which is the graph of the inequality? 3y - 9x ≥ 9

Answer:

a. (x+5)(x-5)

b. 3(x+1)(x-5)

c. (x^2+3)(x+2)

Step-by-step explanation:

a. x^2-25

The given expression can be factorized using the formula:

[tex]a^{2} -b^{2} =(a+b)(a-b)\\So,\\x^{2} -25\\=(x)^{2}-(5)^{2}\\=(x+5)(x-5)[/tex]

b. 3x^2-12x-15

We can see that 3 is common in all terms

=3(x^2-4x-5)

In order to make factors, the constant will be multiplied by the co-efficient of highest degree variable

So,

[tex]3[x^{2} -4x-5]\\=3[x^{2}-5x+x-5]\\=3[x(x-5)+1(x-5)]\\=3(x+1)(x-5)[/tex]

c. x^3+2x^2+3x+6

Combining the first and second pair of terms

[tex]x^{3}+2x^{2}+3x+6 \\=[x^{3}+2x^{2}]+[3x+6]\\Taking\ x^{2}\ common\ from\ first\ two\ terms\\=x^{2} (x+2)+3(x+2)\\=(x^{2}+3)(x+2)[/tex]

Answer:

A positive  number

Step-by-step explanation:

Answer:  [tex]\bold{\sqrt[8]{2^7} }[/tex]

Step-by-step explanation:

[tex]\sqrt[4]{2} \times \sqrt[8]{2} \times \sqrt[2]{2}\\\\={2^{\frac{1}{4}}\times 2^{\frac{1}{8}}\times 2^{\frac{1}{2}}\\\\=2^{\frac{1}{4}+\frac{1}{8}+\frac{1}{2}}\\\\=2^{\frac{2}{8}+\frac{1}{8}+\frac{4}{8}}\\\\=2^{\frac{7}{8}}\\\\\\=\large\boxed{\sqrt[8]{2^7}}[/tex]

Answer:  4.7

Step-by-step explanation:

Use Soh Cah Toa

[tex]sin \theta=\dfrac{opposite}{adjacent}\\\\\\sin(58^o)=\dfrac{4.0}{x}\\\\\\x=\dfrac{4.0}{sin(58^o)}\\\\\\x=4.7[/tex]

Answer:

The value of x = 4.7

Step-by-step explanation:

From the figure we can see aright triangle with height = 4.0 and one angle is 58°

Points to remember

Trigonometric ratios

Sin θ  = Opposite side/Hypotenuse

To find the value of x

Sin 58 = Opposite side/Hypotenuse

 = 4/x

x = 4/Sin (58)

 = 4/0.848

 = 4.71 ≈ 4.7

Therefore the value of x = 4.7

Answer:

25/169

Step-by-step explanation:

We have 13 marbles ( 5+6+2)

P (blue ) = blue marbles/ total marbles = 5/13

P (blue ,blue) = 5/13* 5/13  since the marble is replaced

                      = 25/169

Answer:

Step-by-step explanation:

The trick is not to include anything under and including 150 miles. So A B and C are not to be checked.

D and E are both true.

Answer:

Correct options are:

D.200 miles  

E.250 miles

Step-by-step explanation:

Cary and his brother took a road trip together.

Cary drove for 50 miles.

Let his brother drove x miles

The total number of miles they drove was more than 200.

⇒ 50+x>200

⇒  x>200-50

⇒  x>150

i.e. Cary's brother drove for more than 150 miles

Hence, options which satisfies the above inequality are:

D.200 miles  

E.250 miles

Answer:

(x+1)(x-3)(x-4)=0 is a polynomial equaiton with the zeros mentioned (the answers could vary-means there are multiple answers)

Step-by-step explanation:

If x=-1 is a zero then (x+1) is a factor

If x=3 is a zero then (x-3) is a factor

If x=4 is a factor then (x-4) is a factor

Put it together (while the polynomial equations can be many different polynomial equations) here is one answer (x+1)(x-3)(x-4)=0

Answer:

5pi over 3 cm!

Step-by-step explanation:

The formula used to find the arc length is: [tex]S= r θ[/tex] where, 'r' represents the radius and θ represents the central angle in radians.

We know that r = 5cm and θ=pi/3.

Using the formula:

s =  r θ = 5cm(pi/3) = 5pi/3.

Then, the solution is: 5pi over 3 cm!

Answer:

Option D is correct.

Step-by-step explanation:

The additive inverse of a number is the same number with the negative sign

i.e. if we have a number 1 then it's additive inverse would be -1

So if we add both the number and its additive inverse the answer would be zero.

1+(-1) = 0

So, Option D their sum is always zero is correct.

Answer: Option D

Their sum is always zero

Step-by-step explanation:

Given any number x, the additive inverse of x is -x.

For example, the additive inverse of 3 is - 3, the additive inverse of 2.2 is -2.2.

In this way, note that adding a number with the additive inverse of this number will always result in the number zero.

[tex]x + (-x) = 0[/tex]

Therefore, the correct option is option D

Answer:

30

Step-by-step explanation:

  40

x 0.75

-----------

=  30

Answer: The answer would be -4

Step-by-step explanation:

Answer:

-4

I did the exam trust me ok

Answer:

A

Step-by-step explanation:

458,700 = 4.587 * 10^5

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

y = mx + b

m - slope

b - y-intercept (0, b)

We have the slope m = -9 and the y-intercept (0, -2) → b = -2.

Substitute:

y = -9x + (-2) = -9x - 2

Answer:

That's incorrect. The simplest way to show this is by evaluating the functions at a given point. Let's say x=0, then:

Sin(-x) = Sin(0) = 0

-cos x = -cos (0) = -1

Therefore, Sin(-x)≠-cos x.

The given expression :

        [tex]\sin (-x)=-\cos x[/tex] is a false expression i.e. it is not true for all the values of x.

We are asked to check whether the trignometric expression is true for all the values of x or not.

The expression is given by:

[tex]\sin (-x)=-\cos (x)[/tex]

We consider x=0

Then on taking left hand side of the expression we have:

[tex]\sin (-0)\\\\i.e.\\\\\sin (0)\\\\=0[/tex]

and the right hand side of the expression is:

[tex]-\cos x\\\\i.e.\\\\-\cos 0\\\\i.e.\\\\-1[/tex]

i.e. we have:

[tex]0=-1[/tex]

which is false.

Hence the statement is not true for all the values of x.

Answer:  78.8 ft

Step-by-step explanation:

Similar triangles have proportional sides.

[tex]\dfrac{\text{building shadow}}{\text{building height}}=\dfrac{\text{flagpole shadow}}{\text{flagpole height}}\\\\\\\dfrac{35}{\text{building height}}=\dfrac{8}{18}\\\\\\\dfrac{35\times 18}{8}=\text{building height}\\\\\\\dfrac{35\times 9}{4}=\text{building height}\\\\\\\dfrac{315}{4}=\text{building height}\\\\\\\boxed{78.75=\text{building height}}[/tex]

Answer: Last option.

Step-by-step explanation:

To find which expression in equivalent to the expression [tex]\frac{125^2}{125^\frac{4}{3} }[/tex], you need to remember  :

The Power of a power property:

[tex](a^m)^n=a^{(mn)}[/tex]

The Quotient of powers property:

[tex]\frac{a^m}{a^n} =a^{(m-n)}[/tex]

And the Product of powers property:

[tex](a^m)(a^n)=a^{(m+n)}[/tex]

Knowing that:

 [tex]125=5*5*5=5^3[/tex]

Then, you get:

[tex]\frac{125^2}{125^\frac{4}{3} }=\frac{(5^3)^2}{(5^3)^\frac{4}{3} }=\frac{5^6}{5^4}=5^{(6-4)}=5^2=25[/tex]

Answer:

5

Step-by-step explanation:

Any square root multiplied by the same square root cancels out.

sqr(x) * srt(x) = x

Answer:

5

Step-by-step explanation:

Final answer:

Using the Pythagorean theorem with the given lengths of the sides a=8 and b=15, the hypotenuse c is found to be 17 units.

Explanation:

The question involves finding the length of the hypotenuse c in a right triangle using the Pythagorean theorem, which states that in a right triangle the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Given that a = 8 and b = 15, we can apply the theorem:

c² = a² + b²

c² = 8² + 15²

c² = 64 + 225

c² = 289

c = √289

c = 17

Therefore, the length of the hypotenuse c is 17 units.

Answer:

A; 4,6,8

Step-by-step explanation:

Answer:

angles 4,6,8

Step-by-step explanation: Did it on i-ready and got it right.

Answer:

-4g-3

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

g+2

Step-by-step explanation:

g+1                     5g+4

-------------  -   ------------------

g+2                     g+2

Since the denominators are the same, subtract the numerators

g+1 - (5g+4)

Distribute the negative sign

g+1 -5g-4

-4g-3

Put this back over the denominator

-4g-3

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

g+2

Answer:

-4g-3, g+2

Step-by-step explanation:

Answer:

√a(√a + 2)          a - 2√a

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

    a - 4                a - 4

Step-by-step explanation:

I am assuming that by "sqrt(a)/sqrt(a)-2" you meant:

√a

----------

√a - 2

To rationalize the denom., multiply numerator and denom. of this fraction by the conjugate of √a - 2, which is √a + 2:

√a(√a + 2)

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

    a - 4

ANSWER

The base is 7 and the height is 9.

EXPLANATION

If we consider any two pairs of points and the y-coordinates of these two points are constant (are the same), then that side forms one of the bases of the rectangle.

Consider, Q(-1, 1) and R(6, 1)

The y-values are the same.

The base of the rectangle is the absolute value of difference in the x-values.

[tex]Base = |6 - - 1| = |7| = 7[/tex]

We could have also used S(6,-8), and T(-1,-8) to obtain the same result.

For R(6, 1) and S(6,-8), the x-coordinates are the same. The height is the absolute values of difference in the y-values.

[tex]Height= |1 - - 8| = |9| = 9[/tex]

Therefore, the base is 7 and the height is 9.

Answer:

Base is 7, and Height is 9.

Step-by-step - If we consider any two pairs of points and the y-coordinates of these two points are constant (are the same), then that side forms one of the bases of the rectangle.

Consider, Q(-1, 1) and R(6, 1)

The y-values are the same.

The base of the rectangle is the absolute value of difference in the x-values.

We could have also used S(6,-8), and T(-1,-8) to obtain the same result.

For R(6, 1) and S(6,-8), the x-coordinates are the same. The height is the absolute values of difference in the y-values.

Therefore, the base is 7 and the height is 9.

For this case we must find an expression equivalent to:

[tex]16 ^ 3[/tex]

We can rewrite 16 as [tex]2 * 2 * 2 * 2 = 2 ^ 4[/tex]

Rewriting the expression we have:

[tex](2 ^ 4) ^ 3 =[/tex]

By definition of power properties we have to:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

So, we have:

[tex](2 ^ 4) ^ 3 = 2 ^ {12}[/tex]

Answer:

Option C

Answer:

C

Step-by-step explanation:

edg2021

Answer:

The total surface area is [tex]251\ cm^{2}[/tex]

Step-by-step explanation:

we know that

The total surface area of the composite figure is equal to the lateral area of the pyramid plus the lateral area of the cube plus the area of the base of the cube

The lateral area of the pyramid is equal to the area of the four lateral triangular faces of the pyramid

The lateral area of the cube is equal to the area of the four lateral square faces of the cube

so

[tex]SA=4[\frac{1}{2}(b)(h)]+4(b^{2})+b^{2}[/tex]

we have that

[tex]b=6\ cm[/tex]

[tex]h=5.9\ cm[/tex]

substitute

[tex]SA=4[\frac{1}{2}(6)(5.9)]+4(6^{2})+6^{2}[/tex]

[tex]SA=70.8+144+36[/tex]

[tex]SA=250.8\ cm^{2}[/tex]

Round to the nearest square centimeters

[tex]250.8=251\ cm^{2}[/tex]

Answer:

53+47

Step-by-step explanation:

100-53 is 47. 53-47 gives you 6

Answer:

The numbers are 53 and 47.

Step-by-step explanation:

You didn't write out the problem completely, but this may be the problem:

The sum of two numbers is 100. The difference of the two numbers is 6. What are the numbers?

Let the numbers be x and y.

The sum of two numbers is 100.

x + y = 100

The difference of the two numbers is 6.

x - y = 6

We have a system of two equations in two variables.

x + y = 100

x - y = 6

Add the equations.

2x = 106

x = 53

Now substitute 53 for x in the first equation and solve for y.

53 + y = 100

Subtract 53 from both sides.

y = 47

The numbers are 53 and 47.

Answer:

c. 5

Step-by-step explanation:

Because 15 divided by 3 equals 5

So 25 divided by 5 equals 5 (dont know if it is correct)

From concept of similar triangles, the value of x is Option (C) 5 .

Similar triangles are triangles that have the same shape but their sizes, dimensions may vary. All equilateral triangle, squares of any shape are example of similar objects. If two triangles are similar triangles then their corresponding angles are congruent and the corresponding sides are in equal proportion.  

We know from concept of similar triangles, the corresponding sides are in equal proportion.

Both the triangle given in the diagram are similar.

The unknown side given is x .

Using proportion concept,

⇒  [tex]\frac{15}{3} = \frac{25}{x}[/tex]

⇒  [tex]x = \frac{25}{5}[/tex]

∴   [tex]x = 5[/tex]

Thus, From concept of similar triangles, the value of x is Option (C) 5.  

To learn more about concepts of similar triangles, refer -

https://brainly.com/question/8474273

#SPJ2

Answer:

-35-5

Step-by-step explanation:

-35-5=-40

which is negative

plz mark my answer as the brainliest

The expression  -35-5 has a negative value after adding two negative number we get negative number option fourth is correct.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

We have expressions:

= 2+12

= 14

= (-3)(-8)

= 24

= 10-(-18)

= 10+18

= 28

= -35-5

= -40

Thus, the expression  -35-5 has a negative value after adding two negative number we get negative number option fourth is correct.

Learn more about the arithmetic operation here:

brainly.com/question/20595275

#SPJ2

Check the picture below.  The picture is using feet, but is pretty much the same trajectory for meters.

so the object hits the ground when y = 0, thus

[tex]\bf ~~~~~~\textit{initial velocity} \\\\ \begin{array}{llll} ~~~~~~\textit{in meters} \\\\ h(t) = -4.9t^2+v_ot+h_o \end{array} \quad \begin{cases} v_o=\stackrel{12}{\textit{initial velocity of the object}}\\\\ h_o=\stackrel{62.5}{\textit{initial height of the object}}\\\\ h=\stackrel{}{\textit{height of the object at "t" seconds}} \end{cases} \\\\\\ h(t)=-4.9t^2+12t+62.5\implies \stackrel{\textit{hitting the ground}}{\stackrel{h(t)}{0}=-4.9t^2+12t+62.5}[/tex]

[tex]\bf ~~~~~~~~~~~~\textit{using the quadratic formula} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-4.9}t^2\stackrel{\stackrel{b}{\downarrow }}{+12}t\stackrel{\stackrel{c}{\downarrow }}{+62.5} \qquad \qquad t= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ t=\cfrac{-12\pm\sqrt{12^2-4(-4.9)(62.5)}}{2(-4.9)}\implies t=\cfrac{-12\pm\sqrt{144+1225}}{-9.8} \\\\\\ t=\cfrac{12\mp\sqrt{1369}}{9.8}\implies t=\cfrac{12\mp 37}{9.8}\implies t= \begin{cases} \stackrel{\approx}{-2.55}\\ 5 \end{cases}[/tex]

we can't use -2.55, since it's seconds and can't be negative, so t = 5 seconds later.

Answer:

See below.

Step-by-step explanation:

An example will illustrate the method:

(2/3)^3  

=  2^3 / 3^3

= 8/27.

Answer:100

Step-by-step explanation:

That is the most common number

Hello There!

Mode: The number that occurs most often in a set of numbers

in this case, the number 100 occurs more than any other number in the set.  This means that the mode for this set of data is 100.