Sam initially invested $4,500 into a savings account that offers an interest rate of 3% each year. He wants to determine the number of years, x, for which the account will have less than or equal to $7,020.

Determine the solution set to the inequality that represents this situation.

Answer:

Tony pays $6.75 for his item, & Tanya pays $9 for her items

Step-by-step explanation:

Let Tanya's item be x, and Tony's be y. Set the system of equality:

3x = 4y

y = x - 2.25

Plug in x - 2.25 for y in the first equation

3x = 4(x - 2.25)

Distribute 4 to all terms within the parenthesis

3x = 4x - 9

Isolate the x. Subtract 4x from both sides

3x (-4x) = 4x (-4x) - 9

3x - 4x = -9

-x = -9

Isolate the x. Divide -1 from both sides

(-x)/-1 = (-9)/-1

x = 9

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

Plug in 9 for x in the equation

y = x - 2.25

y = (9) - 2.25

y = 6.75

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

Tony pays $6.75 for his item, & Tanya pays $9 for her items

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

~Rise Above the Ordinary

Your answer would be 1. Hope this helps :)

0.96 rounded to the nearest tenth is:

1

Because 6 is greater than 4. The number has to be greater than 4 for it to be rounded up, but if it's not, then the number only gets rid of the number behind the tenth.

Hope this helped! :D

Hello!

To find the midpoint of the line segment, use the formula: [tex](\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2})[/tex]. In simpler terms, we are finding the average of the two points.

We can assign [tex]x_{1}[/tex] and [tex]y_{1}[/tex] to the point (5, 8), and (-1, 6) to  [tex]x_{2}[/tex] and  [tex]y_{2}[/tex].

[tex](\frac{5+(-1)}{2}, \frac{8+6}{2}) = (\frac{4}{2}, \frac{14}{2}) = (2, 7)[/tex]

Therefore, the coordinates of the midpoint of the line segment is (2, 7).

Final answer:

The coordinates of the midpoint of the line segment with endpoints (5,8) and (-1,6) are (2,7).

Explanation:

To find the coordinates of the midpoint of a line segment, we can use the midpoint formula which states that the x-coordinate of the midpoint is the average of the x-coordinates of the two endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the two endpoints.

Using the formula, we can find the midpoint of the line segment with endpoints (5,8) and (-1,6).

x-coordinate: (5 + (-1)) / 2 = 4 / 2 = 2

y-coordinate: (8 + 6) / 2 = 14 / 2 = 7

Therefore, the coordinates of the midpoint of the line segment are (2,7).

9514 1404 393

Answer:

  a) 7

  b) 20

  c) 14

  d) 24

Step-by-step explanation:

The desired number is found by subtracting the given number from the square of the integer just higher than the root of the given number.

a) √42 ≈ 6.5, so the desired number is 7² -42 = 49 -42 = 7

__

b) √101 ≈ 10.05, so the desired number is 11² -101 = 121 -101 = 20

__

c) √470 ≈ 21.7, so the desired number is 22² -470 = 484 -470 = 14

__

d) √1000 ≈ 31.6, so the desired number is 32² -1000 = 1024 -1000 = 24

Answer:

The answer is [tex]6x^{3} +39x^{2}+54x[/tex]

Step-by-step explanation:

Volume of the rectangular prism = Length * Width * Height

Length (l) = [tex]x+2[/tex]

Width (w) = [tex]3x[/tex]

Height (h) = [tex]2x+9[/tex]

By substituting these values to the equation above,

Volume of the rectangular prism = [tex](x+2)*3x*(2x+9)[/tex]

                                                      =[tex](3x^{2} +6x)*(2x+9)[/tex]

                                                      =[tex]6x^{3} +27x^{2} +12x^{2} +54x[/tex]

                                                      =[tex]6x^{3} +39x^{2}+54x[/tex]

Therefore,

The answer is [tex]6x^{3} +39x^{2}+54x[/tex]

Answer:

Volume = [tex]6x^3+39x^2+54x[/tex]

Step-by-step explanation:

Prism is an object which has two  bases which are parallel to each other and other faces are parallelograms .

Rectangular prism is a three dimensional figure which has 6 faces which are all rectangles .

Let l be the length of rectangular prism , w be the width of prism and h be the height of prism .

Then volume of rectangular prism is equal to [tex]lwh[/tex] .

We will also use formula: [tex]a(b+c)=ab+ac[/tex]

Here,

[tex]l=x+2\\w=3x\\h=2x+9[/tex]

Therefore,

volume of rectangular prism is calculated as follows:

[tex]V=\left ( x+2 \right )\left ( 3x \right )\left ( 2x+9 \right )\\=\left ( 3x^2+6x \right )\left ( 2x+9 \right )\\=3x^2\left ( 2x+9 \right )+6x\left ( 2x+9 \right )\\=6x^3+27x^2+12x^2+54x\\=6x^3+39x^2+54x[/tex]

The product of -0.2 -6.8 = -7          Hope this Helps :)

Answer: Yes it is possible. Angle DCF is also 50 degrees

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

Check out the image attachment below. On that image, I've marked that angle EBA is congruent to angle BAC by the alternate interior angle theorem. Those angles are shown in red. Furthermore, angle BAC is congruent to DCF (corresponding angles) using a green marker. Finally, using the transitive theorem, you can connect the statements in a chain to say that angle EBA is congruent to angle DCF, which is why angle DCF is 50 degrees as well.

Nathan is incorrect. Any number times 0 is equal to 0!

-Abha

To do this you can do (pay) x (hours) to work out how much Johnny makes for example:

8.25 x 29.5 = 243.375$ so the answer is 243.375$

Answer:

The correct answer is B) $243.397

Step-by-step explanation:

Reggie's score changed by 350 points.

Reggie lost 4 spaceships in level 3 of a video game, and he lost 50 points for each spaceship. So, the total points lost would be 4 multiplied by 50, which is 200 points. However, when Reggie completed level 3, he earned a bonus of 550 points. To find out how much his score changed, we need to consider both the points lost and the bonus earned.

Points lost: 4 spaceships x 50 points/spaceship = 200 points

Bonus earned: 550 points

Score change: Bonus earned - Points lost = 550 points - 200 points = 350 points

Therefore, Reggie's score changed by 350 points.

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Answer:

17%

Step-by-step explanation:

Final answer:

Ella owns 15% of Fitz Incorporated, and the remaining 85% is shared equally among 5 other shareholders. Thus, each of these shareholders owns an equal share of 17% of the corporation.

Explanation:

The question asks about corporate stock and how it relates to the percentage of ownership in a corporation. Ella owns 15% of Fitz Incorporated, and the remaining 85% is owned equally by 5 other shareholders. To find the percentage each of these shareholders owns, we divide the remaining percentage by the number of shareholders.

The calculation would be:

Subtract the percentage owned by Ella from the total, which is 100% - 15% = 85%.

Divide this remaining percentage (85%) by the number of other shareholders, which is 5.

85% / 5 = 17% ownership for each of the other shareholders.

So, each of the remaining 5 shareholders owns 17% of the corporation.

1/3    =        7

------      ---------

2 miles     ? miles

using cross products

1/3 * ? = 2 * 7

1/3 ? =14

? = 42 miles

Answer:

42

Step-by-step explanation:

The formula of a midpoint:

[tex]M_{AB}\left(\dfrac{x_A+x_B}{2},\ \dfrac{y_A+y_B}{2}\right)[/tex]

We have:

[tex]A(8,\ 4)\to x_A=8,\ y_A=4\\B(12,\ 2)\to x_B=12,\ y_B=2[/tex]

Substitute:

[tex]\dfrac{8+12}{2}=\dfrac{20}{2}=10\\\\\dfrac{4+2}{2}=\dfrac{6}{2}=3[/tex]

Let's first recall what is known as the Midpoint formula we have, so by the Midpoint formula, we know that, the midpoint of any line segment joining the points [tex]{\bf{A(x_{1},y_{1})}}[/tex] and [tex]{\bf{B(x_{2},y_{2})}}[/tex] is given by

Now, if we assume our points to be A(8,4) and B(12,2) and the midpoint being M, then we will be having :

[tex]{:\implies \quad \sf M=\bigg(\dfrac{8+12}{2},\dfrac{4+2}{2}\bigg)}[/tex]

[tex]{:\implies \quad \sf M=\bigg(\dfrac{20}{2},\dfrac{6}{2}\bigg)}[/tex]

[tex]{:\implies \quad \boxed{\bf{M=(10,3)}}}[/tex]

Hence, the required Midpoint is (10,3)

Constant of proportionality is given by: y=kx oy [tex]k=\frac{y}{x}[/tex]

So lets suppose y = 50 and x = 5 so k will be [tex]\frac{50}{5}=10[/tex]

This 10 will remain constant. For every $50 Michael saves $5, for $100 he will save  $10 , for $150 he will save $15 and so on.

So this 'k' will be same for each value of x and y.

The mean number of people in each spinning class last week is calculated by summing up the total number of attendees and dividing by the number of classes. The mean attendance for last week was 21.

To calculate the mean number of people attending the spinning class each day, you would add up the total number of people for the week and then divide by the number of classes.

The given numbers are:

So the sum of the attendees is: 13 + 23 + 24 + 31 + 14 = 105

The mean is then calculated by dividing the total by the number of days, which is 5 in this case:

Mean = Total ÷ Number of Days = 105 ÷ 5 = 21

So, the mean number of people in each class last week was 21.

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ANSWER TO QUESTION 1

[tex]w(34)=0[/tex]

We multiply both sides by the multiplicative inverse of 34

[tex]w(34)\times \frac{1}{34} =0 \times \frac{1}{34}[/tex]

We apply the multiplicative property of zero to obtain,

[tex]w =0 [/tex]

ANSWER TO QUESTION 2

The dot means multiplication

[tex]7\times x=7[/tex]

By multiplicative inverse property,

[tex]\frac{1}{7}\times7x=\frac{1}{7} \times7[/tex]

[tex]1 \times x=1[/tex]

By the multiplicative identity property,

[tex]x=1[/tex]

ANSWER TO QUESTION 3

[tex]0+r=15[/tex]

By the additive identity property

[tex]r=15[/tex]

ANSWER TO QUESTION 4

[tex]9(0)=a[/tex]

By the multiplicative property of zero

[tex]0)=a[/tex]

or

[tex]a=0[/tex]

ANSWER TO QUESTIONS NUMBER

5. Multiplicative property of zero

Reason: According to this property if you multiply any number by zero, the result is zero.

That is why

[tex](0)3=0[/tex]

6. Multiplicative identity property

Reason: According to this property if we multiply any number by 1 the result is the same number. That is why

[tex]10\times 1=10[/tex]

7. Multiplicative identity property

Reason: According to this property if we multiply any number by 1 the result is the same number. That is why

[tex](1)\times 52=52[/tex]

8. Reflexive property of equality

According to this property for any number [tex]a[/tex],

[tex]a=a[/tex]

That is why

[tex]12+5=12+5[/tex]

9.Additive identity Property

According to this property, if we add any number to zero, the result is the same number. That is why

[tex]17+0=17[/tex]

10. Symmetric Property of Equality

According to this property, if  [tex]a=b[/tex] then  [tex]b=a[/tex]. That is why,

if  [tex]6+7=13[/tex] then  [tex]13=6+7[/tex]

11. Substitution Property of Equality

According to this property,

If if  [tex]a=b[/tex] then we can substitute a and for b in any expression that is why,

[tex](60-20)-10=40-10[/tex] because  [tex]40=60-20[/tex]

12. The Transitive Property of Equality

According to this property is ,if  [tex]a=b[/tex] and  [tex]b=c[/tex]

then [tex]a=c[/tex]. That is why,

If [tex]2^3=8[/tex] and  [tex]8=10-2[/tex]

then  [tex]2^3=10-2[/tex]

Answer:

1. w = 0

2. x = 1

3. r = 15

4. a = 0

5. Multiplicative identity of zero

6. Multiplicative identity of 1

7. Multiplicative identity of 1

8. Reflexive property of equality

9. Additive identity property of 0

10. Symmetric property of equality

11. Substitution property of equality

12. Transitive property of equality

Step-by-step explanation:

1. [tex]w (34) = 0[/tex]

w = 0 / 34

w = 0 (since anything divided by 0 is 0)

2. [tex]7[/tex] · [tex]x = 7[/tex]

7x = 7

x = 7 / 7

x = 1

3. [tex]0 + r = 15[/tex]

r = 15 - 0

r = 15

4. [tex]9 (0) = a[/tex]

Anything multiplied with 0 becomes 0 so

0 = a

a = 0

5. [tex](0) 3 = 0[/tex] ---> Multiplicative identity of 0

Any number multiplied by 0 becomes 0.

6. [tex]10[/tex] · [tex]1 = 10[/tex] ---> Multiplicative identity of 1

Any number multiplied by 1 remains unchanged.

7. [tex]1 (52) = 52[/tex] ---> Multiplicative identity of 1

Any number multiplied by 1 remains unchanged.

8. [tex]12 + 5 = 12 + 5[/tex] ---> Reflexive property of equality

The values are equal to itself.

9. [tex]17 + 0 = 17[/tex] ---> Additive identity property of 0

Sum of 0 and any number is the original number.

10. If [tex]6 + 7 = 13[/tex], then [tex]13 = 6 + 7[/tex] ---> Symmetric property of equality

If a = b then b = a.

11. [tex](60 - 20) - 10 = 40 - 10[/tex] ---> Substitution property of equality

If x = y then x can be substituted in for y in any equation and vice versa.

12. If [tex]2^{3} = 8[/tex] and [tex]8 = 10 - 2[/tex], then [tex]2^{3} = 10 - 2[/tex] ---> Transitive property of equality

If a =b and b = c, then a = c.

Answer:

Kenya’s equation has infinitely many solutions

Step-by-step explanation:

we have

[tex]-6(x-2)+3x=-3(x+3)+21[/tex]

Solve for x

Eliminate the parenthesis

[tex]-6x+12+3x=-3x-9+21[/tex]

Group terms that contain the same variable

[tex]-6x+3x+3x=-9+21-12[/tex]

Combine like terms

[tex]0=0[/tex]  ---> is true for any value of x

therefore

Kenya’s equation has infinitely many solutions

Answer:

D

Step-by-step explanation:

Answer:

Option D

Yes 0.4

Step-by-step explanation:

A sequence is said to be arithmetic if there is a pattern as

nth term is got by adding d to n-1th term.

d = common difference

The sequence will look like

a, a+d,a+2d, a+3d,......

where I term= a and each time d is added to get the next term.

Our given sequence is

-0.3, 0.1, 0.5, 0.9, …

Let us find difference between Ii and I term

=0.1-(-0.3) = 0.4

Similarly iii term - ii term

=0.5-0.1 =0.4

and iv term - iii term = 0.9-0.5 = 0.4

Hence confirmed that this is an arithmetic sequence with I term =-0.3 and common difference = 0.4

38. X>2 and X<1 will give you the answer X3 because X>2+X<1= X3

39. X>2 or X>3 will give you the answer X6 because X>2x X>3=X6

40. your answer would be x=4

Hey there,

Here is your answer:

10/1 = 10

You would just start from the beginning because it is all addition (Pemdas) Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction

the equation will be: 2(v+w)=2z

Answer:

Step-by-step explanation:

[tex]-12-a=4a-7\qquad|\text{add 12 to both sides}\\\\-a=4a+5\qquad|\text{subtract 4a from both sides}\\\\-5a=5\qquad|\text{divide both sides by -5}\\\\\boxed{a=-1}[/tex]

To simplify the expression √7{x 5} ×  √7{x 5}, you can multiply the radicands together and simplify the result.

To simplify the expression √7{x 5} ×  √7{x 5}

We can use the properties of radicals to simplify the expression. When multiplying radicals with the same index, we can simplify by multiplying the radicands together. In this case, the radicands are both x5, so the simplified form will be:

√7{x 5} ×  √7{x 5} = √7{x 5 × x 5} = √7{x10}

Therefore, the simplified form of the expression is √7{x10}.

Answer:

3/6is not a integer.

Step-by-step explanation:

6/3 integer

6/2 integer

3/6 not a integer

Final answer:

The fraction 3/6 is not an integer because it equals 0.5, which is a fraction and not a whole number.

Explanation:

To determine which of these values is not an integer, we need to perform the division for each fraction:

Therefore, 3/6 is not an integer because when you divide 3 by 6, you get a fractional number rather than a whole number.

* First is correct - the height crosses the 0 point between 8 and 10 secs

* Third is correct - 81.6 m is max at 4 secs

all others incorrect