If f(x) = 2x-1 + 3 and g(x) = 5x-9, what is (f-g)(x)?

Answer:

(x) = 2(1/6)^x

Step-by-step explanation:

To easily solve this problem, we can graph each option using a graphing calculator, or any equation plotting tool.

Case 1

f(x) = 2(6)^x

Case 2

f(x) = 1/2*(6)^x

Case 3

f(x) = 2(1/6)^x

Case 4

f(x) = 1/2*(1/6)^x

By looking at the pictures below, we can tell that the correct option is

Case 3

f(x) = 2(1/6)^x

Since the stretch is done by a factor of 2

Answer:

3,5

Step-by-step explanation:

Represent the width by W and the length by L.  L = W + 2 (because L and W are consecutive odd integers).

Then L * W = 15 units^2, and after substitution this becomes:

(W + 2) * W = 15, or W^2 + 2W - 15 = 0.

This factors as follows:  (W + 5)(W - 3) = 0, and the positive root is W = 3.

The length and width of the rectangle are 3 and 5 respectively.

Note that 3 and 5 are consecutive odd integers, and that 3 * 5 = 15 units^2.

Final answer:

The length and width of the rectangle are consecutive odd integers that equate to an area of 15 square units, which are 3 units and 5 units, respectively.

Explanation:

The question at hand involves finding the consecutive odd integers that represent the length and width of a rectangle with an area of 15 square units.

Since the area of a rectangle is the product of its length and width, and in this case both are odd integers, we can list the odd number pairs whose product is 15.

The only odd numbers that multiply together to equal 15 are 3 and 5.

Therefore, the dimensions of this rectangle with the consecutive odd integer sides are: length of 5 units and width of 3 units, or vice versa depending on the interpretation, but typically, length is considered to be greater than width in geometry.

slope is [tex]\frac{rise}{run}[/tex] or [tex]\frac{vertical}{horizontal}[/tex]

Look at the image below:

The red (4) is the rise and the blue (1) is the run

this means the slope is...

[tex]\frac{4}{1}[/tex]

4

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Step-by-step explanation:

Here you estimate the proportion of people in the population that said did not have children under 18 living at home.It can also be given as a percentage.

The general expression to apply here is;

[tex]C.I=p+-z*\sqrt{\frac{p(1-p)}{n} }[/tex]

where ;

p=sample proportion

n=sample size

z*=value of z* from the standard normal distribution for 95% confidence level

Given;

n=5000

Find p

From the question 54% of people chosen said they did not have children under 18 living at home

[tex]\frac{54}{100} *5000 = 2700\\\\p=\frac{2700}{5000} =0.54[/tex]

To calculate the 95% confidence interval, follow the steps below;

The value of z* from the table is 1.96

The value of p=0.54 as calculated above

[tex]0.54(1-0.54)=0.2484[/tex]

Divide the value of p(1-p) with the sample size, n

[tex]\frac{0.2448}{5000} =0.00004968[/tex]

[tex]=\sqrt{0.00004968} =0.007048[/tex]

Here multiply the square-root of p(1-p)/n by the z*

[tex]=0.007048*1.96=0.0138[/tex]

The 95% confidence interval for the lower end value is p-margin of error

[tex]=0.54-0.0138=0.5262[/tex]

The 95% confidence interval for the upper end value is p+margin of error

[tex]0.54+0.0138=0.5538[/tex]

Answer: 0.5262 - 0.5538

Step-by-step explanation:

1) Find the standard deviation with the given information:

n=5000

p=54% ⇒ 0.54

1-p = 1 - 0.54 = 0.46

[tex]\sigma =\sqrt{\dfrac{p(1-p)}{n}}\\\\\\.\ =\sqrt{\dfrac{0.54(0.46)}{5000}}\\\\\\.\ =\sqrt{\dfrac{0.2484}{5000}}\\\\\\.\ =\sqrt{0.00004968}\\\\\\.\ =0.007048[/tex]

2) Find the margin of error (ME) with the given information:

C=95% ⇒ Z = 1.960

σ=0.007048

ME = Z × σ

     = 1.96 (0.007048)

     = 0.01381

3) Find the confidence interval with the given information:

p = 0.54

ME = 0.01381

C = p ± ME

    = 0.54 ± 0.01381

    = (0.5262, 0.5538)

Answer:

54 degrees

Step-by-step explanation:

I would turn this into a quadrilateral by connecting C to O and O to A.

The angles of a quadrilateral add up to 360 degrees.

So we have 90+90+126+angleABC=360

                            180+126+angleABC=360

                                  306+angleABC=360

                                           angleABC=360-306=54

Answer:

ABC = 54°

Step-by-step explanation:

Two tangent have been drawn from an external point B to the circle O.

These tangents touch the circle at points A and C.

Now as per Theorem of arcs and angles.

∠ABC = [tex]\frac{1}{2}[/tex]   [m(major arc AC) - m(minor arc AC)]

          = [tex]\frac{1}{2}[/tex]  [234 - 126]

         = [tex]\frac{1}{2}[/tex]  × (108)

         = 54°

Therefore, ABC = 54°

Answer:

Step-by-step explanation:

If two equations are the same, then the system of equations has infinitely many solutions.

If two equations different only constant number, then the system of equations has no solution (coefficient at x in both equations is the same and coefficient at y is the same).

Therefore for y = 8x + 7 other equation is y = 8x - 7.

Answer:

The markup is $2.48

Step-by-step explanation:

* Lets explain the problem

- There is a cost price we don't know it

- There is a selling price we know it

- There is a markup we want to find it

- The relation between the cost price , the selling price and the markup

 is ⇒ selling price - cost price = markup

∵ The percentage of the selling price is 109%

∵ The percentage of the cost price is 100%

- That means the markup rate = 109% - 100% = 9%

∵ The selling price is $29.99

- Lets use the ratio to find the cost price

∵ selling price / cost price = selling price% / cost price%

∴ 29.99 / cost price = 109 / 100

- By using cross multiplication

∴ cost price × 109 = 29.99 × 100

∴ cost price × 109 = 2999

- Divide both sides by 109

∴ cost price = $27.51

∵ The markup = selling price - cost price

∴ The markup = 29.99 - 27.51 = $2.48

* The markup is $2.48

Answer:

Second option.

Step-by-step explanation:

The angle [tex](3x+17)\°[/tex] and the angle [tex](4x-8)\°[/tex] are alternate exterior angles, then they are congruent. So we can can find "x":

[tex]3x+17=4x-8\\17+8=4x-3x\\x=25[/tex]

Then, the angle  [tex](4x-8)\°[/tex] is:

 [tex](4x-8)\°=(4(25)-8)\°=92\°[/tex]

You can observe that the angle identified in the figure attached as "3" and the angle 46° are Alternate interior angles, then they are congruent.

Since the sum of the measures of the angles that measure 92°, 46° and the angle "2" is 180°, we can find the measure of the angle "2" by solving this expression:

[tex]92\°+46\°+\angle 2=180\°\\\\\angle 2=180\°-92\°-46\°\\\\\angle 2=42\°[/tex]

Answer:I agree that 46 is correct

Step-by-step explanation:

Answer:

p = 35

Step-by-step explanation:

180 - 125 = 55

180 - 90 = 90

55 + 90 = 145

180 - 145 = 35

p = 35

Answer:

9/20 miles

Step-by-step explanation:

we know that

if the bird flies 5/6 miles north for -------------> 3/8 miles east

then

for 1 mile north------------------------------> X miles east?

X=(3/8)/(5/6)-------> 18/40-------> 9/20 miles

the answer is

9/20 miles

The bird flies 18/25 miles east for each mile travelled north.

The question is asking for the ratio of the distance a bird flies east to the distance it flies north. Given that the bird flies 3/5 mile east and 5/6 mile north, we can set up a ratio to express the distance flown east per mile flown north. This is a straightforward ratio problem, where we divide the distance east by the distance north to find the required ratio.

To find the number of miles the bird flies east for every mile it travels north, we can set up the following ratio:

Distance East / Distance North = (3/5) miles / (5/6) miles
To simplify this, we multiply by the reciprocal of the denominator, resulting in:

(3/5) * (6/5) = 18/25.

So, the bird flies 18/25 miles east for every mile it travels north.

Answer:

YZ = XZ

Step-by-step explanation:

Perpendicular Bisector:

A perpendicular bisector of a line segment 'l' is a line that is perpendicular to the line segment 'l' and cuts the line segment 'l' into two equal parts.

Given:

1. A triangle WXY.

2. A perpendicular bisector from vertex W that intersects XY at point Z.

Conclusion based on the drawing:

a. Z is the midpoint of the line segment XY because point Z lies on the perpendicular bisector of XY.

b. Hence, XZ = YZ.

Answer:

Option D.

Step-by-step explanation:

Given information: WXY is a triangle.

Steps of construction:

1. Draw a triangle WXY.

2. Constructs a perpendicular bisector from vertex W that intersects side XY at point Z.

If a line cuts a line segment exactly in half by a 90 degree angle, then it is called a perpendicular bisector.

WZ is a perpendicular bisector on XY. It means point Z divides the side XY in two equal parts.

[tex]YZ=XZ[/tex]

Therefore, the correct option is D.

Answer:

(3, 2)

Step-by-step explanation:

First, we have to eliminate a variable:

3(5x+2y = 19 )

2(4x-3y = 6)

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

15x+6y = 57

8x-6y = 12

Now we add the system of equations together:

15x+8x+6y-6y = 57+12

23x = 69

/23   /23

x = 3

Now we can plug this value back into one of the equations to get y:

5(3)+2y = 19

15+2y = 19

-15         -15

2y = 4

/2     /2

y = 2

Therefore, the solution to these system of equations is (3, 2)

Answer:

The solution of given system of equation is (3,2).

Step-by-step explanation:

The given system of equations is

[tex]5x+2y=19[/tex]            .... (1)

[tex]4x-3y=6[/tex]              .... (2)

Solve the system of equations using elimination method.

Multiply equation (1) by 3 and multiply equation (2) by 2.

[tex]15x+6y=57[/tex]            .... (3)

[tex]8x-6y=12[/tex]              .... (4)

Now, add the equations (3) and (4), to eliminate y.

[tex]15x+8x=57+12[/tex]

[tex]23x=69[/tex]

Divide both sides by 23.

[tex]x=3[/tex]

The value of x is 3. Substitute x=3 in equation (1), to find the value of y.

[tex]5(3)+2y=19[/tex]

[tex]15+2y=19[/tex]

Subtract 15 from both the sides.

[tex]2y=19-15[/tex]

[tex]2y=4[/tex]

Divide both sides by 2.

[tex]y=2[/tex]

The value of y is 2.

Therefore the solution of given system of equation is (3,2).

Answer:

Option D (-1,-2)

Step-by-step explanation:

we know that

The ordered pair is 1 unit to the left of the origin and 2 units down from the origin

so

(x,y) ------> (0-1,0-2)

(x,y) ------> (-1,-2)

therefore

The coordinates of the ordered pair is (-1,-2)

Answer: c: (-1,-2)

Step-by-step explanation:

Just got it right on the quiz

Answer:

[tex]\frac{3}{20}[/tex]

Step-by-step explanation:

Box 1:

Number of pens = 3

Total number of items = pencils + pens = 7 + 3 = 10

Probability that a pen will be picked, P(Pen) = [tex]\frac{3}{10}[/tex]

Box 2:

Number of crayons = 3

Total number of items = color pencils + crayons = 3 + 3 = 6

Probability that a crayon will be picked, P(Crayon) = [tex]\frac{3}{6}[/tex]

P(pen from 1st box and crayon from 2nd box),

= P(Pen) x P(Crayon)

= [tex]\frac{3}{10}[/tex] x [tex]\frac{3}{6}[/tex]

= [tex]\frac{3}{20}[/tex]

Answer:

see explanation

Step-by-step explanation:

Calculate the distance (d) using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (3, 5) and (x₂, y₂ ) = (1, a)

d = [tex]\sqrt{(1-3)^2+(a-5)^2}[/tex]

  = [tex]\sqrt{(-2)^2+(a-5)^2}[/tex]

  = [tex]\sqrt{4+(a-5)^2}[/tex]

Equating d to [tex]\sqrt{8}[/tex], gives

[tex]\sqrt{4+(a-5)^2}[/tex] = [tex]\sqrt{8}[/tex]

Squaring both sides

4 + (a - 5)² = 8 ( subtract 4 from both sides )

(a - 5)² = 4 ( take the square root of both sides )

a - 5 = ± [tex]\sqrt{4}[/tex] = ± 2 ( add 5 to both sides )

a = 5 ± 2, that is

a = 5 - 2 = 3 OR a = 5 + 2 = 7

The speed of the commercial jet is [tex]540mi/h[/tex] while the speed of the private airplane is [tex]330mi/h[/tex]

Let's name the commercial jet as cj and private airplane as pa, so we know the following:

It takes the commercial jet 1.1 hours for the flight, so:

[tex]t_{cj}=1.1h[/tex]

It takes the private airplane 1.8 hours for the flight, so:

[tex]t_{pa}=1.8h[/tex]

The speed of the commercial jet is 210 miles per hour faster than the speed of the private airplane:

Let's name the speed of the commercial jet as [tex]v_{cj}[/tex] and the speed of the private airplane as [tex]v_{pa}[/tex], then:

[tex]v_{cj}=v_{pa}+210[/tex]

From physics we know that:

[tex]v=\frac{d}{t} \\ \\ Where: \\ \\ v: \ speed \\ \\ d: \ distance \\ \\ t: \ time[/tex]

Since the distance from Denver to phoenix is unique, then:

[tex]d_{cj}=d_{pa}=d[/tex]

Thus, from the equation [tex]v_{cj}=v_{pa}+210[/tex] and given the relationship [tex]v=\frac{d}{t}[/tex] we have:

[tex]v_{cj}=v_{pa}+210 \\ \\ \frac{d}{t_{cj}}=\frac{d}{t_{pa}}+210 \\ \\ \\ Plug \ in \ t_{cj}=1.1 \ and \ t_{pa}=1.8 \ then: \\ \\ \frac{d}{1.1}=\frac{d}{1.8}+210 \\ \\ Isolating \ d: \\ \\ d(\frac{1}{1.1}-\frac{1}{1.8})=210 \\ \\ \frac{35}{99}d=210 \\ \\ d=\frac{99\times 210}{35} \\ \\ d=594miles[/tex]

Finally, the speeds are:

[tex]\bullet \ v_{cj}=\frac{d}{t_{cj}} \\ \\ v_{cj}=\frac{594}{1.1} \therefore \boxed{v_{cj}=540mi/h} \\ \\ \\ \bullet \ v_{pa}=\frac{d}{t_{pa}} \\ \\ v_{pa}=\frac{594}{1.8} \therefore \boxed{v_{pa}=330mi/h}[/tex]

Answer:

x² + 4x - 12, remainder - 60

Step-by-step explanation:

Using synthetic division to divide

Since dividing by x - 1, evaluate for x = 1

1 | 1  3  - 16  - 48

   ↓  1     4   - 12

  ---------------------------

   1   4  - 12  - 60 ← degree 2 polynomial

quotient = x² + 4x - 12, remainder = - 60

Hence

[tex]\frac{x^3+3x^2-16x-48}{x-1}[/tex] = x² + 4x - 12 - [tex]\frac{60}{x-1}[/tex]

The division of the given polynomials x³ + 3x² - 16x - 48 by x - 1 using synthetic division results in the polynomial x² + 4x - 12 - 60/(x - 1) with a remainder of -60.

The division of two polynomials can be performed using polynomial long division or synthetic division. In this case, we have a cubic polynomial divided by a linear polynomial: x³ + 3x² - 16x - 48 divided by x - 1.

We can use synthetic division to solve this. Place the coefficients of the dividend (1, 3, -16, -48) in a row and place the zero from the divisor (x - 1= 0, x = 1) to the left. Add down the columns and multiply the result by x in each row, placing the result in the next row.

Following these steps, the coefficients become 1, 4, -12, and -60 which translates to the polynomial x² + 4x - 12 - 60/(x - 1). The remainder (-60) divided by the divisor (x - 1) is added as the last term.

https://brainly.com/question/36507743

#SPJ11

Answer:

Option B is correct.

Step-by-step explanation:

Lateral surface area of cone = π*r*l

where r is the radius and l is the height of cone.

We are given height = l  24 cm

and diameter d = 10.5 cm

we know that radius is half of diameter i.e,

r = d/2

=> r = 10.5/2

r = 5.25

Putting the values in the formula:

Lateral surface area of cone = π*r*l

Lateral surface area of cone = π*5.25*24

Lateral surface area of cone = 126 π cm^2

So, Option B is correct.

Answer: second option.

Step-by-step explanation:

We know that we can calculate the lateral surface area of a cone with this formula:

[tex]LA=\pi rl[/tex]

Where "r" is the radius and "l" is the slant heigth.

We know that the radius is half the diameter, then the radius of this cone is:

[tex]r=\frac{10.5cm}{2}\\\\r=5.25cm[/tex]

Since we know tha radius and the slant height, we can substitute values into the formula. Therefore, we get:

 [tex]LA=\pi (5.25cm)(24cm)\\\\LA=126\pi cm^2[/tex]

Answer:

-3/4

Step-by-step explanation:

You could identify two points and used the slope formula given two points.

OR

You can just count from one point to another.

First step: Identify two points where the line crosses nicely.

I see one at the y-intercept (0,1) and another at (4,-2). So starting at the y-intercept, how much do we need to travel down to get to (4,-2).  Hopefully you say down 3, so the rise is -3.  Now how much to the right after traveling down 3 from (0,1) to we need to travel to get to (4,-2) .  Count the spaces...4 units right so the run is 4.

The slope is -3/4

Answer:

The missing term is 3b

Step-by-step explanation:

step 1

Find the coordinates of point F

Find the midpoint AB

[tex]F(\frac{-3a+3a}{2},\frac{b+b}{2})\\ \\F(0,b)[/tex]

step 2

Find the coordinates of point E

Find the midpoint AC

[tex]E(\frac{-3a-a}{2},\frac{b-5b}{2})\\ \\E(-2a,-2b)[/tex]

step 3

Find the distance EF

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

substitute

[tex]EF=\sqrt{(b+2b)^{2}+(0+2a)^{2}}[/tex]

[tex]EF=\sqrt{(3b)^{2}+(2a)^{2}}[/tex]

therefore

The missing term is 3b

Answer:

its 3b thats the answer

Answer:

Option C

Step-by-step explanation:

we know that

The solution of the system of inequalities is the shaded area above the dashed line y=4 and above the dashed line y=x

therefore

The system of inequalities is equal to

y>4

y>x

0.625 rounded to the nearest hundredth is 0.63

2 is in the hundredths place, and since the next number is 5 the 2 is rounded up one number giving you 0.63

Use the polynomial remainder theorem: the remainder upon dividing a polynomial [tex]p(x)[/tex] by [tex]x-c[/tex] is [tex]p(c)[/tex].

[tex](-b)^4+3(-b)^2-2(-b)+2=b^4+3b^2+2b+2[/tex]

[tex]((-b)^2-3)^2=b^4-6b^2+9[/tex]

Now

[tex]b^4+3b^2+2b+2=b^4-6b^2+9\implies9b^2+2b-7=0[/tex]

[tex]\implies(9b-7)(b+1)=0[/tex]

[tex]\implies b=\dfrac79\text{ or }b=-1[/tex]

Answer:

a)8

b)11

Step-by-step explanation:

given to 23-14

23-3=contains meat

a. Monica has [tex]8[/tex] choices to order from because she dislikes Ham.

b. Andrew has [tex]32[/tex] choices to order from because he likes meat but dislikes mixed meats.

a. Since Monica dislikes Ham, she cannot choose any of the 15 choices that contain Ham. She has [tex]\(23 - 15 = 8\)[/tex] choices left to order from.

b. Andrew likes meat but dislikes mixed meats, which means he can choose from the choices that contain only one type of meat (Ham or Chicken) or the vegetarian options. There are [tex]15[/tex] choices with Ham, [tex]14[/tex] choices with Chicken, and [tex]3[/tex] vegetarian choices.

[tex]\text{Total choices with only one type of meat}: \(15 + 14 = 29\)[/tex]

[tex]\text{Total choices with only one type of meat or vegetarian}: \(29 + 3 = 32\)[/tex]

Andrew has [tex]32[/tex] choices to order from.

Hello :D

Answer:

[tex]\boxed{R>-1}[/tex]

The answer should have a negative sign.

Step-by-step explanation:

First, you do is divide by 17 from both sides of an equation.

[tex]\frac{17r}{17}>\frac{-17}{17}[/tex]

Then, you simplify and solve to find the answer.

[tex]-17\div17=-1[/tex]

[tex]\boxed{R>-1}[/tex], which is our answer.

I hope this helps you!

Have a great day! :D

Answer: [tex]r>-1[/tex]

Step-by-step explanation:

Given the inequality provided [tex]17r > -17[/tex], you need to solve for "r".

To do this, you can divide both sides of the inequality by 17. Then you  get the following solution:

[tex]17r > -17\\\\\frac{17r}{17}>\frac{-17}{17}\\\\(1)r>(-1)\\\\r>-1[/tex]

Now, you can expressed this solution in Interval notation form.

 Therefore, the solution of the inequality in Interval notation is:

[tex](-1, \infty)[/tex]

Answer:

Step-by-step explanation:

you need to double the radius which is 8 cm

then you do 10 * 8 * 3.14 = 251.2

A boy swimming at an elevation of 3 feet below sea level. This is the answer because the boy is only 3 feet away from sea level while the bird is 10 feet away form sea level.

Answer:

B. A boy swimming at an elevation of –3 feet.

Step-by-step explanation:

We have been given that a bird flies at an elevation of 10 feet. We are asked to choose the elevation that is closer to sea level than the bird.

Let us find absolute value of each elevation.

A. A fish swimming at an elevation of –18 feet.

[tex]|-18|=18[/tex]

The fish is 18 feet away from sea level.

B. A boy swimming at an elevation of –3 feet.

[tex]|-3|=3[/tex]

The boy is 3 feet away from sea level.

C. A kite flying at an elevation of 30 feet.

[tex]|30|=30[/tex]

The kite is 30 feet away from sea level.

D. A bird sitting in a tree at an elevation of 12 feet

[tex]|12|=12[/tex]

The bird is 12 feet away from sea level.

Since the distance between the boy swimming and sea level is less than other distances, therefore, the boy is closer to sea level than the bird.

For this case we must indicate an expression equivalent to:

[tex](2 ^ 3) ^ {-5}[/tex]

By definition of power properties we have to:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

We also have to:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

Rewriting the expression we have:

[tex](2 ^ 3) ^ {-5} = 2 ^ {-15} = \frac {1} {2 ^ {15}}[/tex]

Answer:

Option A

[tex]\dfrac{1}{4}+x=\dfrac{20}{3}\Big|\cdot12\\\\3+12x=80\\\\12x=77\\\\x=\dfrac{77}{12}[/tex]

Answer:

x = 77/12 or 6 5/12

Step-by-step explanation:

To solve this one step equation you have to isolate the variable. To isolate the variable you need to to do the inverse of addition which is subtraction.

So you have to subtract 1/4 by 1/4

And what you do to one side of the equation you have to do to the other side.

So 20/3 - 1/4 = 77/12

So x = 77/12 or change it to a mixed number 6 5/12.

Hope this helped you!!

Answer:

correct answer options are ; C and D

Step-by-step explanation:

By definition, vertical angles are those that are opposite each other when two lines cross and are equal.

Observing the given options;

C. ∠LRE and ∠FRA

D.∠TRF and ∠NRL

In the other options given, it could have been correct if stated as;

A. ∠ARS and ∠ERO

B. ∠NRA and ∠TRE