Find the equation of the line.
The perpendicular bisector to the line segment with endpoints (-8,5) and (4,1).
The equation of the line is
y =

Answer:

y = -1/2x +9/2

Step-by-step explanation:

In the proportion (5x + 1):3 = (2x + 2):7, the value of x is -1/29.

In the proportion (6x):(4x) = 7, there is no value of x that satisfies the proportion.

To find the value of x in the given proportions, let's solve them one by one:

(5x + 1) : 3 = (2x + 2) : 7

To solve this proportion, we can cross-multiply:

7(5x + 1) = 3(2x + 2)

35x + 7 = 6x + 6

Subtracting 6x from both sides and subtracting 7 from both sides:

35x - 6x = 6 - 7

29x = -1

Dividing both sides by 29:

x = -1/29

Therefore, the value of x in the first proportion is -1/29.

(6x) : (4x) = 7

To solve this proportion, we can simplify the left side:

6x / 4x = 7

Dividing both sides by 2x:

3/2 = 7

This equation is not true, as 3/2 is not equal to 7.

Therefore, there is no value of x that satisfies the second proportion.

In summary, the value of x in the proportion (5x + 1) : 3 = (2x + 2) : 7 is -1/29, and there is no value of x that satisfies the proportion (6x) : (4x) = 7.

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Answer:

2.088

Step-by-step explanation:

Trust me I am in high school honors algebra with almost an average of 100.

The product of 2.4 x 0.87 is 2.088.

A decimal is represented by a dot which separates the whole part and the fractional part of a number.

According to the given question we have to multiply two decimals numbers  2.4 and 0.87.

Multiplication of decimals numbers can be easily done just by removing the decimas and multiplying them in form of integers and after obtained result we'll put the decimal as many digits before from the rightmost side as the sum of the digits which those two numbers have after the decimal.

So, (24×87) = 2088 now the sum if the digits is 3 so we'll put the decimal 3 places before which is 2.088.

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The vertex of p(x)  is (9, 0).

Vertex of q(x) is (0, 9).

Vertex of r(x) is (-9, 0).

Vertex of t(x) is (0, -9).

What is absolute value function?

The non-negative value of a real number x without regard to its sign is known as its absolute value or modulus in mathematics and is denoted by the symbol |x|. Specifically, |x|=x and |x|=-x, respectively, if x is a positive number, and |0|=0 otherwise.

The vertex form of an absolute value function is f(x) = a |x - h| + k where

(h, k) is the vertex from which the graph starts and a = m is the slope.

So, the absolute value function  p(x) = |x - 9|, means h =-(-9) = 9 and

k = 0, will result in the vertex at (9, 0).

The absolute value function q(x) = |x| +9 , means h = 0 h=0 and k =9, will result in a vertex (0, 9).

The absolute value function r(x) = |x + 9|,  means, h = -9 and, k=0, will result in the vertex at (-9, 0).

The absolute value function t(x) = |x| -9 , means h = 0 and k = -9, will result in the vertex at (0, -9)

Hence,

The vertex of p(x)  is (9, 0).

Vertex of q(x) is (0, 9).

Vertex of r(x) is (-9, 0).

Vertex of t(x) is (0, -9).

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Step-by-step explanation:

180-66=y | 6x-102=66

y=114

x=(66+102)/6-->x=168/6-->x=28

The equation of the line in slope-intercept form is y = 3x + 4.

We can use the combination formula to determine how many different packages can be created from a set of 24 crayons with 36 different colours.

The formula for the mixture is provided by:

n C r equals n!/r! (n-r)!

where r is the number of items we want to choose, n is the total number of items, and! stands for the factorial of a number, which is the sum of all positive integers up to that number.

In this instance, we are trying to determine how many various methods there are to choose 24 crayons from a set of 36 colours, regardless of the sequence in which they are chosen. Consequently, we can apply the following combination formula:

36 C 24 = 36! / (24! * 12!)

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The number of turns the wheel makes is 1.93 ≈ 2.

What is Turns?

This is referred to as a cycle. It is a unit of plane angle measurement that is equivalent to 2π radians, 360 degrees, or 400 gradians.

formular for calculating Turns:

Turns =         Lenght

              Circumference

Circumference of a circle, C= πD

Where,

Diameter=D

            π =22/7

Calculating Circumference;

C= 22  * 66

            7

    =207.4

From the question:

D= 66cm

L  =400m

Calculating Turns:

Turns =  Lenght

              Circumference

          =   400m

               207.4

      Turns =1.93

Turns =1.93≈ 2

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Answer:

35

Step-by-step explanation:

(-5) - (-4 - 32 - 4)

-5 - (-40)

-5 + 40 =35

Answer:

C. 1

Step-by-step explanation:

Use the formula to find slope:

(y2-y1)/(x2-x1)

Plug in the numbers you have.

(9 - 2)/(3 - -4)

7/7

1

Slope of the line shown below is option C. 1

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

Slope can also be defined as the tangent of the angle that the line is making with the positive X axis.

Given is a line.

Slope must be positive since the line is drawn in the positive direction.

Consider two points along the line.

Consider (-4, 2) and (3, 9).

Slope = change in y coordinates / change in x coordinates

          = (9 - 2) / (3 - -4)

          = 7 / 7

          = 1

Hence the slope is 1.

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After handling raw meat the food preparer should: wash hands with soap.

It is important that after handling raw meat the food preparer should endeavor to wash his/her with soap and water and  dry your hand with a clean towel.

Washing of hand with soap will help to prevent bacteria based on the fact that  raw meats can contaminate the area you place your hands on which is why it is advisable to wash your hands after handling raw meat.

Therefore after handling raw meat the food preparer should: wash hands with soap.

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Answer: 20 dollars per ticket

Step-by-step explanation:

Divide the number 480 by 24.

480 ÷ 24 = 20

The answer is 20. Hope this helps!

Step-by-step explanation:

If 24 tickets cost $480 the cost of 1 is:

Let the unit be u

480 ÷ 24= u

\( \frac{480}{24} = u\)

\(20 = u\)

\(u = 20\)

Hope this helps....

Hence the unit = 20

Work Shown:

t = number of hours tutoring

101-t = number of hours working as a waiter

The expressions t and 101-t add to 101.

9t = amount earned as a tutor, at $9 an hour

8(101-t) = amount earned as a waiter, at $8 an hour

9t+8(101-t) = total amount earned from both jobs

This does not account for taxes or other fees. Optionally, you can distribute the 8 through the (101-t) terms, then combine like terms to simplify.

The values of the variables in number 3, in simplest radical form, are:

f = 6;  o = 3.

The simplest radical form, also known as simplified radical form or simplified surd, refers to expressing a square root (√) or other roots in the simplest possible way without any perfect square factors in the root. In other words, it involves reducing the radical expression to its simplest form.

Solving problem 3, we would apply the necessary Trigonometric ratios to find the variables:

sin 60 = opp/hyp

sin 60 = 9√3 / f

f = 9√3 / sin 60

f = 9√3 / √3/2 [sin 60 = √3/2]

f = 9√3 * 2/√3

f = 18/3

f = 6

tan 60 = opp/adj

tan 60 = 9√3 / o

o = 9√3 / tan 60

o = 9√3 / √3 [sin 60 = √3]

o = 9√3 * 1 / √3

o = 9/3

o = 3

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Answer:

o = 9

f = 18

Step-by-step explanation:

Triangle #3 is a right triangle with two of its interior angles measuring 60° and 90°. As the interior angles of a triangle sum to 180°, this means that the remaining interior angle must be 30°, since 30° + 60° + 90° = 180°. Therefore, this triangle is a special 30-60-90 triangle.

The side lengths in a 30-60-90 triangle have a special relationship, which can be represented by the ratio formula a : a√3 : 2a, where "a" represents a scaling factor that can be any positive real number.

In triangle #3, the longest leg is 9√3 units.

As "a√3" is the shortest leg, the scale factor "a" is 9.

The side labelled "o" is the shortest leg opposite the 30° angle. Therefore:

\(o = a=9\)

The side labelled "f" is the hypotenuse of the triangle. Therefore:

\(f= 2a = 2 \cdot 9=18\)

Therefore:

The theoretical probability of spinning red is given as follows:

1/3.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For the spinner in this problem, 2 out of 6 regions are red, hence the theoretical probability is given as follows:

2/6 = 1/3.

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Given data:

The total numbers of guests are n=24.

The given fraction of the guests that have cash gift is f=5/8.

The expression for the gift that are not in cash is,

Substitute the given values in the above expression.

Thus, the numbers of the gift that are not in cash is 9.

Maraging (18% Ni) steel has a better tolerance to defects and fracture toughness compared to Medium strength steel.

The tolerance to defects and fracture toughness of a material can be evaluated using its fracture toughness parameter, Kic. The higher the Kic value, the better the material's tolerance to defects and fracture toughness.

To compare the two materials, we can use the concept of critical stress intensity factor (Kic) and factor of safety (FoS). The critical stress intensity factor is the maximum value of stress intensity factor (K) that a material can withstand without fracturing. The factor of safety is the ratio of the maximum allowable stress to the design stress, and it is used to ensure a safety margin in the design.

Assuming that the two materials have the same defect to tolerance ratio, we can calculate the maximum allowable stress for each material using the following formula:

σmax = FoS * Kic / (π * a)

where σmax is the maximum allowable stress, FoS is the factor of safety (assumed to be 2), Kic is the fracture toughness parameter, and a is the size of the defect.

Let's assume a defect size of 1 mm for both materials. Using the values given in the question, we get:

For Maraging (18% Ni) steel:

σmax = 2 * 82 * 10^6 / (π * 1 * 10^-3) = 52.1 GPa

For Medium strength steel:

σmax = 2 * 50 * 10^6 / (π * 1 * 10^-3) = 31.8 GPa

Therefore, Maraging steel has a higher maximum allowable stress, which indicates that it has a better tolerance to defects compared to medium strength steel.

To compare the fracture toughness of the two materials, we can use their respective Kic values. The higher Kic value indicates a better tolerance to defects and fracture toughness.

Comparing the given values, we can see that Maraging (18% Ni) steel has a higher fracture toughness parameter (Kic= 82 MNm-3/2) compared to Medium strength steel (Kic= 50 MNm-3/2).

Therefore, Maraging (18% Ni) steel has a better tolerance to defects and fracture toughness compared to Medium strength steel.

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Answer:

Part A:

The information on the sign represents a proportional relationship. This can be determined by observing that as the number of DVDs purchased increases, the cost per DVD decreases. Specifically, the cost per DVD decreases as the number of DVDs purchased increases.

Part B:

A reasonable estimate of the cost of the DVDs before tax is added would be $37.50, since Miguel is purchasing 5 DVDs and that is the price advertised on the sign.

The actual cost before tax is $37.50 - (20/100)*$37.50 = $30.

Part C:

The total cost after sales tax has been added would be $30 + (8/100)*$30 = $32.40

Part D:

Anthony's price after tax was $21.60.

The cost of the two DVDs before the sales tax was added is $21.60 / (1+8/100) = $20.

Step-by-step explanation:

Answer:

210 sq in

Step-by-step explanation:

Box dimensions: 5 x 5 x 8

2 faces: 5 x 5 -> 2 * 5 * 5 = 50

4 faces: 5 x 8 -> 4 * 5 * 8 = 160

Total = 50 + 160 = 210 sq in

Answer:

can u speak English I would love to help but I don't understand

Answer:

The blue dot is -19

Step-by-step explanation:

Since every 2 ticks are worth 6 (|-10|-|-4|=6), then one tick is worth 3.

We are going backward, so we can count backward.

We have to go down 3 ticks, so -10-3=-13; -13-3=-16; -16-3=-19.

The blue dot is -19

Answer: The blue dot equals to -19.

Step-by-step explanation:

On the number line, there are the numbers -10 & -4.

-7 would fit in the middle of them. That means the number line goes by minus 3.

Count -10 , -13, -16, then you get on the the blue dot which is -19.

Therefore, -19 is the answer.

The requried, for x < -18, | x- ( - 18) | simplifies to x + 18.

If x is less than -18, then the expression x - (-18) will result in a negative value, since subtracting a smaller number from a larger number yields a positive value. For example, if x = -20, then x - (-18) = -20 + 18 = -2.

Therefore, we can simplify the expression without using the absolute value sign as:

x - (-18) = x + 18

So, for x < -18, | x- ( - 18) | simplifies to x + 18.

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The triangles ABD and CBD has equal angles because of the angle bisector property.

What is angle bisector?

DB is the angle bisector, So ADO = CDB(Angle)

DB = OB (Side)

AD = DC (Side)

So, triangles ABD and CBD has equal angles.

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Making a graph of linear inequalities is similar to making a graph of linear equations. But with inequalities, we find a region instead of a line.

What is linear inequality?

Linear inequalities are mathematical statements that are made up of two expressions which are compared using inequality symbols.

The following steps are to be followed to make a graph of linear inequality:-

1. Solve the inequality for y.

2. Considering the inequality as a linear equation graph the line. ( If the inequality sign does not contain an equal sign then draw a dashed line; if the inequality contains an equal sign then draw a solid line.

3. Shade the region that satisfies the inequality.

Hence, a system of linear inequality is graphed similarly to that of a linear equation, but a region is obtained.

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The number of minutes that the players spend running bases during each hour of practice is the constant of proportionality of the proportional relationship.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

In the context of this problem, the variables x and y are given as follows:

The equation for the constant is given as follows:

k = y/x.

Representing the hourly time spent running times, you can calculate it taking any point (x,y) on the graph of the function.

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Answer:

A = 108 units²

Step-by-step explanation:

The area (A) of a trapezium is calculated as

A = \(\frac{1}{2}\) h (b₁ + b₂ )

where h is the height between the 2 bases and b₁, b₂ are the parallel bases

Here h = 24 , b₁ = 8 , b₂ = 1 , then

A = \(\frac{1}{2}\) × 24 × (8 + 1) = 12 × 9 = 108 units²

Answer:

Step-by-step explanation:

Quotient

X^2+7x+4

The remainder is 1

Answer:

X^2+7x+4

Step-by-step explanation:

Answer:

550g

Step-by-step explanation:

total g in 1 kg is 1000

so 1000 - 550 =450

Answer: What is this free?

Answer:

yes

Step-by-step explanation:

yes+yes(no-no)

=yes

Answer:

5x^2y is the GCF for 15x2y3 and -20x3yz.

Step-by-step explanation:

sin^4x as a product of two squared terms is sin^2(x) * sin^2(x)

The sine expression is given as

sin^4x

The above means

sin x raised to the power of 4

This in other words, the expression is represented as

(sin(x))^4

Express 4 as 2 + 2

(sin(x))^(2 + 2)

Apply the law of indices

(sin(x))^2 * (sin(x))^2

This gives

sin^2(x) * sin^2(x)

Hence, sin^4x as a product of two squared terms is sin^2(x) * sin^2(x)

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