Solve a system by elimination.
8x-2y=2
4x-y=2

Answer:

Counter Clockwise Torque = 360 Nm

Clockwise Torque = 240 Nm

Step-by-step explanation:

The required quotient is given as [tex]7x^3-x^2-8x-24[/tex]  and the remainder term is 119

In the question, it is asked to determine the quotient of the expression, [tex]\frac{\left[7x^4+6x^3-9x^2-32x+95\right]}{x+1}[/tex] .

It is a method for performing the division of polynomials, with little writing and lesser calculations than complex division.

Here,

When performing synthetic division of polynomials, the terms in the product that remain as fractions are referred to as the division's remainder, whereas the polynomial is referred to as the division's quotient.
[tex]= \frac{\left[7x^4+6x^3-9x^2-32x+95\right]}{x+1}\\=7x^3-x^2-8x-24+\frac{119}{x+1}[/tex]

Thus, the required quotient is given as [tex]7x^3-x^2-8x-24[/tex]  and the remainder term is 119

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The number that is thought in the form of expression will be 2x - 4.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Let the number be 'x'. Then the expression is given as,

⇒ (x - 4) × 2

Simplify the expression, then we have

⇒ (x - 4) × 2

⇒ 2x - 4

The number that is thought in the form of expression will be 2x - 4.

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Answer:

The x-intercept is 40, which represents the number of monthly payments needed to repay the loan.

Step-by-step explanation:

The x-axis can be represented as y = $0, and in this graph y represents remaining balance. So, the x-intercept represents when no more money needs to be paid back on the loan.

y=1/3x+4 is perpendicular to y=-3x-4,

y=2/5x-7 is perpendicular to y=-5/2x+7,

y=-5/2x+8 is perpendicular to y=2/5x+6,

y=-2x+6 is perpendicular to y=1/2x+3 and  

y=7/5x-9 is perpendicular to y=-5/7x-11.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We know that the product of slopes of perpendicular lines is -1.

mM=-1

m is slope of one line and M is the slope of perpendicular line.

M=-1/m

y=1/3x+4

The perpendicular line is y=-3x-4

y=2/5x-7

The perpendicular line is y=-5/2x+7

y=-5/2x+8

The perpendicular line is y=2/5x+6

y=-2x+6

The perpendicular line is y=1/2x+3

y=7/5x-9

The perpendicular line is y=-5/7x-11.

Hence, the lines with corresponding perpendicular lines are

y=1/3x+4---> y=-3x-4

y=2/5x-7-----> y=-5/2x+7

y=-5/2x+8----->y=2/5x+6

y=-2x+6---->y=1/2x+3

y=7/5x-9-----> y=-5/7x-11.

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Answer:

  A, C

Step-by-step explanation:

You want to know which answer choices are angles that are coterminal with 3π/2.

Angles are coterminal when their terminal rays lie in the same position. In general, any angle will be coterminal with angles that are an integer multiple of 2π added to the original.

That is, an angle is coterminal with all angles that have the same value modulo 2π.

For the given angle and each of the answer choices, the attachment calculates the coefficient of π modulo 2. The ones that match the given angle are ...

 A. 11π/2 mod 2π = 3π/2

  C. -7π/-2 mod 2π = 3π/2

__

Additional comment

Both -π/-2 and π/2 match the angle π/2, which is not the same as 3π/2.

Of course, the minus signs in numerator and denominator cancel, so -7π/-2 is the same as 7π/2.

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Yes, it wasn't fair because some kids got more pizza.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

A coach took his team out for pizza after their last game.

There were 14 players, so they had to sit in smaller groups at different tables.

Six players sat at one table and got 4 small pizzas to share equally.

Each of them got = 4/6 = 0.67

The other 8 players sat at a different table and got 6 small pizzas to share equally.

Each of them got = 6/8 = 0.75

0.75 > 0.67

Therefore, some kids got more pizza.

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The evaluation of −0.5D of the matrix gives

[9       8]

[-7     -4]

A matrix (plural matrices) is a set of numbers arranged in rows and columns so as to form a rectangular array.

Given:  the matrix

D =  [-18  -16]

       [14     8]

To find −0.5D, multiply every number in the matrix D by -−0.5. Thus:

−0.5D = −0.5 × [-18  -16]

                         [14     8]

−0.5D  =  [9       8]

               [-7     -4]

Therefore, the 1st option is the answer

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Answer: 0=8n

Step-by-step explanation: Add 2n+6n = 8n, so 0=8n

Answer:

0

Step-by-step explanation:

0=2n+6n

add 2n + 6n =8n

0=8n

divide both sides by 8 and you get 0
I'm not sure though unless it's 0=8n

Answer:

sec^2(a) - sin(a)

Step-by-step explanation:

Hope it helps!

Answer:

Step-by-step explanation:the answer is (sin2 A+cos2)/cos A

tan A+cot A =? =sin A/cos A + cosA/sinA. = (sin^2 A+cos^2 A)/cos A.

Answer: first one

Step-by-step explanation: when u divide the equation to (x+2) and (x-1)

Answer:x = -9, y = -3

Step-by-step explanation:

Answer:

17 7/12 gallons of gas.

Step-by-step explanation:

Set the fractions to like denominators. It'll make it a hell of a lot easier to add.

20 2/3rds = 20 8/12

9 1/4ths = 9 3/12

2 1/2 = 2 6/12

Adding those together gets you 31 17/12 which is 32 5/12 simplified.

Take that fraction and subtract it from your 50 gallons and it'll get you 17 7/12

The value of angle x is 161 degree. So the option B is correct.

In the given question, lines h and j are parallel and cut by transversal k.

We have to find the measure of angle x and choose the correct option.

The diagram of the given question is given below:

From the given diagram using the corresponding angle theorem

x = y

As we know that the angle of straight line is 180 degree.

So x+19 = 180

Subtract 19 on both side, we get;

x = 161 degree

Hence, the value of angle x is 161 degree. So the option B is correct.

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Answer:

y=4x-5

Step-by-step explanation:

y=mx+c

m=4

c = y-intercept = -5

y=4x-5

The value of the cosine of the angle of (a - b) will be 0.80.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

It is a function that repeats itself in a particular time interval.

Suppose that sin(a) = 4/6 and cos(b) = 1/5.

Then the value of 'a' is given as,

sin(a) = 4/6

sin(a) = 2/3

a = 41.81°

Then the value of 'b' is given as,

cos(b) = 1/5

b = 78.46°

Then the value of the cosine of the angle of (a - b) will be given as,

⇒ cos(41.81° - 78.46°)

⇒ cos(-36.65°)

⇒ cos 36.65°

⇒ 0.80

The value of the cosine of the angle of (a - b) will be 0.80.

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The translated coordinates of B is B'(97,69).

A translation is a geometric change in Euclidean geometry that involves moving each point in a figure, shape, or space by the same amount in one direction. A translation may alternatively be thought of as moving the origin of the coordinate system or as adding a constant vector to each point.

Given, point B with coordinates (95, 71) is mapped onto B' through a translation by vector (2,-4).

That means, the translation is 2 units right and 4 units down.

A positive number means moving to the right and a negative number means moving to the left.

The number at the second term represents up and down movement. A positive number means moving up, and a negative number means moving down.

So, B (95, 71) → B' (95 + 2, 73 -4)

       B (95, 71) → B' (97, 69)

Therefore, the coordinates of B' is (97, 69).

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The image of the triangle ΔABC under a reflection across the line l can be obtained my making use of the laws of reflection, and the rules of a reflection transformation, to obtain the triangle ΔA'B'C', with vertices at A'(10, -5), B'(13, -6), and C'(12, -3)

Please find attached the plot of the image of the triangle ΔABC, created with MS Excel

A reflection transformation is one that forms a mirror image of the object across the line of reflection, such that lines joining corresponding points on the pre-image and the image are perpendicular to the line of reflection, and the corresponding points on the pre-image and the image are equidistant from the line of reflection.

Taking the coordinate of the vertices of the triangle ΔABC as A(10, 5), B(13, 6), C(12, 3), and the line l as coinciding with the x-axis, we get:

The coordinates of the image of a point (x, y) following a reflection about the x-axis is the point (x, -y)

Therefor, the coordinates of the vertices of the image of the triangle under a reflection across the line l are;

Please find attached the plot of the image of the triangle ABC under a reflection, across line l, created with MS Excel.

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Answer:

-2

Step-by-step explanation:

We can find slope by using change in y over change in x, as shown:

3-(-1) = 4, and 2-4=-2, and 4/-2 = -2, so our answer is -2.

Terms in Algebraic Expression are [tex]4x^{2}[/tex] , -5y , 7

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

Example of Algebraic Expression - 4x + 5y +8

Hence the term is the algebraic expression are -4x , 5y 8

According to the given information

The Algebraic Expression given to us

[tex]4x^{2} -5y+7[/tex]

Hence

The algebraic expression has three terms.

Terms are [tex]4x^{2}[/tex] , -5y , 7

Terms in Algebraic Expression are [tex]4x^{2}[/tex] , -5y , 7

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Answer:11 cones

Step-by-step explanation: She can by 11 since $3x 11 =$33

Answer:

B

Step-by-step explanation:

Reverse the first and second elements of each ordered pair.

Answer:  5.36 × [tex]10^{-8}[/tex]

Step-by-step explanation:

5.36 × [tex]10^{-8}[/tex]

Answer:

  no

Step-by-step explanation:

Tom wants to know if a 70 cm chest will fit in the space left by a 67 in bed in a room 86 in wide.

The space available is 86 in -67 in = 19 in.

An approximate conversion between cm and inches is that 10 cm corresponds to about 4 in. Then 70 cm will correspond to 7×4 = 28 inches, much too wide for a 19-inch space.

The chest will not fit next to the bed.

The cross product or the curl of F, G, and H are zero so they are scaler fields.

The cosine of the angle between the vectors and their magnitude are combined to form the dot product.

The dot product is represented by A.B = ABCos θ.

The sine of the angle between the vectors and their magnitude are combined to form the cross-product.

The cross product is represented by A×B = ABSin θ.

Given, F × (G × H) = (F . H)G - H(F .G).

∴ F × (G × H) = (FHcosФG) - H(FGcosФ).

F × (G × H) = FGHcosФ - FGHcosФ.

F × (G × H) = 0.

We know that cross-product is the curl of a vector field and if the curl is zero it is a scalar field.

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Elena can make 20/3 cups of purple paint

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

WE are given that Elena makes her favorite shade of purple paint by mixing 3 cups of blue paint, 1 1/2 cups of red paint, and 1/2 cup of white paint.

Since Elena has 2/3 cup of white paint. then;

1 1/2 cups of red paint (1 1/2=1.5)

1/2 cup of white paint (1/2=0.5)

Then the ratio is 3:1.5:0.5

Means every 0.5 cups of white paint Elena makes 5 cups of purple paint (3+1.5+0.5)

Let x the number of cups of purple paint

5/ 0.5 = x / (2/5)

x = 20/3 cups of purple paint

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The patient should receive 909 mL of the TPN solution per day.

To determine the amount of the TPN solution the patient should receive per day, we need to use the following formula:

amount of TPN solution = (grams of protein needed / percentage of amino acids in TPN solution) × 100

In this case, we are given that the TPN solution contains 8.25% amino acids and that the patient needs 75 grams of protein per day. Substituting these values into the formula, we get:

amount of TPN solution = (75 / 8.25) × 100

amount of TPN solution = 9.09 × 100

amount of TPN solution = 909 mL

Therefore, the patient should receive 909 mL of the TPN solution per day.

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The player that has a ratio that means they have a better batting average is B. Tasha, because she has the highest ratio since 27 over 30 is greater than 24 over 30

From the information Illustrated, the ratio of hits compared to total attempts is their batting average. Each player on the team wants to have the highest batting average to help their team the most.

For the season so far, Jana has hit the ball 12 times out of 15 attempts. This will be:

= 12/15

= 0.8

Tasha has hit the ball 9 times out of 10 attempts. This will be:

= 9/10

= 0.9

The player that has a ratio that means they have a better batting average is Tasha.

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Using ratios and proportions, he can make 15 batch of muffins from 2 bags of cornmeal

Ratio is used for comparing two quantities of the same kind. The ratio formula for two numbers, a and b is expressed as a : b or a/b. When two or more ratios are equal, they are said to be in proportion. The concept of ratio and proportion is based on fractions.

Proportion refers to the equality of two ratios. Two equivalent ratios are always in proportion. Proportions are denoted by the symbol (: :) and they help us to solve for unknown quantities. In other words, proportion is an equation or statement that is used to depict that the two ratios or fractions are equivalent.

In this problem, we know that he has 2 bags of cornmeal

1 bag of cornmeal = 25 serving

2 bags = x

x = 2 * 25 = 50 servings

When making muffins, he needs 2.5 cups in a batch

But 3/4 cup = 1 serving

x cups = 50 serving

x = 50 * 3/4

x = 37.5 cups

1 batch = 2.5 cups

x batch = 37.5 cups

x = 37.5 / 2.5

x = 15 batch

He can make a 15 batches

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