In the adjoining figure, AB//CD. Show that, AC//BD.
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for

A
70°
C
50%
B
60%D
T

Answer:

x = 3.4

Step-by-step explanation:

\(10x-4.5+3x=12x-1.1\\\\10x+3x-4.5=12x-1.1\\\\13x-4.5=12x-1.1\\\\13x-4.5+4.5=12x-1.1+4.5\\\\13x=12x+3.4\\\\13x-12x=12x-12x+3.4\\\\\boxed{x=3.4}\)

Hope this helps.

Answer:

Step-by-step explanation:

11.04 = 10(1.02)^n

1.104 = 1.02^n

ln 1.104 = ln 1.02^n

ln 1.104 = n ln 1.02

n = ln 1.104/ ln 1.02

n = 4.99630409516

4.99 can be rounded to 5.

So a reasonable domain would be 0 ≤ x < 5

PART B)

f(0) = 10(1.02)^0

f(0) = 10(1)

f(0) = 10

The y-intercept represents the height of the plant when they began the experiment.

f(1) = 10(1.02)^1

f(1) = 10(1.02)

f(1) = 10.2

(1, 10.2)

f(5) = 10(1.02)^5

f(5) = 10(1.1040808)

f(5) = 11.040808

f(1)=10(1.02)^1

f(1)=10.2

Average rate= (fn2-fn1)/(n2-n1)

                     =11.04-10.2/(5-1)

                    =0.22

the average rate of change of the function f(n) from n = 1 to n = 5 is 0.22.  

Answer:

Step-by-step explanation:

There are an infinite amount of possibilities with the solution of (4,1).  As proof, plot the point (4,1) on a coordinate system.  Then, draw straight lines that pass through that point.  These lines can differ in slopes. They can be either be positive, negative, vertical, or horizontal.

x = 4

y = 1

x + y = 5

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Answer:

10

Step-by-step explanation:

56 ÷ 7 = 8 each.

80 ÷ 8 = 10

Answer:

3.2mm

Step-by-step explanation:

Answer:

3.2mm

Step-by-step explanation:

Answer: 5 inspections in 4 hours, because if its 8 hours it would be 10 inspections

Step-by-step explanation:

Answer:

1.25

Step-by-step explanation:

10 ÷ 8 = 1.25

Answer:4

Step-by-step explanation: 9y-8y+2, when y=2

9(2)-8(2)+2=

18-16+2

=4

Answer:

B.  -414,720 x⁷y⁶

Step-by-step explanation:

To find the 4th term of the expansion of (2x - 3y²)¹⁰, we can use the binomial theorem.

The binomial theorem states that for an expression of the form (a + b)ⁿ:

\(\displaystyle (a+b)^n=\binom{n}{0}a^{n-0}b^0+\binom{n}{1}a^{n-1}b^1+...+\binom{n}{r}a^{n-r}b^r+...+\binom{n}{n}a^{n-n}b^n\\\\\\\textsf{where }\displaystyle \rm \binom{n}{r} \: = \:^{n}C_{r} = \frac{n!}{r!(n-r)!}\)

For the expression (2x - 3y²)¹⁰:

Therefore, each term in the expression can be calculated using:

\(\displaystyle \boxed{\binom{n}{r}(2x)^{10-r}(-3y^2)^r}\quad \textsf{where $r = 0$ is the first term.}\)

The 4th term is when r = 3. Therefore:

\(\begin{aligned}\displaystyle &\;\;\;\;\:\binom{10}{3}(2x)^{10-3}(-3y^2)^3\\\\&=\frac{10!}{3!(10-3)!}(2x)^7(-3y^2)^3\\\\&=\frac{10!}{3!\:7!}\cdot2^7x^7(-3)^3y^6\\\\&=120\cdot 128x^7 \cdot (-27)y^6\\\\&=-414720\:x^7y^6\\\\ \end{aligned}\)

So the 4th term of the given expansion is:

\(\boxed{-414720\:x^7y^6}\)

Answer:

Nico's annual premium is A) $5980.

Nico has $11.50 deducted from his weekly paycheck for health care.

So,

Nico's annual deduction are:

Since there are 52 weeks in a year.

So,

11.50*52=$598

His employer pays 90% of the premium, means Nico pays 10%.

And $598 is 10% of total annual premium.

Let annual premium is x.

10%of x =$598

10/100*x=$598

x=$598*10

x=$5980

Hence, Nico's annual premium is $5980

The ladder will reach a Height of approximately 43.46 meters on the building.

To find out how high on the building the ladder will reach, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the ladder forms a right triangle with the ground and the building. The base of the ladder is 7 meters, the height of the building is what we need to find, and the length of the ladder is given as 44 meters.

Using the Pythagorean theorem, we can set up the equation:

(Height of the building)^2 + 7^2 = 44^2

Simplifying the equation, we have:

(Height of the building)^2 + 49 = 1936

Subtracting 49 from both sides, we get:

(Height of the building)^2 = 1887

To find the height of the building, we take the square root of both sides:

Height of the building = √1887

Calculating the square root of 1887, we find that the height of the building is approximately 43.46 meters.

Therefore, the ladder will reach a height of approximately 43.46 meters on the building.

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The equations that has the solution x = all real numbers is 5(3x)+ 7x = 3x + 15 - x and 5(3x) + 7x = 3x + 10 - x,

Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.

A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.

Here given equations,

5(3x) + 6x = 3x + 15 + 2x

15x + 6x = 3x + 15 + 2x

15 x + 6x - 3x -2x = 15

16 x = 15

x = 15/16

5(3x).+ 7x = 3x + 15 - x

15 x + 7x = 3x + 15 - x

15 x + 7x - 3x + x = 15

22x - 3x + x = 15

20 x = 15

x = 15/20

x = 3/4

5(3x) + 7x = 3x + 10 - x

15x + 7x - 3x + x = 10

20x = 10

x = 10/20

x = 1/2

5(3x) + 7x = x + 15 - 3x

15x +7x - x + 3x = 15

24x = 15

x = 15/24

x = 5/8

Therefore the equations that has the solution x = all real numbers are :

5(3x).+ 7x = 3x + 15 - x and 5(3x) + 7x = 3x + 10 - x .

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Answer:

maybe option 1st

Step-by-step explanation:

Hope this will help you dear.

Answer:

3

Step-by-step explanation:

the triangle is a right triangle, meaning that we can use the pythagorean theorem to find a hypotenuse that will satisfy both Rs. if we use 3 as the radius, we get the hypotenuse as 2 + 3 = 5, where one leg is 3 and one is 4.

\( \sqrt{} 3 {}^{2} + 4 { }^{2} = 5 \)

so we know that a radius of 3 is right

Answer: (-5,1)

Step-by-step explanation: that should be right

Answer:

imaginary

Step-by-step explanation:

\(x {}^{2} = 2 - 10 \\ {x}^{2} = - 8 \\ x = \sqrt{ - 8} \)

from the working strp, we know that the number is imaginary

we can't square root the negative number

Answer:

A: 3/5 + 2/5 = 5/5

A: 3/5 + 1/5 = 4/5

B: 3/5 - 2/5 = 1/5

B: 3/5 - 1/5 = 2/5

C: 3/5 x 2/5 = 6/25

C: 3/5 x 1/5 = 3/25

C: 2/5 x 1/5 = 2/25

D: 1/2 + 1/4 = 3/4

D: 4/5 + 4/10 = 6/5

E: 4/6 ÷ 2/6 = 2

E: 1/6 ÷ 1/6 = 1

Step-by-step explanation:

Answer:

In naming a ray, we always begin with the letter of the endpoint (where the ray starts) followed by another point on the ray in the direction it travels. Since the vertex of the angle is the endpoint of each ray and our vertex is , each of our rays must begin with . Only fails to do so.

Answer:

A ray is a part of a line that has one endpoint and goes on infinitely in only one direction. You cannot measure the length of a ray. A ray is named using its endpoint first, and then any other point on the ray (for example, →BA ).

Answer: 5/6

Step-by-step explanation:

The reciprocal of a number is 1 divided by that number. The reciprocal of 6/5 is 5/6.

Answer:

5/6

Step-by-step explanation:

Well to find a fraction's reciprocal all you need is to flop it like this

6/5 => 5/6

so 5 takes the place of 6 and 6 takes the place of 5

that's how 6/5 turns into 5/6

The probability that you win is 6%, and the two choices are dependent events option (B) is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

It is given that:

A standard deck of playing cards contains 52 total cards, 13 of which are "spades".

The probability of the first draw:

Probability = favorable outcomes/total outcomes

First draw: 1/4

For the second draw:

Second draw = 12/51

The probability that you win = (1/4)(12/51) = 3/51

In percent:

= (3/51)x100

= 5.88 = 6%

Thus, the probability that you win is 6%, and the two choices are dependent on events option (B) is correct.

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The probability of the complement of the event is 0.05.

The complement of an event is the probability of that event not occurring. The relationship between the probability of an event and its complement is that they always add up to 1.

Therefore, if the probability of an event occurring is p, then the probability of its complement not occurring is 1-p.

In the case where the probability of an event is 0.95, the probability of its complement not occurring would be 1-0.95 = 0.05. This means that the probability of the complement of the event is 0.05.

This concept is important in probability theory and is used to calculate the probabilities of events and their complements. It allows us to consider all possible outcomes of a given situation and calculate the likelihood of each of them.

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Answer:

400×30= 12000 in 30yrs

12000

Step-by-step explanation:

12000÷.08= 150000

Answer:

(x-2)(x-2) or (x+2)(x+2)

Step-by-step explanation:

since you are squaring it, technically the terms are negative, but the product will be positive. when you multiply two negative factors, you get a positive answer. so either both can be negative or both can be positive.

Answer:

For cobalt-60, which has a half-life of 5.27 years, 50% remains after 5.27 years (one half-life), 25% remains after 10.54 years (two half-lives), 12.5% remains after 15.81 years (three half-lives), and so on.

Step-by-step explanation:

You can figue out the rest.

Answer:

June 26th

Step-by-step explanation:

Answer:

Numer 6 answer is (7.7

Step-by-step explanation:

Sry I don't know the rest

Answer:

Hi

Please mark brainliest ❣️

Thanks

Step-by-step explanation:

The answer is NO

Reason

x= 2 y= 1

Now input in the first inequality

y≤ -x + 4

1 ≤ -2 +4

1≤ 2 i.e 1 is less than two

Next inequality

y≤ x +1

1 ≤ 2 + 1

1≤ 3 i.e 1 is less than 3

But 1 is not equal to 3 and also not equal to 2

Hence our answer is NO

Answer:

27

Step-by-step explanation:

3(6)=18

18+9=27

Answer:

27

Step-by-step explanation:

You would use PEMDAS to solve this equation, P (parenthesis) E (exponates)  M (multiply) D (divide) A (add) S (subtract). The way you use this is by following the steps in the order that you would spell PEMDAS, so 3x+9 would be 3•6+9. So look at the equation 3•6+9, so what would we use first? do we have parenthesis? No, Do we have exponents? No, Do we have multiplication?  Yes, so multiply 3 and 6 = 18. Now the equation will look like this 18+9 = 27.

Hope this helps!

The required set of numbers 5, 9, 11, and 14 satisfies all the given conditions.

In mathematics, a set is a logically arranged group of items that can be represented in either set-builder or roster form. Sets are typically denoted by curly brackets; for instance, A = 1, 2, 3, 4 is a set.

a set of four whole numbers that satisfies the given conditions:

5, 9, 11, 14

To check that this set meets the requirements:

The range of the original set (12 - 4 = 8) increased by 2 to become 10 (14 - 4 = 10).

The mean of the original set ((4 + 9 + 10 + 12) / 4 = 8.75) remains the same in the new set ((5 + 9 + 11 + 14) / 4 = 8.75).

The median of the original set is 9.5 (the average of 9 and 10), and the median of the new set is 10 - 1 = 9.

Therefore, the set of numbers 5, 9, 11, and 14 satisfies all the given conditions.

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