what is 4³ writ
ten in expanded form?
​

The value of angle ∠DEC  = 60 degree.

The complete question is

In the given the figure above, m∠BAC = 64° and m∠CBA = 56°.

Part I: Find the m∠DEC.

Part II: Explain the steps you took to arrive at your answer. Make sure to justify your answer by identifying any theorems, postulates, or definitions used.

A triangle is a polygon with three sides and three vertices and three angles.

As it is given that

AB || CD

Let BC be the transversal , then

∠CBA = ∠DCB (alternate opposite angles)

∠DCB = 56 degree

As the sum of opposite interior angle sis equal to exterior angle therefore ∠ ECB = 120 degree

∠DCE = 120-56 = 64 degree

BC || DE

∠EDC = ∠DCB = 56 degree (alternate opposite angles)

Sum of all the interior angles of a triangle is equal to 180 degree

56 +64+∠DEC = 180

∠DEC  = 60 degree.

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The graph of the linear inequality 2x – 3y < 12 is given below. Then the correct option is A.

The missing options are given below.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality is given below.

2x – 3y < 12

Then the correct graph will be given below.

Then the correct option is A.

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Based on my experiences so far, the approach to geometry that I prefer is: Euclidean Geometry. This is because the problems are easy to visualize since they are restricted to two-dimensional planes.

The approach that is easier to extend beyond two dimensions is Euclidean Geometry. Again, this is because of how it deals with shapes and visualization of the same.

Take for instance a triangle; it is easy to go from a two-dimensional equilateral triangle  to a square pyramid.

Analytical geometry is a superior technique for discovering objects (points, curves, and planes) based on their qualities in some situations than Euclidean geometry is in others (for example, when employing topography or building charts).

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Answer:

(-5, -7) and the x-axis

Step-by-step explanation:

when looking for a point that is 7 points away, we are looking for a difference of 7 in either the x-value or the y-value.

[remember: a point is written as (x, y) ]

We know that the x-value is -7, meaning that it is 7 units under the x-axis (meaning that it is 7 units away)

We know that our point, (2 , -7) has the same y-value as (-5, -7), so we are looking for a change in x. The difference (which is the change) between:

-5 and 2 is 7

(2 - (-5) = 2 + 5 = 7)

so, both the x-axis and the point (-5, -7) are 7 units away from (2, -7)

(the other point (-7, 7) is not near (2 , -7) at all--they have a larger difference on both the y-values, the x-values, and the length of if you made a diagonal line)

(I've attached an image to help you visualize what we're doing)

hope this helps!!

Answer:

180

Step-by-step explanation:

Find the LCM of 12, 18, and 20

[tex]12 = 2 \times 2 \times 3[/tex]

[tex]18 = 2 \times 3 \times 3[/tex]

[tex]20 = 2 \times 2 \times 5[/tex]

LCM = 2 × 2 × 3 × 3 × 5 = 180

basically you treat y like a number and not a variable

Answer:

a is 4

b is 2y

c is -10y²+9

discriminant is 4(41y²-36)

Step-by-step explanation:

4x²+2xy-10y²+9=0

rewrite in standard form of a quadratic equation like ax² + bx + c = 0

4x²+2yx-10y²+9=0

basically you treat y like a number and not a variable

a is the number with the x²

right away we know a is 4 because of 4x²

b is the one with x so in this formula b is 2y

c is the number without the x which in this case is -10y²+9

discriminant is

b² - 4ac

(2y)²- (4)(4)(-10y²+9)

4y²-(16)(-10y²+9)

4y²-(16)(-10y²+9)

4y²+160y²-144

164y²-144 =

4(41y²-36)

For the function F(x)=[tex]a(x+k)^{1/n}+C[/tex] the value of a is less than zero and the correct option is option d.

Given the value of function  F(x)=[tex]a(x+k)^{1/n}+C[/tex].

We have to put the function equal to 0 for finding the nature of a and C is a fixed number in the function :

a[tex](x+k)^{1/n}[/tex]+C=0

a[tex](x+k)^{1/n}[/tex]=-C

a=-C/[tex](x+k)^{1/n}[/tex]

Since negative sign is coming before a and the value of rest of the expression cannot be negative so the value of a should b negative which means less than 0. The rest of the expression cannot be negative because it has a power of 1/n which only gives positive values like modulas.

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The graph of the parent absolute value function decreases over Option B(–∞, 0) interval.

An absolute value function is defined as a function that contains an algebraic expression within absolute value symbols.

The absolute value function is f(x) = |x| is defined as,

f(x )

x = x < x = 0 < x = -x

Observe that the graph is V-shaped.

The vertex of the graph is (0,0).

The domain is the set of all real numbers.

The x-intercept and the y-intercept are both 0.

Hence, The graph of the parent absolute value function decreases over Option B(–∞, 0) interval.

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Answer: [tex]\frac{5\pi}{3}[/tex]

Step-by-step explanation:

[tex]A=(\sqrt{20})^{2}(\pi)\left(\frac{30}{360} \right)=\boxed{\frac{5\pi}{3}}[/tex]

Answer:

a = -9

b = -3

c = 11

d = 19

Step-by-step explanation:

a. x = -2

y= x² + 3x + 1

y= -2²+ 3(-2)+1

y= -4-6+1

y = -9

b. x= -1

y= x² + 3x+ 1

y= -1² + 3(-1) +1

y= -1 -3 + 1

y = -3

c. x =2

y = x² + 3x +1

y= 2²+ 3(2) +1

y= 4 +6 +1

y = 11

d. x= 3

y = x² +3x +1

y = 3² +3(3) +1

y= 9 +9 +1

y = 19

N = 0

2(0)² + 4(0) = 0

0 + 0 = 0

Answer:

See below

Step-by-step explanation:

Area of a circle = pi * r^2

  for this circle  :    Area = 3.142 * 10 * 10 =  314.2 cm^2

The formula for area of a circle is [tex]\pi r^{2}[/tex]

So using pi as 3.142, we can do 3.142 • 100 which is 314.2 when moving place values.

Even though you did not ask, the circumference formula is 2[tex]\pi[/tex]r.

If we were given the same information, where the radius is 10, and we were solving circumference, then we would do 3.14 • 20 = 62.8.

Brainliest if helpful.

Answer:

50.24 mm^2

Step-by-step explanation:

The area of a circle is given by

A = pi r^2  where r is the radius

A = 3.14 ( 4)^2

   = 50.24 mm^2

Answer:

c. 50.24 square millimeters

Step-by-step explanation:

Radius of circle = 4 milimeters.

Area of a circle = πr²

Area = 3.14 × 4² (π = 3.14)

= 50.24 square millimeters

Answer: -1

Step-by-step explanation:

[tex]f(-1)=(-1)^2 - (-1)-1=1\\\\f(1)=1^{2}-1-1=-1\\\\\therefore \frac{f(-1)-f(1)}{-1-1}=\frac{1-(-1)}{-1-1}=\frac{2}{-2}=\boxed{-1}[/tex]

Step-by-step explanation:

please mark me as brainlest

Answer: 4.5

Step-by-step explanation:

[tex]\frac{6+3}{2}=\boxed{4.5}[/tex]

We want to find the median for the given density curve.

The value of the median is 4.5. ({3+6)/2}

Let's see how to solve this.

First, for a regular set {x₁, ..., xₙ} we define the median as the middle value.

The difference between a set and a density curve is that the density curve is continuous, so getting the exact middle value can be harder.

Here, we have a constant density curve that goes from 3 to 6.

Because it is constant, the median will just be equal to the mean, thus the median is the average between the two extreme values.

Remember that the average between two numbers a and b is given by:(a + b)/2

So we get: m = (6 + 3)/2 = 4.5

So we can conclude that the value of the median is 4.5, so the correct option is the second one, counting from the top.

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Answer:

A.

Step-by-step explanation:

let me know if you want an explanation :))

Answer:

A

Step-by-step explanation:

Part A:

The greatest common factor is 2k

2k(2ck + 5k - 8c - 20)

Part B:

factor by grouping

2k(k - 4)(2c + 5) is the final factored form

..................................

The fraction of the journey Sapna traveled by car and train is 3/8 and 5/8 respectively.

We know that fraction is an expression in mathematics used to denote the division of two whole numbers.

Given that the total distance = 48 km.

The distance Sapna traveled by car = 18 km.

So, the fraction is = distance traveled by car/total distance = 18/48 = 3/8

The distance Sapna traveled by train = 48 - 18 km = 30 km.

So, the fraction is = distance traveled by train/total distance = 30/48 = 5/8

Therefore the fraction of the journey Sapna traveled by car and train is 3/8 and 5/8 respectively.

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Answer:

x + 3y = 30

Step-by-step explanation:

We are given that a line contains the points (12,6) and (-3,11)​.

We want to write the equation of this line in standard form.

Standard form is written as ax+by=c, where a, b, and c are free integer coefficients, however a and b cannot be 0, and a cannot be negative.

Regardless, before we write an equation in slope-intercept form, we must first write the equation in a different form, such as slope-intercept form.

Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y-intercept.

So first, let's find the slope of the line.
The slope (m) can be found using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points.

Even though we already have 2 points, let's label their values to avoid any confusion and mistakes when calculating.

[tex]x_1=12\\y_1=6\\x_2=-3\\y_2=11[/tex]

Now substitute these values into the formula.

m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m=[tex]\frac{11-6}{-3-12}[/tex]

Subtract

m=[tex]\frac{5}{-15}[/tex]

Simplify

m=[tex]-\frac{1}{3}[/tex]

The slope is -1/3

Here is the equation of the line so far in slope-intercept form:

[tex]y=-\frac{1}{3} x + b[/tex]

We need to solve for b.

As the equation passes through (12,6) and (-3,11)​, we can use either one to help solve for b.

Taking (12, 6) for example:

[tex]6=-\frac{1}{3}(12) + b[/tex]

Multiply

[tex]6=-\frac{12}{3} + b[/tex]

Divide

6 = -4 + b

Add 4 to both sides.

10 = b

Substitute 10 as b in the equation.

[tex]y = -\frac{1}{3} x + 10[/tex]

Here is the equation in slope-intercept form, but remember, we want it in standard form.

In standard form, the values of both x and y are on the same side, so let's add -1/3x to both sides.

[tex]\frac{1}{3} x + y = 10[/tex]

Remember that a (the coefficient in front of x) has to be an integer, 1/3 is not an integer.

So, let's multiply both sides by 3 to clear the fraction.

[tex]3(\frac{1}{3} x + y) = 3(10)[/tex]
Multiply.

x + 3y = 30

Topic: finding the equation of the line (standard form)

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The proportion can be used to find the distance on the map (x) that represents 50 miles will be x/50 = 5 / 200. Then the correct option is A.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

The scale on a map shows that 200 miles is represented by 5 inches on a map.

Then the proportion can be used to find the distance on the map (x) that represents 50 miles will be

x/50 = 5 / 200

Then  the correct option is A.

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The simplified expression of [tex]\frac{x^3 + (-y)^3}{(x - y}[/tex] is [tex]x^2+xy+y^2[/tex]

Simplify the expression: (x³ + (-y)³) / (x - y)

Do not include parentheses in your answer.

The expression is given as:

[tex]\frac{x^3 + (-y)^3}{(x - y}[/tex]

Open the inner bracket

[tex]\frac{x^3 -y^3}{(x - y}[/tex]

Apply the difference of two cubes to the numerator

[tex]\frac{(x-y)(x^2+xy+y^2)}{(x - y}[/tex]

Cancel out the common factors

[tex]x^2+xy+y^2[/tex]

Hence, the simplified expression of [tex]\frac{x^3 + (-y)^3}{(x - y}[/tex] is [tex]x^2+xy+y^2[/tex]

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The allowable weights are 30 lbs and 40 lbs if the weight of the bag is 35 lbs option (d) is correct.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

We have:

Henry is working in a packed room. He is filling a bag with dry seasoning. The net weight of the bag is stated as 35

lbs. His tolerance is +/-5 lbs.

Weight of the bag = 35 lbs

Tolerance = ± 5 lbs

Allowable weights = 35 ± 5

= 35 + 5 = 40 lbs

= 35 - 5 = 30 lbs

Thus, the allowable weights are 30 lbs and 40 lbs if the weight of the bag is 35 lbs option (d) is correct.

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Answer:

93 boxes

Step-by-step explanation:

sixth row has 23 boxes

fifth row has 20 boxes

fourth row has 17 boxes

third row has 14 boxes

second row has 11 boxes

first row has 8 boxes

the total is thus 23+20+17+14+11+8=93

The factored form of the polynomial function is y(x) = (x + 3)²(x - 4)(x - 2)

The given parameters are:

Rewrite the zeros as:

x = -3, x = -3, x = 4 and x = 2

Set the zeros to 0

x + 3 = 0, x + 3 = 0, x - 4 = 0 and x - 2 = 0

Multiply the zeros

(x + 3) * (x + 3) * (x - 4) *(x - 2) = 0

Express as a function

y(x) = a(x + 3) * (x + 3) * (x - 4) *(x - 2)

Substitute 1 for a

y(x) = (x + 3)²(x - 4)(x - 2)

Hence, the factored form of the polynomial function is y(x) = (x + 3)²(x - 4)(x - 2)

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Answer:

the answer is 13.73 %

Answer:

The square root of 36 is a rational number. A rational number is a number that can be written as a fraction, a/b, where a and b are integers.

Answer:

Step-by-step explanation:

Hi, let me help you out.

The square root of 36 is 6.

6 belongs to the following subsets.

Overall, 6 belongs to 4 sub-sets.

__________________

Hope I helped! Best wishes.

___________________

Answer:

The cost of 1 taco = $4

The cost of 1 quesadilla = $7.50

Step-by-step explanation:

Let the cost of tacos be x and the cost of quesadillas be y.

x + 3y = 26.50 ------------------(1)

3x + y = 19.50 -------------------(2)

Multiply Eq. (2) by 3

3(3x + y) = 19.50 * 3

9x + 3y = 58.5 -----------------(3)

Subtract Eq. (3) from (1)

x + 3y - 9x - 3y = 26.50 - 58.50

x - 9x = -32

-8x = -32

8x = 32

Divide 8 to both sides

x = $4

Put x = 4 in (1)

4 + 3y = 26.50

Subtract 4 to both sides

3y = 26.50 - 4

3y = 22.50

Divide 3 to both sides

y = $7.50

So,

The cost of 1 taco = $4

The cost of 1 quesadilla = $7.50

[tex]\rule[225]{225}{2}[/tex]