The principal P is borrowed at a simple interest rate r for a period of time t.

Answer:

[tex]g(x)= -3x^{2} +4x +5[/tex]

Step-by-step explanation:

Five more = Addition of 5

Opposite = (-)

3 times = Multiplication by 3

Square = To the power (exponent) of two

4 times the number = Multiplication by 4

The number = unknown number = x

The complete inequality is y < x and y< -x

The expressions are given as:

y[ ]x and y[ ]-x

From the graph, we can see that:

Only the lower regions are shaded

This represents the less than inequality sign

Hence, the complete inequality is y < x and y< -x

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Answer:

Step-by-step explanation:

This problem is similar to many others in which the sum of two quantities and their difference are given. The solution can be found easily when the equations for the relations are written in standard form.

Let s and h represent numbers of sodas and hot dogs sold, respectively. The given relations are ...

Adding the two equations eliminates one variable.

  (s +h) +(s -h) = (235) +(59)

  2s = 294 . . . . simplify

  s = 147 . . . . . .divide by 2

  h = 147 -59 = 88 . . . . h is 59 less

147 sodas and 88 hot dogs were sold.

__

Additional comment

The solution to a "sum and difference" problem is always the same. One of the numbers is half the sum of those given, and the other is half their difference. ((235-59)/2 = 88)

Answer:

[tex]C-\frac{1}{3(lnx- \pi)^3}.[/tex]

Step-by-step explanation:

[tex]\int\ {\frac{1}{x(lnx- \pi)^4} } \, dx=\int\ {\frac{d(lnx- \pi)}{(lnx- \pi)^4}} \, dx=-\frac{1}{3(lnx- \pi)^3} +C.[/tex]

A) A parallelogram has 4 sides.

B) The opposite angles of parallelogram are congruent.

C) [tex]\angle A \cong \angle C, \angle B \cong \angle D\\\\\implies m\angle C=115^{\circ}, m\angle D=65^{\circ}[/tex]

By using the table, we see that the correct options are:

a) f(2) = 7

b) f(x) = 3 when x = 8.

c) f⁻¹(7) = 2

d) f⁻¹(x) = 8 when x = 3.

Here we have a table of x and f(x).

First, we want to find f(2). To get that, we need to go to the row where we have x = 2.

In that same row we can see that f(x) = 7.

Then f(2) = 7.

Then it says:

"if f(x) = 3, then x = ?"

This time we do the opposite. We find the row where f(x) = 3, and then we see the value of x in that row.

In the second row (counting from the bottom) we can see that when x = 8, f(x) = 3.

Then:

"if f(x) = 3, x = 8"

Then we want to get the inverse of f(x) evaluated in 7.

Here we use the rule:

[tex]f(x) = y\\f^{-1}(y) = x[/tex]

Then

[tex]f(2) = 7\\f^{-1}(7) = 2[/tex]

The answer here is 2.

Finally:

"if the inverse evaluated in x si 8, then what is the value of x"

Similar to before, we know that when we evaluate f(x) in 8, the outcome is 3.

Then when we evaluate the inverse in 3, the outcome is 8.

So here we must have x = 3.

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The two factors multiplied together to make a trinomial is (x-1)(3x-2).

Given equation is 3x²-5x+2.

An algebraic equation which of the second degree in x is known as quadratic equation. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

In the given equation,

Multiply the first coefficient 3 with the last coefficient 2  so we get 2×3=6

Use any two numbers which on multiply give 6 and on adding or subtracting give -5.

Such two numbers are -2 and -3

On multiplying, (-3)×(-2)=6

On Adding, -3-2=-5

So, break -5x into -3x and -2x and we get

3x²-3x-2x+2

Taking out 3x common from the first two terms and -2 from the last two terms as

3x(x-1)-2(x-1)

Taking out the common term (x-1) as common and get

(x-1)(3x-2)

Hence, the two factors of the equation 3x²-5x+2 that can be multiplied together to make this trinomial is (x-1)(3x-2).

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Answer:

x^2=ab

Step-by-step explanation:

Please mark as brainlist

Answer:

Step-by-step explanation:

Answer:

f-(g/h) is an algebraic expression of the difference of f and the quotient of g and h.

Step-by-step explanation:

[tex]f - ( \frac{g}{h} )[/tex]

I hope it was helpful for you..m

The requried algebraic expression of English phrase is given as f - g/h.

The algebraic expression consists of constants and variables. eg x, y, z, etc.

the equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

here,
The difference between f and the quotient of g and h.
The difference represents the subtraction of values, and the quotient can be obtained by division of g by h.
So,
Required algebraic expression,
= f - g/h

Thus, the required expression is given as f - g/h.

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The product is equal to:

[tex]\frac{18}{25}(cos(165) + i*sin(165))[/tex]

Remember that we can write a complex number in polar form as:

[tex]R*e^{i*a} = R*(cos(a) + i*sin(a))[/tex]

Then the given product:

[tex]\frac{6}{5}*(cos(120) + i*sin(120))*\frac{3}{5}*(cos(45) + i*sin(45))[/tex]

can be rewritten to:

[tex](\frac{6}{5}*e^{i*120})*(\frac{3}{5}*e^{i*45})[/tex]

Now is easier to solve the product:

[tex](\frac{6}{5}*e^{i*120})*(\frac{3}{5}*e^{i*45})\\\\= \frac{6}{5} *\frac{3}{5} *e^{i*(120 + 45)}\\\\= \frac{18}{25}*e^{i*165}\\\\= \frac{18}{25}(cos(165) + i*sin(165))[/tex]

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Answer:

  22

Step-by-step explanation:

The segment addition theorem tells us the whole is the sum of the parts. We can use this to write an equation relating the expressions for segment length.

  OQ = OP +PQ . . . . . segment addition theorem

  4x +2 = (3x -3) +(4x -10) . . . . substitute given expressions

  15 = 3x . . . . . . add 13 -4x to both sides

  5 = x . . . . . . . divide by 3

  OQ = 4x +2 = 4(5) +2 = 22

The length of OQ is 22 units.

The equation solved for w is w = 6g - 40

The complete question is in the attached image

The equation is given as:

g = 1/6(w + 40)

Multiply both sides by 6

6g = w + 40

Subtract 40 from both sides

w = 6g - 40

Hence, the equation solved for w is w = 6g - 40

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Answer:

.

Step-by-step explanation:

Answer: W = 113/20

What we know:

Set up equation                                                W + 3/5 = 6 1/4

Expand                                                              W + 3/5 = 6*4+1 /4

Simplify                                                              W + 3/5 = 25/4

Common denominator                                     W + 3*4/5*4 = 25*5 / 4*5

Simplify                                                              W + 12/20 = 125/20

Subtract                                                                   -12/20    -12 /20

Solve                                                                  W = 113/20

Check:

By converting our answers into decimals, we can see if the sides are equal:

113/20 = 5.65

3/5 = 0.6

5.65 + 0.6 = 6.25

Does 6.25 = 6 1/4?

1/4 = 0.25

6 + 0.25 = 6.25

6.25 = 6.25

Therefore, W = 113/20 is the correct answer.

Answer:

  B.  360 meters

Step-by-step explanation:

The triangles shown are similar, so their corresponding parts are proportional.

There are a couple of useful proportions here. We can equate the ratio of horizontal segments to the ratio of diagonal segments:

  (600 m)/(250 m) = ??/(150 m)

Or, we can equate the ratios of the diagonal segment to the corresponding horizontal segment:

  ??/(600 m) = (150 m)/(250 m)

Either way, when we multiply the equation by the denominator of ??, we get the result ...

  ?? = (600)(150/250) m = 360 m

The distance from F to G is 360 meters.

Answer:

Original Salary: [tex]5,957.14[/tex]

Increase in 3%: [tex]6,135.85[/tex]

Step-by-step explanation:

So when something increases by x%, the new value is (100+x)% the original value. So 6255, is 105% the original value. This means to find the original value, we have to find the number that has 6255 as 105% of it's value. Whenever you try to find x% of a number, you multiply it by the decimal value of the percentage, which is found by dividing by 100. So to find x%, you do: [tex]o*\frac{x}{100}[/tex] where o = original value, x=percent. In this case the percent is 105%, which when divided by 100 is 1.05. So this gives us the equation: [tex]o*1.05=6255 \implies o = \frac{6255}{1.05} = 5,957.14[/tex]. This is his original salary. You need to do this process, do not make the mistake of subtracting 5% from 6255. This is because 5% of 6255 does not equal the 5% of the original value. 5% of 6255 should be greater than 5% of the original value, since the new value is an increase of 5%. So since we have his original salary, we can calculate the salary increase had it been 3%. to do this we multiply by 1.03 (103% divided by 100). This gives us the equation: [tex]5,957.14*1.03=6,135.85[/tex]

Answer:

8

Step-by-step explanation:

12+4=16

16 divided by 2= 8

Answer:

-1

Step-by-step explanation:

Simply plug in (-1) to both equations and add.

Equation 1:

2(-1)^2 = 2

3(-1) = -3

2 + -3 - 1 = -2

Equation 2:

-( - 1) = 1

Add both together:

-2 + 1 = -1

Answer:

The equation is 2x² + 3x - 1 and here f(x) is -1

Putting f(x) = -1.

[tex]f(x) = 2 {( - 1)}^{2} + 3( - 1) - 1[/tex]

[tex]f(x) = 2 (1) - 3 - 1[/tex]

[tex]f(x) = 2 - 3 - 1[/tex]

[tex]f(x) = - 1 - 1[/tex]

[tex]f(x) = - 2[/tex]

For g(x) put as -1

[tex]g(x) = - ( - 1)[/tex]

[tex]g(x) = 1[/tex]

Last step,

-2 + 1 = -1

So, option ( a) is correct

The range of the given relation is:   range = { 3, 9, 10}

Range is the out come of the event is know as y.

Here, the given relation:

               R = {(0,3), (8,9), (16,10)

Now, range = { 3, 9, 10}

Thus, the range of the given relation is: range = { 3, 9, 10}

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Answer:

Step-by-step explanation:

The attached graph shows the graph opens downward, so the vertex at (-2, 6) is a maximum. The y-intercept is the constant, +2.

The range is the vertical extent of the function. Its upper limit is the maximum value of the function (6), and its lower limit is negative infinity.

  The range is {y l y ≤ 6}.

The graph opens downward, so it is increasing to the left of its maximum value, and decreasing to the right of its maximum. The x-coordinate of the maximum (-2) defines the upper limit of the increasing interval.

  The function is increasing over the interval (-∞, -2).

The y-intercept of the graph is where it crosses the y-axis. The value of x is zero there, so the value of the function is the value of its constant, +2.

  The function has a positive y-intercept.

The multiples of 5 and 6 based on the information have been illustrated below.

It should be noted that a multiple is a number that can be divided by another number without a remainder.

Here, the multiples of 5 will be:

5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60.

6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...

In this case, the multiples of the numbers have been illustrated.

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Answer:

N=15

Step-by-step explanation:

The calculation of 129 ÷ 3.332 rounded to the appropriate number of significant digits is 39.

Given that;

129 ÷ 3.332

First we convert 3.332 to fraction

3.332 = 3.332/1

3.332 = 3.332/1 × 1000/1000 = 3332/1000

3.332 = 833/250

Hence we have;

129 ÷ 833/250

This can be written as

= 129 × 250/833

= 32250/833

= 38.71549 ≈ 39

Therefore, the calculation of 129 ÷ 3.332 rounded to the appropriate number of significant digits is 39.

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Answer:

Step-by-step explanation:

x=40

Answer:

here is

Step-by-step explanation:

5x-20=180

5x=180+20

=200

X=200/5

40

Answer:

Proof:

By the inscribed angle theorem, we know that angle BAC is equal to angle DEC. By the second corollary to the inscribed angle theorem, we know that line segment AE is perpendicular to line segment AC. Therefore, line segment AE is tangent to circle C.

Step-by-step explanation:

Analyze and ensure the answer is correct.

Answer:

Step-by-step:

By the inscribed angle theorem, we know that angle BAC is equal to angle DEC. By the second corollary to the inscribed angle theorem, we know that line segment AE is perpendicular to line segment AC. Therefore, line segment AE is tangent to circle C.

Answer:

2.75 is the median

Answer:

1.25 is the median

Step-by-step explanation:

it is the middle of the number sequence.

to find the median, place the numbers in value order and find the middle

since there is an even amount of numbers, add 2.5 and 0 (the two middle numbers) and divide them by two