In the given figure, identify a pair of perpendicular lines.
A) I and p
B) o and p
C) m and n
D) m and o

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Answer:

a) 128°

b) Opposite angles of a cyclic quadrilateral add up 180°

Step-by-step explanation:

→ Work out ABD

180 - 116 = 64°

→ Use the theorem 'The angle at the centre is twice the angle at the centre'

2 × 64 = 128°

→ Use the cyclic quadrilateral theorem

Opposite angles of a cyclic quadrilateral add up 180°

The value of x is 128 degree when the angle CBD is of 116 degree.

It is a four sided polygon having four angles and four corners.

Firstly we find angle ABD which is 180-116=64 Degrees because the angle at the center is twice the angle on the any point of circle.

So the value of x becomes 2*64=128 degrees.

By using the cyclic quadrilateral theorem opposite angles of a cyclic quadrilateral has a sum of 180 degrees.

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The solution of the given quadratic equation is x = -2.

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

Given is a quadratic equation x²+4x+4 = 0, we need to solve it using the Quadratic Formula:

The formula for the same is given by -

x = -b ± √b²-4ac / 2a

Here,

a = 1, b = 4 and c = 4

Put in the formula,

x = -4 ± √4²-4(1)(4) / 2

x = -4 ± √16-16 / 2

x = -4 ± √0 / 2

x = -4/2

x = -2

Hence, the solution of the given quadratic equation is x = -2.

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Answer:

B

Step-by-step explanation:

Mathematically, the numbers that are divisible by 7 here forms an arithmetic sequence, with 203 being the first term

Now, we need the last term

The last term before 800 is 798

Now, the nth term of a sequence (arithmetic) can be represented as;

Tn = a + (n-1)d

Kindly note that the numbers have 7 as their common difference

Thus;

798 = 203 + (n-1)7

798-203 = 7n - 7

7n = 798 -203 + 7

7n = 602

n = 602/7

n = 86

Answer:

A) -6x9 will change the end behavior of the graph.

OAmalOHopeO

a. –6x9 when added to the given polynomial, will change the end behavior of the graph.

hope it helps :)

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Answer:

4

Step-by-step explanation:

Step-by-step explanation:

Answer:f(x)=-5x^(2)-3x+9 this is the standard form

Answer:

Step-by-step explanation:

a) 8 * 3 = 24 cm^2

b) 5.2 * 7.7 = 40.04 cm^2

Answer: [tex]26,400\ ft[/tex]

Step-by-step explanation:

Given

Each side of the pentagon measures [tex]1760\ ft[/tex]

A complete trip is equivalent to the perimeter of the perimeter

[tex]\Rightarrow \text{Perimeter of the Pentagon P=}5\times 1760\\\Rightarrow P=8800\ ft[/tex]

For Three rounds, he completed a distance of  

[tex]\Rightarrow P=3\times 8800\\\Rightarrow P=26,400\ ft[/tex]

Answer:

Mean

Step-by-step explanation:

Finding the mean, or the average, of the different weights that were measured, would best estimate the true mass of the solid.

This would find the average mass, which would be the most accurate estimate of the solid's actual mass.

Using the minimum, maximum, and mode will not take into account the other weights that were measured. This makes it much more inaccurate.

So, the correct answer is Mean.

Answer:

(0,1,3,5)

Step-by-step explanation:

Set g(x) equal to each respective range and solve for x

[tex]3x + 2 = 2[/tex]

[tex]3x + 2 = 5[/tex]

[tex]3x + 2 = 11[/tex]

[tex]3x + 2 = 17[/tex]

If we solve for each, we get

[tex]x = 0[/tex]

[tex]x = 1[/tex]

[tex]x = 3[/tex]

[tex]x = 5[/tex]

So our domain is

(0,1,3,5)

Answer:

These figures are not similar

Step-by-step explanation:

The two sides are proportional, but the angle between them are not congruent.

One angle is marked with one arc.

The other is marked with two arcs.

They must have the same number or arcs to be considered congruent.

Tricky

Answer:

4628

Step-by-step explanation:

We are given that

In 2000

The population of a small industrial town  in 2000=12910

Depreciation rate, r=5% per year

We have to find the  population in the year 2020.

Time from 2000 to 2020=20 years

[tex]FV=PV(1-\frac{r}{100})^n[/tex]

Where FV=Future value

PV=Present value

Using the formula

[tex]FV=12910(1-\frac{5}{100})^{20}[/tex]

[tex]FV=12910(\frac{95}{100})^{20}[/tex]

FV=4628

Hence, the population in 2020 =4628

Answer:

1/7

Step-by-step explanation:

negative reciprocal

Answer:

11 minutes and 20 seconds. or 11.33

Step-by-step explanation:

Reciprocal of .75 is 1.33. Multiply 1.33 times 8.5 minutes to find how long it would take to run one mile.

or

Divide 8.5 minutes by 3 to find how long it takes to run 1/4 of a mile, and multiply that time by 4 to see how long it takes to run one mile.

Answer:

Since curved surface area of a cyclinder = 154 cm2 [given]

Total surface area of cyclinder = 3 × curved surface area

2πrh + 2πr2 = 3 × 154

154 + 2πr2 = 462

2πr2 = 462 - 154 = 308

r2 = 308 × 7 / 2 × 22 = 49

r = 7 cm

Now, 2πrh = 154

2 × 22 / 7 × 7 × h = 154

h = 154 / 44 = 3.5 cm

∴ Volume of cyclinder = πr2h

= 22 / 7 × 7 × 7 × 3.5 = 539 cm3

=======================================================

Work Shown:

x = length of PQ

3x-20 = length of QS, since its 20 less than 3 times PQ

The triangles are similar (we can prove this through the AA similarity theorem), so we can set up a proportion like shown below to solve for x.

PT/RS = PQ/QS

6/8 = x/(3x-20)

6(3x-20) = 8x ..... cross multiplying

18x-120 = 8x

18x-8x = 120

10x = 120

x = 120/10

x = 12

So PQ is 12 units long.

This then means QS = 3x-20 = 3*12-20 = 36-20 = 16

Answer:

Step-by-step explanation:

Answer: 6, 7

Step-by-step explanation:

x · y = 42

x · (13 - x) = 42

13x - x² = 42

-x² + 13x - 42 = 0

(-1)(-x² + 13x - 42) = 0(-1)

x² - 13x + 42 = 0

(x - 6)(x - 7) = 0

y = 13 - x

Answer:4

Step-by-step explanation:

but they said it would have toend

Answer:

(a) 25

(b) $4816

Step-by-step explanation:

Let's say the starting amount of ducks is d, and the starting amount of chickens is c. Since there are only ducks and chickens, we can say that d + c= 455.

Next, the farmer sells 2/5 of the ducks, so we subtract 2/5 of the ducks so that the ending duck amount is d - (2/5)d = (3/5) d

After that, the farmer buys another 104 chickens, so we add 104 chickens to the current amount of chickens to get the ending chicken number as 104+c

Given the ending duck and chicken count, we can say that the ending farm animal count (we can represent this as a) is (3/5)d + 104 + c = a

The number of ducks is 2/3 the total number of animals at the end, so (3/5)d = (2/3)a

Let's list our equations out so it is easier to solve:

d+c = 455

(3/5)d + 104 + c = a

(3/5)d = (2/3)a

We have three equations and need to solve for three variables. One common variable in all three equations is d, so it might help if we put everything in terms of d.

Starting with d+c=455, if we subtract d from both sides, we get c=455-d. We can substitute this in the second equation to get

(3/5)d + 104 + 455 - d = a

-(2/5)d + 559 = a

(3/5)d = (2/3)a

Next, we can substitute for a. If we multiply both sides by 3 and then divide by 2 in (3/5)d = (2/3)a , we get

(9/10)d = a

Substitute that in to the second equation to get

-(2/5)d + 559 = (9/10) d

-(4/10)d + 559 = (9/10) d

add (4/10)d to both sides to isolate the variable and its coefficient

(13/10)d = 559

multiply both sides by (10/13) to isolate the coefficient

d = 430

Therefore, the starting number of ducks is 430 and the starting amount of chickens is 455-430 = 25

For (b), 2/5ths of the ducks are sold, so this is (430) * (2/5) = 172. Each duck is sold for 28 dollars, so this is 172*28=$4816 as the total price

Answer:

Let the MP of 1 article = Rs 1

MP of 15 article = Rs 15

SP of (15+1) articles = 15 x 96/100

= Rs 14.40

CP of 16 article = 14.40/135 x 100

= Rs 32/3

CP of 1 article = 32/3x16

= Rs 2/3

Required % = 1/3 x 3/2 x 100

= 50

Answer:

110.8 feet

Step-by-step explanation:

Find the difference in sea level by subtracting 236 from 346.8:

346.8 - 236

= 110.8

So, the difference in sea level is 110.8 feet

Given:

The graph of data points.

To find:

The equation of the best fit line by using the graphing calculator.

Solution:

The general form of a best fit line is:

[tex]y=mx+b[/tex]                 ...(i)

Where, m is the slope and b is the y-intercept.

Using the graphing calculator, we get

[tex]m\approx 1.423[/tex]

[tex]b\approx 11.698[/tex]

Substituting [tex]m\approx 1.423, b\approx 11.698[/tex] in (i), we get

[tex]y=1.423x+11.698[/tex]

Therefore, the equation of the best fit line is [tex]y=1.423x+11.698[/tex] and its graph is shown below.

Answer: $15927.183

Step-by-step explanation:

Price of good= $29,000

Trade discount = 40½ 20¼/5

The first discount will be:

= 40½ × $29000

= $11745

Then, the price after the first discount will be:

= $29000 - $11475

= $17255

Then, the second discount will be:

= $17255 × 20¼%

= $3494.14

Then, the price after the second discount will be:

= $17255 - $3494.14

= $13760.86

The third discount will be:

= $13760.86 × 5%

= $688.043

Then, the total discount will be:

= $11745 + $3494.14 + $688.043

= $15927.183

Therefore, the trade discount is $15927.183.

Answer:

y=58°

x=122°

Step-by-step explanation:

y=58°[°•°being corresponding angles]

Now,

x+y=180[°•°co-interior angles]

or, x=180-58

•°•x=122

Expression given:-

Substaract 7 from sum of 9 and 8

Convert it to algebraic term

[tex]\\ \sf\longmapsto (9+8)-7[/tex]

[tex]\\ \sf\longmapsto 17-7[/tex]

[tex]\\ \sf\longmapsto 10[/tex]

Answer:

D

Step-by-step explanation:

Answer:

There are no solutions.

Step-by-step explanation:

im assuming that the equation is x^2+20=2x, but if not, x=10.

quadratic formula is

(-b+-√(b^2-4ac))/2a, and a=1, b=-2, and c=20. plug these values in and you will find that you are asked to square root a negative number. There are no solutions.