Question is in the image. I need help with #19

The angle bisector theorem states that a triangle's opposite side is divided into two halves by an angle bisector that is proportional to the triangle's other two sides.

A point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects, therefore if mACD = 90°, point D is equidistant from points A and B.

Any point on the perpendicular bisector is simply equal distance from both endpoints of the line segment on which it is drawn, according to the perpendicular bisector theorem.

The answer is that point  is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it makes up. Therefore, if a pillar is stationed at the middle of a bridge at an angle, all the points on the pillar will be equidistant from the end points of the bridge intersects.

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The function translation / transformation rules:

Function transformations specify how a function is moved on a graph and how its shape is altered. Translation, dilatation, and reflection are the three main categories of function transformations.

The technique of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation. In particular, the change of algebraic equations is a typical kind of algebraic problem.

The function translation / transformation rules:

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Answer:

8/15

Step-by-step explanation:

Multiply the numerators:

2*4 = 8

Multiply the denominators:

3*5 = 15

Now we have 8/15.

This cannot be simplified, so this is our final answer.

[tex]\frac{2}{3} \times\frac{4}{5}[/tex]

Multiply numerator by numerator and denominator by denominator:

[tex]2*4=8\\3*5=15[/tex]

[tex]\frac{8}{15}[/tex]  would be your final answer.

The number of 1/4 pound bags that can be filled with this amount of nails is 2 1/3 bags.

The large bag contains 7/12 pound of nails.

We also want to fill them into 1/4 pounds of bags. The number of bags needed will be calculated through division. This will be:

= Amount in large bags / Smaller bags

= 7/12 ÷ 1/4

= 7/12 × 4/1

= 28/12

= 2 1/3

Therefore, 2 1/3 1/4 bags are required

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Taking into account the definition of a system of linear equations, the first number is x= -14 and the second number y= -13.

A system of linear equations is a set of linear equations (that is, a system of equations in which each equation is of the first degree) in which two or more unknowns are related.

Systems of linear equations have as a solution set all ordered pairs (x, y) that satisfy the equation, where x and y are real numbers. That is, solving a system of equations consists of finding the values of the unknowns, with which, when replaced in the equations, they must give the proposed solution.

In this case, a system of linear equations must be proposed taking into account that

You know:

The system of equations to be solved is

x-y= -1

x+y= -27

It is decided to solve the system of equations using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable "x" from the first equation:

x= -1 +y

Replacing this expression in the second equation:

-1 +y +y= -27

Solving:

y +y= -27 +1

2y= -26

y= (-26)÷2

y= -13

Remembering that x=-1 +y, you get

x= -1 -13

x= -14

Finally, the numbers are -13 and -14.

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The values of the first and second numbers are - 13 and - 14 respectively.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Let us assume that the two numbers are x and y.

Given, The difference between the two numbers is -1.

∴ x - y = - 1...(i)

And, Their sum is - 27 which is,

x + y = - 27...(ii)

Now, if we add eqn (i) to eqn (ii)

    x + y = - 27

+  x - y =     -1

---------------------

  2x     = - 28

+ y and - y get canceled and we get

∴ 2x = 26.

x = - 13.

Now, substitute the value of x in any of the eqn(i). we get y = - 14.

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Answer:

slope = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

3x + y = 8  ( subtract 3x from both sides )

y = - 3x + 8 ← in slope- intercept form

with slope m = - 3

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex]

The value of a³b for the value of a=3 and b=-5-2i is -135-54i for the given complex number that defines "Complex numbers are the numbers that are expressed in the form of a+ib where, a, b are real numbers and 'i' is an imaginary number called “iota”."

Complex numbers are those that are expressed as a+ib, where a and b are real numbers and I is a fictitious number called a "iota." I has the value (√-1). As an illustration, the complex number 2+3i is made up of the real number 2 (Re) and the imaginary number 3i (Im). In the 19th century, the term "complex numbers"—which denotes that they have both real and imaginary components—became widely used. Occasionally, the term "imaginary number" is used to describe a complex number that is not real or, more commonly, a number whose real part is zero (a.k.a "pure imaginary").

Here,

The value of a³b

=3³(-5-2i)

=27(-5-2i)

=-135-54i

For the given complex number that defines "Complex numbers are the numbers that are expressed in the form of a+ib where, a, b are real numbers and I is an imaginary number called "iota," the value of a³b is -135-54i.

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Answer:

(x² -5x +13) + (x² +3x -6)

Step-by-step explanation:

(x² -5x +13) + (x² +3x -6)

x² -5x +13 + x² +3x -6

|x² + x²| |-5x + 3x| |+13 -6|

2x² -2x +7

The vertex of the function is (1, -25) Correct

Because

f(x) = (x + 4)(x - 6)

Substitution

-25 = (1 + 4)(1 - 6)

Simplification

-25 = (5)(-5)

Result

-25 = -25 As both sides of the equation are equal this option is true

5) The graph is negative on the entire interval - 4 < x < 6 because the graph is below the x-axis

Using the Pythagorean Theorem, it is found that:

A. The straight line distance between the school and the fire station is of 4.62 miles.

B. The distance between the school and the hospital is of 2.08 miles.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following rule:

[tex]h^2 = l_1^2 + l_2^2[/tex]

In the context of this problem, the distance between the school and the fire station is the hypotenuse of a right triangle with sides 4.3 and 1.7, hence:

d² = 4.3² + 1.7²

d = sqrt(4.3² + 1.7²)

d = 4.62 miles.

The hospital is 3.1 miles west of the fire station, hence the distance between the school and the hospital is the hypotenuse of a right triangle of sides 1.7 and 4.3 - 3.1 = 1.2, hence:

d² = 1.2² + 1.7²

d = sqrt(1.2² + 1.7²)

d = 2.08 miles.

The complete problem is given by the image at the end of the answer.

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the data are normally distributed with a mean of 74.674.6 hours and a standard deviation of 9.19.1 hours. So  10.2% of gadgets were powered by batteries for fewer than 63 hours.

Given that,

Data have a mean of 74.6 hours and a standard deviation of 9.1 hours, and they are regularly distributed.

The standard deviation is defined as ?

The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.

[tex]p(X\leq 63) = p(Z\leq 63-74.6/9.1)[/tex]

From standard deviation,

         [tex]p(X\leq 63) = p(Z\leq -1.279)= 0.1061[/tex]

a certain percentage of gadgets have battery life of less than 63 hours.

X= 63 hours

Percentage of devices ran on the batteries for fewer than 63 hours = 10.2%

Therefore, 10.2% of electronic devices had battery life of less than 63 hours

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Answer:

-4

Step-by-step explanation:

12/-3=-4

The difference quotient of f(x) is:[ f(x + h) - f(x)]/h =  8x + 4h + 3

Here we have the function:f(x) =4x^2 +3x - 5

And we want to get the difference quotient that can be written as:

[f(x + h) - f(x)]/h

Replacing the function we get:

[f(x + h) - f(x)]/h = [4*(x + h)^2 + 3*(x + h) - 5 - 4*x^2 - 3x + 5]/h

Solving further (open the brackets), we have

[f(x + h) - f(x)]/h = [4x^2 + 8*x*h + 4h^2 + 3x + 3h  -5 - 4x^2 - 3x + 5]/h

Evaluate the like terms

So, we have

[f(x + h) - f(x)]/h = [8*x*h + 4h^2 + 3h]/h

Evaluate the quotients

[f(x + h) - f(x)]/h = 8x + 4h + 3

That is the difference quotient.

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Answer:

6.25 weeks

Step-by-step explanation:

Take 18.75 ÷ 3. The construction crew finishes 3 km per week. You should receive 6.25 by solving the equation. So, this is the answer.

Answer:

2(x + 9)

Explanation:

Let x represent the unknown value.

Double a quantity increased 9 means;

*We'll multiply the quantity by 2

*Increased by signifies addition

*Quantity means we'll put the expression after it in brackets

Let's go ahead and write the required algebraic expression;

Answer: ∠BDG = 50°

Step-by-step explanation:

    We know that a straight line is equal to 180°, meaning that line CDF is 180°.

     Next, we know that angle CDB, angle BDG, and angle GDF should all add up to be 180°, since we know CDF is equal to 180°.

     Lastly, with all this information in mind, we will set up an equation and solve.

130° + BDG = 180°

∠BDG = 50°

The figure above is a rectangle

The classifications of a rectangle are:

1. A rectangle has 4 sides and angles, therefore, it is a quadrilateral.

2. Each interior angle is a right-angle, that is 90⁰

3. The sum of the interior angles equals 360

4. The opposite sides are parallel

5. The opposite sides are equal

6. The diagonals bisect each other

7. The diagonals have the same length

The percentage of adult females with pulse rates between 49.0 bpm and 86.5 bpm - 81.86%

The percentage of adult females have pulse rates below 90 bpm - 89.97%

a)

X ~  N ( µ = 74 , σ = 12.5 )

P ( 49 < X < 86.5 )

Standardizing the  value

Z = ( X - µ ) / σ

Z = ( 49 - 74 ) / 12.5

Z = -2

Z = ( 86.5 - 74 ) / 12.5

Z = 1

P ( -2 < Z < 1 )

P ( 49 < X < 86.5 )  =  P ( Z < 1 ) - P ( Z < -2 )

P ( 49 < X < 86.5 )  = 0.8413 - 0.0228

P ( 49 < X < 86.5 )  = 0.8186  ≈  81.86%

b)

X ~ N ( µ = 74 , σ = 12.5 )

P ( X < 90 )

Standardizing the value

Z = ( X - µ  ) / σ

Z = ( 90 - 74 ) / 12.5

Z = 1.28

P (  ( X - µ ) / σ )  < ( 90 - 74 ) / 12.5 )

P ( X < 90 ) =  P ( Z < 1.28 )

P ( X < 90 ) = 0.8997  ≈  89.97%

The pulse rate, or the number of times the heart beats each minute, is gauged by the pulse rate. The arteries enlarge and constrict with the flow of blood as the heart pumps blood through them. An elevated heart rate, or tachycardia, can occur for any reason. Exercise-induced or stress-related heart rate increases are two possible causes (sinus tachycardia). Sinus tachycardia is not seen as an illness but rather a symptom. Another factor contributing to tachycardia is an unsteady heartbeat (arrhythmia).

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Answer:

$134.50

Step-by-step explanation:

4200 x .035 = 134.50

3.5% Percent means per 100

3.5/100 when you divide by 100, you move the decimal two places to the left.

The commission amount is $147

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Mr. Webster sells vacation rentals and earns a 3.5% commission on every vacation rental he sells.

He sold $4200.

So, 3.5% of commission:

4200 x 3.5  / 100

= 147

Therefore, the commission is $147.

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The current exchange rate is 1 US dollar = 1 euro.

The exchange rate of a currency is the worth of one currency in respect to another, or the rate at which one currency will be exchanged for another.

The foreign exchange market, commonly known as Forex or FX, is a global decentralized market for currency trading that determines the exchange rates of such currencies.

A currency exchange rate is the rate at which one currency can be exchanged for another. In other words, the exchange rate is the price of one currency in terms of another.

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Betty takes 6 hours to paint a house alone, that indicates she can paint 1/6 of the house in 1 hour then Karen working alone will paint a house in 3 hours.

Since Betty takes 6 hours to paint a house alone, that indicates she can paint 1/6 of the house in 1 hour.

Karen can even paint 1/x in 1 hour

Both of them will paint the house in 3/2 hours.

We then add them together which gives:

1/6 + 1/x = 3/2x

The lowest common multiple is 6x

1x/6x + 6/6x = 9/6x

We then leave out the denominators

1x + 6 = 9

simplifying the above equation, we get

x = 9 - 6

x = 3

Therefore, the value of x = 3.

Karen working alone will paint a house in 3 hours.

The complete question is:

Betty and Karen have been hired to paint the houses in a new development. Working together, the women can paint a house in two-thirds the time that it takes Karen working alone. Betty takes 14 h to paint a house alone. Betty takes 6 h to paint a house alone.

Required:

How long does it take Karen to paint a house working alone?

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The area of the region within the square and without the circle is equal to 13.7 square inches.

In this problem we find the case of figure generated by a square and an inscribed circle. Then, the area of the region is found by subtracting the area of the circle from the area of the square. Then, the area is:

A = L² - 0.25π · D²

Where:

If we know that D = L = 8 in, then the area of the region is:

A = (8 in)² - 0.25π · (8 in)²

A = 64 in² - 50.265 in²

A = 13.735 in²

The area of the region is equal to 13.7 square inches.

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Answer:

D. Negative

Step-by-step explanation:

Always read the graph from left to right

The graph is going down thus it is negative

Answer: Negative.

Step-by-step explanation: The graph of the line falls from left to right which makes it negative.

Answer:

p = 3

Step-by-step explanation:

y = mx + b They gave us the slope of -1.  We need to find the y intercept.  We will use the x of 9 and the y of 2 to find b.  We will plug these numbers in to find b.

y = mx + b

2 = -1(9) + b

2 = -9 + b  Add 9 to both sides

11 = b

y = -x +11

Now, plug in 8 for x

y = -1(8) + 11

y = -8 + 11

y = 3

In this case p is 3.

Given the graph, you can identify that x-axis represents the number of the corresponding month, and the y-axis represents the Number of Newspapers distributed (in hundreds).

You know these points:

Notice that 200 school newspapers were distributed in the second month, and 300 school newspapers were distributed in the fourth month. Therefore, you can conclude that the number of school newspapers that were distributed in the second month must be between 200 and 300. You can set up that, for:

The y-value is:

Hence, the answer is: Second option.

The equation that passes through (-12, 15 with a slope of -1 in point slope form is y - 15 = - 1(x + 12)

Linear equation can be represented in different form such as point slope form, slope intercept form  and standard form.

Therefore, let's represent the line that passes through (-12, 15) with a slope of -1 in point slope form.

Hence,

y - y₁ = m(x - x₁)

where

Therefore,

m = slope = -1

using (-12, 15)

Hence,

y - 15 = - 1(x - (-12))

Therefore,

y - 15 = - 1(x + 12)

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Answer: [tex]f(1)=1, f(2)=0, f(3)=2[/tex]

Step-by-step explanation:

[tex]0 \leq 0 \leq 1 \implies f(1)=1^2 =1\\\\1 < 1 \leq 2 \implies f(2)=-2+2=0\\\\2 < 3 \leq 3 \implies f(3)=3^2 -3(3)+2=2[/tex]

Answer:

6.5625 gal per hour

Step-by-step explanation:

Since there are 60 minutes per hour, we need to multiply 14 by 60 to change per minute into per hour. Combining these: 14 fl oz / min x (1 gal / 128 fl oz) x (60 min / hr) = 6.5625 gal per hour. Written as a mixed fraction: 6 9/16 gal per hour.