Mathematics College

What is the area of polygon EFGH?

Answers

Answer 1

Answer:

C. 42 square units

Step-by-step explanation:

This is a rectangle and to calculate the area of a rectangle we multiply length and width

The length of this rectangle is 7 units and the width is 6 units

6 × 7 = 42 square units

Related Questions

In RST, RS = 7, RT = 10, and ST = 8. Which angle of RST has the smallest measure? A T BCANNT BE DETERMINDED C R D S

Answers

Answer:

Correct answer is option A. T

Step-by-step explanation:

Given that

In a [tex]\triangle RST[/tex], RS = 7, RT = 10, and ST = 8.

To find:

Smallest angle = ?

Solution:

We can use cosine rule here to find the angle.

Formula for cosine rule:

[tex]cos B = \dfrac{a^{2}+c^{2}-b^{2}}{2ac}[/tex]

Where

a is the side opposite to [tex]\angle A[/tex]

b is the side opposite to [tex]\angle B[/tex]

c is the side opposite to [tex]\angle C[/tex]

Using the cosine rule:

[tex]cos T = \dfrac{ST^{2}+RT^{2}-RS^{2}}{2\times ST \times RT}\\\Rightarrow cos T = \dfrac{8^{2}+10^{2}-7^{2}}{2\times 8 \times 10}\\\Rightarrow cos T = \dfrac{64+100-49}{160}\\\Rightarrow cos T = \dfrac{115}{160}\\\Rightarrow \angle T = cos^{-1}(0.71875)\\\Rightarrow \angle T = 44.05^\circ[/tex]

Now, let us use Sine rule to find other angles:

[tex]\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}[/tex]

[tex]\dfrac{RS}{sinT} = \dfrac{ST}{sinR} = \dfrac{RT}{sinS}\\\Rightarrow \dfrac{7}{sin44.05} = \dfrac{8}{sinR} = \dfrac{10}{sinS}\\\Rightarrow \dfrac{7}{0.695} = \dfrac{8}{sinR} = \dfrac{10}{sinS}\\\Rightarrow sin R = \dfrac{8 \times 0.695}{7}\\\Rightarrow R = 52.58^\circ[/tex]

[tex]\Rightarrow sin S = \dfrac{10 \times 0.695}{7}\\\Rightarrow S = 83.14^\circ[/tex]

Smallest angle is [tex]\angle T[/tex]

Correct answer is option A. T

a radion station usa 1\6 of its time for the news. in a 12 hour day, how many hours are used for music & entertainment?

Answers

Answer:

10 hours

Step-by-step explanation:

In order to answer this question, you must assume that all air time not spent on news is spent on music & entertainment. That would usually not be the case, as there would usually be advertisements and public service programming along with everything else.

The time spent on news is ...

(1/6)(12 hours) = 2 hours

If the rest is spent on music and entertainment, then ...

12 -2 = 10 . . . hours are used for music and entertainment

Twelve apples cost $2.00. How much will 50 apples cost?

Answers

Answer:

$8.33

Step-by-step explanation:

[tex]Solve \:using \: proportion\\\\12\:apples = \$ 2\\50\:apples = \$ x\\Cross \: Multiply\\\\12x = 100\\\\\\\frac{12x}{12} = \frac{100}{12} \\\\x = \$ 8.333[/tex]

Answer:

About $8.33.

Step-by-step explanation:

Write a proportion. Make sure the values line up horizontally:

[tex]\frac{12\text{ apples}}{\$2} =\frac{50\text{ apples}}{\$x}[/tex]

Cross multiply:

[tex]100=12x\\x=25/3\approx\$8.33[/tex]

Help please!!! Tyyyyy

Answers

Answer:

D) 60 degree

Step-by-step explanation:

Let's connect the remaining diagonal, which forms a triangle containing angle x.

As a property of regular hexagon, all diagonals are equal.

=> The formed triangle is a regular triangle and it has three equal angles, which are 60 degrees.

A household survey of 10 families was conducted by students of 4th year MBBS. In the collected data, the ages of heads of families were: 32, 34, 35, 36, 36, 42, 44, 46, 48, and 52. The mean age of heads of families is
a. 36
b. 38.5
c. 40
d. 40.5
e. 42

Answers

Answer:

Which polynomial is prime?

7x2 – 35x + 2x – 10

9x3 + 11x2 + 3x – 33

10x3 – 15x2 + 8x – 12

12x4 + 42x2 + 4x2 + 14

Step-by-step explanation:

Which polynomial is prime?

7x2 – 35x + 2x – 10

9x3 + 11x2 + 3x – 33

10x3 – 15x2 + 8x – 12

12x4 + 42x2 + 4x2 + 14 SO IT IS RIGHT

I will name you Brainly hurryyyy What two integers are in between 0.7142

Answers

Answer:

0.71419 &0.71421 are the correct.

find the greatest common factor of 108d^2 and 216d

Answers

Answer:

Below

Step-by-step explanation:

If d is a positive number then the greatest common factor is 108d.

To get it isolate d and d^2 from the numbers.

108 divides 216. (216 = 2×108)

Then the greatest common factor of 216 and 108 is 108.

For d^2 and d we will follow the same strategy

d divides d^2 (d^2 = d*d)

Then the greatest common factor of them is d.

So the greatest common factor will be 108d if and only if d is positive. If not then 108 is the answer

Answer:

[tex]\boxed{108d}[/tex]

Step-by-step explanation:

Part 1: Find GCF of variables

The equation gives d ² and d as variables. The GCF rules for variables are:

The variables must have the same base.If one variable is raised to a power and the other is not, the GCF is the variable that does not have a power.If one variable is raised to a power and the other is raised to a power of lesser value, the GCF is the variable with the lesser value power.

The GCF for the variables is d.

Part 2: Find GCF of bases (Method #1)

The equation gives 108 and 216 as coefficients. To check for a GCF, use prime factorization trees to find common factors in between the values.

Key: If a number is in bold, it is marked this way because it cannot be divided further AND is a prime number!

Prime Factorization of 108

108 ⇒ 54 & 2

54 ⇒ 27 & 2

27 ⇒ 9 & 3

9 ⇒ 3 & 3

Therefore, the prime factorization of 108 is 2 * 2 * 3 * 3 * 3, or simplified as 2² * 3³.

Prime Factorization of 216

216 ⇒ 108 & 2

108 ⇒ 54 & 2

54 ⇒ 27 & 2

27 ⇒ 9 & 3

9 ⇒ 3 & 3

Therefore, the prime factorization of 216 is 2 * 2 * 2 * 3 * 3 * 3, or simplified as 2³ * 3³.

After completing the prime factorization trees, check for the common factors in between the two values.

The prime factorization of 216 is 2³ * 3³ and the prime factorization of 108 is 2² * 3³. Follow the same rules for GCFs of variables listed above and declare that the common factor is the factor of 108.

Therefore, the greatest common factor (combining both the coefficient and the variable) is [tex]\boxed{108d}[/tex].

Part 3: Find GCF of bases (Method #2)

This is the quicker method of the two. Simply divide the two coefficients and see if the result is 2. If so, the lesser number is immediately the coefficient.

[tex]\frac{216}{108}=2[/tex]

Therefore, the coefficient of the GCF will be 108.

Then, follow the process described for variables to determine that the GCF of the variables is d.

Therefore, the GCF is [tex]\boxed{108d}[/tex].

All sacks of sugar have the same weight. All sacks of flour also have the same weight, but not necessarily the same as the weight of the sacks of sugar. Suppose that two sacks of sugar together with three sacks of flour weigh no more than 40 pounds and that the weight of a sack of flour is no more than 5 pounds more than the weight of two sacks of sugar. What is the largest possible weight (in pounds) of a sack of flour?

Answers

Answer:

The largest possible weight of flour is 11.25 pounds.

Step-by-step explanation:

To start with, we will assume that the weight of 1 sack of sugar = x pounds

We will also assume that the weight of 1 sack of flour = y pounds

So, the weight of 2 sacks of sugar = 2 * (x) = 2x

Same thing goes for the weight of 3 sacks of flour = 3 * (y) = 3y

Supposing that the weight of (2 sacks of sugar + 3 sacks of flour) ≤ 40 pounds

= 2x + 3y ≤ 40............ we'll call that equation 1.

Also, suppose that the weight of ( 1 sack of flour) ≤ 2 sacks of sugar + 5 pounds

= y ≤ 2x + 5........................ we'll call that equation 2

Therefore, we'll solve for the values of x and y in the two equations and we will get:

2x + 3y ≤ 40

y ≤ 2x + 5

Now, substitute the value of y into equation 1

2x + 3y ≤ 40 ⇒ 2x + 3(2x +5) =40

⇒ 2x + 6x + 15= 40

⇒ 8x + 15 = 40

⇒ 8x = 25

⇒ x = 25/8

⇒ x = 3.12

x cannot be more than 3.12 pounds, so we solve for y

Putting the value of x into equation 2, we'll get

⇒ 2y + 5 = 2(3.12) + 5

⇒ y = 11.25 pounds.

So, n cannot be more than 11.25 pounds

Determining the normal form of the equation of a line is like finding the equation of a tangent line to a circle of radius p.

Please select the best answer from the choices provided

True

False

Answers

Answer:

True

Step-by-step explanation:

The normal form of equation of a line is the radius of p. Tangent to a circle is the line that touches one point on the circle. The radius is the circumference of the circle. The tangent line on the circle is always perpendicular to the radius. The statement is correct.

Let f(x) and g(x) be polynomials as shown below. Which of the following is true about f(x) and g(x)? f(x) and g(x) are not closed under multiplication because when multiplied, the result will not be a polynomial. f(x) and g(x) are not closed under multiplication because when multiplied, the result will be a polynomial. f(x) and g(x) are closed under multiplication because when multiplied, the result will not be a polynomial. f(x) and g(x) are closed under multiplication because when multiplied, the result will be a polynomial. Reset Submit

Answers

Answer:

f(x) and g(x) are closed under multiplication because when multiplied, the result will be a polynomial.

Step-by-step explanation:

The set of all polynomials is closed under addition, subtraction, and multiplication, because performing any of these operations on a pair of polynomials will give a polynomial result.

Comment on the question

The wording is a bit strange, because f(x) and g(x) are elements of a set (of polynomials), so cannot be said to be "closed." "Closed" is a property of a set with respect to some function, it is not a property of an element of the set.

Answer:

f(x) and g(x) are closed under multiplication because when multiplied, the result will be a polynomial.

Step-by-step explanation:

Its correct trust

Solve for x: the quantity of x plus 4 over 3 = 2.

Answers

Answer:

x =2

Step-by-step explanation:

(x+4) /3 = 2

Multiply each side by 3

(x+4) /3 *3= 2*3

x+4 = 6

Subtract 4

x+4-4 = 6-4

x =2

━━━━━━━☆☆━━━━━━━

▹ Answer

x = 2

▹ Step-by-Step Explanation

[tex]\frac{x + 4}{3} = 2\\\\3 * 2 = 6\\\\x + 4 = 6\\\\x = 2[/tex]

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Complete parts (a) through (c) below.

(a) Determine the critical value(s) for a right-tailed test of a population mean at the alpha = 0.10 level of significance with 15 degrees of freedom.

(b) Determine the critical value(s) for a left-tailed test of a population mean at the alpha = 0.01 level of significance based on a sample size of n = 20.

(c) Determine the critical value(s) for a two-tailed test of a population mean at the alpha = 0.05 level of significance based on a sample size of n = 14.

Answers

Answer:

(a) 1.341

(b) -2.539

(c) -2.160 and 2.160

Step-by-step explanation:

(a) We have to find the critical value(s) for a right-tailed test of a population mean at the alpha = 0.10 level of significance with 15 degrees of freedom.

Since the degrees of freedom are included here, so we will use t table here for a population mean test.

In the table there are two values given, one is the degrees of freedom and another is the value of P.

P is the level of significance at which the critical values are calculated.

So, here the degrees of freedom (n - 1) = 15 and the level of significance for a right-tailed test is 0.10, i.e. P = 10%

Now, looking in the t table with P = 10% and [tex]\nu[/tex] = 15, we get the critical value of 1.341.

(b) We have to find the critical value(s) for a left-tailed test of a population mean at the alpha = 0.01 based on a sample size of n = 20.

Since the degrees of freedom are included here, so we will use t table here for a population mean test.

In the table there are two values given, one is the degrees of freedom and another is the value of P.

P is the level of significance at which the critical values are calculated.

So, here the degrees of freedom (n - 1) = 20 - 1 = 19 and the level of significance for a left-tailed test is 0.01, i.e. P = 1%

Now, looking in the t table with P = 1% and [tex]\nu[/tex] = 19, we get the critical value of 2.539. But since it is a left-tailed test, so the critical value will be -2.539.

(c) We have to find the critical value(s) for a two-tailed test of a population mean at the alpha = 0.05 level of significance based on a sample size of n = 14.

Since the degrees of freedom are included here, so we will use t table here for a population mean test.

In the table there are two values given, one is the degrees of freedom and another is the value of P.

P is the level of significance at which the critical values are calculated.

So, here the degrees of freedom (n - 1) = 14 - 1 = 13 and the level of significance for a two-tailed test is [tex]\frac{0.05}{2}[/tex] is 0.025, i.e. P = 2.5%.

Now, looking in the t table with P = 2.5% and [tex]\nu[/tex] = 13, we get the critical value of -2.160 and 2.160 for a two-tailed test.

BOND VALUATION Asiana Fashion's bonds have 10 years remaining to maturity. Interest is paid annually; they have a $1,000 par value; the coupon interest rate is 8% and thebyield to maturity is 9%.What is the bond's current market price?

Answers

Answer:

$935.76

Step-by-step explanation:

Step 1

We find the Present value factor of sum

The formula =

(1 + i)^n

Where

i = maturity rate = 9% = 0.09

n = number of years = 10 years

Present Value = ( 1 + 0.09)^-10

= 0.4224

Step 2

We find the present value factor of annuity

The formula is given as:

1 - (1+i)^-n / i

i = maturity rate = 9% = 0.09

n = number of years = 10 years

= 1 - (1 + 0.09)^-10 /0.09

= 1 - 0.4224 /0.09

= 0.5775 /0.09

= 6.417

Step 3

The bond's current market price is calculated as:

= PV factor of Sum × Par Value + PV factor of annuity × coupon payment

Coupon payment is calculated as:

= Coupon interest × par value

= 8% × 1000

= 80

Hence,

= 0.4224 × 1,000 + 6.417 × 80

= 422.4 + 513.36

= 935.76

In this exercise we have to use the knowledge of finance to calculate the corrective value of the market place, in this way we find that:

[tex]\$935.76[/tex]

We find the Present value factor of sum, by the formula of:

[tex](1 + i)^n[/tex]

Where:

i = maturity rate = 9% = 0.09 n = number of years = 10 years

Substituting the values in the formula as;

[tex]Present \ Value = ( 1 + 0.09)^{-10} = 0.4224[/tex]

We find the present value factor of annuity, by the formula as:

[tex]1 - (1+i)^{-n} / i[/tex]

Where:

i = maturity rate = 9% = 0.09 n = number of years = 10 years

Substituting the values in the formula as;

[tex]= 1 - (1 + 0.09)^{-10} /0.09\\= 1 - 0.4224 /0.09\\= 0.5775 /0.09\\= 6.417[/tex]

The bond's current market price is calculated as:

[tex]= PV \ factor\ of\ Sum * Par\ Value + PV\ factor\ of\ annuity * coupon\ payment[/tex]

Coupon payment is calculated as:

[tex]= Coupon\ interest * par\ value\\= 8\% * 1000= 80[/tex]

So continue the calcule;

[tex]= 0.4224 *1,000 + 6.417 * 80\\= 422.4 + 513.36\\= 935.76[/tex]

See more about market place at brainly.com/question/24518027

When x=5 what would the value of expression

Answers

Answer:

Step-by-step explanation:

6 more than the product of 8 and a number x

6 more means 6+

product of 8 and a number x means 8x

6+8x

when x=5

6+8(5)=6+40=46

use a paragraph, flow chart, or two column proof to prove the angle congruency

Answers

Answer: see proof below

Step-by-step explanation:

Statement Reason

1. ∠CAX ≅ ∠ BAX 1. Given

2. AC ≅ AB 2. Given

3. AY ≅ AY 3. Reflexive Property

4. ΔCAY ≅ ΔBAY 4. SAS Congruency Theorem

5. CY ≅ BY 5. CPCTC

6. ∠CYA ≅ ∠BYA 6. CPCTC

7. ∠CXY ≅ ∠ BXY 7. Given

8. ΔCYX ≅ ΔBYX 4. AAS Congruency Theorem

9. ∠XCY ≅ ∠XBY 9. CPCTC

Step-by-step explanation:

Hope it helps u

plz mark it as brainlist

In a stable matching problem, if every man has a different highest-ranking woman on his preference list, and given that women propose, then it is possible that, for some set of women's preference lists, all men end up with their respective highest-ranking woman.a. Trueb. False

Answers

Answer:

True

Step-by-step explanation:

The statement given above in the question is correct. It is mentioned that men are free to create a list of women's according to their preferences. There will be order sequence of women and men places them in queue of their preference. The men proposes the women with highest ranking in the list then it is possible that all men gets their preferred choice.

What is the domain of the set of ordered pairs?
(8, -13); ( 0,-5); (4, -9); (-3,2)

Answers

The domain is the input values, which are the x values.

The x values in the given pairs are: 8, 0,4,-3

The domain set is (-3, 0, 4, 8)

The required domain of the set of ordered pairs is [8, 0, 4, -3]

Given that,

Set of ordered pair; (8, -13); ( 0,-5); (4, -9); (-3,2).

We have to determine,

The domain of the set of ordered pair.

According to the question,

The domain refers to the set of possible input values.

The domain of a graph consists of all the input values shown on the x-axis.

A relation is a set of ordered pairs.

The domain is the set of all the first components of the ordered pairs.

Then,

Set of ordered pair; (8, -13); ( 0,-5); (4, -9); (-3,2).

Here, Set of all the input values on the x-axis.

Therefore,

The set of values of x is { 8,0,4,-3 }

Hence, The required domain of the set of ordered pairs is [8, 0, 4, -3]

To know more about Domain click the link given below.

https://brainly.com/question/19704059

f(x)=6x+2 and g(x)=-9x-5 Find the product of f and g.

Answers

Answer: See below

Explanation:

(f • g)(x) = (6x+2)(-9x-5)
(f • g)(x) = 54x^2 - 30x - 18x - 10
(f • g)(x) = 54x^2 - 48x - 10

The product of the functions f(x) and g(x) will be negative 2 times (27x² + 24x + 5).

What is a function?

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The functions are given below.

f(x) = 6x + 2 and g(x) = -9x - 5

The product of the functions f(x) and g(x), then we have

⇒ f(x) × g(x)

⇒ (6x + 2) × (-9x - 5)

Simplify the expression, then we have

⇒ (6x + 2) × (-9x - 5)

⇒ 6x(-9x - 5) + 2(-9x - 5)

⇒ -54x² - 30x - 18x - 10

⇒ -(54x² + 48x + 10)

⇒ -2(27x² + 24x + 5)

The product of the functions f(x) and g(x) will be negative 2 times (27x² + 24x + 5).

More about the function link is given below.

https://brainly.com/question/5245372

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A doctor orders Quinidine for an adult patient weighing 110 lb at a dosage of 25 mg/kg/day q6h. How many
milligrams should the patient receive each day?

Answers

Answer:

Total amount receive each day = 1250 mg per day

Number of dosage = 1250 / 4 = 312.5 mg per meal

Step-by-step explanation:

Given:

Weight of patient = 110 lb

Dosage = 25 mg/kg/day

Find:

Total amount receive each day

Computation:

Weight of patient = 110 lb

1 lb = 0.453592

Weight of patient = 110 (0.453592)

Weight of patient = 49.89

Weight of patient = 50 kg (Approx)

Total amount receive each day = 50 kg × 25 mg/kg/day

Total amount receive each day = 1250 mg per day

Number of dosage = 1250 / 4 = 312.5 mg per meal

PLEASE PLEASE PLEASE HELP ME ANSWER THIS QUESTION QUICK!! The picture of the question is down below. The answer choices are increased or decreased.

Answers

Answer:

NEGATIVE; DECREASED.

Step-by-step explanation:

A correlation coefficient of -0.76 indicates that there is a "fairly" strong negative relationship between the daily temperature and the number of people who visit the store.

This implies that, as the daily temperature increases, number of customers who come to the store decreases.

Therefore, the interpretation of the situation is:

"There is a NEGATIVE association between x and y. As the high temperature of the day increases across days, the number of customers who come to the store DECREASED.

Why is 12 * 10-8 is NOT a correct representation of scientific notation?

Answers

Answer:

see below

Step-by-step explanation:

Scientific notation is a * 10 ^b

a must be a number between 1 ( including 1 ) and less than 10

12 is greater than 10 so it is not scientific notation

Given the following three points, find by the hand the quadratic function they represent (0,6, (2,16, (3,33)

Answers

Answer:

[tex] f(x) = 4x^2 - 3x + 6 [/tex]

Step-by-step explanation:

Quadratic function is given as [tex] f(x) = ax^2 + bx + c [/tex]

Let's find a, b and c:

Substituting (0, 6):

[tex] 6 = a(0)^2 + b(0) + c [/tex]

[tex] 6 = 0 + 0 + c [/tex]

[tex] c = 6 [/tex]

Now that we know the value of c, let's derive 2 system of equations we would use to solve for a and b simultaneously as follows.

Substituting (2, 16), and c = 6

[tex] f(x) = ax^2 + bx + c [/tex]

[tex] 16 = a(2)^2 + b(2) + 6 [/tex]

[tex] 16 = 4a + 2b + 6 [/tex]

[tex] 16 - 6 = 4a + 2b + 6 - 6 [/tex]

[tex] 10 = 4a + 2b [/tex]

[tex] 10 = 2(2a + b) [/tex]

[tex] \frac{10}{2} = \frac{2(2a + b)}{2} [/tex]

[tex] 5 = 2a + b [/tex]

[tex] 2a + b = 5 [/tex] => (Equation 1)

Substituting (3, 33), and c = 6

[tex] f(x) = ax^2 + bx + x [/tex]

[tex] 33 = a(3)^2 + b(3) + 6 [/tex]

[tex] 33 = 9a + 3b + 6 [/tex]

[tex] 33 - 6 = 9a + 3b + 6 - 6 [/tex]

[tex] 27 = 9a + 3b [/tex]

[tex] 27 = 3(3a + b) [/tex]

[tex] \frac{27}{3} = \frac{3(3a + b)}{3} [/tex]

[tex] 9 = 3a + b [/tex]

[tex] 3a + b = 9 [/tex] => (Equation 2)

Subtract equation 1 from equation 2 to solve simultaneously for a and b.

[tex] 3a + b = 9 [/tex]

[tex] 2a + b = 5 [/tex]

[tex] a = 4 [/tex]

Replace a with 4 in equation 2.

[tex] 2a + b = 5 [/tex]

[tex] 2(4) + b = 5 [/tex]

[tex] 8 + b = 5 [/tex]

[tex] 8 + b - 8 = 5 - 8 [/tex]

[tex] b = -3 [/tex]

The quadratic function that represents the given 3 points would be as follows:

[tex] f(x) = ax^2 + bx + c [/tex]

[tex] f(x) = (4)x^2 + (-3)x + 6 [/tex]

[tex] f(x) = 4x^2 - 3x + 6 [/tex]

Researchers have collected data on the hours of television watched in a day and the age of a person. You are given the data below.

HOURS OF TV AGE
1 45
3 30
4 22
3 25
6 15

a. Determine which variable is the dependent variable.
b. Compute the least squares estimated line.
c. Compute the coefficient of determination. How would you interpret this value?