What is the value of x?



Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.

x =

cm

A scalene triangle G E F. Side E F is labeled as x. Side E G is labeled as 13 centimeters. Angle E is labeled as 40 degrees. Angle G is labeled as 87 degrees.

[tex] 3 \ln 3 - \ln 9 = 3 \ln 3 - \ln 3 ^2 = 3 \ln 3 - 2 \ln 3 = \ln 3[/tex]

Answer: [tex]\ln 3[/tex]

Answer:

ln 3

Step-by-step explanation:

Using the rules of logarithms

• log [tex]x^{n}[/tex] ⇔ n logx

• log x - log y = log ([tex]\frac{x}{y}[/tex] )

Given

3 ln3 - ln9, then

= ln 3³ - ln 9

= ln 27 - ln 9

= ln ([tex]\frac{27}{9}[/tex] ) = ln 3

Answer:

6 hopes this helps

Step-by-step explanation:

The degree of the polynomial [tex]x^{6} + 4x - 3[/tex] is 6 .

The degree of a polynomial is the highest power of the variable in a polynomial expression. For any given polynomial function, the degree refers to the highest power of the dependent variable in the given polynomial.

For the given polynomial function, f(x) =  [tex]x^{6} + 4x - 3[/tex] , we have the dependent variable of the function as x .

Thus, degree of the given polynomial, refers to the highest power of x in the polynomial.

As the highest power of x is 6, thus the degree of the polynomial is also 6.

Therefore, the degree of the polynomial [tex]x^{6} + 4x - 3[/tex] is 6 .

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Answer:

x=5

Step-by-step explanation:

We can solve this using the Pythagorean theorem

[tex]13^2-12^2=x^2\\\\x=\sqrt{169-144} \\\\x=\sqrt{25} \\\\x=5[/tex]

It should be 5. You would need to use the Pythagorean theorem, a^2 + b^2 = c^2 to find the length of the missing side. So it would be x^2 + 144=169, which leads to 169-144 = 25. Then you would need to get the square root of 25, which is 5. I hope that helps.

Answer: B

Step-by-step explanation:

There are 4 quarts in a gallon. 12 / 4 = 3.

A contains 3 gallons. B contains 2 gallons. If you divide the price by the number of gallons, b will be cheaper.

Answer:

B.

Step-by-step explanation:

A quart is approximately 1/4 of a gallon. Therefore 8 quarts is 2 gallons. 8/12 is 2/3

2/3 of $44.04 is $29.36. Therefore A is more expensive and B is the better buy.

The answer is:

The domain for the function is:

Domain:(-∞,-3)∪(-3,∞)

Since we are working with fractions, the only restriction that we will have for the function is when the denominator of the function tends to 0.

We are given the function:

[tex]f(x)=\frac{x^3} +27}{x+3}[/tex]

We have two expressions:

The first expression (numerator) has no restriction, however, we can find a restriction at the second expression (denominator) because when a fraction has a denominator equal to 0, the function does not exist on the real numbers.

For the denominator, we have that it tends to 0 at:

[tex]x=-3[/tex]

So, the domain for the given function will be:

Domain:(-∞,-3)∪(-3,∞)

Hence, the answer is the second option, the domain for the function is:

Domain:(-∞,-3)∪(-3,∞)

Have a nice day!

The area of the rhombus with diagonals of 8m each is 32 square meters.

The area of a rhombus can be calculated using the formula:

Area = (diagonal1  diagonal2) / 2

Given that the diagonals of the rhombus are 8m and 8m, we can plug these values into the formula:

Area = (8  8) / 2

Area = 64 / 2

Area = 32 square meters

To explain the calculation step by step:

1. Identify the diagonals: In a rhombus, the diagonals are perpendicular bisectors of each other and they bisect each other at right angles. Here, both diagonals are 8m each.

2. Plug into the formula: Substitute the lengths of the diagonals into the formula for the area of a rhombus.

3. Calculate the product: Multiply the lengths of the diagonals together.

4. Divide by 2: Since the formula for the area of a rhombus involves dividing the product of the diagonals by 2, perform this division to find the final answer.

5. Final answer: The area of the rhombus is 32 square meters.

So, the area of the rhombus with diagonals of 8m each is 32 square meters.

Complete question:

Find the area of the rhombus.

8 m

8 m

8 m

8 m

Answer:

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

Step-by-step explanation:

perimeter of the rectangle = 2( length + width )

Answer:

The degree is zero

Step-by-step explanation:

we know that

The degree of a constant monomial is always zero

so

In this problem we have

-2

The number -2 represent a constant monomial

therefore

The degree is zero

Answer:

i)

-2

ii)

a0 = 5.5

a1 = -44

Step-by-step explanation:

i)

Given a geometric sequence, the common ratio is the ratio between any two adjacent values. In our case we have the following geometric sequence;

a0, -11, 22, a1, 88, -176

To find the common ratio we can simply divide 22 by -11 or divide -176 by 88;

common ratio = 22/(-11) = -2

ii)

To find a0, we use the common ratio;

(-11)/a0 = -2

a0 = (-11)/(-2)

a0 = 5.5

We do the same for a1;

88/a1 = -2

a1 = 88/(-2)

a1 = -44

Solve for x: (2x + 40)° = (3x - 85)°. The solution is x = 125.

To find the value of x, you can set the expressions for the angles equal to each other since the two lines are parallel and corresponding angles are equal.

The given angles are:

- Line p: [tex]\(2x + 40\)[/tex] degrees

- Line q: [tex]\(3x - 85\)[/tex] degrees

Set them equal to each other and solve for x:

[tex]\[ 2x + 40 = 3x - 85 \][/tex]

Combine like terms:

[tex]\[ 40 + 85 = 3x - 2x \][/tex]

[tex]\[ 125 = x \][/tex]

So, the value of x is 125 degrees.

The complete question is here:

if line p is (2x+40)°and line q is (3x-85) what is the value of x​

The value of ( x ) is [tex]\( 125^\circ \)[/tex].

To find the value of ( x ), we can use the properties of parallel lines cut by a transversal. When two parallel lines are cut by a transversal, alternate interior angles are congruent.

Given:

- Angle [tex]\( 2x + 40^\circ \) and angle \( 3x - 85^\circ \)[/tex] are alternate interior angles.

So, we can set up an equation:

[tex]\[ 2x + 40^\circ = 3x - 85^\circ \][/tex]

Let's solve for ( x ):

[tex]\[ 2x - 3x = -85^\circ - 40^\circ \][/tex]

[tex]\[ -x = -125^\circ \][/tex]

To isolate ( x ), we divide both sides by -1:

[tex]\[ x = \frac{-125^\circ}{-1} \][/tex]

[tex]\[ x = 125^\circ \][/tex]

So, the value of ( x ) is [tex]\( 125^\circ \)[/tex].

complete question given below:

In the diagram, parallel lines P and Q are cut by transversal R.

(2x + 40°

(3x - 85)°

What is the value of x?

15/x = 9/4

9x = 60

x = 60/9 = 20/3 = 6.6666

Answer:

20/3

Step-by-step explanation:

9/4=15/x

cross multiply and get:

9x=15x4

9x=60

divide both sides by 9 so

x=60/9 which when reduced is equal to 20/3

Answer:

The area of triangle D'E'F' is four times the area of triangle DEF.

Answer:

first things first which one is angle B. if would be easier if you labeled them .

Step-by-step explanation:

but any ways see if the image attached can help out

Answer:

b

Step-by-step explanation:

Answer:

The answer is $9669.65 ≈ $9670.

Step-by-step explanation:

The formula to be used is :

[tex]A=P(1+r)^{nt}[/tex]

For first part :

p = 7800

r = [tex]5.2/100/12=0.00433[/tex]

t = 5

[tex]A=7800(1.00433)^{5}[/tex]

A = $7970.04

For second part:

p = 7970.04

r = [tex]33.6/100/12=0.028[/tex]

t = 7

[tex]A=7970.04(1.028)^{7}[/tex]

A = $9669.65

So, the answer is $9669.65 ≈ $9670.

Answer:

A) 47

B) 65

C) 01

Step-by-step explanation:

A stem and Leaf is a unique way of representing data, in which every data value is split into a “stem” and “a leaf” . The “Stem” is the first Digit of the number and The “Leaf” is the second digit of the data value.

As we seen in the Key provided to us at the foot of the page, 6│3 represent 63,also

6│0 3 4 represents : 60,63,64

0│1 5 8 represents : 01,05,08

Using this rule we expands the data given to us and answer the questions given to us.

A) Number of people represented in data

0│1 1 2 2 3 4 4 4 4 5 8 = 01 01 02 02 03 04 04 04 04 05 08 = 11 Entries

In the same way , we count the other data and see that

Total number of data values are : 11+8+8+9+4+5+2= 47

B) The range of the Data: It the Difference of the largest Data value and the Lowest Data Value

Largest Data Value : 66

Smallest Data Value : 01

Range = 66-01 = 65

C) The mode : It the Data value which is repeated the most:

01 : 4 times

10 : 3 times

31 : 3 times

32 : 3 times

Hence the mode is 01

0.95c

100% minus 5% is 95%, or 0.95. This means Sally only has to pay 0.95 times the grocery bill, or c, which represents 0.95c.

the correct answer would be 16 you add (2+2) first and the do 8/2 then multiple 4 x 4 and you get 16

[tex]\bf 8\div 2(2+2)\implies 8\div 2(\stackrel{\downarrow }{4})\implies \stackrel{\downarrow }{4}(4)\implies 16[/tex]

recall PEMDAS

Parentheses first off

MD multiplication and division from left-to-right.

ANSWER

C. 35 men

EXPLANATION

Let m represent the number of men needed and d represent the number of days.

From the question,the number of men needed varies inversely to the time needed to complete the project.

We can write the inverse variation equation.

[tex]m = \frac{k}{d} [/tex]

where k is the constant of variation.

When m=28, d =90.

We substitute these values into the variation equation to determine the value of k.

[tex]28 = \frac{k}{90} [/tex]

[tex]k = 90 \times 28[/tex]

[tex]k = 252[/tex]

Now the equation becomes:

[tex]m= \frac{2520}{d} [/tex]

When d=72,

[tex]m = \frac{2520}{72} [/tex]

[tex]m = 35[/tex]

Therefore he needs to have 35 men working.

Answer:

The number of messages sent by Justin was [tex]180\ messages[/tex]

The number of messages sent by David was [tex]270\ messages[/tex]

Step-by-step explanation:

Let

x-----> number of messages sent by Justin

y----> number of messages sent by David

we know that

[tex]\frac{x}{y}=\frac{8}{12}[/tex]

[tex]x=\frac{8}{12}y[/tex] ----> equation A

[tex]x+y=450[/tex] -----> equation B

substitute equation A in equation B and solve for y

[tex]\frac{8}{12}y+y=450[/tex]

[tex]\frac{20}{12}y=450[/tex]

[tex]y=450*12/20=270\ messages[/tex]

Find the value of x

[tex]x=\frac{8}{12}(270)=180\ messages[/tex]

therefore

The number of messages sent by Justin was [tex]180\ messages[/tex]

The number of messages sent by David was [tex]270\ messages[/tex]

Answer:

5

Step-by-step explanation:

Evaluate (5 x)/8 + 10 where x = -8:

(5 x)/8 + 10 = 10 - 8×5/8

5/8 (-8) = (5 (-8))/8:

(-8×5)/8 + 10

(-8)/8 = (8 (-1))/8 = -1:

5×-1 + 10

10 - 5 = 5:

Answer: 5

Answer:

Step-by-step explanation:

Part A: Company A charges $6 for a window and $12 for a service clean. If you add that up it would be 6 + 12 =18 so company A would be making $18 per customer. Company B charges $15 + $5 for a whole cleaning which would make them $20 per customer. That is better then $18 so business B would be making more money.

Part B: For cleaning 8 windows company B would charge less because 8 x 5 = $40 for all the windows and company A would be charging $6 for a window which is more so 8 x 6 = 48. Company B charges less.

Part C: Company B charges 5 dollars for thier services on windows as Company A charges 6. You would be saving a dollar by buying at company B.

The expression 5x + 5 ( x-3y ) + 1/2 (4x - 6y) simplifies to 12x - 18y by distributing the multiplication over addition, combining like terms, and checking the answer for reasonableness.

To simplify the algebraic expression 5x + 5 ( x-3y ) + ½ (4x - 6y), let's start by distributing the multiplication over addition for each term inside the parentheses:

Multiply 5 by each term inside the first set of parentheses: 5 × x and 5 × (-3y), which gives us 5x - 15y.

Multiply ½ by each term inside the second set of parentheses: ½ × 4x and ½ × (-6y), resulting in 2x - 3y.

Now, combine the like terms:

The x-terms: 5x + 5x + 2x = 12x.

The y-terms: -15y - 3y = -18y.

So, the expression in standard form is 12x - 18y.

Lastly, we should check the answer to see if it is reasonable:

No like terms are left to combine.

The coefficients are summed up correctly.

The expression is simplified as much as possible.

the only equation that seems to describe the pattern is:

[tex]\( b = a - 5 \)[/tex]. Therefore, option C is correct

To determine whether the given equations can describe the pattern in the table, we need to look at the values in the table and see if they satisfy the equations. However, the provided image is not completely clear, and it seems like part of the table or the values might be missing.

From what is visible in the image, it seems we have a table with two columns labeled 'a' and 'b', with 'a' taking on values from 5 to 9 and 'b' from 0 to 4. We need to check if the equations given describe the relationship between 'a' and 'b' according to the table.

The equations given are:

1. [tex]\( b + a = 5 \)[/tex]

2. [tex]\( b = a + 5 \)[/tex]

3. [tex]\( b = a - 5 \)[/tex]

4. [tex]\( a = b - 5 \)[/tex]

Without the complete table, we can't perform a full analysis, but we can explain how you would generally approach this:

- For equation 1 [tex](\( b + a = 5 \))[/tex], check if the sum of each pair of 'a' and 'b' equals 5.

- For equation 2 [tex](\( b = a + 5 \))[/tex], check if 'b' is always 5 more than 'a'.

- For equation 3 [tex](\( b = a - 5 \))[/tex], check if 'b' is always 'a' minus 5.

- For equation 4 [tex](\( a = b - 5 \))[/tex], check if 'a' is always 'b' minus 5.

Given the values for 'a' and 'b' in the table:

a | 5 | 6 | 7 | 8 | 9

b | 0 | 1 | 2 | 3 | 4

We can analyze each equation to see if it describes the pattern in the table.

1. [tex]\( b + a = 5 \)[/tex]

Let's check if the sum of 'a' and 'b' equals 5 for each pair:

- For [tex]\( a = 5 \), \( b = 0 \): \( 5 + 0 = 5 \)[/tex] (True)

- For [tex]\( a = 6 \), \( b = 1 \): \( 6 + 1 = 7 \)[/tex] (False)

- Since it is false for [tex]\( a = 6 \), \( b = 1 \)[/tex], we can already conclude that this equation does not describe the pattern.

2. [tex]\( b = a + 5 \)[/tex]

Let's check if 'b' equals 'a' plus 5:

- For [tex]\( a = 5 \), \( b = 0 \): \( 5 + 5 = 10 \)[/tex] (False)

- Since it is false for [tex]\( a = 5 \), \( b = 0 \)[/tex], this equation does not describe the pattern.

3. [tex]\( b = a - 5 \)[/tex]

Let's check if 'b' equals 'a' minus 5:

- For [tex]\( a = 5 \), \( b = 0 \): \( 5 - 5 = 0 \)[/tex] (True)

- For [tex]\( a = 6 \), \( b = 1 \): \( 6 - 5 = 1 \)[/tex] (True)

- Continuing this pattern, this equation seems to be true for all given pairs of 'a' and 'b'.

4. [tex]\( a = b - 5 \)[/tex]

This is not likely to be true since subtracting 5 from 'b' would result in negative numbers, which are not present in the 'a' values.

From the analysis, the only equation that seems to describe the pattern is:

[tex]\( b = a - 5 \)[/tex]

Let's confirm that this equation is true for all pairs of 'a' and 'b'.

The equation [tex]\( b = a - 5 \)[/tex] holds true for all pairs of 'a' and 'b' values in the table. Therefore, this equation correctly describes the pattern in the table.

The answer would be A

The solution of ⁶P₂ would be,

⇒ ⁶P₂ = 30

We have to given that,

An expression to solve,

⇒ ⁶P₂

Now, By definition of permutation, we get;

⇒ ⁶P₂

⇒ 6! / (6 - 2)!

⇒ 6! / 4!

⇒ 6 × 5

⇒ 30

Therefore, The solution of ⁶P₂ would be,

⇒ ⁶P₂ = 30

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17 and -17. The opposite of a number is usually the negative or positive version of that #

Answer:

I think its D

Step-by-step explanation:

Forgive me if im wrong.

The following system of equations has only one solution, which is (2,0), because you can use the method of substitution to find the value of x and if it has multiple solutions.

y = x - 2

y = - x + 2

x - 2 = - x + 2

2x = 4

x = 2 (substituting this back into the equation)

y = 2 - 2

y = 0

Answer:

Probability the first is a communications major and the second is a business major = 0.03

Step-by-step explanation:

let the total number of students be 100

Event A= Business Majors = 15%

Event B = Communication Majors = 20%

P(A) = [tex]\frac{15}{100}[/tex]   ⇒  P(A) = 0.15

P(B) = [tex]\frac{20}{100}[/tex]  ⇒ P(B) = 0.2

P( A and B) = P(A) × P(B)

                  = 0.15 × 0.2

                  = 0.03                      

Answer:

3*3*3=27

The answer is B 1 1/27

Step-by-step explanation:

As a formula:  

volume = s3  

where:

s  is the length of any edge of the cube.

Read as "s to the power 3"

The answer is d

[tex]x = \sqrt{{20}^{2}-{7}^{2}} [/tex]

The expression x = √(20² - 7²) can be used to determine the side length of side AC option (d) is correct.

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

We have:

Triangle ABC is a right triangle with sides shown in the figure.

From the Pythagoras theorem:

20² = 7² + x²

x² = 20² - 7²

x = √(20² - 7²)

Thus, the expression x = √(20² - 7²) can be used to determine the side length of side AC option (d) is correct.

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