The star Sirius is more than 4 light years farther from Earth than the star
Proxima Centauri. Write an inequality that represents the distances of Sirius
and Proxima Centauri from Earth.

Answer: (2x + 5) (4x^2 -10 + 25)

Step-by-step explanation:

I use the equation a^3 + b^3 = (a+b) ( a^2 -ab + b^2)

You can factor the answer (2x + 5) (4x^2 -10 + 25) out to check and will get 8x^3 +125

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Answer:

7.14 km

Step-by-step explanation:

the total time that the bus takes to travel from Deltaville to Eastwick  12:42 - 11:32 = 00:10

Convert to hours 00:10 / 60 minutes/hour = 0.17 hours.

distance = speed * time

distance = 42 km/h * 0.17 hours

distance = 7.14 km

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The number of chicken sandwiches is 60.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 - 6 is an equation.

We have,

Number of ham sandwiches = H

Number of chicken sandwiches = C

Cost of ham sandwiches = $3.50

Cost of chicken sandwiches = $4

Now,

The total number of sandwiches = 110

The total amount earned = $415

Now,

The two equations are:

H + C = 110 _____(1)

3.50H + 4C = 415 _____(2)

From (1) we get,

C = 110 - H _____(3)

Now,

Putting (3) in (2) we get,

3.50H + 4(110 - H) = 415

3.50H + 440 - 4H = 415

-0.5H = 415 - 440

-0.5H = -25

H = 25/0.5

H = 50

Now,

Putting H = 50 in (3) we get,

C = 110 - H

C = 110 - 50

C = 60

Thus,

The number of chicken sandwiches is 60.

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The required linear functions are A(t) = 50t + 100 and B(t) = 25t + 200  which are represented in the attached graph. Company A is cheaper if the time is less than 4 hours.

As per the given question, we can write the linear functions as:

A(t) = 50t + 100

B(t) = 25t + 200

We can determine time t when both companies charge the same rate by equating the two equations.

50t + 100 = 25t + 200

Subtract 25t from both sides and subtract 100 from both sides

25t = 100

Divide both sides by 25

t = 4

At 4 hours both companies charge the same rate. So Company A is cheaper if the time is less than 4 hours.

After 4 hours, company B is cheaper.

Since both functions are linear, we only need two points to plot each one onto a graph.

Thus, the required linear functions are A(t) = 50t + 100 and B(t) = 25t + 200  which are represented in the attached graph.

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The correct option d. 90 - 95%, is the percentage of diabetes patients having type 2.

A disorder in the body's ability to control and utilize sugar (glucose) as fuel is type 2 diabetes.

The recipe for diabetes management is a healthy diet.

Thus, one in ten Americans, or more than 37 million people, have diabetes, and 90–95% of them suffer from type 2 diabetes.

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Answer:

D

Step-by-step explanation:

90-95

Answer: I believe it is 18/5

 or Decimal Form:

3.6

or Mixed Number Form:

3 3/5

Step-by-step explanation

4/5 x 4 1/2

Answer: $69

Step-by-step explanation: 562-148=414 & 414/6=69

Answer:

x=2173

Step-by-step explanation:

Step-by-step explanation:

where is the diagram?

please

Answer:

56

Step-by-step explanation:

Take two points as far apart on the line (for maximum accuracy), preferably on grid points, and then calculate the vertical difference divided by the horizontal difference.

So (4, 224) and (0,0) are on the line, and (224-0)/(4-0) = 56

Answer:

Stretches vertically by 2, shifts right by 1

Step-by-step explanation:

changes to y are direct, but you have to take the inverse for changes to x. This is because for a given value of y, with x-1, you would have to add one to x to make it the same value(to get the same point before the transformation)

The surface area of the rectangular prism is 76cm^2

Geometry is the study of various mathematical or actual-world shapes, figures, and sizes. In geometry, we study various angles, transformations, and figure-to-figure similarities. The fundamental concepts of geometry primarily depend on point, line, angle, and plane.

The three most popular types of geometry are solid geometry (which deals with objects like the line, sphere, and polyhedron) and spherical geometry. Plane geometry deals with objects like the point, line, circle, triangle, and polygon.

According to the question:-

The surface area of the rectangular prism is:_

surface area= 2*(lb+bh+hl)

                    =2*(5*4+4*2+2*5)

                    =76 cm^2

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Each of the three angles measures 75°, 65°, and 40°.

What is an angle measure?

An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Here, we have

Let the largest angle be x degrees, the median y, and the smallest z.

x = 2y - 55

z = y - 25

x + y + z = 180

Substituting for x in the last equation:

2y - 55 + y + z = 180

3y + z = 235  

From the second equation:

- y + z = -25     Subtract this from the last equation:

4y = 260

y = 65 degrees

z = 65 - 25 = 40 degrees.

and x = 180 - 65 - 40 = 75 degrees.

Hence, each of the three angles measures 75°, 65°, and 40°.

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The measures of each of the three angles are 40,65 and 75 degrees.

What is angle ?

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle.

Give that:

Let us consider X,Y,Z re the largest ,medium and smallest angle in the triangle.

Sum of the measures of the angles of any triangle is 180 degrees .

                            X + Y + Z = 180 degree

The largest angle measures 55degrees less than twice the medium angle,

                            Z = 2Y - 55 degree

The smallest angle measures 25 degrees less than the medium angle,

                          X = Y - 25 degree

Now ,replace X by (Y - 25) and Z by (2Y - 55) in the first equation

Y - 25 +Y + 2Y - 55 = 180 degree

4Y = 180 + 25 + 55

4Y = 260

Y = 65   Degree of the medium angle

X = 65 - 25

X = 40   Degree of the smallest angle

Z = 2 * 65 -55

  = 130-55

Z = 75   Degree of the largest angle.

40 + 65 + 75 = 180

180 = 180

Hence proved.

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Answer: X=0

Step-by-step explanation: X is equal to zero. This is the only way the equation can be true.

Another estimate is given as L6, R6, and M3 using the velocities at the conclusion of the time periods.

The table provides speedometer readings of velocity for a moving vehicle at 7-second intervals. t (sec) v (ft/s) 0 7 14 21 28 Using the speeds at the start of the time intervals, calculate the distance the car went during this 35-second span. travel distance in feet

Just figure out the rectangles' surface areas. Always draw the picture; it will be really helpful.

L6 = 10(0+9+31+56+71+68) \sR6 = 10(9+31+56+71+68+50) \sM3 = 20(9+56+68)

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Answer:

2

Step-by-step explanation:

you take 1 and add 1 to it... and bam... 2

Answer:

2

Step-by-step explanation:

1+1=2 because 2-1=1 :0

Answer:

-4v³ - v² - v - 9

Step-by-step explanation:

1. Subtract the numbers

7v - 4 - 4v³ - v² - 8v - 5

7v - 9 - 4v³ - v² - 8v

2. Combine like terms

7v - 9 - 4v³ - v² - 8v

-v - 9 - 4v³ - v²

3. Rearrange Terms

-v - 9 - 4v³ - v²

-4v³ - v² - v - 9

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Answer:

He spent 4&1/10 hours

Step-by-step explanation:

2&1/2+1&3/5

=5/2+8/5

=25/10+16/10

=41/10

4&1/10

question: 4m^2 - 5mn^2 + 8m^2 - 6n^2m - m^2

answer:

11m^2-11mn^2 (see pictures)

Time required to diffuse the F2 gas under the same conditions pressure and temperature with same volume is equal to 14 mins( approximately).

As given in the question,

Time taken by 1.5L sample of He gas to diffuse = 4.55 min.

Molar mass of He gas = 4g

Volume of He gas = 1.5L

Volume of F2 gas = 1.5L

Molar mass of F2 = 38gm

Formula of Rate of diffusion is given by :

Rate of diffusion of He / Rate of diffusion of F2

= √Molar mass of F2 / √Molar mass of He

Now,

Rate of He = Volume of He / time taken

                  = 1.5 / 4.55  

Rate of F2 = [ ( Rate of He ) ×√ Molar mass of He ] / √ Molar mass of F2

                 = ( 1.5 / 4.55 ) × ( √4 / √38)

                 = 3 / 28.028

                 = 0.107 L / min

Time of F2 = Volume of F2 / Rate of F2

                  = 1.5 / 0.107

                  = 14.02 minutes

                  ≈ 14 minutes.

Therefore, the time taken by F2 to diffuse under the same condition of He is equal to 14 minutes.

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Answer:

4

Step-by-step explanation:

 The lines are perpendicular because they intersect at a right angle.

The linear equation of the relationship is L = -8t + 40.

The amount Austin paid back each week is: $8.

A linear equation is straight line graph, which can be expressed as y = mx + b, in slope-intercept form. In the slope-intercept form, we have:

Slope = change in y / change in x.

Using two pairs of values from the table given, (1, 32) and (2, 24):

Slope (m) = (32 - 24) / (1 - 2)

m = 8/-1

m = -8.

Find the y-intercept (b) by substituting m = -8 and (x, y) = (1, 32) into y = mx + b:

32 = -8(1) + b

32 = -8 + b

32 + 8 = b

40 = b

b = 40

Substitute b = 40 and m = -8 into L = mt + b:

L = -8t + 40

Using the linear equation, the amount Austin paid back each week is: $8.

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Answer:

y + 3 = (-5/3) × (x - 1)

Step-by-step explanation:

                     5

(1, -3); m = - -------

x₁, y₁              3

y - y₁ = m(x - x₁)

y - (-3) = (-5/3)(x - 1)

y + 3 = (-5/3)x + (5/3)

   -3                   -3

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

y = (-5/3)x - (4/3) :Slope-intercept form

I hope this helps!

Assuming that h(x) = 7x4 - 9x3 - 41x2 + 13x + 6 and h(-2) = 7, (-2) 4 - 9(-2) (-2) 3 - 41(-2) (-2) 2 + 13(-2) + 6 = 7(16) - 9(-8) (-8) - 41(4) + 13(-2) + 6 = 0;

This indicates that (x + 2) is a synthetic polynomial factor.

(7x4 - 9x3 - 41x2 + 13x + 6) ÷ (x + 2):

The balance is zero.

A polynomial of degree 3 makes up the quotient: g(x) = 7x3 - 23x2 + 5x + 3.

The Rational Zeros Theorem shows that p: 1, 3, which are factors of the constant term 3, and q: 1, 7, which are factors of the leading coefficient 7, respectively

All potential outcomes are p/q: 1, 3, 1/ 7, and 3/7 g(3) = 7. (3)

3 - 23(3) +(3)

By artificial division:

The balance is zero.

The polynomial quotient is quadratic.

7x2 - 2x - 1 = 0

Equation for quadratics = [-b (b2 - 4ac)]/2a

x = -(-2) ± √[(-2)2 - (4 × 7 × -1)]/ (2 × 7) = (2 ± √32)/14 = (1 ± 2√2)/7

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By using exponent properties we will find the equivalent expression:

(-2)⁴/(-2)² = (-2)² = 4

Here we need to use the exponent property:

xⁿ/xᵇ = xⁿ⁻ᵇ

Here the expression we have is:

(-2)⁴/(-2)²

Using the above property we can rewrite the expression as:

(-2)⁴/(-2)² = (-2)⁴⁻² = (-2)²

Now we can solve this:

(-2)² = (-2)*(-2) = 4

Then the equivalent expression is 4.

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A=[e to the power of π/2-2] when the height and breadth of a typical approximate rectangle that you have drawn. then locate the region's area. y=eˣ, x=π/2, y=cos x

Given that,

We have to draw the area that the provided curves surround. Choose x or y as the integration direction. Label the height and breadth of a typical approximate rectangle that you have drawn. then locate the region's area. y=eˣ, x=π/2, y=cos x

We know that,

y=eˣ, x=π/2, y=cos x

Now area of the shaded region is

A=[tex]\int\limits^\pi/2_ x=0 \int\limits^e^{2} _y=cosx {dy} \, dx[/tex]

A=[tex]\int\limits^\pi/2_0 {e^{x}-cosx } \, dx[/tex]

Now we integrate with respect to x.

A=[eˣ-sinx]₀π/2

A=[e to the power of π/2- sin(π/2)]-[e⁰-sin(0)]

A=[e to the power of π/2-1]-[1-0]

A=[e to the power of π/2-1-1]

A=[e to the power of π/2-2]

Therefore, A=[e to the power of π/2-2] when the height and breadth of a typical approximate rectangle that you have drawn. then locate the region's area. y=eˣ, x=π/2, y=cos x

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The largest value less than 500 that the arithmetic progressions have in common = 479

In this question, we have been the arithmetic progressions {2,5,8,11, . . .} and {3,10,17,24, . . .}

We need to find the largest value less than 500 that they have in common.

We know that the formula for the n-th term of arithmetic progression is: an = a + (n – 1)d

For arithmetic progression {2,5,8,11, . . .}

a_m = 2 + (m - 1)3

For arithmetic progression {3,10,17,24, . . .}

a_n = 3 + (n - 1)7

if we solve for m, n then m =160 and n =69

2 + (160 -1)*3 = 479  which is the 160th term in the arithmetic progression {2,5,8,11, . . .}

3 + (69 - 1)*7  =479 which is the 69th term in the arithmetic progression {3,10,17,24, . . .}

Therefore, the value which less than 500 that both the progressions have in common = 479

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The rectangle has a length of 40 cm and width of 34 cm.

Given,

The length of a rectangle = x cm

The width of the rectangle = x - 6 cm

The perimeter of the rectangle = 148 cm

We have to find the length and width of the rectangle;

Here,

Perimeter of rectangle = 2(length + width)

That is,

148 = 2(x + x - 6)

148/2 = 2x - 6

74 = 2x - 6

74 + 6 = 2x

x = 80/2

Length, x = 40 cm

Width, x - 6 = 40 - 6 = 34 cm

Therefore,

The length of the rectangle is 40 cm and the width of the rectangle is 34 cm

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Answer: $4368

Step-by-step explanation:

Find 4% of 1400 by taking 1400 times 0.04 = $56

So a year he has 1456$

After 3 years just need to take 1456 times 3 = $4368

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