Given: ​△ACE,BD¯¯¯¯¯∥AE¯¯¯¯¯​

Prove: BACB=DECD

A triangle with vertices labeled as A, C, and E, and base A E. Sides C A and C E contain midpoints B and D, respectively. A line segment parallel to base A E is drawn from point B to D. Angle C A E is labeled as 4 and angle C E A is labeled as 3. Angle C B D is labeled as 1 and angle C D B is labeled as 2.

Question
Drag an expression or phrase to each box to complete the proof.

The minimum value of the objective function is -15, which occurs at the corner point (0, 5).

The corner points of a linear programming problem are the points where the constraints intersect. These points can be found by solving the system of inequalities for each pair of constraints.

For this problem, we can find the corner points by solving the system of inequalities for each pair of constraints:

3x – y >= 2 and x + y <= 5:
- Add y to both sides of the first inequality: 3x >= 2 + y
- Subtract 2 from both sides of the first inequality: 3x - 2 >= y
- Substitute 3x - 2 for y in the second inequality: x + (3x - 2) <= 5
- Simplify: 4x <= 7
- Divide by 4: x <= 7/4
- Substitute 7/4 for x in the first inequality: 3(7/4) - 2 >= y
- Simplify: 5/4 >= y

The first corner point is (7/4, 5/4).

3x – y >= 2 and x >= 0:
- Set x = 0 and solve for y: 3(0) - y >= 2, y <= -2
- Set y = 0 and solve for x: 3x - 0 >= 2, x >= 2/3

The second corner point is (2/3, 0).

x + y <= 5 and x >= 0:
- Set x = 0 and solve for y: 0 + y <= 5, y <= 5
- Set y = 0 and solve for x: x + 0 <= 5, x <= 5

The third corner point is (0, 5).

x + y <= 5 and y >= 0:
- Set x = 0 and solve for y: 0 + y <= 5, y <= 5
- Set y = 0 and solve for x: x + 0 <= 5, x <= 5

The fourth corner point is (5, 0).

Now we can plug each corner point into the objective function to find the minimum value:

C = 3x – 3y

C = 3(7/4) - 3(5/4) = 3
C = 3(2/3) - 3(0) = 2
C = 3(0) - 3(5) = -15
C = 3(5) - 3(0) = 15

Therefore, the solution to the linear programming problem is (0, 5).

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The notation f(x) means:
- the value of the function at the number x
- f of x

These two options are the correct ones. The notation f(x) typically refers to a mathematical function named "f" that takes an input value "x" and returns an output value. The function f maps the input value x to a unique output value f(x). The symbol "f" is often used to represent a generic function, and the variable inside the parentheses, "x", represents the argument or input value of the function.

For example, if we have the function f(x) = x + 2, then f(3) = 3 + 2 = 5. This means that when we input the number 3 into the function, the output is 5.

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Answer:

angle 1 will be 32

angle 2 will be 2

hope it helps u mark me BRAINLIST

The requried measure of the angle x in at the point of intersection of tangent and secant of the circle is 30°.

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by

(x - h)² + (y - k)² = r²

Where h, k is the coordinate of the center of the circle on a coordinate plane and r is the radius of the circle.

Here,
From the figure the,
From a point, a tangent and a secant are drawn to the circle.
Since an equilateral triangle is formed with the help of a cord intersects the tangent and secant on the circumference of triangle.

Again from the figure, the sum of the angle in the triangle is equal to 180°.
90 - 60 + 180 - 60 + x = 180
30 + 120 + x = 180
x = 30°

Thus, the requried measure of the angle x at the point of intersection of tangent and secant of the circle is 30°.

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Therefore , the solution of the given problem of triangle comes out to be NL =  √(100 + 20LM2) * 10 * 4 .

A triangular is a polygon because it has 2 different or more additional parts. It has a straightforward rectangle form. Only the sides A, B, and C can differentiate a triangle from a parallelogram. When the sides are not exactly collinear, Euclidean geometry results in a singular surface rather than a cube. If a shape has three edges and three angles, it is said to be triangular. The intersection of a quadrilateral's three edges is known as an angle. The sum of a triangle's edges is 180 degrees.

Here,

By removing NP:, we can resolve this system of equations.

NL Equals NP(LM + NL + 5). (5 - LM)

NL = NP(LM - PQ + 5) (LM)

NL(5 - LM) = NP(LM + NL + 5)(LM - PQ + 5) (LM)

By enlarging and condensing, we obtain:

NP = 2NL Plus LM / 5LM

Now that we know this, we can put it into one of the equations to find NL:

(2NL Plus LM / 5LM)

NL = (LM Plus NL + 5) (5 - LM)

By condensing and rearrangeing, we obtain:

(2NL Plus LM) = 0 when (NL2 - 10NL - 5LM2)

The quadratic algorithm yields:

NL =  √(100 + 20LM2) * 10 * 4 alternatively,

=> NL = (10 -  √(100 + 20LM2)) / 4

NL can never be negative, so we pick the positive root:

NL =  √(100 + 20LM2) * 10 * 4

Now that we have this, we can put it into one of the equations to find NP:

NP = 2NL Plus LM / 5LM

NP = 5LM / (2(10 + √100 + 20LM^2)) / 4 + LM)

NP is equal to 5LM / (5 +  √(25 + 5LM2)).

The widths of NP and NL are as follows:

NP is equal to 5LM / (5 + sqrt(25 + 5LM2)).

NL = (10 -  √(100 + 20LM2)) / 4

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When 1 is put in the box, it generates an equation that is equal to 2 - 5. The expressions |-3 -2|, |2-(-3)|, |-3 + (-2)|, |-3 - (-2)|, etc., represent the distance between the two points  integers on number line.

A number line is used to display integers. A number line is a graphic representation of a straight line of numbers. It consists of positive and negative integers such as 1, 2, and so forth, as well as a zero that is neither positive nor negative.

Part A:

2 - 5 = -3

2 + 1 = 3

The absolute value of a number is the distance on the number line between that number and 0.

That distance is always positive.

b. The absolute value symbol is " | | ".

Part B: |-3 -2| = 1

On the number line, this point represents the distance of one unit from -3 to -2.

|2-(-3)| = 5

On the number line, this point represents the distance of 5 units between 2 and -3.

|-3 + (-2)| = 5

The 5 units at this point on the number line reflect the distance from -3 to -2.

|-3 - (-2)| = 1

On the number line, this point represents the distance of one unit between -3 and -2.

It's a good idea to have a backup plan in place in case something goes wrong. The expressions |-3 -2|, |2-(-3)|, |-3 + (-2)|, |-3 - (-2)|, etc., represent the distance between the two points on the number line.

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4(3)(2)/2 + 2² = 12 + 4 = 16

The number of students who voted for each mascot is given as follows:

Then the difference is given as follows:

nT - nC.

The difference between the two amounts is obtained applying the proportions in the context of the problem.

The circle graph gives the percentage of each type of vote.

Hence the amounts relative to each type of vote are given as follows:

In which:

The problem is incomplete, hence the general procedure is given to solve the problem.

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Answer:

D

Step-by-step explanation:

Answer:

The outputs are in order:

5

2

1

2

5

Answer:

5.2.1.2.5

Step-by-step explanation:

The equation for the given tangent function is f(x) = 3 tan(x - π/2) - 1.

What is Trigonometric function ?

Trigonometric functions are mathematical functions that relate to angles of a right-angled triangle. The three most common trigonometric functions are sine, cosine, and tangent, which are denoted by sin, cos, and tan, respectively.

The general form of a tangent function is given by:

f(x) = A tan(B(x - C)) + D

where A is the amplitude, B is the frequency (inverse of the period), C is the horizontal shift, and D is the vertical shift.

Given the information, we have:

A = 3

period = π

frequency = 1/period = 1/π

horizontal shift = π/2 to the right

vertical shift = down 1

So, we can plug in the values into the general form and get:

f(x) = 3 tan(1(x - π/2)) - 1

Simplifying:

f(x) = 3 tan(x - π/2) - 1

Therefore, the equation for the given tangent function is f(x) = 3 tan(x - π/2) - 1.

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When x = 4, y = 320/27.

If y varies directly as x, it means that y = kx, where k is a constant. To find k, we can use the given information:

When x = 3, y = 12

12 = k * 3

k = 4

Now that we know k, we can find y when x = 20:

y = k * x

y = 4 * 20

y = 80

Therefore, when x = 20, y = 80.

25. If y varies directly as the square of x, it means that y = k * x^2, where k is a constant. To find k, we can use the given information:

When x = 2, y = 16

16 = k * 2^2

k = 4

Now that we know k, we can find y when x = 8:

y = k * x^2

y = 4 * 8^2

y = 4 * 64

y = 256

Therefore, when x = 8, y = 256.

26. If y varies directly as the cube of x, it means that y = k * x^3, where k is a constant. To find k, we can use the given information:

When x = 3, y = 5

5 = k * 3^3

k = 5/27

Now that we know k, we can find y when x = 4:

y = k * x^3

y = 5/27 * 4^3

y = 5/27 * 64

y = 320/27

Therefore, when x = 4, y = 320/27.

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a) At the time the article was published, the federal minimum wage was $5.85 per hour.

b) According to the US Department of Labor website, the federal minimum wage in 2008 was $6.55 per hour.  

c) To earn the current federal minimum wage of $7.25 per hour, a person must pick up a penny in 4.97 seconds.

d) The phrase "penny dreadful" is a British expression referring to cheaply printed stories of sensational and sometimes gruesome content that were sold for a penny in the 19th century.

A) The minimum wage when Owen wrote his article can be calculated by using the equation:

Minimum wage = (Amount of money earned)/(Amount of time taken to earn it)

In this case, the amount of money earned is $0.01 (the value of a penny) and the amount of time taken to earn it is 6.15 seconds. Therefore:

Minimum wage = ($0.01)/(6.15 seconds) = $0.00162601626 per second

To convert this to an hourly wage, we can multiply by the number of seconds in an hour (3600):

Minimum wage = ($0.00162601626 per second) x (3600 seconds per hour) = $5.85365854 per hour

Minimum wage =  $5.85

B) According to the U.S. Department of Labor, the federal minimum wage in 2008 was $6.55 per hour.

Therefore, Owen's arithmetic was slightly off, as his calculated minimum wage is lower than the actual minimum wage at that time.

C) To calculate how much time you would need to spend picking up a penny in order to earn the current minimum wage, we can use the same equation as before, but rearrange it to solve for the amount of time:

Amount of time = (Amount of money earned)/(Minimum wage)

The current federal minimum wage is $7.25 per hour, or $0.00201388889 per second. Therefore:

Amount of time = ($0.01)/($0.00201388889 per second) = 4.97 seconds

So you would need to spend 4.97 seconds picking up a penny in order to earn the current minimum wage.

D) The phrase "penny dreadful" refers to a type of cheap, sensationalist fiction that was popular in the 19th century. These stories were typically published in weekly installments and sold for a penny each, hence the name "penny dreadful."

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The vertex form of the equation for function g is g(x) = a(x + 1)² - 38, where a is the same as in function f.

A quadratic function is one of the forms f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero.

The vertex form of the equation of a quadratic function is given by:

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex. To find the vertex form of the equation for function g, we need to determine the vertex of function f and then adjust it to 2 units below and 3 units to the left.

To find the vertex of function f, we can use the formula:

h = -b / 2a

where a and b are the coefficients of the quadratic term and the linear term, respectively.

For function f(x) = x² - 4x - 32, we have a = 1 and b = -4, so the vertex has an x-coordinate of:

h = -b / 2a = -(-4) / 2(1) = 2

To find the y-coordinate of the vertex, we can substitute this value of h into the function:

f(2) = 2² - 4(2) - 32 = -36

So the vertex of function f is (2, -36).

To adjust the vertex of the function f 2 units below and 3 units to the left, we need to subtract 2 from the y-coordinate and add 3 to the x-coordinate. Therefore, the vertex of function g is:

(h, k) = (2 - 3, -36 - 2) = (-1, -38)

Therefore, the vertex form of the equation for function g is g(x) = a(x + 1)² - 38, where a is the same as in function f.

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The cost of the meal, including the 20% discount, 8% sales tax, and 15% tip, is $43.72.

Suppose a number is 'a'

Suppose another number is 'b'

We want to know how much percent of 'b' is 'a'.

Then, it is calculated as:

[tex]\dfrac{a}{b} \times 100[/tex]

(in percentage)

We are given that;

Items ordered= a 12 piece Grilled Tuscan Chicken Wings, Mozzarella

Fritta and Pan Sauteed Mussels.

Coupon percent off =20%

Sales tax= 8%

Waiter tip= 15%

Now,

Let's start by finding the cost of the appetizers and the pizza before any discounts or taxes are applied:

Grilled Tuscan Chicken Wings: let's assume this is $12

Mozzarella Fritta: let's assume this is $8

Pan Sauteed Mussels: let's assume this is $14

Craft Your Own Pizza: let's assume this is $10 for a small 2-topping pizza

So the total cost of the food before any discounts or taxes is:

$12 + $8 + $14 + $10 = $44

With the 20% coupon, we can apply a discount of:

0.2 x $44 = $8.80

So the new total before taxes is:

$44 - $8.80 = $35.20

Now we can calculate the sales tax on this amount:

0.08 x $35.20 = $2.82

Adding the sales tax to the discounted amount gives:

$35.20 + $2.82 = $38.02

Finally, we can calculate the total cost of the meal after adding the 15% tip:

$38.02 + 0.15 x $38.02 = $43.72

Therefore, by the given percentages the answer will be $43.72.

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The intersection of sets A and B

The intersection of two sets is the set of elements that are common to both sets. To find the intersection of sets A and B, we simply look for the elements that are in both sets. In this case, the intersection of A and B is {h, o, e}.

The union of two sets is the set of elements that are in either one of the sets or both. To find the union of sets A and B, we simply combine the elements from both sets, making sure to not include any duplicates. In this case, the union of A and B is {h, o, m, e, u, s}.

So, the intersection of sets A and B is {h, o, e} and the union of sets A and B is {h, o, m, e, u, s}.

Here is the solution in HTML:

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Two families attended a baseball game, where they bought popcorn and souvenir. popcorn cost $4 and cost of souvenir is $7.

An equation is an expression that shows the relationship between two or more variables and numbers. Through equations the given information can be denoted as,

Let x = price of 1 bag of popcorn

Let y = price of 1 souvenir cup

First family:

3x + 4y = 40 (equation 1)

Second family:

8x + 4y = 60 (equation 2)

We have a system of 2 equations with 2 variables.

3x + 4y = 40

8x + 4y = 60

We are asked for the price of 1 bag of popcorn, x, so we will eliminate y and solve for x.

[tex]8x+4y=60\\4y=60-8x\\[/tex]

divide both sides by 4

[tex]\frac{4y}{4} =\frac{60-8x}{4} \\y=\frac{60-8x}{4} \\y=15-2x[/tex]

now putting the value of y in equation 1

[tex]3x+4y=40\\3x+4(15-2x)=40\\3x+60-8x=40\\-5x+60=40\\-5x=40-60\\-5x=-20\\x=\frac{-20}{-5} =4\\x=4[/tex][tex]y=15-2x\\y=15-2(4)\\y=15-8\\y=7\\[/tex]

Therefore, the cost of one bag of popcorn is $4.

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The polynomial expressions are P(x) = x(x - 5)(x - 2), P(x) = (x + 3)(x + 5)(x - 3)(x + 1), P(x) = (x + 5)(x² - 4x + 5) and P(x) = (x + 5)(x² + 4)

Zeros (1): 0, 5, 2

This means that

Roots: x = 0, x = 5 and x = 2

The equation can be represented as

P(x) = (x - root)

So, we have

P(x) = (x - 0)(x - 5)(x - 2)

Evaluate

P(x) = x(x - 5)(x - 2)

Zeros (2): 0, 5, 2

Here, we have

Roots: x = -3, x = -5, x = 3 and x = -1

Using the form in (a), we have

P(x) = (x + 3)(x + 5)(x - 3)(x + 1)

Zeros (3): 0, 5, 2

Here, we have

Roots: x = -5, x = 2 + i

Using the form used abov]e, we have

P(x) = (x + 5)(x - 2 - i)(x - 2 + i)

Expand

P(x) = (x + 5)((x - 2)² + 1)

So, we have

P(x) = (x + 5)(x² - 4x + 5)

Zeros (4): -1 and 2i

Here, we have

Roots: x = -1, x = 2i

Using the form used abov]e, we have

P(x) = (x + 1)(x - 2i)(x + 2i)

Expand

P(x) = (x + 5)(x² + 4)

Zeros (5):2 mult.2, -4

The zeros here are not clear

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The rate of change of with respect to for this function is 1.75.

From the question, we have the following parameters that can be used in our computation:

P = (-2, -7.5)

Q = (4, 3)

Using the two given points, we can find the slope of the line passing through them using the slope formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) = (-2, -7.5) and (x2, y2) = (4, 3)

slope = (3 - (-7.5)) / (4 - (-2))

= 10.5 / 6

= 1.75

Hence, the rate of change (i.e., the slope) of the line passing through points P and Q is 1.75.

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the expression for 5,364 in terms of x is 5x³ + 3x² + 6x + 4, where x = 10.

why it is and what is multiple?

a) The number 5,364 can be written as the sum of multiples of powers of 10 as follows:

5,364 = 5 × 1,000 + 3 × 100 + 6 × 10 + 4 × 1

= 5 × 10³ + 3 × 10² + 6 × 10¹ + 4 × 10⁰

(b) If x = 10, then we can write 5,364 as:

5,364 = 5 × 10³ + 3 × 10² + 6 × 10¹ + 4 × 10⁰

= 5x³ + 3x² + 6x + 4

Therefore, the expression for 5,364 in terms of x is 5x³ + 3x² + 6x + 4, where x = 10.

A multiple is a product of a given number and any other whole number. In other words, if a number 'a' can be expressed as the product of another number 'b' and a whole number 'c', then 'a' is a multiple of 'b'. For example, 10 is a multiple of 5 because 10 can be expressed as 5 multiplied by 2. Similarly, 15 is a multiple of 3 because 15 can be expressed as 3 multiplied by 5.

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So, the value of the car after 2 years, rounded to the nearest dollar, is $8450.

To determine the value of the car after 2 years, we need to plug in x=2 into the exponential function y=20000*(13000/20000)^x.

y=20000*(13000/20000)^2

y=20000*(0.65)^2

y=20000*0.4225

y=8450

Therefore, the value of the car after 2 years is $8450.

To round to the nearest dollar, we can look at the decimal part of the number. Since the decimal part is less than 0.5, we can round down to the nearest whole number.

So, the value of the car after 2 years, rounded to the nearest dollar, is $8450.

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No common factors

For the first set of fractions, the inequality symbol would be <, as 8/9 is less than 10/12. The rationale for this is that when fractions have different denominators, the fraction with the smaller denominator is always less. For the second set of fractions, the inequality symbol would be >, as -5/6 is greater than -6/8. The rationale for this is that when two fractions have the same denominator, the fraction with the larger numerator is always greater. The fractions that are completely simplified are 8/9, -5/6, and -6/8. This is because they cannot be reduced any further as they have no common factors.

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Answer:

I don't know dude...............

Answer:5:7

Step-by-step explanation:

From the given graph it is clear that

The total number of circles = 12

The total number of patterned circles = 5

The total number of plain circles = 7

We need to find the ratio of patterned circles to plain circles.

Substitute patterned circles = 5 and plain circles = 7 in the above formula.

Therefore, the ratio of patterned circles to plain circles is 5:7.

Answer is 240 centigrams = 2400 milligrams, 240 centigrams = 24 decigrams, 240 centigrams = 0.024 kilograms.

Measurement is the process of quantifying an attribute or property of an object or event using a numerical or quantitative scale. The result of a measurement is a number or value that represents the magnitude or amount of the attribute being measured.

Centigrams, milligrams, decigrams, and kilograms are all units of measurement of mass in the metric system.

1 centigram (cg) = 10 milligrams (mg) in the metric system.

240 centigrams =  10×240 milligrams,

So, 240 centigrams is equal to 2400 milligrams.

1 centigram (cg) = 0.1 decigrams (dg)

240 centigrams =  0.1×240 decigrams

So, 240 centigrams is equal to 24 decigrams.

1 centigram (cg) = 0.0001 kilograms (kg)

240 centigrams =  0.0001×240 kilograms

So, 240 centigrams is equal to 0.024 kilograms.

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Answer: B

Step-by-step explanation:

Answer: 256

Step-by-step explanation: This is a rectangular prism and shows the length, width, and height, so we need to use the formula length times width times height. So 8 * 8 * 4 equals 256.

The value of x is -11

The sum of angles of a triangle equals the straight angle (180 degrees, π radians, two right angles, or a half-turn). A triangle has three angles, one at each vertex, bounded by a pair of adjacent sides.

represent the other two base angles as z and y

z= 80(opposite angles)

y = 60( opposite angles)

z+y +x+51 = 180

80+60 +x +51 = 180

140+51+x = 180

x+191 = 180

x = 180-191

x = -11

therefore the value of x is -11

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The amount of interest she will earn at the end of 3 years would be = $375

The principal amount of money saved by Chantal (p)= $5000

The interest rate that the amount generates (r)= 2.5%

The total time for the savings(t) = 3 years.

The simple interest generated S.I = P×T×R/100

= 5000×3×2.5/100

= 37500/100

= $375

Therefore the amount of money she will earn as interest after three years of savings would be = $375.

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