In the right ∆ABC, BL is an angle bisector. If LB = 1.2 in and LC = 0.6 in. Find:

- The distance from L to AB.

- m∠ABC

Answer:

141 minus 3 equals 123

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

'cause yan Ang answer

The equation in slope-intercept form of the line that passes through (6, −1) and (3, −7) is:y = 2x − 13.

To write an equation in slope-intercept form of the line that passes through (6, −1) and (3, −7), you will use the point-slope form, as follows:

y − y1 = m(x − x1),

where:

m = slope (or gradient) of the line, and

(x1, y1) = the coordinates of a point on the line.

Let us calculate the slope (gradient) of the line using the given points:

(6, −1) and (3, −7).

m = (y2 − y1)/(x2 − x1)

m = (−7 − (−1))/(3 − 6)

= −6/−3

= 2

Thus, the slope of the line is 2.

Using the coordinates of one of the points, say (6, −1), in the point-slope form, we obtain:

y − y1 = m(x − x1)y − (−1)

= 2(x − 6)y + 1

= 2x − 12

Subtracting 1 from both sides, we get:

y = 2x − 13

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The evaluation of the quadratic equations are as follows;

Question 5

Question 6

Question 7

Sometimes; Factoring

Always; Quadratic formula

Always; Completing the square

Sometimes; Square root method

Sometimes; Factoring by group

Question 8

The numerator are;

(a) 8

4

(b) The denominator value;

4

(c) The roots are;

2

1

A quadratic equation is an equation of the form; a·x² + b·x + c = 0

Question 5

The quadratic equation, x² + 6·x + 10 = 0

The discriminant is 6² - 4×1×10 = -4

The discriminant < 0, therefore, the equation does not have solution

Question 7

Factoring;

Method of solving equations work more when the coefficient of x and the constant can be expressed as a + b and a·b

Where;

a·b = The constant

a + b = The coefficient of x

Therefore, factoring works sometimes

Sometimes; Factoring

Quadratic formula

The quadratic formula is an equation that involves the use of the constant and the coefficients of x

The quadratic formula therefore works all the time

Always; Quadratic formula

Complete the square

The completing the square method works by rearranging the equation in the form;

a·x² + b·x + c ⇒ a·(x + m)² + n

Where;

m = b/(2·a),

n = c - (b²/(4·a))

The method therefore works all the time

Always; Completing the square

Square root method

The square root method involves placing the square term of the equation on one side of the equation and the constant term on the other side

The square root method  works for equations that can be expressed in the form x² = b

The method  works sometimes

Sometimes; Square root method

Factoring by group

The method involves finding the common factors and grouping based on the common factors

The method only works when there are common factors

Sometimes; Factoring by group

Question 8

The  equation is 2·x² - 5·x = x - 4,

Writing the equation so that we have;

2·x² - 5·x - x + 4 = 0

2·x² - 6·x  + 4  = 0

x = (6 ± √((6² - 4× 2 × 4))/(2×2) =

Therefore;

x = 8/(2×2)  or x =  4/(2×2)

The numerators are 8 and 4

8

4

(b) The denominator is (2 × 2) = 4

(c) The two roots of the quadratic equation are;

x = 8/4 = 2 and x = 4/4 = 1

2

1

Question 6

The equation, x² - 16·x + 64 = 4

The left side of the equation can be factored as follows;

x² - 16·x + 64 = 4

x² - 8·x - 8·x + 64 = 4

(x² - 8·x) + (64 - 8·x) = 4

x·(x - 8) - 8·(x - 8) = 4

(x - 8)·(x - 8) = (x - 8)² = 4

Yes; (x - 8)² = 4

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Answer:

P (greater than 3) = 1/2

Step-by-step explanation:

A standard number cube has 6 sides, numbered 1 through 6.

We want to find the probability of rolling a number greater than 3. To find this probability, create a fraction. The numerator is the amount of numbers greater than 3 and the denominator is the total amount of numbers.

P(greater than 3)= numbers greater than 3/ total numbers

There are 3 numbers that are greater than 3 (4, 5 and 6).

There are 6 total numbers (1, 2, 3, 4, 5, and 6)

P (greater than 3) = 3/6

This fraction can be simplified. Both the numerator and denominator can be divided by 3.

P (greater than 3) = (3/3) / (6/3)

P (greater than 3)= 1/ (6/3)

P(greater than 3) = 1/2

The probability of rolling a number greater than 3 is 1/2.

Answer:

First one- y = -13

Step-by-step explanation:

27 + y = 14 (Rearrange equation)

y = 14 - 27 (Combine like terms)

y = -13

Answer:

10

Step-by-step explanation:

P.s. Coefficient always goes before the variable

= 2b + 4

= 2(3) + 4    Substitute b for 3

= 6 + 4

= 10

Answer:

v = 1

Step-by-step explanation:

v -10= -9

Add 10 to each side

v -10+10= -9+10

v = 1

Answer:

7

Step-by-step explanation:

σ = 4 ; μ =?

8.52 to the left of X

.

P(X < 8.52) = 64.8%

P(X < 8.52) = 0.648

Using the Z relation :

(x - μ) / σ

P(Z < (8.52 - μ) / 4)) = 0.648

The Z value of 0.648 of the lower tail is equal to 0.38 (Z probability calculator)

Z = 8.52 - μ / 4

0.38 = 8.52 - μ / 4

0.38 * 4 = 8.52 - μ

1.52 = 8.52 - μ

μ = 8.52 - 1.52

μ = 7

Let's assume the sum of the scores of the 28 students who took the test yesterday is 28 * 72 = 2016.

We know that the sum of the scores of all 30 students is (28 * 72) + x + y, where x and y are the scores of the two students who took the test this morning.

We also know that the mean of all 30 scores is 73. So we can write an equation:

[(28 * 72) + x + y]/30 = 73

Multiplying both sides by 30, we get:

2016 + x + y = 2190

So, x + y = 174.

We are given that the difference of the two scores is 22, so we can write another equation:

y - x = 22

Solving these two equations simultaneously, we get y = 98 and x = 76.

Therefore, the lower score from this morning is 76.

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The value of x is 10

The perimeter of the triangle is 30 units

An equilateral triangle can be defined as a triangle which has all its sides equal or congruent to each other.
The properties of an equilateral triangle includes;

From the information given, we have the sides as;

Since all of its sides are equal, we have to  equate two side, we have;

x + 5 = 2x - 5

collect like terms

x - 2x = -5 - 5

subtract the like terms

-x = -10

make 'x' the subject

x = 10

But the perimeter of an equilateral triangle = 3a = 3(10) = 30 units

Thus, the value is 10

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Betrys needs another 400 grams of diced potatoes to make her vegetable stew for 8 people.

We know that Betrys is cooking for 8 people, and we know that a recipe for 2 people needs 10 ounces.

8 people is 4 times 2 people, then for 8 people you need 4 times 10 ounces, this is 4*10 oz = 40 ounces.

Now we can apply a change of units, remember that:

1 oz = 28 grams

Then the total amount she needs is:

40 oz = 40*28 g = 1,120 g

So she needs in total 1,120 grams, and in the balance, she already has 720 grams, so the amount that she needs is given by the subtraction:

1,120 g - 720g = 400

Betrys needs another 400 grams of diced potatoes to make her vegetable stew for 8 people.

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Therefore , the solution to the given problem of trigonometry comes out to be tanθ = - √35 .

Trigonometry is the discipline of mathematics that studies correlations between angles and sides of triangles. Trigonometry is present in all of geometry because every straight-sided shape may be reduced to a set of triangles. Remarkably intricate connections exist between trigonometry and other areas of mathematics, particularly calculus, real or complicated, exponentials, logarithms, and infinite series.

Here.

Given : Cosθ = -1/6

To find : Tanθ

Since cosθ is in second quadrant

Thus,

Cosθ = B/H

According to pythagoras theorem,

H²= B²+ P²

=> 6² = 1² + P²

=> 36-1 =P²

=>P= √35

So ,

value of Tanθ comes out to be

=> tanθ = - √35 /1

=>tanθ = - √35

Therefore , the solution to the given problem of trigonometry comes out to be tanθ = - √35 .

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Answer:  y=1/2x+-4

(You cant give a certain number of points btw)

Answer:domain is x and range is y

Step-by-step explanation:

Answer:

the slope is 2

Step-by-step explanation:

using the slope formula

Answer: true

Step-by-step explanation:

Answer: True

Step-by-step explanation: Has to be true if a b and c are all numbers

The average cost per item over the interval (1,000,1,010] is (C(1010) - C(1000)) / (1010 - 1000) = (10,000 + 5(1010) - 10,000 - 5(1000)) / 10 = $5.50.

The average cost per item over the interval [999.5, 1000] is (C(1000) - C(999.5)) / (1000 - 999.5) = (10,000 + 5(1000) - 10,000 - 5(999.5)) / 0.5 = $5.00.

The given function C(x) represents the cost in dollars to manufacture x items. To find the average cost per item over a given interval, we use the formula: (C(b) - C(a)) / (b - a), where a and b are the endpoints of the interval.

For the interval (1,000,1,010], we substitute a = 1000 and b = 1010 into the formula to obtain (C(1010) - C(1000)) / (1010 - 1000). Simplifying the expression using the given function C(x) yields ($10,000 + $5(1010) - $10,000 - $5(1000)) / 10 = $5.50 per item.

For the interval [999.5, 1000], we substitute a = 999.5 and b = 1000 into the formula to obtain (C(1000) - C(999.5)) / (1000 - 999.5). Simplifying the expression using the given function C(x) yields ($10,000 + $5(1000) - $10,000 - $5(999.5)) / 0.5 = $5.00 per item.

To find C'(1000), we differentiate the function C(x) with respect to x, which gives C'(x) = 5. The value of C'(1000) is therefore 5, rounded to 1 decimal place.

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Answer:

A and E

Step-by-step explanation:

The ratio of the hypotenuse to the shorter leg to the longer leg is 2:1: root 3

Answer:

A. and E.

Step-by-step explanation:

The length of the hypotenuse is always double the length of the shortest leg and you can find the long leg by multiplying the short by the square of 3.

The probability of getting at least one head is 15/16.

What is probability?

The ratio of positive outcomes to all possible outcomes of an event is known as the probability.

Formula for probability = favourable outcomes/ total outcomes

Main body:

if 4 coins are tossed , total no. of outcomes = 2⁴ = 16

In a toss there are 2 outcomes T or H

so, Probability of getting Head = 1/2

The probability of getting at least 1 head = 1- probability of getting no heads

⇒1 - Probability of getting tail in 4 tosses

⇒ 1 - (1/2)⁴

⇒ 1 - 1/16

⇒ 15/16

So the probability of getting at least one head is 15/16.

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Answer:

Step-by-step explanation:

(5 - 1)/2= 4/2 = 2

(5+3)/2= 8/2= 4

(2,4)

The regular expression (xy | zy)* describes a language that consists of zero or more repetitions of either "x" followed by zero or more "y"s or "z" followed by one or more "y"s. "zyyxz" is part of the language generated by the given regular expression.

In the given string, "zyyxz", we can break it down into individual components based on the regular expression. The first "z" matches the pattern "z" followed by one or more "y"s. The "yyx" part matches the pattern "x*y", where "y" occurs zero or more times after "x". Finally, the "z" at the end also matches the pattern "z" followed by one or more "y"s.

Since all parts of the string "zyyxz" match the regular expression pattern, we can conclude that "zyyxz" indeed belongs to the language described by the regular expression (xy | zy)*.

Therefore, "zyyxz" is part of the language generated by the given regular expression.

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Answer:

12x-4

Step-by-step explanation:

8x+4(x-1)

multiply whats inside the parenthesis by 4

8x+4x-4

add like terms

12x-4

Answer:

A heptagon has 7 sides, so we take the hexagon's sum of the interior angles and add 180 to it getting us, 720+180= 900 degrees

Step-by-step explanation:

The formula for calculating the sum of the interior angles of a regular polygon is: (n-2) x 180 degrees. N is the number of sides

The use the numbers 5, 6, and 7 and the operations of addition, subtraction, multiplication, and/or division to create three different number expressions with three different values will be:

1. 5 × 6 + 7 = 37

2. 5 + 6 - 7 = 4

3. 5 + 6 + 7 = 18

Addition simply means the sum of the numbers that are given. It should be noted that addition is represented by the sign +.

In this case, we are told to use 5, 6 and 7 to create different values. These are represented above. The addition of 5, 6, and 7 gives 18.

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The probability that the person is over 40 given that he or she is a root beer drinker is 62.75%

The fact that

The ratio of the event space's size to the sample space's size represents an event's probability.

The total number of outcomes equals the size of the sample space.

The number of outcomes in the event you are interested in is the event space.

so

P = event space size divided by sample space size

step 1

determine the likelihood that the person is over 40 years old.

The sample size is 255.

event space size = 85

P=85/255------> P=1/3

step 2

determine the likelihood that they consume root beer.

The sample size is 255.

event space size = 75

P=75/255------> P=5/17

step 3

determine the likelihood that the individual is over 40 years old or that

They consume root beer.

so

P=(1/3)+(5/17)——-> P=(17*1+3*5)/51------> P=32/51-----> 0.6275——> 62.75%

therefore, the response is

32/51 or 62.75%

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Answer:

-(44a+9/24)

Hope this helps

Answer: 5a/3 - 3/8 - a/6

Step-by-step explanation:

\(\begin{array}{l}-\frac{5}{3}a+\frac{1}{8}-\frac{1}{6}a-\frac{1}{2}\\\\=-\frac{5a}{3}+\frac{1}{8}-\frac{a}{6}-\frac{1}{2}\ {\longrightarrow-\frac{5}\{3}=-\frac{5a}{3};\ \frac{1}{6}a=\frac{a\cdot a}{6}=\frac{a}{6}}\\\\=\frac{5a}{3}-\frac{3}{8}-\frac{a}{6}{\longrightarrow{\frac{1}{8}-\frac{1}{2}=\frac{1}{8}-\frac{4}{8}=-\frac{3}{8}}}}}\end{array}\)

The actions which is taken to ensure "data-integrity" is maintained during  "simultaneous-transactions" are called concurrency control  actions, option (c) is correct.

The "Concurrency-Control" refers to techniques and mechanisms which is used to manage and coordinate concurrent access to shared resources, such as databases, to prevent conflicts and maintain data consistency.

It involves managing the execution of multiple transactions in a way that ensures data integrity, avoids conflicts, and preserves the correctness of the overall system.

The "Concurrency-Control" actions can include locking mechanisms, isolation levels, transaction scheduling, and conflict resolution strategies. These actions are crucial in maintaining data integrity and ensuring that multiple transactions can safely execute concurrently without interfering with each other.

Therefore, the correct option is (c).

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The given question is incomplete, the complete question is

The actions that must be taken to ensure data integrity is maintained during multiple simultaneous transactions are called ________ actions.

(a) logging

(b) multiple management

(c) concurrency control

(d) transaction authorization.

Answer:

A. 20%

Step-by-step explanation:

% Increase = 12−10/10x100

= 2/10x100

= 20%

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