Which of the following constants can be added to x2 - 3x to form a perfect square trinomial?

The greater common divisor between 10 and 15 is 5, so we can factor it out:

[tex]10x^2-15x = 5(2x^2-3x)[/tex]

The greater common exponent between 1 and 2 is 1, so we can factor x out:

[tex]10x^2-15x = 5x(2x-3)[/tex]

The equations are as follows where x represents the number of minutes the cell phone is used.

For plan one: Total cost = $20 + $0.15x

For plan two: Total cost = $35 + $0.10x

For both the costs to be the same, we need to use the cell phone for

300 minutes.

Equations are relations showing the value of one quantity related to another quantity when it can change. The changing value is the variable.

We are informed that one cell phone plan charges $20 per month plus $0.15 per minute used. A second cell phone plan charges $35 per month plus $0.10 per minute used.

We are asked to write and solve an equation to find the number of minutes you must talk to have the same cost for both calling plans.

Let the number of minutes the cell phone is used be x minutes.

Now we solve for equations for both plans in the following way:-

Plan one:

Charges $20 per month plus $0.15 per minute used.

When the use is for x minutes, the additional charge = $0.15*x = $0.15x

∴ Total cost = Fixed cost + Additional cost

or, Total cost = $20 + $0.15x.

Plan two:

Charges $35 per month plus $0.10 per minute used.

When the use is for x minutes, the additional charge = $0.10*x = $0.10x

∴ Total cost = Fixed cost + Additional cost

or, Total cost = $35 + $0.10x.

We are asked to find the number of minutes used so that the costs in both the plans are equal. To find this we equate the equation of total costs in both the cases to get:

$20 + $0.15x = $35 + $0.10x.

Subtracting ($20 + $0.10x) from both sides of the equation, we get

$20 + $0.15x - ($20 + $0.10x) = $35 + $0.10x - ($20 + $0.10x).

or, $20 + $0.15x - $20 - $0.10x = $35 + $0.10x - $20 - $0.10x.

or, $0.05x = $15

Dividing both sides of the equation by $0.05, we get

$0.05x/$0.05 = $10/$0.05

or, x = 300.

∴ We must talk for 300 minutes for both the plans to cost the same to us.

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Answer:

Option A and C are correct

Step-by-step explanation:

A polynomial is defined as an algebraic expression that consists of variables and constants involving operations of addition, subtraction, multiplication and non-negative exponents.

A. 4x^2+9x+12 is a polynomial

B. 3-√2x is not a polynomial

C. 15x^4 is a polynomial

D. 6x^2+2/x is not a polynomial

So, Option A and C are correct.

Answer: Option A and Option C

Step-by-step explanation:

Polynomials always have the following form:

[tex]ax ^ n + bx ^{n-1} + cx^{n-2} +...+ d[/tex]

Where a, b, c, and d are constant and are real numbers

The exponents of the variable x are always greater than or equal to zero.

Then identify among the options the expressions that have these characteristics

The answer are:

Option A.

[tex]4x^2 +9x+12[/tex]

Option C.

[tex]15x^4[/tex]

Answer:

last choice

Step-by-step explanation:

sin(theta) is positive

tan(theta)=sin(theta)/cos(theta) is negative

If sin(theta) is positive and tan(theta) is negative, then cos(theta) is negative because +/-=-

So we are looking for the quadrant where sine is positive and cosine is negative or when x is negative and y is positive.

This is in quadrant 2 so our angle theta is between 90 and 180 degrees.

Answer:

Step-by-step explanation:

The correct answer is the second one. The function g(x) is increasing "faster" than f(x), and this is true of exponential functions in general. This should make sense if you're familiar with the concept of limits at infinity.

Answer: 0 is the answer, the 1/7 and -1/7 cancel each other out. Leaving zero as the answer!

Answer:

maybe

[tex] y = \frac{1}{2} x + 0.5[/tex]

Answer:

x - 2y = - 1

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

Obtain the equation in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 3, - 1) and (x₂, y₂ ) = (3, 2) ← 2 points on the line

m = [tex]\frac{2+1}{3+3}[/tex] = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]

y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (3, 2), then

2 = [tex]\frac{3}{2}[/tex] + c ⇒ c = [tex]\frac{1}{2}[/tex]

y = [tex]\frac{1}{2}[/tex] x + [tex]\frac{1}{2}[/tex] ← in slope- intercept form

Multiply all terms by 2

2y = x + 1 ( subtract 2y from both sides )

0 = x - 2y + 1 ( subtract 1 from both sides )

- 1 = x - 2y , that is

x - 2y = - 1 ← in standard form

Answer:

C

Step-by-step explanation:

Girls - 28-12 = 16

16:12 = 4:3 - so answer choice C

We know that out of the 28 students 12 of them are boys. To find how many girls there are subtract 12 from 28

28 - 12 = 16

That means that there are 16 girls in the class

Now you need a ratio of girls : boys so...

16 : 12

This can be further simplified to the following...

4 : 3 (C)

This means that for every four girls there are 3 boys

Hope this helped!

~Just a girl in love with Shawn Mendes

Check the picture below.

bearing in mind that ⌈some expression⌉ means "ceil" or the ceil() function, which means any number in between one integer and the next, "ceils" or gets bumped up to the next integer.

namely for example, for y = ⌈x⌉ will yield

y(0.5) = 1

y(0.7) = 1

y(0.0000001) = 1

y(3.0000001) = 4

y(-2.000001) = -2

y(-5.00001) = -5

and so on

the same is true btw for the y = ⌊x⌋ or the "floor" floor() function, but it "floors" or drops down instead.

y(0.5) = 0

y(3.9999999) = 3

y(-5.0000001) = -6

and so on.

in this case is y = 4⌈x⌉, so any values in between each integer for "x" gets bumped up.

The graph which represents the given function is first graph.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given a function,

f(x)=4[x]

The step function [x] is defined as the piecewise constant function which has a countable or finite number of pieces.

Here a step function is multiplied to 4.

The correct graph which represents the step function is first graph.

Hence the correct option is A.

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Answer:

Step-by-step explanation:

[tex]z-2+8=24\\\\z+(-2+8)=24\\\\z+6=24\qquad\text{subtract 6 from both sides}\\\\z+6-6=24-6\\\\z=18[/tex]

Answer:

Z = 18

Step-by-step explanation:

Z- 2 + 8 = 24

Combine like terms

Z +6 = 24

Subtract 6 from each side

Z+6-6 =24-6

Z = 18

Answer:

Step-by-step explanation:

To create a system of equations, write an equation to model each condition that must be satisfied in the given situation.

It is given that x represents the width of the flower bed and that y represents the area of the base of the birdbath.

Write an equation to represent the condition regarding the planting area in the flower bed. It is given that there is 35 square feet of planting area. The flower bed is 3 feet longer than the width.

x(x+3) - y = 35

Write an equation to represent the condition regarding the cost of the soil and the birdbath. The question gives that the soil will cost $5 per square foot and the birdbath will cost $18 per square foot of the base.

5x(x+3)+18y=150

Combining both of the equations gives the following system of equations.

x(x+3)-y=35

5x(x+3)+18y=150

Answer:

1.25

Step-by-step explanation:

Calculate the scale factor as the ratio of the corresponding sides of the image to the original.

here the image is 6.25 and the original is 5

scale factor = [tex]\frac{6.25}{5}[/tex] = 1.25

This represents an enlargement

Answer:

Part 1) The vertex is the point (-83,-9)

Part 2) The focus is the point (-82.75,-9)

Part 3) The directrix is [tex]x=-83.25[/tex]

Step-by-step explanation:

step 1

Find the vertex

we know that

The equation of a horizontal parabola in the standard form is equal to

[tex](y - k)^{2}=4p(x - h)[/tex]

where

p≠ 0.

(h,k) is the vertex

(h + p, k) is the focus

x=h-p is the directrix

In this problem we have

[tex]x=y^{2} +18y-2[/tex]

Convert to standard form

[tex]x+2=y^{2} +18y[/tex]

[tex]x+2+81=y^{2} +18y+81[/tex]

[tex]x+83=(y+9)^{2}[/tex]

so

This is a horizontal parabola open to the right

(h,k) is the point (-83,-9)

so

The vertex is the point (-83,-9)

step 2

we have

[tex]x+83=(y+9)^{2}[/tex]

Find the value of p

[tex]4p=1[/tex]

[tex]p=1/4[/tex]

Find the focus

(h + p, k) is the focus

substitute

(-83+1/4,-9)

The focus is the point (-82.75,-9)

step 3

Find the directrix

The directrix of a horizontal parabola is

[tex]x=h-p[/tex]

substitute

[tex]x=-83-1/4[/tex]

[tex]x=-83.25[/tex]

Answer:

B  (the second graph)

Step-by-step explanation:

3.55g<-28.4

Divide each side by 3.55

3.55g/3.55<-28.4/3.55

g < -8

This would be an open circle at 8  (because g is less than not less than or equal to)  and it goes to the left ( since g is less than)

Answer:

C. s= 75

Step-by-step explanation:

One radian is the angle subtended by an arc length equal to the radius of the circle.

∅=s/r where s is the arc length ∅ the angle and r the radius of the circle.

Thus s=∅×r

In the circle provided arc s subtends and angle of 5 radians.

s= 5 radians× 15

=75

Answer:

-3, -2, -1, 0, 1, 2

Step-by-step explanation:

Note that "integer" means whole numbers, and "consecutive" means continuously following. Also, note that you are starting with -3:

-3 , -2 , -1 , 0 , 1 , 2, is your answer, because you just need to add 1 each time until you have 6 numbers.

~

Answer:

Look to the attached graph

Step-by-step explanation:

* Lets explain the difference between the graphs of f(x) and g(x)

∵ f(x) = IxI

∵ g(x) = IxI - 4

- If we add are subtract f(x) by k, where k is a constant that means

 we translate f(x) vertically

- If g(x) = f(x) + k

∴ f(x) translated vertically k units up

- If g(x) = f(x) - k

∴ f(x) translated vertically k units down

∵ g(x) = IxI - 4

∵ f(x) = IxI

∴ g(x) = f(x) - 4

∴ f(x) translated vertically 4 units down

∴ The graph of f(x) will translate down 4 units

∵ The origin point (0 , 0) lies on f(x)

∴ The origin point (0 , 0) will translate down by 4 units

∴ Its image will be point (0 , -4)

∴ Point (0 , -4) lies on the graph of g(x)

- So you can translate each point on the graph of f(x) 4 units down to

 graph g(x)

# Two point on the left part

∵ Point (-2 , 2) lies on f(x)

∴ Its image after translation 4 units down will be (-2 , -2)

∴ Point (-2 , 2) lies on g(x)

∵ Point (-7 , 7) lies on f(x)

∴ Its image after translation 4 units down will be (-7 , 3)

∴ Point (-7 , 3) lies on g(x)

# Two point on the right part

∵ Point (3 , 3) lies on f(x)

∴ Its image after translation 4 units down will be (3 , -1)

∴ Point (3 , -1) lies on g(x)

∵ Point (8 , 8) lies on f(x)

∴ Its image after translation 4 units down will be (8 , 4)

∴ Point (8 , 4) lies on g(x)

* Now you can draw the graph with these 5 points

Answer:

c = 2s + 3

Step-by-step explanation:

Let c be Carly's age.

Carly is 3 more . . . than twice her sister's age.

We can translate "twice her sister's age" into 2s.

Carly is 3 more than 2s.

We can translate this into:

Carly is 3 + 2s.

c = 2s + 3

Carly's age, given that it's three more than twice her sister's age, can be expressed with the mathematical expression 2s + 3. This translates the stated relationship into an algebraic context.

The question is asking for an expression that represents Carly's age in relation to her sister's age. Given that Carly's age is three more than twice the age of her sister, we can express Carly's age (C) as 2s + 3, where s is her sister's age.

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bearing in mind that the hypotenuse is never negative, since it's just a distance unit, so if an angle has a sine ratio of -(5/13) the negative must be the numerator, namely -5/13.

[tex]\bf cos\left[ sin^{-1}\left( -\cfrac{5}{13} \right) \right] \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{then we can say that}~\hfill }{sin^{-1}\left( -\cfrac{5}{13} \right)\implies \theta }\qquad \qquad \stackrel{\textit{therefore then}~\hfill }{sin(\theta )=\cfrac{\stackrel{opposite}{-5}}{\stackrel{hypotenuse}{13}}}\impliedby \textit{let's find the \underline{adjacent}}[/tex]

[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{13^2-(-5)^2}=a\implies \pm\sqrt{144}=a\implies \pm 12=a \\\\[-0.35em] ~\dotfill\\\\ cos\left[ sin^{-1}\left( -\cfrac{5}{13} \right) \right]\implies cos(\theta )=\cfrac{\stackrel{adjacent}{\pm 12}}{13}[/tex]

le's bear in mind that the sine is negative on both the III and IV Quadrants, so both angles are feasible for this sine and therefore, for the III Quadrant we'd have a negative cosine, and for the IV Quadrant we'd have a positive cosine.

Answer:

Step-by-step explanation:

[tex](f-g)(x)=f(x)-g(x)\\\\f(x)=5x-2,\ g(x)=2x+1\\\\\text{Substitute:}\\\\(f-g)(x)=(5x-2)-(2x+1)\\\\=5x-2-2x-1\qquad\text{combine like terms}\\\\=(5x-2x)+(-2-1)\\\\=3x-3[/tex]

Your answer is the first option, "One is a factor of every whole number since every number is divisible by itself".

This is true because whenever you multiply 1 by anything you always get the thing you multiplied by, which makes it a factor of every number.

You can also find this by eliminating the other options, for example a prime number is any number whose factors are 1 and itself, 2 factors, so since 1 only has 1 factor it is not prime and option 3 is eliminated.

This also eliminates option 4 because 1 cannot be a composite number if it only has 1 factor.

I hope this helps!

The true statement among the given options is that one is a factor of every whole number since every number is divisible by itself.

A prime number is that number that is only fully divisible by 1 and that number itself.

Since we know that every number is divisible by 1. Thus 1 is also a factor of every number.

Thus one is a factor of every number.

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Answer:

Third Option

Step-by-step explanation:

Given expression is:

[tex]\sqrt{\frac{55x^7y^6}{11x^11y^8}}[/tex]

Simplifying

[tex]=\sqrt{\frac{11*5*x^7*y^6}{11*x^11*y^8}}\\=\sqrt{\frac{5*x^7*y^6}{x^11*y^8}}\\Combining\ exponents\ with\ same\ base\\=\sqrt{\frac{5}{11*x^{(11-7)}*y^{(8-6)}}}\\=\sqrt{\frac{5}{x^{4}*y^{2}}}\\Applying\ radical\\=\frac{5^{\frac{1}{2}}}{x^{(4*\frac{1}{2})}*y^{(2*\frac{1}{2})}}}\\=\frac{\sqrt{5}}{x^2y}[/tex]

As 5 cannot be taken out of the square root, it will remain inside the square root.

Hence, Third option is the correct answer ..

The area of a parallelogram is the base times the height.

Area = 14 x 8 = 112 square inches.

-4 times -2 equals 8.

8 times -1 equals -8.

Therefore, the point on your number line that is on -8 is your answer!

Answer:

(a+2) Is your answer

Step-by-step explanation:

You could try synthetic division, but it's pretty complicated (not to mention for much harder problems), so you should try factoring this. What two numbers multiply up to 10 and add up to 7? Using trial and error, we would find these two numbers to be 2 and 5. Therefore, it factors into (a+5)(a+2).

Answer:

2

Step-by-step explanation:

Answer:

y - 2 = 2(x - 3).

Step-by-step explanation:

The point -slope form of a line is:

y - y1 = m(x - x1) where m = the slope and (x1, y1) is a point on the line.

Here m = 2, x1 = 3 and y1 = 2. So we have the equation:

y - 2 = 2(x - 3).

Answer:

[tex]y=2x-4[/tex]

Step-by-step explanation:

Given: The line passes through (3, 2) and has a slope of  2.

To find: Point slope form of the equation.

Solution: We know that the point slope form of the line passing through [tex]\left ( x_{1},y_{1}\right )[/tex] and slope m is [tex]y-y_{1}=m\left ( x-x_{1} \right )[/tex]

Here, [tex]x_{1}=3,\ y_{1}=2, \text{and} \:\:m=2[/tex]  

So we have,

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

[tex]y-2=2x-6[/tex]

[tex]y=2x-4[/tex]

Hence, the point slope form of the line is [tex]y=2x-4[/tex].

Answer:

x=-1

Step-by-step explanation:

2x -2= -4

2x = -2

x = -1

Answer:

-1

Step-by-step explanation:

Answer:

x ≈ 56.7°

Step-by-step explanation:

Since the triangle is right use the sine ratio to solve for x

sin x° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{66}{79}[/tex], hence

x = [tex]sin^{-1}[/tex] ( [tex]\frac{66}{79}[/tex] ) ≈ 56.7°

Answer:

x = 56.7

Step-by-step explanation:

Step-by-step explanation:

formula of square= width x length

width = length

each sides = √ 64

= 8 cm

area of the rectangle = 1 & 1/2 x 64

= 96 cm²

formula for area of rectangle = " square

8 x length = 96 cm²

length= 96/8

= 12 cm

perimeter= 4 (8 + 12 + 12)

= 128 cm

*multiple with 4 cuz issa cross (??) i hope you get what i mean(??)

correct me if i'm wrong i'm learning too

So the x-axis represents the age of the car and the y represents the value of the car

As you can see as the x values increase the y value decreases

This means that the answer is C. As the age of the car increases the value of the car decreases

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

3

Step-by-step explanation: