In 5 years, Dad will be three times as old as his daughter Jill will be then. If the sum of their present ages is 50, how old are they now?

If x + 5 is Jill's age five years from now, which of the following equations could be used to solve the problem?
a.3x + 5 = 55 - x
b.3x + 15 = 55 - x
c.3x + 15 = 45 - x ...?

The solution to the first problem is that Julia can watch up to 3.5 more hours of TV this week. The solution to the second problem is that you need to watch 30 more movies to earn a free movie pass. An example of an equation with infinitely many solutions is x = x.

19. To represent this scenario as an inequality, we let T be the amount of television Julia can still watch this week. Since she can watch no more than 5 hours per week and she has already watched 1.5 hours, we subtract 1.5 from 5. So we have the inequality T + 1.5 <= 5. Subtracting 1.5 from both sides gives us the inequality T <= 3.5. So Julia can watch 3.5 more hours of TV this week.

20. Let m be the number of movies you need to watch to get a free movie pass. Each movie gives you 2 advantage points and you currently have 40 points. The equation to model this situation is 2m + 40 = 100. Subtracting 40 from both sides gives 2m = 60. Dividing by 2 gives m = 30. So you need to watch 30 more movies to get a free movie pass.

21. An equation with infinitely many solutions is one where all the terms on one side can be made identical to all the terms on the other side. A simple example is x = x. For every value of x, the equation holds, meaning it has an infinite number of solutions.

https://brainly.com/question/29731212

#SPJ3

The question requires solving various problems involving projectile motion, a physics topic, using kinematic equations and algebraic techniques to determine height, flight time, and impact speeds.

The question involves calculating various aspects of projectile motion, which is a topic in physics. In these problems, equations of motion are used to determine the maximum height, time of flight, and speed at impact of objects thrown or released from certain heights.

Example Calculations

Each of these problems requires an understanding of the kinematic equations for vertical projectile motion and the ability to apply algebraic and calculus techniques.

In fraction,

175% = 35/20

In mixed fraction,

175%  = [tex]1\frac{15}{20}[/tex]

In simplest form,

175%  = 1.75

The given percentage is,

175%

Now to write it into fraction,

Divide it by 100 we get

175% = 175/100

         = 35/20

Thus,

175% = 35/20

Now divide 35 by 20 to write it into mixed fraction

20  ) 35 ( 1

     - 20

     ___

        15

Hence in simple fraction

175%  = [tex]1\frac{15}{20}[/tex]

Now again proceed the division,

20  ) 35 ( 1.75

     - 20

     ___

        15  0

      - 14 0

     _____

           10 0

         - 10 0

           ____

               x

Hence in simplest form,

175%  = 1.75

To learn more about division visit:

https://brainly.com/question/2273245

#SPJ6

The correct option is:

4(3x² + 1)(x – 5)

To find the completely factored form of the expression 12x³ – 60x² + 4x – 20, we can first factor out the greatest common factor, which is 4.

4(3x³ – 15x² + x – 5)

Next, we can factor the quadratic expression 3x³ – 15x² + x – 5 by grouping:

4[3x²(x – 5) + 1(x – 5)]

4(3x² + 1)(x – 5)

Therefore, the completely factored form of 12x³ – 60x² + 4x – 20 is:

4(3x² + 1)(x – 5

So, the correct option is:

4(3x² + 1)(x – 5)

Answer:

(D)

Step-by-step explanation:

Given: Triangle ABC is a right triangle. Point D is the midpoint of side AB and point E is the midpoint of side AC. The measure of angle ADE is 28°.

To prove: The measure of angle ECB is 62°.

Proof:

Step1. Segment DE joins the mid points of segments AB and AC (GIVEN).

Step 2. Segment DE is parallel to segment BC (MIDSEGMENT THEOREM)

Step3. Angle ECB is congruent to angle AED (CORRESPONDING ANGLES ARE CONGRUENT) that is ∠AED≅∠ACB.

Step 4. Measure of angle DAE is 90° (Definition of right angle)

Step 5.  Measure of angle ADE is 28° (Given)

Step 6. Thus, by triangle sum theorem, we have

∠DAE+∠ADE+∠AED=180°

∠AED=180-118

∠AED=62°

Step 7. Thus, by substitution, we have

∠AED≅∠ACB that is ∠ECB=62°

Hence proved.

By applying the PEMDAS rule, the coefficient of x is equal to 7.

In Mathematics and Euclidean Geometry, a coefficient simply refers to a constant quantity or numerical value (number or numeral) that is typically placed before the variable in an algebraic expression.

Based on the information provided, we have the following mathematical expression:

[tex]10x^2+8x-6x^3+4x^2+12x^3-x+20\\\\12x^3-6x^3+10x^2+4x^2+8x-x+20\\\\6x^3+14x^2+7x+20[/tex]

In this context, we can reasonably and logically deduce that the coefficient of x is 7.

Complete Question:

When this polynomial is simplified, what is the coefficient of x?

[tex]10x^2+8x-6x^3+4x^2+12x^3-x+20[/tex]

Answer:

Option C. (n + 1)/(n +2).

Step-by-step explanation:

The given sequence is 2/3, 3/4, 4/5, 5/6, 6/7.

and we have to find the general term of the given sequence.

Since first term of the sequence is 2/3

So numerator can be represented as (n + 1) and the denominator as (n + 2)

Therefore the general term will be (n + 1)/(n + 2)

Option C is the answer.

c The probability that event A occurs, given that event B occurs, is 83%.

P = the principal

t = 25 years the time in years

r = 0.0525 or 5.25% annual rate

m = 1 compounding periods per year

i = 0.0525 or 5.25% interest rate per period

n = t*m = 25 total number of compounding periods

A = $75,000 future value

A = P(1 + i)^n

P(1 + i)^n = A

P(1 + 0.0525)^25 = 75000

by solving we find:

P = $20,869.34

Final answer:

The question is about solving a system of equations to find the number of nickels and dimes in a piggy bank, given a total amount and quantity of coins. The solution involves using either the substitution or elimination method to find the values of the two variables representing nickels and dimes.

Explanation:

The question involves solving a system of equations to find the number of nickels and dimes in Keana’s piggy bank. Given the total amount is $4.30 and there are 59 coins in total, we can set up the following equations:

Let N represent the number of nickels and D the number of dimes.

The value equation is 0.05N + 0.10D = 4.30 or 5N + 10D = 430

The quantity equation is N + D = 59.

To solve these equations, we will use the substitution or elimination method. First, solve the quantity equation for one variable, for example, N = 59 - D. Then, substitute this expression for N in the value equation and solve for D. After finding D, substitute its value back into any of the original equations to find N. The sum of the digits in the number of nickels in Keana's bank is then found by adding together the digits of N.

we get,  5(59 - D) + 10D= 430

295 - 5D + 10D = 430

5D = 135 , Therefore D = 27

and N = 59 - D = 59 - 27 = 32.

To find the sum of the digits in the number of nickels (n=32), we add the digits 3+2=5

Therefore, the sum of the digits in the number of nickels in Keana’s bank is 5.

Answer: The explicit rule for the sequence will be

[tex]a_n=15.5-2.5n[/tex]

Step-by-step explanation:

Since we have given that

[tex]13,10.5,8,5.5,3,0.5.....[/tex]

Here,

a = first term = 13

d = common difference

[tex]a_2-a_1 = 10.5-13=-2.5[/tex]

Since it forms an A.P. ;

[tex]a_n=a+(n-1)d\\\\a_n=13+(n-1)(-2.5)\\\\a_n=13-2.5n+2.5\\\\a_n=15.5-2.5n[/tex]

Hence, the explicit rule for the sequence will be

[tex]a_n=15.5-2.5n[/tex]

Answer:

[tex]a_n[/tex]  [tex]= 15.5-2.5n[/tex]

Step-by-step explanation:

Laplace transformation is the transformation in the integral form which convert a function of a real variable to a complex variable.

The Laplace transform of the given function is,

[tex]L[t^{2}\sin(2t)]=\left [\dfrac{4(3s^2-4)}{(s^2+4)^2} \right ]\\[/tex]

Laplace transformation is the transformation in the integral form which convert a function of a real variable to a complex variable.

Given information-

The function given in the problem is,

[tex]t^{2}\sin(2t)[/tex]

By the Laplace transform we can write that,

[tex]L[t^{2}\sin(2t)]=(-1)^2\dfrac{d^2}{ds^2}L(\sin 2t)\\L[t^{2}\sin(2t)]=\dfrac{d}{ds}\;\dfrac{d}{ds}\dfrac{2}{s^2+4}\\L[t^{2}\sin(2t)]=\dfrac{d}{ds}\left [\dfrac{-4s}{(s^2+4)^2} \right ]\\[/tex]

Solve further to get the final result,

[tex]L[t^{2}\sin(2t)]=\left [\dfrac{(s^2+4)^2(-4)+4s(s^2+4)\times2s}{(s^2+4)^2} \right ]\\[/tex]

Simplify the above equation as,

[tex]L[t^{2}\sin(2t)]=\left [\dfrac{4(3s^2-4)}{(s^2+4)^2} \right ]\\[/tex]

Hence, the Laplace transform of the given function is,

[tex]L[t^{2}\sin(2t)]=\left [\dfrac{4(3s^2-4)}{(s^2+4)^2} \right ]\\[/tex]

Learn more about the Laplace transform here; https://brainly.com/question/17062586

Answer:

its c on edge babes, yw <3

Step-by-step explanation:

Grant should remove approximately 7.33 gallons of water to obtain a 24% ammonia solution from the initial 16% ammonia solution.

Let x be the number of gallons of water that Grant needs to remove.

The equation you can use to represent this situation is based on the principle of maintaining the amount of ammonia in the solution:

The amount of ammonia in the original solution = The amount of ammonia in the final solution

The amount of ammonia in the original solution is the product of the initial concentration (16%) and the initial volume (22 gallons).

The amount of ammonia in the final solution is the product of the desired concentration (24%) and the final volume (22 - x gallons, where x is the amount of water removed).

So, the equation becomes:

0.16 * 22 = 0.24 * (22 - x)

Now, you can solve this equation for "x" (the number of gallons of water to remove) to achieve the desired concentration:

0.16 * 22 = 0.24 * (22 - x)

3.52 = 5.28 - 0.24x

Now, isolate the variable "x" by subtracting 3.52 from both sides:

0.24x = 5.28 - 3.52

0.24x = 1.76

Now, divide both sides by 0.24 to solve for "x":

x = 1.76 / 0.24

x ≈ 7.33

To know more about ammonia solution click here :

https://brainly.com/question/1642219

#SPJ12

Answer:

The student's conclusion is incorrect because the solution to the system of equations 3x + 4y = 32 and 5x + 5y = 50 is (8, 2).

Step-by-step explanation:

To see if the answer to an equation is right, you just have to put the value of X and Y into the equation system, since we don´t have the equation system that the student used, we will make our own, so we will start by stating that Notebooks are represented by X and index cards are represented by Y.

Your equation would look like this:

3x+ 4y=34

The student said that the price of the notebook is $5 and the index card would be $1, now we put those values into the equation.

3(5)+4(1)=32

15+4=32

19=32

Since 19 is not equal to 32, the equation is wrong, therefore the student is wrong.

Now to solve it you get your other equation, since if he had bought 5 and 5 he would have needed 18 extra dollars that means that

5x+5y= 32 +18

5x+5y=50

With the two equations you just use elimination process to create a single equation:

(5x+5y=50)-3=  -15x-15y=-150

(3x+4y=32)5 =   15x+20y= 160

You eliminate the x from the equation and are left with:

-15y+20y= -150+160

5y=10

y=[tex]\frac{10}{2}[/tex]

y=2

Now that you have the value of Y you just put it into the equation to know the value of x:

5x + 5(2) = 50

5x+10=50

You clear the x and the result would look like this:

x= [tex]\frac{50-10}{8}[/tex]

x=8

Answer:

Option 2 is correct.

Step-by-step explanation:

In the given graph x-axis represents the numbers and y-axis represent the frequency.

Number         Frequency              Cumulative frequency

100                        14                              14

200                       6                               20   (20<36)

300                       18                              38  (38>36)

400                       12                              50

500                       2                               52

600                       12                              64

700                       8                               72

Total                     72          

Mode is the number which has highest frequency. From the above table it is noticed that the highest frequency is 18 at 300. Therefore mode of the data is 300.

Sum of frequency is 72, which is an even number.

[tex]Median=\frac{n}{2}\text{th term}[/tex]

[tex]Median=\frac{72}{2}\text{th term}[/tex]

[tex]Median=36\text{th term}[/tex]

We have to find the number whose cumulative frequency is more than 36 but preceding cumulative frequency is less than 36.

Median of the graph is 300.

Since the value of median and mode are same, therefore

[tex]median=mode[/tex]

Option 2 is correct.

Final answer:

The number that, when multiplied by itself 4 times equals 81, is 3, as 3 to the fourth power (3^4) is 81.

Explanation:

To find what number multiplied by itself 4 times equals 81, we need to find the fourth root of 81. The fourth root is the same as raising a number to the 0.25 power. To calculate manually, we may take two square roots in succession, since the square root of a number squared is the original number. The square root of 81 is 9, and the square root of 9 is 3, thus the fourth root of 81 is 3. Indeed, 34 = 3 × 3 × 3 × 3 = 81.

In the diagram, the pair of angles ∠1 and ∠7 form a pair of alternate exterior angles.

Here is the reason:

Within the graph, ∠1 and ∠7 are on the inverse sides of transversal t and exterior lines a and b. Subsequently, they are a combination of substitute outside points.

The other answer choices are not correct since:

Answer:

Step-by-step explanation:

Yes