The coordinates of 3 of the vertices of a parallelogram are (-3, 4), (-2, 1), and (2, 6). What is the equation for the
line containing the side opposite the side containing the first two vertices? (Remember, opposite sides of a
parallelogram are parallel.)

9514 1404 393

Answer:

  5x^2 -55x +150 = 0

Step-by-step explanation:

A root of p means (x-p) is a factor. So, the factored form of the equation you want is ...

  5(x -5)(x -6) = 0

  5(x^2 -11x +30) = 0 . . . . . multiplying binomials

  5x^2 -55x +150 = 0 . . . . applying the leading coefficient

According to question,

= 8x² + 6x - 2 = 228

= 8x² + 6x - 230 = 0

= 2(4x² + 3x - 115) = 0

= 2(4x² + 23x - 20x - 115) =0

= 2(x(4x +23) -5(x - 23) )= 0

= 2((x-5)(4x+23)) = 0

x = 5 , x = -23/4

let x = 5

so length 4x - 1

= 4 × 5 - 1

= 19 ft

width = 2x + 2

= 2 × 5 + 2

= 22 ft

_______

gosh! finally did it.. was too big -_-

Therefore, Becky must combine 25.6 grams of the second ingredient (25 percentage protein) with 2.4 grams of the first ingredient (50 percent protein) to create 28 grams of

A percentage (%) is a number that can alternatively be written as a decimal or fraction and represents a quantity as a proportion of 100. You can change a percentage to a fraction by putting 100 in the numerator and also the percentage number in the numerator.

Here,

Becky will need to blend several substances to obtain the necessary level of protein in order to generate 28 grams of a material that is 30% protein.

Let's name the first ingredient's percentage of protein (50%) "x" and the second ingredient's percentage of protein (25%) "y".

That which we are aware of is

28 grams of the combination are present in total.

It has 30% protein.

50% of the first component is protein.

25% protein makes up the second component.

To express the issue, we can build up the following equations:

x + y = 28 (the total amount of the mixture is 28 grams) (the total amount of the mixture is 28 grams)

(0.50)x + (0.25)y = 0.30(28) (the mixture is 30% protein)

Now we can use the first equation to solve for one variable in terms of the other. If we solve for y, we get:

y = 28 - x

We can substitute this into the second equation:

(0.50)x + (0.25)y = 0.30(28) (28) (30% of the mixture is protein)

We may now solve for one variable in terms of the other using the first equation. If we figure out y, we obtain:

y = 28 - x

This can be used as a substitution in the second equation:

(0.50)x + (0.25)(28-x) = 0.30(28) (28)

which results in:

0.50x + 7 - 0.25x = 8.4

And simplifying even more

0.25x = 0.6

x = 2.4

We now know that 2.4 grams of the combination are made up of the first component, which is 50% protein. Using this knowledge, we can calculate the quantity of the second ingredient:

y=28 - x=28 - 2.4=25.6 grams

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The angle with the measure 360° is known as a complete angle. A complete angle is one full rotation measuring 360°.

When the final point coincides with the initial point, after one whole rotation, then the angle so created is known as the complete angle. A complete angle is also known as a full angle or a round angle.

The measure of a complete angle is equal to 2π radians = 360 degrees which is the central angle of a circle. Also, if we combine four right angles or two straight angles it makes a complete angle. A complete angle is identical to a zero angle but the difference is only the amount of rotation.

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The amount of a program that can be parallelized limits the amount of time it takes to run. For example, if 90% of the program can be parallelized, the theoretical maximum speedup utilizing parallel computing would be 10 times regardless of the number of processors employed.

The amount of a program that can be parallelized limits the amount of time it takes to run. For example, if 90% of the program can be parallelized, the theoretical maximum speedup utilizing parallel computing would be 10 times regardless of the number of processors employed. Parallel computing is a sort of computation in which several computations or processes are performed at the same time. Large issues are frequently broken into smaller ones, which may then be tackled concurrently.

Here,

Parallelization can only speed up a program so much. For example, if 90% of the program can be parallelized, the theoretical maximum speedup utilizing parallel computing would be ten times regardless of the number of processors employed.

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Question: in a deck of 52 cards, how many different groups five cards can you be dealt.

Answer: the number of ways of choosing an unordered set of 5 cards from a 52-card deck. Your 52! 47! is the number of ways to deal 5 cards: it counts each of the 5! =120 possible dealing orders of a given hand separately.

have a good day

Answer:

P = 14.9

Step-by-step explanation:

i used distance formula:  

d = √(difference of y-values, squared, + difference of x-values, squared)

distance from (-2,1) and (2,4):  [tex]\sqrt{25}[/tex] = 5

distance from (-2,1) and (-1,-2):  [tex]\sqrt{10}[/tex]

distance from (-1,-2) and (2,4):  [tex]\sqrt{45}[/tex] = 3[tex]\sqrt{5}[/tex]

P = 5 + [tex]\sqrt{10}[/tex] + 3[tex]\sqrt{5}[/tex]  ≈  14.9

The polynomial's zero is 2 since the value of k = -2 is  [tex]3x^{2}[/tex]  +4x+2k . A polynomial is an equation that combines variables, constants .

Using just the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables, a polynomial is an expression in mathematics made up of variables (also known as indeterminates) and coefficients. Using addition, subtraction, multiplication, and division of numbers, a polynomial is an equation that combines variables, constants, and exponents (No division operation by a variable).

given

−2 is a zero of f(x)=[tex]3x^{2}[/tex]+4x+2k

f(−2)=0

∴[tex]3(-2)^{2}[/tex] +4(−2)+2k=0

=>12−8+2k=0

=>2k=−4

=>k=−2

The polynomial's zero is 2 since the value of k = -2 is  [tex]3x^{2}[/tex]  +4x+2k .

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Answer:

The radius of a similar circle with center (-2, 0) has a length of 10 units.

Step-by-step explanation:

The radius of the new circle ([tex]R[/tex]) is the product of the former radius ([tex]r[/tex]) and the scale factor ([tex]k[/tex]), that is to say:

[tex]R = k\cdot r[/tex] (1)

If we know that [tex]k = \frac{5}{2}[/tex] and [tex]r = 4[/tex], then the radius of the new circle is:

[tex]R = k\cdot r[/tex]

[tex]R = \left(\frac{5}{2} \right)\cdot (4)[/tex]

[tex]R = 10[/tex]

The radius of a similar circle with center (-2, 0) has a length of 10 units.

Answer:

elected Council

Step-by-step explanation:

In the given case, Matthew would have a negative z score and John would have a positive z score.

A z-score is a measurement of how far an observation or data point is from the distribution's mean. An observation is said to be above the mean if the z-score is positive, while it is said to be below the mean if the z-score is negative. Therefore, it is possible that John's z-score would be positive, showing that he is taller than the average for his age group if he is one of the tallest children in his class at the age of 7.

In contrast, if 12-year-old Matthew is among the smallest students in his class, it is likely that his z-score will be negative, suggesting that he is shorter than the norm for his age group. Therefore, John would have a positive z-score but Matthew would have a negative one if he is shorter than average for his age group.

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Answer:

[tex]T = 3 + {S}^{2} [/tex]

Step-by-step explanation:

Fill in the table and you will see the formula above gives you the total. Substitute S=10 for you answer

How derive the formula?

You have to realize that you are give 3 to start with, so that's your starting constant. Filling in the table and subtracting 3 show help you see that the square of want is left after the subtraction is the square of the step.

Let me know is you need more clarification

Answer:

B it will have to be 7 to make this true

Step-by-step explanation:

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here's the solution ~

[tex]\qquad \sf  \dashrightarrow \: 4x - 6 = x + 9[/tex]

[tex]\qquad \sf  \dashrightarrow \: 4x - x = 9 + 6[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3x = 15[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 15 \div 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 5[/tex]

Answer:

Step-by-step explanation:

4x-6=x+9

4x-x=9+6

3x=15

Final answer: x = 5

Avogadro's number is a unitless object. It represents a number.

What is unit?

The mass of a particular piece of metal or the length of a particular rod are examples of quantities (specific properties) of objects that have historically been used to define measurement units. An object that has no units is known as unitless.

The proportionality factor that connects the number of constituent particles (often molecules, atoms, or ions) in a sample with the amount of material in that sample is called the Avogadro constant, also known as NA or L. It has a precise value of  6.02214076 × 10²³ reciprocal moles and serves as a SI defining constant.

The value of Avogadro's number is 6.02214076 × 10²³.

One mole of the chemical compound consists of 6.02214076 × 10²³ atoms.

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'v' visits.... would get her 12.5v points

She needs at least 155 points... Meaning the least she needs is 155. Also meaning she needs 155 or More...

We would represent that with a "Greater than or Equal to Sign ≥"

12.5v + 70 ≥ 155

12.5v≥155-70

v= 85/12.5

v=6.8.

Our answer can't be in decimal. She can't make 6.8 visits... Rather

The answer would be 7 Visits.

She needs a Minimum of 7visits.

The inequality that can be used to represent  the number of visits is

12.5v + 70 ≥ 155.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, Genesis has a points card for a movie theater.

Assuming no. of visits to the movie theater to be 'v'.

∴  An inequality that can be used to determine v, the number of visits

Genesis can make to earn her first free movie ticket as she needs 155 points and already has 70 points is,

12.5v + 70 ≥ 155 we have chosen greater than or equal to as she needs at least 155 points.

12.5v + 70 ≥ 155.

12.5v ≥ 85.

v ≥ 85/12.5.

v ≥ 6.8 but she needs to visit at least 7 times.

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Answer: 27

Step-by-step explanation:

Given

In the first sequence, the first term is [tex]a_1=15[/tex]

Common difference is [tex]d_1=4[/tex]

In the second sequence, the first term is [tex]b_1=18[/tex]

Common difference is [tex]d_2=3[/tex]

The nth term of the sequence is [tex]a_n=a+(n-1)d[/tex]

for the same number to appear on both sequence, the nth term must be equal

[tex]\Rightarrow 15+(n-1)4=18+(n-1)3\\\Rightarrow 3=(n-1)\\\Rightarrow n=4[/tex]

Put n=4

[tex]\Rightarrow 15+(4-1)4\\\Rightarrow 15+12=27[/tex]

Therefore, 27 is the first common term in both sequences.

First look at one of the point covered by the black shape, example of which being (2,2).

Next look at where the corrosponding point on the dilated figure is, so keeping with the sample, (10,10).

With this, knowing that both of the shapes are centered around the origin and that they are dilations of each other, do 10/2. to give you 5.

This would be the dilation needed to get the black shape to become the black shape.

Hope that helps.

Answer:

X = 11

Step-by-step explanation:

since the angles are supplementary that means their sum is 180

[tex]5x + 15 + 10x = 180 \\ 15x + 15 = 180 \\ 15x = 180 - 15 \\ 15x = 165 \\ x = 165 \div 15 \\ x = 11[/tex]

Answer:

-2

Step-by-step explanation:

If a1 = 7 and an = An-1 – 3

a4 = a3 - 3

Get a2;

a2 = a1 - 3

a2 = 7 - 3

a2 = 4

Get a3;

a3 = a2 - 3

a3 = 4 - 3

a3 = 1

GEt the required a4

a4 = a3 - 3

a4 = 1 - 3

a4  = -2

Hence the value of a4 is -2

Answer:

[tex]\bold{\boxed{Check explaination for better understanding!}}[/tex]

z=65,y=65,x=50

Step-by-step explanation:

Firstly,  let's identify the only angle provided. The angle is an exterior angle.

The exterior angle theorm states that greater than either of the measures of the remote interior angles.

Let's remember that and start solving!

The exterior angle and x form a supplimentary line which means they create 180 degrees.

130+x=180

x=50

Now by the theorm the sum of z+y should be equal to the exterior angle which is 130.

Simply, z+y=130.

So z  is equal to 65, and y is equal to 65.

Let's check our answers now.

z=65,y=65,x=50

z+x+y=180

65+50+65=180! That works :)

Hope it helps! :))

Using the Pythagoras Theorem the value of c=11.40 and the number that goes beneath the radical is 130.

What is Pythagoras Theorem?

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.

The rectangle is divided into two triangles which have exactly same sides.

So take any one triangle.

Apply the Pythagoras theorem since it is a right-angled triangle with base = 9 and perpendicular = 7.

So, according to Pythagoras theorem -

(Hypotenuse)^2=(Base)^2+(Perpendicular)^2

Plugging in the values in the equation -

c^2=(9)^2+(7)^2

c^2=81+49

c^2=130

c=[tex]\sqrt{130}[/tex]

c=11.40

Therefore, the value of c is obtained as 11.40.

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Answer:

It would be 8

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let's make Mark x as he is in both equations.

For Gregory in Marks view = x+20

For Marks's sister Louanne = x-6

Now you just add everything!

> x+x+20+x-6

> 3x+14

The sum of their ages is 3x+14

Hope that helped!

Answer:

B. Domain: {-∞ < x < ∞}; Range: {y ≤ 2}

Step-by-step explanation:

In simple terms, the domain of a graphed function refers to all the possible x-values while the range refers to all the possible y-values. Therefore, based on the graph the answer would be.

B. Domain: {-∞ < x < ∞}; Range: {y ≤ 2}

This is because x is in a slope and extends infinitely both to the left and to the right, therefore having all possible values. The y-axis starts at and includes the value 2 and all values less than 2. A black filled in dot in a graph indicates that the value is included.

The null hypothesis is that the linear regression model does not exist. This essentially means that the value of all the coefficients is equal to zero.

What is the null hypothesis?

The null hypothesis is a common statistical theory that contends that there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable.

Here,

We have to find out the slope of the line predicted by the null hypothesis if we are doing a linear regression.

We concluded that the null hypothesis states that the slope is equal to zero, and the alternative hypothesis states that the slope is not equal to zero.

Hence, the null hypothesis is that the linear regression model does not exist. This essentially means that the value of all the coefficients is equal to zero.

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Answer:

[tex]x {}^{2} - 4x - 12 = 0 \\ (x - 6)(x + 2) = 0 \\ x = 6 \: \: x = - 2[/tex]

Answer:

Obtuse and isosceles

Step-by-step explanation:

obtuse because an angle is more than 90* and isosceles because two sides are equal.

Hope this helps!

Answer:

24%

Step-by-step explanation:

assign a variable x:

Find the average and solve for x by isolating the variable:

(x+60%)÷2=42%

multiply on both sides, left side cancels, multiply right side

(x+60%)÷2 *2= 42%*2

x+60% = 84%

subtract on both sides, left side cancels, subtract right side

x+60% - 60%=84% - 60%

x=24%