Fully factorise 3h² + 12h​

Okay, here are the steps to solve this system of linear equations:

3x1 + x2 + 2x3= 6

4x1 - 3x2 + 5x3 = 8,

2x1 + x2 + 3x3 = 10

1) Add 4 times the first equation to the second equation:

7x1 + 2x2 + 7x3 = 22

2) Add -2 times the first equation to the third equation:

5x1 - x2 + 5x3 = 12

3) Divide both sides by 5 to get:

x1 = 2

x2 = -2

x3 = 1

Therefore, the solution to the system is:

x1 = 2

x2 = -2

x3 = 1

Let me know if you have any other questions!

Answer:

Like the ellipse, the hyperbola can also be defined as a set of points in the coordinate plane. A hyperbola is the set of all points

(

x

,

y

)

in a plane such that the difference of the distances between

(

x

,

y

)

and the foci is a positive constant.

Notice that the definition of a hyperbola is very similar to that of an ellipse. The distinction is that the hyperbola is defined in terms of the difference of two distances, whereas the ellipse is defined in terms of the sum of two distances.

Answer:

10

Step-by-step explanation:

it is one of the properties and derived "abilities" of a hyperbola that the distance of a point on one branch to the focal point of the other branch is the sum of the minimum distance of both branches (in our case 4) and the distance to its "own" focal point (in our case 6).

so, the length of the dotted line is

4 + 6 = 10

to extend and clarify the information from the other answer :

there are 3 different curves when slicing a double-cone (2 cones standing straight on top of each other with their tips touching - in other words, each cone is the mirrored upside-down version of the other).

1. ellipse

a plane is slicing through one of the cones, so that it never touches the other cone.

the ellipse is the outline of that cut around the cone.

a circle is an extreme case, where the plane cuts perpendicular to the central axis of the cone.

2. parabola

an infinite ellipse (another extreme case of ellipse). the slicing plane is parallel to the outline of the cone(s).

but still, only one of the 2 cones is touched.

3. hyperbola

the slicing plane is so inclined that it cuts through both cones. the 2 branches of a hyperbola are the outlines of the cuts through both cones.

usually shown as example is the extreme case, where the slicing plane is parallel to the central axis of the double-cone.

all 3 forms are therefore related.

Answer: - 1.4

Step-by-step explanation: 1.7 minus 3.1 equals -1.4

Answer: A.

Step-by-step explanation: 5 is in one of the first 2 quadrants, and since the second number is a negative, it goes in the 2nd quadrants.

Answer:

\(8 {x}^{2} - 6x - 5 = x\)

\(8 {x}^{2} - 7x - 5 = 0\)

x = (7 + √((-7)^2 - 4(8)(-5)))/(2×8)

= (7 + √(49 + 160))/16

= (7 + √209)/16

= -.4661, 1.3411 (to 4 decimal places)

Answer:

x=-7/2

Step-by-step explanation:

Answer:

x = -7/2 or -3.5

Step-by-step explanation:

7x - 2 = 9x + 5

Add 2 to both sides

7x = 9x + 7

Subtract 9x from both sides

-2x = 7

Divide both sides by -2

x = -7/2

x = -3.5

Answer:

3,952 ft

Step-by-step explanation:

Use the sine function since you need to find the hypotenuse but know the opposite side of the angle, since sine is equal to opposite/hypotenuse.

sin8°=\(\frac{550}{c}\)

csin8°=550

c=550/sin8°

c= 3,952

The statement "Every set can be considered a class" means that every object in set theory, including sets, can be considered a class. This is because classes are simply collections of objects, and sets are a type of collection.

The statement "If S is a set, consider the formula x S and the class {x: x = S}" means that if S is a set, then we can consider the formula x S, which states that x is an element of S, and the class {x: x = S}, which is the class of all objects that are equal to S.

In other words, the statement is saying that every set can be considered a class, and that we can define a class for any set by considering the formula that defines the set and the class of all objects that satisfy that formula.

For example, the set {1, 2, 3} can be considered a class by considering the formula x ∈ {1, 2, 3}, which states that x is an element of the set {1, 2, 3}, and the class {x: x ∈ {1, 2, 3}} is the class of all objects that are elements of the set {1, 2, 3}. This class is equal to the set {1, 2, 3}.

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Answer:

54

Step-by-step explanation:

They look about the same so it could be 54 but at the same time the angles on EDF seem bigger so it could be 63. To be one the safe side though I would choose 54.

Answer:

Domain: (−∞,∞)

Range: (−∞,∞)

Answer:

\(r \geqslant - 16\)

Step-by-step explanation:

\( \frac{ - 10 + r}{2} \geqslant - 13\)

multiply both sides by 2:

\( - 10 + r \geqslant - 26\)

add 10 on both sides:

\(r \geqslant - 16\)

Answer:

\(r \ge -16\)

Step-by-step explanation:

To solve any equation/inequality:

1. get the variable to show up exactly once

2. isolate it

\(\frac{-10+r}{2} \ge -13\)

Multiply both sides by 2 and simplify (note that we're multiplying by a positive, not a negative, so the direction of the inequality stays the same, whereas multiplying or dividing by a negative would have changed the direction of the inequality)

\(\frac{-10+r}{2} *2 \ge -13 *2\)

\(-10+r \ge -26\)

Add 10 to both sides, and simplify

\((-10+r)+10 \ge (-26)+10\)

\(r \ge -16\)

x² +3x+9 and x² + 9 are prime polynomials.

A whole number higher than 1 whose only elements are 1 and itself is referred to as a prime number. A whole number that may be split evenly into another number is referred to as a factor. 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29 are the first few prime numbers. Composite numbers are those that have more than two components. A prime number is one that can only be divided without leaving a residue by itself and one.

Given Data

x² +9

x² + 9 cannot be divided into factors of rational numbers. It is a prime polynomial as a result.

x²+3x+9

It is impossible to factorize x² + 3x + 9 using rational values. It is a prime polynomial as a result.

x²-9

Factoring x² - 9 results in (x - 3)(x + 3). It is not a prime polynomial, therefore.

-2x² +8

The factorization of -2x² + 8 results in -2(x - 2)(x + 2). It is not a prime polynomial, therefore.

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Answer:

please send the picture of the number line.

Answer:me not know

Step-by-step explanation:

Hehuehuejejejje

Answer:

A paired sample t-test

Step-by-step explanation:

A paired sample t-test is most of the time used when in determining the difference between two related dependent variables and in this context; we have

approval ratings before the senator's decision variables and

approval rating after the senator's decision variables for the same subject

These revolves around the senator's decision causing a decrease in approval ratings. Often the two variables are separated by time.

It is used to determine whether the mean of the dependent variable (approval ratings) is the same in the two related groups (the before and after decision groups).

Okay, here we have this:

Considering the provided information, we are going to identify what is the horizontal shift of y, so we obtain the following:

We obtain that the correct answer is the option A, because:

To find:

Round $43,569.14 the nearest dollar

Solution:

The number after the decimal is less than 50. So, the amount $43,569.14 rounded to the nearest dollar is $43,569.

Thus, the answer is $43569.

Just add the powers while it is multiply

-1+(-3)

= -1 - 3

= -4

So it is \(2^{-4}\)

y=55x is the expression for the amount of money obtained from the sale of x units of product.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation. Linear equations are classified into three types: point-slope, standard, and slope-intercept.

Here,

Let sale of x units of product.

y=55x

The expression for the amount of money received from sale of x units of product is y=55x.

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You must charge the customer to achieve your profit target it should be more than $328.

Given that, on a service call, your technician used one contractor the cost you $17.50.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Now,

Total cost = 17.50+6.75+134+11.5+3.5×28.20

= 169.75+98.7

= $268.45

22% net margin

So, 22% of 268.45

= 0.22×268.45

= $59.059

Final cost = 268.45+59.059

= 327.509

≈ $328

You must charge the customer to achieve your profit target it should be more than $328.

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The solution to the quadratic equation 3x² + 5x + 4 = 0 is -5 ±√23/6

Using the quadratic formula, we have the general equation;

ax + bx + c = 0

The general formula is given as;

= (-b±√(b²-4ac))/(2a)

Now, substitute the values, we get;

= -(5) ± √(-5)² - 4 × 3 × 4)/2(3)

find the square value and multiply

= -5± √25- 48/6

Then, we have;

= -5 ±√23/6

Hence, the solutions is -5 ±√23/6

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Answer:

(x, -y)

Step-by-step explanation:

When you reflect across the x-axis, the point moves vertically up or down to the other side of the x-axis. The x-coordinate of the point remains the same. The y-coordinate of the point becomes the opposite of the original value.

x remains x. y becomes -y.

Answer: (x, -y)

Answer:

1000

Step-by-step explanation:

=> \(\frac{1}{10^{-3}}\)

According to the law of exponents, \(\frac{1}{a^{-m}} = a^{m}\)

So, it becomes

=> \(10^{3}\)

=> 1000

The amount of money that Nora would need to invest is $25913.

In Mathematics and Financial accounting, compound interest can be calculated by using the following mathematical equation (formula):

\(A(t) = P(1 + \frac{r}{n})^{nt}\)

Where:

By substituting the given parameters into the formula for compound interest, we have the following;

\(72,000 = P(1 + \frac{0.064}{365})^{365 \times 16}\\\\72,000 = P(1 + 1.75 \times 10^{-4})^{5,840}\\\\72,000 = P(1.000175)^{5,840}\)

P = 72,000/2.77849825425152

Principal, P = $25913.28 ≈ $25913

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Answer:

x = 11

Step-by-step explanation:

8x - 8 + 30 = 11x -11

3x = 33

x = 11

Answer:

x=11

Step-by-step explanation:

8x-8+30+11x-11

3x=33

x=11

hehe the same as her/him

The solution is:  the rate of change is 3.

Here, we have,

Since the graph of f(x) is translated 1 unit down, we need to decrease the value of f(x) by 1 to find g(x):

g(x) = f(x) - 1

f(x) = 3|x| – 4

so, we get,

g(x) = 3|x| – 4 - 1

      = 3|x| – 5

Now, to calculate the rate of change over the interval 2 <= x <= 5, we can use the formula below:

rate = g(5) - g(2)/ 5-2

so, we get,

rate = 9/3 = 3

Therefore the rate of change is 3.

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Answer:

29.5735 milliliters (can be rounded to 30 ml)

Step-by-step explanation:

1(fluid ounce) x 29.5735(Milileters) = 29.5735

1 fluid ounce is 29.5735 millileters

Answer:

Step-by-step explanation:

y

=

1

3

x

−

3

Use the slope-intercept form to find the slope and y-intercept

Slope:

1

3

y-intercept:

(

0

,

−

3

)

Any line can be graphed using two points. Select two

x

values, and plug them into the equation to find the corresponding

y

values.

x

y

0

−

3

3

−

2

Graph the line using the slope and the y-intercept, or the points.

Slope:

1

3

y-intercept:

(

0

,

−

3

)

x

y

0

−

3

3

−

2

image of graph

The value of the sum of twice a number and 7 is 17.

An expression is used to show the relationship between the variables that are given.

Let the number in this situation be 5. This will be illustrated as:

2n + 7

where n = number = 5

= 2n + 7

= 2(5) + 7

= 10 + 7

= 17

Therefore, the number is 17.

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Answer:

A. the angular speed is 3771.4 rad/min

b. 5921 rpms

Step-by-step explanation: I just got this same question right on a test.

In the proportion (5x + 1):3 = (2x + 2):7, the value of x is -1/29.

In the proportion (6x):(4x) = 7, there is no value of x that satisfies the proportion.

To find the value of x in the given proportions, let's solve them one by one:

(5x + 1) : 3 = (2x + 2) : 7

To solve this proportion, we can cross-multiply:

7(5x + 1) = 3(2x + 2)

35x + 7 = 6x + 6

Subtracting 6x from both sides and subtracting 7 from both sides:

35x - 6x = 6 - 7

29x = -1

Dividing both sides by 29:

x = -1/29

Therefore, the value of x in the first proportion is -1/29.

(6x) : (4x) = 7

To solve this proportion, we can simplify the left side:

6x / 4x = 7

Dividing both sides by 2x:

3/2 = 7

This equation is not true, as 3/2 is not equal to 7.

Therefore, there is no value of x that satisfies the second proportion.

In summary, the value of x in the proportion (5x + 1) : 3 = (2x + 2) : 7 is -1/29, and there is no value of x that satisfies the proportion (6x) : (4x) = 7.

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