Use the intermediate value theorem to determine whether f(x)=8x^4-9x^2-9 has a real zero between 1 and 2

Answers

Answer 1

ANSWER:

There is a real zero in this interval

STEP-BY-STEP EXPLANATION:

We have the following function:

[tex]f\mleft(x\mright)=8x^4-9x^2-9[/tex]

To determine if there is a real zero between 1 and 2, we must evaluate the function at these points, if there is a change from positive to negative or vice versa, by the intermediate value theorem we can say that it has a real zero in that interval.

[tex]\begin{gathered} f(1)=8\left(1\right)^4-9\left(1\right)^2-9 \\ \\ f(1)=8\cdot1-9\cdot1-9 \\ \\ f(1)=8-9-9 \\ \\ f(1)=-10 \\ \\ \\ f(2)=8\left(2\right)^4-9\left(2\right)^2-9 \\ \\ f(2)=8\cdot16-9\cdot4-9 \\ \\ f(2)=128-36-9 \\ \\ f(2)=83 \end{gathered}[/tex]

We can observe that it goes from a negative value to a positive value in this small interval, which by means of the theorem we can say that if there is a real zero in this interval


Related Questions

A force of 250 newtons stretches a spring 30 centimeters . Please find how much work is done in stretching the spring from 20 centimeters to 50 centimeters.

Answers

Force required to stretch the spring(F)=250 n answer is 87.5 J

Whoever helps me first with this gets a free gift card. Comment on the problem with my email. after that you can claim your reward plus a bonus of 30+ points

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The table of 3 × 3 such that the sum of any row, column, or even diagonal is 30.3 has been created below.

What is the arithmetic operator?

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

Subtraction = Minus of any two or more numbers.

The third grid in first raw will be → 39.3 - (14.9 + 10.7) =  13.7

The third grid in second raw will be→ 39.3 - (13.7 + 11.3) = 14.3

The 2nd grid of 2nd raw will be → 39.3 - (17.9 + 11.3) = 13.1

The 1st grid in 2nd column will be→ 39.3 - (13.1+14.3) = 11.9

The 1st grid of 3rd raw will be → 39.3 - (14.9+11.9) = 12.5

The 2nd grid of 3rd raw will be → 39.3 - (12.5 + 11.3) = 15.5

Hence "The table of 3 × 3 such that the sum of any row, column, or even diagonal is 30.3 has been created below".

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Mike solved a system of equations and found that it had infinite solutions. Which could be the system of equations mike solved?

Answers

A system of equations has infinite solutions when both equations are equivalent.

To check if two equations are equivalent, write both of them in the same form. If the coefficients are proportional, including the constant terms, then they are equivalent.

Option 1

The first equation is written in general form. Isolate the constant term on the second equation to write it in general form:

[tex]\begin{gathered} y=-2x-1 \\ \Rightarrow2x+y=-1 \end{gathered}[/tex]

Notice that if we multiply the second equation by 3 on both sides, we will get the same coefficients as in equation 1:

[tex]\begin{gathered} 3(2x+y)=3(-1) \\ \Rightarrow6x+3y=-3 \end{gathered}[/tex]

Then, both equations are equivalent.

Therefore, this system has infinite solutions.

Option 2

Since there is no constant term in the secon

more help need 50 points

Answers

50p-40p+25-p
9p+25 is the answer.

Answer:

9p-25

Step-by-step explanation:

always do parentheses first

-5(-10p + 8p -5)-p

multiply negative with negative gives positive

-5(-2p-5)-p

variable always has a 1 in front

10p-1p-25

9p-25

The function shown can be used to determine the amount of money, indollars, in a savings account after m months. If no money is added orwithdrawn, which of the following is closest to the amount of money inthe account after 30 months?f(m) = 1500(1.003)^m

Answers

Given data:

The given function of amount of mmoney after m months is f(m)=1500(1.003)^m.

Substitute 30 for m in the given expression.

f(30)=1500(1.003)^(30)

=1500(1.094)

=1641

Thus, the total amount of money after 30 monnths is 1641.

Try Again3Graph the line with slopepassing through the point (-4,5)

Answers

[tex]\begin{gathered} \\ \end{gathered}[/tex]

hello I'm a 7th grader can you please help me with my math summer package and explain it in a way that a 7th grader can understand it.....I need help with number 1 ...

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Suppose that both Brian and Kristen pay $18.42 in order to diminish their checkbook balance. Then, after the payment, their current balances would be

[tex]\begin{gathered} Brian:-23.45+18.42=-5.03 \\ Kristen:18.42-18.42=0 \end{gathered}[/tex]

Therefore, after paying the same amount ($18.42), Kristen's debt has reduced to zero while Brian still owes $5.03.

Thus, Brian owes more money than Kristen.

Which set of numbers are integers but not whole numbers or natural numbers?{V1, –4, V=5}IO{*}O {V2, , V3}O {0,1,2,3}O {-2, -3, - 4}

Answers

The set of whole numbers or natural numbers are the ones that appear naturally, which would go from 0 and beyond. While the set of integers are the numbers that don't have any decimal point, which would include negative numbers. Therefore the correct answer is the last option.

Sam weighed and measured an infant at the clinic today The baby weighed 8.5 kg and was 60.5 cm long The baby's mather wanted the baby's weight in pounds and length in inches . Use the lowing conversion factors 22 1in = 2.54 cm Round your answers to the nearest tenths place .

Answers

We know that

• The baby weighed 8.5 kg and was 60.5 cm long.

We have to transform 8.5 kg into pounds. We know that 1 kg is equivalent to 2.2 pounds. So, we just have to multiply.

[tex]8.5\operatorname{kg}\cdot\frac{2.2lb}{1\operatorname{kg}}=18.7lb[/tex]Therefore, the baby weighed 18.7 pounds.

Then, we transform 60.5 cm into inches. We know that 1 inch is equivalent to 2.54 cm. So,

[tex]60.5\operatorname{cm}\cdot\frac{1in}{2.54\operatorname{cm}}=23.82in[/tex]Therefore, the baby was 23.82 inches long.

state the value of as a 5/7 recurring decimal

Answers

Answer:

The value of 5/7 recurring numbers is 714285

Explanation:

The given fraction 5/7 is the equivalent of

0.7142857142857142857142857142857142857142857142857142857142857142...

Notice that the recurring numbers are:

714285

what is the answer to 8+2(6-3)÷6 in pemdas form

Answers

8 + 2(6 - 3) / 6

we will be using order of operation

pemdas

firstly we will solve the parentheses

= (6 - 3)

= 3

8 + 2(3) / 6

Secondly we will open the parentheses with 2

= 8 + 6/6

thirdly, we will do the division

= 6/6 = 1

Lastly, Addition

8 + 1

= 9

The answer is 9

Help pleasee i want it today

Answers

Polynomials are used in engineering, computer, business, and math based jobs. (and more)

Answer:

Since polynomials are used to describe curves of various types, people use them in the real world to graph curves. For example, roller coaster designers may use polynomials to describe the curves in their rides. Combinations of polynomial functions are sometimes used in economics to do cost analyses, for example. Polynomials are used in engineering, computer and math based jobs, in management, business and even in farming. In all careers requiring knowledge of polynomials, variables and constants are used to create expressions defining quantities which are known and unknown.

Step-by-step explanation:

hope this helps you

Camille attended a music store's banjo sale. She counted the types of banjos and made note of their discounts. 4 strings 5 strings 6 strings 25% off 4 4 8 50% off 6 8 3 What is the probability that a randomly selected banjo has 6 strings or 5 strings? Simplify any fractions.

Answers

[tex]\text{probability = }\frac{\text{ number of favorable outcomes}}{\text{ total number of outcomes}}[/tex]

number of banjos with 6 or 5 strings: 4 + 8 + 8 + 3 = 23

total number of banjos: 4 + 6 + 4 + 8 + 8 + 3 = 33

The probability that a randomly selected banjo has 6 strings or 5 strings is:

[tex]p=\frac{23}{33}[/tex]

write a complete sentence that makes a relative comparison of the density of castle in the two countries

Answers

Before we write the sentence comparing the densities, let's first calculate them. The density is given by the ratio between the amount of cattle and the area of the country.

The ratio for United States is:

[tex]\frac{75.9}{3.797}=19.9894653674\ldots\approx19.989[/tex]

The density of cattle for United States is 19.989 cattle/square mile.

Doing the same calculation for the other country:

[tex]\frac{41.1}{1.013}=40.5725567621\ldots\approx40.573[/tex]

The density of cattle for Republica is 40.573 cattle/square mile.

To do a relative comparison, we can do it by finding the ratio between those densities.

[tex]\frac{19.989}{40.573}=0.49266753752[/tex]

A sentence that makes a relative comparison would be:

The density of cattle in United States is less than the density of cattle in Republica, representing only 49.27% of the density of cattle in Republica.

A bank tellers’ hourly wage will increase from $24 to $27.60. What percent increase does this represent? An employee’s salary for Alar Services is $37,500. Next year, she will get an 8% increase in salary. How much is her new salary?

Answers

(a).A bank tellers’ hourly wage will increase from $24 to $27.60.

The increament n wage is

[tex](27.60-24)=3.6[/tex]

Therefore, the percent of increament is

[tex]\frac{3.6}{24}\times100=15[/tex]

Therefore, it represents 15% increament.

(b). An employee’s salary for Alar Services is $37,500. Next year, she will get an 8% increase in salary.

So, new salary is

[tex]37500+(37500\times\frac{8}{100})=40500[/tex]

Therefore, new salary is $40500.

It takes a sheet metal worker 2/3 of an hour to fabricate a fitting, How many fittings can a sheet metal worker
make in an 8 hour day?

Answers

12 fittings can a sheet metal worker make in 8 hours.

What is ratio calculator?

Ratio Calculator is a formula used to solve ratio problems to express two or three numbers ratio to its simplest form.

2/3 hours taken to  fabricate = 1 sheet

8 hours taken to fabricate = 8/2/3

= 4(3)

= 12

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What type of correlation is shown in this scatterplot 1. Perfect positive 2. Perfect Negavite 3. Low positive 4.High Negavite

Answers

SOLUTION

A Scatter Plot has points that show the relationship between two sets of data.

When the line shows a negative slope, the correlation is a negative correlation

Consider the image below

This shows a perfect Negative correlation between the set of data.

Hence

The Second option is Right(2)

1. 3y=-3x+6
Slope_
y-intercept

Answers

Answer:

Slope = -1

y-intercept = 2

Step-by-step explanation:

Equation of a line in slope-intercept form is

y = mx + b

where m = slope and b =y-intercept

Here we have

3y = -3x + 6

Dividing by 3 on both sides:
y = -1x + 2

So slope m = -1, y-intercept b = 2

3. David’s watch broke. He decides to get it fixed instead of replacing it. Since David is a loyal customer, he received a coupon in the mail for a discount. The total cost to repair the watch can be represented by 0.07r + (r – 20), where r represents the original cost of the repair. Explain what each part of the expression represents in the context of the problem.

Please show work :)

Answers

What each part of the expression represents in the context of the problem include the following:

r represents the original cost of the repair.0.07r represents the tax.(r – 20) represents the discount.

What is an algebraic expression?

An algebraic expression is a mathematical equation that can be used for showing the relationship which exist between two or more variables, numerical quantities, as well as in conjunction with different mathematical operations.

What is a coefficient?

In Mathematics, a coefficient simply refers to a constant numerical value (number or numeral) that written before the variable in any algebraic expression.

Given the following algebraic expression:

0.07r + (r – 20)

In the context of fixing David’s broken watch, the variable r represents the original cost of the repair while 0.07r most likely represents the amount of money charged as tax. Lastly the expression (r – 20) represents the discount on fixing David’s broken watch.

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solve the system of equations for each variable x, y, and z. please show your work 2xy=z 4x+z=4y y=x+1

Answers

The solution of the system of equations 2xy = z, 4x + z = 4y, y = x + 1 are:

x = 1, y = 2, z = 4 and;

x = - 2, y = - 1, z = 4.

Consider the system of equations,

2xy = z                                                                                              ------------(1)

4x + z = 4y                                                                                       ------------(2)

y = x + 1                                                                                            -------------(3)

Substituting equation (3) in equation (2),

4x + z = 4y

4x + z = 4( x + 1)

4x + z = 4x + 4

z = 4

Substituting equation (3) in equation (1),

2xy = z

2x( x + 1 ) = z

2x² + 2x = 4

x² + x = 2

Hence, x = 1, - 2

Therefore,

When x = 1,

y = x + 1 = 2

When x = - 2, y = x + 1 = - 1

So, the solution for the system of the equations are x = 1, y = 2, x = 4 and x = - 2, y = - 1, z = 4.

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A RICH DONOR GIVES A HOSPITAL $500000ONE YEAR FROM TODAY.

Answers

Answer:

what do you need to be helped with please

(Real-World Proportional Problems MC)

Three students are participating in a walkathon. The data for each student is shown.

Student A: The equation y = 14x represents the amount of money raised (y) for walking (x) miles.

Student B: $42 is raised after walking 3 miles.

Student C:

Miles Walked 6 9
Money Raised $72 $108


Determine which student raised the least amount of money after walking 8 miles.
Student A
Student B
Student C
All three students raised the same amount of money after walking 8 miles.

Answers

Student C raised the least amount of money after walking 8 miles.

What is mean by Ratio?

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.

Where, x and y are individual amount of two quantities.

Given that;

Condition for A;

The equation y = 14x represents the amount of money raised (y) for walking (x) miles.

Condition for B;

$42 is raised after walking 3 miles.

Condition for C;

Miles Walked =    6           9

Money Raised =  $72      $108

Now, For student A;

The amount of money raised for walking 8 miles will be;

⇒ y = 14x

⇒ y = 14 × 8

⇒ y = $112

So, The amount of money raised for walking 8 miles = $112

For student B;

The amount of money raised for walking 1 miles will be;

= $42 / 3

= $14 per mile

Hence, The amount of money raised for walking 8 miles will be;

= $14 x 8

= $112

So, The amount of money raised for walking 8 miles = $112

For student C;

The amount of money raised for walking 1 miles will be;

= $72 / 6

= $12 per mile

Hence, The amount of money raised for walking 8 miles will be;

= $12 x 8

= $96

So, The amount of money raised for walking 8 miles = $96

Therefore,

Student C raised the least amount of money after walking 8 miles.

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Which of the following represents a linear function?                    these are the options a, c or b How do you know?these are the options it creates a simple shapeit passes the vertical line testit is a straight line

Answers

We want to identify the linear function.

Of course,

a linear function is going to be a line

The vertical line test is for understanding whether it is a function or not.

By vertical line test,

Picture 1 [passes]

Picture 2 [passes]

Picture 3 [fails]

Now, we can clearly see that Option B is the a straight line, hence a linear function.

a survey about favorite sports. suppose 200 people were surved. how many more people favor soccer than swimming. 40% soccer 10% swimming 20%tennis 30%basketball

Answers

People surveyed P = 200

Then

40% soccer= 200x40/100= 80

10% swimming= 200x10/100= 20

20% tennis= 200x 20/100= 40

30% basketball= 200x 30/100= 60

))How many favor soccer than swimming?

= 80 - 20= 60

Then answer is 60 people

The value of c must be greater than 0 1 3 7

Answers

The true statement about the triangle is the value of c must be greater than 3.

How to complete the statement

The figure that completes the question is added as an attachment

From the figure, we have the following parameters

The length of segment AB is 12 units.The length of segment AC is 15 units.

The length of segment of BC is represented by the variable c

By the triangle inequality theorem, we have:

The sum of any two sides length is greater than the third length

This means that

12 + 15 > c

c < 27

Also, we have

15 + c > 12

c >-3

Lastly, we have

12 + c > 15

c >3

Using the list of options as a guide, we have x > 3 to be true

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Determine whether the coordinate plane shows a reflection in the x-axis, y-axis, or neither.O neitherO X-axisy-axis

Answers

1) To determine a reflection across the x-axis, the rule to be followed is

Pre-Image Image

(x,y) --------------------> (x, -y)

A reflection across the y-axis follows this one:

Pre-Image Image

(x,y) --------------------> (-x, y)

2) Let's pick one point from the pre-image and the image on the graph

Since A (-2,0) and F (1,-3) then we cannot state that there was a reflection across the x-axis or y-axis.

3) The answer is neither

Which equation represents the relationship shown in
the graph?

Answers

Answer:

[tex]y\le-\frac{1}{4}x^{2}+\frac{1}{2}x+12[/tex]

Step-by-step explanation:

It has to have a y-int of +12 so that eliminates the first 2.

It needs to be contained inside the parabola therefore the x^2 value needs to be negative.

It needs to be shifted 1/2 to the right, therefore it needs a pos x value.

Hope that helps

What is 201 divided by 12

Answers

Answer: 16.75

Step-by-step explanation:

201/12

In 5 months, firefighters responded to 80wildfires. At this rate, how many wildhres will the frefighters respond to in 8 months?

Answers

Given that, in 5 months, firefighters responded to 80 wildfires:

• You can determine the rate of wildfires per month firefighters respond to by dividing 80 wildfires by 5 months:

[tex]\frac{80\text{ }wildfires}{5\text{ }months}=16\text{ }\frac{wildfires}{month}[/tex]

You can determine that each rectangle of the diagram provided in the exercise represents the rate obtained above.

• Assuming that the rate is the same in 8 months, you can multiply the rate obtained before by 8 months, in order to determine the number of wildfires the firefighters will respond to in 8 months:

[tex](16\text{ }\frac{wildfires}{month})(8\text{ }months)=128\text{ }wildfires[/tex]

Hence, the answer is:

THE RECTANGLE BELOW IS DILATED BY A SCALE FACTOR OF 3.6 TO CREATE A NEW RECTANGLE. WHICH OF THE FOLLOWING COILD BE THE DIMENSIONS OF THE NEW RECTANGLE? A: 14.4 CM x 5.4 B: 5.4 cm x C: 7.2 cm x 1.8 cm D: 14.4 cm x 7.2 cm.

Answers

ANSWER:

A: 14.4 CM x 5.4

STEP-BY-STEP EXPLANATION:

We must multiply the value of the scale factor by the original measures of the rectangle, like this:

[tex]\begin{gathered} AB=3.6\cdot1\frac{1}{2}=5.4 \\ BC=3.6\cdot4=14.4 \end{gathered}[/tex]

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