Determine whether each function is an example of exponential growth or decay. Then, find the y -intercept. y=0.0015(10) x

Here we need to evaluate some mathematic expressions in some given values, we will get:

3x-  4 is equal to 17 when x = 7.

-5x + 8 is equal to -7 when x = 3.

Here we have some expressions that we need to evaluate. Evaluating an expression means that we replace the variables (usually denoted by letters) with numerical values.

The first expression is:

3x-  4

And we we want to evaluate it in x = 7.

So just replace the x by the number 7 and then do the operations:

3*7 - 4 = 21 - 4 = 17

The expression is equal to 17 when x = 7.

Now let's do it again for second expression:

-5x + 8  with x = 3.

Replacing the variable by the number we get:

-5*3 + 8 = -15 + 8 = -7

So that is the basic procedure to evaluate mathematic expressions.

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Answer:

9ft by 9ft

Step-by-step explanation:

Answer:

The two smaller angles equal 24 and together they equal 48

Step-by-step explanation:

The bisector tells us that the smaller angles equal each other

3x + 6 = 7x - 18  Subtract 3x from both sides

6 = 4x - 18  Add 18 to both sides

24 = 4x  Divide both sides by 4

6 = x

Now, plug 6 back into each equation.

3x + 6

3(6) + 6

18 + 6

24

7x - 18

7(6) - 18

42 - 18

24

After dividing and simplifying the expression 4√162 x⁴ / 4√2 y⁸, we get the result as 9 x ² / y⁴.

We are given the expression

4√162 x⁴ / 4√2 y⁸

We need to divide the expression and simplify it.

First, cancelling the terms that are same in the numerator and the denominator:

√162 x⁴ / √2 y⁸

Now , using the properties of the exponents, we get that:

= √81 x² / y⁴

= 9 x ² / y⁴

Therefore, after dividing and simplifying the expression 4√162 x⁴ / 4√2 y⁸, we get the result as 9 x ² / y⁴.

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Answer:

The graph of g(x) = -|x| - 8.

Answer:

∠ GRS = 74°

Step-by-step explanation:

∠ GRS + ∠ QRG = ∠ QRS , that is

∠ GRS + 105° = 179° ( subtract 105° from both sides )

∠ GRS = 74°

Answer:

75°

Step-by-step explanation:

While it may appear that QRS is a straight line, it is not so since m∠QRS = 179° and if it was a straight line, it would be 180°

The figure actually represents three rays with endpoint at R

The three rays are RQ, RS and RG

Draw another ray RT with endpoint at R and opposite to ray RG. Opposite rays have angles that add up to 180°

Therefore m∠GRT = 180°

m∠SRT = m∠QRG since they are opposite angles

Since m∠QRG = 105°, therefore m∠SRT = 105°

m∠GRS + m∠SRT=180° since these angles are formed by two opposite rays

Substituting we get
m∠GRS + 105 = 180

m∠GRS = 180-105 = 75°

The values of  f(−4), f(−2), and f(3) for given piecewise function are 0, -4, and -3.5 respectively.

What is piecewise function ?

Whenever the summation of two functions is different over different intervals, the sum is a piecewise function.

Here, the given piecewise function f(x) is :

[tex]\begin{aligned}f(x)&=\left\{\begin{matrix}\frac{-1}{2}x-2 \text{ if} \:x \neq -2&\\-4 \:\:\:\:\:\:\;\;\text{ if }x = -2\end{matrix}\right.\end{aligned}[/tex]

Now, let us find the value of f(-4) :

for x = -4 the function f(x) is (-1/2)x -2, substituting x = -4 in place x :

f(x) =  (-1/2)x - 2

f(-4) = (-1/2)*(-4) - 2  

f(-4) = 2 - 2

f(-4)  = 0

similarly, for f(-2) :

for x = -2 the function f(x) is -4 only that is :

f(-2) = -4

For, let us find the value of f(3) :

for x = 3 the function f(x) is (-1/2)x -2, substituting x = 3 in place x :

f(x) =  (-1/2)x - 2

f(3) = (-1/2)*(3) - 2  

f(3) = -3/2 - 2

f(3)  = - 3.5

Therefore, the values of  f(−4), f(−2), and f(3) are 0, -4, and -3.5 respectively.

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Answer: electronics worth $1,650

1500 (1+5%)^2 = $1653.75

3.75 dollars will be left over.

Step-by-step explanation:

The original price of a ticket is a  $56.95.

According to the statement

We have to find that the linear equation.

So, For this purpose, we know that the

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.

From the given information:

An amusement park offers a ticket for $12.95 off the original price p.

Then

Discounted price is that the amount of sum that extracted from the initial price when buyers receive some style of leverage from the vendor. during this case, discounted price of the ticket is $44 which was $12.95 but the initial price.

Then the first price would be:

$44 + $12.95 = $56.95

So, The original price of a ticket is a  $56.95.

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Answer:

arccos(51/100)

Step-by-step explanation:

By the Law of Cosines,

[tex]a^2 = b^2 + c^2 - 2bc \cos A \\ \\ a^2 - b^2 - c^2=-2bc \cos A \\ \\ \cos A=\frac{b^2 + c^2 - a^2}{2bc} \\ \\ m\angle A=\arccos \left(\frac{b^2 + c^2 - a^2}{2bc} \right) \\ \\ =\arccos \left(\frac{10^2 + 5^2 - 8^2}{2(5)(10)} \right) \\ \\ =\arccos(51/100)[/tex]

Answer:

10000

Step-by-step explanation:

Answer:

a = 9

Step-by-step explanation:

Step 1: Add 3 to both sides

2a – 3 = 15

2a – 3 + 3 = 15 + 3

Step 2: Simplify

add the numbers ( 2a = 18 )

Step 3: Divide both sides by the same factor

2a = 18

2a 18

––– = –––

2 2

Step 4: Simplify

l

Cancel the terms that are in both the numerator and the denominator

l

l

Divide the numbers

l

a = 9

Answer: a = 9

Answer:

B store is cheaper since 790.56<823

B price<A price

Step-by-step explanation:

A:

549(0.5)=274

264+549=823

Josh need to pay the refrigerator for $823 in this store without tax.

B:

549(0.6)= 329.4

329.4+549=878.4

878.4(09)=790.56

Josh need to pay $790.56 in this store without the tax.

C:

B, department store is cheaper so he could pay less

Expression as a single logarithm of 5 log₇2-2 log₇y is Log (2x/3y).

Log a + Log b = Log ab

Log a - Log b = Log (a/b)

so starting with the bracket, we have;

Log 2 + Log X - Log 3y

Furthermore, we have;

Log 2x - Log 3y

Finally, we have;

Log (2x/3y)

The inverse of an exponential function, the natural log is the logarithm to the base of the number e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues.

The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).

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Answer: 9/9^4 in Simplest form is 1 / 729

Answer:

2/375

Step-by-step explanation:

We can multiply 8/15 by 1/100 to get

[tex]\frac{8}{15} *\frac{1}{100}=\frac{8}{1500}[/tex]

Now we simplify this fraction into simplest form.

2/375

The equation which models the number of calculators packed by the machine in certain minutes is x = 2.5y

No. of calculators packed after 10 minutes = 25 calculators

No. of calculators packed after 30 minutes = 75 calculators

Using the unitary method for finding calculators packed in a minute,

10 minutes = 25 calculators

1 min = 25/10 = 2.5 calculators

Let x be the number of minutes the machine is running

Let y be the number of calculators packed

Formulation of the equation we get:

x = 2.5y

Hence, the equation which gives the number of calculators packed after certain minutes is given by: x = 2.5y

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The inverse of the fuction y=2x³+10 is y = [tex]\sqrt[3]{\frac{x-10}{2} }[/tex].

So,

All we have to do to find the inverse of an equation is switch the variables x and y.

Now, solve for y as follows:

Therefore,  the inverse of the fuction y=2x³+10 is y = [tex]\sqrt[3]{\frac{x-10}{2} }[/tex].

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The number that should fill in the blank is 10. Therefore, the complete equation is 0.05 × x = 0.5.

Given that, 0.05 × ----- = 0.5.

To multiply decimals, first, multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor. Finally, put the same number of digits behind the decimal in the product.

Let the number should fill in the blank be x.

So, 0.05 × x = 0.5

⇒ x = 0.5/0.05

⇒ x = 10

The number that should fill in the blank is 10. Therefore, the complete equation is 0.05 × x = 0.5.

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The value of x for the equation log₈2=x is 0.333

Logarithmic function properties. You have encountered several characteristics during your study of algebra, including the commutative, associative, and distributive properties. These characteristics make it easier to simplify a complex statement or equation. With logarithms, the same holds true.

Given,

log₈2=x

It can be expressed in the form -

2 = 8ˣ

2 =  2³ˣ

As base is same -

1 = 3x

x = 1/3

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Answer:

1 1/2+4/5 and the vertical would be graphed?

The total walking distance of the week is 12.1 km.

So, let the total walking distance be 'x'.

Then,

Therefore, the total distance of walking in the week is 12.1 km.

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Answer:

17x and 3x

Step-by-step explanation:

like terms are terms that have the same variables and powers. The coefficients do not need to match. Unlike terms are two or more terms that are not like terms, i.e. they do not have the same variables or powers. The order of the variables does not matter unless there is a power.

Triangle ABC with coordinates A (2, 4),

B (3, 6), and C (5, 1) is translated

4 units horizontally is (6,4), (7,6) ,( 1,9)

A triangle is a basic polygon with three sides and three internal angles. It is one of the fundamental shapes in geometry in which the three vertices are connected together, and it is represented by the symbol. Triangles are categorized into many sorts based on their sides and angles. All geometrical shapes have unique qualities relating to sides and angles that aid in their identification. The following are some of the most important qualities of a triangle.

There are three sides, three vertices, and three internal angles in a triangle.

The angle sum property of a triangle asserts that the sum of a triangle's three internal angles is always 180°. Consider the triangle PQR shown above .

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Answer:

A) y =  2.91x + 64.61 with x hours after 6:00 am

B) at 2:00pm, temperature is 87.89°

Step-by-step explanation:

(>>Regression Equation y = bx + a )With b- Sum of products/Sum of Square = sq/SSx. a = My- bMx,)

set 6.00 am is an original time, when x = 0

use the unit: hour to get a new table

X time 0, 0.75, 1.5, 2.5, 3, 3.75, 4.5, 5

Y temp 65°, 67", 68° ,72° ,74", 75° ,77° ,78°

a). with temperature y and x hour after 6:00 am,

can get Sum of x = 21 Mx = 2.63

Sum of - 578 My = 72.25

SSx = Sum of (X-Mx)² = 22.25

= sum of (X-Mx)(}-My)= 64.75

So b= sq/SSx =64.75/22.25 = 2.91

a= My- bMx = 72.25 - 291 x 2.63 = 64.61

So regressing equation Y= 2.91x + 64.61

b). at 02:00 pm , means 8 hours after 6:00 am

meaning X-8, )= 2.91×8 + 64.61 = 87.8)

The required equation of regression is y = 2.91x + 64.6 and at 2.00 pm temperature is 87.8°

Given that,
The table shows the recorded temperature on a certain day starting at 6:00 am.

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

Here,
The standard form of the regression equation,
y = bx + a,
where b = sum of product/sum of squares a = My - bMx
Since
b = 2.91 , My = 72.25, Mx = 2.63
a = 72.25 - 2.91 * 2.63
a = 64.6
The required regression equation is,
y = 2.91x + 64.6

B)
For 2.00 PM, x = 8
Now,
y = 2.91 * 8 + 64.6
y = 87.8°

Thus, the required equation of regression is y = 2.91x + 64.6 and at 2.00 pm temperature is 87.8°

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Sides of Quadrilateral A is 6, 9, 9 and 12.

It is given that Quadrilateral B is a scaled copy of Quadrilateral A,

and have shortest side = 2

To find the length of sides of quadrilateral, first we will find the ratio of the shortest side of quadrilateral A to that of quadrilateral B as shown below :

B : A = 2 : 6 = 1 : 3

This shows that the quadrilateral B is 3 times smaller than A.

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Answer:

  0

Step-by-step explanation:

You want the sum of numerator and denominator such that their difference is 2 and the reciprocal is equal to the original fraction.

We want a fraction such that ...

  x/y = y/x

  y = x +2

Substituting for y, we have ...

  x/(x +2) = (x +2)/x

  x^2 = x^2 +4x +4 . . . . . cross multiply

  0 = 4(x +1) . . . . subtract x^2, factor

  x = -1 . . . . . . . . the value of x that satisfies the equation

Then the denominator is ...

  y = x +2 = (-1) +2 = 1

The sum is ...

  x +y = (-1) +1 = 0

The sum of numerator and denominator is zero (0).

The expression is equivalent to quantity y raised to the negative third power times z raised to the fifth power end quantity over quantity z raised to the negative fourth power times y raised to the sixth power end quantity all raised to the negative second power is  [tex]z^{-18}.y^{18}[/tex] .

The given expression is [tex](\frac{y^{-3}.z^5}{z^{-4.y^6}} )^{-2}[/tex]

Let us take the numerator terms to denominator.

When shifting numerator terms to denominator the sign of the power will be changed.

[tex](\frac{1}{z^{-4.y^6.y^{3}.z^{-5}}} )^{-2}[/tex]

Combine like terms in denominator:

[tex](\frac{1}{z^{-9}.y^9} )^{-2}[/tex]

[tex](z^9.y^{-9})^{-2}[/tex]

[tex]z^{-18}.y^{18}[/tex]

Hence, [tex]z^{-18}.y^{18}[/tex]  is equivalent to quantity y raised to the negative third power times z raised to the fifth power end quantity over quantity z raised to the negative fourth power times y raised to the sixth power end quantity all raised to the negative second power.

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