Given that f(x) = x + 4 and g(x) = x + 7, find (g - 4(x).

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

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

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]

Step-by-step explanation:

22

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a. Determine which variable is the dependent variable.

b. Compute the least squares estimated line.

c. Compute the coefficient of determination.22

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a. Determine which variable is the dependent variable.

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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 you interpret22

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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 this value22

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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 value22

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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

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a. Determine which variable is the dependent variable.

b. Compute the least squares estimated line.

c. Compute the coefficient of determination. How would 22

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a. Determine which variable is the dependent variable.

b. Compute the least squares estimated line.

c. Compute the coefficient of determination. How would you 22

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a. Determine which variable is the dependent variable.

b. Compute the least squares estimated line.

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a. Determine which variable is the dependent variable.

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a. Determine which variable is the dependent variable.

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a. Determine which variable is the dependent variable.

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c. Compute the coefficient of determination.22

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a. Determine which variable is the dependent variable.

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c. Compute the coefficient of determination.22

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a. Determine which variable is the dependent variable.

b. Compute the least squares estimated line.

c. Compute the coefficient of determination.22

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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 How22

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6 15

a. Determine which variable is the dependent variable.

b. Compute the least squares estimated line.

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Answer:

Q1= 2, Q2 = 4.5, Q3 = 7.5

Step-by-step explanation:

firstly, put the data is other;

0 1 1 1 2 2 2, 2 2 3 3 4 4 4, 5 6 7 7 7 7 7, 8 8 8 8 8 8 9

the Q1 = (2+2)/2 = 2

Q2 = (4 + 5)/ 2 = 4.5

Q3 = (7 + 8)/2 = 7.5

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

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

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.

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 ❁

━━━━━━━☆☆━━━━━━━

Answer:

77:44

Step-by-step explanation:

Since 7:4 is equal to 11 and 121/11, each ratio can be multiplied by 11.

Answer:

0.71419 &0.71421 are the correct.

Answer:

D. There is sufficient information because if two angles and a side included between them are known, the third angle can be determined using the angle sum formula and the remaining two sides can be determined using the law of sines.

Step-by-step explanation:

A triangle is a plane shape that consists of 3 sides and 3 angles. There are different ways of solving for any unknown sides or angles of a triangle.

If any two angles and just one side of a triangle are known, then other angles and sides can also be determined using the sine rule.

For example, if a, b and c are the sides of the triangle and <A, <B and <C are the angles. The sine law is expressed as shown;

a/sinA = b/sinB = c/sinC

Any two can be equated to get any unknown sides and angles.

Also, if two of the angles are known, the third angle can be determined since the sum of angle in a triangle is 180°. If <A and <B are known for example, the third angle <C can be determined using the expression.

<C = 180°-(<A+<B)

Based on the explanation, option D is therefore the correct option i.e There is sufficient information because if two angles and a side included between them are known, the third angle can be determined using the angle sum formula and the remaining two sides can be determined using the law of sines.

Answer:

840 ( D )

Step-by-step explanation:

GIVEN DIGITS : 1,2,3,4,5,6,7,8  

Number of odd numbers = 4

Number of even numbers = 4

therefore the number of odd numbers with 4 different digits can be formed by the same way the number of even numbers ( without repetition )

Hence the number of ways odd numbers with 4 different digits = Total number of ways of forming 4 digit numbers / 2

8*7*6*5 = 1680 / 2 =  840 ways

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

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

#SPJ2

Answer:

C). $3523.83

Step-by-step explanation:

loan of principles p= $9,300,

at rate R= 12 1 /8 % interest

Rate R = 12.125%

for duration year T = 37.5 months

T= 37.5/12 = 3.125 years

Interest I=PRT/100

Interest I =( 9300*12.125*3.125)/100

Interest I = (352382.8125)/100

Interest I = 3523.83

Interest I= $3523.83

Answer:

46

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

Answer:

3780.  

Step-by-step explanation:

To solve this we will start by just considering the number of ways to arrange 9 objects. We can do this in  9!  ways.

However since we have 3 reoccurring letters in Tennessee namely n,s and e we need to remove the times these form the same arrangement. Let me give an example to show what this means. Lets say we have the arrangement:

ennetssee

Now what happens if we exchange the places of the letters n for example? Of course we get the same arrangement of letters. We don’t want to count these as 2 different arrangements since for our interests they are the same. We therefore divide  9!  by the number of times this type of double counting occurs.

Since the word has the letter n occurring twice we will start by diving by  2! .

The letter s occurs 2 times as well so we will have to divide by  2!  again.

Finally the letter e occurs 4 times and so we will have to divide by  4!  here.

Now we get the following result:

9/(2 x 2 x 4)=3780.  

So in conclusion there are 3780 different ways to arrange the letters in Tennessee.

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

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.

Answer and Step-by-step explanation:

Suppose that we have a number y which is a positive integer and that:

y = [tex]x_n...x_5x_4x_3x_2x_1x_0[/tex]

Where;

[tex]x_{0}[/tex] = digit at 10⁰ => one's place (units place)

[tex]x_1[/tex] = digit at 10¹ => 10's place (tens place)

[tex]x_{2}[/tex] = digit at 10² => 100's place (hundreds place)

[tex]x_{3}[/tex] = digit at 10³ => 1000's place (thousands place)

.

.

.

[tex]x_{n}[/tex] = digit at 10ⁿ place

Then;

y = [tex]x_{0}[/tex] * 10⁰ + [tex]x_1[/tex] * 10¹ + [tex]x_{2}[/tex] * 10² + [tex]x_{3}[/tex] * 10³ + [tex]x_{4}[/tex] * 10⁴ + [tex]x_5[/tex] * 10⁵ + . . . + [tex]x_{n}[/tex] * 10ⁿ

Since 10⁰ = 1, let's rewrite y as follows;

y = [tex]x_{0}[/tex]  + [tex]x_1[/tex] * 10¹ + [tex]x_{2}[/tex] * 10² + [tex]x_{3}[/tex] * 10³ + [tex]x_{4}[/tex] * 10⁴ + [tex]x_5[/tex] * 10⁵ + . . . + [tex]x_{n}[/tex] * 10ⁿ

Now, to test if y is divisible by 11, replace 10 in the equation above by -1. Since 10 divided by 11 gives -1 (mod 11)     [mod means modulus]

y = [tex]x_{0}[/tex]  + [tex]x_1[/tex] * (-1)¹ + [tex]x_{2}[/tex] * (-1)² + [tex]x_{3}[/tex] * (-1)³ + [tex]x_{4}[/tex] * (-1)⁴ + [tex]x_5[/tex] * (-1)⁵ + . . . + [tex]x_{n}[/tex] * (-1)ⁿ

=> y =  [tex]x_{0}[/tex]  - [tex]x_1[/tex] + [tex]x_{2}[/tex] - [tex]x_{3}[/tex] + [tex]x_{4}[/tex] - [tex]x_5[/tex] + . . . + [tex]x_{n}[/tex] (-1)ⁿ (mod 11)

Therefore, it can be seen that, y is divisible by 11 if and only if alternating sum of its digits [tex]x_{0}[/tex]  - [tex]x_1[/tex] + [tex]x_{2}[/tex] - [tex]x_{3}[/tex] + [tex]x_{4}[/tex] - [tex]x_5[/tex] + . . . + [tex]x_{n}[/tex] (-1)ⁿ is divisible by 11

Let's take an example

Check if the following is divisible by 11.

i. 1859

Solution

1859 is divisible by 11 if and only if the alternating sum of its digit is divisible by 11. i.e if (1 - 8 + 5 - 9) is divisible by 11.

1 - 8 + 5 - 9 = -11.

Since -11 is divisible by 11 so is 1859

ii. 31415

Solution

31415 is divisible by 11 if and only if the alternating sum of its digit is divisible by 11. i.e if (3 - 1 + 4 - 1 + 5) is divisible by 11.

3 - 1 + 4 - 1 + 5 = 10.

Since 10 is not divisible by 11 so is 31415 not divisible.

Answer:

[tex]\huge\boxed{6 ( 3d + 2 )}[/tex]

Step-by-step explanation:

18d + 12

The greatest common factor is 6, So we need to factor out 6

=> 6 ( 3d + 2 ) [Distributive property has been applied and this is the simplest form]

Answer:

6(3d+2)

Step-by-step explanation:

6 is the gcd of the two terms.

Answer:

f of x

Or

f-function of x

Answer:

f(x) is pronounced in mathematics as if one were saying "f of x"

Answer:

73%

Step-by-step explanation:

Complete Question

Statistics professors believe the average number of headaches per semester for all students is more than 18. From a random sample of 15 students, the professors find the mean number of headaches is 19 and the standard deviation is 1.7. Assume the population distribution of number of headaches is normal.the correct conclusion at [tex]\alpha =0.001[/tex] is?

Answer:

There is no sufficient evidence to support the professor believe

Step-by-step explanation:

From the question we are told that

     The population mean is  [tex]\mu = 18[/tex]

     The sample size is  [tex]n = 15[/tex]

      The sample mean is  [tex]\= x = 19[/tex]

      The standard deviation is  [tex]\sigma = 1.7[/tex]

      The level of significance is  [tex]\alpha = 0.001[/tex]

The null hypothesis is  [tex]H_o: \mu = 18[/tex]

The  alternative hypothesis is  [tex]H_a : \mu > 18[/tex]

 The critical value of the level of significance from the normal distribution table is    

         [tex]Z_{\alpha } = 3.290527[/tex]

The test hypothesis is mathematically represented as

           [tex]t = \frac{\= x - \mu }{ \frac{\sigma}{ \sqrt{n} } }[/tex]

substituting values  

         [tex]t = \frac{ 19 - 18}{ \frac{1.7}{ \sqrt{15} } }[/tex]

         [tex]t = 2.28[/tex]

Looking at the value of  t and  [tex]Z_{\alpha }[/tex] we can see that [tex]t < Z_{\alpha }[/tex] so we fail to reject the null hypothesis.

This mean that there is no sufficient evidence to support the professor believe

Answer:

c=18

Step-by-step explanation:

5/30=3/c

1/6=3/18

1✖️3=3

6✖️3=18

Answer:

2 sqrt(41) = x

Step-by-step explanation:

This is a right triangle so we can use the Pythagorean theorem

a^2 + b^2 = c^2

8^2 + 10 ^2 = x^2

64+ 100 = x^2

164 = x^2

Take the square root of each side

sqrt(164) = sqrt(x^2)

sqrt(4) sqrt(41) = x

2 sqrt(41) = x

Answer:

3

Step-by-step explanation:

[tex]f(-1)g(-1) \text{ is the same thing as } f(-1)\cdot g(-1). \\\text{Therefore, find f(-1) and g(-1)}[/tex]

[tex]f(-1)=(-1)^2-4\\f(-1)=1-4\\f(-1)=-3[/tex]

[tex]g(-1)=3(-1)+2\\g(-1)=-3+2\\g(-1)=-1[/tex]

Therefore:

[tex]f(-1)\cdot g(-1)\\=(-3)(-1)=3[/tex]

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.

Answer:x ≤ 3

Step-by-step explanation:

Answer:

x ≥ -3

Step-by-step explanation:

x - 6 ≥ 15 + 8x

x - 8x ≥ 15 + 6

-7x ≥ 21

x ≥ 21/-7

x ≥ -3

x greater than equal to -3

check:

-3 - 6 ≥ 15 + 8*-3

-9 ≥ 15 - 24

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