C is the point (1;-2) .The point D lies in the second quadrant and has coordinates (x;5) . If the Length of CD is the square root of 53 units , determine the value of x

Step-by-step explanation:

a linear function must follow the structure

y = ax + b

we use the given data point numbers for x and y to solve for the 2 variables a and b.

we use 2 data points to get a solution for the 2 variables. if the third data point then fits into the same equation, then all 3 points are on a line, and the function is therefore linear. if not, then not.

-8 2/5 = a×-7 1/2 + b

-6 = a×-1 1/2 + b

let's subtract the second from the first equation to eliminate b and solve for a :

-8 2/5 = a×-7 1/2 + b

- -6 = a×-1 1/2 + b

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

-2 2/5 = a×6 0

6a = -2 2/5 = (-2×5 - 2)/5 = -12/5

a = -12/5 / 6 = -2/5

and now we use one of the 2 original equations with the newly found information to solve for b :

e.g.

-6 = -2/5 × -1 1/2 + b = -2/5 × -3/2 + b = 6/10 + b = 3/5 + b

-6 - 3/5 = b

(-6×5 - 3)/5 = b

-33/5 = b

so, our proposed linear function is

y = -2x/5 - 33/5

let's see, if the third point is on the line (then the equality is true for its coordinates) or not :

-2 = -2/5 × 8 1/2 - 33/5 = -2/5 × (8×2 + 1)/2 - 33/5

-2 = -2/5 × 17/2 - 33/5 = -34/10 - 33/5 = -34/10 - 66/10

-2 = -100/10 = -10

that is not true (-2 is not equal to -10), so the third point is not on the line between the first 2 points.

that means the function is nonlinear.

Cost of the TV before sale £350

We come across phrases like cost price, tagged price, discount, and selling price when making a purchase. Shop owners give discounts to customers to encourage product sales. Discount is the term used to describe a rebate or an offer made to clients on the listed price of goods. Let's examine the connections between these concepts.

Given,

Sale% = 20%

The cost of TV after the sale = £280

Finding the original price:

                   100% - 20% = 80%

So 80% is the price £280

We have to find the 20% which has been less

Or, £280 = 0.80 x T

Let the original price be T,

                               280 = 0.80 x T

                               280/0.80 = T

                                      350 = T

Hence, the original price of the TV was £350.

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The solution is TRUE

What is union and intersection of sets?
The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B

The union of two sets is a new set that contains all of the elements that are in at least one of the two sets

The intersection of two sets is a new set that contains all of the elements that are in both sets

Given data ,

Let the equation be x

x = A ∩ ( B' ∪ C' )

Now , from Distributive law of set

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

And , ( A ∩ B' ) = A - B

So , substituting the formulas in the equation , we get

x = A ∩ ( B' ∪ C' )

x = ( A ∩ B' ) ∪ ( A ∩ C' )

x = ( A - B ) ∪ ( A - C )

Hence , the solution is TRUE

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We proved that [tex]\angle2\cong\angle4[/tex].

Given: [tex]\angle2[/tex] and [tex]\angle4[/tex] are vertical.

We have to prove [tex]\angle2\cong\angle4[/tex]

The [tex]\cong[/tex] means congruence which means [tex]\angle2[/tex] and [tex]\angle4[/tex] both have same size and angle. We have to show that they both have same size or angle to prove them congruence.

As we know that the value of straight line is [tex]180^{o}[/tex].

From the given figure we can see that

[tex]\angle1+\angle2=180^{o}[/tex]

[tex]\angle3+\angle4=180^{o}[/tex]

[tex]\angle1+\angle4=180^{o}[/tex]

[tex]\angle2+\angle3=180^{o}[/tex]

To prove the [tex]\angle2\cong\angle4[/tex] we subtract [tex]\angle1+\angle2=180^{o}[/tex] and [tex]\angle1+\angle4=180^{o}[/tex]

[tex]\angle1+\angle2-(\angle1+\angle4)=180^{o}-180^{o}[/tex]

We first simplify bracket. When we multiply with the subtraction sign then the sign under the bracket will changed.

[tex]\angle1+\angle2-\angle1-\angle4=0[/tex]

There have [tex]\angle1[/tex] in addition and subtraction then there only remains

[tex]\angle2-\angle4=0[/tex]

We can write that notation as

[tex]\angle2=\angle4[/tex]

Since [tex]\angle2=\angle4[/tex], that means they both have same angle.

So we proved that [tex]\angle2\cong\angle4[/tex].

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Answer:

x = 6

Step-by-step explanation:

8x + 7x = 90

15x = 90

x = 6

For dilation, a figure's size and shape only change during transformation, but during translation, the size of the figure's image and preimage are congruent.

Congruent in geometry refers to being the same size and shape. Congruence can be used with figures, angles, and line segments. If any two line segments are equal in length, they are said to be congruent. If two angles have the same measure, they are said to be congruent.

Techniques for transformation: In a xy-plane, transformation involves changing the size and shape of an item.

Translation and dilation are a couple of the transformation methods used.

For dilation, a figure's size and shape only change during transformation, but during translation, the size of the figure's image and preimage are consistent.

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5x + 4y = -40

4y = -40 -5x

4y/4 = -40/4 -5x/4

y = -10 -5x/4

hence the y-intercept is -10

Answer:

dog

Step-by-step explanation:

Answer:

Step-by-step explanation:

5. A n B = ∅  (the empty set)

6. A u B = {x|x is an integer, x ≠ 0}

7. B n C = {x|x<0}

8. B u C = {x|x<0 or a positive odd integer}

Answer:

  C) The circumcenter is on the outside of an obtuse triangle.

Step-by-step explanation:

You want to know where the circumcenter is in relation to the sides and vertices of different triangles.

The circumcenter of a triangle is the center of the circle through its vertices. As such, it will never lie on a vertex of the triangle.

As you can see in the attached figure, the circumcenter of an acute triangle is inside the triangle.

For a right triangle, the circumcenter is the midpoint of the hypotenuse.

The circumcenter of an obtuse triangle is outside the triangle.

__

Additional comment

The circumcenter is located at the point where the perpendicular bisectors of the sides meet.

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Answer:

0.315

Step-by-step explanation:

The fraction of the hour that remained is 1/4 hour.

The portion or part of the complete item is represented by a fraction. It stands for the equal components of the whole. The denominator and numerator are the two components of a fraction. The top number is referred to as the numerator, and the bottom number is referred to as the denominator.

The students have to submit the book reports in 1 hour.

After the first report, 2/3 hours remained. The next two reports took 1/6 hour and 1/4 hour respectively.

After the first report, 2/3 hours remained.

The next two reports took 1/6 and 1/4 hours.

So, the total time to complete the next two reports is:

= 1/6 + 1/4

= 10/24

= 5/12 hours

Therefore, the fraction of hour remained will be:

= 2/3 - 5/12

= ( 2/3 ) × ( 4/4 ) - 5/12

= 8/12 - 5/12

= 3/12

= 1/4 hour

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Answer:

a. x=5

b. x=4

Step-by-step explanation:

The value of [tex]2\frac{1}{2} -1\frac{5}{6}[/tex] as an fraction is 2/3 .

In the question ,

the expression is given as

[tex]2\frac{1}{2} -1\frac{5}{6}[/tex]

To convert a mixed fraction [tex]a\frac{b}{c}[/tex] into a improper fraction , we use the  formula

[tex]a\frac{b}{c}[/tex] = (a*c+b)/c

let us first convert the given mixed fraction into improper fraction ,

using the formula of conversion , we get

[tex]2\frac{1}{2}[/tex] = (2*2+1)/2 = 5/2

and

[tex]1\frac{5}{6}[/tex] = (1*6+5)/6 = 11/6

Substituting the values , the expression becomes

= 5/2-11/6

taking the LCM as 6 and solving further , we get

= 15/6 - 11/6

= (15-11)/6

= 4/6

= 2/3

Therefore , The value of [tex]2\frac{1}{2} -1\frac{5}{6}[/tex] as an fraction is 2/3 .

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An example of a graph with 4 vertices, with at least one vertex having a degree of 1 is a square graph.

There are 11 simple graphs on 4 vertices.

A graph is a set of points, known as vertices, and lines between those points are referred to as edges. there are many exclusive styles of graphs, along with linked and disconnected graphs, bipartite graphs, weighted graphs, directed and undirected graphs, and simple graphs.

This sort of graph with an even wide variety of vertices of diploma 4 has an even length, so our graphs must have 1, three, or 5 vertices of degree four. as much as isomorphism, there is precisely one graph of each type. A related graph G is known as a Hamiltonian graph if there's a cycle that includes each vertex of G and the cycle is referred to as a Hamiltonian cycle. Hamiltonian stroll in graph G is a walk that passes via every vertex precisely as soon as.

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The entrepreneur make a profit of 200 BD .

In the question ,

it is given that ,

Amount for which the bookshop owner sells educational books to school students = 500 BD .

Amount of money paid to install new shelves = 300 BD .

So, the profit can be calculated using the formula

profit = (Amount for which the bookshop owner sells educational books to school students) - (Amount of money paid to install new shelves) .

Substituting the values from above , we get

profit = 500BD - 300 BD

= 200BD

hence , profit is 200 BD .

Therefore , the entrepreneur make a profit of 200 BD .

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From the graph we get that:

The vertex of the parabola 1 has coordinates (5,4), and its equation is:

The vertex of parabola 2 has coordinates (-3,-2), and its equation is:

Answer: 60% chance or 3:5

Step-by-step explanation: well, 40/24 is 0.6, which is 60%, or you can see 4 is 10%, and 20 is 50%, and add them together to get 60%. 60% is also 6:10, which can be simplified to 3:5

The area of the iPhone 5s in the nearest hundredth is 7252.72 mm².

The iPhone 5s is rectangular in shape and has a base of 58.57 mm and a height of 123.83 mm.

The area of the iPhone 5s can be found as follows:

Therefore,

area of the iPhone 5s = lw

where

Therefore,

l = 58.57 mm

w = 123.83 mm

Hence,

area of the iPhone 5s = 58.57 × 123.83

area of the iPhone 5s = 7252.7231

Therefore,

area of the iPhone 5s = 7252.72 mm²

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The amount Annika should give to Susan is $3.12

What is Algebra?

One of the many branches of mathematics is algebra. Algebra is a common thread that runs through nearly all of mathematics. It involves the study of mathematical symbols and the rules for using them in formulas.

Given,

The amount of money Annika spend = $15.95

The amount of money Tamara spend = $18.46

The amount of money Susan spend = $22.80

The total amount of money:

$15.95 + $18.46 + $22.80 = $57.21.

The average money spent :

= $57.21/3

= $19.07 ,  for each girl.

Thus Annika should give Susan

= $19.07 - $15.95

= $3.12

Hence, Annika should give $3.12 to Susan

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The system is sadly flawed ._.

After decreasing £16870 by 3% we get, £16363.90

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

First, find the percentage of £16870 by 3%

%value = 3% * 16870

            = (3 / 100) * 16870

            = 506.1

Now, just minus with actual value

New value = actual value - %value

We know, actual value = £16870 and %value = 506.1

so, New value = 16870 - 506.1

we get, New value = £16363.90

Therefore, After decreasing £16870 by 3% we get, £16363.90

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The equivalent expression of 8(x+3)−14(20x−56)​ is - 272x + 808.

Two algebraic expressions are equivalent, when the two expressions have the same value when we plug in the same value(s) for the variable(s).

In other words, two algebraic expressions are said to be equivalent if their values obtained by substituting the values of the variables are same.

Therefore, the equivalent expression of 8(x+3)−14(20x−56)​ can be found as follows;

8(x+3) − 14(20x−56)​

open the parenthesis

8x + 24 -  280x + 784

combine the like terms

8x + 24 -  280x + 784

8x -  280x + 24 + 784

Therefore, the equivalent expression is as follows:

- 272x + 808

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Answer:6 trays

Step-by-step explanation:

36 people two cupcakes each means 36x2=72

on tray holds 12 cupcakes 72/12=6 trays

Answer:

y-intercept= (0,0)

Step-by-step explanation:

4x+5y=0

4(0)+5y=0

5y/5=0/5

y=0

4x+5(0)=0

4x/4=0/4

x=0

same for x-intercept (0,0)

endpoint: (14, 28) coordinates of the other endpoint c.

The x-value at the midpoint lies halfway between the values at the two positions. The y-value midway between the two positions is known as the midpoint.

I start by placing the endpoint coordinate at the top and the halfway coordinate at the bottom.

(2, 10)

(6, 9)

I then calculate the difference between endpoint 1 and the midpoint.

+8 and+19

Applying that to the second coordinate's midpoint

(6 ,9)

 8 +19

endpoint: (14, 28)

you can check using the midpoint formula ( x + x / 2, y + y / 2)

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Answer:

Step-by-step explanation:

We know that:

Use the given to find the missing function:

Answer:

[tex]{ \rm{f(x) = 4 - {x}^{2} }}[/tex]

[tex]{ \rm{(f - g)(x) = - {x}^{2} + x + 2}}[/tex]

- From functions;

[tex]{ \boxed{ \tt{(f - g)(x) = f(x) - g(x)}}} \\ \\ { \rm{ - {x}^{2} + x + 2 = (4 - {x}^{2} ) - g(x) }} \\ \\ { \rm{g(x) = (4 - {x}^{2}) + {x}^{2} - x - 2 }} \\ \\ { \boxed{ \rm{g(x) = 2 - x}}}[/tex]

The area of a parallelogram is:

a = bh

The base, b, of the parallelogram is 14.

The issue with this particular figure? We need the perpendicular height. We are given the side width, but that cannot be used in the final equation. So, we employ the Pythagorean Theorem.

We know that in the right triangle, a = 4, and c = 8.

a^2 + b^2 = c^2
4^2 + b^2 = 8^2
16 + b^2 = 64
16 - 16 + b^2 = 64 - 16
b^2 = 48
√b^2 = √48
b ≈ 6.93

So, b in this right triangle is equal to h in the parallelogram. So:

a ≈ 14(6.93)
a ≈ 97.02

There are 120 quarters if Norman has a total of 72 dimes option (D) 120 if there are 3 dimes for every 5 quarters.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

Norman has a coin collection. There are 3 dimes for every 5 quarters in his collection.

3 dimes → 5 quarters

72 dimes →  x quarters

x = (5x72)/3

x = 120 quarters

Thus, there are 120 quarters if Norman has a total of 72 dimes option (D) 120 if there are 3 dimes for every 5 quarters.

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Answer:

120

Step-by-step explanation:

Part a

we have the function

R=-0.1x^3+11x62-100x

using a graphing tool

Part b

we have that

The value of x cannot be a negative number

The value of R can be a negative number

therefore

part c

the answer part c is the option A and C