Given the equation cosx = x^2 prove that it has at least one root in the [0, pi] interval. Justify answer by indicating the theorem used.

The amount that Tom’s most recent book earn is 10^7.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

Since Tom’s most recent book earned 10*4 times as much money as his first book which was 10³.

The total amount of the recent book will be:

= 10⁴ × 10³

= 10^(4 + 3)

= 10^7

The amount is 10^7.

Learn more about exponents on:

brainly.com/question/13669161

#SPJ1

Answer:

4(x-2 +y) = 4x-8+4y

Step-by-step explanation:

You have to apply the distributive law

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

Then solve it which equals

4 x +4 (-2) + 4y

Then multiply the numbers

4 (-2) = -8

Which gets you 4x-8+4y

The adjusting journal entries for the following unrelated transactions are as follows:

a) Dec. 31, 2020: Debit Interest Expense Php. 6,667

Credit Interest Payable Php. 6,667

(To record the adjusting entry.)

b) Dec. 31, 2020: Debit Insurance Expense Php. 12,500

Credit Prepaid Insurance Php. 12,500

(To record the adjusting entry under the asset method.)

Debit Prepaid Insurance Php. 17,500

Credit Insurance Expense Php. 17,500

(To record the adjusting entry under the expense method.)

c) Dec. 31, 2020: Debit Interest Revenue Php. 12,000

Credit Interest Receivable Php. 12,000

(To record the adjusting entry.)

d) Dec. 31, 2020: Debit Unearned Rent Revenue Php. 133,333

Credit Rent Revenue Php. 133,333

(To record the adjusting entry under the Liability method.)

Debit Rent Revenue Php. 66,667

Credit Unearned Rent Revenue Php. 66,667

(To record the adjusting entry under the income or revenue method.)

One of the methods is the asset method (similar to the liability method) that records the asset when cash is received.

Another is the expense method (similar to the revenue or income method) that records the amount as expense until adjusted.

a) Dec. 31, 2020: Interest Expense Php. 6,667 Interest Payable Php. 6,667

b) Dec. 31, 2020: Insurance Expense Php. 12,500 Prepaid Insurance Php. 12,500

Prepaid Insurance Php. 17,500 Insurance Expense Php. 17,500

c) Dec. 31, 2020: Interest Revenue Php. 12,000 Interest Receivable Php. 12,000

d) Dec. 31, 2020: Unearned Rent Revenue Php. 133,333 Rent Revenue Php. 133,333

Rent Revenue Php. 66,667 Unearned Rent Revenue Php. 66,667

Learn more about adjusting journal entries at https://brainly.com/question/13035559

#SPJ1

Answer:

2x - y - 2 = 0

Step-by-step explanation:

A (1,0)

B (0,-2)

(y-0)/(-2-0) = (x-1)(0-1)

y/-2 = (x-1)/-1

-y/2 = -x + 1

-y = 2(-x+1)

-y = -2x + 2

2x - y - 2 = 0

The correct answers are:

1) 1/2

2) 1/10

3) 3/4

Step-by-step explanation:

[tex]\boxed{50=0.5\\}\\\boxed{10=0.1\\\\\\} \boxed{75=0.75}[/tex]

50% means 0.5. This 0.5 was (multiplied before by 100) to get this percentage.

Therefore, the answer is true

Answer:

slope is 7/4

y intercept (0,2)

Step-by-step explanation:

m= 7/4 y=mx + b to find slope.

(2, 11) is the vertex of f(x) = 4(x - 2)² +11.

A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .

The given equation is f(x) = 4(x - 2)² +11.

The vertex form is y=a(x-h)²+k

y=a(x-h)²+k of a parabola is said to be in vertex form because the vertex can be determined by examining the equation: (h, k) is the vertex.

(h, k) are the vertices of the given equation.

a=4,

h=2 and

k=11

so the (2,11) is the vertex of the function.

Hence, the vertex of f(x) = 4(x - 2)² +11 is (2, 11).

To learn more on Quadratic equation click:

https://brainly.com/question/17177510

#SPJ1

The equations for parallel lines:

y = -1/2 x - 2  ----- y = -1/2 x + 6

y = 1/2 x + 4   ----- y = 1/2 x - 4

y = 2x -4       -----  y =2/1x + 2

y = 5x + 2     -----  y = 5x - 1

y = 1/5 x + 10 ----   y = 1/5 x + 3

What is slope of line?

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).

If an equation in the form y = mx + c then m is the slope of the line.

Equation of line               slope          Slope parallel line

y = -1/2 x - 2                        -1/2                        -1/2

y = 1/2 x + 4                          1/2                           1/2

y = 2x -4                                2                            2

y = 5x + 2                               5                           5

y = 1/5 x + 10                          1/5                         1/5

Now identify the lines from the option whose slope are  -1/2,  1/2, 2, 5,  1/5.

The slope of the line y = -1/2 x + 6 is  -1/2.

The slope of the line y = 1/2 x - 4 is  1/2.

The slope of the line y = 2x -4 is 2.

The slope of the line y = 5x + 2  is 5.

The slope of the line y = 1/5 x + 10 is 1/5.

To learn more about the equation of parallel line click on below link:

brainly.com/question/402319

#SPJ1

The surface area of the prism is 84 square centimeters.

What is a prism?

A prism is a polyhedron in geometry that has n parallelogram faces that connect the n-sided polygon basis, the second base, which is a translated duplicate of the first base, and the n faces. The bases are translated into all cross-sections that are parallel to them.

In the figure,

The surface area of the figure consists of 2 triangles, 3 rectangles.

The area of the triangle and rectangle is the surface area of the triangle.

The area of the triangle is (1/2) × base × height

The base of the triangle  ABC is BC and the height is AB.

The area of triangle ABC is (1/2) × 4 × 3 = 6 square centimeters.

The area of triangle DEF is (1/2) × 4 × 3 = 6 square centimeters.

The area of the rectangle ACDE  is 5 × 6 = 30 square centimeters.

The area of the rectangle ABEF  is 4 × 6 = 24 square centimeters.

The area of the rectangle BCDF  is 3 × 6 = 18 square centimeters.

The total surface area of the figure is ( 6 + 6 + 30 + 24 + 18) square centimeters = 84 square centimeters

To learn more about surface area, click on below link:

https://brainly.com/question/23463460

#SPJ1

Answer:

p(x) = (x+7)(x+5)(-x+1)(x-35).

Step-by-step explanation:

To factor p(x), we can use the following steps:

Find the factors of 35 that add up to 4, which is the coefficient of the quadratic term (x^2). In this case, the factors of 35 that add up to 4 are 7 and 5.

Use these factors to rewrite the quadratic term as the product of two binomials. In this case, we can write the quadratic term as (x+7)(x+5).

Substitute this expression into the original polynomial to get p(x) = (x+7)(x+5) + 2x + 35.

To complete the factorization, we need to find two numbers that multiply to 35 and add up to 2. These numbers are -1 and -35.

Use these numbers to rewrite the remaining linear term as the product of two binomials. In this case, we can write the linear term as (-x+1)(x-35).

Substitute this expression into the polynomial to get p(x) = (x+7)(x+5) + (-x+1)(x-35).

Finally, we can factor p(x) as the product of two quadratics: p(x) = (x+7)(x+5)(-x+1)(x-35).

The required equations can be used to model the situation is x = 1/2y - 3 and y = 10(x-1)

What is equation ?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."

Equations can be classified as either conditional equations or identities. Any value of the variables results in an identity being true. Only certain values of the variables in a conditional equation result in truth. When two expressions are joined together by the equals sign ("="), the result is an equation.

If the smaller number is 3 less than half a larger number, this is expressed as:

x = 1/2y - 3 ⇒(1)

If the larger number is 10 times 1 less than the smaller number, this is expressed as;

y = 10(x-1) ⇒ (2)

Substitute equation 2 into 1 as shown;

x = 1/2y - 3

x = 1/2(10x-10)- 3

x = 5x - 5 - 3

-4x = -8

x = 2

The required equations can be used to model the situation is x = 1/2y - 3 and y = 10(x-1)

To learn more about equation from the given link  

https://brainly.com/question/2972832

#SPJ1

Answer:

a d

Step-by-step explanation:

The slope of the function is which describes the direction and steepness and the slope for the equation will be m = (-30)

This is the process of finding the rate of change of the value y (dependent variable) of the function changes with respect to that of the variable x (independent variable). The slope itself describes the direction and steepness of the line.

slope = m = rise / run = [tex]\frac{y2 - y1}{x2 - x1}[/tex],

To find the slope , In the case of a straight line y=mx+b, the slope m=Δy/Δx measures the change in y per unit change in x. This can be interpreted as a measure of "sensitivity''; for example, if y=100x+5, a small change in x corresponds to a change one hundred times as large in y, so y is quite sensitive to changes in x.

To know more about slope of function

https://brainly.com/question/29110980

#SP4

The equation of the exponential function represented in this table is;

y = 6(1.8)ˣ

We are given the table of values of the exponential function and we can write the coordinates as;

(3, 34.99)

(4, 62.99)

(5, 113.37)

(6, 204.07)

(7, 367.33)

The general formula for an exponential function is;

y = a(b)ˣ

where;

a is the initial value

b is the constant multiplier

For the third coordinate, we have;

a(b)³ = 34.99    ------(1)

For the fourth coordinate, we have;

a(b)⁴ = 62.99    ------(2)

Divide eq 1 by eq 2 to get;

b = 1.8

Put 1.8 for b in eq 1 to get;

a(1.8)³ = 34.99

a = 6

This gives the exponential equation as; y = 6(1.8)ˣ

Read more about exponential function at; https://brainly.com/question/2456547

#SPJ1

Answer: 27/16

Step-by-step explanation: evaluate

(a)  The corresponding angles are congruent.

So, m ∠ TLC = 66°

(b)  m ∠KGX = m ∠DNK = 120°

"Information available from the question"

In the question:

A graphic artist created a design for a flower using four congruent hexagons as shown:

B P⊥M K, m ∠ M Y F=m ∠ F H B, m° W M C=m ∠ W P T, m ∠G X R=66°, m ∠ D N K=(3 x+18)°, and m ∠ W B R=(5 x-8)°.

The sum of the angles in WKNDSP is 720°.

Now, According to the question:

Part(a) Since the four hexagons are congruent

So, the corresponding angles are congruent.

Thus, m ∠ T L C=  m ∠ 6 x R

Since, m ∠ 6 x R = 66°

So, m ∠ TLC = 66°

Part(b) In WKNDSP

m  ∠KWP + m ∠ WPS + m ∠ PSD + m ∠ SDN + m ∠ DNK + m ∠ NKW = 720°

Since, 1)  B P⊥M K => m ∠KWP = 90°

2) m ∠WPS =m ∠NKW =m ∠WBR = (5x - 8)°

3) m ∠PSD = m ∠DNK = (3x + 18)°

4) m ∠SDN = m ∠GXR = 66°

So, 90 + (5x + 8) + (3x + 18) + 66 + (3x + 18) + (5x - 8) = 720°

90 + 5x + 8 + 3x + 18 + 66 + 3x + 18 + 5x - 8 = 720

176 + 16x = 720

16x = 720 - 176

16x = 544

x = 34

=> m ∠DNK = (3x + 18)° = (3 × 34 + 18)° = 120°

So, m ∠KGX = m ∠DNK = 120°

Learn more about Hexagon at:

https://brainly.com/question/3295271

#SPJ4

The direction of the point (-3, 2) is 3 units to the left and 2 units up from the origin (0, 0). Obtained by applying the translation rules.

The translation rules are:

(x, y) → (x + a, y); translated by 'a' units to the right

(x, y) → (x - a, y); translated by 'a' units to the left

(x, y) → (x, y + a); translated by 'a' unit up

(x, y) → (x, y - a); translated by 'a' units down

The given points are (-3, 2) and (0, 0).

The point (-3, 2) is 3 units to the left and 2 units up from the origin (0, 0).

This is obtained by the rules:

(x, y) → (x - a, y); translated by 'a' units to the left

(x, y) → (x, y + a); translated by 'a' unit up

Thus, option C is correct.

Learn more about translation rules here:

https://brainly.com/question/15123583

#SPJ1

Answer:

45 pounds of meat.

Step-by-step explanation:

= 120 ( 3/8)

= 360 / 8

= 45

Trigonometry is the application of certain functions to determine the value of a quantity. The tree stands 10.77 meters tall.

Some trigonometric functions can be used to solve the given problem. Let s represent the distance from the tip of the tree's shadow to where Aria stands, so that;

s = 27.75 - 23.5

= 4.25 m

s = 4.25 m

Also, let the angle formed by the line connecting the tree's tip and the shadow's tip be, so that;

Tan θ = opposite / adjacent

Here given,

Opposite side = 1.65

Adjacent side = 4.25

          = 1.65 / 4.25

          = 0.3882

θ = Tan⁻¹ 0.3882

  = 21.216

θ = 21.216°

We get θ = 21.216°

The tree's height, h, can be calculated as follows:

Tan 21.216° = h/27.75

h = Tan 21.216° x 27.75

  = 0.3882 x 27.75

h = 10.77m

As a result, the tree's height is 10.77m.

To learn more about trigonometry function refer to :

https://brainly.com/question/25618616

#SPJ1

Answer:

The value of x is equal to tan^-1(0.5961538461538461). This is the angle opposite to the side with length 3.1 in the given right triangle.

Step-by-step explanation:

To find the value of x, you can use the inverse tangent function, which is denoted as tan^-1. To use the inverse tangent function, you need to know the length of the adjacent side and the length of the opposite side of the right triangle. In this case, the length of the adjacent side is 3.1 and the length of the opposite side is 5.2. So, the value of x is equal to tan^-1(3.1/5.2) or tan^-1(0.5961538461538461).

Answer: d

Step-by-step explanation:

edge 2023

Answer:

It sounds like you want to use the equation h = "-5" - 2 t + 36 to calculate how many seconds it will take for a coin to fall from a balcony to a fountain below. The only problem is that the equation you provided is not correct. The correct equation for the height of an object in free fall is h = -16t^2 + vt + h0, where t is the time in seconds, h0 is the initial height of the object, and v is the initial velocity of the object.

To solve for the time it will take for the coin to fall to a height of 12 feet, you need to know the initial height of the balcony and the initial velocity of the coin. Assuming the initial height of the balcony is 36 feet and the initial velocity of the coin is 0 (since it is not moving when it is released), you can plug these values into the equation to solve for t:

h = -16t^2 + 0 + 36

12 = -16t^2 + 36

-24 = -16t^2

t^2 = 1.5

t = sqrt(1.5)

t = approximately 1.22 seconds

So it will take approximately 1.22 seconds for the coin to fall from the balcony to a height of 12 feet.

Answer:

  $11,127.75

Step-by-step explanation:

You want to use the compound interest formula A=Pe^rt to find the value of an $8000 investment compounded continuously at 11% for 3 years.

Put the values of the variables into the formula and do the arithmetic.

  A = $8000·e^(0.11·3) ≈ $11127.75

The accumulated value after 3 years will be $11,127.75.

The range of Sanders support among millennials in within 90% confidence interval is between 53% and 57%.

Percentage is defined as "out of 100." Similar to fractions and decimals, percentages are being used in mathematics to represent subsets of a whole. When expressing a sum as a percentage, 100 equal components are regarded to make up the entire.

In order to answer this question, a statistical power (90% CI) must be calculated for the percentage of millennials who had a favorable impression of Sanders.

The sample size is n=1,754.

The p-hat, taken from the poll, is

[tex]$\hat{p}=0.55$[/tex]

The estimated standard deviation is equal to:

[tex]$$\sigma_p=\sqrt{\frac{p(1-p)}{N}}=\sqrt{\frac{0.55 * 0.45}{1754}}=0.012$$[/tex]

For a 90% CI, the z-value is z = 1.645.

Then, the confidence interval is

[tex]$$\begin{aligned}& \hat{p}-z * \sigma_p \leq p \leq \hat{p}-z * \sigma_p \\& 0.55-1.645 * 0.012 \leq p \leq 0.55-1.645 * 0.012 \\& 0.55-0.02 \leq p \leq 0.55+0.02 \\& 0.53 \leq p \leq 0.57\end{aligned}$$[/tex]

To know more about Percentages visit:

https://brainly.com/question/28269290

#SPJ4

The complete question is-

Throughout the 2016 Presidential election primaries, Millennials (those aged 20 t 36 years) consistently supported Senator Bernie Sanders over Secretary Hillary Clinton. According to the 2016 Gallup poll of 1,754 Millenials, 55% had a favorable opinion of Sanders than Hillary Clinton (38%). Calculate the 90% confidence interval for Bernie Sanders. *round to two decimals (Please read the rules for rounding in the preface page xvi. If the number you are rounding is followed by 5, 6, 7, 8, 9 round the number up. If the number is followed by 0,1,2,3,4, you are rounding down, meaning you do not change the number). The 90% confidence interval for Bernie Sanders is to

Answer:

To factor out the GCF from the given expression, we can use the distributive property. This property states that we can distribute a common factor to all of the terms in an expression by multiplying the common factor by each term separately. In this case, the common factor is n, so we can distribute it to each term by multiplying it by -26, 7, and 13:

(-26n * n) + (7n * n) + (13n * n)

This gives us:

-26n^2 + 7n^2 + 13n^2

We can then combine like terms by adding the coefficients of n^2:

(-26 + 7 + 13) * n^2

This gives us the final result:

-6 * n^2

Therefore, we can factor out the GCF of -6n^2 from the given expression.

Step-by-step explanation:

The solution of the given inequalities will be the common region between the two (refer to the graph).

What is an inequality ?

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.

Nachelle has x dimes and y nickels.

We know that, A nickel is worth 5 cent, A dime is worth 10 cent and have maximum of $0.8 combined.

So, 5% x + 10% y ≤ 0.8

     5x + 10y ≤ 80

She has at least 11 coins.

So, x + y ≥ 11

Hence, We have two inequalities as:

5x + 10y ≤ 80 and x + y ≥ 11

Similarly, x≥ 0 and y≥ 0.

Now, We'll find the points that lie on the given lines and draw the lines ( refer the given figure )

After drawing the graph, we'll check the inequalities where the portion is true.

If take point (0,0),

5x + 10y ≤ 80

5(0) + 10(0) ≤ 80

0 ≤ 80 which is true, hence we will shade the region which is down because the point (0,0 ) lies in downward region.

Similarly,

x + y ≥ 11

0 + 0 ≥ 11

 0 ≥ 11 which is false hence, we will shade the region which is up because the point (0,0 ) lies in downward region.

In result, We get the common region which is the solution.

Learn more about Inequalities from the link given below:

https://brainly.com/question/25275758

#SPJ1

The least amount possible is $25 and the number of miles is 25 miles

From the question, we have the following parameters that can be used in our computation:

Yellow Taxi service charges a $15 flat fee plus $2.50

This means that

Yellow Taxi: y = 15 + 2.5x

For the graph, we have

y-intercept = 10

(x, y) = (0, 10) and (2, 16)

So, the slope is

slope = (y₂ - y₁)/(x₂ - x₁) = (16 - 10)/(2 - 0) = 3

So, we have

Black and White Taxi service: y = 10 + 3x

Yellow Taxi: y = 15 + 2.5x

When he travels for 5 miles, we have

Black and White Taxi service: y = 10 + 3 * 5 = 25

Yellow Taxi: y = 15 + 2.5 * 5 = 27.5

Hence, the least amount possible is $25

This means that we equate the above equations

So, we have

15 + 2.5x = 10 + 3x

Evaluate the like terms

0.5x = 5

Divide

x = 25

Hence, the distance is 25 miles

Read more about system of equations at

https://brainly.com/question/13729904

#SPJ1

There are 7 packs of candy, but only two people can share it equally. 7/2= 3.5. If each person gets 3.5 bags, they both have an equal amount.

Credit to: primebunny24

Answer:(22.5/3)-1.75=e

Step-by-step explanation:

3x/3=22.5/3

x=7.5 per book

7.5-1.75=5.75 per book after coupon

Answer:

1/82.

Step-by-step explanation:

In a cross country race with 40 athletes, 10 of them are on the same team. The probability that the top four finishers are all from that same team is given by the expression 10P4/40P4.

The expression 10P4 represents the number of ways that the top four finishers can be chosen from the team of 10 athletes. Since the order in which the athletes finish does not matter, this is equivalent to choosing 4 athletes from a group of 10 without regard for order, which can be done in 10!/(4!6!) = 210 ways.

The expression 40P4 represents the number of ways that the top four finishers can be chosen from the entire group of 40 athletes. Since the order in which the athletes finish does not matter, this is equivalent to choosing 4 athletes from a group of 40 without regard for order, which can be done in 40!/(4!36!) = 34,650 ways.

Therefore, the probability that the top four finishers are all from the same team is given by the expression 10P4/40P4 = 210/34,650 = 1/164. This can be simplified to 1/82 by dividing the numerator and denominator by 2, so the final answer is 1/82.

a) The range of values that the game operator can use to represent a winner getting a basketball is of: 50 to 100.

b) The percentage of the 10 simulated winners who got a basketball is of: 40%.

The range of values is the set that contains all possible values that can result in a person getting a basketball.

There is a 51% probability of the winner getting a basketball, hence supposing that the last 51 values represent the winner getting a basketball, the range of values is given as follows:

50 to 100.

From the 10 simulated winners, 4 had numbers ranging from 50 to 100, hence the percentage of them who won a basketball is calculated as follows:

p = 4/10 x 100% = 40%.

More can be learned about the range of a data-set at https://brainly.com/question/24326172

#SPJ1

Answer:

see explanation

Step-by-step explanation:

N(t)=4|t+5|+3, evaluate N(2).

Evaluate: Plug in a number for each variable.

4(|t+5|)+3

t=2

Evaluate for t=2

4(|2+5|)+3

4(|2+5|)+3

=31

(Hope this answer does you some good )