Which answer is an equation in point-slope form for the given point and slope?
Point:
(5, 9); slope: 2

Answer:

\(\\\sf7x^3 - 2x^2 - 5\)

Step-by-step explanation:

\(\\\sf(6x^3 + 3x^2 - 2) + (x^3 - 5x^2 - 3)\)

Remove parenthesis.

6x^3 + 3x^2 - 2 + x^3 - 5x^2 - 3

Rearrange:

6x^3 + x^3 + 3x^2 - 5x^2 - 2 - 3

Combine like terms to get:

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

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Answer:

7x³ - 2x² - 5

Step-by-step explanation:

(6x³ + 3x² - 2) + (x³ - 5x² - 3)

Remove the round brackets.

= 6x³ + 3x² - 2 + x³ - 5x² - 3

Put like terms together.

= 6x³ + x³ + 3x² - 5x² - 2 - 3

Do the operations.

= 7x³ - 2x² - 5

____________

hope this helps!

Answer:

Step-by-step explanation:

Vertices of ΔABC are,

A(-3, 6), B(2, 1) and C(9, 5)

Use the formula to get the distance between two points \((x_1,y_1)\) and\((x_2,y_2)\),

Distance = \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

By using the formula,

AB = \(\sqrt{(1-6)^2+(2+3)^2}\)

     = \(\sqrt{50}\) units

BC = \(\sqrt{(5-1)^2+(9-2)^2}\)

     = \(\sqrt{65}\) units

AC = \(\sqrt{(6-5)^2+(-3-9)^2}\)

     = \(\sqrt{145}\)

Use cosine rule to find the measure of ∠ABC.

AC² = AB² + BC²- 2(AB)(BC)cos(B)

\((\sqrt{145})^2=(\sqrt{50})^2+(\sqrt{65})^2-2(\sqrt{50})(\sqrt{65})\text{cosB}\)

145 = 50 + 65 - 2(√3250)cosB

cos(B) = \(-(\frac{145-115}{2\sqrt{3250}})\)

          = -0.26312

B = \(\text{cos}^{-1}(-0.26312)\)

B = 105.26°

Answer:

2 times

Step-by-step explanation:

3/4 × 2 = 6/4, simplified down is 3/2

Answer: the answer is a

John is likely to choose a root beer from the cooler 5/27 times, or 18.5% of the time.

p(root beer)=5/27=18.5%

John is likely to choose a root beer from the cooler 5/27 times, or 18.5% of the time. Divide the number of root beers in the cooler (five) by the total number of things in the cooler to arrive at this calculation (27). In this instance, the cooler is filled with 12 Coke cans, 10 water bottles, and 5 root beers. Hence, there are 27 things in the cooler, and the likelihood that John will choose a root beer is 5/27. By dividing the fraction by 100, this figure can be stated as a percentage, giving the answer of 18.5%.Hence, John has an 18.5% chance of grabbing a root beer from the cooler.

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Answer:

\(5x^{2}(x+7)(x-3)\)

Step-by-step explanation:

5x4+20x3-105x2

5x2( x^2 +4x -21)

\(5x^{2}(x+7)(x-3)\)

Answer:

x = -27

Step-by-step explanation:

Apply the Distributive Property to 5(x - 4):  5x - 20.  

Then we have 5x - 20 + 3x - 9x + 7.

Combining like terms, we get -x = 7 + 20 = 27, so that x = -27.

Answer: 3.7

Step-by-step explanation: In this case you're just multiplying by (10) usually this is done to make a decimal to a whole number

There are ten centimeters in one decimeter. How many decimeters are in thirty seven centimeters?

Divide 37/10=3.7

Another way is 3. 7*10=37

Answer:

3

Step-by-step explanation:

The slope is positive since it goes from the bottom left to top right so 3 is the only choice

Answer: 3

Step-by-step explanation:

The line is increasing (meaning it's pointing to the right), so that means the slope must be a positive value. When the slope is 0, the line is flat. When the slope is negative, it's decreasing (pointing to the left).

The speed of red light in a diamond, denoted as vred, is approximately equal to the speed of light in a vacuum, c, which is 2.998 × 10^8 m/s, rounded to four significant figures.

According to the principles of optics and the refractive index of a material, the speed of light in a medium is generally lower than its speed in a vacuum. The refractive index of a diamond is approximately 2.42.

To calculate the speed of red light in a diamond, we can use the formula vred = c / n, where c represents the speed of light in a vacuum and n represents the refractive index of the diamond.

Substituting the given values, we have vred = (2.998 × 10^8 m/s) / 2.42. Evaluating this expression yields a result of approximately 1.239 × 10^8 m/s.

Rounding this value to four significant figures, we obtain the speed of red light in a diamond, vred, as approximately 1.239 × 10^8 m/s.

Therefore, the speed of red light in a diamond, rounded to four significant figures, is approximately 1.239 × 10^8 m/s, which is slightly lower than the speed of light in a vacuum, c.

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Explicación paso a paso:

Workdone = Fuerza * distancia movida en la dirección de la fuerza

Dado

Fuerza f = 40N

Distancia = 6 m

El trabajo realizado por la fuerza F es:

Trabajo hecho = 40 * 6

Trabajo terminado = 240 Nm

El trabajo realizado por la fuerza de la gravedad es el trabajo realizado por el cuerpo de 2 kg:

W = mg

W = 2 * 10

W = 20N

Trabajo realizado = 20 * 6

Trabajo terminado = 120 Nm

The explicit rule in simplified form that can be used to find the number of homes sold in the nth month of the year is H(n) = 6(n - 1) + 12.

A list of numbers that adhere to a pattern or rule is referred to in mathematics as a sequence. Every number in the sequence is referred to as a term, and its location within the sequence is referred to as its index. As an illustration, the numbers 1, 3, 5, 7, 9,... are an example of an odd number sequence. Each word is two more than the one before it, which is the pattern of the sequence. Sequences might have an unlimited number of terms or a finite number of terms (having an infinite number of terms). Mathematical sequences come in a variety of shapes and sizes, including arithmetic, geometric, and Fibonacci sequences.

The pattern shows that the number of homes sold is increasing by 6 each month.

Thus, the explicit rule is given as:

H(n) = 6(n - 1) + 12

Hence, the explicit rule in simplified form that can be used to find the number of homes sold in the nth month of the year is H(n) = 6(n - 1) + 12.

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if 6 litres cost £7.20

then 1/2 of it will cost 'x'(algebraic value)

we form equation

\( \frac{ 7.2}{6} \times \frac{1}{2}x\)

which is equal to 0.6

Cost of 1/2 liter is £0.6.

It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

According to the question

Cost of 6 liters ⇒ £7.20

Cost of 1/2 liter ⇒ X

According to the unitary method

6X = \(7.20\times\frac{1}{2}\)

X  = \(\frac{7.20}{6}\times\frac{1}{2}\)

X = \(\frac{3}{5}\)

X = £0.6

Cost of 1/2 liter is £0.6

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Given the matrix \(\[ A=\left[\begin{array}{ll} x & -7 \\ y & -3 \end{array}\right] \]\)

We are to determine the values of\(\( x \) and \( y \) for which \( A^{2}=A \).\[ A^{2} = A \]\[ \Right arrow A \c dot A = A \]\)

Multiplying A with itself,

we get \(\[ \left[\begin{array}{ll} x & -7 \\ y & -3 \end{array}\right] \c dot \left[\begin{array}{ll} x & -7 \\ y & -3 \end{array}\right] = \left[\begin{array}{ll} x & -7 \\ y & -3 \end{array}\right] \]\) After multiplying the matrices,

we get,\(\[\begin{array}{ll} x^2-7y&=-6x-7\\ yx-3y&=-6y-3 \end{array}\]\)Simplifying the above equations, we get,\(\[\begin{array}{l} x^2-7y+6x+7=0\\ y(x-3)=3(x+1) \end{array}\]\) Solving for x,\(\[\begin{array}{l} x^2-7y+6x+7=0\\ x=\frac{-3y-7 \pm \sqrt{4y^2+22y+29}}{2} \end{array}\]And solving for y,\[\begin{array}{l} y(x-3)=3(x+1)\\ y=\frac{3x+3}{x-3} \end{array}\]\)

Substituting the value of y in equation (1), we get,\(\[\begin{array}{l} x^2-7(\frac{3x+3}{x-3})+6x+7=0 \end{array}\]\)

Solving the above equation, we get two values of x.

One of the values is negative.

The only value that makes sense is,\[ x = -1 \]

Now, substituting the value of x in equation (2), we get,\(\[\begin{array}{l} y=\frac{3x+3}{x-3} \end{array}\]\)

Solving for y, we get,\(\[ y = -\frac{3}{4} \]\)

The values of \( x \) and \( y \) for which\(\( A^{2}=A \) are,\[ \begin{array}{l} x=-1\\ y=-\frac{3}{4} \end{array} \]\)

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Yes the statement that is assume that an is a symmetric matrix. If v and u are eigenvectors of the same matrix with eigenvalues of 3 and 10, respectively, then u must be orthogonal to v is true.

A scalar matrix is ​​a type of diagonal matrix. Diagonal elements of a scalar matrix are equal or equal. If the elements of a scalar matrix are all ones, then it is an identity matrix.

A square matrix A = [aij]n x n is called a scalar matrix.

aij = 0 if i ≠ j

aij = k (for i = j), for some constant k

Facts about scalar matrix :

Eigenvectors are a special set of vectors associated with a linear system of equations

If suppose u is an eigenvector of a corresponding to eigenvalue 3, v is an eigenvector of a corresponding to eigenvalue 10, then u must be orthogonal to v .

u.v=0.

So therefore the statement is true for the given data.

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Answer:

3.25

Step-by-step explanation:

total 18.25 - 2.00 tip = 16.25

16.25/5=3.25

Answer:

W' = 54.4  pounds

Step-by-step explanation:

Given that,

The weight of a bag of books = 40 pounds

After picking up some books at school, the weight has increased by  36%.

We need to find the weight of the bag now. Let the new weight is W'.

So,

W' = 40 +36% of 40

i.e.

\(W'=40+\dfrac{36}{100}\times 40\\W'=54.4\ pounds\)

So, the new weight of the bag is equal to 54.4  pounds.

Answer:

13)

Line A - slope/constant of proportionality = 5/2

Line B - slope/constant of proportionality = 2/3

14)

unit rate = 3/2 or 1.5

The unit rate, 3/2, is greater than line B's unit rate but is less than line A's unit rate.

Step-by-step explanation:

To find the constant of proportionality for question 13 you use the graph. k = y/x so you find the point at (4, 10) and you go up 10 (y) and over 4 (x). So now you have 10/4 and then you simplify to 5/2. Use the same method for line B to find the slope. Now for question 14 you subtract 10 - 5 to get 5 which is your x and 15- 7.5 to get 7.5 which is the y. So this is now 7.5/5 (y/x) or 3/2. 3/2 is less than 5/2 and greater than 2/3.

Thank you so much!!! Hope this helps!!!

Answer:

5/2 = 2.5

2/3 = 0.66667

Step-by-step explanation:

13)  From graph

for A  Constant of proportionality is 10/4 = 20/8 = 5/2 = 2.5

for B  Constant of proportionality is 8/12 12/18 = 2/3 = 0.66667

14) for Object C unit rate / Constant of proportionality is

y / x = 7.5/5 = 15/10 = 30/20 = 1.5

unit rate = 1.5

Object C rate is in between A and B 's rate

A > C > B

The value of the equation is A = ⁵√32,768 is A = 8

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = ⁵√32,768   be equation (1)

On simplifying the equation , we get

A = 8 x 8 x 8 x 8 x 8 = 32,768

So , the 5th root of ( 32,768 ) is 8

Therefore , the value of A = 8

Hence , the equation is A = 8

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Answer:

£4.80

Step-by-step explanation:

We know

A shop advertises 15% off

100% - 15% = 85%

So, £4.08 is the price at 85%

Find 1% by taking

4.08 divided by 85 = £0.048

Now find the price before the reduction by taking

0.048 times 100 = £4.80

So, it was £4.80 before the price reduction.

Answer:

Answer is Lee Ann wrote the right equation.

Step-by-step explanation:

2/8 equals 25%, which equals 1/4, half of 25% is 12.5%, so 25% plus 12.5% equals 37.5%.

37.5% in decimal form is 0.375.

Therefore Lee Ann is correct.

The performance is likely to increase, as the feature size will be reduced, leading to increased efficiency of the processor.

Effect of Decreasing Feature Size on Processor Performance

The performance of a processor is largely determined by its feature size. As the feature size decreases, the processor can process more information in a given time due to the increased efficiency of its components. In this case, the designer has chosen to use a manufacturing process that decreases the feature size of the processor. This means that the processor will be able to process more information in a given time, leading to an increase in performance. All else being constant, the performance of the processor is likely to increase.

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Answer:

a.c,means ac or ca and 5.5=25,So 10 ac is not equivalent

Answer:

165.0

30 plus 50 plus the 85 equals 165

The magnitude of the resultant force acting on the box is 126.4 pounds.

Hence the correct answer is C.

Given that Kiera pulls at an angle of 30below the horizontal and with a force of 80 pounds Nathan pulls at an angle of 50 degrees above the horizontal and with a force of 85 pounds.

We need to determine the magnitude of the resultant force acting on the box.

To find the magnitude of the resultant force acting on the box, we can use the law of cosines.

The law of cosines states that for any triangle with sides of lengths a, b, and c, and an angle θ opposite to side c, the following equation holds:

c² = a² + b² - 2ab × cos(θ)

In this case, we have a triangle formed by the two forces exerted by Keira and Nathan, and we want to find the magnitude of the resultant force, which corresponds to side c.

Let's assign the following values:

a = 80 pounds (force exerted by Keira)

b = 85 pounds (force exerted by Nathan)

θ = 180° - 30° - 50° (angle opposite to the resultant force)

θ = 100°

Now we can plug these values into the law of cosines equation:

\(F = \sqrt{80^2 + 85^2 -2\times 80 \times 85\times \cos100}\)

Solving we get,

F = 126.4

Hence the magnitude of the resultant force acting on the box is 126.4 pounds.

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The number of guests that must attend the picnic for the sophomores to pay for the permit is 82.

The sophomore class is planning a picnic. The cost of the permit to use a city park is $250. To pay for the permit, there is a fee of $.74 for each sophomore and $1.25 for each guest who is not a sophomore. A total of two hundred sophomores plan to attend the picnic. Let the number of guests who attend the picnic be "x". We can form an inequality to find the value of x.

0.74*200 + 1.25*x ≥ 250

148 + 1.25x ≥ 250

1.25x ≥ 102

x ≥ 81.6

Hence, the minimum number of guests is 82.

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The question refers to the plot of the plate's function of the angle of inclination. When the hot side is tilted both upward and downward over the range of +90°, the discontinuous formulas must be used in different ranges of 0.

It refers to the plot of the function of the angle of inclination of a plate. It is a graph that shows the relationship between the angle of inclination and the plate's function. A plate is tilted on its hot side both upward and downward over a range of +90°. The graph shows that different discontinuous formulas are needed for different ranges of 0. A discontinuous formula refers to a formula that consists of two or more parts, each with a different equation. The two or more parts of a discontinuous formula have different ranges, such that each range requires a different equation. These formulas are used in cases where the same equation cannot be applied throughout the entire range.

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Answer: 5 cents

Step-by-step explanation:

Let's assume the ball costs "x" dollars.

According to the problem, the bat costs a dollar more than the ball, which means the bat costs "x+1" dollars.

Together, the bat and ball cost $1.10.

So, we can add the cost of the ball and bat:

x + (x+1) = 1.10

Combining like terms, we get:

2x + 1 = 1.10

Subtracting 1 from both sides:

2x = 0.10

Dividing both sides by 2:

x = 0.05

Therefore, the ball costs 5 cents.

There are 8+9+10=27 equal parts, so Ben has 1/3 of the total amount of money.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.

Ratios compare two numbers, usually by dividing them. If you are comparing one data point (A) to another data point (B), your formula would be A/B. This means you are dividing information A by information B. For example, if A is five and B is 10, your ratio will be 5/10.

For n/(8+9+10), where n is an integer <27

 Ali : Ben : Cathy

   8 : 9 : 10

Thus, there are 8+9+10=27 equal parts, so Ben has 1/3 of the total amount of money.

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