I am a square. One of my sides is 9 feet long. what is my area?

Answer:

9°

Step-by-step explanation:

You can make use of any of the trigonometric ratios to determine N, or you can let your calculator tell you what it is by solving the triangle.

SOH CAH TOA reminds you that

... sin(N) = 13/85 . . . . N = arcsin(13/85)

... cos(N) = 84/85 . . . N = arccos(84/85)

... tan(N) = 13/84 . . . . N = arctan(13/84)

all will tell you N ≈ 8.79741° ≈ 9°

_____

If you use inverse functions on your calculator, be sure it is in degrees mode.

Answer:

2.3x + 1.23y = 23

Step-by-step explanation:

The bag of chips is x because it is getting multiplied by 2.3.

The candy is y because it is getting multiplied by 1.23.

The reason they equal 23 is to figure out the maximum amount of each snack you can get without going over the money limit.

Answer:

A

Step-by-step explanation:

First discount is the original price reduced by 35% prior to the annual clearance.

So, 35% of 1325 = 0.35 × 1325 = 463.75.

After the discount of $463.75, the price that remains =  1,325 -  463.75 = $861.25.

Then, additional disount of 10%.

10% of $1,325. = 0.10  × 1,325. = 132.50

The final price after discount of 10% = 861.25 - 132.50. =  728.75.

Round to the nearest cent, we get 728.75.

Therefore, you would pay $ 728.75 after applying the discounts.

Answer:

B. 775.13

Step-by-step explanation:

Edge says A was wrong.

Answer:

16 mm  

Step-by-step explanation:

Since ABC is an equilateral triangle, all three sides are the same length.  The perimeter is found by adding together all of these equal sides; letting x represent the length of a side of the triangle, this gives us

x + x + x = 96

Combining like terms,

3x = 96

Dividing both sides by 3,

3x/3 = 96/3

x = 32

Since AM is a perpendicular bisector, it splits BC into two congruent sections. This means the length of MC, half of BC, will be 32/2 = 16.

Option (B) is correct which is 24 mm

Step 1:

Find the length of each side.

Let the side be a,

3×a = 96mm

⇒ a = 96/3

⇒ a = 32 mm

Step 2:

Length of MC = length of BC/2      (As AM is a perpendicular bisector)

⇒ MC = 32/2 = 16 mm

Step 3:

Now, in the triangle, AMC, using Pythagoras theorem,

AC² = MC² + AM²

⇒ (32)² = MC² + (16)²

After solving,

⇒ MC = 16√3 = 27.77 mm

This is closest to option (B) which is 24 mm

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We can simply multiply the roots together to find the original function.

(x + 2)(x - 4)(x - 4)(x - 3)

FOIL.

x^2 - 4x + 2x - 8(x - 4)(x - 3)

Combine like terms.

x^2 - 2x - 8(x - 4)(x - 3)

FOIL.

x^3 - 2x^2 - 8x - 4x^2 + 8x + 32(x - 3)

Combine like terms.

x^3 - 6x^2 + 32(x - 3)

FOIL.

x^4 - 6x^3 + 32x - 3x^3 + 18x^2 - 96

Combine like terms.

A quartic polynomial function with roots at -2,4,4,and 3 can be written in standard form as f(x) = (x + 2) * (x - 4)^2 * (x - 3)

A quartic polynomial function is a function of the fourth degree. Its general form is f (x) = ax^4 + bx^3 + cx^2 + dx+ e, where a, b, c, d, and e are constants, and a ≠ 0. Given the roots or zeros of the function (-2,4,4,3), we can construct the quartic polynomial function.

The quartic polynomial with roots r1, r2, r3, r4 is represented by: f(x) = a(x - r1)(x - r2)(x - r3)(x - r4). The roots of your polynomial function are -2, 4, 4, and 3. So, we substitute those roots into the equation:

f(x) = a(x - (-2)) * (x - 4) * (x - 4) * (x - 3). We may choose the leading coefficient a to be 1 (a ≠ 0) for simplicity's sake. Thus, the quartic polynomial function in standard form with zeros -2,4,4, and 3 is:

f(x) = (x + 2) * (x - 4)^2 * (x - 3)

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Answer:

5

Step-by-step explanation:

So the triangle to the right is similar to the big triangle by SAS similarity with a ratio of 1:2. So (3x-5):20 is 1:2. So 3x-5=10 or 3x=15. So x=5.

Answer:

5

Step-by-step explanation:

good luck on the test babes <3

Answer:

Step-by-step explanation:

This development is ugly, but it works.

Let area ΔABC = 6a. Then area ΔAMC = 3a, and area ΔAPC = a. Similarly, area ΔBMC = 3a, and area ΔBPC = a.

Let area ΔCPQ = x. Then ...

... area ΔACQ = area ΔAPC + area ΔCPQ

... area ΔACQ = a + x

Define k such that BQ : CQ = k : 1. Then ...

... area ΔBPQ + area ΔCPQ = area ΔBPC

... kx + x = a = (k +1)x

The division of BC into parts of ratio k : 1 means ...

... area ΔABQ = k × area ΔACQ

... area ΔABQ + area ΔACQ = area ΔABC

... k × area ΔACQ + area ΔACQ = area ΔABC

... (k +1)(x +a) = 6a . . . . . . . area ΔACQ = x+a

... (k +1)x +(k +1)a = 6a . . . . . distributive property

... a + (k +1)a = 6a

... k +2 = 6 . . . . . . . . . . . . . . . divide by a, simplify

... k = 4

Now, we know BQ : CQ = 4 : 1, so ...

... BQ = 4/5 × 12 cm = 9.6 cm

... CQ = 1/5 × 12 cm = 2.4 cm

Answer:

10% of 650 visitors is:

650 visitors* (10/100)= 65 visitors.

650 visitors+ 65 visitors= 715 visitors.

There are 715 visitors on Saturday

Step-by-step explanation:

Ans7wer:

715 people

Step-by-step explanation:

650÷100=6.5

6.5X10=65

650+65=715

7.65%

There are 200 times $100 in $20,000, so the interest amount per $100 is ...

... $3,279/200 = $16.395 per hundred

In the row of the given table corresponding to 48 months, the smallest amount of interest listed is $23.48 per $100. The APR on the loan of concern is clearly less than 10.75%.

A financial calculator says the interest rate on a loan of $20,000 with 48 monthly payments of ($20,000 +3,279)/48 = $484.98 is about 7.65%.

Answer:

B) The maximum y-value of f(x) approaches 2

C) g(x) has the largest possible y-value

Step-by-step explanation:

f(x)=-5^x+2

f(x) is an exponential function.

Lim x→∞ f(x) = Lim x→∞ (-5^x+2) = -5^(∞)+2 = -∞+2→ Lim x→∞ f(x) = -∞

Lim x→ -∞ f(x) = Lim x→ -∞ (-5^x+2) = -5^(-∞)+2 = -1/5^∞+2 = -1/∞+2 = 0+2→

Lim x→ -∞ f(x) = 2

Then the maximun y-value of f(x) approaches 2

g(x)=-5x^2+2

g(x) is a quadratic function. The graph is a parabola

g(x)=ax^2+bx+c

a=-5<0, the parabola opens downward and has a maximum value at

x=-b/(2a)

b=0

c=2

x=-0/2(-5)

x=0/10

x=0

The maximum value is at x=0:

g(0)=-5(0)^2+2=-5(0)+2=0+2→g(0)=2

The maximum value of g(x) is 2

Answer:

x = −4 and x = 4

Step-by-step explanation:

4x² = 64

Lets get x² on its own. To do this we divide each sides by 4:

x² = 16

Now to get just x, we need to square root this answer:

√x² = √16

x = √16

x = 4

But this can be ±4 as it -4 and 4 squared both give 16.

So your answer is x = −4 and x = 4

Answer:

x = −4 and x = 4

Step-by-step explanation:

c on edg

A. 28

We assume m is the measure of the marked unknown angles: ∠BZY ≅ ∠BZA

(5x +3)° = (2x +18)°

Divide by ° and subtract 2x+3:

... 3x = 15

... x = 5

Then ∠BZA = (2·5 +18)° = m = 28°

-2

20 greater than 8x +5 is ...

... 8x +5 +20 = 8x +25

We want this value to be -3(2x +1), so we want to solve the equation ...

... 8x +25 = -3(2x +1)

... 8x +25 = -6x -3 . . . . . . eliminate parentheses

... 14x = -28 . . . . . . . . . . . add 6x-25

... x = -2 . . . . . . . . . . . . . . divide by the coefficient of x

The desired value of the variable is -2.

_____

Check

-3(2x+1) = -3(2(-2)+1) = -3(-3) = 9

8x+5 = 8(-2) +5 = -11

9 is 20 greater than -11, so the answer checks OK.

Answer:

X = -2

Step-by-step explanation:

Answer:

hundreds

Step-by-step explanation:

The quotient of 3216/8 is 402. 4 is the first digit, and is in the hundreds place.

Answer:

7. The sum of the measures of the interior angles of this polygon is 900°.

8. The sum of the measures of the interior angles of this polygon is 540°.

9. The polygon has 10 sides.

10. The polygon has 5 sides.

Step-by-step explanation:

7. Vertices: A, B, C, D, E, F and G

Number of vertices: n=7

Sum of the measures of the interior angles of the polygon: S=?

S=180°(n-2)

Substituting n by 7 in the formula above:

S=180°(7-2)

S=180°(5)

S=900°

8. Vertices: A, B, C, D and E

Number of vertices: n=5

Sum of the measures of the interior angles of the polygon: S=?

S=180°(n-2)

Substituting n by 5 in the formula above:

S=180°(5-2)

S=180°(3)

S=540°

9. Each interior angle of a regular polygon (i) measures 144°:

i=144°

How many sides does the polygon have?

n=?

i=180°(n-2)/n

Substituting i by 144° in the formula above:

144°=180°(n-2)/n

Solving for n: Cross multiplication:

144°n=180°(n-2)

Eliminating the parentheses on the right side of the equation applying the distributive property:

144°n=180°(n)-180°(2)

Multiplying

144°n=180°n-360°

Grouping n's on the right side of the equation: Subtracting 144°n both sides of the equation:

144°n-144°n=180°n-360°-144°n

Subtracting:

0=36°n-360°

Adding 360° both sides of the equation:

0+360°=36°n-360°+360°

Adding:

360°=36°n

Dividing both sides of the equation by 36°:

360°/36°=36°n/36°

10=n

n=10

The polygon has 10 sides.

10. Each interior angle of a regular polygon (i) measures 108°:

i=108°

How many sides does the polygon have?

n=?

i=180°(n-2)/n

Substituting i by 108° in the formula above:

108°=180°(n-2)/n

Solving for n: Cross multiplication:

108°n=180°(n-2)

Eliminating the parentheses on the right side of the equation applying the distributive property:

108°n=180°(n)-180°(2)

Multiplying

108°n=180°n-360°

Grouping n's on the right side of the equation: Subtracting 108°n both sides of the equation:

108°n-108°n=180°n-360°-108°n

Subtracting:

0=72°n-360°

Adding 360° both sides of the equation:

0+360°=72°n-360°+360°

Adding:

360°=72°n

Dividing both sides of the equation by 72°:

360°/72°=36°n/72°

5=n

n=5

The polygon has 5 sides.

[tex]a_n=3a_{n-1}-4[/tex]

Try the answers

You can try the answers to see what works. You can expect all of the choices to match the first two terms, so try some farther down. Let's see if we can get -25 from -7.

a) 3*(-7) -4 = -21 -4 = -25 . . . . this one works

b) -7 -2 = -9 . . . . ≠ -25

c) -3(-7) +2 = 21 +2 = 23 . . . . ≠ -25

d) -2(-7) +1 = 14 +1 = 15 . . . . ≠ -25

The formula that works is the first one.

_____

Derive it

All these formulas depend on the previous term only, so we can write equations that show the required relationships. Let the unknown coefficients in our recursion formula be p and q, as in ...

[tex]a_n=p\cdot a_{n-1}+q[/tex]

Then, to get the second term from the first, we have

... 1·p +q = -1

And to get the third term from the second, we have

... -1·p +q = -7

Subtracting the second equation from the first gives ...

... 2p = 6

... p = 3 . . . . . . . this is sufficient to identify the first answer as correct

We can find q from the first equation.

... q = -1 -p = -1 -3 = -4

So, our recursion relation is ...

[tex]a_n=3a_{n-1}-4[/tex]

Answer:

$6

Step-by-step explanation:

The graph shows you that 4 pounds of apples (and no cranberries) can be purchased for $24. Thus each pound costs ...

... $24/(4 pounds) = $6/pound

The exercise is asking you to compute the volume of five different spheres and cylinders, choosing 5 different random values.

Remember the formulas for the volumes: given a radius [tex] r [/tex], the volume of the sphere is

[tex] \dfrac{4}{3}\pi r^3 [/tex]

Whereas the volume of the cylinder is

[tex] \pi h r^2[/tex]

In this specific case, you're told that the height of the cylinder is the same as the diameter of the sphere (i.e. twice the radius). So, the formula of the cylinder updates to

[tex] \pi (2r) r^2 = 2\pi r^3 [/tex]

So, all you need to do is to pick 5 random numbers, use them as the radius [tex] r [/tex], and for each of them compute the volume and cylinder sphere as indicated above.

For example, if you choose a radius [tex] r=5 [/tex], you will have

[tex] \text{Sphere: } V = \dfrac{4}{3}\pi 5^3 = \dfrac{500\pi}{3} [/tex]

[tex] \text{Cylinder: } V = 2\pi 5^3 = 250\pi [/tex]

Now choose your 5 random values and do the same!

y = 10(√3)/3

unnamed side = 5(√3)/3

Side ratios in a 30°-60°-90° triangle are 1 : √3 : 2.

Multiplying these by 5/√3 gives ...

... unnamed side : 5 : y = 5/√3 : 5 : 10/√3

Then ...

... unnamed side = 5/√3 = 5(√3)/3

... y = 10/√3 = 10(√3)/3

Answer:

Choice D) which is f(0) = g(0) - 2

Step-by-step explanation:

Plug x = 0 into the g(x) function to find that....

g(x) = f(2*x) + 2

g(0) = f(2*0) + 2 .... replace every x with 0

g(0) = f(0) + 2

g(0) - 2 = f(0) + 2 - 2 .... subtract 2 from both sides

g(0) - 2 = f(0)

f(0) = g(0) - 2

Answer:

80 adult tickets were sold

Step-by-step explanation:

If you subtract the extra 20 adult tickets from ticket numbers and revenue, you get ...

equal numbers of $4 and $8 tickets were sold for a total of $720 collected

Since that is some number of ticket pairs worth $12 per pair, there must have been ...

$720/12 = 60 pairs of $4 and $8 tickets

The number of adult tickets is 20 more than this, so is

60 + 20 = 80 . . . . adult tickets sold

_____

If you feel better with an equation, rather than numerical reasoning, you can let n represent the number of adult tickets. Then n-20 is the number of student tickets and total revenue is ...

8n +4(n-20) = 880

12n -80 = 880 . . . . . simplify

12n = 960 . . . . . . . . . add 80

n = 80 . . . . . . . . . . . . divide by 12

_____

Comment on the different solutions

Using n for the number of adult tickets, we effectively chose a scenario where we added 20 student tickets to bring the total to $960 for some number of $12 pairs of tickets. That number is 80, the number of adult tickets.

In the "word solution" given at first, we effectively solved for the number of student tickets, then added 20 to get the number of adult tickets. The corresponding equation would be ...

4s +8(s+20) = 880 . . . s = number of student tickets sold

12s = 720 . . . . . . . . . subtract 160, the price of the 20 extra adult tickets

You are given the length of every side, except for two, that can be easily derived from the others:

The sum of all sides, including these two, will give you the perimeter of the polygon.

The perimeter of the polygon is determined as P = 210 feet.

Given data:

The polygon of the perimeter is the total side length of all the sides of the polygon.

Let the perimeter be represented as P.

From the attached figure of the polygon:

P = ( 15 + 22 + 10 + 18 + 10 + 14 + 5 + 16 + ( 15 + 5 + 5 ) + 16 + 5 + ( 14 + 18 + 22 )

On simplifying the equation:

P = 210 feet

So, the value of P is 210 feet.

Hence, the perimeter is 210 feet.

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Answer:

q/mc=t

Step-by-step explanation:

q=mct

q/mc=t

Answer:

The formula for t is [tex]T=\frac{Q}{MC}[/tex]

Step-by-step explanation:

Consider the provide formula.

[tex]Q=MCT[/tex]

Where Q=heat flow M=mass, C specific heat, and T is the change of temperature is used to calculate heat flow.

We need to solve the above formula for T.

Divide both the sides by MC.

[tex]\frac{Q}{MC}=\frac{MCT}{MC}[/tex]

[tex]\frac{Q}{MC}=T[/tex]

[tex]T=\frac{Q}{MC}[/tex]

Hence, the formula for t is [tex]T=\frac{Q}{MC}[/tex]

Answer:

Step-by-step explanation:

1. You can use a calculator if your knowledge of arithmetic fails you.

... 98 +17 +37 -176 = 152 -176 = -24

___

2. -37/8 = -(32 +5)/8 = -4 5/8 = -4.625

This number is on the left side of zero on the number line, but is slightly closer to zero than -4.63, so is "greater than" -4.63.

Answer:

-2

Step-by-step explanation:

From the given graph, the point A(1, -4) and B(-1, 0)

Slope (m) = (y2 - y1) / (x2 - x1)

x1 = 1, y1 = -4, x2 = -1 and y2 = 0

Slope (m) = (0 - (-4))/(-1 - 1)

= 4/-2

Slope = -2

Thank you.

Answer:

-5(x² -2x +3)

Step-by-step explanation:

5 is a factor common to all of the coefficients. It is convenient to have the x² coefficient be positive in the factored form, so the result of factoring out -5 is ...

... -5((-5x²/-5) +(10x/-5) +(-15/-5)) = -5(x² -2x +3)

Answer:

-5(x² -2x +3) your welcome

Step-by-step explanation:

f(x) factors as ...

... f(x) = (x² -4)(x² +3) = (x -2)(x +2)(x² +3)

The real roots are x = ±2.

The complex roots are x = ±i√3.

___

We don't know what "no real complex roots" means. We suspect your answer may be C. 2.

Answer:

Step-by-step explanation:

Assuming the categorization is mutually exclusive (customers either text or internet, but not both), the total number of Plan B customers in the sample is the sum of those in each category:

.... 13 + 10 = 23 . . . . plan B customers

The problem statement tells you

... 23 plan B customers text

Since 13 out of 23 customers surveyed use the phone for text, the empirical probability that a plan B customer will use the phone for texting is ...

... 13/23 . . . . probability that text is used most

There are 23 customers are on payment plan B.

There are 13 customers who are on plan B text.

The probability that a randomly selected customer who is on plan B uses the phone most often to text is 13/23.

Given

A phone company surveys a sample of current customers to determine if they use their phones most often to text or use the Internet.

They sort the data by payment plans, as shown below.

Plan A: 27 texts, 21 Internet

Plan B: 13 texts, 10 Internet

The probability is defined as the ratio of the sum of all observations and the total number of observations.

The total number of observation is;

= 13 +10 = 23

1. How many customers are on payment plan B?

There are 23 customers are on payment plan B.

2. How many of the customers are on plan B text?

There are 13 customers who are on plan B text.

3. What is the probability that a randomly selected customer who is on plan B uses the phone most often to text?

[tex]\rm Probability = \dfrac{Customer \ plan \ B}{Total \ number \ of \ customers}\\\\Probability = \dfrac{13}{23}[/tex]

The probability that a randomly selected customer who is on plan B uses the phone most often to text is 13/23.

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Answer:

$9275

Step-by-step explanation:

Selma earns 5% on the first $40,000, which is $2000.

She earns 5.5% on the next $35,000, which is $1925.

She earns 6% on the next $25,000, which is $1500.

And she earns 7% on the last $55,000 (the amount over 100,000), which is $3850.

Altogether, Selma's commission is ...

... $2000 +1925 +1500 +3850 = $9275.

_____

Comment on the sliding scale

Each of the segments of this sliding scale could be rewritten to simplify its computation. For example, for amounts above $100,000, the formula could be either of ...