oan, omb, apb and mpn are straight lines and an = 3oa. m is the midpoint of ob. oa = a ов = b ap = kab where k is a scalar quantity. express ab and mn in terms of a and b. express mp in terms of a, b and k. finally, find the value of k.

First step is to write the equation in slope-intercept form

[tex]x - 5y = 5\\-5y = -x+5[/tex]      To make simplification easier, multiply negative to both sides

[tex]5y = x-5\\[/tex]  Now, you must divide 5 to both sides to isolate the variable

[tex]y = \frac{x}{5} - 1[/tex] To tell the slope more easily, turn [tex]\frac{x}{5}[/tex] into [tex]\frac{1}{5} x[/tex]

To rewrite the equation: [tex]y = \frac{1}{5} x - 1[/tex]

Now, you are able to see the slope(m) being [tex]\frac{1}{5}[/tex]

Next, you use the formula y=mx+b to solve for b (replace your newly found slope and points "x" and "y"

[tex]20 = (\frac{1}{5} *-15) + b\\20 = -3 + b\\b -3 = 20\\b = 23[/tex]

Final Answer:   [tex]y = \frac{1}{5} + 23[/tex]

Hope this helps :)

The equation that represent the relationship model that will reach $0 in the same number of days as the scenario gave is: y = -2x + 12

To solve this problem, we have to state the equation using the information of the problem.

Information about the problem:

Writing the equation according to the information gave, we have:

y = -2x + 12

Where:

So that (y) equals zero, the number of days (x) should be = 6

y = -2x + 12

0 = -2*6 + 12

0 = -12 + 12

0 = 0

The "y" variable is the dependent variable, because it will change according to the number of days passed (x).

The "x" variable is the independent variable, because it doesn't depend on any other value, just the number of days passed.

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

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As per the angle sum property, the value of x is 125°

Angle sum property:

According to the angle sum property, the sum of interior angles of a triangle is 180°.

Given,

In the given diagram, PQR and SQT are straight line.

Now we need to find the value of x.

As per the angle sum property, we know that the sum of all the angles of the triangle is 180 degrees.

While we equate the given values within this property, we get.

x° + 55° = 180°

x° = 180° - 55°

x° = 125°

Therefore, the value of x is 125°.

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Step-by-step explanation:

Deshaun is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices. Company A charges $84 and allows unlimited mileage. Company B has an initial fee of $75 and charges an additional $0.60 for every mile driven. For what mileages will Company A charge less than Company B? (Use m for the number of miles driven, and solve your inequality for m.)

inequality: 0.6m + 75 < 84

subtract 75 from both sides:

0.6m + 75 - 75 < 84 - 75

0.6m  < 9

divide both sides by 0.6:

0.6m/0.6 < 9/0.6

m < 15

SO:

For anything less than 15 miles, Company A charges less than Company B.

The slope of the line is given as -2/3.

We are also given the point (1, 1) in which this line passes through.

Before we can plot the graph of the line, we need to know the equation of the line first.

The values given are more than enough to find the equation of the line.

The formula used to get the equation of the line is given below:

Now, with this formula, let us find the equation of the line.

Thus, the equation of the line is:

Now, using a graph calculator, let us plot this equation.

After doing this, the following is the result:

The identified acute angles in the diagram are: D. Angle WZY and angle WXY.

An acute angle can be described as any angle that has a degree measure that is below 90 degrees, in order words, it is smaller than a right angle.

For example, an acute angle is attached below, which is 62°, and it is less than a right angle or 90 degrees. Angles 30°, 45°, 60°, 75°, etc are all regarded as acute angles because they are less than a right angle or 90 degrees.

In quadrilateral WXYZ, the acute angles that are less than a right angle, and are below 90 degrees are: D. Angle WZY and angle WXY.

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According to the given graph, the given angles are alternate interior angles that are always equivalent.

Having said that, we can express the following equation.-

Solving for x, we have

1) According to the exponent's law, any exponent whose base is 1, that yields 1. For example

2) The same does not happen to 0.1

Since 0.1 is a fraction, we'll raise to the 4th power 1 and 10 simultaneously, as a ratio.

3) So the answer is

1) The general form of a cosine function is:

2) Let's pick from the graph, the amplitude, the period, the horizontal and the vertical shift.

We can tell that half of the distance between the maximum point and the minimum point is 2

Let's find the period

3) Let's resort to the picture. The only cosine function that has an amplitude of 2 and a period of 3 is C and y=2cos(3x) has a vertical shift =0

Answer:-1a+2

Step-by-step explanation:

add like terms

Hey there!

(2a - 5) - (3a + 5)

= 2a - 5 - 3a + 5

COMBINE the LIKE TERMS

= (2a - 3a) + (-5 + 3)

= 2a - 3a + (-5) + 3

= -1a - 2

Therefore, your answer should be:

-1a - 2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

In the images, we are given an exercise which is solved by taking T as the midpoint of SU. This is the

Answer:

59 degrees(triangle on the right)

Step-by-step explanation:

The total degrees of a triangle is 180 so add 76+45=121.

180-121=59

Answer:

12

Step-by-step explanation:

The numbers from greatest to least is - 1 2/3, -1 5/6, -2.1 and -2.2.

Based on the information, we want to arrange the numbers from the greatest to the least.

In this case, it will be illustrated thus:

-2.1

-1 5/6 = -1.83

-1 2/3 = -1.67

-2.2

This will be arranged as - 1 2/3, -1 5/6, -2.1 and -2.2. In this case, it can be deduced that - 1 2/3 is the greatest and the least number is -2.2. This shows the concept of descending numbers.

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The amount to be paid after paying interest of 7% for 10 years is 10,2000

The amount to be borrowed from the bank = 6000

Interest rate for the amount per year = 7%

The total time period of the loan = 10 years

Thus , the final amount can be calculated by using the formula

                    A = P(1 + rt)

where A is the final amount

          P is the principal amount to be borrowed

          r is the rate of interest

          t is the time period

Now, let us substitute the known values in the above equation , we get

             A = 6000 ( 1 + 0.07 x 10)

                 = 6000 (1 + 0.7)

                 = 6000 (1.7)

             A = 10,200

Therefore , the final amount to be paid is 10,200

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In a case whereby the the shortest side of a right triangle measures 6, and the longest side measures 10 the measurement of the unknown side is 8.

We can use this expression from trigonometry to know the third side of the triangle as:

a^2 + b^2 = c^2

Then since the longest side measures 10 which is the c side of the triangle then the unknown side can be calculated as :

10^2 - 6^2

The we can simplify as

100-36=64

Then [tex]\sqrt{64}[/tex] = 8.

Therefore, the second option is correct.

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Answer:

Explanation:

Here, we want to write the equation of a line in point-slope form

Mathematically, we have that as:

where m, which is the slope is -2/3 and (x1,y1) which is the point is (-3,2)

Substituting the values, we have it that:

The outer perimeter of the no-slip surface is 78 feet if the swimming pool has a 3-ft-wide no-slip surface around it.

The outer perimeter of an area or land can be described as the whole of its outer edge or can be described as the sum total of the outside edge lengths.

We can find the outer perimeter of this swimming pool by adding 3 feet twice to all the sides of this rectangular swimming pool followed by the addition of these sides together.

As the swimming pool is 12-ft-by-15-ft, this represents that two sides of this rectangular swimming pool are 15 feet and the other two sides are 12 feet, therefore;

12 + 6 = 18

15 + 6 = 21

Now we can find the perimeter by the addition of all the sides as follows;

18 + 18 + 21 + 21 = 78 feet

Therefore, the outer perimeter of the no-slip surface is found to be equal to 78 feet.

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To solve the exercise you can rewrite the fractions in decimal form and then we order.

To write them in decimal form divide the numerator by the denominator, then we have

The exact value of cos(A - B) is -2√5 /25.

Therefore,

sin A = 0.3

sin B = (1/√5)

cos A = 0.7

cos B = (-1/√5)

cos(A-B) = cos a cos b + sin a sin b

⇒ cos(A-B) = 0.7(-1/√5) + 0.3((1/√5))

⇒ cos(A-B) = -0.7/√5 + 0.3/√5

⇒ cos(A-B) = -0.4/√5

On multiplying, √5 on the numerator and denominator,

⇒ cos(A-B) = -0.4 x √5 / 5

⇒ cos(A-B) = -2√5 /25

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For the given points B(-1, -10) is reflected over the line y = x , the coordinates of B' is given by ( -10 , -1).

As given in the question,

Given points :

B (-1, -10)

Reflected over the line y = x

Reflected represents the transformation which shows the movement of original points to the new location. There are different types of transformation such as reflection, rotation, dilation , and translation.

Reflection represents the flipping of the points over the line y =x.

B(x, y) and B'(y, x).

For the given points B (x, y) = (-1,-10) is reflected over the line y =x , the coordinates of B'(y, x) = ( -10 , -1).

Therefore, for the given points B(-1, -10) is reflected over the line y = x , the coordinates of B' is given by ( -10 , -1).

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The location of the center of dilation in the figure and the image formed following the dilation is the point N

The scale factor of the dilation is 0.5

A dilation transformation resizes an object such that the lengths of the sides of the image (the object formed) following the dilation of the original image has sides that are a constant multiple of the side lengths of the original object.

The center of dilation is a reference and fixed point, such that the center of is in the same location relative to the preimage and the image.

The location or point shared by both the figure LMNO and the image of LMNO formed following the dilation, which is figure L'M'N'O' is the point N.

Therefore;

The scale factor of the dilation is found using the definition of a scale factor, which is the ratio of the scale of a new figure to the scale of an original figure, therefore:

[tex]The \ scale \ factor,\, s.f. = \mathrm{\dfrac{Length \ of \ the \ sides \ of \ L'M'N'O'}{Length \ of \ the \ sides \ of \ LMNO}}[/tex]

MN = 6 units

LO = 6 units

ML = ON = √(6² + 2²) = 2·√(10)

M'N' = L'O' = 3 units

M'L' = O'N' = √(3² + 1²) = √(10)

Which gives:

[tex]s.f. = \dfrac{M'L'}{ML} =\dfrac{\sqrt{10} }{2 \cdot \sqrt{10} } = \dfrac{1}{2}=0.5[/tex]

The scale factor of the dilation is, s.f. = 0.5

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Answer:

a) Yes, the graph is proportional.  It is linear and it goes through the point (0,0)

b) No shells cost no dollars

c)  3 shells cost 1.20

Step-by-step explanation:

To graph this, you only need 2 points.  You have the points (0,0).  You can put a point at (0,0) and at the point ( (3, 1.20) and then draw a line through those 2 points.

Answer:

Angle 1: 159

Angle 2: 21

Angle 4: 21

Step-by-step explanation:

The simplified form of the expression [tex](3x^2+4x+2)-(7x^2+2x+5)[/tex] is [tex]-4x^2+2x-3[/tex].

In the given question,

The given expression is [tex](3x^2+4x+2)-(7x^2+2x+5)[/tex].

We have to solve the given expression.

To solve this question we use have to follow some rule.

Some Rules are

In this given question to solve the expression we firstly solve the bracket.

When we multiply the term under the bracket with minus sign then all sign under the bracket will also be changed

Now simplifying the expression.

[tex]=3x^2+4x+2-7x^2-2x-5[/tex]

Now we combine the similar term.

[tex]=(3x^2-7x^2)+(4x-2x)+(2-5)[/tex]

[tex]=-4x^2+2x-3[/tex]

Hence, the simplified form of the expression [tex](3x^2+4x+2)-(7x^2+2x+5)[/tex] is [tex]-4x^2+2x-3[/tex].

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Answer:

The answer is option A.

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given equation

STEP 2: Find the value of x

Cross multiply the equation

Divide both sides by 4

Hence, the value of x is -18

If Sarah is 148 centimeters tall. Sarah's height in inches is 58.27 inches

Information given in the question include

Sarah is 148 centimeters tall

Round to the nearest tenth inch

Sarah's height in inches is is determined using conversion from centimeters to inches

centimeters = cm

inches = in

The unit conversion factor is given as

1 centimeter = 0.393701 inches

148 cm = ?

cross multiplying gives

? * 1 = 148 * 0.393701

? = 58.2677 in

? = 58.27 in ( to the nearest tenth of inch )

Therefore Sarah's height when converted form cm to inches is 58.27 in

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Answer:58.3 inches

Before rounding:58.2677

A 20-ounce bottle of lotion costs $3.95 then each of the ounce of the bottle will cost 0.173 ounce.

we were told that the cost of the 20-ounce bottle of lotion is  $3.95

then we can know the value cost of just one of the bottle of notion by using the expression below

X = the cost of each of the  bottle of lotion

then X=  $3.95 / 20-ounce bottle= 0.173 ounce

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