Write the expression 5x(x + 9) - 7(x + 9) in complete factored form.
A. (x + 9)(x + 9)
B. (5x - 7)(x+9)
C. (5x – 7)(x + 9)(x + 9)
D. (5x2 + 45x)(-7x - 63)

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:

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.

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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:

B

Step-by-step explanation:

So, for this problem, it is only asking for vertex A, so you only have to apply the transformations to one point (unless you want to find out where the other points are at).

Vertex A is at (-4,2).

The triangle is first translated 2 units right and 5 units down.

So to find the coordinate of that you have to understand that is you translate something right or left, the x value will change. And if it's up or down, the y value will change. If you are going right or up, the amount it's moved will be added. And left or down will be subtracted.

-4+2=-2 (so the new x-value will be -2)

2-5=-3 (so the new y-value will be -3)

Thus vertex A' is (-2,-3).

Now for the next transformation.

(-2,-3) is moved 5 units right and 4 units up.

-2+5=3 (so x-value will be 3)

-3+4=1 (so the y-value will be 1)

SO, the new coordinate of vertex A" is...

(3,1)! aka B

(Also, you can just illustrate this on a graph but i'm showing it to you this way because when you get more advanced the amount it is being translated will be much higher.)

Answer: The answer is B

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]

Answer:

[tex]x = 5+\sqrt{31}\,\, and\,\, x=5-\sqrt{31}[/tex]

Step-by-step explanation:

We need to solve the quadratic equation

6 = x^2 -10x

Rearranging we get,

x^2-10x-6=0

Using quadratic formula to solve the quadratic equation

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

a= 1, b =-10 and c=6

Putting values in the quadratic formula

[tex]x=\frac{-(-10)\pm\sqrt{(-10)^2-4(1)(-6)}}{2(1)}\\x=\frac{10\pm\sqrt{100+24}}{2}\\x=\frac{10\pm\sqrt{124}}{2}\\x=\frac{10\pm\sqrt{2*2*31}}{2}\\x=\frac{10\pm\sqrt{2^2*31}}{2}\\x=\frac{10\pm2\sqrt{31}}{2}\\x = 5\pm\sqrt{31}[/tex]

So, [tex]x=5+\sqrt{31}\,\, and\,\, x=5-\sqrt{31}[/tex]

Answer:

The solutions are:

x1= 5 +√31

x2= 5 -√31

Step-by-step explanation:

We have 6=x^2-10x

Balance the equation by adding the same constant to each side

x^2-10x+25=6+25

x^2-10x+25=31

Rewrite as perfect square,

(x-25)^2=31

Taking square root at both sides

√(x-5)^2 = √31

x-5 = (+/-)√31

x1= 5 +√31

x2= 5 -√31

Therefore the solutions are x1= 5 +√31 , x2= 5 -√31

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:

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:

-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:

25

Step-by-step explanation:

2x + 2 + 5x + 3 = 180      

2 lines that cross make consecutive angles supplementary.

Combine the left.

7x + 5 = 180        Subtract 5 from both sides.

7x +5-5=180-5    Combine

7x = 175               Divide by 7

7x/7=175/7          

x = 25

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:

[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:

$1424.10

Step-by-step explanation:

APEX is obnoxious, I understand.

Answer:1424.10

Step-by-step explanation:

Answer:

(2x^2)(y^16)

Step-by-step explanation:

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:  The correct option is (B) 7.

Step-by-step explanation:  Given that a karate studio charges $35 for the first course and $22.50 for each course after that, even if the student leaves the course early.

Cena paid $170 for her son to take courses.

We are to find the number of courses that he took.

Let x represents the number of courses that Cena took.

Then, according to the given information, we have

[tex]35+22.50\times (x-1)=170\\\\ \Rightarrow 22.50(x-1)=170-35\\\\ \Rightarrow 22.50(x-1)=135\\\\ \Rightarrow x-1=\dfrac{135}{22.50}\\\\\Rightarrow x-1=6\\\\ \Rightarrow x=7[/tex]

Thus, the required number of courses that Cena took is 7.

Option (B) is CORRECT.

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!

When point D in shape ABCDE is reflected over the x-axis, the y-coordinate changes its sign. If it is then translated 3 units to the left, the x-coordinate of D decreases by 3. Therefore, if the original coordinates of D are (d1, d2), after these transformations, its new coordinates will be (d1-3, -d2).

To answer this question, we need to understand how the reflection and translation transformations affect the coordinates of point D in the shape ABCDE.

First, when a point is reflected over the x-axis, the y-coordinate changes sign. For example, if the original coordinates of D are (d1, d2), after reflection over the x-axis, the new coordinates will be (d1, -d2).

Next, a translation of 3 units to the left (in the negative x direction), lowers the x coordinate by 3 units. Thus, after this translation, the final coordinates of point D will be (d1-3, -d2).

So, if you know the original coordinates of point D in the shape ABCDE, you can calculate its new position after these transformations in the described way.

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The new coordinates of point D after reflection over the x-axis and translation 3 units left is

The coordinates is solved by considering the sequence of transformation that took place

Reflection over the x-axis will result to

D (-3, -1) → D' (-3, 1)

Translation of 3 units left will result to

D' (-3, 1) → D"(-6, 1)

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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:

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

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:

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  

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Answer:

5 sqrt(5) =c

Step-by-step explanation:

We can use the Pythagorean theorem to find the length of the hypotenuse

a^2 + b^2 = c^2 since this is a right triangle

5^2 + 10^2 = c^2

25+100 = c^2

125 = c^2

Take the square root of each side

sqrt(125) = sqrt(c^2)

sqrt(25*5) = c

sqrt(25) sqrt(5) = c

5 sqrt(5) =c

Alright, in a right-angled triangle, the lengths of the three sides are related by the Pythagorean Theorem, which states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
This can be written as:
c² = a² + b²
In the question you provided, you've given that side a is 5 and side b is 10, and you'd like to find side c, the hypotenuse.
Following the Pythagorean Theorem :
c² = a² + b² = 5² + 10² = 25 + 100 = 125
Now we need to find the length of side c by taking the square root of c²:
c = √125
This can be further simplified by recognizing that 125 is equal to 25 * 5, and the square root of 25 is 5.
c = √(25 * 5) = √25 * √5 = 5√5
Therefore, the length of side c in its simplified radical form is:
c = 5√5
That would be the value of the hypotenuse of the right triangle with side lengths 5 and 10.

Answer:  B) F(x) = √x and G(x) = 3x + 2

Step-by-step explanation:

The composite function G(F(x)) is when you replace every x-value in the G(x) function with the F(x) function.

[tex]A)\ G(3x+2) = \sqrt{3x+2}\\\\B)\ G(\sqrt{x})=3(\sqrt{x})+2\quad =3\sqrt{x}+2\\\\C)\ G(\sqrt{x}+2) = 3\quad \text{there are no x-values in the G(x) function to replace}\\\\D) G(3\sqrt{x})=2\quad \text{there are no x-values in the G(x) function to replace}[/tex]

The only one that matches G(F(x)) = 3√x + 2 is OPTION B

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:

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:

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:

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:

748 in^3.

Step-by-step explanation:

This consists of a triangular prism and a  rectangular cuboid .

Volume of the prism =  .1/2 * 8 *11 * 17 = 748 in^3

Volume of the cuboid =  5*8*17 = 680 in^3

Therefore the volume of the whole figure

= 680 + 748 =  1428 in^3.

Answer:

What is the volume of the composite figure?

748 cubic inches

Step-by-step explanation: