Find the measure of the numbered angles in each rhombus.

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.

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:

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:

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:

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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-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:

For this case, we have that by definition:

Let "x" be an angle of any vertex of a right triangle.

[tex]tangent (x) = \frac {Cathet \ opposite} {Cathet \ adjacent}[/tex]

So, if we want to find the tangent of angle A:

[tex]tangent (A) = \frac {6} {8}[/tex]

Thus, the tangent of angle "A" is [tex]\frac {6} {8}[/tex]

Answer:

[tex]\frac {6} {8}[/tex]

Option b

DAY 15: The measures of the angles in a certain triangle are in the ratio 1: 5: 6. Find the measure of the smallest angle.  

x +5x +6x=180  

12x =180  

x=15º  

DAY 16: In triangle ABC, the measure of angle A = 7x - 32, the measure of angle B = 3x + 4, and the exterior angle at C has measure 12 (x - 5). Find the value of x.  

exterior angle = sum of two remote (other) interiors  

7x -32 +3x+4 =12(x-5)  

10x -28 =12x -60  

32-2x  

x=16  

DAY 17: Find the slope of the line perpendicular to the line through the points (21, 11) and (-4, -12).  

11 - -12 / 21 - -4 =23/25  

slope of perpendicular line is negative reciprocal =  

-25/23 ( no 17!)  

DAY 18: In a certain triangle, the largest angle is 6 times the smallest. The third angle is 18 less than 4 times the smallest. What is the measure of the smallest angle?  

x= smallest  

6x =largest  

third angle =4x-18  

x+6x +4x-18 =180  

11x =198  

x=18º

Answer:

Second Option is the correct answer 3/2

Step-by-step explanation:

Tangent of an angle in a triangle is given by Perpendicular of that triangle / Base of that triangle , with resoect to angle in consideration.

Tangent Ratio for angle B = Perpendicular / Base

Tangent Ratio for angle B = AC / BC

Tangent Ratio for angle B = 3/2

Hope it helps.

Thank you.

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.

Numerical Reasoning

Consider a set of prints that consists of 2 small prints and one large print (that is, twice as many small prints as large). The value of that set will be ...

... 2×$20 +45 = $85

To have revenue of at least $510, the studio must sell ...

... $510/$85 = 6

sets of prints. That is, the studio needs to sell at least 6 large prints and 12 small ones.

_____

With an equation

Let x represent the number of large prints the studio needs to sell. Then 2x will represent the number of small prints. Total sales will be ...

... 20·2x +45·x ≥ 510

... 85x ≥ 510

... x ≥ 510/85

... x ≥ 6

The studio needs to sell at least 6 large prints and 12 small prints.

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:

y = 1 + 1/((x -1)(x -4))

Step-by-step explanation:

To get vertical asymptotes at 1 and 4, you need factors (x -1) and (x -4) in the denominator. As x approaches 1 or 4, one of these will approach zero, and the function value will approach infinity.

To get a horizontal asymptote of 1, the function must approach the value 1 when the value of x gets large (positive or negative). This can generally be accomplished by simply adding 1 to a fraction that approaches zero when x is large.

Here, we make the fraction be the one that gives the vertical asymptotes, and we simply add 1 to it.

... y = 1 + 1/((x -1)(x -4))

If you like, this can be "simplified" to ...

... y = (x² -5x +5)/(x² -5x +4)

_____

In this rational expression form, please note that the numerator and denominator have the same degree. That will be the case when there is a horizontal asymptote. (When a slant asymptote, the numerator degree is 1 higher than the denominator.) The ratio of the coefficients of the highest degree terms is the horizontal asymptote value (or the slope of a slant asymptote).

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

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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Total -

Right-handed: 214! Left-handed: 22!

Total of students: 236 students

I hope this helped! :D

Step-by-step explanation:

9th Grade: Right Handed: 111! Left Handed: 10!

10 Grade: Right Handed: 103! Left Handed: 22!

Add left handed for both grades. Add right handed for both grades. And add total numbers.

I hope this helped :D    

There are 121 students in 9th grade and 115 students in 10th grade at Jefferson High School.

This question involves counting and analyzing data about grade levels and handedness of students at Jefferson High School. To answer the question, we need to use the given information:

- There are 236 students in 9th and 10th grades combined.

- Out of these, 121 students are in 9th grade.

- Among the 214 right-handed students, 103 are in 10th grade.

We can use these numbers to find out how many students are in each grade level.

Let's denote the number of 9th-grade students as 'x' and 10th-grade students as 'y'.

From the given information:

x + y = 236 (total number of students)

x = 121 (number of 9th-grade students)

y = 103 (number of 10th-grade students)

To find the value of 'y', we can substitute the given value of 'x' into the first equation:

121 + y = 236

y = 236 - 121

y = 115

Therefore, there are 121 students in 9th grade and 115 students in 10th grade.

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:

$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 ...

Answer:

I do believe the answer is C

Step-by-step explanation:

.004 / .0004 =

Answer:

c 10

Step-by-step explanation:

If we want to know how much bigger object A is than object B is we take object A and divide it by object B

object A        4 * 10^-3

-----------   = -------------

Object B        4 * 10 ^-4

When dividing exponents with the same base

We can subtract them.  The numbers out front get divided

4/4 * 10 ^ (-3- -4)

1 * 10 ^(-3+4)

1 * 10 ^1

10

half-turn

There is a point of rotational symmetry at the center of the pattern. Thus, turning it 180° (a half-turn) will map it to itself.

_____

Comment on other choices

Any sort of reflection will change it to bqbqbqbqbq. Translation puts its somewhere else, not on top of itself.

Answer:

A half turn reversal of direction (as in a staircase) either by one 180-degree turn or two right-angle turns

Step-by-step explanation:

Hope this helps :) -Mark Brainiest Please :)

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:

y= 35/2  when x=5

x=6 when y =21

Proportinal relatiionships:  y=−x ,  y=15x

Step-by-step explanation:

The formula for direct variation is

y= kx

If y=7 and x=2, we can solve for k

7 =k*2

Divide by 2

7/2 =k

y =7/2 x

Now if x=5

y =7/2 * 5

y =35/2

Now if y=21

21 =7/2 * x

Multiply by 2/7

21 * 2/7 = 7/2 * 2/7 x

6 =x

Which equation represents a proportional relationship?

y=−x

YES  k = -1   Some people debate about having a negative constant, but everything I have read and taught says you can have a negative constant.

y=−5(x+1)

This does not go through the origin so no

if x=0  y = -5

y = 5x + 1

if x = 0 y =1   so no

y=15x

YES  k = 15

Answer:

17.5

i just did it on my quiz and it was wrong(the other guy is wrong)

Answer:

Step-by-step explanation:

1. First differences in the y-values are ...

... -5-0 = -5; -8-(-5) = -3; -9-(-8) = -1; -8-(-9) = 1; -5-(-8) = 3; 0-(-5) = 5

Second differences are ...

... -3-(-5) = 2; -1-(-3) = 2; 1-(-1) = 2; 3-1 = 2; 5-3 = 2

These 2nd differences are constant, so the points can be described by a 2nd-degree polynomial.

2. Values on the graph range from 0 to a low of -9 and back up to 0. There is a minimum at (1, -9).

3. The value at x=-1 is -5; at x=1, it is -9, which is less than -5. The function is decreasing on the interval -1 to 1.

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

5.51 seconds

y = 0 when the stone hits the ground. At that point, t can be found from ...

... 0 = -16t^2 +486

... 0 = t^2 -30.375 . . . . divide by -16

... 30.375 = t^2 . . . . . . add the opposite of the constant

Take the square root to get ...

... √30.375 = t ≈ 5.51 . . . . seconds

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

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:

B. side-angle-side

Step-by-step explanation:

You are given that side SR matches its counterpart; angle SRT matches its counterpart; and you know side ST matches its counterpart, because they are the same segment.

Hence, you have two matching sides and the angle between them. This set of side-angle-side lets you invoke the theorem that matches that name.

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