do not immediately suggest a common factor, and since 67 is a prime number, we can reasonably conclude that the fraction is already in its simplest form. Therefore, the experimental probability is:

                        = 67 / 450

So there you have it, answers to both questions in their simplest form:

a. The theoretical probability of rolling a 3 on a number cube is 1/6.
b. The experimental probability of rolling a 3 given the cube is rolled 450 times and 3 comes up 67 times is 67/450.

Answer:

The shorter piece is 10 in. and the longer one is 50 in.

Step-by-step explanation:

First, let's set the shorter piece to be length x. Then the longer piece is 5x, or 5 times longer than the shorter piece.

Since both pieces combined equals to the length of the entire board, we can set these two lengths equal to it:

x + 5x = 60

And now solve for x:

6x = 60

x = 10 in (length of shorter piece)

Now let's find the length of the longer piece:

Longer = 5x = 5(10) = 50 in.

Answer:

LCM of 24, 36  = 72

Step-by-step explanation:

24 = 24, 48, 72, 96

36 = 36, 72, 109

Answer:

The LCM of 24 and 36 = 72

Step-by-step explanation:

Find and list multiples of each number until the first common multiple is found. This is the lowest common multiple.

Multiples of 24:

24, 48, (72), 96, 120

Multiples of 36:

36, (72), 108, 144

Hope this helped!

Answer:

see below

Step-by-step explanation:

y > 6x + 7  

y < 6x + 9  

check one by one  

A. (3, 26)  

26 > 6(3) + 7→ 26 > 25 yes  

26 < 6(3) + 9→ 26 < 27 yes  

B. (-4, 32)  

32 > 6(-4) + 7→ 32 > -17 yes  

32 < 6(-4) + 9→ 32 < -15 no  

C. (3, 25)  

25 > 6(3) + 7→ 25 > 25 no  

25 < 6(3) + 9→ 25 < 27 yes  

DB. (4, 33)  

33 > 6(4) + 7→ 33 > 31 yes  

33 < 6(4) + 9→ 33 < 33 no  

Final answer:

Points a (3, 26) and b (-4, 32) are solutions to the system of inequalities y>6x+7 and y<6x+9. Points c (3, 25) and d (4, 33) do not satisfy both inequalities, so they are not solutions.

Explanation:

To determine which points are solutions to the given system of inequalities, y > 6x + 7 and y < 6x + 9, we need to check if they satisfy both inequalities:

Point a (3, 26): 26 > 6(3) + 7 and 26 < 6(3) + 9, which simplifies to 26 > 25 and 26 < 27. Both are true, so point a is a solution.

Point b (-4, 32): 32 > 6(-4) + 7 and 32 < 6(-4) + 9, which simplifies to 32 > -17 and 32 < -15. Both are true, so point b is also a solution.

Point c (3, 25): 25 > 6(3) + 7 and 25 < 6(3) + 9, which simplifies to 25 > 25 and 25 < 27. The first inequality is not true (it is equal, not greater), so point c is not a solution.

Point d (4, 33): 33 > 6(4) + 7 and 33 < 6(4) + 9, which simplifies to 33 > 31 and 33 < 33. Similar to point c, the second inequality is not true (it is equal, not less), so point d is not a solution.

Points a and b satisfy both inequalities and are correct solutions to the system.

Answer:

3x^2-x-6

Step-by-step explanation:

f-g means you are going to do (3x^2-4)-(x+2)

3x^2-4-x-2

Combine like terms

3x^2-x-6

Answer:

[tex](f-g) (x) = 3x ^ 2- x - 6[/tex]

Step-by-step explanation:

We have the following functions

[tex]f (x) = 3x ^ 2-4[/tex]

[tex]g (x) = x + 2[/tex]

To find [tex](f-g) (x)[/tex] we must subtract the function f(x) with the function g (x)

Then we perform the following operation

[tex](f-g) (x) = 3x ^ 2-4- (x + 2)[/tex]

[tex](f-g) (x) = 3x ^ 2-4- x - 2[/tex]

[tex](f-g) (x) = 3x ^ 2- x - 2-4[/tex]

Finally we have that:

[tex](f-g) (x) = 3x ^ 2- x - 6[/tex]

Answer:

yes you start solving whats in the parentheses

Step-by-step explanation:

In algebra you use the order of operations or PEMDAS

PEMDAS is a way to help you remember what you solve first

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Answer:

A cone is a three dimensional solid with a circle at its cross section

Answer:

The answer is cone.

Step-by-step explanation:

A cone is a three dimensional figure, whose cross section parallel to its base, gives a circle because the base of the cone is a circle.

A cross section is defined as the slicing of a three dimensional figure to get a two dimensional figure.

Here, cone is a three dimensional figure and circle is a two dimensional figure.

So, the answer is cone.

Answer:

(2x^2)(y^16)

Step-by-step explanation:

Answer:

y=-ax(x-500)^2(x-1000)

Step-by-step explanation:

The slope is given as 1.

The Y-intercept is where the line crosses the Y axis when X is 0. This is also given by the point (0,5/6). X is 0 and Y is 5/6, so the Y-intercept is 5/6.

The equation of a line is given as y = mx +b where m is the slope and b is the y-intercept.

The equation is: y = x +5/6

Answer:

y = x+5/6

Step-by-step explanation:

The slope intercept form of the equation of a line is

y = mx +b

We are given the slope of 1 and the y intercept of 5/6 (The y intercept is when x=0)

y = 1x+5/6

y = x+5/6

Answer:

Step-by-step explanation:

The intercept form of a quadratic equation (parabola):

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

p, q - x-intercepts

Therefore

The function f(x) = x(x - 6) = (x - 0)(x - 6) has two x-intercepts at (0, 0) and (6, 0)

The function f(x) = (x - 6)(x - 6) has only one x-intercept at (6, 0)

The function f(x) = (x + 6)(x - 6) = (x - (-6))(x - 6)

has two x-intercept at (-6, 0) and (6, 0)

The function f(x) = (x + 1)(x + 6) = (x - (-1))(x - (-6))

has two x-intercepts at (-1, 0) and (-6, 0).

Answer:

the answer is d on edge

Step-by-step explanation:

Answer:

D.) x^2-3x-5

Step-by-step explanation:

f(x)=3x+5

g(x)=x^2 .

Find g(x)-f(x)

g(x) - f(x)=  x^2 -(3x+5)

Distribute the minus sign        

 x^2 -3x-5

Answer:

x² - 3x - 5 ⇒ answer D

Step-by-step explanation:

* Lets explain how to solve the problem

- There are two functions f(x) ang g(x)

- f(x) = 3x + 5 ⇒ it is a linear function

- g(x) = x² ⇒ it is a quadratic function

- Both functions have a domain the set of real numbers

- We want to subtract f(x) from g(x)

* Lets solve the problem

∵ g(x) = x²

∵ f(x) = 3x + 5

∵ f(x) will subtracted from g(x)

∴ g(x) - f(x) = (g - f)(x)

- Lets make the subtraction

∴ (g - f)(x) = x² - (3x + 5)

- Open the bracket by multiply the negative sign by the two terms

 of the bracket

∵ -(3x) = - 3x

∵ -(5) = - 5

∴ (g - f)(x) = x² - 3x - 5

∴ g(x) - f(x) = x² - 3x - 5

Answer:

[tex]2x^2 - 8x + 6[/tex]

Step-by-step explanation:

Use the FOIL method of multiplying binomials.

First term in each binomial: [tex]x * 2x = 2x^2[/tex]

Outside terms: [tex]x * -2 = -2x[/tex]

Inside terms: [tex]-3 * 2x = -6x[/tex]

Last term in each binomial: [tex]-3 * -2 = 6[/tex]

Now, add them all together.  [tex]2x^2 - 2x - 6x + 6[/tex]

Simplified, this equals [tex]2x^2 - 8x + 6[/tex], which is the answer.

Answer:

34 degrees

Step-by-step explanation:

The measure of the angle ∠VXZ will be 34°. Then the correct option is C.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

The measure of the angle ∠VXZ will be given as,

∠VXZ = 1/2(93 – 25)

∠VXZ = 1/2(68)

∠VXZ = 34°

Then the correct option is C.

More about the angled link is given below.

https://brainly.com/question/15767203

#SPJ2

Answer:

[tex](x-3)^{2}+(y+2)^{2}=49[/tex]

Step-by-step explanation:

The center-radius form of the equation of a circle is in the format;

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

with the center being at the point (h, k) and the radius being r units.

We simply plugin the values of the center and radius given in order to determine the equation of the circle;

The equation of the circle with center (3, -2) and radius 7 is;

[tex](x-3)^{2}+(y+2)^{2}=49[/tex]

Answer:

[tex](x-3)^2 + (y+2)^2 = 49[/tex]

Step-by-step explanation:

The general equation of a circle has the following form:

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

Where the point (h, k) represents the center of the circle and r represents the radius

In this case we know that the center is (3, -2) and the radius is 7.

Therefore:

[tex]h=3\\k = -2\\r=7[/tex]

Finally the equation of the circle is:

[tex](x-3)^2 + (y-(-2))^2 = 7^2[/tex]

[tex](x-3)^2 + (y+2)^2 = 49[/tex]

Answer:

$1424.10

Step-by-step explanation:

APEX is obnoxious, I understand.

Answer:1424.10

Step-by-step explanation:

Answer: area of the base = 32 m²

Step-by-step explanation:

Cylinder volume is the product of area of the base by height.

Then, area of the base = cylinder volume/height = 288m³/9m = 32 m²

Answer: area of the base = 32 m²

[tex]\textit{\textbf{Spymore}}[/tex]

total bill before any discounts $13.

she is a student, so she gets 20% off.

she brought an item of clothing, so she gets 5% off.

so she's really getting 20% + 5% off, namely 25% off her bill.

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{25\% of 13}}{\left( \cfrac{25}{100} \right)13\implies 3.25}~\hfill \stackrel{\textit{bill with all discounts}}{13-3.25\implies 9.75}[/tex]

Answer:

see explanation

Step-by-step explanation:

Given

[tex]\frac{1-\sqrt{5} }{1+\sqrt{5} }[/tex]

Multiply the numerator and denominator by the conjugate of the denominator

The conjugate of 1 + [tex]\sqrt{5}[/tex] is 1 - [tex]\sqrt{5}[/tex], hence

[tex]\frac{(1-\sqrt{5})(1-\sqrt{5})  }{(1+\sqrt{5})(1-\sqrt{5})  }[/tex]

Expand numerator/ denominator

= [tex]\frac{1-2\sqrt{5}+5 }{1-5}[/tex]

= [tex]\frac{6-2\sqrt{5} }{-4}[/tex]

= [tex]\frac{6}{-4}[/tex] + [tex]\frac{-2\sqrt{5} }{-4}[/tex]

= - [tex]\frac{3}{2}[/tex] + [tex]\frac{1}{2}[/tex] [tex]\sqrt{5}[/tex]

Answer:

-3/2  + (1/2)*sqrt(5)

Note: a=-3/2 , b=1/2 , c=5

Step-by-step explanation:

I think this is meant to be written as (1-sqrt(5))/(1+sqrt(5)).

First step: Multiply top and bottom by the conjugate of the bottom which is 1-sqrt(5).

When you multiply conjugates, you do have to do the whole foil thing... just do first and last  because the others will cancel.

So what I'm saying is when multiply (1+sqrt(5))(1-sqrt(5)) you will get 1-5=-4.

Second step: Multiply top out... you have to do the whole foil here because you aren't multiplying conjugates. So (1-sqrt(5))(1-sqrt(5))=1-sqrt(5)-sqrt(5)+5=

1-2sqrt(5)+5=6-2sqrt(5).

Third step:  Second step/first step =(6-2sqrt(5))/-4

Fourth step: Separate fraction 6/-4       -      2sqrt(5)/-4

Fifth step:  Simplify each fraction:  -3/2  + (1/2)*sqrt(5)

Sixth step:  If you compare the form you want it in to the form I wrote my answer in, then you should see that a=-3/2 , b=1/2 , c=5

Answer:

x = 9

Step-by-step explanation:

Use the equation of the line, and let y = 0. Then solve for x.

y = 2/3 x - 6

Let y = 0:

0 = 2/3 x - 6

Add 6 to both sides.

6 = 2/3 x

Multiply both sides by 3/2.

3/2 * 6 = x

x = 9