Nelson has half of his investments in stock paying a 6% dividend and the other half in a stock paying 9% interest. if his total annual interest is $660 how much does he have invested?

Answer:

x = 3

or

x = -3

(explanation in the picture above)

Answer: x = 3 or x = -3

Step-by-step explanation:

Absolute values make the answer always positive, as they cancel out the negative sign. So to solve an absolute value equation, we must solve for both the positive and negative of the answer.

3x = 9

3x = -9

x = 3 or x = -3

The answers are given below.

First of all, we will know about GCF and expressions.

GCF (GREATEST COMMON FACTOR) - The largest number, which is the factor of two or more number is called the Greatest Common Factor (GCF). It is the largest number (factor) that divide them resulting in a Natural number. Once all the factors of the number are found, there are few factors which are common in both.

Expression are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

1). 5/6(-2y+3) (simply multiply 5/6 with both terms using expansion)

=-2(5/6)+3(5/6)

=-5/3+5/2

2). 6(3s-2.5-5s)= 18s-15-30s = -12s-15

3). 3/10(4m-8)+9m = 12/10m-24/10+9m

= 6/5m-12/5+9m

=6/5m+9m-12/5

=51/m-12/5

4). 2.25-2(7.5-4h)= 2.25-15+8h

= 8h-12.75

5). 3(a-7)= 3a-21

6). -6(2+x)= -12-6x

7). -5(3m-4)= -15m+20

8).  -9(-5-4c)= 45+36c

9).  4.5(3s+6)= 13.5s+27

10).  -1.4(-5+7g)= 7-9.8g

11). 2/5(6-5p)= 12/5-2p

12).  -4/3(3q-10)= -4q+40/3

13). 2(3+4y+5)= 6+8y+10 = 8y+10

14. The expression 8x + 2 factored using the GCF is= 2(4x+1)

15. The expression 3y-24 factored using the GCF is = 3(y-8)

16. The expression 14p-28 factored using the GCF is= 14(p-2)

17. The expression 6+16k factored using the GCF is= 2(3+8k)

The coefficient of the variable terms of following are given below

18. The expression 1/7a + 1/7 factored is= 1/7

19. The expression 1/3b - 1/3 factored is= 1/3

20. The expression 3/8d + 3/4 factored is= 3/8

21. The expression 2.2x+ 4.4factored is= 2.2

22. The expression 0.15c - 0.072 factored is= 0.15

23. The expression 3/8z + 1 factored is=3/8

24. The expression 6s - 3/4 factored is=6

25. The expression 5/2k - 2 factored is=5/2

26. Factor -4 out of 8d + 20 The factored expression is= -4(-2d-5)

27. Factor -6 out of 18z - 15 The factored expression is=-6(-3z+5/2)

28. Factor -0.25 out of 7g + 3.5 The factored expression is=-0.25(-28g-14)

29. Factor -1/2 out of -1/2x+ 6 The factored expression is=-1/2(x-12)

30. Factor -1.75 out of -14m - 5.25n The factored expression is=-1.75(8m+3n)

31. Factor -1/4 out of -1/2x - 5/4y The factored expression is=-1/4(2x+5y)

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Answer:

7

Step-by-step explanation:

since 3x-6 and x+8 are congruent x had to make both the equations equal eachother. 7 is the only number that does that

Answer:  72

Step by step explanation:

sum of the masses of the 25 goats take as x then x/25=74 so 74×25=x x=1850 after buying a new goat number of goats =26

hope i helped <3

the answer is 2f

Re-order terms so constants are on the left

f×2=2f

The room's temperature when Quinn returned home is the y-intercept of the equation, which is: 40 degrees Celsius.

The equation of a linear relationship between two variables, x and y, can be expressed in slope-intercept form as y = mx + b, where we have the initial value or the y-intercept as "b", and the rate of change or unit rate as "m".

Alternatively, it can be rewritten as y = b + mx.

R = 42 - 0.7t represents the equation for the Quinn's room's temperature, R, in degrees Celsius, and t in minutes after Quinn turned on the air conditioner.

Interpreting the equation, we can deduce the following:

The initial value or the y-intercept (b) was the room's temperature when Quinn returned home.

The unit rate or rate of change (m) = -0.7 degrees per minute.

Thus, Quinn's room's temperature when she returned was 40 degrees Celsius.

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Answer:

Dog be 28

Phosphors apparently

Step-by-step explanation:

We know that

Based on the given information, we define the following

The cost to rent a moving van is $51 plus an additional $7 per hour.

Based on the given information,

Select red from A and B then the probability of getting cards of same color is  12/24 * 24/48 = 1

Box A: 12 Red

          12 Black

Box B: 24 Red

          24 Black

One card is selected from Box A and placing the selected card into Box B.

One card is selected from Box B.

What is the probability that a red card is selected from Box B?

Two things can occur:

1) Select red from A and B:

12/24 * 24/48 = 1

2) Select black from A and red from B:

12/24 * 24/48 = 1

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answer

11

Step-by-step explanation:

4x+1/3y^24(2)+1/3(3)^28+1/3(9)8+3

Answer:

D

Step-by-step explanation:

-3 ft means that it is three feet below zero. That means 0 means the sea level.

We can see that the holes of the piece are already oriented in a way the piece will fit in the missing hole of the puzzle, so it doesn't need a rotation or reflection.

Then, in order to fit the piece in the hole, we need to move the piece 3 positions to the left and 1 position down.

Therefore the transformation needed is: a translation of 3 units to the left and 1 unit down.

Step-by-step explanation:

d

since you add them up you will have a certain answer that will match up

The translation of Quadrilateral ABCD with coordinates A(-3, 4), B(1, 3), C(3, 6), and D(1, 6) using the given transformation rule is; E(3, -1), F(7, -2), G(9, 1), H(7, 1)

We are given the vertices of Quadrilateral ABCD as;

A(-3, 4), B(1, 3), C(3, 6), and D(1, 6)

Now, we are told that it is first translated right by 6 units. This means that we would add 6 units to each x-value to get;

A'(-3 + 6, 4) = A'(3, 4)

B'(1 + 6, 3) = (7, 3)

C'(3 + 6, 6) = C'(9, 6)

D'(1 + 6, 6) = D'(7, 6)  

It is now translated by 5 units downwards and we subtract 5 from each y-value and this gives us;

E(3, -1), F(7, -2), G(9, 1), H(7, 1)

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Complete question is;

Quadrilateral ABCD has vertices A(-3, 4), B(1, 3), C(3, 6), and D(1, 6) is translated 6 units right and 5 units down to create quadrilateral EFGH. Determine the correct orientation and location of quadrilateral EFGH.

If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.

Definition of the proportionality constant?

The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.

K = y/x is the equation for the proportionality constant. The equation for the slope of a line through the origin, m = y/x, is the same as this. One can determine the value by using the equation for the line's slope.

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Answer:

Answer: 7.5 or 7 1/2.

Answer:

52

Step-by-step explanation:

52 is a bigger number than 33?

Answer:

$100.00

Step-by-step explanation:

5 and above ex: 150 =200 140=100 under 5 keep the first letter then turn the other numbers into 0's 5 and above make the first number go up one then turn the rest of the numbers in to 0's

The dimensions that yield the minimum surface area of the open-top square-based, rectangular metal tank that will have a volume of 48.5 ft³ are:

The dimensions of an area, which is a two-dimensional object, refer to the length and the width.

On the other hand, the dimensions of the volume refer to the length, width, and height.

The volume of the square-based rectangular tank = 48.5ft³.

The length of each side of the surface area = 3.6468 ft (∛48.5ft)

Check:

Volume = height x length x width

= 3.6468 x 3.6468 x 3.6468

= 48.499 ft³

= 48.5 ft³

Thus, the dimensions of the surface area include the length and the width without the height.

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Answer:

Axis interception points [tex]97x-9[/tex] x intercepts: [tex](\frac{9}{97} ,0),[/tex]Y intercepts:[tex](0,-9)[/tex]

Step-by-step explanation:

Slope of 97x-9 :     m=97

Domain: 97 x - 9

Range: 97 x - 9

The polynomial in standard form is  2x³+200x-36x²-3600

A polynomial is a mathematical formula that involves only the operations subtraction, addition,  multiplication, and powers of positive integers of the variables and is composed of coefficients and indeterminates.

We know the roots of the polynomial as 18, 10i, and −10i.

therefore the polynomial is of the form.

a(x-18)(x-10i)(x+10i)

= a (x-18)(x²-100i²)

= a (x-18)(x²+100)

= a (x³+100x-18x²-1800)

Now at x =1 The value of the polynomial is -3434

Therefore

-3434 = a(1+100-18-1800)

or, a = 2

Therefore the polynomial is of the form: (2x³+200x-36x²-3600)

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Step-by-step explanation:

in general, a linear function is always of the structure

y = ax + b

"a" is the slope of the line and is the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another.

"b" is the y-intercept (the y-value when x = 0).

so, if we don't see the solution right away with experience, we have to use the data points (usually starting with the first 2) to solve them 2 equations with 2 variables a, b :

2 = a×1 + b = a + b

1 = a×2 + b = 2a + b

now we can simply subtract the first equation from the second and get

1 = 2a + b

- 2 = a + b

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

-1 = a + 0

a = -1

1 = 2×-1 + b = -2 + b

b = 3

and the equation is

y = -x + 3

therefore, when the input is n (that means f(n))

y = output = -n + 3

1. (3/4)x = 9. Multiply both sides by the reciprocal of 3/4: (4/3)(3/4)x = (4/3)(9)

x = 12.

2 . -4=4/7*x

        4x/7=-4

             x=-7

3. -1/5*x=6

     -x/5=6

Multiply all terms by the same value to eliminate fraction denominators

Cancel multiplied terms that are in the denominator

x=-30

With an example, what is a reciprocal equation?

An inverse of a number or value is referred to as reciprocal. If x is any real number, then 1/x will be the reciprocal of that number. For instance, 1/8 is the reciprocal of 8, which is 1 divided by 8. 1/8's reciprocal is equal to 8.

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The rate of interest was 5%.

The rate of interest and simple interest can be related through the formula -

S.I. = PRT/100, where S.I. stands for simple interest, P stands for principal, R stands for rate of interest and T stands for time.

Amount = Principal + Interest

Interest = 106.05 - 101

Performing subtraction on Right Hand Side of the equation

Interest = $5.05

Rate of interest = (5.05×100)/(101×1)

Performing multiplication in numerator and denominator

Rate of interest = 505/101

Performing division

Rate of interest = 5

Therefore, to earn $106.05 from $101 in one year, the rate of interest should be 5%.

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The hexadecimal value from the operation is 6385A7

To solve this problem, we have to subtract the hexadecimal numbers from one another.

In doing so, we would subtract 3F2E1D from A2B3C4.

This would give us,

[tex]A2B3C4 - 3F2E1D = 6385A7[/tex]

The value of the expression is 6385A7.

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123

[tex]123 > x = 10 > 6[/tex]

The speed of the boat in still water is 6miles/hour miles per hour.

The speed of the current is 3miles/hour miles per hour.

The distance travelled by the boat downstream(with the flow current of river) is 240 miles.

The distance travelled by the boat upstream(Against the flow current of river) is 240 miles.

Time taken to travel downstream = 20 hours.

Time taken to travel upstream = 60 hours.

Let us say the velocity of the boat is V and the velocity of the current flow of river is U.

The relative velocity of boat with respect to ground while going downstream is,

velocity of boat in downstream = V + U.

As we know,

Velocity = distance/time

Putting values of downstream motion,

V + U = 240/20

V + U = 10

Let us say this is our equation 1.

The relative velocity of boat with respect to ground while going upstream is,

velocity of boat in upstream = V - U

As we already know,

Velocity = distance/time

Putting the values of upstream motion,

V - U = 240/60

V - U = 3

Let us say this is our equation 2.

Now, on adding equation 1 and 2.

V+U+V-U = 10 + 3

2V = 13

V = 6.5 miles per hour.

Rounding off to the nearest integer,

V = 6 miles/hour.

Putting V = 6.5 miles/hour in equation 1,

6.5 + U = 10

U = 3.5 miles/hour.

Rounding off to the nearest integer,

U = 3 miles/hour

The velocity of river current is 3 miles/hour and velocity of boat is 6miles/hour.

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A boat traveled 240 miles downstream, then 240 miles back up stream. The trip downstream took 20 hours. The trip back up stream took 60 hours. Use this information to fill in the following blanks.

The speed of the boat in still water is ______ miles per hour.

The speed of the current is ______ miles per hour.

Answer:

Step-by-step explanation:
(the small double lines like = means that the length of those sides are all same)
So, if one length is considered as x
     the other two will also be x
      we see that the length of one side is given which is 27
      to find x
      x + x + x = 27
        3x = 27
    so, x = 27/3
          x = 9m

(the small vertical single line means that those sides are equal)
so if one side is y, the other two are also y
so , y + y+ y = 30
       3y = 30
       y = 10m

If we imagine the stairs to be made of small rectangles of length 10m and base 9m , finding area will be easier.
we will see that there are 9 rectangles in total
area of rectangle = length x base
so, area of 1 rectangle = 9x10
                                       = 90[tex]m^{2}[/tex]
so area of 9 identical rectangles = 9 x 90
                                                      = 810 [tex]m^{2}[/tex]

Step-by-step explanation:

1st

[tex]area = \frac{1}{2} base \times hight[/tex]

2nd

[tex]32 = \frac{1}{2} base \times 4[/tex]

3rd

[tex]32 \div 4 = \frac{1}{2} base[/tex]

4th

[tex]8 \times 2 = base[/tex]

answer

[tex]base = 16ft[/tex]