The length of DE is ? and m angle cab is blank degrees

Answer: C

Step-by-step explanation:

12/4=3

16/4=4

3*8=24

4*8=32

To simplify 12/16 to lowest terms, we can divide both the numerator and denominator by their greatest common factor, which is 4:

12/16 = 3/4

Now we need to find an equivalent fraction with a denominator of 32. To do this, we can multiply both the numerator and denominator of 3/4 by 8:

3/4 = (38)/(48) = 24/32

So the answer is C. 3/4, 24/32.

\(\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &19\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=minutes\dotfill &13\\ \end{cases} \\\\\\ A = 19(1 - 0.05)^{13} \implies A = 19( 0.95 )^{13}\implies A \approx 9.75\)

Answer:

110

Step-by-step explanation:

10×8=80

14-8=6

6×10/2=30

80+30=110

The equations that has the solution x = all real numbers is 5(3x)+ 7x = 3x + 15 - x and 5(3x) + 7x = 3x + 10 - x,

Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.

A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.

Here given equations,

5(3x) + 6x = 3x + 15 + 2x

15x + 6x = 3x + 15 + 2x

15 x + 6x - 3x -2x = 15

16 x = 15

x = 15/16

5(3x).+ 7x = 3x + 15 - x

15 x + 7x = 3x + 15 - x

15 x + 7x - 3x + x = 15

22x - 3x + x = 15

20 x = 15

x = 15/20

x = 3/4

5(3x) + 7x = 3x + 10 - x

15x + 7x - 3x + x = 10

20x = 10

x = 10/20

x = 1/2

5(3x) + 7x = x + 15 - 3x

15x +7x - x + 3x = 15

24x = 15

x = 15/24

x = 5/8

Therefore the equations that has the solution x = all real numbers are :

5(3x).+ 7x = 3x + 15 - x and 5(3x) + 7x = 3x + 10 - x .

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1.57 meters of barbed wire are needed to fence the circular piece of land with a radius of 25 cm.

We have,

To calculate the amount of barbed wire needed to fence the circular piece of land, we need to find the circumference of the circle.

Given:

Radius (r) = 25 cm

The formula for the circumference (C) of a circle is:

C = 2πr

Substituting the given radius into the formula, we have:

C = 2π x 25 cm

Now, we can calculate the circumference in centimeters.

C = 2 x 3.14 x 25 cm

C ≈ 157 cm

Now,

To convert centimeters to meters, we divide the circumference by 100.

C (in meters) = 157 cm / 100

C (in meters) ≈ 1.57 meters

Therefore,

Approximately 1.57 meters of barbed wire are needed to fence the circular piece of land with a radius of 25 cm.

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The complete question.

A circular piece of land with a radius of 25 cm is going to be fenced. How many meters of barbed wire are needed?

Answer:

its x=1/3 :)))

Answer:

A. 64,80,100,125, 625/4

Explanation:

Given a geometric sequence with the following:

• First term, a1 = 64

• Common ratio, r = 5/4

We want to determine the first five terms of the sequence.

The nth term of a geometric sequence is calculated using the formula below:

Thus, the 2nd to 5th terms are calculated below.

Therefore, the first five terms of the geometric sequence are:

Option A is correct.

Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

The Operating income is $172,500.

To calculate the margin of safety, contribution margin ratio, and operating income, we need to use the given information.

a. Margin of Safety:

Margin of Safety = Actual Sales - Break-even Sales

Given that the break-even point is at $750,000 in sales revenue and actual sales are $1,100,000, we can calculate the margin of safety:

Margin of Safety = $1,100,000 - $750,000 = $350,000

Therefore, the margin of safety is $350,000.

b. Margin of Safety as a Percentage of Sales:

Margin of Safety Percentage = (Margin of Safety / Actual Sales) * 100

Using the values from the previous calculations:

Margin of Safety Percentage = ($350,000 / $1,100,000) * 100 = 31.82%

Therefore, the margin of safety expressed as a percentage of sales is approximately 31.82%.

c. Contribution Margin Ratio:

Contribution Margin Ratio = (Contribution Margin / Sales) * 100

To calculate the contribution margin, we need to subtract variable costs from sales:

Contribution Margin = Sales - Variable Costs = $1,100,000 - $645,000 = $455,000

Using the values, we can calculate the contribution margin ratio:

Contribution Margin Ratio = ($455,000 / $1,100,000) * 100 = 41.36%

Therefore, the contribution margin ratio is approximately 41.36%.

d. Operating Income:

Operating Income = Sales - Variable Costs - Fixed Costs

Using the values provided:

Operating Income = $1,100,000 - $645,000 - $282,500 = $172,500

Therefore, the operating income is $172,500.

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The sentence that best describes the paragraph is: "The pirates didn't believe Caesar would kill them because he was their prisoner." So, the correct option is c) Pirates didn’t believe Caesar will kill them because he was their prisoner.

The paragraph recounts the events of Caesar's kidnapping by pirates while crossing the Aegean Sea. Despite being held captive, Caesar maintained an attitude of superiority. The pirates demanded a ransom of 20 talents of silver, but Caesar insisted they ask for 50. This indicates that Caesar saw himself as more valuable than the initial ransom amount suggested by the pirates.

After the ransom was paid, Caesar did not forget the pirates' actions. He raised a fleet, pursued the pirates, and captured them. The sentence implies that the pirates didn't believe Caesar would actually kill them because he was their prisoner and they likely saw his promises as mere jest.

However, Caesar, true to his word, had the pirates crucified on his own authority.

This sequence of events highlights Caesar's determination, strategic thinking, and his ability to command respect even in dire circumstances. Despite being initially taken prisoner, he managed to turn the tables on the pirates, assert his authority, and exact his revenge. So, the correct option is c) Pirates didn’t believe Caesar will kill them because he was their prisoner.

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The values are;

Length = 6 inches

Width = 14 inches

The formula for determining the perimeter of a rectangle is expressed as

P = 2( l + w)

Where;

From the information given, we have;

Length = x

Width = 2(x + 1) = 2x + 2

Now, substitute the values

40 = 2( x + 2x + 2)

expand the bracket

40 = 2(3x + 2)

40 = 6x + 4

collect like terms

6x = 40 - 4

6x = 36

x = 36/6

Divide the values

x = 6 inches

Length = 6 inches

Width = 2( 6 + 1) = 2(7) = 14 inches

Hence, the values are 6 and 14 inches

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The values are;

Length = 6 inches

Width = 14 inches

How to determine the values

The formula for determining the perimeter of a rectangle is expressed as

P = 2( l + w)

Where;

P is the perimeter

l is the length

w is the width

From the information given, we have;

Length = x

Width = 2(x + 1) = 2x + 2

Now, substitute the values

40 = 2( x + 2x + 2)

expand the bracket

40 = 2(3x + 2)

40 = 6x + 4

collect like terms

6x = 40 - 4

6x = 36

x = 36/6

Divide the values

x = 6 inches

Length = 6 inches

Width = 2( 6 + 1) = 2(7) = 14 inches

Hence, the values are 6 and 14 inches

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Juliet will earn the same amount of money whether she chooses a monthly salary of ​$1900 from the company or a base salary of ​$1800 plus a ​5% commission on furniture sales if her sales amount to $2000.

To find the amount of sales for which the two salary choices are equal, we set the equation for the base salary plus commission equal to the equation for the flat monthly salary. The equation can be written as:

1800 + 0.05x = 1900

where x is the amount of furniture sales in dollars.

Simplifying and solving for x, we get:

0.05x = 100

x = 2000

If she sells less than $2000 of furniture, she will earn more with the flat monthly salary of $1900. If she sells more than $2000 of furniture, she will earn more with the base salary plus commission. This calculation provides an important decision-making tool for Juliet, as she can tailor her salary choice based on her expected sales for the month.

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Using the normal distribution, the area underneath the shaded region between the two z-scores is given by:

C. 0.6766.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

Hence, for this problem, the area is the p-value of z = 0.75 subtracted by the p-value of z = -1.3.

Looking at the z-table, the p-values are given as follows:

Then:

0.7734 - 0.0968 = 0.6766.

Which means that option C is correct.

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The functions g(x) = x² - 4x + 3 and f(x) = x² - 4x are:

The functions have the same range.

The functions have the same domain.

The functions have the same x-intercepts.

Let's analyze the given functions g(x) = x² - 4x + 3 and f(x) = x² - 4x and determine which statements about them are true.

Here are the options:

The functions have the same graph.

The functions have the same range.

The functions have the same domain.

The functions have the same vertex.

The functions have the same y-intercept.

The functions have the same x-intercepts.

The functions have the same graph:

This statement is false. While both functions are quadratic functions, their additional terms make them different. g(x) has an additional constant term (+3) compared to f(x).

Their graphs will be different, with g(x) being shifted upward by 3 units compared to f(x).

The functions have the same range:

This statement is true.

Both functions are quadratic functions, and their range will be the same. The range of a quadratic function is either all real numbers (if the parabola opens upward) or the set of real numbers greater than or equal to (or less than or equal to) the vertex of the parabola.

The functions have the same domain:

This statement is true.

The domain of both functions, unless restricted by any other factors, is all real numbers.

Quadratic functions have a domain of (-∞, ∞).

The functions have the same vertex:

This statement is false.

The vertex of a quadratic function is determined by the values of "a," "b," and "c" in the general form of the quadratic function (ax^2 + bx + c).

Since g(x) has an additional constant term, its vertex will be different from the vertex of f(x).

The functions have the same y-intercept:

This statement is false.

The y-intercept of a function is the value of y when x = 0.

For f(x), when x = 0, we have f(0) = (0)² - 4(0) = 0.

For g(x), when x = 0, we have g(0) = (0)² - 4(0) + 3

= 3.

Their y-intercepts are different.

The functions have the same x-intercepts:

This statement is true.

To find the x-intercepts of both functions, we set y (or f(x) and g(x)) equal to zero and solve for x.

The quadratic equation x² - 4x + 3 = 0 can be factored as (x - 1)(x - 3) = 0, giving x = 1 and x = 3 as the x-intercepts.

Both functions have the same x-intercepts.

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The matching expressions are:

\(i) 3a x 4 = C (12a)\\ii) a^2 x a = A (a^3)\\iii) 6 × 1/2 a^2 = D (3a^2)\)

i) 3a x 4 can be represented as C (12a) since multiplying 3a by 4 gives 12a.

ii) a^2 x a can be represented as A (a^3) since multiplying a^2 by a gives a^3.

iii) \(6 \times 1/2 a^2\) can be represented as D (3a^2) since multiplying 6 by 1/2 and then by a^2 gives 3a^2.

To understand the matching expressions, let's break down each one:

i) 3a x 4:

This expression represents multiplying a variable, 'a', by a constant, 4. The result is 12a, which matches with C (12a).

ii) a^2 x a:

This expression represents multiplying the square of a variable, 'a', by 'a' itself. This results in a^3, which matches with A (a^3).

iii) 6 × 1/2 a^2:

This expression involves multiplying a constant, 6, by a fraction, 1/2, and then multiplying it by the square of 'a', a^2. The final result is 3a^2, which matches with D (3a^2).

Therefore, the matching expressions are:

i) 3a x 4 = C (12a)

ii) a^2 x a = A (a^3)

iii) 6 × 1/2 a^2 = D (3a^2)

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Answer:

15/4 +6y

Step-by-step explanation:

See Image below:)

Answer:

x = 45

Step-by-step explanation:

the sum of the angles round a point is 360°

sum the angles and equate to 360

3x + 2x + x + 2x = 360

8x = 360 ( divide both sides by 8 )

x = 45

The strand of straight hair would be most accurately classified as a ray.

The definition of ray in math is that it is a part of a line that has a fixed starting point but no endpoint.

Given is the strand of straight hair.

Considering the strand of hair to be straight. We can call it as a ray as ray originates from one point and extends away from that point towards infinity.

Therefore, the strand of straight hair would be most accurately classified as a ray.

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Answer:

x = 15

Step-by-step explanation:

3x+1+4x-3 = 103

7x = 105

x = 15

Answer:

See the answers below

Step-by-step explanation:

Name two characteristics of the Fibonacci Series that you observed. ​

If we take a closer look at the Fibonacci series, we will notice the following characteristics

1.The next number is the sum of the two preceding numbers

2. Another interesting characteristic is evidenced in the convergence of the sequence

Answer:

x = -1,375

y = -5

Step-by-step explanation:

{-8x + y = 6, / : (-1)

{-8x + 3y = -14;

Multiply the first equation by -1, so that we could eliminate 8x:

+ {8x - y = -6,

{-8x + 3y = -14;

----------------------

4y = - 20 / : 4

y = -5

Now, make x the subject from the first equation (you can do it from the 2nd one instead):

8x = -6 + y / : 8

x = -0,75 + 0,125y

x = -0,75 + 0,125 × (-5) = -0,75 - 0,625 = -1,375

Answer:

for y = - (x-1)^2 + 1 its B the second graph

Step-by-step explanation:

find the vertex

y = -x^2 + 2x

its (1,1)

and x is negative so it must be that one.

On the coordinate plane, the parabola opens down, it goes through (0, 0), has a vertex at (1, 1), and goes through (2, 0).

A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point and from a fixed straight line.

According to the given problem,

y = - ( x - 1 )² + 1 is in the form of y = ( x - h )² + k where, (h , k) is the vertex of the parabola which is ( 1 , 1) as h = 1

                                                       k = 1

Now, after plotting the graph we can find out that the parabola passes through ( 2 , 0 ) and the minus sign indicates a parabola that opens down.

Hence, the parabola has a vertex at (1 , 1), goes through (0 , 0) and (2 , 0).

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Answer:112

Step-by-step explanation:multiply and divide for your answer

Answer:

|-5|

Step-by-step explanation:

I hope this helps!

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation: