Is 6 a solution to the equation below. Yes or No?

6x + 4 = 42

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

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:

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:

the required answer of this question is 1/10

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.

Answer:

a. 6 + 2(x + 4) = (3 – x)

Step-by-step explanation: just took the test

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 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:

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:

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

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: 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.

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

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

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:

1/5 for both of them is your answer.

Step-by-step explanation:

Lets see so 5 numbers on a spinner and you want a 3 and a 4, so their is only one 3 and one 4 on a spinner so your fraction would be for both of them 1/5.

Hope my answer has helped you!

Answer:

4

Step-by-step explanation:

The geometric mean finds the typical value of a set of numbers through multiplication. To find the geometric mean of two numbers, you take the square root of the product of the two numbers.

So in this instance, multiply the two numbers together:

[tex]2*8=16[/tex]

And take the positive square root of the product:

[tex]\sqrt{16}=4[/tex]

The geometric mean is different than the commonly-used arithmetic mean, which finds the central value of a set of numbers by dividing the set's sum total by how many numbers are in the set.

Final answer:

The geometric mean of 8 and 2 is calculated as the square root of their product, which is 4.

Explanation:

To find the geometric mean of 8 and 2, we use the formula for geometric mean which is the square root of the product of the numbers. Therefore, the geometric mean of 8 and 2 is the square root of 8 multiplied by 2, which is √(8×2).

Let's calculate it step by step:

Hence, the geometric mean of 8 and 2 is 4.

[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:

= 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:

Step-by-step explanation:

"Rectangular" includes "square," and in fact treating the rectangle as a square is the fastest way to "solve" this problem.  The perimeter of the rectangular area is 160 ft; dividing that by 4 yields 40 ft.  "40 ft square" describes the rectangle maximum area:  (40 ft)^2 = 1600 ft^2.

Alternatively, let W and L represent the width and length of the rectangle.  Then:

P = perimeter = 2W + 2L = 160 ft, or W + L = 80 ft, or W = 80 ft - L.

A = area = L*W = L(80 ft - L) = 1600 ft^2.  Rewriting this as a proper quadratic:

80L - L^2 - 1600 = 0, or  L^2 - 80L + 1600.  Note that this last result factors into (L - 40)^2 = 0, so L = 40 ft.  Then W = 80 ft - 40 ft = 40 ft.

This confirms that the max area is 1600 ft^2 = (40 ft)^2.

Final answer:

To find Tina's dog's fenced area dimensions, use an algebraic model with area and perimeter equations to solve for the dimensions optimizing the given constraints.

Explanation:

To determine the dimensions of the rectangular area for Tina's dog:

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:

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

Step-by-step explanation:

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:

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:

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:

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:

[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) 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:

√ 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]