Which angle is congruent to ∠DFE?

An illustration shows two right angled triangle A B C and D E F; triangle A B C is larger than triangle D E F.

A.
∠ABC

B.
∠FDE

C.
∠FED

D.
∠ACB

Applying the inscribed angle theorem, we have:

1. Measure of inscribed angle EDF = 53°

2. m<DCB = 92°

3. m<VWS = 37°

In a circle, the measure of an inscribed angle is equal to half of the measure of the measure of the intercepted arc, based on the inscribed angle theorem. In order words, the measure of the intercepted arc in a circle, is always twice the measure of the inscribed angle in the circle.

1. Measure of intercepted arc EF = 106° [given]

Measure of inscribed angle EDF = 1/2(measure of arc EF) [inscribed angle theorem]

Substitute

Measure of inscribed angle EDF = 1/2(106)

Measure of inscribed angle EDF = 53°

2. m<DCB + m<DQB = 180° [opposite angles of a cyclic quadrilateral add up to 180 degrees]

Substitute

m<DCB + 88 = 180

m<DCB + 88 - 88 = 180 - 88

m<DCB = 92°

3. m<VWS = 1/2(measure of arc VS) [inscribed angle theorem]

Substitute

m<VWS = 1/2(74)

m<VWS = 37°

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11*21+11*19+17*18/3=746/3=248.3

The measure of side n is √(m^2 - 64).

According to the given question.

We have a right angle triangle.

Here, we have to find the measure n.

Since, the given triangle is divided into two right angle triangles.

Now in the right angled triangle with the side measure m, n and 8.

By the Pythagoras theorem we can say that

m^2 = 8^2 + n^2

⇒ m^2 = 64 + n^2

⇒ m^2 -64 = n^2 ...(i)

⇒ n = √(m^2 - 64)

Hence, the measure of side n is √(m^2 - 64).

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We need to prove

(1 + cos a)(1 - sec a) = -sin a tan a

LHS

= (1 + cos a)(1 - sec a)

= 1 -sec a + cos a - cos a sec a

= 1 - sec a + cos a - cos a (1/cos a)

= 1 - sec a + cos a - 1

= cos a - sec a

= cos a - 1/cos a

= [tex]\frac{cos^{2}a - 1}{cos a}[/tex]

We know that [tex]sin^{2}a+ cos^{2}a = 1[/tex],

Then [tex]1 - cos^{2}a = sin^{2} a[/tex]

        [tex]cos^{2}a - 1 = -sin^{2}a[/tex]

= [tex]-\frac{sin^2a}{cos a}[/tex]

= [tex]-\frac{(sina)(sina)}{cosa}[/tex]

=[tex]- (sin a)(\frac{sin a}{cosa} )[/tex]

We know that tan a = sin a / cos a

= - sin a tan a

= RHS

                                        LHS = RHS

                                     Hence Proved

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The probability of getting yellow marbles is 0.23.

Probability is the measure of the likelihood that an event will occur in a Random Experiment.

Experiment: A trial or an operation conducted to produce an outcome is called an experiment.

Sample Space: All the possible outcomes of an experiment together constitute a sample space. For example, the sample space of tossing a coin is head and tail.

Favorable Outcome: An event that has produced the desired result or expected event is called a favorable outcome. For example, when we roll two dice, the possible/favorable outcomes of getting the sum of numbers on the two dice as 4 are (1,3), (2,2), and (3,1).

Trial: A trial denotes doing a random experiment.

Given:

Total marbles= 100

blue marbles = 21

green marbles= 19

red marbles = 37

yellow marbles= 23

So, the probability of randomly selecting a yellow marble

= 23/100

= 0.23

Hence, the probability of randomly selecting a yellow marble is 0.23.

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Answer:

S₆ = - 364

Step-by-step explanation:

the sum to n terms of a geometric series is

[tex]S_{n}[/tex] = [tex]\frac{a_{1}(r^{n}-1) }{r-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = 2 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-6}{2}[/tex] = - 3 , then

S₆ = [tex]\frac{2((-3)^{6}-1) }{-3-1}[/tex]

    = [tex]\frac{2(729-1)}{-4}[/tex]

   = [tex]\frac{2(728)}{-4}[/tex]

   = [tex]\frac{1456}{-4}[/tex]

  = - 364

Answer: C= 60 milligrams

Step-by-step explanation:

apply the formula

C = Divide[a,\(40)a+2\(41)]A

The inequality that can be used to determine the minimum number of sets of glasses Bella bought is x ≥ 20.8.

She needs to order some new supplies for the restaurant where she works.

The restaurant needs at least 503 glasses.

Each set on sale contains 10 glasses.

The inequality that can be used to determine the minimum number of sets of glasses Bella bought is as follows:

Therefore,

x =  number of sets

Hence,

295 + 10x ≥ 503

10x ≥ 503 - 295

10x ≥ 208

x ≥ 208 / 10

x ≥ 20.8

Therefore, the inequality that can be used to determine the minimum number of sets of glasses Bella bought is x ≥ 20.8.

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Inequality represents number of months (m) it will take Gabriela to save at least $5,600 is m ≥ 6.

As given in the question,

Amount Gabriela plans to save to buy a car = at least $5,600

Amount she already has = $2500

Amount she needs to save at least = $(5600 -2500)

                                                          =$3100

Plans to save each month =$500

Inequality to represents the number of months to save at least $5600

m ≥ 3100/500

⇒ m ≥ 6

Therefore, inequality represents number of months (m) it will take Gabriela to save at least $5,600 is m ≥ 6.

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(a) The average rate of change for the height from 0 seconds to 4.6 seconds is 30 meters per second.

(b) The average rate of change for the height from 9.2 seconds to 11.5 seconds is -10 meters per second.

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Answer:

Length of the rectangle = 43 inches

Width of the rectangle= 20 inches

Step-by-step explanation:

The value of f-¹(x) for the function f(x) = (x + 2)/x is y = 2/(x-1).

The inverse of a function f is denoted by f-¹ and it exists only when f is both one-one and onto function. An inverse function in mathematics is function which "reverses" the another function.

For example, If function f which is applied to input a gives result b and then applying inverse of the function g to b, it gives result a and vice versa.

It can be written as:

f(a) = b if and only if g(b) = a or, f⁻¹ (b) = a

In order to calculate the inverse of function f(x) = (x + 2)/x just simply swap the x and y, and solve the resulting equation for the x.

So, we have f(x) = (x + 2)/x, swap the variable x by y, we get

f(x) = (y + 2)/y ............(1)

Now, solving the above equation x = y+2/y for y.

⇒y = 2/(x-1)

∴ The value of f-¹(x) for the function f(x) = (x + 2)/x is y = 2/(x-1).

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The system of inequalities is,

The total hours will be X+Y≤4.

The total amount she can earn 8.5X + 10Y ≤ 22.85.

First let us assume that she work 7 days in the week.

If she works for 28 hours a week, Then the hours of work done by her in a day will be,

28hours/7days

Per day working hours are 4 hours per day.

now, if she has to earn at least 160$ a week. Then, the amount she has to earn in one day will be 160$/7days,

Amount needed to be earned in one day is 22.85$,

Now, if she work for X hours as cashier, then she can work Y hours as florist.

The total hours for which she can can be represented by,

X+Y≤4

The amount she will earn in one day can be represented by the inequality,

8.5X + 10Y ≤ 22.85.

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The equation of the linear least-squares regression line is given by:

[tex]\sqrt[3]{\text{Volume}} = -0.006 + 0.64(\text{Time})[/tex]

A linear function is modeled by the following rule:

y = mx + b

In which:

For this problem, we have that:

From the table, we get that:

Water is being poured into the cone, hence the volume is increasing and the slope is positive. The equation will be given by:

[tex]\sqrt[3]{\text{Volume}} = -0.006 + 0.64(\text{Time})[/tex]

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Answer:

[tex]f(x) = x^2 + 6x+9[/tex]

Step-by-step explanation:

[tex]y=(x+3)^2 = x^2 + 6x+9[/tex]

Answer:

all the correct answers are the correct answers of

Step-by-step explanation:

step by step explanation no needed because answer already answered okay there answer needed.

Answer:

1. 740 students

2. 4 years

3. 185 students per year

4. 357 students

5. 185t+357

6. 3132 students

Work:

1. 1837 - 1097 = 740

2. 2008 - 2004 = 4

3. (1837 - 1097) / (2008 - 2004) = 185

4. 185(0) + 357 = 357

5. 185t + 357

6. 185(15) + 357 = 3132

Answer: I hope this helps.

Step-by-step explanation:

Based on the demand curves and the movement of the demand curve, the equilibrium price before the demand shift is b and the equilibrium quantity before the demand shift was e.

The equilibrium price refers to the price at the point where the supply and demand curves meet on the graph.

Before the shift in demand, the equilibrium price was at Price b which was the intersection between demand curve d1 and the Supply curve.

The equilibrium quantity was the quantity at this equilibrium price and this was Quantity e.

Rest of the question is:

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Answer:

45 (-3 i + 2)

Step-by-step explanation:

Simplify the following:

(8 + 7) (-sqrt(-81) + 6)

Hint: | Evaluate 8 + 7.

8 + 7 = 15:

15 (-sqrt(-81) + 6)

Hint: | Express sqrt(-81) in terms of i.

sqrt(-81) = sqrt(-1) sqrt(81) = i sqrt(81):

15 (6 - i sqrt(81))

Hint: | Factor common terms from -(i sqrt(81)) + 6.

Factor 3 out of 6 - 9 i giving 3 (2 - 3 i):

15×(3 (-3 i + 2))

Hint: | Multiply 15 and 3 together.

15×3 = 45:

Answer: 45 (-3 i + 2)

The missing number so that the equation has no solutions is -7/3.

The equation given is represented by:

x+1 = -2x–6

It should be noted that we just have to find the value of x. This will be

x+1 = -2x–6

x + 2x = -6 - 1

3x = -7

x = -7/3

Therefore, the value of x is -7/3.

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Step-by-step explanation:

supplementary angles are two angles that are together 180°.

they don't have to be adjacent, but the fact that the 2 angles can be placed "randomly" in a scenario is rarely used, except maybe for intersection angles of a line with parallel lines.

a linear pair are 2 angles that are truly adjacent (neighbors, touching each other) that are together 180°.

so, our original statement is

if 2 angles are supplementary, then the angles are a linear pair.

that by itself is (as described) not true in all cases. angles can be non-adjacent (and therefore not a linear pair) and still be supplementary.

so the original statement is false.

(a)

the inverse is

if 2 angles are not supplementary, then the angles are not a linear pair.

that is true.

as per the definition, linear pair angles are a true subset of supplementary angles (every linear pair is a pair of supplementary angles, but not every pair of supplementary angles is a linear pair).

so, if they are not a member of the set of supplementary angles, they cannot be a member of a subset either.

(b)

the converse is

if 2 angles are a linear pair, then the angles are supplementary.

that is true.

because linear pair angles are a true subset of supplementary angles. if something is a member of a subset, it is also a member of any superset.

(c)

the contrapositive is

if 2 angles are not a linear pair, then the angles are not supplementary.

that is false.

as described, linear angles are a true subset of supplementary angles. so, an element can be outside a subset but still inside a superset.

like in the original example, 2 angles across intersected parallel lines can be supplementary, but they are not a linear pair.

The two numbers that are (1/16) away from -(1/5) are -(11/80) and -(21/80).

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

The two numbers that are 1/16 away form -(1/5) can be found by adding 1/16 to -(1/5) and subtracting 1/16 from -(1/5). Therefore, we can write,

-(1/5) + (1/16) = -(11/80)

-(1/5) - (1/16) = -(21/80)

Hence, the two numbers that are (1/16) away from -(1/5) are -(11/80) and -(21/80).

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Answer:

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Answer:

X+Y-3

Step-by-step explanation:

I don’t know what X/Y is, but “three less than” means you need to subtract 3 from the sum of X+Y

The value of x in the given expression 8 = x over 2.5 minus 6 is (-1/8)^(2/7)

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

given expression is :

-8 = x^(2.5-6)

Now, solving for x by transferring power of x to -1/8 that will become -8 to the power (2/7) :

-8 = x^(-3.5)

-8 = 1/x^(3.5)

x^(3.5) = -1/8

x^(7/2) = -1/8

x = (-1/8)^(2/7)

Therefore, the value of x in the given expression is (-1/8)^(2/7)

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