Which inequality represents all the solutions of 8(6x-7) <5(9x - 4)?
O A.
OB.
OOO
O C.
OD.
X> 12
x < 12
x> 20
x < 20

This shows that 154mm is equivalent to 15centimeters 4millimeters

Units are measure of a quantity. From the given question, we are to convert 15cm4mm to millimeters

Since 10mm =1cm, hence;

15cm4mm = (15 * 10) + 4

15cm4mm = 150+ 4

15cm4mm = 154mm

This shows that 154mm is equivalent to1 5centimeters 4millimeters

Learn more on unit conversion here: https://brainly.com/question/3371568

#SPJ1

The coordinates of point P along AB so that the ratio of AP to PB is 3 to 1 is (4,13).

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.

Given that the ratio of the two lines is 3:1, therefore, we can write,

m:n = 3:1

Also, the coordinate of the endpoints of the line are,

A = (x₁, y₁) = (1, 7)

B = (x₂, y₂) = (5, 15)

Now, Using the Section formula the coordinate of the point P can be written as,

[tex]P = (\dfrac{mx_2+nx_1}{m+n}\ , \dfrac{my_2+yx_1}{m+n})\\\\P = (\dfrac{3(5)+1(1)}{4}\ , \dfrac{3(15)+1(7)}{4})\\\\P = (4, 13)[/tex]

Hence, the coordinates of point P along AB so that the ratio of AP to PB is 3 to 1 is (4,13).

Learn more about Coordinates:

https://brainly.com/question/23450276

#SPJ1

The inequality equation of the lines are given as 4x – y ≤ 4 and 2x – 2y ≤ 3. Then the correct option is A.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The graph is given below.

From the graph, equation of the lines are given as

4x - y = 4 and 2x - 2y = 3

But for the inequality is shown in graph. Then the inequality equation of the lines are given as

4x – y ≤ 4 and 2x – 2y ≤ 3

Then the correct option is A.

More about the inequality link is given below.

https://brainly.com/question/19491153

#SPJ1

The confidence interval of employes individuals from home

Construction of hypothesis:

0.10 - 0.047 < p < 0.10 + 0.047

A simple random sample size n = 250 . Of the 250 employed individuals ​surveyed,42 responded that they did work home a minimum of once per week.

Construct 99% confidence interval for population

For proportion : 42 / 250 = 1/10 = 0.16

Mean = 2.5 * sqrt [ 0.1 * 0.9 / 250]

= 2.5 * 0.01

= 0.47

Construction of hypothesis:

0.10 - 0.047 < p < 0.10 + 0.047

To know more about confidence interval

https://brainly.com/question/24131141

#SPJ4

Answer:

60 in²

Step-by-step explanation:

Area of a Regular Polygon

  [tex]\textsf{A}=\dfrac{n\:s\:a}{2}[/tex]

where:

From inspection of the diagram:

Substitute the values into the formula and solve for A:

[tex]\implies \sf A = \dfrac{5 \times 6 \times 4}{2}[/tex]

[tex]\implies \sf A = \dfrac{120}{2}[/tex]

[tex]\implies \sf A = 60\:in^2[/tex]

Therefore, the area of the given regular pentagon IJKLM is 60 in².

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{First thing, let's get the formula for}\\\huge\textbf{the regular pentagon/polygon.}[/tex]

[tex]\mathbf{\dfrac{1}{2}\times \boxed{a}pothem\times\boxed{p}erimeter = {\boxed{a}rea}}[/tex]

[tex]\huge\textbf{Or we could simply say....}[/tex]

[tex]\mathbf{\dfrac{\boxed{n}umber\ of\ sides\ you\ have \times \boxed{s}ide \ length\ on\ one\ side\times \boxed{a}pothem}{2} = \boxed{a}rea}[/tex]

[tex]\huge\textbf{Let's plug the pieces to the equation,}\\\huge\textbf{since we have that information out the}\\\huge\textbf{way.}[/tex]

[tex]\bullet\mathbf{\ Number\ of\ sides \rightarrow \boxed{\bf 5}}[/tex]

[tex]\bullet\mathbf{\ Side\ length\ of\ one\ side \rightarrow \boxed{\bf 6\ inches}}[/tex]

[tex]\bullet\mathbf{\ Apothem \rightarrow \boxed{\bf 4\ inches}}[/tex]

[tex]\huge\textbf{Making the equation for you:}[/tex]

[tex]\mathbf{\dfrac{5\times 6 \times 4}{2} = \boxed{a}rea}[/tex]

[tex]\huge\textbf{Solving for the result:}[/tex]

[tex]\mathbf{\dfrac{5\times 6 \times 4}{2} = \boxed{a}rea}[/tex]

[tex]\mathbf{\dfrac{30\times 4}{2} = \boxed{a}rea}[/tex]

[tex]\mathbf{\dfrac{120}{2} =\boxed{a}rea}[/tex]

[tex]\mathbf{\dfrac{120\div2}{2\div2} = \boxed{a}rea}[/tex]

[tex]\mathbf{\dfrac{60}{1} = \boxed{a}rea}[/tex]

[tex]\mathbf{60\div1 = \boxed{a}rea}[/tex]

[tex]\mathbf{60 = \boxed{a}rea}[/tex]

[tex]\huge\textbf{Met the result....}[/tex]

[tex]\huge\text{Thus, your answer should be: \boxed{\mathsf{60\ in^2}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assingment \& enjoy your day!}[/tex]

Answer:

D

21√2/2

C

C

C

Step-by-step explanation:

For all problems, the ratios of the lengths of the sides are:

30-60-90 triangle 1 : √3 : 2

45-45-90 triangle 1 : √2 : √2

Problem 3:

30-60-90 triangle at left

Hypotenuse = 11

Short leg = 11/2

Long leg = 11/2 × √3

45-45-90 triangle at right

x = 11/2 × √3 × √2 = 11√6/2

Answer: D

Problem 4:

30-60-90 triangle at top

Hypotenuse = 7√3

Short leg = 7√3/2

Long leg = 7√3/2 × √3 = 7 × 3/2 = 21/2

45-45-90 triangle at right

x = 21/2 × √2 = 21√2/2

Answer: 21√2/2

Problem 7:

30-60-90 triangle

Long leg = 4√3

Short leg = y = 4√2/2 = 2√2

Answer: C.

Problem 6:

30-60-90 triangle at left

Hypotenuse = 12√6

Short leg = 12√6/2 = 6√6

Long leg = 6√6 × √3 = 6√2√3√3 = 18√2

45-45-90 triangle at right

x = 18√2/√2 = 18

Answer: C.

Problem 8:

45-45-90 triangle

Hypotenuse = 2

Leg = y = 2/√2 = 2√2/(√2√2) = √2

Answer: C.

Answer:

c=104.1 ft

Step-by-step explanation:

Law of Cosines

c^2 = 66^2 + 120^2 - 2 (66)(120)cos 60

c = 104.1 ft

The width of the rectangle is 10 inches

The given parameters are:

Length = 3x + 6

Width = 3x + 4

Area = 120

The area of a rectangle is

Area = Length * Width

So, we have:

(3x + 6) *(3x + 4) = 120

Expand

9x^2 + 12x + 18x + 24 = 120

Evaluate the like terms

9x^2 + 30x - 96 = 0

Using a graphing calculator, we have:

x = 2

Substitute x = 2 in Width = 3x + 4

Width = 3 * 2 + 4

Evaluate

Width = 10

Hence, the width of the rectangle is 10 inches

Read more about areas at:

https://brainly.com/question/11952845

#SPJ1

Answer:

3rd option : 5

Step-by-step explanation:

https://brainly.com/question/8346797

its a slope question

f(x) is y

y2-y1/x2-x1

-10+25/-1+4

15/3

5

Since we know that the equation of a line in slope-intercept form is: , where, m= Slope and b= y-intercept.

Upon substituting m = 5 in slope-intercept form of equation we will get,

Now let us find y-intercept by substituting coordinates of one point in our given line.

So the equation of given line will be,

Now let us find value of n by substituting x = n and y = 20 in our equation.

Therefore, the value of n is 5.

The value of k is  [tex]-h^2 -2xh -5x + 6[/tex]

Given;

x^(2)-5x+6=(x+h)^(2)+k

Expand the expression on the right side, we have

[tex]x^2 - 5x + 6 = (x+ h) (x+ h) + k[/tex]

[tex]x^2 -5x + 6 = x^2 +xh + xh + h^2 +k[/tex]

Collect like terms

[tex]x^2 -5x + 6 = x^2 + 2xh + h^2 + k[/tex]

[tex]x^2 -5x + 6 -x^2 - 2xh -h^2 = k[/tex]

We then have

[tex]-5x + 6 -2xh -h^2 = k[/tex]

[tex]k = -h^2 -2xh -5x + 6[/tex]

Thus, we have k as [tex]-h^2 -2xh -5x + 6[/tex]

Learn more about algebraic expression here:

https://brainly.com/question/723406

#SPJ1

Answer:

Step-by-step explanation:

Comment

Find the number of square yards

Area = L * w

L = 2

w = 1

Area = 2 * 1

Area = 2

Now for the counter top

1 sq yard costs 204.63

2 sq yards cost 2 * 204.63

2 sq yards cost 409.26

Answer: 409.26

Answer:

9 sq cm

Step-by-step explanation:

If you join the two triangles it will become a square of side 3cm.

3cm * 3cm = 9cm squared.

Hope you have a nice day :)

Any questions please comment.

The equation of the parabola which has a vertex at (-2,0) is; y = x² +4x +4.

From the task content, it follows that the vertex of the of the parabola described by the graph in discuss is given by the point; (-2,0).

Hence, the vertex form of the equation is;

y = (x-(-2))² +0

Hence, the equation is; y = x² +4x +4.

Read more on the equation of a parabola;

https://brainly.com/question/4148030

#SPJ1

Answer: B

Step-by-step explanation:

Edge 2023

In the given diagram, the value of the side labelled x is 10.8 cm

From the question, we are to determine the value of side x

Using the law of sines

In any given triangle XYZ,

[tex]\frac{x}{sinX}=\frac{y}{sinY}=\frac{z}{sinZ}[/tex]

Thus,

In the given triangle,

[tex]\frac{x}{sin81^\circ} =\frac{7}{sin40^\circ}[/tex]

∴ [tex]x=\frac{7 \times sin81^\circ}{sin40^\circ}[/tex]

x = 10.75599

x ≈ 10.8 cm

Hence, the value of the side labelled x is 10.8 cm

Learn more on Law of sines here: https://brainly.com/question/2807639

#SPJ1

Answer:

4x+22

Step-by-step explanation:

distribute 4(x+4)

it would become 4x+16+6

16+6 = 22

4x+22

The maximum volume of the cylinder is 27147.355 at the maximum point  [tex]r = \frac{50}{\sqrt{3} }[/tex] .

The formula for the volume of the cylinder v = [tex]\pi[/tex][tex]r^{2}[/tex]h, To find the maximum volume of the cylinder we apply the condition of maxima  [tex]\frac{\mathrm{d} v}{\mathrm{d} r}[/tex] = 0.

Let r cm be the radius and h cm be the height of the closed cylinder.

Then, Total surface area of the cylinder = [tex]2\pi r(r+h)[/tex]

                                                        [tex]5000[/tex] = [tex]2\pi r^{2} +2\pi rh[/tex]

                                                             [tex]h[/tex] =   [tex]\frac{5000-2\pi r^{2} }{2\pi rh}[/tex] .............(1)

Volume of the cylinder v = [tex]\pi r^{2} h[/tex]

Substitute the value of [tex]h[/tex] in the above equation

[tex]\Rightarrow[/tex]                                       = [tex]\pi r^{2}[/tex] × [tex]\left [ \frac{5000-2\pi r^{2}}{2\pi r} \right ][/tex]

[tex]\Rightarrow[/tex]                                      = [tex]\frac{r}{2}[/tex] ×  [tex](5000-2\pi r^{2} )[/tex]

[tex]\Rightarrow[/tex]                                    v = [tex]2500r-\pi r^{3}[/tex] ..............(2)

Now, for the maximum volume of the cylinder  [tex]\frac{\mathrm{d} v}{\mathrm{d} r}[/tex] = 0

[tex]\Rightarrow[/tex]                                                            [tex]\frac{\mathrm{d} (2500r-\pi r^{3})}{\mathrm{d} r} = 0[/tex]

[tex]\Rightarrow[/tex]                                                                      [tex]3\pi r^{2} = 2500[/tex]

[tex]\Rightarrow[/tex]                                                                          [tex]r^{2} = \frac{2500}{3\pi }[/tex]

[tex]\Rightarrow[/tex]                                                                          [tex]r = \frac{50}{\sqrt{3\pi } }[/tex]

Volume is maximum for  [tex]r = \frac{50}{\sqrt{3\pi } }[/tex]  

Then, v = [tex]2500r-\pi r^{3}[/tex]

[tex]\Rightarrow[/tex]              =  [tex]2500 \frac{50}{\sqrt{3\pi } } -\pi (\frac{50}{\sqrt{3\pi } } )^{3}[/tex]                              

[tex]\Rightarrow[/tex]             = [tex]\frac{125000}{\sqrt{3\pi } } - \frac{125000}{3\sqrt{3\pi } }[/tex]

[tex]\Rightarrow[/tex]             = [tex]\frac{125000}{\sqrt{3\pi } }[/tex]×[tex]\frac{2}{3}[/tex]

[tex]\Rightarrow[/tex]             = [tex]\frac{250000}{3\sqrt{3\pi } }[/tex]                                                              

[tex]\Rightarrow[/tex]          v = 27147.355

Hence, The maximum volume of the cylinder is 27147.355 at the maximum point  [tex]r = \frac{50}{\sqrt{3} }[/tex] .                                                

To learn more about total surface area and volume of the cylinder from the given link

https://brainly.com/question/16095729

#SPJ4                                                                                   

The graphs show a parabola with a vertex that has Roots are -2 and 4.

We have given that,

vertex of (1,-9) and solutions of (-2,0) and (4,0).

y=k*(x+2)(x-4)

Vertex = (1,-9) is a point of the parabola

-9=k*(1+2)(1-4) implies k=1

Equation of the parabola is y=(x+2)(x-4).

The graphs show a parabola with a vertex that has Roots are -2 and 4.

To learn more about the parabola visit:

https://brainly.com/question/4148030

#SPJ1

Answer:

B

Step-by-step explanation:

cable subscribers

Answer:

table A

Step-by-step explanation:

A direct variation can be expressed as: [tex]\frac{y}{x}=k[/tex]. The y/x is equal to a constant value k. Multiply both sides by x you get: [tex]y=kx[/tex]. So as x increases by 1, y increases by some constant value. So to find which one will create a direct variation, see which of the tables has a constant y/x

Table A:
   7/2 = 3.5

   14/4 =3.5

   17.5/5=3.5

   21/6 = 3.5

   this has a constant y/x so it is a direct variation

Table B:

   7/2 = 3.5

   14/4 = 3.5

   21 / 5 = 4.2

   this is not a direct variation, it doesn't have a constant y/x

table C:

   7 / 2 = 3.5

   14 / 4 = 3.5

   15/5 = 3

   This is not a direct variation, it doesn't have a constant y/x

table d:
   7/2 = 3.5

   14/4 =3.5

   17/5=3.4

   This is not a direction variation, it doesn't have a constant y/x

The statement that is true about the estimate is that the number will be less than 1 because when adding the exponents, 11 + (negative 14) = negative 3, and a number in scientific notation with a negative exponent is less than 1 (option D).

According to this question, Bethany wants to estimate the value of (4.296 times 10 Superscript 11) (1.8614 times 10 Superscript negative 14).

This expression can be mathematically written as:

(4.296 × 10¹¹) (1.8614 × 10-¹⁴)

The result of this expression is 7.996 × 10-³, which is value less than 1.

Therefore, the number will be less than 1 because when adding the exponents, 11 + (negative 14) = negative 3, and a number in scientific notation with a negative exponent is less than 1.

Learn more about exponentiation at: https://brainly.com/question/11487261

#SPJ1

The data can be shown in the frequency table with only 4 intervals and the histogram is shown in the picture.

It is defined as the depiction of numerical data in a graph using a bar with no space. The histogram depicts the approximate distribution of the data.

We have data:

6, 5, 4, 3, 0, 7, 1, 5, 4, 4, 3, 2, 2, 3, 2, 4, 3, 4, 0, 7

Intervals   Frequency

 0 - 3     6

 3 - 6     11

 6 - 9     3

 9 - 12     0

The histogram is shown in the attached picture.

Thus, the data can be shown in the frequency table with only 4 intervals and the histogram is shown in the picture.

Learn more about the histogram here:

brainly.com/question/16819077

#SPJ1

Answer:

7.76

Step-by-step explanation:

0.22×20=4.4

3.36(base amount ,average of the others)+4.4=7.76

[tex]x=57^{\circ}[/tex] (alternate segment theorem)

[tex]y=67^{\circ}[/tex] (alternate segment theorem)

Answer:

gradient = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

calculate the gradient m using the gradient formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 6, 0) and (x₂, y₂ ) = (0, 2) ← 2 points on the line

m = [tex]\frac{2-0}{0-(-6)}[/tex] = [tex]\frac{2}{0+6}[/tex] = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]

x+3 is not a factor of f(x)=x^4+6x^3+5x^2-15x-2 because there is a remainder of 7 when we use the long division method to divide x+3 with the given function f(x).

The factors of a quadratic equation are the simplified form of the quadratic equation, that if multiplied together, results in the original quadratic equation.

Given that:

[tex]\mathbf{=\dfrac{x^4+6x^3+5x^2-15x-2}{x+3} }[/tex]

[tex]\mathbf{=x^3+3x^2-4x-3+\dfrac{7}{x+3} }[/tex]

x+3 is not a factor of f(x)=x^4+6x^3+5x^2-15x-2 because there is a remainder of 7 when we use the long division method to divide x+3 with the given function f(x).

Learn more about finding the factors of a quadratic equation here:

https://brainly.com/question/3400933

#SPJ1

The pattern in the values as the exponents increase is multiply the previous value by 2.

Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.

Given:

Powers of 2      Values

[tex]2^{-5}[/tex]                         1/32

[tex]2^{-4}[/tex]                           1/16

[tex]2^{-3}[/tex]                           1/8

[tex]2^{-2}[/tex]                           1/4

[tex]2^{-1}[/tex]                           1/2

As, from the given data we can see that negative powers of 2 reducing by 1.

as, 2^-5 * 2= 2^-4

Hence, multiply the previous value by 2 to obtain the next value.

Learn more about exponents and powers here:

https://brainly.com/question/16649216

#SPJ1

Therefore, the measures of the angles in triangle ABC is as follows:

The measure of the angles in the right triangle can be found as follows:

Using trigonometric ratios,

sin ∅ = opposite / hypotenuse

sin ∅ = 7 / 25

∅ = sin ⁻¹ 0.28

∅ = 16.2602047083

∅ = 16.3°

Hence,

m∠B = 16.3°

m∠C = 90°

m∠A = 180 - 90 - 16.3 = 73.7°

learn more on right triangle here: https://brainly.com/question/27899600

#SPJ1

The scale factor of the image under a dilation centered at the origin is 2.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Translation is the movement of a point either up, down, left or right on the coordinate plane.

Let us assume that quadrilateral ABCD have vertices at A(2, 1) while its image has vertices at A'(4, 2), hence:

Scale factor = 4/2 = 2/1 = 2

The scale factor of the image under a dilation centered at the origin is 2.

Find out more on transformation at: https://brainly.com/question/4289712

#SPJ1

The rate at which the distance from the plane to the station increases is 537 miles/hour. Computed using Pythagoras Theorem and Differentiation.

We assume the station to be at point A.

The plane when directly over the station, takes point C.

As it is flying horizontally continuously at an altitude of 1 mile, AC = b = 1 mile.

The plane flies continuously, and when it is at a distance of 3 miles from the station, it is at point B.

The distance between the plane and the station of 3 miles can be shown as AB = c = 3 miles.

The movement of the plane from C to B can be shown as BC = a.

Now, from the given case, we get a right triangle ABC.

By Pythagoras' Theorem,

a² + b² = c² ... (i).

or, a² + 1² = 3²,

or, a² = 9 - 1 = 8,

or, a = 2√2 miles.

We are told that the plane is moving at a speed of 570 miles/hour.

This can be shown as, da/dt = 570 miles/hour.

As the plane is moving horizontally, the vertical distance between the plane and the station doesn't change, that is, db/dt = 0.

In the question, we are asked to find the rate at which the distance from the plane to the station is increasing, that is, we are asked to find dc/dt.

Differentiating (i), with respect to time t, we get:

2a(da/dt) + 2b(db/dt) = 2c(dc/dt).

Substituting values of a = 2√2 miles, b = 1 mile, c = 3 miles, da/dt = 570 miles/hour, and db/dt = 0, we get:

2(2√2)(570) + 2(1)(0) = 2(3)(dc/dt),

or, 2280√2 + 0 = 6(dc/dt),

or, dc/dt = 380√2 miles/hour = 537.40 miles/hour ≈ 537 miles/hour.

Thus, the rate at which the distance from the plane to the station increases is 537 miles/hour. Computed using Pythagoras Theorem and Differentiation.

Learn more about the Pythagoras Theorem and Differentiation at

https://brainly.com/question/15291822

#SPJ4