Given the figure below, find BD.
А
B
8
6
X + 3
2x
D

Answer:

x(x-7)+4(x-1)/(x-1)(x+1)(x-7)

Step-by-step explanation:

Given the expression x/x²-1 + 4/x²-6x-7

Factorize x²-6x-7

x²-6x-7

= x²-7x+x-7

= x(x-7)+1(x-7)

= (x+1)(x-7)

Replace back into the expression given

x/x²-1 + 4/x²-6x-7

= x/x²-1 + 4/ (x+1)(x-7)

= x/(x+1)(x-1) + 4/(x+1)(x-7)

Find the LCM

=  x(x-7)+4(x-1)/(x-1)(x+1)(x-7)

This gives the required expression

The missed value in the frequency tree is 224.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Given that 400 people are asked if they drink tea.

7/10  say Yes and  20% of the people who say Yes drink at least 3 cups each day

7/10 of 400 is 280

Which means 280 people drink tea.

The remaining people does not drink tea.

Remaining =400-280=120.

Now let us find 20% of 280

20/100×280

0.2×280=56

So 56 drink at least 3 cups each day.

280-56=224

So 224 people drink tea but not three cups.

Hence, the missed value in the frequency tree is 224.

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Answer: 36 are red

Step-by-step explanation:

3 out of every 5

5*12 = 60

so do 3*12 which = 36

36/60

Answer:

3

Step-by-step explanation:

12 × 3 = 36

12 × 5 = 60

36 + 60

Have a good day :)

Answer:

3

Step-by-step explanation:

Let's double check:

12 x 3 = 36

12 x 5 = 60

36 + 60, it fits!

Answer:

Step-by-step explanation:

Aubrey's Pie Shop recently sold [tex]20[/tex] pies in total, [tex]6[/tex] of them being cherry pies, so the experimental probability is [tex]\dfrac{6}{20} = \dfrac{3}{10} = 30\%[/tex] chance of the next one being a cherry pie.

Answer: HL

Step-by-step explanation:

HL because the hypotenuse leg theorem shows how a given set of right triangles are congruent if the corresponding lengths of their hypotenuse and one leg are equal.

Using long division convert 1/4 to a decimal

To convert a fraction into a decimal, we'll just divide the numerator by the denominator:

4√1

we'll divide 1 by 4.

1 divided by 4 equals 0

0

4√1

To keep dividing, we'll add a decimal point and a zero after the 1, we'll also add a decimal point after the 0 on top

0.

4√1.0

Now we can divide 10 by 4, 10 divided by 4 equals 2.

0.2

4√1.0

Now we'll multiply 4 by 2, 4 times 2 equals 8. So we'll subtract 8 from 10.

0.2

4√1.0

-8

______

2

Since 2 is greater than 0, we're not finished dividing yet. We'll add another 0 after the decimal point and bring it down.

0.2

4√1.00

-8

________

20

20 divided by 4 equals 5.

0.25

4√1.00

-8

______

20

Now we'll multiply. 4 times 5 equals 20. When we subtract 20 from 20, we get 0. The 0 means we're done dividing.

0.25

4√1.00

-8

______

20

20

________

0

So 1/4 is equal to 0.25.

The process to find the asymptote and zeros of the function is explained below.

The term asymptote is referred as a horizontal/vertical/slant line to which the curve is very close to but the curve doesn't touch the asymptote.

Here we need to find the way to identify the asymptotes and zeros of a function.

The process of finding the asymptote is defined as,

If you want to find the horizontal asymptotes, then apply the limit x→∞ or x→ -∞.

Where as if you want to find the vertical asymptotes, then apply the limit y→∞ or y→ -∞.

Finally, if you want to find the slant asymptote, then divide the numerator by the denominator.

The process of finding the zero of the function is defined as the way to find the values of x where f(x) = 0.

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Christian Mansell (born 9 February 2005) is an Australian racing driver set to compete in the 2023 FIA Formula 3 Championship with Campos Racing. He previously competed in the 2022 Neuroforamina Open Championship for Crypto Tower Racing, finishing in third overall in the standings.

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Answer:

a) 4.2 - 2.8 = 1.4

b) 72.1 - 45.6 = 26.5

c) 82.2 - 41.3 - 29.2 = 11.7

d) 17.1 - 11.7 - 0.8 = 4.6

e) 29.2 - 12.5 - 0.9 = 15.8

f) 21 - 14 = 7

g) 71 - 37 - 18 = 16

h) 50 - 19 - 8 = 23

i) 92 - 57 - 16 = 19

j) 44 - 18 - 9 = 17

Answer:

X=5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

15+x=20

or, x=20-15

or, x=5

Answer:

A)

Step-by-step explanation:

Answer: A perimeter is the total length of all the sides of a polygon. It is calculated by adding up the lengths of all the sides of the polygon. For a polygon with distinct and non-overlapping sides, each side length contributes exactly once to the perimeter. So in such case, a side length of a polygon can never produce two different perimeters.

However, it's worth mentioning that, one side length of a function could be a side of a polygon and the other could be a side of another shape. Also, it's possible that a single side length of an object is connected to a different set of side length, generating different perimeters.

For example, the length of an arc of a circle can be considered as a "side length" of the circle and it can be used to calculate both the perimeter of the arc and the circumference of the full circle, which are different measurements.

Also, a circular pool has a radius, but it's perimeter is the circumference, and this length is produced by the same radius but it's a different perimeter from the length of the radius.

In summary, a side length can produce different perimeter if we are talking about different shapes and measurements.

Step-by-step explanation:

The required inequality expression for the third side is 1 < m < 25. The correct option is (B).

Linear inequality refers to the relation between a linear algebraic expression to some known value that contains inequality sign.

Unlike a linear equation it can have a range of values inside an interval.

The sides of the triangle are given as 12 and 13 units respectively.

As per the rule for sides of a triangle, the third side is always less than the sum and greater than the difference of two sides.

Then, the inequality can be written as,

13 - 12 < m < 13 + 12

⇒ 1 < m < 25

Hence, the measure of third side can be written in inequality as 1 < m < 25.

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Answer:

Step-by-step explanation:

Answer:

1. (-4,-2) (4,-2)

2. (4,1)(7,1)

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

90÷6=15×8=120

As per the decimal number system, the cost of 25 tickets is $32.5

The term decimal in math is defined as the numbers, which consist of two parts namely, a whole number part and a fractional part separated by a decimal point.

Here we have given that the product of 3 student tickets at $4.

Here we have know that the ticket cost for 3 students is $4.

Then the cost of one person is calculated by dividing the cost by the number of students then we get,

=> 4/3

=> 1.3

So, if the cost for one person or ticket is $1.3 then the cost of 25 tickets is calculated as,

=> 25 x 1.3

=> 32.5

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20 dodgeballs have been pumped up by Ttaloc.

Ttaloc has 36 additional pumped-up balls.

The complete ball's original number is 14.

The relationship between two or more numbers is expressed by the ratio. It displays the frequency of how often one value is encapsulated by another value (s).

The number of dodgeballs Ttaloc pumped up = (5/14) x 56 = 20

The number of other balls Ttaloc pumped up = (9/14) x 56 = 36.

A ratio in mathematics demonstrates how many times one number is present in another.

A ratio can have any number of quantities, such as counts of people or things or measurements of length, weight, time, etc. Both numbers must be positive in most situations.

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The equation of the line perpendicular to x - 4y = 7 can be written as:

y = 4*x + b

Where b could be any real number.

Two lines are perpendicular if the product between the slopes of the lines is equal to -1.

Where a general line in the slope-intercept form is written as:

y  =a*x +b

And the given line is:

x - 4y = 7

Writing this in the slope-intercept form we will get:

-4y = -x - 7

y = (-1/4)*x + 7/4

So the slope is -1/4, then the slope of our line must be such that:

a*(-1/4) = -1

a = -4*-1 = 4

a =4

So the line perpendicular to the given one is:

y = 4*x + b

Where b can be any real number.

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The company is likely to sell 3,120 copies of rock music per week.

If the company estimates sales of 6,000 copies a week at its online store, it is likely that 78/150 x 6,000 = 3,120 copies will be from the rock genre.

To find this, we first need to calculate the proportion of visitors that preferred rock music by dividing the number of visitors who preferred rock (78) by the total number of visitors surveyed (150). This gives us 78/150 = 0.52.

Next, we multiply this proportion by the estimated number of weekly sales at the online store (6,000) to find the number of sales that are likely to be from the rock genre. 0.52 x 6,000 = 3,120.

So, the company is likely to sell 3,120 copies of rock music per week.

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Answer:

Step-by-step explanation:

Answer:

The function that correctly depicts the scenario is:

cost(n) = 18.50 * 1.06^n

This function takes the number of years n as input and returns the cost of eating at the all-you-can-eat buffet after n years.

The cost of eating at the all-you-can-eat buffet 10 years from now can be calculated as follows:

cost(10) = 18.50 * 1.06^10 ≈ $30.59

The cost of eating at the all-you-can-eat buffet 15 years ago can be calculated as follows:

cost(-15) = 18.50 * 1.06^(-15) ≈ $8.01

Step-by-step explanation:

Answer:

58 units²

Step-by-step explanation:

Using Pythagoras identity

The square on the hypotenuse ( third side ) is equal to the sum of the squares on the other 2 sides, then

area = 7² + 3² = 49 + 9 = 58

Step-by-step explanation:

Firstly: using pythagoras theorem

Hyp^2=adj^2+opp^2

Let the hyp be x

X^2=7^2+3^2

X^2=49+9

X^2=58

X=Square root 58

Let the side is root 58

Area of a square is L^2

Root 58×root 58

The area of the square is 58unit squ

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The third side of a triangle can be calculated using the Pythagorean Theorem.

This theorem states that in a right triangle, the sum of the squares of the two sides is equal to the square of the hypotenuse. The hypotenuse is the longest side of the triangle and is opposite the right angle.

Formula:

[tex]a^2 + b^2 = c^2[/tex]

Determine the two side lengths of the triangle

Calculate the sum of the squares of the two side lengths.

Calculate the square root of the sum of the squares of the two side lengths. This is the length of the third side (the hypotenuse).

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Answer:

first term(a)= 80

common ratio(r)= t2/t1 =40/80 =1/2

T4= ar^n-1

= 80*1/2^4-1

=80*1/2^3

=80*1/8

=10

then

t5=ar^n-1

= 80*1/2^5-1

=80*1/16

=5

Some polynomials have specific names indicated by their prefix like monomial is a polynomial with exactly one term (“mono”—means one) binomial is a polynomial with exactly two terms (“bi”—means two) trinomial is a polynomial with exactly three terms (“tri”—means three).

Some polynomials have unique names that are denoted by their prefix, such as monomial, which is a polynomial with precisely one term ("mono"—means one). A binomial polynomial has precisely two terms ("bi" indicates two). A trinomial is a polynomial with three terms ("tri"—three). A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive-integer powers of variables. x2 4x + 7 is an example of a polynomial with a single indeterminate x.

Here,

Some polynomials have unique names that are denoted by their prefix, such as monomial, which is a polynomial with precisely one term ("mono"—means one). A binomial polynomial has precisely two terms ("bi" indicates two). A trinomial is a polynomial with three terms ("tri"—three).

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Answer:

the lateral area of the regular prism is 30 cm².

Step-by-step explanation:

Given;

the base of the regular prism, b 4cm

height of the prism, h = 2.5 cm

The lateral area of the regular prism is calculated as the product of the base perimeter and height of the prism.

L.A = P x h

where;

P is the perimeter of the base = 3 x 4cm (equilateral triangle has equal sides)

P = 12 cm

L.A = 12 cm x 2.5 cm

L.A = 30 cm²

Therefore, the lateral area of the regular prism is 30 cm².

Answer:

30 cm2

Step-by-step explanation:

Answer:

x = -8 (10

Step-by-step explanation:

x (x + 16) = -64

-8(10 + 16) = -64

-80 + 16 = -64

-64 = -64

Answer:

i think the answer is 45.5 because you have 91 and you know the diameter of 2 circle so you would divide 91 by 2

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The probability is 0.4444.

Probability is a measure of the likelihood of a particular outcome occurring in a given situation. It is the chance that something will happen or is true. Probability is expressed as a number between 0 (impossible) and 1 (certain). Probability is a mathematical way of predicting what will happen in the future based on a given set of data. It is used to analyze the likelihood of various outcomes in a range of scenarios, such as gambling, finance, insurance, and weather forecasting.

The probability of a randomly selected tester from the group of college-bound seniors having a score between 1497 and 1507 can be calculated using the standard normal distribution. First, we need to convert the scores to standard scores, or z-scores. Subtract the mean from the scores and divide by the standard deviation to get z-scores.

For XXX = 1497, z = (1497 - 1497) / 322 = 0.
For XXX = 1507, z = (1507 - 1497) / 322 = 0.31.

Using a standard normal table, we can calculate the area under the normal curve between 0 and 0.31. The probability of randomly selecting a tester with a score between 1497 and 1507 is 0.4444. The probability is therefore P(1497 ≤ XXX ≤ 1507) = 0.4444.

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Complete questions as follows-
The distribution of SAT scores of all college-bound seniors taking the SAT in 2014 was approximately normal with a mean of 149714971497 and standard deviation of 322322322. Let XXX represent the score of a randomly selected tester from this group. Find P(1497 ≤ XXX ≤ 1507).