Write each equation in exponential form.
log₂1/2=-1

Answer:

Naryam

Step-by-step explanation:

Murphy is incorrect because when subtracting integers, you have add the addictive inverse of the others. (keep, change, change) which would lead to the equation of 9 + 8. What Murphy did wrong is subtract 9 and -8 without finding -8 addictive inverse.

The value of -4(7/10) - 9(7/15) is -85 / 6.

A fraction represented with its quotient and remainder is a mixed fraction.

For example:

3 4/5 is a mixed fraction, where 3 is the quotient, and 4 is the remainder.

We have,

-4(7/10) - 9(7/15)

Convert each term into a proper fraction.

4 7/10 = (40+7) / 10 = 47 / 10

9 7/15 = (135 + 7) / 15 = 142 / 15

Now,

= -47 / 10 - 142 / 15

The LCM of 10 and 15 is 30

= [3 x (-47) - (2 x 142)] / 30

= (-141 - 284) / 30

= -425 / 30

We can divide by a common factor of 5

= - 85 / 6

Thus the value of -4(7/10) - 9(7/15) is -85 / 6.

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The complete question is

Evaluate -4(7/10) - 9(7/15)

Since their dot product is not equal to zero, then (8,-4) and (-2,4) are not normal to each other.

Two vectors are said to be normal or perpendicular to each other if the result of their dot product is equal to zero.

These two vectors are also called orthogonal to each other.

Let u = (u₁, u₂) and  v = (v₁, v₂), then the dot product u . v is defined as:

u . v = u₁v₁ + u₂v₂

To check whether the vectors are normal to each other, let us check their dot product.

The given vectors are: (8,-4) and (-2,4)

Let u = (8,-4) and  v = (-2,4), then,

u . v = 8 . (-2) + (-4) . 4

       = -16 + (-16) = -32 (not equal to zero)

Since u.v ≠ 0, then (8,-4) and (-2,4) are not normal to each other.

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Answer:

Below in bold.

Step-by-step explanation:

(√5)² * (√3)²

= 5 * 3

= 15

(∛9))³  (√30)²

= 9 * 30

= 270

Answer:

(3 3/4) : (3/4) = 5/1 = 5

Step-by-step explanation:

Answer:

0.03773584905

or 0.04

Step-by-step explanation: if this was not what you were looking for,

The number of years for which the money was invested is 5.0 years

From the question, we are to determine how long (in years) the money was invested

From the given information,

Lina invested $7,800 at a simple interest rate of 4.35%

and

She earned $1,696.50 in interest

From the formula for simple interest

I = PRT

Where I is the simple interest

P is the principal

R is the rate

and T is the time in years

From the given information,

I = $1,696.50

P = $7,800

R = 4.35% = 0.0435

Thus,

1696.50 = 7800 × 0.0435 × T

1696.50 = 339.3 × T

T = 1696.50/339.3

T = 5.0 years

Hence, the money was invested for 5.0 years

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Answer:

Step-by-step explanation:

As we know that a-b=7 and ab=8(a times b is equal to 8) If we find the factors of 8 we know that 8 times 1 make 8 and if u try 8-1= 7 so 1 squared is 1 and 8 squared is 16 so 16+1=17

Answer:

A = 8

B = 1

A squared + B squared = 65

Step-by-step explanation:

8 - 1 = 7

A - B = 7

8 x 1 = 8

A x B = 8

8 x 8 = 64

1  x 1 = 1

64 + 1 = 65

A squared + B squared = 65

Answer: Shape A is congruent to Shape B because If you were to rotate one of the two and flip it, it would  match.

Step-by-step explanation:

hope it helps :)

Answer:

[tex] {3}^{x} = 243 = {3}^{x} = {3}^{5} = 5[/tex]

Answer:

-2g-2f

Step-by-step explanation:

Hope it helps you

Answer: -2g-2f

Step-by-step explanation: Combine like terms

-3g+2f+g-4f

-2g-2f

Answer:

Thabo had 51 crayons at the start.

Step-by-step explanation:

Sam has three times as many crayons as Thabo. Then

x = 3y.

If Sam gives 17 crayons to Thabo, then he will have twice as many crayons as Thabo. Then

(x-17) = 2(y+17).

Thabo had 51 crayons to start with.

Given that Sam has three times more crayons than Thabo does. He will have twice as many crayons as Thabo if he gives him 17 of them.

We need to determine the number of crayons Thabo had in starting.

Let's use algebra to solve this problem step-by-step.

Let's assume that Thabo starts with "x" crayons.

According to the given information:

Sam has three times as many crayons as Thabo, which means Sam has 3x crayons.

If Sam gives Thabo 17 crayons, he will have (3x - 17) crayons left.

Thabo will have (x + 17) crayons after receiving the 17 crayons from Sam.

Now, the second condition states that if Sam gives Thabo 17 crayons, he will have twice as many crayons as Thabo.

Mathematically, it can be expressed as:

2(x + 17) = 3x - 17

Let's solve this equation to find the value of x:

2x + 34 = 3x - 17

Subtract 2x from both sides:

34 = x - 17

Now, add 17 to both sides:

x = 51

So, Thabo had 51 crayons to start with.

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Answer:

the amount he is charged for being overdrawn each day

Step-by-step explanation:

The value of algebraic expression 2³x + 4 for x = - 1 will be equal to - 4.

2³ x + 4 =  ( 2 )³ x + 4 = 8x + 4

8x + 4 =  8(-1) + 4

          = -8 + 4

          = -4

Therefore, the value of algebraic expression 2³x + 4 for x = - 1 will be equal to - 4.

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The situation which is represented by the inequality (7x + 50 > 4x + 100) is: A. Molly has $50 and Mary has $100. Molly saves $7 per week and Mary saves $4 per week. How long will it be before Molly has more money than Mary?

An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments:

In this scenario, the number of week for saving money by each person is represented by the variable x. Therefore, the situation which is represented by the inequality (7x + 50 > 4x + 100) is that "Molly has $50 and Mary has $100. Molly saves $7 per week and Mary saves $4 per week. How long will it be before Molly has more money than Mary?"

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Answer: x = 2

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

Given equation,

→ 5(2x + 1) = 25

Solving for the value of x,

→ 5(2x + 1) = 25

→ 10x + 5 = 25

→ 10x = 25 - 5

→ x = 20/10

→ [ x = 2 ]

Hence, the value of x is 2.

The correct unit price is $1.24 per pair of padded gloves such that the contractor's unit price is incorrect because total cost was divided by number of dozens bought instead of the number of units in 6 dozens

How many units are in a dozen?

The dozen of pairs of padded  gloves contains 6 pairs of padded  gloves, in other words, the number of units in 6 dozens is 6 dozens multiplied by 12 units in a dozen

number of units in 6 dozens=6*12

number of units in 6 dozens=72

unit price=total cost/number of units in 6 dozens

unit price=$89.28/72

unit price=$1.24

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Answer:   [tex]2\text{x}^4, \ 2\text{x}^7, \ 2\text{x}^{10}, \ 2\text{x}^{13}[/tex]

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

Explanation:

The first term is [tex]a_1 = 2\text{x}[/tex] and the common ratio is [tex]r = \text{x}^3[/tex]

To get the second term, we multiply the first term by that common ratio

[tex]a_2 = a_1*r = 2\text{x}*\text{x}^3 = 2\text{x}^4[/tex]

Repeat a similar idea for the third term

[tex]a_3 = a_2*r = 2\text{x}^4*\text{x}^3 = 2\text{x}^{4+3} = 2\text{x}^7[/tex]

and the fourth term is

[tex]a_4 = a_3*r = 2\text{x}^7*\text{x}^3 = 2\text{x}^{7+3} = 2\text{x}^{10}[/tex]

The fifth term is

[tex]a_5 = a_4*r = 2\text{x}^{10}*\text{x}^3 = 2\text{x}^{10+3} = 2\text{x}^{13}[/tex]

Something to notice: The exponents of the first five terms are: 1, 4, 7, 10, 13. The sequence of exponents is arithmetic even though the original underlying sequence is geometric.

The reason why the exponent sequence is arithmetic is because we keep multiplying by [tex]\text{x}^3[/tex], and hence we keep adding 3 to each exponent to get the next exponent.

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

To summarize, the first five terms are:

[tex]2\text{x}, \ 2\text{x}^4, \ 2\text{x}^7, \ 2\text{x}^{10}, \ 2\text{x}^{13}[/tex]

We will ignore the first term 2x since your teacher wanted you to find the next four terms after that first term (i.e. term2 through term5).

Answer:

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Step-by-step explanation:

There are 0 or no real solutions for the equation 4x²=-4x-4.

So,

Given the equation: 4x²=-4x-4

Then,

No factor for this equation.

Therefore, there are 0 or no real solutions for the equation 4x²=-4x-4.

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The equation that can be formed with the unit and total costs of filling up the Sedan with 12 gallons of gas is 12p = 50.04, where p = 4.17.

An equation is a mathematical statement that expresses two equal variables.

Equations use the equation sign (=).

The quantity of gas per the Sedan's tank = 12 gallons

The unit cost of a gallon of gas = $4.17

The total cost of filling 12 gallons with gas = $50.04

In equation form, the expression can be written as:

12p = 50.04

Where p = 4.17

Thus, the equation of the total cost is 12p = 50.04, where p = 4.17.

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The equation of the circle where the given parameters are Center = (6, 15) and Radius = 2 is (x - 6)^2 + (y - 15)^2 = 4

The given parameters are

Center = (6, 15)

Radius = 2

Rewrite the above parameters properly as

Center, (h, k) = (6, 15)

Radius, r = 2

The equation of the circle is represented as

(x - h)^2 + (y - k)^2 = r^2

Substitute the known values in the above equation

So, we have

(x - 6)^2 + (y - 15)^2 = 2^2

Evaluate the exponent of 2

So, we have

(x - 6)^2 + (y - 15)^2 = 4

Hence, the equation of the circle where the given parameters are Center = (6, 15) and Radius = 2 is (x - 6)^2 + (y - 15)^2 = 4

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Complete question

Write an equation of the circle with Center = (6,15) and Radius = 2

According to the question,  solution for the inverse variation function. Using standard concept which defines inverse variation function is as follows:

Inverse variation function: [tex]yx=k[/tex]

Therefore, the number of inverse variation function which has[tex](2,3)[/tex] as a solution is : one

What is inverse variation function?

Inverse variation function defines the relationship which are in inverse function. Like, direct variation define direct relationship between the two variables. In inverse variation function, one variable is inversely related to the another variable.

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Answer:

81.1111111111111

Step-by-step explanation:

Becuse

Answer:

80 (Estimate, we'll get to the exact result at the end.)

Step-by-step explanation:

[tex]\mathrm{(Round)~If~x < 5,~x=y.0}[/tex]

→ y is the number, for instance, 60.0 since 63.0 in the ones/tenths place is less than 5 or 0.5

[tex]20 \times 70 = 1,400[/tex]

→ imagine the newly rounded 73 as 2 × 7 which is 140, but it's 2 more 0's, so it's 1,400.

[tex]\bold{77}\\18|1,400\\18 \times 7 = 126\\140 - 126 = 14\\18 \times 7 = 126\\140 - 126 = 14[/tex]

→ long division was performed. for each time a 0 appeared in 14 when 140 was subtracted by 126(18 • 7), a zero was either borrowed from 1,400 or dropped from 1,400 which became our remainder of 14 both ways around.

→ 77 is close to 75 but not below 5, so it round to 80. therefore, your estimate result is 80.

(The exact result is 81.1)

I hope this helped, let me know if you have concerns.

The face of the rhombus ( length of one side) is found to be 13 cm.

A rhombus is a special parallelogram because it meets the definition of a parallelogram, which is a quadrilateral to two pairs of parallel sides.

As per the given question;

The circumference of the rhombus is 52 cm.

Let us consider the one side of the rhombus is of length 'x'.

As, we known that the sides of the rhombus are equal.

Thus,

4x = 52

x = 52/4

x = 13.

Therefore, the face or the length of the one side of the rhombus is found as 13 cm.

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Answer:

47 23

Step-by-step explanation:

calculator

on the internet in brainly lol

The surface area needed to be paint is 3,008 sq. ft. The cans requires for the paint are 15.

A cuboid is a 3 solid with six (rectangular) faces, eight vertices, and twelve edges.

Total Surface Area (TSA) = 2(lb + bh + hl) sq.units

where, i is the length, b is the breadth and h is the height.

The given values are;

length l = 12 ft

breadth b = 10 ft

height h = 16 ft

Put the values in the formula;

Total Surface Area (TSA) = 2(12×10 + 10×16 + 16×12)

                                         = 2×(120 + 160 +192)

                                          = 2×(472)

Total Surface Area (TSA) = 1504

Now, reduce the area of the floor as it is not to be painted;

Painted area = Total Surface Area (TSA) - area of floor

                     = 1504 -12×10

Painted area = 3,008 sq. ft

The area covered by 1 paint can is 200 sq. ft.

Can required = total painted area/painted area by one can

Can required = 3,008/200

                      = 14.44

Can required = 15 (as half can is not considered)

Therefore, the area painted is 3,008 sq. ft with the total number of cans as 15.        

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Answer:

3rd option, y<=x^2-3

Step-by-step explanation:

y<=x^2-3 is the graph of the function. The vertex of the graph is (0, -3), so when x=0, y=-3. Also, for every x-coordinate, the shaded region is below the corresponding y-coordinate. For example, when x=0, the shaded area for that x-coordinate is below y=-3.