Rodney opens a savings account with $75 and also deposits $40 each month. Morgan opens an account with $50 and also deposits $40 each month. Will they have the same amount in their account at any point? If so, after how many months? Explain.
Show an equation

The line through (1, 0, 1) and (4, −4, 4) intersect the plane x + y + z = 6 at point (7,-8,7).

As given,

Equation of the line passes through two points (1, 0, 1) and (4, −4, 4) is:

[tex]\frac{x-4}{4-1}=\frac{y+4}{-4-0}=\frac{z-4}{4-1}[/tex]

From the above equation we have

(x-4)/3 =(y+4)/-4

⇒-4x+16= 3y+12

⇒y=(-4x +4)/3  __(1)

And

(x-4)/3=(z-4)/3

⇒z=x __(2)

Substitute the value of y and z in the plane x +y+ z=6 to get point of intersection of line and plane

x+ [(-4x +4)/3] +x=6

⇒3x-4x+4 +3x =18

⇒2x=14

⇒x=7

Substitute value of x in (1) and (2)

y=-8 and z=7

Therefore, the line through (1, 0, 1) and (4, −4, 4) intersect the plane x + y + z = 6 at point (7,-8,7).

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Answer:

6.3071, 6.408, 6.47, 6.7

Step-by-step explanation:

6.3071, 6.408, 6.47, 6.7, hope this helped!

Answer:

In bold below.

Step-by-step explanation:

6.3071, 6.7 6.408, 6.47

= 6.3071, 6.408, 6.47, 6.7

Answer:

f(-2) = 18

Step-by-step explanation:

In order to calculate a function of x, we replace x
For example
f(x) = x
f(-2) = -2

In this specific scenario

f(x) = 3 * (4 - x)
f(-2) = 3 * (4 - -2)

- -2 turns positive
f(-2) = 3 * (4 + 2)

Now we use PAMDAS (parentheses, exponents, multiplication, division, addition) as an operation order, so we first solve the parantheses
f(-2) = 3 * 6

f(-2) = 18

Answer:

2/17, 8/17, and 11/17
7/21, 7/18, 7/14, 7/12, and 7/8
2/12, 2/10, 2/8, 2/6, and 2/4.

Step-by-step explanation:

the order would be 2/17, 8/17, and 11/17 since the bottom number (denominator) stays the same while the numerator (top number) increases.

the order for the 2nd one would be:
7/21, 7/18, 7/14, 7/12, and 7/8. The reason for this is that when the numerator stays the same and the denominator increases, the value of the fraction decreases. For example, 1/2 is greater than 1/4, and 1/4 is more than 1/5 because 5 is greater than 4. This only works when the numerator (top number) stays the same.
The order for the 3rd one would be:
2/12, 2/10, 2/8, 2/6, and 2/4. Again, the numerator stays the same while the denominator changes. As the denominator goes down, the value of the fraction goes up.
Also if possible label your question the correct difficulty this is like middle school not college

Given

9h-27

Answer

Greatest common factor = 9

Answer:

(1) y = 8.45x

(2) Total cost: $42.25

Step-by-step explanation:

Let's see by constructing a first-hand example of the information we have.

$101.40 = 12x

Divide 12 on both sides.

When we divide 12 from both sides, we get the simplified answer of:

x = 8.45

This means that each pizza will be $8.45 each, therefore this will be out=r equation

y = 8.45x

(where x is the number of pizzas and y is the total amount cost.

To find the cost of 5large pepperoni pizzas, we use our equation above (y = 8.45x) and input a 5 in x;

y = 8.45(5)

y = 42.25

The total cost for the 5 pizzas will be $42.25.

The attached figure shows the location of P' and R' in the figure, after the dilation

Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor, where the scale factor does not equal one.

The figure that completes the question is added as an attachment

From the figure, we have the following parameters

The image of dilation using the above parameters is the scaled factor of the given figure

As a general rule, the following are the properties of a scaled copy of another figure

The above means that

New lengths = Old lengths * Scale factor

So, we have

P'R' = PR * Scale factor

C'R' = CR * Scale factor

This gives

P'R' = 5 * 3

P'R' = 15

C'R' = 2.6 * 3

C'R' = 7.8

Using the above as a guide, the location of P' and R' are identifies in the figure

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The true statement  is that both √15 and √0.001 are irrational , the correct option is (c).

Rational Numbers can be defined as the  numbers that can be expressed in the form of p/q , where p and q are integers and q not equal to 0 .

For Example : 2/3 , 2, 8/3 are all Rational Numbers.

Irrational Numbers can be defined as the  numbers that cannot be expressed in the form of p/q where , p and q are integers and q not equal to 0 .

For Example : √2 , √37 are irrational as they cannot be expressed in the form of p/q.

In the question ,

two numbers √15 and √0.001 are given .

the first number √15 is not a perfect square , hence not an integer ,

So, √15 is an irrational number .

the second number

√0.001 = √(1/1000) = 1/√1000 = [tex]\frac{1}{10\sqrt{10} }[/tex]

we see that √10 is not an integer , hence √0.001 is an irrational number .

Therefore , the true statement  is that both √15 and √0.001 are irrational , the correct option is (c).

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The unknown variables and angles are as follows:

The sum of angles on a straight line is 180 degrees.

Therefore, the sum of angles on line STA is 180 degrees.

CT bisect STE

Angle STE Is a right angle.

Therefore,

5x + y + 3 + 3x + 12 = 90

5x + 3x + y + 12 + 3 = 90

8x + y + 15 = 90

8x + y = 90 - 15

8x + y = 75

Ty bisect ETA

Angle ETA Is a right angle.

Therefore,

y + 41 + 5x + 4 = 90

5x + y + 45 = 90

5x + y = 90 - 45

5x + y = 45

Combine the equation

8x + y = 75

5x + y = 45

subtract equation(ii) from equation(i)

3x = 30

x = 30 / 3

x = 10

y = 75 - 80

y = -5

Therefore,

m∠YTE = y + 41 = -5 + 41 = 36°

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Betty spent $90 and Nan spent $ 30

Mathematical expressions can be used to depict situations or issues, and algebra is the field of mathematics that does this. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in every area of mathematics, including coordinate geometry, calculus, and trigonometry. A straightforward algebraic expression is 2x + 4 = 8.

Given that :While shopping, Betty spent three times as much as Nan. And they spent a total of $120,

Let the Betty spent total $x and Nan spent total $Y

then,

x = 3y ....(i)

x +y =120 .....(ii)

put value of c from i equation to equation ii

4y = 120

y = 30

x = 90

Hence Betty spent $90 and Nan spent $ 30

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Answer:

$48

Step-by-step explanation:

Simple interest (I) = PRT/100

Where P = principal

R= rate

T = time

.: Simple Interest = 120 × 8 × 5

---------------

100

S. I = $48

.: the approximate value of the investment at the end of 5 years will be = $48

The set A ∪ B ∪ C will be {1, 2, 3, 4, 5, 7, 9, 11},  (A – B) ∩ C is ∅, and A' ∪ B is {2, 3, 5, 7, 9, 11}.

It is defined as a diagram that shows a logical relation between sets.

The Venn diagram consists of circles to show the logical relation.

The universal set will be:

U = {1, 2, 3, 4, 5, 7, 9, 11}

Let:

A = {1, 2, 3, 4, 5}

B = {2, 3, 5, 7, 11},

C= {3, 5, 7, 9}

1) A ∪ B ∪ C = {1, 2, 3, 4, 5, 7, 9, 11}

3) (A – B) ∩ C = {1, 4} ∩ C= {3, 5, 7, 9}

(A – B) ∩ C = ∅

5) A' ∪ B = {7, 9, 11} ∪ {2, 3, 5, 7, 11}

A' ∪ B = {2, 3, 5, 7, 9, 11}

Thus, the set A ∪ B ∪ C will be {1, 2, 3, 4, 5, 7, 9, 11},  (A – B) ∩ C is ∅, and A' ∪ B is {2, 3, 5, 7, 9, 11}.

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[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the end of the period}}{\textit{Future Value of an ordinary annuity}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right] \\\\\\ ~~~~~~ \begin{cases} A=\textit{accumulated amount}\\ pmt=\textit{periodic payments}\dotfill &100\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{each months, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &20 \end{cases}[/tex]

[tex]A=100 \left[ \cfrac{\left( 1+\frac{0.06}{12} \right)^{12 \cdot 20}-1}{\frac{0.06}{12}} \right] \\\\\\ A=100 \left[ \cfrac{\left( 1.005 \right)^{240}-1}{0.005} \right]\implies A \approx 46204.09[/tex]

The number of shoes that have to be purchased until both companies earn the same amount is 21.

Based on the information, the profit rates for Nike and Adidas are illustrated as:

Nike -2 (x - 2)

Adidas -17 + x

In this case, x represents the number of shoes purchased,

The number of shoes that have to be purchased until both companies earn the same amount will. be:

2(x - 2) = 17 + x.

2x - 4 = 17 + x

2x - x = 17 + 4

x = 21

The number of shoes will be 21.

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Answer:

$2

Step-by-step explanation:

To find the unit cost, divide the entire price of all the songs (22), by how many songs you bought (11)

22 Dollars / 11 Songs   =    2 Dollars / Song   (2 Dollars per Song)

Answer:

02987329619

Step-by-step explanation:

02987329619

Answer:

kk

Step-by-step explanation:

Answer: $2.75

Step-by-step explanation:

2) Judy spent 3*5.25 = 15.75 on popcorn bags, 13.60 on a jumbo bag of chips and 7.90 for a dip. This means that overall she spent $37.25. If she had $40, this means that she have left $40 - $37.25 = $2.75.

1) Your answer is right.

The formulas that will appear in D2, E2, and F2, respectively are

B$2, C$2, D$2. Option A

This is further explained below.

Generally, A mathematical formula or a chemical formula, for example, are both examples of formulas, which are condensed ways of expressing information via the use of symbols.

When used informally within the realm of science, the word "formula" refers to the overall construction of a connection between a set of determinable variables.

Because of the formula =A$2, row 2 is considered to be anchored.

At this point, D2 is located to the right of C2, but still in the same row.

And the cell that is direct to the right of A2 is labeled B2.

As a result, the formula for D2 will equal B times 2.

In the same manner, the formula in E2 will be C$2, and the formula in F2 will be D$2.

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-1000 represents Jenny's change in elevation.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the corresponding positive numbers are the negative numbers. The boldface Z is a common mathematical symbol for the set of integers. A number that contains both positive and negative integers, including zero, is called an integer. There are no fractional or decimal parts in it. Integers include things like -5, 0, 1, 5, 8, 97, and 3,043.

Given Data

Jenny ended a hike at an elevation of 3, 000 feet above sea level.

She had started at an elevation of 2, 000 feet above sea level.

Hike remaining = 3000 - 2000

Hike remaining = 1000

-1000 represents Jenny's change in elevation.

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Answer:Explanation:

• T

• 0.320

The player's on-base percentage = 0.320

This is equally the relative frequency of the player being on base.

Thus, the appropriate method is the relative frequency method.

Thus, the probability that the player will get on base in his next appearance is 0.320.

D. moving red blood cells around the body

The customer must purchase 80 gallons of 50% solution if they wish to create a 40% soap solution.

A customer has 40 gallons of a cleaning solution that contains 20% soap.

The company sells a cleaning solution that contains 50% soap.

The customer wishes to create a 40% solution.

Solution:

By mixture and allegation method,

1 gallon                              1 gallon

  50%                                   20%

                         40%

  20                                       10

To create a 40%Soap solution, one must mix 20 gallons of 50%  soap solution and 10 gallons of  20% Soap solution.

Therefore, the ratio is 20 : 10 = 2:1

The customer has 40gallons of a cleaning solution that contains 20% soap, therefore in a 2:1 ratio, 1 part is 40 gallons.

Then for 2 parts = 2*40 = 80 gallons.

The customer must purchase 80 gallons of 50% solution if they wish to create a 40% soap solution.

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Answer:

12

Step-by-step explanation:

(8+11+14+13+14+9+15)/7 = 12

Answer:

Total obs. = 7

Average = (n + 1 )/2

Average = 7 + 1 /2

= 8/2 = 4th obs.

= Sum of obs./ Total obs.

= 8,11,14,13,14,9,15/7

= 84/7

The time taken to fill the bathtub by cold water is 14.4 minutes.

Given,

Time taken to fill a bathtub by both cold and hot water = 8 minutes

Time taken to fill the bathtub by hot water = 18 minutes

Time taken to fill the bathtub by cold water = t minutes

We have to find t.

We can take the full bath tub as 1.

Now,

We can equate the given data:

We get,

(8/18) + (8/t) = 1

Now, solve the equation:

((8 × t) + (8 × 18) ) ÷ (18 × t) = 1

(8t + 144) ÷ 18t = 1

8t + 144 = 18t

18t - 8t = 144

10t = 144

t = 144/10

t = 14.4

That is,

The time taken to fill the bathtub by cold water is 14.4 minutes.

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Answer: g=-16.3

Step-by-step explanation:

ya welcome

Answer:

Hhhhhhhhhhhhhhhhhh : x=-2

Given:

There is a graph given in the question

Required:

We want to find the solution of the given graph

Explanation:

As we can see that, both lines are parallel so there is no chance for intersection

now if there is no intersection point means there is no solution

Final answer:

No solution

The continents that have a lower elevation than North America are Africa and Asia.

It should be noted that elevation simply had to do with the height above sea level of a particular thing. Any of numerous huge landmasses is referred to as a continent. Up to seven geographical regions are usually regarded as continents, based on convention rather than precise requirements.

A continent is one of the seven major land divisions on Earth. Asia, Africa, North America, South America, Antarctica, Europe, and Australia are the continents, in order of size.

In this case, the table shows negative integers to represent the lowest elevations below sea level on each of the 7 continents.

In the table, Africa has -512 and Asia had -1312. It should be noted that these are lower than in North America.

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A point that lies in the middle of a line and is equally spaced from its ends is the line's midway. The formula for the line's midpoint is [(x)1 + (x)2]/2, [(y)1 + (y)2]/2 if the line's endpoints are (x)1, (y)1, and (x), (y), respectively.

Using the equations [(x)1 + (x)2]/2, [(y)1 + (y)2]/2, one may get the midway. Here, the coordinates of two points are (x), (y), (x)2, (y)2, and the midway is a location that is equally spaced from both of these positions.

The exact middle number between two numbers is referred to as the midway. The midpoint calculation is the same as the two-number average calculation. Therefore, by adding any two numbers together and dividing by two, you may find the halfway between any two integers.

The distance formula, which is derived from the Pythagorean Theorem, is employed to determine the separation between two points in the plane. The Pythagorean Theorem is based on a right triangle where the angles are a and b.

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