Mr Ankomah bought some story books at Ghc5.00 each from a bookshop. Twelve of the books got missing. He then sold the rest at Ghc 7.00 each and made a profit of Ghc150.00. How many books did Mr. Ankomah buy?​

Answers

Answer 1

From the calculation below, the number of books bought by Mr. Ankomah was 87 books.

How do we calculate the number of units bought?

Let x represent present the number of books bought.

Therefore, we have:

Number of books sold = x - 12

Total revenue from units sold = Number of books sold  * Unit selling price = (x - 12) * 7 = 7x - 84

Total cost of units sold = Number of books sold  * Cost price per unit = (x - 12) * 5 = 5x - 60

Profit = Total revenue from units sold - Total cost of units sold ........... (1)

Since he made a profit of Ghc150.00, we substitute all the relevant values into equation (1) and solve for x as follows:

150 = (7x - 84) - (5x - 60)

150 = 7x - 84 - 5x + 60

150 + 84 - 60 = 7x - 5x

174 = 2x

x = 174 / 2

x = 87

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Related Questions


Position and label each triangle on the coordinate plane.isosceles Δ A B C with base AB that is a units long

Answers

The  Δ A B C with base AB that is a unit long has been drawn below.

What is a triangle?

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

Δ A B C is a isosceles triangle.

Now isosceles triangle is a triangle whose two sides are equal.

In the Δ A B C, AC = BC

Hence "The  Δ A B C with base AB that is a unit long has been drawn below".

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I NEED HELP, it’s for baking

Answers

Put in 2 of the second spoon (1 teaspoon) and 1 of the third spoon (1/2 teaspoon).


How many tiles are in the 25th figure in this pattern? Show a table of values with a process column.

Answers

52 tiles are there in the 25th figure in this pattern.

What is a pattern?

A pattern is described as a series of recurring symbols, figures, or numbers. Any form of event or object can be related to a pattern.

A pattern has a rule that specifies which items fall within the pattern's umbrella and which do not.

A pattern in mathematics is a recurring arrangement of numbers, forms, colors, and other elements.

Any kind of event or object can be connected to the Pattern.

A pattern is referred to as a rule or a way in which a group of numbers is related to one another.

Sometimes a pattern is also referred to as a sequence.

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Do the following side lengths form a right triangle?

14, 20, 15

Answers

Answer:  No, the sides do not form a right triangle.

============================================================

Explanation:

Let c = 20 be the largest or longest side. If we had a right triangle, then this side is the hypotenuse.

a = 14 and b = 15 are the other sides in either order.

Plug the values into the pythagorean theorem equation. Evaluate each side separately until getting a single numeric value.

[tex]a^2 + b^2 = c^2\\\\14^2 + 15^2 = 20^2\\\\196 + 225 = 400\\\\421 = 400\\\\[/tex]

The last equation is false, so the first equation is false for those a,b,c values mentioned. This shows us we do not have a right triangle.

For more information, check out the pythagorean theorem converse.

no

Does a triangle with sides 14, 15 and 20 can form a right triangle?

To check if a triangle is a right one, we can follow these steps:

Step 1: Take the longest side as the candidate for the hypotenuse (c). Here, the longest side is that of lenght 20. So, c = 20. The other sides are leg A (a) and leg B (b). In this case we can assume that a = 14 and b = 15 .

Step 2: Now plug in these values in the formula below to check its validity:

c2 = a2 + b2

202 = 142 + 152

400 ≠ 421

As both sides of the above equation are not equal, we can surely say that the triangle [14 15 20] is NOT a right triangle.

Give the answer okkk

Answers

Step-by-step explanation:

b(h) = 212 - 1.72×h/1000

what is h, when b = 190 ?

190 = 212 - 1.72×h/1000

-22 = -1.72×h/1000

22000 = 1.72×h

h = 22000/1.72 = 12,790.69767... ≈ 12,791 ft

50 points
Write the equation of the line in slope-intercept form (picture here)

Answers

Answer:

[tex]f(x)=\frac{1}{2}x+-6[/tex] or y=1/2x+-6

Step-by-step explanation:

You can use any two points on a line to find slope. For example, I used:

(x1, y1) 2, -5

(x2, y2) 4, -4

To find slope, the following formula is needed:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Input our values:

[tex]m=\frac{(-4)-(-5)}{4-2}[/tex] which means m=1/2

b is equal to y-intercept which is -6

The equation is:

[tex]y=\frac{1}{2}x+-6[/tex]

to get the equation of any straight line, we simply need two points off of it, let's use the points from the picture below.

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-4}-\stackrel{y1}{(-8)}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{(-4)}}} \implies \cfrac{-4 +8}{4 +4} \implies \cfrac{ 4 }{ 8 }\implies \cfrac{1}{2}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-8)}=\stackrel{m}{\cfrac{1}{2}}(x-\stackrel{x_1}{(-4)}) \implies y +8= \cfrac{1}{2} (x +4) \\\\\\ y+8=\cfrac{1}{2}x+2\implies {\LARGE \begin{array}{llll} y=\cfrac{1}{2}x-6 \end{array}}[/tex]


Solve each equation. Check your answer. 7 y+4=3-2 y

Answers

The solution of the given equation 7y + 4 = 3 - 2y is 29/2.

According to the given qestion.

We have a linear equation in one variable 7y + 4 = 3 - 2y.

So, the solution of the given linear equation in one variable  7y + 4 = 3 - 2y is given by

7y + 4 = 3 - 2y

⇒ 7y + 2y + 4 = 3    ( adding 2y both the sides)

⇒ 9y  = 3 - 4

⇒ 9y = -1

⇒ y = -1/9

Now, we will check whether y = -1/9 is the solution of the given equation 7y + 4 = 3 - 2y  or not.

Thereofore,

LHS

= 7(-1/9) + 4

= -7/9 + 4

= -7 + 36/9

= 29/9

Similarly

RHS

= 3 - 2(-1/9)

= 3 + 2/9

= (27 + 2)/9

= 29/2

Here, LHS = RHS

Hence, the solution of the given equation 7y + 4 = 3 - 2y is 29/2.

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Solve each system by substitution. Check your answers.
4p + 2q = 8 , q = 2p+1

Answers

By substitution, the solution of the system of equations, 4p + 2q = 8 and q = 2p + 1, is (p , q) = (3/4 , 5/2).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given two linear equations in p and q,

4p + 2q = 8     (equation 1)

q = 2p + 1     (equation 2)

Since the second equation is already expressed in q in terms of p, substitute the second equation to the first equation.

4p + 2q = 8     (equation 1)

4p + 2(2p + 1) = 8

4p + 4p + 2 = 8

Combining all terms containing the variable p on one side and the constants on the other side of the equality, and solving for p.

4p + 4p + 2 = 8

4p + 4p = 8 - 2

8p = 6

p = 6/8

p = 3/4

Substitute the value of p in the second equation and solve for q.

q = 2p + 1

q = 2(3/4) + 1

q = 6/4 + 1

q = 5/2

Hence, the solution of the given system of equations is (p , q) = (3/4 , 5/2).

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workings.
Karina is making a 3-digit number by choosing three different
numbers from the following list:
2, 4, 5, 7, 9
How many different 3-digit numbers could Karina make?

Answers

The number of different 3-digit number if each of those digits is only allowed to be used once is 60

How to determine the number of different 3-digit number codes if each of those digits is only allowed to be used once?

The digits are given as:

2, 4, 5, 7, 9

There are 5 digits represented in the above list

If each of those digits is only allowed to be used once, then we have the following possibilities

First character: Any of the 5 digitsSecond character: Any of the remaining 4 digitsThird character: Any of the remaining 3 digits

The number of 3-digit number codes is

Number =  5 * 4 * 3

Evaluate the product

Number = 60

Hence, the number of different 3-digit number if each of those digits is only allowed to be used once is 60

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A certain mapping in the plane has the following property: Each pair of points A and B is mapped to another pair or points A' B' such that quadrilateral AA'BB' is parallelogram. What type of transformation is that? Explain how you know.

Answers

When certain mapping in the plane has the following property: Each pair of points A and B is mapped to another pair or points A' B' such that quadrilateral AA'BB' is parallelogram, the transformation is reflection.

How to illustrate the information

Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.

When a figure is translated, it is moved in any direction.

Flipping a figure over a line is called reflection.

Rotation is the process of turning a figure a specific amount around a point.

When we dilate a figure, we increase or decrease its size.

In this case, since the figure is flipped, over a line is called reflection.

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Help please. I’ll give you Brainly

Answers

Answer:

13

Step-by-step explanation:

divide the 24 by two so you can find one side of the two right triangles. you get 12. now that you have 12 and the 5 from the other side use a^2+b^2=c^2 to solve for the missing side where a=5 b=12 and c=? so 12 squares is 144 and 5 squared is 25 so add then up and you get 169=c^2. lastly square the 169 and you end up with 13 :)

13 because your dividing 48 by 2 so u get 24 and divide that by 2 u get 12 and you square two by the missing sides so then multiply 12 by 12 equals 144 and so since u have 5 square it which is 5 add and u get 169 and then u square that and you get 13


What is an equation of the line y=9.1 x+3.6 in standard form?

Answers

y - 9.1x - 3.6 = 0 is an equation of the line y=9.1 x+3.6 in standard form

How to solve an equation?

To solve linear equations, utilize the steps that are provided below.

Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

Standard form of an equation is given as ax + by + c = 0

Here is given

⇒ y = 9.1 x+3.6

y - 9.1x - 3.6 = 0

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SHOW YOUR WORK OR I DELETE UR ANSWER

can √3 + 5 be simplified if yes show your work if not explain why


can √2x/3y be simplified if yes show your work if not explain why


...........4
can (x↑y)3/2 be simplified if yes show your work if not explain why

Answers

It is true that the expressions √3 + 5 and √2x/3y  cannot be simplified while the expression (x + y)3/2 can be simplified

What are expressions?

Expressions are mathematical statements that are represented by variables, coefficients and operators

How to determine if the expression can be simplified?

Expression 1

The expression is given as

√3 + 5

The above expression is a combination of a radical expression and an integer

The radical expression √3 cannot be simplified

This means that the expression √3 + 5 cannot be simplified

Hence, the expression √3 + 5  cannot be simplified

Expression 2

The expression is given as

√2x/3y

The above expression is a combination of radical expressions

However, the radical expressions do not have a common factor

This means that the expression √2x/3y cannot be simplified

Hence, the expression √2x/3y  cannot be simplified

Expression 3

The expression is given as

(x + y)3/2

Open the bracket

(x + y)3/2 = 3/2x + 3/2y

This means that the expression (x + y)3/2 can be simplified

Hence, the expression (x + y)3/2 can be simplified

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write a two-column proof for the property reflective property of segment congruence

Answers

Hence, proved the reflective property of segment congruence.

We need to write a two-column proof for the property reflective property of segment congruence.

What is the reflective property of congruence?

In geometry, the reflexive property of congruence states that an angle, line segment, or shape is always congruent to itself.

Two angles are congruent if and only if they have equal measures. Two segments are congruent if and only if they have equal measures. Two triangles are congruent if and only if all corresponding angles and sides are congruent.

Consider, XY≅AB

Prove that, AB≅XY

Proof: XY≅AB (given)

XY=AB (Definition of the congruent segment)

AB=XY (Symmetric property of equality)

AB≅XY (Definition of the congruent segment)

Hence, proved the reflective property of segment congruence.

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Find the 17 th term of each sequence. a₁₆ =21, d=-3

Answers

The 17th term of the arithmetic progression (A.P) is given as 18.

What is defined as arithmetic progression?

An arithmetic progression (AP) is a succession in which the differences between each successive term are the same.

An arithmetic progression is a series in which each term (except the first) is derived by adding a fixed number to the term before it.The following arithmetic progression formulas are frequently used to solve various AP problems for the initial term 'a' of an AP and the common difference 'd':Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ......      = an - an-1.nth term of an AP: an = a + (n - 1)dSum of n terms of an AP: Sn = n/2(2a+(n-1)d) = n/2(a + l), where l defines last term of an AP.

Now, as per the given question;

16th term; a₁₆ = 21Common difference; d = -3

Then, the 17th term will be;

Apply the difference formula;

d = a₁₇ - a₁₆

a₁₇ = a₁₆ + d

a₁₇ = 21 + (-3)

a₁₇ = 21 - 3

a₁₇ = 18.

Therefore, the value of the 17th term of an AP is found to be 18.

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what is the range of 40, 41, 52, 54, 50, 39, 43, 54,

Answers

The range of given set of data is 15.

We have a set of numbers.

We have to determine its range.

What is range of a given set of elements?

The range is the difference between the smallest and highest number in a list.

According to the question, we have the following set of elements -

40, 41, 52, 54, 50, 39, 43, 54.

Arrange it in ascending order -

39  40  41  43  50  52  54  54

Now -

Range = Highest number - Lowest number

Range = 54 - 39

Range = 15

Hence, the range of given set of data is 15.

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[tex]\huge\text{Hey there!}[/tex]


[tex]\huge\textbf{Question reads..}[/tex]

[tex]\large\boxed{\text{What is the range of 40, 41, 52, 54, 50, 39, 43, 54 \bf ?}}[/tex]


[tex]\huge\textbf{To find your range, you have to..}}[/tex]

[tex]\large\boxed{\text{You have to find the difference between the largest number in the}}\\\\\large\boxed{\text{data plot from the smallest number in data plot.}}[/tex]

[tex]\huge\textbf{The range formula is..}[/tex]

[tex]\large\boxed{\rm{largest\ number - smallest\ number = range}}[/tex]


[tex]\huge\textbf{The data plot..}[/tex]

[tex]\large\boxed{\rm{40, \ 41, \ 52, \ 54, \ 50, \ 39, \ 43, \ 54}}[/tex]


[tex]\huge\textbf{Now let us answer the question..}[/tex]

[tex]\large\boxed{\rm{40, \ 41, \ 52, \ 54, \ 50, \ 39, \ 43, \ 54}}\\\\\large\boxed{\rm{The\ largest\ number\ in \ the \ plot\rightarrow 54}}\\\\\large\boxed{\rm{The \ smallest \ number\ in\ the\ data plot\rightarrow 39}}[/tex]


[tex]\huge\textbf{Your equation should be:}[/tex]

[tex]\large\boxed{\rm{54 - 39}}}\\\\\large\boxed{\rm{Simplify \ it}}\\\\\large\boxed{\rightarrow 15}}[/tex]


[tex]\huge\textbf{Therefore your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{15}}}\huge\checkmark[/tex]


[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]




~[tex]\frak{Amphitrite1040:)}[/tex]

notre prof de math vient de nous envoyer se travaille pour lundi je ne comprends rien sil vous plait aider moiii

Answers

Answer: f(2)=-10     f(-3)=15

Step-by-step explanation:

Let the number conceived be x.

Hence,

f(x)=(x+5)(-3)-2x+15

f(x)=-3x-15-2x+15

f(x)=-5x

Thus,

f(2)=(-5)(2)

f(2)=-10

f(-3)=(-5)*(-3)

f(-3)=15


Determine whether each sequence is arithmetic. If so, identify the common difference. 10,20,30,40, ...........

Answers

The given sequence 10,20,30,40, ........... forms an arithmetic sequence. The common difference is found to be 10.

How does the AP arithmetic progression succession?

The difference between the two mathematical orders is a fixed value in Arithmetic Progression (AP). Another name for it is Arithmetic Sequence.

We'd come around a few specific words in AP that were labeled as:

The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)

Some formulas related to AP are-

The AP could be defined in terms of common differences, as shown below: a, a + d, a + 2d, a + 3d, a + 4d, ………. ,a + (n – 1) d.The procedure for appraising an AP's n-th term is as follows: an = a + (n − 1) × dThe following is the arithmetic progression sum: Sn = n/2[2a + (n − 1) × d].

Now, for the stated sequence is: 10,20,30,40, ...........

Let us suppose the first term is'a₁' = 10.

Let us suppose 'a₂' = 20 is the second term.

Let us suppose the third term is 'a₃' = 30.

Let us suppose the fourth term be 'a₄' = 40.

d = a₂ - a₁      

Substitute the values;

d = 20 - 10 = 10       ........(equation 1)

Now consider the other set;

d = a₃ - a₂    

d = 30 - 20 = 10      .......(equation 2)

Comparing equation 1 and 2, the common difference is same.

Thus, the given sequence forms an AP.

The common difference is found to be 10.

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The points B(2,-8), C(2, 1), D(-3, 5), and E(-3,-4) form parallelogram BCDE.
Plot the points then click the "Graph Quadrilateral" button. Then find the perimeter
of the parallelogram. Round your answer to the nearest tenth if necessary

Answers

The perimeter of parallelogram BCDE is 38 .

The distance between two points is the length of the line segment connecting the two points. The distance between two points on the xy plane can be found using the distance formula. The ordered pair (x,y) represents the coordinates of the point, where the x-coordinate (or abscissa) is the distance from the x-axis to the point, and the y-coordinate (or ordinate) is the distance to the point. from the y-axis which is given by [tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] where [tex](x_1 , y_1)[/tex] is the coordinate of first point and [tex](x_2 , y_2)[/tex] is the coordinate of second point .A shape's perimeter is defined as the total length of its bounds. The perimeter of a shape is determined by summing all  sides and side lengths that enclose the shape.

The plotting of the points B(2,-8), C(2, 1), D(-3, 5), and E(-3,-4) is given below.

Using distance formula , put [tex]x_1=2, \ y_1 =-8[/tex] and [tex]x_2=2, \ y_2 =1[/tex] in equation (1) , we get BC

      [tex]BC=\sqrt{(2-2)^2+(1-(-8))^2} \\BC=\sqrt{0+(1+8)^2} \\BC=\sqrt{(9)^2} \\BC= 9[/tex]

Using distance formula , put [tex]x_1=2, \ y_1 =1[/tex] and [tex]x_2=-3, \ y_2 =5[/tex] in equation (1) ,we get CD

       [tex]CD=\sqrt{(-3-2)^2+(5-1)^2} \\CD=\sqrt{(-5)^2+(4)^2} \\CD=\sqrt{25+16} \\CD=\sqrt{100} \\CD=10[/tex]

Using distance formula , put [tex]x_1=-3, \ y_1 =5[/tex] and [tex]x_2=-3, \ y_2 =-4[/tex] in equation (1) ,we get DE

       [tex]DE=\sqrt{(-3-(-3))^2+(-4-5)^2} \\DE=\sqrt{(-3+3)^2+(-9)^2} \\DE=\sqrt{0+81} \\DE=\sqrt{81} \\DE=9[/tex]

Using distance formula , put [tex]x_1=2, \ y_1 =-8[/tex] and [tex]x_2=-3, \ y_2 =-4[/tex] in equation (1) ,we get BE

     [tex]BE=\sqrt{(-3-2)^2+(-4-(-8))^2} \\BE=\sqrt{(-5)^2+(-4+8)^2} \\BE=\sqrt{25+(4)^2} \\BE=\sqrt{25+16} \\BE=\sqrt{100} \\BE=10[/tex]

Perimeter [tex]=10+10+9+9=38[/tex]

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What is the equation of a line parallel to y=x that passes through the point (0,1) ?
a. y=x+1
b. y=2 x+2
c. y=x-1
d. y=-x

Answers

Answer: Maybe D, I'm not sure

Step-by-step explanation:

(3x3+4x2)−(2x3+3x2−x

Answers

Answer:

9+8-6+6=29

Step-by-step explanation:

MATHAMATICS please check this i don't know x or×


Use your results from Exercise 13 to determine whether the given measures define 0,1, 2, or infinitely many obtuse triangles. Justify your answers.
a=10, b=8, m

Answers

We can make an unlimited number of obtuse triangles when given two sides but no angle measurement, such as a = 10 and b = 8.

For illustration:

If we have side lengths of 10 and 8 and an angle value of 90 to 360 degrees, how many different obtuse triangles can we create?

Make a triangle with sides of 10 and 8 metres, an angle of 120 degrees, and a third side that may be adjusted to your preferred length using a protractor. You have built a triangle.

By changing the length and angle of the third side, we can produce a completely different triangle that is similar to this one.

It's imperative to keep in mind that you choose the side lengths and angle. It's implied that you could make a different decision. By employing the same angles, an unlimited number of different triangles can be formed.

Thus, using a single angle and a single side length, we may create an unlimited number of triangles.

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Kudzu is a fast-growing vine found in the southeastern United States. An initial measurement of the length of a kudzu vine was 0.5 meter. Seven days later the plant was 4 meters long.

c. Assuming that the growth rate of the plant continues, how long will the plant be after 15 days?

Answers

The height of the Kudzu vine after 15 days is 8 m.

The initial measurement of length of Kudzu vine =

0.5 metres

Length of the Kudzu vine after seven days = 4 m

[tex]Let \: the \: (x _{1},y _{1}) =(0 ,0.5)[/tex]

[tex]Let \: the \: (x _{2},y _{2}) =( 7,4)[/tex]

The rate of the growth of the Kudzu vine per day is,

The slope formula is,

[tex]m = \frac{(y _{2} - y _{1}) }{ (x _{2} - x _{1}) }[/tex]

[tex]m = \frac{4 - 0.5}{7 - 0} [/tex]

[tex] = \frac{3.5}{7} [/tex]

= 0.5

Rate of growth of Kudzu vine per day is 0.5 per day.

Let the height of the Kudzu vine after fifteen days be y2.

The height of the Kudzu vine after fifteen days is,

[tex]m = \frac{(y _{2} - y _{1}) }{ (x _{2} - x _{1}) }[/tex]

[tex]0.5= \frac{y _{2} - 0.5 }{15 - 0} [/tex]

Now, multiplying 15 on both the sides. [tex]7.5 = y _{2} - 0.5[/tex]

[tex]y _{2} = 8[/tex]

Therefore, the height of the Kudzu vine after fifteen days is 8 m.

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Alana is writing a coordinate proof to show that the diagonals of a rectangle are congruent. She
starts by assigning coordinates to a rectangle as shown. Then she uses the coordinates to
write and simplify expressions for the lengths of the diagonals.

What is the length of one of the diagonals of the rectangle?

A: 12.4
B: 6
C: 6.3
D: 8

Answers

The expression for diagonal of a rectangle is d= √ (a2 + b2).

Consider a rectangle PQRS in which let PR and QS be the diagonals.

Then, there are two triangles obtained and they are ΔRPS and ΔRPQ

The angle that is common between the two triangles is ∠p

The common side is PQ

Hence, PS=QR

Therefore, ΔRPS≅ΔRPQ

Also, QS=PR the diagonals of a rectangle are equal in length.

By using the Pythagorean theorem, the length of the diagonal of rectangle is                   d = √ (l2 + w2)

From the given data the length of the rectangle(l) PQ =a

The width of the rectangle(w) QR = b

Hence the expression for diagonal of rectangle is d= √ (a2 + b2).

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Answer:

The formula for a rectangle's diagonal is d=(a2 + b2).

Step-by-step explanation:

Let PR and QS be the diagonals of the rectangle PQRS.

Following that, two triangles—RPS and RPQ—are obtained.

The common angle between the two triangles is p.

PQ is the common side.

So, PS=QR.

Consequently, RPSRPQ

A rectangle's diagonals are also equal in length since QS=PR.

The Pythagorean theorem shows that d = (l2 + w2) is the length of the diagonal of a rectangle.

The length of the rectangle (l) PQ =a from the provided data

Rectangular width (w) = QR = b

Therefore, d=(a2 + b2) is the expression for the diagonal of a rectangle.

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In this problem, you will investigate the relationship between the arcs of a circle that are cut by two parallel chords.
b. Use a protractor to find m

Answers

The measures of m [tex]\angle[/tex] A = 30º, m [tex]\angle[/tex] D = 30º, measure of arc AC = 60º and measure of arc BD = 60º.

The arcs exists congruent because they have equal measures.

What is meant by Congruent arcs?

Congruent arcs are arcs on circles that have the same degree measure and have congruent radii. A minor arc is one with a degree measure between and 180º. A semicircle is an arc with a degree measure of 180º. A major arc is one with a degree measure between 180º and 360º.

If two arcs have the same length and are segments of congruent circles, they are congruent arcs. Because any circle is congruent to itself, two arcs of equal length that are part of the same circle are congruent arcs.

The measures of m [tex]\angle[/tex] A = 30º, m [tex]\angle[/tex] D = 30º, measure of arc AC = 60º and measure of arc BD = 60º.

The arcs exists congruent because they have equal measures.

The complete question is:

In this problem, you will investigate the relationship between the arcs of a circle that are cut by two parallel chords.

Use a protractor to find m \angle A and m \angle D. Then determine the measure of arc AC and BD. What is true about these arcs? Explain

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Determine whether y varies directly with x . If so, find the constant of variation.
y=-2 x

Answers

The required value of the constant of proportion is 2.

What is the constant of proportion?

A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.

Solving for the value of constant of variation

When a quantity varies directly with others, then we have a relation, y = kx, where k is the constant of the proportion     —-- 1

Given the relation is y = 2x            —-- 2

On comparing both the equation 1 and 2, we have,

k = 2

Hence, the required value of constant of variation is 2.

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Moira solved a problem on the board. what error did moira make and how can she correct it? use the drop-down menus to explain your answer. 12x 10 = 54 â€" 10x 12x 10 â€" 10 = 54 â€" 10x â€" 10 12x = 44 â€" 10x 12x â€" 10x = 44 â€" 10x 10x 2x = 44 x = 22 on the left side of the equation, moira choose... 10x, but on the right side of the equation, moira choose... 10x. she needs to choose... 10x to both sides of the equation.

Answers

The value of the linear equation 12x+10=54-10x, X=22.

What is linear equation?

An algebraic equation of the form y=mx+b is referred to as a linear equation involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a linear equation of two variables, where y and x are the variables.

Given that,

Moira chooses 10x on the left side of the equation,

And on the right side she chooses 10x

Given equation is 12x+10=54-10x

12x+10-10=54-10x-10 (subtract -10 on both sides)

12x=44-10x

12x-10x=44 (sending 10x on left side of the equation)

2x=44

X=22

Therefore the value of linear equation 12x+10=54-10x is X=22.

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Is the equation -2(4-x) = 2x+8 an identity?

Answers

Answer:

No

Step-by-step explanation:

-2(4-x) = 2x+8

Distribute the -2 on the left hand side

-2 *4 -2*-x = 2x+8

-8 +2x = 2x+8

They are not equal so it is not an identity

Answer: not an idenfity

Step-by-step explanation:

[tex]-2(4-x)=2x+8\\(-2)(4)+(-2)(-x)=2x+8\\-8+2x=2x+8\\2x-8\neq 2x+8[/tex]


State whether each sentence is true or false. If false, replace the underlined word or phrase to make a true sentence.
The three types of congruence transformations are rotation, reflection, and translation.

Answers

The three types of congruence transformations are rotation, reflection, and translation is TRUE.

What is the transformation of a graph?

Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.

Reflection is a mirror image of a graph about any axis.

If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).

If we rotate a triangle by any angle in any direction either clockwise or anti the dimension will remain the same so it will be congruent.

If we reflect a triangle about any axis then also it will remain the same so it will be congruent.

If we transform by any amount either horizontal or vertical then it will remain the same so it will be congruent.

Hence "The three types of congruence transformations are rotation, reflection, and translation is TRUE".

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I cant figure out this problem...

Answers

The required first term is 100 and the common ratio is 1.1 and the 11th term is 285.

What is geometric progression?

Geometric progression is a sequence of series whose ratio with adjacent values remains the same.

Here,
Orignal price iss 100
Appreciates 10% each year,
So price on next year = 100 + 100 * 10 / 100
So the price next year = 110
Similarly price on the next year becomes in a series = 100, 110, 121,
Now, the first term of geometric progression = 100
Common difference = 110 / 100 = 1.1
11 the term = 100 * 1.1 ¹¹
11the term = 285

Thus, the required first term is 100 and the common ratio is 1.1 and the 11th term is 285.

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