One year ago liz was three times as old as her brother jack. in two years she'll be only twice as old as jack. how old are liz and jack now?

Rewriting 4 x 3/6 as the product of a unit fraction and a whole number is: 12 * 1/6

The parameters are given as:

Number - 4

Fraction - 3/6

The following steps can be used to determine the product as the product of a whole number and a unit fraction:

Step 1 - Remember the whole number are those numbers that involve all positive integers and zero.

Step 2 - Also remember that the unit fraction is nothing but a fraction whose numerator is 1.

Step 3 - Write the given expression.

4 * 3/6

Step 4 - Convert the given fraction into a unit fraction by multiplying 4 by 3 in the above expression.

4 * 3 * 1/6

Step 5 - Simplify the above expression.

12 * 1/6

Read more about Fraction Multiplication at: https://brainly.com/question/415490

#SPJ1

Answer: 803.84cm3

Step-by-step explanation:
The formula for finding the volume of a cylinder is πr2h.
In other words, the area of the top face's circle times the height.

To find the circle's area, we first find the radius of the circle. Since the diameter is 8cm, we divide by 2 to get the radius, which is 4cm.

4cm squared is 4cm x 4cm, which is 16cm. 16cm times 3.14 is 50.24cm squared.

Now, we have the area of the circle. 50.24cm squared!

The height is 16cm, so to find the cylinder, we times the area of the circle by the height of the cylinder! So,

16cm x 50.24cm squared = 803.84cm cubed.

The volume of the can of soup is 803.84cm cubed.

Answer: b = 11.62

Step-by-step explanation:

We can use this formula to solve for b:

\(b^{2} =\) \(\sqrt{c^{2}-a^{2} }\)

\(b^{2} =\) \(\sqrt{12^{2}-3^2 }\)

\(b^2= \sqrt{144-9}\)

= 11.61895004

We can round that to 11.62.

Hope this helped!

Answer:

456

Step-by-step explanation:

Product means an answer derived from multiplication.  Therefore, if the product is 155952, and one value is 342, then the following equation is true:

342x = 155952, or 342 * x = 155952

Divide 155952 by 342 to get: 456.

Check the work in the equation:

342(456) = 155952

155952 = 155952, which is true, so the answer is 456.

If I helped, please make this answer brainliest! ;)

============================================================

Explanation:

As you probably expect, the first number 80 refers to the percentage the first loan covers. If the house is say $100,000, then the first loan is $80,000 while the second loan is the remaining $20,000.

An 80/20 mortgage, or similar, will have two monthly payments because you are getting two mortgages bundled together. Usually you should pay a down payment, though it may likely depend on your credit history. Those with good credit will pay less or no down payment, compared to those with worse credit will have to pay more down payment. A good rule of thumb is that 20% of the home's value is made as down payment, though this isn't what the "20" in "80/20" is referring to.

An 80% down payment is extremely high and unreasonable. Not many people have that kind of money laying around. A similar story applies to a 20% interest rate which is incredibly large for a mortgage rate (typically they are in the single digits such as 3%).

Answer:

Step-by-step explanation:

This is a related rates problem from calculus using implicit differentiation. The main equation is Pythagorean's Theorem. Basically, what we are looking for is \(\frac{dx}{dt}\) when y = 6 and \(\frac{dy}{dt}=-2\).

The equation for Pythagorean's Theorem is

\(x^2+y^2=c^2\) where x and y are the legs and c is the hypotenuse. The length of the hypotenuse is 10, so when we find the derivative of this function with respect to time, and using implicit differentiation, we get:

\(2x\frac{dx}{dt}+2y\frac{dy}{dt}=0\) and divide everything by 2 to simplify:

\(x\frac{dx}{dt}+y\frac{dy}{dt}=0\). Looking at that equation, it looks like we need a value for x, y, \(\frac{dx}{dt}\) and \(\frac{dy}{dt}\).

Since we are looking for \(\frac{dx}{dt}\), that can be our only unknown and everything else has to have a value. So what do we know?

If we construct a right triangle with 10 as the hypotenuse and use 6 for y, we can solve for x (which is the only unknown we have, actually). Using Pythagorean's Theorem to solve for x:

\(x^2+6^2=10^2\) and

\(x^2+36=100\) and

\(x^2=64\) so

x = 8.

NOW we can fill in the derivative and solve for \(\frac{dx}{dt}\).

Remember the derivative is

\(x\frac{dx}{dt}+y\frac{dy}{dt}=0\) so

\(8\frac{dx}{dt}+6(-2)=0\) and

\(8\frac{dx}{dt}-12=0\) and

\(8\frac{dx}{dt}=12\) so

\(\frac{dx}{dt}=\frac{12}{8}=\frac{6}{4}=\frac{3}{2}=1.5 m/sec\)

Answer:

x = 88

Step-by-step explanation:

All angles in a triangle equal 180 degrees. So our equation will be:

x + 48 + (x - 44) = 180

x + 48 + x - 44 = 180

2x + 48 - 44 = 180

2x + 4 = 180

2x = 176

x = 88

Hope this helps!

Answer:

107º

Step-by-step explanation:

Okay, if 135 is adjacent to an ungiven side, then to find that, you subtract 135 from 180.

180 - 135 = 45

So the other side is 45. Now we find the last unknown given side, and since we know 180 degrees is the sum of the degrees in a triangle, we do:

28 + 45 + x = 180

73 + x = 180

Subtract 73 on both sides you get,

x = 107.

Measure DEF is 107.

Answer:

The answer is 3 days

Step-by-step explanation:

Divide 48/16=3

Answer:

No, 3:15 is not equivalent to 1:

Step-by-step explanation:

3:15 cannot be equivalent to 1: because they are completely different numbers. You could try to find the factors of them to see if they are equivalent or not. So the answer would be no, 3:15 isn't equivalent to 1:

Thank you.

Answer:

I have completed the answers and attached them to the explanation.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question asks for a subtraction expression:

length is always a positive number so bigger number first here.

OB = 4-(-1)              >only moves in x direction so subtract x's

AB = 4-(-2)             >only moves in y direction so subtract y's

Answer:

its c. y>1/3x-2

Step-by-step explanation:

Just took the quiz

Answer:

y = - x - 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (2, - 4) and (x₂, y₂ ) = (- 1, - 1)

m = \(\frac{-1+4}{-1-2}\) = \(\frac{3}{-3}\) = - 1 , thus

y = - x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (- 1, - 1 ), then

- 1 = 1 + c ⇒ c = - 1 - 1 = - 2

y = - x - 2 ← equation of line

Step-by-step explanation:

it seems you solved the tricky part yourself already.

just to be sure, let's do the first derivative here again.

the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...

f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =

= 3t⁴ + 18t³ + 24t² + 18t + 21

f'(t) = 12t³ + 54t² + 48t + 18

and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).

we simply put the input number (2) at every place of the input variable (t).

so,

f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =

= 426

Answer:

Step-by-step explanation:

Answer:

For month 1, the current balance is $2750.00, the interest is $45.38, and the payment is $75.00. The amount applied to principal is $29.62.

For the remaining months, the interest and payment amount will stay the same, but the current balance and amount applied to principal will change based on the previous month's numbers.

Point of view:

Here's your answer but I prefer you to focus and study hard because school isn't that easy. But i'm glad I could help you!

:)

Among the four options provided in the reference diagram for the question attached thereby along with the question statement, {(-5, 8), (-5, 2), (-3, 3), (-3, 1), (0, 4), (0, 5), (-5, 7), (-3, 6)} is the relation that has a domain of {(-5), (-3), 0} and a range of {1, 2, 3, 4, 5, 6, 7, 8}.

As per the question statement, we are required to determine the relation which has a domain of {-5, -3, 0) and a range of {1, 2, 3, 4, 5, 6, 7, 8).

To solve this question, we will use the trial-and-error method on the options provided. We have to find out possible (x, y) combination, where "x" belongs to the set of {(-5), (-3), 0} and "y" belongs to the set of {1, 2, 3, 4, 5, 6, 7, 8}, and match these combinations with the options.

The first option has x values from the set of {1, 2, 3, 4, 5, 6, 7, 8} and y values from the set of {(-5), (-3), 0}. Hence, it is not the correct answer.

The second option has x values from the set of {(-5), (-3), 0} and y values from the set of {1, 2, 3, 4, 5, 6, 7, 8}. Hence, it is one possible correct answer.

The third and fourth options have values out of the sets of {(-5), (-3), 0} and {1, 2, 3, 4, 5, 6, 7, 8}. Hence, they are not the correct answers.

Therefore,  {(-5, 8), (-5, 2), (-3, 3), (-3, 1), (0, 4), (0, 5), (-5, 7), (-3, 6)} is the relation that has a domain of {(-5), (-3), 0} and a range of {1, 2, 3, 4, 5, 6, 7, 8}.

To learn more about Range & Domain of a Function, click on the link below.

https://brainly.com/question/1632425

#SPJ9

Answer:

39

Step-by-step explanation:

assuming the angles are 57 & 84

141 + 57 > 180

123 + 57 = 180 (no room for an 8)

96 + 57 = 153

180 - 153 = 27 (an 8 doesn't work for this answer)

57 + 39 = 96

180 - 96 = 84 ( we have a winner!)

Answer: x = 19

These two angles are equal to each other.

so 135 = (7x+2), and now solve for x.

135 = 7x +2

133 = 7x

Divide both sides by 7.

133/7 = 7x

19 = x

Check to see if it's correct

7x+2 = 135

7(19) + 2 = 135

133 + 2 = 135

135 = 135

Answer:

10.315

Step-by-step explanation:

The transformations taking place in the given function is a horizontal left ward shift of 9 units and 1 unit upward vertical shift.

A Transformation in Math is a process of moving an object (two-dimensional shape) from its original position to a new position.

Given that, a function f(x) undergo some transformations to become f(x+9)-1,

We know that,

Vertical Shifting:

Adding a constant to a function will shift its graph vertically (i.e. y = f (x) + c). Adding a positive constant c will shift the graph upward c units, while adding a negative constant c will shift it downward c units.

Horizontal Shifting:

Horizontal shifts are inside changes that affect the input (x-) axis values and shift the function left or right. Combining the two types of shifts will cause the graph of a function to shift up or down and right or left.

Therefore, there is transformation of a horizontal and vertical shift.

Hence, the transformations taking place in the given function is a horizontal left ward shift of 9 units and 1 unit upward vertical shift.

Learn more about transformations, click;

https://brainly.com/question/29194193

#SPJ9

The sale price of the item when displayed on sales costs $8.75 based on the stated original price and percentage discount offered.

The formula to calculate sale price of the item according to discount and original price will be -

Sale price = 25% × original price

Keep the value of original price in the formula to find the sale price

Sale price = 25% × 35

Performing multiplication and division by solving the percentage on Right Hand Side of the equation to find the value of sale price of the item

Sale price = 8.75

Hence, the item on sale costs $8.75.

Learn more about percentage -

https://brainly.com/question/843074

#SPJ1

Answer:

The value of x is 15.

Step-by-step explanation:

Since the base is 40 inches long, and the two triangles are congruent - both are right triangles and have sides x and their bases equal - you know that each base of a triangle is 20 inches long. Using the Pythagorean Theorem, you can get that \(x^2+20^2=25^2\). Solve for x by isolating the variable on one side: \(x^{2} =25^{2} - 20^{2}\) ⇒ \(x^{2} = 625 - 400\) ⇒ \(x^{2} = 225\) ⇒ \(x^{2} =225\) ⇒ \(x=\sqrt{225}\) ⇒ \(x=15\) inches.

For the plant which manufactures bars of steel, the conclusions are as follows;

A.  The scatter graph is shown.

B.  The equation is y = 2.204 + 1.007x

C.  Null hypotheses (H₀); β = 0

    Alternative hypotheses (Hₐ); β ≠ 0

D.  P-value (0.0001) is less than the significance level (α = 0.05).

In null hypotheses, there is no relationship between the two phenomenon's under the assumption or it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.

At a plant that manufactures bars of steel, a machine is used to cut the bars to specific lengths.

The machine has a dial that sets the length of the bars to be cut.

The dial is currently out of alignment and the plant manager is collecting data to assess the situation.

The following table shows 8 trials at different dial settings along with the actual output length of the bars that were cut.

All measurements are in millimeters.

Dail setting    Output length

    75                     78

    77                     79

    79                     82

    80                     83

    81                      85

    82                     83

    83                     86

    85                     88

A. The scatter plot is shown below.

Based on the scatter plot, a linear model seems appropriate to the model relationships between the dial setting of the machine and the output length of the steel bar.

The scatter plot shows the strong (r = 0.965), positive, linear association. There do not appear to be any outliners.

B.  From the data to construct a least-squares regression line to predict output length from dial setting. Then

y = (a + bx)

Let x be the dial setting machine and y be the output length of steel bars (in mm).

y = 2.204 + 1.007 x

C.  All conditions for inference are met. Indicate the hypotheses appropriate to test whether there is a linear relationship between output length and dial setting.

Let β be the true slope of the population regression line relating the dial setting of the machine (x) and the output length of the steel bars (y) at the manufacturing plant.

Null hypotheses (H₀) ; β = 0

Alternative hypotheses (Hₐ) ; β ≠ 0

Appropriate test = slope of regression line t-test.

D.  The test statistic for the appropriate test is t = 9.018 with 6 degrees of freedom (7 - 1)

The normal curve is shown;

Using calculator command t-CDF, with the alternative hypotheses as β≠0, then P-value = 0.0001.

In probability notation;

P(b≥0.017) = P(t≥9.018) = 0.00005

P-value = (2) × (0.00005) = 0.0001

P-value = 0.0001

Assume α = 0.05

Since our P-value (0.0001) is less than the significance level (α = 0.05), we do not convince statistical evidence that there is a linear relationship between output length and dial setting.

As the dial setting (x) increases, the output length of the steel bar (y) increases as well.

More about the null hypotheses and alternative hypotheses visit:

brainly.com/question/9504281

#SPJ1

Answer: 3.2

Step-by-step explanation: (2/5)/(1/8)=(2/5)*8= 16/5=3 1/5=3.2

Yes, there is a difference in the shapes of the displacement-time graphs for uniform acceleration towards the positive direction, uniform acceleration towards the negative direction, uniform deceleration towards the positive direction, and uniform deceleration towards the negative direction.

Uniform acceleration towards the positive direction:

In this case, the object's velocity increases in the positive direction over time. The displacement-time graph will have a concave-upward shape, forming a curve that starts with a small slope and gradually becomes steeper as time progresses.

Uniform acceleration towards the negative direction:

Here, the object's velocity increases in the negative direction, meaning it accelerates in the opposite direction to its positive direction.

The displacement-time graph will have a concave-downward shape, forming a curve that starts with a steep slope and gradually becomes less steep as time progresses.

Uniform deceleration towards the positive direction:

In this scenario, the object's velocity decreases in the positive direction, but it still moves towards the positive direction.

The displacement-time graph will show a curve with a decreasing slope, forming a concave-downward shape, indicating that the object is slowing down.

Uniform deceleration towards the negative direction:

Here, the object's velocity decreases in the negative direction, opposing its initial direction.

The displacement-time graph will have a curve with a decreasing slope, forming a concave-upward shape, indicating that the object is slowing down but still moving in the negative direction.

In summary, the shapes of the displacement-time graphs differ based on the direction and type of acceleration (positive or negative) and whether the object is undergoing uniform acceleration or uniform deceleration. These differences can be observed through the concavity and slope of the graphs.

For similar question on displacement-time.

https://brainly.com/question/28357012  

#SPJ8

Equations are used to represent functions, and vice versa.

The equation of y as a function of x is \(y=\sqrt{6 - x^2\)

The function is given as:

\(\sqrt{6-y^2}=x\)

Square both sides

\(6-y^2=x^2\)

Subtract 6 from both sides

\(-y^2=x^2 - 6\)

Multiply both sides by -1

\(y^2=6 - x^2\)

Take square root of both sides

\(y=\sqrt{6 - x^2\)

Express as a function

\(f(x) = \sqrt{6- x^2\)

Hence, the equation of y as a function of x is \(y=\sqrt{6 - x^2\)

Read more about functions and equations at:

https://brainly.com/question/13336451