Describe the x-values for which (a) f is increasing or decreasing, (b) f(x) > 0 and (c) f(x) < 0

The Area of Rectangle would be Decreased by 16% of the original Area. Now the Area of Rectangle is 84%.

Let the Length of rectangle be ‘x’

And width of rectangle be ‘y’

Area of Rectangle = Length X Width

Original Area of rectangle = x X y = xy square units

As the length is increased by 40% then, the new length would be 1+40% i.e 1.4 and,

The width is decreased by 40% then, the new width would be 1-40% i.e  0.6

New Length = 1.4x

New Width = 0.6y

Now , New Area of Rectangle = 1.4x X 0.6y

                    = 0.84xy square units

The effect is that the New Area of the rectangle is 84% of the original area. There is a decrease of 16% in the area.

To know more about Rectangle, Click here :

https://brainly.com/question/27924963

#SPJ4

Answer:

Bruce is 10 years old.

Step-by-step explanation:

m - Madge age.

b - Bruce age.

Madge is six years older than Bruce.

m=b+6 or m-6=b

In five years the sum of their ages will be 36.

m+5 - Madge age after 5 years.

b+5 - Bruce age after 5 years.

m+5+b+5=36

m=b+6

b+6+5+b+5=36

2b+16=36

2b=36-16

2b=20 /:2

b=10

m=b+6=10+6=16

.

The graph that represents the solutions of the given system of equations is attached below.

We are given a system of equations. The first equation is a quadratic polynomial. The second equation is linear in nature. The equations are given below.

x² - y = -2

4y - 8 = x

We need to find the solution to the equations using a graph. The graph of the equations is attached below. The graph of the first equation is represented by an upward parabola. The graph of the second equation is represented by a straight line. The intersection points of the two curves are the solutions to the given system of equations.

To learn more about equations, visit :

https://brainly.com/question/10413253

#SPJ1

Answer:6978

Step-by-step explanation:304585

The number of polio vaccinations is 32  and measles vaccination is 28

Let p represent the number of polio vaccines and let m represent the number of measles vaccines.

We know that each polio vaccine consists of 4 doses, and each measles vaccine consists of 2 doses.

Dr. Potter gave a total of 60 vaccinations last year. Therefore, the sum of the number of polio vaccines and measles vaccines must total 60. Therefore:

p+m=60

Together, they consisted of 184 doses.

Since each polio vaccine has 4 doses, the amount of doses for p polio vaccines is 4p.

And since each measles vaccine has 2 doses, the amount of doses for m measles vaccines is 2m.

So:

4p+2m=184

We now have a system of equations:

p+m=60

4p+2m=184

We can solve using elimination. Let’s multiply the first equation by -2. So:

-2p-2m=-120

Now, we can add this to the second equation. Hence:

(-2p+4p)+(-2m+2m)=(-120+184)

2p=64

p=32

Therefore, Dr. Potter gave out 32 polio vaccinations

p+m=60

By the first equation:

p+m=60

Substitute 32 for p to get

32+m=60

m=60-32

m=28

So, 28 measles vaccinations were given out.

To Learn more linear equations visit:

https://brainly.com/question/11897796

#SPJ4

Answer:

x=12.99

h=7.5

Step-by-step explanation:

the triangle OCB is an isosceles triangle whereby angleOCB=120,angleCOB=angleCBO=30

thus length of BC is 15

[tex]cosine \: rule \\ a {}^{2} = b {}^{2} + c {}^{2} - 2bc \cos(a) [/tex]

=(15^2+15^2)-(2×15×15×cos 120)

=450-(-225)

a^2 =675

a=25.98=OB

x=15sin 60

=12.99

h=15sin 30

=7.5

(x+2)(3x+1)

x(3x+1)+2(3x+1)

3x²+x+6x+2

3x²+7x+2

(3x²+7x+2)(x-3)

x(3x²+7x+2)-3(3x²+7x+2)

3x³+7x²+2x-9x²-21x-6

3x³+7x²-9x²+2x-21x-6

3x³-2x²-19x-6

The gal in the first mixes is nine-halves, the constant of proportionality is one-twelfth and the white paint required in 7 gals is seven twelfths

Given:

White paint = 3/8 gal

Blue paint =  2 7/8 gal

Red paint = 5/4 gal

Gallons of  first mixes = White paint + Blue paint + Red paint

Gallons of first mixes = 3/8 + 2 7/8 + 5/4 = 9/2 gal

The constant of proportionality of white paint to gallons of mixed paint:

constant of proportionality = white paint volume/ mixed paint volume

constant of proportionality = (3/8) / (9/2) = 1/12  

The constant of proportionality of white paint to gallons of mixed paint gives the fraction of white color in the total volume

In order to make 7 gallons of the same color paint, the quantity of white paint he will need is:

White paint in 7 gallons = 1/12 x 7 =  7/12

Therefore, blank one is nine-halves, blank two is  one-twelfth and blank three is seven twelfths

Learn more about fractions on:

https://brainly.com/question/29356621

#SPJ1

Nathan can drive 83 miles without exceeding the budget.

Let us assume the number of miles Nathan can go in $75 budget be x. Now forming the equation based on the mentioned information -

The total budget = daily rental charge + number of miles × cost per mile

Keep the values in formula -

75 = 29.50 + 0.55x

Rewriting the equation according to variable x

0.55x = 75 - 29.50

Performing subtraction on Right Hand Side of the equation

0.55x = 45.5

x = 45.5 ÷ 0.55

Performing division on Right Hand Side of the equation

x = 82.7

As 0.7 will be counted a mile, thus, Nathan can drive 83 miles.

Learn more about equation -

https://brainly.com/question/21405634

#SPJ4

Answer:

43

Step-by-step explanation:

to find mean we add all the terms together and them divide by the amount of terms so lets add what we know first

2+3+4+5+6+7

27

there are 7 terms including the y so for there to be a mean of 10 the terms will have to equal 70 when added so we just subtract

70-27

43

hopes this helps please mark brainliest

The system that models the equation is m = 2.5 lb.

This is a mixed-up issue.  The combination of

80% almonds and 20% peanuts make up combination A.

Completely peanuts in mixture B

both the

As a combination, use 60% peanuts and 40% almonds.

Since mixture C is created by combining mixtures A and B, we may calculate its combined weight in pounds to be 5 pounds.

Hence, we

Let m be the weight in pounds of mixture A (20% peanuts, 80 % almonds).

and

50-m is the quantity of mixture B in pounds.

Consequently, the set of equations that models this circumstance is:

0.20m + 1(50-m) = 0.60(5) (5)

0.80m + 0(50-m) = 0.40(5)

Equation 2's solution for m gives us

m = 2.5 lb.

Learn more about system of equations at

https://brainly.com/question/1379570

#SPJ4

The answer is 3.6 and 2 respectively.

What is the proportionality constant?

The proportionality constant is the ratio that connects two given values in a proportional relationship. The constant of proportionality is also known as the constant ratio, constant rate, unit rate, constant of variation, and even the rate of change.

We have,

R = k / A

where,

k is the proportionality constant

12 = k / 1.5

k = 12 * 1.5

k = 18

now

a) The value of R is?, when A=5.

R = 18 / 5

= 3.6

b) The value of A is? R=9.

A = 18 / 9

= 2

Hence, the answer is 3.6 and 2 respectively.

To learn more about the proportionality constant visit,

https://brainly.com/question/920111

#SPJ9

The expression represents the time she spent driving is       [tex]\frac{228.95}{x}[/tex]

The expression represent the time she spent driving can be calculated as follows:

We know that

Time = [tex]\frac{distance}{ speed}[/tex]

Let x be her speed on the first half of the trip.

Then for first half , the tiime she takes is

T1= [tex]\frac{150}{x}[/tex]

while in a second half the time taken by her is

T2= [tex]\frac{150}{1.9x}[/tex]

T2= [tex]\frac{78.95}{x}[/tex]

the total time she spent on driving is

T1 + T2 =    [tex]\frac{150}{x}[/tex] + [tex]\frac{78.95}{x}[/tex] =    [tex]\frac{228.95}{x}[/tex]

Hence, the expression represents the time she spent driving is       [tex]\frac{228.95}{x}[/tex]

Learn more on the expression here : https://brainly.com/question/2506869

#SPJ1

Answer:

See attachment...

Hope this helps! :)

The percent error of the meaurement is 6.21%

Julia meaured a line to be 16. 1 inche long

The actual length of the line i 17. 1 inche

Error in length = actual length - measured length

Error in length = 17.1 - 16.1 = 1 inch

Percent of error is defined as the difference between a measured or experiment value and an accepted or known value, divided by the known value, multiplied by 100

error percent = error/ known value x 100

= 1/16.1 x 100

= 6.21%

Therefore, the percent error of the meaurement is 6.21%

To learn more about error percentage refer here

https://brainly.com/question/28746643

#SPJ4

The probability that the mean contents of the 784 sample cans are less than 9.995 ounces is 0.081. The correct option is B

Probability is the ability to happen. The subject of this area of mathematics is the occurrence of random events. From 0 to 1 is used to express the value. Probability has been introduced in mathematics to determine how likely events are to occur.

Given mean = 10

standard deviation = 0.10

sample  = 784

The probability that the 784 sample cans' average contents will be less than 9.995 ounces

P ( X < 9.995 ) =  x - μ/ σ / √n

 = 9.995-10/0.10/√784

 = -0.005 / 0.10 /28

 = -1.400

P(Z < -1.400)  = 0.081

Therefore the probability that the mean contents of the 784 sample cans are less than 9.995 ounces is 0.081

To learn more about probability visit

https://brainly.com/question/11234923

#SPJ4

Answer:

Step-by-step explanation:

m = E / c²

Hives, itching, and pale or flushed skin are examples of allergies. reduced blood pressure (hypotension) breathing difficulties and wheezing can result from airway constriction and swelling of the tongue or throat.

What causes allergies?

Why do allergies occur?

If your immune system overreacts to something that is typically harmless but causes an allergic reaction in someone who is sensitive to it, you will experience allergy symptoms. We call this chemical an allergy.

Learn more about allergic

brainly.com/question/13092376

#SPJ4

Step-by-step explanation:

4.

p(-2) = 6×-2 + 2 = -12 + 2 = -10

p(4) = 6×4 + 2 = 24 + 2 = 26

so,

p(-2) is smaller than p(4)

3.

r(-1) = -2×-1 - 5 = 2 - 5 = -3

Answer:

64

Step-by-step explanation:

Hope this helps!

Answer:

2nd answer is the right one

Step-by-step explanation:

the square root of 9 is 3. The square root of 8 is a little smaller because 8 is smaller than 9.

Answer:

∴ x = 90

Step-by-step explanation:

(180 - x)° = x° (vertically opposite angles)

  180 - x = x

        -2x = -180

         2x = 180

        ∴ x = 90

Step-by-step explanation:

the slope is the inclination of a line, or of the tangent (also a line) on a point of a bent curve.

it is expressed as ratio (y coordinate change / x coordinate change) when going from one point on the line or curve to another point on the line.

it tells us how many units y changes when x changes a certain number of units (like 1).

it is positive, if the line goes up (when going from left to right). the larger the value, the steeper the line goes up.

it is negative, if the line is going down (again, going from left to right). the lower the value, the steeper the line goes down.

a horizontal line has a slope of 0/x = 0.

a vertical line has a slope of y/0, which is undefined, or sometimes expressed as infinite.

Using the range idea, the following scenario is represented by the inequality 0 ≤ y ≤ 2000. Here option D is the correct answer.

A function's range is the set that contains all of the output values that the function can take. In the context of this problem, the following input and output are provided:

Input the number of crates that have been loaded into the vehicle. Total weight of the crates loaded into the vehicle as output.

Because the weight of an amount can never be negative, and the greatest weight is 2,000 pounds, as stated in the issue, the range in this context is reflected by the following inequality: 0 ≤ y ≤ 2000.

To learn more about inequality

https://brainly.com/question/28823603

#SPJ4

Answer:

Step-by-step explanation:

In the given triangle AED, segments GB and FC are parallel to base ED. Points G and F are on segment AE in that order. Lengths AG=2, GF=5, FE=3, GB=6, and CD=7 are given. You want the lengths of AB, BC, FC, and ED.

Segments of transversals crossed by parallel lines are proportional:

  AG : GF : FE = AB : BC : CD

  2 : 5 : 3 = AB : BC : 7

Multiplying the first ratios by 2 1/3 will give the second ratios:

  2 : 5 : 3 = 4 2/3 : 11 2/3 : 7

This lets us conclude ...

  AB = 4 2/3

  BC = 11 2/3

Corresponding segments of similar triangles are proportional:

  AG : GB = FA : FC = AE : ED

  2 : 6 = (5+2) : FC = (5+2+3) : ED

We notice the second number in the first ratio is 3 times the first number. That means these ratios are ...

  2 : 6 = 7 : 21 = 10 : 30

This lets us conclude ...

  FC = 21

  ED = 30

The lengths of the missing sides are calculated to be

The parallel lines in the figure created similarity between the dimensions, this makes the ratio of the dimensions equal

The given dimensions that is used to find the missing sides

Solving for AB

AB / CD = AG / FE

AB / 7 = 2 / 3

cross multiplying

3 * AB = 7 * 2

AB = 14/3 = 4.667

Using AB, GF is calculated

AB / BC = AG / GF

14/3 / BC = 2 / 5

cross multiplying

BC = (5 * 14/3) / 2

BC = 35/3 = 11.667

Solving for FC

GB / FC = AG / A'F

6 / FC = 2 / (2 + 5)

cross multiplying

2 * FC = 6 * 7

FC = 42/2 = 21

Solving for ED

GB / ED = AG / AE

6 / ED = 2 / (2 + 5 + 3)

cross multiplying

2 * ED = 6 * 10

ED = 60/2 = 30

Learn more about similar polygons at:

https://brainly.com/question/1493409

#SPJ1

Answer:

-7.8n+7.9

Step-by-step explanation:

Answer: [-1, ∞)

Step-by-step explanation:

     First, we will simplify the equation.

     Given:

t - 1/3 ≥ -12/9

     Add 1/3 to both sides of the equation:

t ≥ -1

     Next, we know that a bracket is used when representing greater than or equal to and less than or equal to. Here, it's greater than or equal to so we will use a bracket on the left side.

     Then, t can be any value to infinity above -1, so we will use ∞) on the right side.

[-1, ∞)

The numeric value of the expression 8n at n = 6 is different of 56, hence n = 6 is not a solution to the expression 8n = 56.

A number a is a solution to an expression if the numeric value of the expression at input a generates an identity with the expression.

In this problem, the expression is given as follows:

8n = 56.

We want to verify if the number six is a solution to the presented expression.

The numeric value of the expression at n = 6 is found replacing the lone instance of n by 6, hence it is obtained as follows:

8n = 8 x 6 = 48.

(the product of 8 and 6 is 48).

Then the equality would be of:

48 = 56.

Which is a contradiction, hence n = 6 is not a solution to the expression 8n = 56.

The problem is:

Explain how to determine if the number is a solution to the equation. 56 = 8n for n = 6

More can be learned about the numeric values of a function at brainly.com/question/28367050

#SPJ1

The expression that could represent the amount of sodium per serving, in milligrams, in the new soup recipe is y = 0.67x

From the information, the new soup recipe contains 33% less sodium per serving than the old soup recipe.

Let's say Sodium in an old soup recipe per serving = x mg

Let's say Sodium in a new soup recipe per serving = y mg

The new soup recipe contains 33% less sodium per serving than the old soup recipe

y = x  - (33/100)x

100y = 100x  - 33x

100y = 67x

Divide through by 100

y = 0.67x

Learn more about expressions on:

https://brainly.com/question/723406

#SPJ1

x = 1.53347526

Take the log of both sides of the equation.

[tex]ln(2^{3x-1} ) = ln(3^{x-2} )[/tex]

Expand [tex]ln(2^{3x-1} )[/tex] by moving 3x-1 outside the logarithm

[tex](3x-1)ln(2)= ln(3^{x-2} )[/tex]

Move x-2 outside the logarithm      [tex]ln(3^{x-2} )[/tex]

[tex](3x-1)ln(2) = (x-2)ln(3)[/tex]  

Solve the equation for x

[tex]x = -[\frac{{2ln(3)-ln(2)}}{3ln(2)-ln(3)} ][/tex]

The value of x is 1.53347526(After applying the log values)

Learn about logarithmic equations

https://brainly.com/question/14411365

Answer:

Step-by-step explanation:

3/10 < 1/3