(03.06 LC)
The functions f(x) = (x+4)2+2 and g(x) = (x - 2)2-2 have been rewritten using the completing the
square method. Is the vertex for each function a minimum or a maximum? Explain your reasoning for
each function (10 points)
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Answer:

cos60° = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Using the trigonometric identity

sin²x + cos²x = 1 ⇒ cos x = [tex]\sqrt{1-sin^2x}[/tex]

Given

sin60° = [tex]\frac{\sqrt{3} }{2}[/tex], then

cos60° = [tex]\sqrt{1-(\frac{\sqrt{3} }{2})^2 }[/tex] = [tex]\sqrt{1-\frac{3}{4} }[/tex] = [tex]\sqrt{\frac{1}{4} }[/tex] = [tex]\frac{1}{2}[/tex]

Final answer:

The cosine of 60 degrees is 1/2.

Explanation:

To find cos 60 degrees, we can use the trigonometric identity: cos² 0 = 1 - sin² 0. Since sin 60 degrees = √3/2, we can substitute this value into the equation:

cos² 60 degrees = 1 - (√3/2)²

cos² 60 degrees = 1 - (3/4)

cos² 60 degrees = 1/4

cos 60 degrees = ±√(1/4)

cos 60 degrees = ±1/2

However, since 60 degrees is in the first quadrant, cos 60 degrees is positive:

cos 60 degrees = 1/2

Answer:

The answer is 25/31 because it equals 56

Final answer:

The smaller number is 25 and the larger number is 31, obtained by setting up an equation with x for the smaller number and x + 6 for the larger one, to represent the described relationship.

Explanation:

To solve the problem, let's denote the smaller number as x and the larger number as x + 6, because the problem states that the larger number is 6 more than the smaller number. The sum of the two numbers is given as 56, so we can set up the following equation:

x + (x + 6) = 56

This simplifies to:

2x + 6 = 56

Subtract 6 from both sides to get:

2x = 50

Now, divide both sides by 2 to find x:

x = 25

Since x is the smaller number, the larger number would be x + 6. Plugging in the value of x, we get:

Larger number = 25 + 6 = 31

Therefore, the smaller number is 25 and the larger number is 31.

Answer:

Length = 25 inches and width = 15 inches.

Step-by-step explanation:

Let us assume that the length of the rectangle is L inches and the width of the rectangle is W inches.

Now, the area of the rectangle is A = LW = 375 sq. inches ........... (1)

Now, given that the length to width ratio of the rectangle is 5 : 3.

Let L = 5x and W = 3x, then from equation (1) we get,

(5x)(3x) = 375

⇒ 15x² = 375

⇒ x² = 25

⇒ x = 5 {Neglecting the negative root, as length can not be negative}

Now, Length = L = 5x = 25 inches and Width = W = 3x = 15 inches. (Answer)

Answer:

Part 1) [tex]x=\frac{g}{c}[/tex]

Part 2) [tex]a=\frac{1}{3b}[/tex]

Part 3) [tex]a=\frac{n+p}{m}[/tex]

Part 4) [tex]x=g-y+c[/tex]

Part 5) [tex]x=\frac{z}{m-1}[/tex]

Part 6) [tex]a=\frac{g+b}{c}[/tex]

Part 7) [tex]b=\frac{A}{h}[/tex]

Part 8) [tex]W=\frac{P}{2}-L[/tex]

Part 9) [tex]d=2Q-c[/tex]

Part 10) [tex]a=\frac{Q}{3+5c}[/tex]

Part 11) [tex]N=\frac{A)}{P-IR}[/tex]

Part 12) [tex]b=P-a-c[/tex]

Step-by-step explanation:      

Part 1) we have

[tex]g=xc[/tex]

solve for x

That means---> Isolate the variable x

Divide by c both sides

[tex]\frac{g}{c}=\frac{xc}{c}[/tex]

simplify

[tex]x=\frac{g}{c}[/tex]

Part 2) we have

[tex]12ab=4[/tex]

solve for a

That means---> Isolate the variable a

Divide by 12b both sides

[tex]\frac{12ab}{12b}=\frac{4}{12b}[/tex]

simplify

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

Part 3) we have

[tex]am=n+p[/tex]

solve for a

That means---> Isolate the variable a

Divide by m both sides

[tex]\frac{am}{m}=\frac{n+p}{m}[/tex]

simplify

[tex]a=\frac{n+p}{m}[/tex]

Part 4) we have

[tex]g=x-c+y[/tex]

solve for x

That means---> Isolate the variable x

Subtract y both sides

[tex]g-y=x-c+y-y[/tex]

[tex]g-y=x-c[/tex]

Adds c both sides

[tex]g-y+c=x-c+c[/tex]

[tex]g-y+c=x[/tex]

rewrite

[tex]x=g-y+c[/tex]

Part 5) we have

[tex]xm=x+z[/tex]

solve for x

That means---> Isolate the variable x

Subtract x both sides

[tex]xm-x=x+z-x[/tex]

[tex]xm-x=z[/tex]

Factor x left side

[tex]x(m-1)=z[/tex]

Divide by (m-1) both sides

[tex]\frac{x(m-1)}{m-1}=\frac{z}{m-1}[/tex]

[tex]x=\frac{z}{m-1}[/tex]

Part 6) we have

[tex]g=ca-b[/tex]

solve for a

That means---> Isolate the variable a

Adds b both sides

[tex]g+b=ca-b+b[/tex]

[tex]g+b=ca[/tex]

Divide by c both sides

[tex]\frac{g+b}{c}=\frac{ca}{c}[/tex]

[tex]a=\frac{g+b}{c}[/tex]

Part 7) we have

[tex]A=bh[/tex]

solve for b

That means---> Isolate the variable b

Divide by h both sides

[tex]\frac{A}{h}=\frac{bh}{h}[/tex]

simplify

[tex]b=\frac{A}{h}[/tex]

Part 8) we have

[tex]P=2L+2W[/tex]

solve for W

That means---> Isolate the variable W

Subtract 2L both sides

[tex]P-2L=2L+2W-2L[/tex]

simplify

[tex]P-2L=2W[/tex]

Divide by 2 both sides

[tex]\frac{P-2L}{2}=\frac{2W}{2}[/tex]

simplify

[tex]W=\frac{P-2L}{2}[/tex]

[tex]W=\frac{P}{2}-L[/tex]

Part 9) we have

[tex]Q=\frac{c+d}{2}[/tex]

solve for d

That means---> Isolate the variable d

Multiply by 2  both sides

[tex]2Q=(2)\frac{c+d}{2}[/tex]

simplify

[tex]2Q=c+d[/tex]

subtract c both sides

[tex]2Q-c=c+d-c[/tex]

[tex]2Q-c=d[/tex]

rewrite

[tex]d=2Q-c[/tex]

Part 10) we have

[tex]Q=3a+5ac[/tex]

solve for a

That means---> Isolate the variable a

Factor the variable a in the right side

[tex]Q=a(3+5c)[/tex]

Divide by (3+5c) both sides

[tex]\frac{Q}{3+5c}=\frac{a(3+5c)}{3+5c}[/tex]

simplify

[tex]a=\frac{Q}{3+5c}[/tex]

Part 11) we have

[tex]I=\frac{PN}{RN+A}[/tex]

solve for N

That means---> Isolate the variable N

Multiply in cross

[tex]I(RN+A)=PN[/tex]

Apply distributive property left side

[tex]IRN+AI=PN[/tex]

subtract PN both sides

[tex]IRN+AI-PN=PN-PN[/tex]

[tex]IRN+AI-PN=0[/tex]

subtract AI both sides

[tex]IRN+AI-PN-AI=-AI[/tex]

[tex]IRN-PN=-AI[/tex]

Factor N left side

[tex]N(IR-P)=-AI[/tex]

Divide by (IR-P) both sides

[tex]\frac{N(IR-P)}{IR-P}=-\frac{A}{IR-P}[/tex]

simplify

[tex]N=-\frac{A}{IR-P}[/tex]

[tex]N=\frac{A}{P-IR}[/tex]

Part 12) we have

[tex]P=a+b+c[/tex]

solve for b

That means---> Isolate the variable b

subtract (a+c) both sides

[tex]P-(a+c)=a+b+c-(a+c)[/tex]

simplify

[tex]P-(a+c)=b[/tex]

rewrite

[tex]b=P-a-c[/tex]

For this case we have that by definition, the equation of the line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It is the slope of the line

b: It is the cut-off point with the y axis

We have two points through which the line passes:

[tex](x_ {1}, y_ {1}) :( 8,5)\\(x_ {2}, y_ {2}): (- 6,5)[/tex]

We found the slope:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {5-5} {- 6-8} = \frac {0} {- 14} = 0[/tex]

The slope is zero.

Thus, the equation is of the form:

[tex]y = b[/tex]

We substitute one of the points and find b:

[tex](x, y) :( 8,5)\\5 = b\\b = 5[/tex]

Finally, the equation is:

[tex]y = 5[/tex]

Answer:

[tex]y = 5[/tex]

Answer:

y=5

Step-by-step explanation:

Answer:

150=6x

Step-by-step explanation:

Let x = height of the tree.

Set up the ratio %28Height%29%2F%28Shadow%29+=5%2F6=x%2F30

Since a%2Fb=c%2Fd means ad=bc,

5%2F6=x%2F30 means 5%2A30=6%2Ax

150=6x

the answer is 173 square units

Answer: 84 un squared

Step-by-step explanation:

area of parallelogram = bh

area = 14 x 6 = 84 un squared

Answer:

She did not drive consistently because if 65 = 1 hour, the two-hour mark would be 130, not 120 and the second-hour mark would be 185, not 195. You have to have the same mileage added to each hour to make it consistent.

Answer:

The original fraction was less than 1/2. Since the result was a mixed number, the original fraction must have contained less than 1 unit of 1/2.

Step-by-step explanation:

The fraction will be less than 1/2. An example will be 1/2 divided by 1/3. You'll need to do 1/2 x 3/1, which will result in 3/2, or 1 1/2.

The original fraction was greater than 1/2. Dividing by 1/2 is the same as doubling, so for the result to be a mixed number, the original fraction must have exceeded 1/2.

The original fraction was greater than 1/2. Since the result was a mixed number, the original fraction must have contained more than 1 unit of 1/2.

This is because when you divide a fraction by 1/2, you are essentially doubling that fraction. If the original fraction were less than or equal to 1/2, doubling it would still result in a fraction that is less than or equal to 1 (not a mixed number). Therefore, in order for the result to be a mixed number, the original fraction must have been more than 1/2. For example, if the original fraction was 3/4 (which is greater than 1/2), when divided by 1/2, the result would be 1 1/2, a mixed number.

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Answer:

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.

Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42.

Step-by-step explanation:

Answer:

6,3,2,1

Step-by-step explanation:

the factors of 36 are 36, 18, 12, 9, 6, 4, 3, 2, 1

The factors of 42 are 42, 21, 14, 7, 6, 3, 2, 1

The factors that they have in common are therefore 6,3,2, and 1 when compared

Answer:

1.25 miles/hr

Step-by-step explanation:

5miles in 4 hours, this means  5miles/ 4hrs

To find the rate per hour:

5/4 = 1.25 miles/hr

Hope this helps!

Please mark brainliest if you think I helped! Would really appreciate!

Answer:

5/4

Step-by-step explanation:

Divide the miles by the hours. It gives you the ratio.

RootIndex 12 StartRoot 8 EndRoot Superscript x

12th root of 8^x = (12th root of 8)^x

[tex]\sqrt[12]{8^{x}} = \left(\sqrt[12]{8}\right)^{x}[/tex]

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

Explanation:

The general rule is

[tex]\sqrt[n]{x} = x^{1/n}[/tex]

so any nth root is the same as having a fractional exponent 1/n.

Using that rule we can say the cube root of 8 is equivalent to 8^(1/3)

[tex]\sqrt[3]{8} = 8^{1/3}[/tex]

-----

Raising this to the power of (1/4)x will have us multiply the exponents of 1/3 and (1/4)x like so

(1/3)*(1/4)x = (1/12)x

In other words,

[tex]\left(8^{1/3}\right)^{(1/4)x} = 8^{(1/3)*(1/4)x}[/tex]

[tex]\left(8^{1/3}\right)^{(1/4)x} = 8^{(1/12)x}[/tex]

-----

From here, we rewrite the fractional exponent 1/12 as a 12th root. which leads us to this

[tex]8^{(1/12)x} = \sqrt[12]{8^{x}} [/tex]

[tex]8^{(1/12)x} = \left(\sqrt[12]{8}\right)^{x} [/tex]

Answer:

C 8 x/3

Step-by-step explanation:

Answer:

$0.10x + $0.25y = $0.80

The equation in standard form that represents the situation is 10x + 25y = 80.

To represent the situation in terms of the number of dimes and quarters, we can use the equation 0.10x + 0.25y = 0.80. This equation states that the value of the dimes (0.10x) plus the value of the quarters (0.25y) equals $0.80. Rearranging the equation to standard form, we have:

0.10x + 0.25y = 0.80

10x + 25y = 80

So, the equation in standard form that represents the situation is 10x + 25y = 80.

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Answer:

$75.26

Step-by-step explanation:

base cost = $49.95

total mile cost = 1.19*18 =$21.42

gas cost = $3.89

total cost =$(49.95 +21.42+3.89)=$75.26

The expression to represent total cost of the trip is $49.95 + $1.19m + (m/18)($3.89).

Given that, the rental has a base cost of 49.95, plus an additional cost of 1.19 per mile driven.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

If we let m = total distance, then we can set up an equation to find the total cost.

The additional cost for distance would be $1.19m

The cost for gas would be (m/18)($3.89)

So the total cost of the trip could be represented by $49.95 + $1.19m + (m/18)($3.89).

Therefore, the expression to represent total cost of the trip is $49.95 + $1.19m + (m/18)($3.89).

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To find equivalent fractions, multiply the numerator and denominator of a given fraction by the same number to achieve the desired denominator. For example, 3/4 becomes 9/12 and 1/2 becomes 3/6 when transformed to have denominators of 12 and 3 respectively.

To solve the question of completing each equation so that it shows equivalent fractions, we will use the concept of multiplying the numerator and denominator of a fraction by the same number to find an equivalent.

For the fraction 3/4, to find its equivalent with a denominator of 12, we would multiply both the numerator and denominator by 3, because 4 times 3 equals 12. Thus, we get the equivalent fraction: 3/4 = 9/12.

To find an equivalent fraction for 1/2 with a denominator of 3, we multiply both the numerator and denominator by 3/6 because 2 times 3 equals 6. The equivalent fraction is 1/2 = 3/6.

If we need an equivalent for 2/1 with a denominator of 4, we multiply both the numerator and denominator by 4 because the common denominator we are aiming for is 4. The equivalent fraction is then 2/1 = 8/4.

Note that we always ensure the multiplication factor makes the denominators equal, since that is the requirement for fractions to be equivalent.

The equivalent fractions are:

1. [tex]\( \frac{1}{4} = \frac{3}{12} \)[/tex]

2. [tex]\( \frac{4}{5} = \frac{8}{10} \)[/tex]

3. [tex]\( \frac{1}{6} = \frac{2}{12} \)[/tex]

To complete each equation and show equivalent fractions, we need to find the missing numerator or denominator that, when filled in, will make the fractions equivalent.

1. [tex]\( \frac{1}{4} = \frac{3}{12} \)[/tex]

  Explanation: To find an equivalent fraction for [tex]\( \frac{1}{4} \)[/tex] with a denominator of 12, we notice that we can get from 4 to 12 by multiplying 4 by 3 (4 * 3 = 12). So, to make the fractions equivalent, we also multiply the numerator by 3 (1 * 3 = 3). This gives us [tex]\( \frac{3}{12} \)[/tex], which is equivalent to [tex]\( \frac{1}{4} \)[/tex].

2. [tex]\( \frac{4}{5} = \frac{8}{10} \)[/tex]

  Explanation: To find an equivalent fraction for [tex]\( \frac{4}{5} \)[/tex] with a denominator of 10, we notice that we can get from 5 to 10 by multiplying 5 by 2 (5 * 2 = 10). So, to make the fractions equivalent, we also multiply the numerator by 2 (4 * 2 = 8). This gives us [tex]\( \frac{8}{10} \)[/tex], which is equivalent to [tex]\( \frac{4}{5} \)[/tex].

3. [tex]\( \frac{1}{6} = \frac{2}{12} \)[/tex]

  Explanation: To find an equivalent fraction for [tex]\( \frac{1}{6} \)[/tex], we want the denominator to be 12. To do this, we notice that we can get from 6 to 12 by multiplying 6 by 2 (6 * 2 = 12). So, to make the fractions equivalent, we also multiply the numerator by 2 (1 * 2 = 2). This gives us [tex]\( \frac{2}{12} \)[/tex], which is equivalent to [tex]\( \frac{1}{6} \)[/tex].

The complete question is given below:

Complete each equation below so that it shows equivalent fractions.

1/4 = __/12

4/5 = __/10

1/6 = __/__

Answer:

5/2 is the scale factor.

Step-by-step explanation:

To calculate scale factor, divide the similar sides.

According to the problem, EFGH is the drawing, or the "result".

Divide a side of the result by the original.

EFGH / ABCD = scale factor

We can use the widths.

Width of EFGH / Width of ABCD

= 10 / 4

= 5/2

Check using the lengths:

Length of EFGH / Length of ABCD

= 20 / 8

= 5/2

The scale factor is 5/2.

Answer:

Step-by-step explanation:

Answer: 7

Step-by-step explanation:

3(n+3) = - (1 - 5n) – 4

3n+9=-1+5n-4

n=7

Answer:

n=7

Step-by-step explanation:

3(n+3)=-(1-5n)-4

3n+9=-1+5n-4

3n+9=-5+5n

3n+14=5n

14=2n

7=n

I used PEMDAS and moving numbers and combing like terms

Answer:

m = 0 or 5

Step-by-step explanation:

m² − 5m = 0

Factor out m:

m (m − 5) = 0

Set each term to 0:

m = 0

m − 5 = 0

Solve for m:

m = 0

m = 5

Final answer:

The point estimate for the proportion of homeowners in the given sample is 75%, calculated by dividing the number of homeowners (24) by the total number surveyed (32).

Explanation:

To obtain a point estimate of the proportion of homeowners from the given sample, we would calculate the proportion of those who did not rent, since owning and renting are the only two options provided. Out of 32 people, 8 said they rented, which means 32 - 8 = 24 owned their home. The point estimate for the proportion of homeowners is then given by the number of homeowners divided by the total number of people surveyed:

Point estimate for homeowners = (Number of homeowners) / (Total number surveyed) = 24 / 32 = 0.75 or 75%

This mean 75% of the surveyed individuals are estimated to be homeowners.

Answer:

2/5

Step-by-step explanation:

if one red ball was pulled that mean that now we have 2 red balls 2 green balls and 1 blue ball

and the sum of them is 5 and we have 2 . Soo it is 2/5

Answer:

False

True

Step-by-step explanation:

Initially, there were 50 bacteria. It is observed that the bacteria triple in population every 8 hours.

Therefore, the situation can be interpreted as  

[tex]f(x) = 50\times (3)^{\frac{x}{8} }[/tex] .......... (1)

where, f(x) represents the population of bacteria after x hours.

So, the model equation [tex]f(x) = 3 (50)^{\frac{x}{8}}[/tex] is false. (Answer)

Again, from the equation (1) we get, after 36 hours, the bacteria population will be given by [tex]f(36) = 50 \times (3)^{\frac{36}{8}} = 7014.8[/tex] ...... (2)

So, 7014.8 ≈ 7015 is the population of bacteria after 36 hours.  

Hence, this statement is true. (Answer)

Answer:

Annual rate of interest is 8%.

Answer:

The answer would be 3; 1.3

Answer:

Each box has 800 spoons.

Step-by-step explanation:

4800/6=800

The answer is -.75 because y=mx+b, and the slope is m.

Answer:

The two numbers are 12 , 10

Step-by-step explanation:

Given as :

The least common multiple of two numbers = LCM = 60

The ratio of the greater number to lesser number = 6 : 5

let the greater number = 6 x

And The smaller number = 5 x

∵ The LCM of numbers = 60

So, 6 × 5 × x = 60

Or,  30 × x = 60

∴  x = [tex]\frac{60}{30}[/tex]

I.e x = 2

So The greater number = 6 x = 6 × 2 = 12

And  The smaller number = 5 x = 5 × 2 = 10

Hence The two numbers are 12 , 10 Answer

Answer:

The answer is 300. Use an online calculator.

Step-by-step explanation:

Answer:300

Step-by-step explanation:

Write your equation down in long division format and the see how many times you can get 7 into 2,100 and then you put 300 at the top and that’s how you solve a perfect division equation.

Answer:

3

Step-by-step explanation:

11-8=3

3 saves were left out of the 11 for the second game

Answer:

He has made 3 saves in the second game

Step-by-step explanation: