What positive value of b makes 9 x²-b x+4 a perfect square trinomial?

The function rule g(x) after the given transformations of the graph of f(x)= 3x is g(x) = 1/9x

Transformation techniques -

The act of shifting an object's location on the xy plane is referred to as transformation.

Given the parent function

f(x) = -3x

If the function is not reflected over x-axis, the resulting function will be f(x) =  3x

If the resulting function is compressed by a factors of 1/8, hence the final function rule will be;

g(x) = 1/9( 3x)

g(x) = 1/9x

Hence the function rule g(x) after the given transformations of the graph of f(x)=3x is g(x) = 1/9x.

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The value of the expression log₄2 is 1/2.

The logarithmic function is the inverse of the exponential function. This means that the logarithm of a given number, say x, is the exponent to which another fixed number that is the base b, must be raised, so as to produce that number x.

Log a to the base b can be written as- log a/ log b.

Moreover, log [tex]a^{k}[/tex] = k log a, for all non negative values of a

Here, we are given a logarithmic expression- log₄2

We can expand this as-

log₄2 = log 2/ log 4

= log 2/ log [tex]2^{2}[/tex]

= log 2/ 2 log 2

= 1/2

Thus, the value of log₄2 is 1/2.

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Answer:

x = 0.5, −0.5 i think

Step-by-step explanation:

bc 0.5 x 0.5 is 0.25 and in multiplication 2 negs equal a positive

Based on the diameter of the pie, and the cost of the apple pie, the approximate cost per square inch of the apple pie is $0.32

First, find the area of the apple pie sold by the bakery because this will be needed to find the approximate cost per square inch.

Area of the pie will be the area of a circle:

= π x radius x radius

Radius is:

= 6 / 2

= 3 inches

The area of the apple pie is:

= π x 3 x 3

= 28.29 inch²

The approximate cost per square inch is:

= 9.15 / 28.29

= $0.32

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Answer: the answer is C $0.32

Step-by-step explanation:

This answer is proving the other person's answer correct

I got the questions on this test correct so I know the answer

Here is photo proof that it is correct

You can trust me because I always try my best to provide the correct answers on these tests. Have a good day FLVS students :)

Answer:

0.926

Step-by-step explanation:

Simplify exponents

[tex](3^2*3^{-5})/5^{-2}\\(3^2*0.004)/5^{-2}\\(9*0.004)/5^{-2}\\(0.037)/5^{-2}\\0.037/0.04\\= 0.926[/tex]

1. The domain of the function in interval g(x) = 13x-15/x+4

Domain: (−∞,0)∪(0,∞),{x|x≠0

Range: (−∞,∞),{y|y∈R}

2. The domain of the function in interval y=x2-10x+2

Domain: (−∞,∞) {x|x∈R}

Range: (−23,∞),{y|y≥-23}

3. By rearranging the equation so that C is in terms of F, you may determine the inverse:

F= 5/9C+32

32 is deducted from both sides.

F−32= 5/9C

Add five to both sides:

5(F−32)=9C

multiply both sides by 9.

C= 5/9(F−32)

C=− 25​/9

−2.78C o 2.dp

The inverse is, in fact, a one-to-one function.

4. We are looking for the height at t=0 in order to determine the beginning height. To do this, replace t with 0 and find h.

h(t)= -16t2 + 32t + 24

h(0) = -16(0)2 + 32(0) + 24

h(0) = 24

24 feet is the initial height

The constant in the equation often represents height. 24 in this instance.

The coefficient of x, in this case 32, represents the beginning velocity.

32 feet per second is the beginning velocity.

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Answer:

whether the transaction

is a purchase or sale. Write a formula for the advisor's

commission. Let D represent the value of one transaction.

Give two examples of how this financial advisor could earn a

commision of $1000

Step-by-step explanation:

Answer:

none

Step-by-step explanation:

The value of y is equal to 18.

In this problem we have a geometric system generated by two lines intersecting each other and generating two pairs of angles supplementary to each other. The system of linear equations representing the situation is presented below:

(8 · y - 13) + (3 · x + 4) = 180

3 · x + 8 · y = 189                                 (1)

(10 · x - 19) + (3 · x + 4) = 180

13 · x = 195                                           (2)

The solution to this system is (x, y) = (15, 18). The value of y is equal to 18.

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Answer:

the ratio of distance descended over time

Step-by-step explanation:

It's  a simple linear (first degree) equation in ' a '.

It has no solution.

Answer:

Step-by-step explanation: 4=3a-14 then you add 14 to both sides and to isolate 3a should it look like this 18=3a then you divide 3 and to isolate "a" and you should 6=a

hope this helped :D

Answer:

a = 6

Step-by-step explanation:

Switch the sides

[tex]4=3a-14\\= 3a-14=4[/tex]

Group(right side)

[tex]3a-14=4\\3a-14+14=4+14[/tex]

Simplify arithmetic

[tex]3a=4+14\\3a=18[/tex]

Isolate "a"

[tex]3a=18\\\frac{3a}{3}=\frac{18}{3}[/tex]

Simplify this improper fraction by splitting it into its least common multiples

[tex]a=\frac{6 \times 3}{1 \times 3}[/tex]

Factor(Cancel GCF)

[tex]a = 6[/tex]

Concerns, let me know, otherwise, have a great day!

Answer:

Step-by-step explanation:

Question 1:

0.42 repeating is rational. A rational number is any integer, fraction, terminating decimal, or repeating decimal.

11/3 = rational. A rational number is any integer, fraction, terminating decimal, or repeating decimal.

6.25 is a rational number. A rational number is any integer, fraction, terminating decimal, or repeating decimal.

16[tex]\pi[/tex] = irrational irrational number, any real number that cannot be expressed as the quotient of two integers.

0.01045 is rational. A rational number is any integer, fraction, terminating decimal, or repeating decimal.

[tex]\sqrt{\frac{3}{16} }[/tex] = Irrational number because it cannot be expressed as a fraction of two whole numbers and it has no accurate decimal equivalent.

[tex]\sqrt{48}[/tex] = The square root of 48 is not a rational number, as it cannot be expressed in the p/q form.

[tex]\sqrt{\frac{16}{81} }[/tex] = rational. The square root of (16/81) is the same as the square root of 16 divided by the square root of 81. You can divide the fraction inside the radical before or after you calculate the square root. The result will be the same.Here we first calculate the square root of the numerator and the square root of the denominator separately, and then we divide the two:  √16   √81  =    4   9  ≈  0.4444 Alternatively, we first divide 16 by 81 and then do the square root of the quotient:√16/81 ≈ √0.1975 ≈ 0.4444

Question 2:

[tex]\frac{\sqrt{6} }{\sqrt{5} }[/tex] = irrational. Irrational number because it cannot be expressed as a fraction of two whole numbers and it has no accurate decimal equivalent.

[tex]\frac{\sqrt{6} }{5}[/tex] = irrational number because it cannot be expressed as a fraction of two whole numbers and it has no accurate decimal equivalent.

[tex]\sqrt{30}[/tex] = the square root of 30 is not a rational number. It is an irrational number, as it cannot be expressed in the form of p/q.

[tex]\frac{\sqrt{5} }{6}[/tex] = irrational number, as it cannot be expressed in the form of p/q.

[tex]\frac{\sqrt{30} }{5}[/tex] = irrational since there is no exact square root for 30 and 5.

Question 3:

[tex]\sqrt{68}[/tex] = 68 is not an exact square root so it is about 8.24621125124….. about 8.25 or 8.3 or just 8.

[tex]\sqrt{45}[/tex] x [tex]\sqrt{96}[/tex] = 12[tex]\sqrt{30}[/tex]

Answer: $44.02

Step-by-step explanation: 180 - 135.98  =

44.02

The customer will pay 27% of the original price

The discounts are given as:

70% and 10%

This means that

Selling price = (1 - 0.7) * (1 - 0.1) * original price

Evaluate the differences

Selling price = (0.3) * (0.9) * original price

Evaluate the products

Selling price = 0.27 * original price

Express as percentage

Selling price = 27% * original price

Hence, the customer will pay 27% of the original price

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3.62 years

Or

3 years

7 Months

12 days

9 hours

18 minutes

40 seconds

Answer:

x = 6

Step-by-step explanation:

Subtract, simplify, subtract

[tex]2x+36-36=8x-36\\2x=8x-36\\2x-8x=8x-36-8x\\[/tex]

Simplify

[tex]-6x=-36[/tex]

Divide

[tex]\frac{-6x}{-6}=\frac{-36}{-6}[/tex]

Reverse the equation by the fraction rule

[tex]\rightarrow \frac{6x}{6}\\= x\\\rightarrow \frac{36}{6}\\= 6\\6 = x\\\uparrow\downarrow\\x = 6[/tex]

The Volume of the cone with base radius 5cm and Total Surface Area 907cm² is   1374.5cm³.

The Volume of the cone is denoted by

V = (1/3)*π*r²*h

where r = base radius

h = height of the cone

In the given question

the base radius r = 5cm

the total surface area of the cone = 907cm²

Total Surface Area of the cone is denoted by = πr(L+r)

where L is the slant height .

Step1: we first calculate Slant height "L"

Substituting the values in Total Surface Area formula we get

907 = π*5(L+5)

Simplifying further we get

L+5 = 907/5π

L = 907/5π - 5

L = 57.77 - 5

L = 52.77

Step2: Use L to find the height of cone

Using Pythagoras Theorem

L²=r²+h²

(52.77)² = (5)² + h²

Simplifying further we get

2784.67 = 25 +  h²

h² = 2759.67

h = √2759.67

h = 52.53

Step 3: use h to find the Volume

Substituting the value of h and r in Volume formula we get  ,

V = (1/3)*π*5²*52.53

= (1/3)*(3.14)*25*52.53

= 4123.605 / 3

= 1374.535

≅1374.5

Therefore , the volume of the cone is 1374.5cm³.

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Answer: 0.000000000115

Step-by-step explanation: 1.15e-10 = 1.15x10^-10

The perimeter of the shape is => 50cm.

Here, we have,

given that,

from the given diagram, we get,

there are two rectangles.

we get,

perimeter of one rectangle is:

2( 3+ 7) cm

=20 cm

perimeter of the other rectangle is:

2(4+11)

= 30cm

so, total perimeter = (20+30) =50cm

Hence, the perimeter of the shape is => 50cm.

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The cost of each bag of gummy bears= $1

Let,s take the cost of a bag of gummy bears to be x and the cost of each chocolate bar to be y.

So from the given question, we get out the first equation as

7 x + 3 y = $22 ------(1)

and the second equation is

3 x + 1 y = $ 8 -------(2)

We have to find the value of x and y by which we will get to know about the cost of each bag of gummy bears and chocolate bar respectively.

Now we have to multiply the second equation with 3

(3 x + 1 y = $8 ) *

we will get :

9 x + 3 y = $ 24 -------( 3)

After equating equations (1 ) and (3)

we get

7 x + 3y = $22-------(1)

9x + 3 y= $24-------(3)

By subtracting of the equation (1) and (3) we get

-2 x = - $2

i.e., x = $1

Now to get the value of y we can put the value of x in any of the above- given equation

Let us put it on equation number (2)

3x + 1 y = $8

= 3 * 1 + y = $ 8

= 3 + y = $ 8

=y = $5

From this, we get the value of x = $1 and y = $ 5 which are the value of gummy bear and chocolate bar

We have to find the value of each gummy bar which is $1

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The exponential form of the given equation is 0.0001 = [tex]10^{-4}[/tex]

The exponential function is the inverse of the logarithmic function and vice versa. This means that the logarithm of a given number, say x, is the exponent to which another fixed number that is the base b, must be raised, so as to produce that number x. Mathematically this means,

logₐ x = y

then x = [tex]a^{y}[/tex]

Here, we are given a  logarithmic function- log 0.0001 = -4

since no base is given, we always assume it to be 10

thus, the function can be written as- 0.0001 = [tex]10^{-4}[/tex]

Hence, the exponential form of this equation is 0.0001 = [tex]10^{-4}[/tex].

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The postulate is which illustrated the above expression is the multiplication identity.

As we  are the given expression for the real numbers 5 . 1  =5, Jere the ". " depicts the multiplication symbol,  and the here 1 is called the identity  element. According to the postulate, it is said that the  identity element which is the 1 in the group of rational numbers,  when multiplied  with any real number in a given mathematical system leaves the result of the product unchanged.

Such as  4 . 1=4

              7 . 1 =7

              12 . 1= 12

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Answer:

x = 22

Step-by-step explanation:

14,040 - 50x = 12,500 + 20x

14,040 - 12,500 = 20x + 50x

1540 = 70x

x = 22

Answer: She forgot to add there signs

Step-by-step explanation:

Since both numbers are negative, you have to add their absolute values and then add their signs so its -9

Answer:

Step-by-step explanation:

She forgot to keep the same sign as the numbers being added (SAK) same , add , keep

The product of 4.5 x 1012  and  5.12 x 109 written in scientific notation is 23.04 x 110308

It is given that,

Two numbers are 4.5 x 1012 and  5.12 x 109

Using scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation. For instance, 650,000,000 can be represented as 6.5 X 10^8 in scientific notation.

We need to find the product of both numbers and then find the final answer in scientific notation form

(4.5 x 1012) x ( 5.12 x 109 )

(4.5 x 5.12) x ( 1012 x 109)

23.04 x 110308

Hence, the product of 4.5 x 1012  and  5.12 x 109 written in scientific notation is 23.04 x 110308

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A function which can be used to determine the velocity V(L(p)) at the bottom of the pendulum released from the same angle for any period, p is V(L(p)) = p/2π√192.08.

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable to an output variable.

Given the following data:

L(p) = 9.8(p/2π)².

V(L) = √19.6L

A function which can be used to determine the velocity V(L(p)) at the bottom of the pendulum released from the same angle for any period, p is given by:

V(L(p)) = √[19.6 × 9.8(p/2π)²]

V(L(p)) = √(19.6 × 9.8) × √(p/2π)²)

V(L(p)) = 192.08 × (p/2π)

V(L(p)) = p/2π√192.08

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Answer:

its B V(L(p)) = p/2π√192.08

Step-by-step explanation:

Answer:

Monomial

Step-by-step explanation:

This is a monomial because there is only one term.

Monomial = one term.

Binomial = two terms

Trinomial = three terms

Hope this helps!

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The number of possible ways to create the flag with 6 colors in total and 3 colors to be used in the flag is 30 ways.

We are given that:

Total colors in a palette = 6 colors.

Colors to be used in making of the flag = 3 colors.

So, by using the permutations, we get that:

Number of possible ways to create the flag = 6 × 5 ways.

Number of possible ways to create the flag = 30 ways.

Therefore, we get that, the number of possible ways to create the flag with 6 colors in total and 3 colors to be used in the flag is 30 ways.

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Answer:

8 would come on the 3rd notch past 5( is behind 10 2 notches.

1 would come one notch after 0.

-3 would come 3 notches befor 0 and 2 notches after -5.

Step-by-step explanation:

Hope it helps! =D