What is the simplified form of the following expression?
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Answer: First option.

Step-by-step explanation:

You know that the product obtained by multiplying a binomial and a trinomial is:

[tex]x^3+3x^2-x+2x^2+6x-2[/tex]

Then, in order to simplify this product, it is necessary to add the like terms.

Therefore, the expression that is equivalent to this product after it has been fully simplified is:

 [tex]=x^3+(3x^2+2x^2)+(6x-x)-2\\\\=x^3+5x^2+5x-2[/tex]

You can  observe that this matches with the first option.

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{3}{ h},\stackrel{2}{ k})\qquad \qquad radius=\stackrel{5}{ r} \\\\\\ (x-3)^2+(y-2)=5^2\implies (x-3)^2+(y-2)=25[/tex]

Answer:

(x-3)² + (y-2)² = 25

Step-by-step explanation:

apeex

Answer:

6

Step-by-step explanation:

Given (x1, y1) and (x2, y2) dot product = (x1*x2 + y1*y2)

SO... given (2, 4) and (-1, 2) dot product = (2*-1 + 4*2)

= -2 + 8

= 6

Answer:

The mean point estimate is 593

Step-by-step explanation:

650 + 550 + 380 + 720 + 710 + 550 = 3560

3560/6 = 593.33

Answer:

593.3

Step-by-step explanation: plato family

Answer:

Option C is correct.

A reflection over the x-axis and then a reflection over the y-axis

Step-by-step explanation:

From the given figure:

The coordinates of ABC are:

A(-4, -3), B(-5, -2) and C(-3, -2).

and the coordinate of A'B'C' are:

A'(4, 3), B'(5, 2) and C(3, 2)

The rule of reflection over x-axis is given by:

then,

The rule of reflection over y-axis is given by:

Therefore, the triangle ABC is rotated 180 degree using the origin as the center of rotation is: A reflection over the x-axis and then a reflection over the y-axis

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer:

It's C

Step-by-step explanation:

Just took the test

Answer:

a: 5.25 b: -0.33

Step-by-step explanation:

a:

4x - 5 = 16

isolate the variable. this is done by putting only the variable on the left side and the numbers on the right side. when moving the 5 to the right side, it is counted as a -5 because of the minus in front. when moving it, be sure to change from - to + and vice versa.

4x = 16 + 5

4x = 21

x = 21/4

x = 5.25

b:

same process

35 + 3x - 11 = 23

move the 35 to the right, changing it to a -35

3x - 11 = 23 - 35

move the -11

3x = 23 - 35 + 11

3x = -12 + 11

3x = -1

x = -1/3

x = -0.33

Hope I could help! If you have any trouble, tell me in the comments.

Answer:

a. [tex]x=5.25[/tex]

b. [tex]x=-0.33[/tex]

Step-by-step explanation:

You need to solve for the variable "x" in each equation. Then:

a. You need to add 5 to both sides of the equation:

[tex]4x - 5 +(5)= 16+(5)\\\\4x= 21[/tex]

Now you need to divide both sides of the equation by 4, getting:

[tex]\frac{4x}{4}=\frac{21}{4}\\\\x=5.25[/tex]

b. You need to subtract 35 from both sides of the equation:

[tex]35 + 3x - 11-(35)= 23-(35)\\\\3x-11=-12[/tex]

Add 11 to both sides:

[tex]3x-11+(11)=-12+(11)\\\\3x=-1[/tex]

Now you need to divide both sides of the equation by 3, getting:

[tex]\frac{3x}{3}=\frac{-1}{3}\\\\x=-0.33[/tex]

Answer:

A

Step-by-step explanation:

let y = f(x) and rearrange making x the subject

Given

y = [tex]\frac{1}{9}[/tex] x - 2

Multiply through by 9

9y = x - 18 ( add 18 to both sides )

x = 9y + 18

Change y back into terms of x, hence

[tex]f^{-1}[/tex] (x) = 9x + 18

Answer:A

Step-by-step explanation:Right on edge

Step-by-step explanation:

f(g(10))

This is called a composite function.  It's when you plug one function into another.

First, find g(10):

g(x) = √(x-9)

g(10) = √(10-9)

g(10) = √1

g(10) = 1

Then plug that into f(x):

f(x) = -9x - 9

f(g(10)) = -9 g(10) - 9

f(g(10)) = -9 (1) - 9

f(g(10)) = -9 - 9

f(g(10)) = -18

By having two coworkers pay for a quarter of the tank each, the student saves $20.70 per month on gasoline.

The question asks us to calculate how much a student would save on gasoline for a month by having two coworkers pay for a quarter of a tank each. With gasoline costing $2.76\/gallon and the tank capacity of 15 gallons, the cost of a full tank is 15 gallons x $2.76\/gallon = $41.40.

Each coworker would pay for a quarter of that amount, which is 0.25 x $41.40 = $10.35. Since there are two coworkers, the total contribution would be 2 x $10.35 = $20.70. Therefore, the student saves $20.70.

Answer:

= 70.2 ± 3.761  bpm

Step-by-step explanation:

The question is on calculating the confidence interval for a population mean

The general expression is

CI = x ± z * δ/√n   where;

CI = confidence interval,

 x = mean of sample,

 δ = standard deviation,

  n= is sample size

   z = z* value from standard normal distribution according to   confidence level given.

Given that;

n= 30   x =70.2    δ=10.51          z* for 95% CI = 1.96

Then applying the expression

CI = x ± z * δ/√n

[tex]=\sqrt{n} = \sqrt{30} =5.477\\\\=\frac{10.51}{5.477} =1.919*1.96=3.761\\\\[/tex]

Cl = 70.2±3.761

= 70.2 ± 3.761  bpm

Answer:

x < -5 + 3b

Step-by-step explanation:

-x + 3b >5

-x > 5 - 3b ..... flip inequality when multiplying both sides by -1

x < -5 + 3b (Answer)

Answer:

x<-5/2 + 3b/2 ( the fractions are supposed to be 5 over 2  and 3b over 2 btw)

Step-by-step explanation:

pls mark brainiest.

Answer:

Offer lots of information. Consumers look for trustworthy, knowledgeable individuals to educate them on a purchase. .

Step-by-step explanation:

Answer:

√ 41 (or  6.40 in decimal form)

Step-by-step explanation:

By Pythagorean theorem,

for a right triangle with sides a and b and hypotenuse h, the following formula is true:

a² + b²  = h²

or

h = √ (a² + b²).

in this case, it is given that a and b are 4 and 5 units respectively

hence

h = √ (4² + 5²) = √ (16 + 25) = √ 41 = 6.40

Answer: last option.

Step-by-step explanation:

You need to apply the Pythagorean Theorem, which states that:

[tex]a^2=b^2+c^2[/tex]

Where "a" is the hypotenuse of the right triangle and "b" and "c" are the legs of the right triangle.

Knowing that the legs of this right triangle have lengths of 4 units and 5 units, you can solve for the hypotenuse "a".

Then:

[tex]a^2=(4units)^2+(5units)^2\\\\a=\sqrt{(4units)^2+(5units)^2}\\\\a=6.4units[/tex]

Answer:

the answer is 12. hoped this helped

Step-by-step explanation:

first find out what 5* 12  is. 5* 12= 60

then 12* 4. 12* 4=48

finally subtract 60 and 48 witch is 12

Answer:

The possible dimensions are  y, 5y + 2 and y + 7.

Step-by-step explanation:

V = 5y^3 + 37y^2 + 14 y

y is common  to all 3 terms so

V = y(5y^2 + 37y + 14)

V = y (5y  + 2)(y + 7)

The expressions for the possible dimensions of the rectangular prism.

[tex]V = 5y^3 + 37y^2 + 14 y[/tex]. The possible dimensions are y, 5y + 2, and y + 7.

Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units,

then its volume is given as:

[tex]V = a\times b \times c \: \: unit^3[/tex]

The given expressions for the possible dimensions of the rectangular prism.

[tex]V = 5y^3 + 37y^2 + 14 y[/tex]

y is common to all 3 terms

so,

[tex]V = y(5y^2 + 37y + 14)\\V = y (5y + 2)(y + 7)[/tex]

By the comparison of the volume

[tex]V = a\times b \times c \: \: unit^3[/tex]

Therefore, the dimensions are a = y, b = 5y + 2, c = y + 7.

Learn more about the volume of a right rectangular prism here:

https://brainly.com/question/21308574

#SPJ2

64 large boxes and 60 small boxes.

Here we must use the concept of multiples. A multiple of a number result of the multiplication of that number by an integer. For instance, 2, 4, 6, 8 are multiples of 2. The following chart shows our statement:

[tex]\begin{array}{cccccccccc}Number\,of\,boxes & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9\\Large & 8 & 16 & 24 & 32 & 40 & 48 & 56 & 64 & 72\\Small & 10 & 20 & 30 & 40 & 50 & 60 & 70 & 80 & 90\end{array}[/tex]

So we need to choose the number of small and large boxes such that the sum is 124 boxes of sunglasses and the number of large boxes is greater than the number of small boxes. From the table, the correct solution is:

64 large boxes and 60 small boxes because 64 + 60 = 124 and 64 > 60

Answer:

A merchant selling sunglasses can place 8 large boxes or 10 small boxes into a carton for shipping.

If a total of 124 boxes are shipped, then the large boxes in the cartons must be a multiple of 8 which means either 16,56,64, 72,104.

We will choose that multiple of 8, which when subtracted from 124, gives the number that is divisible by 10.

As the larger boxes are more in quantity, we will choose 64 and 104.

[tex]124-64=60[/tex]

[tex]64/8=8[/tex] cartons

[tex]60/10=6[/tex] cartons

Total cartons are =[tex]8+6=14[/tex]

Also, [tex]124-104=20[/tex]

[tex]104/8=13[/tex] cartons

[tex]20/10=2[/tex] cartons

So, total cartons shipped = [tex]13+2=15[/tex]

So, both can be answers. As any options are not given, you can solve it whatever way you like.

To solve the equation 4x + 2 = 12, we subtract 2 from both sides and then divide by 4, finding that x = 2.5. The change of base formula mentioned is not needed for solving this equation.

The question asks to solve the equation 4x + 2 = 12 for x, but references the change of base formula which is not relevant to solving this linear equation. Instead, we will solve it through simple algebraic manipulation.

Therefore, the solution to the equation 4x + 2 = 12 is x = 2.5.

Answer:

Approximately 7.3%.

Step-by-step explanation:

What is percentage increase?

[tex]\displaystyle \text{Percentage Increase} = \frac{\text{Final Value} - \text{Initial Value}}{\text{Initial Value}} \times 100\%[/tex].

For this question:

Let [tex]\text{Initial Value} = x[/tex].

[tex]\displaystyle \frac{0.089 - x}{x} = 0.217[/tex].

Assume that [tex]x \ne 0[/tex]. Multiply both sides of the equation by [tex]x[/tex]:

[tex]0.089 - x = 0.217x[/tex].

Add [tex]x[/tex] to both sides of the equation:

[tex]0.089 = (1 + 0.217)x[/tex].

[tex]\displaystyle x = \frac{0.089}{1 + 0.217} = 0.0731 \approx 7.3\%[/tex].

In other words, the initial percentage is approximately 7.3%.

Answer:

C). 0 degrees

Step-by-step explanation:

The given equation is:

-4 + 6 sinx = -4 + 4 sinx

adding 4 on both sides:

4 - 4 + 6 sinx = 4 - 4 + 4 sinx

6sinx = 4sinx

dividing by 2 on both sides, we get:

6sinx/2 = 4sinx/2

3 sinx = 2 sinx

subtracting 2 sinx from both sides we get:

sin x = 0

x = sin⁻¹ (0)

x = 0 degrees

Answer:

The vertex is (-2, 2).

Step-by-step explanation:

2x^2 + 8x + 10

Convert to vertex form:

= 2(x^2 + 4x) + 10

= 2 [ (x + 2)^2 - 4] + 10

= 2(x + 2)^2 - 8 + 10

= 2(x + 2)^2 + 2.

Compare this with a(x - b)^2 + c:

b = -2 and c = 2.

The vertex is at

Answer:

2

Step-by-step explanation:

Answer:

the required answer of this question is 1/10

Answer:

see explanation

Step-by-step explanation:

Using the intercept form of the equation of a straight line

[tex]\frac{x}{a}[/tex] + [tex]\frac{y}{b}[/tex] = 1

where a is the x- intercept and b the y- intercept

here a = - 2 and b = 3, hence

[tex]\frac{x}{-2}[/tex] + [tex]\frac{y}{3}[/tex] = 1

Multiply through by - 6

3x - 2y = - 6 ← equation in standard form

Substitute x = 2 and y = 6 into the left side of the equation and if equal to the right side then (2, 6) lies on the line

left side = (3 × 2) - 2(6) = 6 - 12 = - 6

Hence line passes through (2, 6)

Answer:

2.5 pesos/mango

Step-by-step explanation:

You are looking for the price per mango. "Per" means to divide.

Price per mango means to divide the price of all the mangoes by the number of mangoes.

(15 pesos)/(6 mangoes) = (5 pesos)/(2 mangoes) = 2.5 pesos/mango

Answer:

The maximum length (x) of the rectangular box

The minimum volume (y) of the rectangular box

The minimum height (8-x) of the rectangular box

Step-by-step explanation:

we have

[tex]y=3x(8-x)[/tex]

This is the equation of a vertical parabola open downward

The vertex is a maximum

Remember that

The x-intercept is the value of x when the value of y is equal to zero

The x-intercepts of the equation are

(0,0) and (8,0)

therefore

The greatest x-intercept is the point (8,0)

see the attached figure

Remember that x represent the length of the box

therefore

The greatest x-intercept of the graph of this polynomial equals to

The maximum length (x) of the rectangular box

The minimum volume (y) of the rectangular box

The minimum height (8-x) of the rectangular box

Answer:

[tex](3x+5)[/tex]

Step-by-step explanation:

The given polynomial expression is:[tex]6x^2+x-15[/tex]

We compare to [tex]ax^2+bx+c[/tex] and have a=6,b=1,c=-15

The product [tex]ac=6\times -15=-90[/tex]

Two factors of -90 that sums to 1 are -9 and 10

We split the middle term to get:

[tex]6x^2+10x-9x-15[/tex]

[tex]2x(3x+5)-3(3x+5)[/tex]

[tex](3x+5)(2x-3)[/tex]

Therefore the other factor is:

[tex](3x+5)[/tex]

Answer: B

Step-by-step explanation:

Answer:

a. 6 + 2(x + 4) = (3 – x)

Step-by-step explanation: just took the test

Answer:

a) 3x + y = 5

Step-by-step explanation:

Insert the coordinates into the Point-Slope Formula FIRST, y - y₁ = m(x - x₁), with their CORRECT signs. Remember, in the Point-Slope Formula, all the negative symbols give the OPPOSITE term of what they really are. So, with that being stated, here is how you will set it up: y + 1 = -3(x - 2). After this [Distributive Property], convert to Slope-Intercept Form by moving "-1" to the right side of the equivalence symbol, resulting in y = -3x + 5. Go to your answer choices and see if this is there. No. So then, we try going from Slope-Intercept to Standard by moving "3x" to the left side of the equivalence symbol to end up with 3x + y = 5. This answer choice is found, there you are finished.

Answer:

A) A = 30m + 13           B = 28m + 15

B) Company B would charge $6 less for 4 mattresses

C) Company B would charge $12 less for 7 mattresses

Step-by-step explanation:

A. : Write equations to represent Company A's and Company B's total mattress cleaning charges for a certain number of mattresses. Define the variable  used in the equations.

Let's define the variable m to represent the number of mattresses to be cleaned.

For company A, we have a cost per mattress of $30 plus a fixed service fee of $13.  So the equation will be:

A = 30m + 13  

While company B charges $28 per mattress, with a fixed service fee of $15:

B = 28m + 15

That way, we have a good representation of both price structures, using a meaningful variable.

B. Which company would charge less for cleaning 4 mattresses? Justify your answer.

We just have to calculate the cost of cleaning 4 mattresses at both companies:

A = 30m + 13 = 30 (4) + 13 = 120 + 13 = $133

B = 28m + 15 = 28 (4) + 15 = 112 + 15 = $127

Company B would charge $6 less for 4 mattresses

C. How much money is saved by using the services of Company B instead of Company A to clean 7 mattresses?

Again, all we have to do is calculate the cost to clean 7 mattresses at both companies:

A = 30m + 13 = 30 (7) + 13 = 210 + 13 = $223

B = 28m + 15 = 28 (7) + 15 = 196 + 15 = $211

Company B would charge $12 less for 7 mattresses

Answer:

Step-by-step explanation:

Replace tan^2(x) with sin^2 (x ) / cos^2(x)

2 sec(x) sin^3(x) = cos(x) * sin^2(x) / cos^2(x)    Cancel cos(x) with cos^2(x)

2 sec(x) sin^3(x) = sin^2(x) / cos(x)                     Multiply by cos(x) both sides

2 sec(x)*cos(x)*sin^3(x) = sin^2(x)                      Divide sin^2(x) both sides

Note sec(x) and   cos(x) will cancel when multiplied. giving you one

2 sin^3(x) / sin^2(x) = sin^2(x) / sin^2(x)             Do the division

2 sin(x) = 1                                                           Divide by 2

sin(x) = 1/2

x = sin-1(1/2)

x = 30 degrees or 150 degrees.

So the answers are pi/6 and 5/6 pi