Which angle is vertical angle to

The value of the expression when z = -19 is 25.

Here we have the expression:

(33 + 2z)²

And we want to evaluate this on z = -19

Evaluating just means that we need to replace the variable in the expression by the given number.

By doing that we will get:

(33 + 2*(-19))^2

(33 - 38)^2

(-5)^2 = 25

The expression is equal to 25.

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The monthly repayment on the following hire-purchase agreement is £22.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a colour TV costs £640. The deposit was £200. The interest rate was 10% p.a. and it was paid off in two years.

The monthly repayment will be calculated as,

Total interest for two years = ( 640 - 200 ) x 1.2

Total interest for two years = ( 440 x 1.2 )

Total interest for two years = £528

The value of monthly repayment = 528 / 24 = £22

Therefore, the monthly repayment on the following hire-purchase agreement is £22.

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The longest and the shortest distances are 1 mile and 5 miles

The greatest number of miles left is 4.5 miles

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

Luke = 3 miles

Logan = 2 miles

This means that

Shortest = 3 - 2 = 1 mile

Longest = 3 + 2 = 5 miles

Represent the distance with x

So, we have

3 - 2 < x < 3 + 2

Evaluate

1 < x < 5

The number line is | 1 | 2 | 3 | 4 | 5 |

In (a), we have

Longest = 5 miles

So, we have

Greatest = 5 - 0.5

Greatest = 4,5 miles

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Cases (iii) and (iv) are left as exercises, meaning the proof for those cases is not provided in the given information. To fully establish the Characterization Theorem, the proof for these remaining cases needs to be completed.

Theorem 2.5.1 (Characterization Theorem):

If S is a subset of R that contains at least two points and has the property that if x, y ES and x < y, then (x, y)C S, then S is an interval.Proof.

There are four cases to consider:

(i) S is bounded,

(ii) S is bounded above but not below,

(iii) S is bounded below but not above, and

(iv) S is neither bounded above nor below.

Case (i): Let a = inf S and b = sup S.

Then SC[a, b] and we will show that (a, b)C S. If a < z < b, then there exist x, y

ES such that x < z < y. Since x < y and S has property (1), we have (x, y)C S.

Since zEP(x, y), it follows that zES.

Thus (a, b)C S.

Now if a S and b S, then S =[a, b].

If a S and b S, then S=(a, b).

The other possibilities lead to either S = (a, b) or S = [a, b].

Case (ii): Let b = sup S.

Then SC (-[infinity]o, b] and we will show that (-oo, b)C S. For, if z < b, then there exists y

ES such that z < y < b.

Since b is the least upper bound of S and yES, it follows that y 6S. But then (z, y)C (-oo, b) and (z, y)C S.

Thus (-oo, b)C S. Now if S contains its smallest element a, then S = [a, b]. Otherwise, S=(a, b).

Cases (iii) and (iv) are left as exercises.

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Answer:  4/7

Step-by-step explanation:

the number of chairs = 7

the number of cushions = 11

Every chair has at least 1 cushion. There are 7 chairs so 7 cushions are used.

There is a total of 11 cushions and 7 cushions are already distributed to the chairs so there are 4 chairs with a 2nd cushion.

Chairs with 2 cushions ÷ Total chairs = 4/7

Answer:

x = 2

Step-by-step explanation:

If x is a prime number, then x + 1 is not a prime number.

A counterexample is x = 2.

x = 2

2 is prime

x + 1 = 2 + 1 = 3

3 is also prime

Answer:

1 inch represents 60 feet.

Step-by-step explanation:

120/2

= 60

So his scale is 1:60

Answer:

Its 1 inch represents 60 ft

Step-by-step explanation:

you have to divide 120 by 2 and thats 1 inch per 60 feet

Answer:

The completed proportions are;

ED/A_F = CE/CA = CF/CD

Step-by-step explanation:

The given m∠CED = m∠A

∴ Angle ∠CDE = Angle ∠A_FC, (corresponding angles)

Angle ∠ECD = Angle ∠ACF (reflexive property)

Triangle ΔDCE is similar to triangle ΔACF (Angle Angle Angle (AAA) similarity)

In triangle ΔDCE and triangle ΔACF

m∠A is bounded by CA and A_F

m∠CED is bounded by CE and ED

∠DCE is bounded by CE and DE

∠C is bounded by CA and CF

Based on the orientation of the two triangles, we have

ED is the corresponding side to A_F, CD is the  corresponding side to CF, CE is the corresponding side to CA

Therefore, we have;

ED/A_F = CE/CA = CF/CD.

The width that is left on each side of the mirror is 10 1/4 inches.

Mirrors, due to their size, weight, and combination of robustness and fragility, present a challenge for drywall and plaster walls.

The mounting gear for most new mirrors is already included, but it is important to take great consideration when choosing the anchors, screws, and bolts that will connect the mirror to the wall.

Use the following guidance on how to hang a heavy mirror safely so you may update your space while safeguarding your walls and décor after deciding what kind of wall you have and selecting the appropriate materials.

25 - 14 3/4 = 10 1/4

5 1/8 inches broad on each side of the mirror when 10 1/4 are split by two.

5 1/8 + 5 1/8 + 14 3/4 = 25.

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Answer:

D

Step-by-step explanation:

-9x-9=18

plus 9 on both sides

-9x=-9

divide both sides by -9

x=1

The  |120-x| simplifies to 120-x when x is less than 120.

S If x is less than 120, then the expression |120-x| simplifies to 120-x. This is because the absolute value bars mean that the result must be positive,

so if x is already less than 120, then subtracting x from 120 will give a positive result.

For example, if x is 115, then |120-x| would equal |120-115|, which simplifies to |5|, which equals 5.  

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1/7 of the animals in the zoo are male monkeys.

To find the fraction of animals in the zoo that are male monkeys, we have to calculate the product of the fractions representing the proportion of monkeys and the proportion of male monkeys among them.

Given that 1/5 of the animals in the zoo are monkeys, we will then represent this as:

= 1/5

= 5/25.

And 5/7 of the monkeys are male which is written as 5/7.

To get fraction of male monkeys, we will multiply these two fractions:

= (5/25) * (5/7)

= 25/175

= 1/7.

Full question:

1/5 of the animals in the zoo are monkeys 5/7 of the monkeys are male. What fraction of the animals in the zoo are male monkeys?

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The sum of an arithmetic-series can be found using the formula:

Sum = n/2 × (\(a_{1}\) + \(a_{n}\))

where n is the number of terms, \(a_{1}\) is the first term, and \(a_{n}\) is the last term.

In this case, the first term is \(a_{1\) = 3 × 1 - 13 = -10 and the last term is  \(a_{n}\)  = 3 × 35 - 13 = 88.

The number of terms is n = 35.

Substituting the values into the formula:

Sum = 35/2 × (-10 + 88)

= 35/2 × 78

= 2630

Therefore, the sum of the arithmetic series is 2630.

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Step-by-step explanation:

Step 1: To calculate the time it takes to cook a 3 kg chicken, use the following equation: Time (minutes) = Mass (kg) × Constant

Step 2: Substitute 3 for the mass (kg) and solve for the time (minutes): Time (minutes) = 3 kg × Constant

Step 3: To calculate the constant, use the given information that it takes 100 minutes to cook a chicken of unknown mass (M). Substitute 100 minutes and M for the time and mass, respectively: 100 minutes = M kg × Constant

Step 4: Solve for the constant by dividing both sides by M kg: Constant = 100 minutes / M kg

Step 5: Substitute the value of the constant into the first equation and solve for the time it takes to cook a 3 kg chicken: Time (minutes) = 3 kg × (100 minutes / M kg)

Step 6: Simplify the equation to find the number of minutes it takes to cook a 3 kg chicken: Time (minutes) = 300 minutes

Therefore, it will take 300 minutes, or 5 hours, to cook a 3 kg chicken.

To calculate the mass of a chicken that takes 100 minutes to cook, use the same equation and substitute 100 minutes for the time: Mass (kg) = Time (minutes) / Constant

Substituting 100 minutes and the value of the constant, which is 100 minutes/M kg, yields Mass (kg) = 100 minutes / (100 minutes / M kg) = M kg

Therefore, the mass of a chicken that takes 100 minutes to cook is M kg.

Answer:1 only solution

Step-by-step explanation:

If the discriminant is equal to 4, the number of solutions there are is; 2 solutions.

According to the question;

When the discriminant is a perfect square as in 4 above; Then the solutions to the equation are not only real, but also rational.

However, If the discriminant is positive but not a perfect square, then the solutions to the equation are real but irrational.

There are 2 rational solutions if the discriminant is equal to 4.

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Answer:

  2.7 < x < 12.3 meters

Step-by-step explanation:

You want to know the possible lengths of the third side of a triangle, given that two sides are 7.5 m and 4.8 m.

The triangle inequality requires the sides of a triangle have the relationship ...

  a + b > c

for any assignment of side lengths to the letters a, b, c. In effect, this means the length of a third side must lie between the sum and the difference of the other two sides.

  7.5 -4.8 < x < 7.5 +4.8

  2.7 < x < 12.3 . . . . . meters

(a) The correct option is C

(b) The correct option is B

Given the expression:

To write this in logarithmic form, we first add 6 to both sides of the equation

From

Take logarithm of both sides

The collection gadget with the given transfer function and an enter of x(t) = cos(t) has a frequency response given through Y(s) = cos(t) * \([8(s+1)/(s+2)(s^2 + 4)]\). The gadget is solid due to the poor real part of the pole at s = -2. The absence of zeros in addition contributes to system stability.

To set up the frequency reaction of the collection system, we want to calculate the output Y(s) inside the Laplace domain given the input X(s) = cos(t) and the transfer function of the device.

The switch function of the series machine, as proven in Figure 1, is given as H(s) = \(8(s+1)/(s+2)(s^2 + 4).\)

To locate the output Y(s), we multiply the enter X(s) with the aid of the transfer feature H(s) and take the inverse Laplace remodel:

Y(s) = X(s) * H(s)

Y(s) = cos(t) * \([8(s+1)/(s+2)(s^2 + 4)]\)

Next, we want to determine the stability of the overall gadget. The stability is determined with the aid of analyzing the poles of the switch characteristic.

The poles of the transfer feature H(s) are the values of s that make the denominator of H(s) equal to 0. By putting the denominator same to zero and solving for s, we are able to find the poles of the machine.

S+2 = 0

s = -2

\(s^2 + 4\)= 0

\(s^2\) = -4

s = ±2i

The machine has one actual pole at s = -2 and complicated poles at s = 2i and s = -2i. To investigate balance, we observe the actual parts of the poles.

Since the real part of the pole at s = -2 is poor, the system is stable. The complicated poles at s = 2i and s = -2i have 0 real elements, which additionally contribute to stability.

Sketching the poles and zeros at the complex plane, we see that the machine has an unmarried real pole at s = -2 and no 0. The pole at s = -2 indicates balance because it has a bad real component.

In conclusion, the collection gadget with the given transfer function and an enter of x(t) = cos(t) has a frequency response given through Y(s) = cos(t) *\([8(s+1)/(s+2)(s^2 + 4)]\). The gadget is solid due to the poor real part of the pole at s = -2. The absence of zeros in addition contributes to system stability.

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The correct question is:

" Establish the frequency response of the series system with transfer function as specified in Figure 1, with an input of x(t) = cos(t). Determine the stability of the connected overall system shown in Figure 1. Also, sketch values of system poles and zeros and explain your answer in terms of the contribution made by the poles and zeros to overall system stability. x(t) 8 5 s+1 s+2 Figure 1 Block diagram of series system s+2 S² +4"

Step-by-step explanation:

Parallel lines have the same slope so they can therefore never touch. Just change the y-int. (Any number as long as it's not the same as the previous)

I.E.:

y = -3x - 12

The solutions for each statement are given below.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

The initial amount of the company = -$200,000

Earnings for selling one batch = $40,000

Now,

1.

The two quantities that are changing in this situation are:

The number of batches.

The amount of profit.

2.

The independent variable is the number of batches.

The dependent variable is the profit.

3

The number of batches = x

The amount of profit = y

The equation for the profit.

P = -200,000 + B x 40,000

Where B is the number of batches.

4.

Batches of tires   Profits

   B                        P

0                         -200,000

1                          -160,000

2                          -120,000

3                           -80,000

4                           -40,000

5                            0

5.

The unit rate of change.

= (-120,000 + 160,000) / (2 - 1)

= 40,000

Thus,

The statements are given above.

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Answer:

0.45

Step-by-step explanation:

You divided 2.25 by 5

Answer: A: Slope = -4, y-intercept 1

Step-by-step explanation:

To find slope, do rise over run. The y-intercept is where the line crosses the y-axis.

The solution to the given system of linear equations is x = 3, y = -3. That is, (3, -3)

The graph of the system of equations is shown below

From the question, we are to determine the apparent solution to the given system of linear equations

The given system of equations is

y = -2x + 3

y = 1/3x - 4

Set the two equations equal

That is,

-2x + 3 = 1/3x - 4

Multiply through by 3

-6x + 9 = x - 12

Add 6x to both sides of the equation

-6x + 6x + 9 = x + 6x - 12

9 = 7x - 12

Add 12 to both sides of the equation

9 + 12 = 7x - 12 + 12

21 = 7x

x = 21/7

x = 3

Substitute the value of x into the first equation

y = -2x + 3

y = -2(3) + 3

y = - 6 + 3

y = - 3

The solution is (3, -3)

The graph is shown below

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Answer:

Step-by-step explanation:

ED :  DL = FD : DM

or

ED / DL = FD / DM

FD = ED·DM / DL

FD = 88 ·  84  / 48 = 154

We have proved that Angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

To prove that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, we can use the following steps:

Step 1: Join points A and C with a line segment. Let's label the point where AC intersects with line segment BD as point E.

Step 2: Since line segment AC is drawn, we can consider triangle ABC and triangle ADC separately.

Step 3: In triangle ABC, we have angle B + angle ABC + angle BCA = 180 degrees (due to the sum of angles in a triangle).

Step 4: In triangle ADC, we have angle D + angle ADC + angle CDA = 180 degrees.

Step 5: From steps 3 and 4, we can deduce that angle B + angle ABC + angle BCA + angle D + angle ADC + angle CDA = 360 degrees (by adding the equations from steps 3 and 4).

Step 6: Consider quadrilateral ABED. The sum of angles in a quadrilateral is 360 degrees.

Step 7: In quadrilateral ABED, we have angle BAD + angle ABC + angle BCD + angle CDA = 360 degrees.

Step 8: Comparing steps 5 and 7, we can conclude that angle B + angle BCD + angle D = angle BAD + angle ABC + angle ADC.

Step 9: Rearranging step 8, we get angle BCD = angle BAD + angle ABC + angle ADC.

Therefore, we have proved that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

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Given: Quadrilateral \(\displaystyle\sf ABCD\)

To prove: \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\)

Proof:

1. Draw segment \(\displaystyle\sf AC\) and extend it to point \(\displaystyle\sf E\).

2. Consider triangle \(\displaystyle\sf ACD\) and triangle \(\displaystyle\sf BCE\).

3. In triangle \(\displaystyle\sf ACD\):

4. In triangle \(\displaystyle\sf BCE\):

5. Since \(\displaystyle\sf \angle BCE\) and \(\displaystyle\sf \angle BCD\) are corresponding angles formed by transversal \(\displaystyle\sf BE\):

6. Combining the equations from steps 3 and 4:

Therefore, we have proven that in quadrilateral \(\displaystyle\sf ABCD\), \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\).

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Answer:

\(f'(x)= \frac{13}{(2x+3)^2}\\\)

Step-by-step explanation:

\(f(x)= \frac{3x-2}{2x+3} \\\)

\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)

\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)