Which matrix represents the system of equations shown below? 3x - 4y = -8 4x+3y = -19
​

Answer:

B; There is only one (x,y) solution and y is negative

Step-by-step explanation:

First, I graphed the two equations. Attached is an image of the equations graphed. Next, I looked for overlapping points. Wherever the two points overlap, there is a solution. When looking at the graph, we can see the lines overlap at only one point, (0,-1). Since y is negative, the answer must be B; there is only one (x,y) solution and y is negative.

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The required solution of the given algebraic expression is x = 6.

The algebraic expression consists of constants and variables using mathematical operators. eg x + y + z, or y = x + z etc.

Here,
Given an algebraic expression,
x + 1 +1 +1 +1 +1 +1 +1  = 1 +1 +1 +1 +1 +1 +1 + 1 +1 +1 +1 +1 +1

Combining like terms on each side of the equation, we get,
According to the question

x + 7 = 13
x = 6

Thus, the required solution of the given algebraic expression is x = 6.

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Answer:

x + 7 = 13

Step-by-step explanation:

(in case you also need it) x = 6

Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.

Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.

Given the equation x² + xy + y² = 5,

we can differentiate both sides with respect to x using the chain rule as follows:

2x + (x(dy/dx) + y) + 2y(dy/dx) = 0

Simplifying this equation yields:

(x + 2y)dy/dx = -(2x + y)

Hence, dy/dx = -(2x + y)/(x + 2y)

Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.

That is:

d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))

= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))

Simplifying this equation yields:

d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³

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Therefore, **x < 7** is the inequality that may be utilized to find x

A mathematical statement known as an inequality compares two expressions using an inequality sign, such as (less than), > (greater than), or (less than or equal to).

For instance, the inequality x + 2 5 signifies that "x + 2 is less than 5".

Let x represent how many days the client paid for pet sitting.

$15 per day plus a $20 fixed service fee equals the total cost of pet sitting.

We are aware that the customer's purchase was under $125. Consequently, we can write:

20 + 15x < 125

Putting this disparity simply:

15x < 105

x < 7

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3x - 14 here, 2x + 10 here. Consequently, X has a value of 14. In algebra, the letter "x" is frequently used to denote a value that is still unknown. It is referred to as a "variable" or "unknown" at times.

In algebra, the letter "x" is frequently used to denote a value that is still unknown. The term "variable" or "unknown" is used to describe it. x in x+2=7 is a variable. Not only can a variable be "y," "w," or any other letter, name, or symbol, it can also be "x." Examine: Variable

Bring the variable to one side of the equation, and then move all the other values to the other side by performing arithmetic operations on both sides of the equation to find the value of x. To determine the answer, simplify the values.

An experiment's independent variable is a variable that stands in for a variable that is being altered. In equations, the independent variable is frequently denoted by the variable x. X is the variable here.

\($$3 x-14-(2 x)=0$$\\\)

We shift every term to the left:

\($3 x-14-(2 x)=0$\)

We combine all the numbers and all the variables.

\($$x-14=0$$\)

All terms containing x are shifted to the left, and all other terms are shifted to the right.

\($$x=14$$\)

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The surface area of the cylinder has a radius of 9.4cm and a height of 18.6 cm is 1098.56 square centimeters.

The surface area of this cylinder is defined as the product of the radius of the base and the height of the cylinder.

The surface area of this cylinder = (2π x r)h

We have given a radius of the base is 9.4 cm and the height of the cylinder is 18.6 cm.

The surface area of this cylinder = (2π x r)h

= (2π x 9.4)18.6

= (59.06)18.6

= 1098.56

Thus, The surface area of the cylinder has a radius of 9.4cm and a height of 18.6 cm is 1098.56 square centimeters.

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The distance traveled by airplane is 180 miles.

The speed of the airplane is 3 miles per minute and the angle of direction from the origin is 51.34°

The airplane landed 100 miles north and 80 miles east from its origin and it flew for one hour.

Then, the total distance traveled by airplane will be:

= 100 miles + 80 miles = 180 miles.

The speed can be defined as the distance traveled by the total time taken.

Speed = distance/time

Speed = 180 miles/ 1 hour

Speed = 180 miles/60 minutes

Speed = 3 miles per minute

The angle of direction from its origin will be:

tan (x) = 100 miles/80 miles

x = tan⁻¹ ( 100/80)

x = tan⁻¹ ( 10/8) =  tan⁻¹ ( 5/4)

x = 51.34°

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Answer:

( − ∞ , ∞ ) hope i help

Step-by-step explanation:

First, solve each inequality. I'll solve the first one first.

7 ≥ 2 x − 5

12 ≥ 2 x

6 ≥ x

Therefore, x could be any number less than or equal to 6. In interval notation, this looks like:

( − ∞ , 6 ]

The parenthesis means that the lower end is not a solution, but every number above it is. (In this case, the lower end is infinity, so a parenthesis must be used, since infinity is not a real number and so it cannot be a solution.) The bracket means that the upper end is a solution. In this case, it indicates that not only could  

x

be any number less than 6, but it could also be 6.

Let's try the second example:

3 x − 2 4 > 4

3 x − 2 > 16    3 x > 18 x > 6

Therefore, x could be any number greater than 6, but x couldn't be 6, since that would make the two sides of the inequality equal. In interval notation, this looks like:

( 6 , ∞ )  

The parentheses mean that neither end of this range is included in the solution set. In this case, it indicates that neither 6 nor infinity are solutions, but every number in between 6 and infinity is a solution (that is, every real number greater than 6 is a solution).

Now, the problem used the word "OR", meaning that either of these equations could be true. That means that either  x  is on the interval  ( − ∞ , 6 ] or the interval  ( 6 , ∞ )

. In other words,  x

is either less than or equal to 6, or it is greater than 6. When you combine these two statements, it becomes clear that  

x

could be any real number, since no matter what number  

x

is, it will fall in one of these intervals. The interval "all real numbers" is written like this:

( − ∞ , ∞ )

The length of z in the triangle is 97 inches.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

Therefore, let's find the side z of the triangle XYZ using sine law as follows:

a / sin A = b / sin B = c / sin C

Hence,

500 / sin 117 = z / sin 10

cross multiply

500 sin 10 = z sin 117

divide both sides by sin 117

z = 500 sin 10  / sin 117

z = 86.8240888335 / 0.89100652418

z = 97.4410774411

Therefore,

z = 97 inches

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Answer:

\((a)\ m = \frac{4}{3}\) --- slope of OA

\((b)\ y = \frac{4}{3}x\) --- the equation

Step-by-step explanation:

Given

The attached graph

Solving (a): Slope of OA

First, we identify two points on OA

\((x_1,y_1) = (0,0)\)

\((x_2,y_2) = (3,4)\)

So, the slope (m) is:

\(m = \frac{y_2 -y_1}{x_2 - x_1}\)

This gives:

\(m = \frac{4-0}{3-0}\)

\(m = \frac{4}{3}\)

Solving (b): The equation

This is calculated as:

\(y = m(x - x_1) + y_1\)

Recall that:

\((x_1,y_1) = (0,0)\)

\(m = \frac{4}{3}\)

So, we have:

\(y = \frac{4}{3}(x - 0) + 0\)

\(y = \frac{4}{3}(x)\)

\(y = \frac{4}{3}x\)

Answer:

\(4\sqrt{3}\)

Step-by-step explanation:

\(48\\\\=2*24\\\\=2*2*12\\\\=2*2*2*6\\\\=2*2*2*2*3\\\\=2^2*2^2*3\\\\\Rrightarrow \sqrt{48}\\\\=\sqrt{2^2*2^2*3}\\\\=2*2\sqrt{3}\\\\=4\sqrt{3}\)

Answer:

MOoo

Step-by-step explanation:

MOoo

Answer:

Angle 6 = 70

Step-by-step explanation: Using vertical angles if you look across from angle 6 you would see the angle of 70 degrees which means they are equal because they're across from each other.

Answer:

21.

Step-by-step explanation:

On my test

Answer:

32 kilometers

Step-by-step explanation:

65 - 33 = 32 kilometers

Hope this helps

Answer:

b = 56km is the answer.

Step-by-step explanation:

a (Northbound train) = 33km

b (Eastbound train) = ?

c (Distance between them) = 65km

According to the Pythagorean theorem,

a² + b² = c²

33² + b² = 65²

1089 + b² = 4225

b² = 4225 - 1089

b² = 3136

b = 56km

∴ the eastbound train has travelled 56km.

Answer:

a) -73°C, -15°C, -12°C, 0°C, 16°C, 37°C, 96°C

a) 96°C, 37°C, 16°C, 0°C, -12°C, -15°C, -73°C

b) -36°C, -15°C, -7°C, -1°C, 0°C, 20°C, 23°C

b) 23°C, 20°C, 0°C, -1°C, -7°C, -15°C, -36°C

The value of the expression \(\sqrt[4]{a}^3\) when evaluated is \(a^\frac34\)

From the question, we have the following parameters that can be used in our computation:

\(\sqrt[4]{a}^3\)

Consider an expression expressed as xⁿ

The expression can be expanded as

xⁿ = x * x * x .... in n places

Using the above as a guide, we have the following:

\(\sqrt[4]{a}^3 = \sqrt[4]{a} * \sqrt[4]{a} * \sqrt[4]{a}\)

Apply the exponent rule of indices

\(\sqrt[4]{a}^3 = a^\frac14 * a^\frac14 * a^\frac14\)

Apply the power rule of indices

\(\sqrt[4]{a}^3 = a^\frac34\)

Hence, the expression \(\sqrt[4]{a}^3\) when evaluated is \(a^\frac34\)

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Answer:

Please check the explanation.

Step-by-step explanation:

Let us consider

\(y = f(x)\)

To find the area under the curve \(y = f(x)\) between \(x = a\) and \(x = b\), all we need is to integrate \(y = f(x)\) between the limits of \(a\) and \(b\).

For example, the area between the curve y = x² - 4 and the x-axis on an interval [2, -2] can be calculated as:

\(A=\int _a^b|f\left(x\right)|dx\)

    = \(\int _{-2}^2\left|x^2-4\right|dx\)

\(\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx\)

   \(=\int _{-2}^2x^2dx-\int _{-2}^24dx\)

solving

\(\int _{-2}^2x^2dx\)

\(\mathrm{Apply\:the\:Power\:Rule}:\quad \int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1\)

   \(=\left[\frac{x^{2+1}}{2+1}\right]^2_{-2}\)

    \(=\left[\frac{x^3}{3}\right]^2_{-2}\)

computing the boundaries

     \(=\frac{16}{3}\)

Thus,

\(\int _{-2}^2x^2dx=\frac{16}{3}\)

similarly solving

\(\int _{-2}^24dx\)

\(\mathrm{Integral\:of\:a\:constant}:\quad \int adx=ax\)

     \(=\left[4x\right]^2_{-2}\)

computing the boundaries

      \(=16\)

Thus,

\(\int _{-2}^24dx=16\)

Therefore, the expression becomes

\(A=\int _a^b|f\left(x\right)|dx=\int _{-2}^2x^2dx-\int _{-2}^24dx\)

  \(=\frac{16}{3}-16\)

  \(=-\frac{32}{3}\)

  \(=-10.67\) square units

Thus, the area under a curve is -10.67 square units

The area is negative because it is below the x-axis. Please check the attached figure.

Answer: My teacher told me to use 180 and divide something.

Step-by-step explanation:

Answer:

isnt itjust 15?

Step-by-step explanation:

1 +1+1+1 = 4  5+3+3 = 11 then 11+4 = 15 if this is incorrect im sorry

Answer:

x=5

Step-by-step explanation:

2(x−1)/4=2(x+8)/13

Step 1: Cross-multiply:

2(x−1)*(13)=2(x+8)*(4)

26x−26=8x+64

Step 2: Subtract 8x from both sides.

26x−26−8x=8x+64−8x

18x−26=64

Step 3: Add 26 to both sides.

18x−26+26=64+26

18x=90

Step 4: Divide both sides by 18.

18x/18= 90/18

x=5

~Hope this helps~

\( \huge \boxed{\mathbb{QUESTION} \downarrow}\)

\( \tt\frac { 2 ( x - 1 ) } { 4 } = \frac { 2 ( x + 8 ) } { 13 } \\ \)

\( \large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}\)

\( \tt\frac { 2 ( x - 1 ) } { 4 } = \frac { 2 ( x + 8 ) } { 13 } \\ \)

Cross multiply the equations on both sides.

\( \tt13\times 2\left(x-1\right)=4\times 2\left(x+8\right) \)

Multiply 13 and 2 to get 26.

\( \tt26\left(x-1\right)=4\times 2\left(x+8\right) \)

Use the distributive property to multiply 26 by x-1.

\( \tt26x-26=4\times 2\left(x+8\right) \)

Multiply 4 and 2 to get 8.

\( \tt \: 26x-26=8\left(x+8\right) \)

Use the distributive property to multiply 8 by x+8.

\( \tt \: 26x-26=8x+64 \)

Subtract 8x from both sides.

\( \tt \: 26x-26-8x=64 \)

Combine 26x and -8x to get 18x.

\( \tt \: 18x-26=64 \)

Add 26 to both sides.

\( \tt \: 18x=64+26 \)

Add 64 and 26 to get 90.

\( \tt \: 18x=90 \)

Divide both sides by 18.

\( \tt \: x=\frac{90}{18} \\ \)

Divide 90 by 18 to get 5.

\( \boxed{ \boxed{ \bf \: x=5 }}\)

Answer:

choice 4

Step-by-step explanation:

complementary angles sum to 90

Answer:

B. one

Step-by-step explanation:

y = x² + 4                            y = 4x

x^2 + 4 = 4x

x^2 - 4x + 4 = 0

This is a quadratic equation in x, which can be factored as:

(x - 2)^2 = 0

The only solution to this equation is x = 2. Substituting this value of x into either of the original equations, we get y = 8.

So, there is only one real solution to the system of equations, which is (2, 8).

\( \Large{\boxed{\sf Option \: B \text{:} \: One}} \)

\( \\ \)

Given system of equations:

\( \begin{cases} \sf y &=\sf x^2 + 4 \\ \sf y &=\sf 4x \end{cases} \)

\( \\ \)

We notice that both 'x² + 4' and '4x' are equal to y, which means that we can write the following equality:

\( \sf x^2 + 4 = 4x \)

\( \\ \)

Subtracting 4x from both sides, we get:

\( \sf x^2 + 4 - 4x = 4x - 4x \\ \\ \\ \sf x^2 - 4x + 4 = 0 \)

\( \\ \)

This is a quadratic equation, which means that it can be written as ax² + bx + c = 0, with a ≠ 0.

\( \\ \)

The number of real solutions a quadratic equation has is determined by the value of its discriminant, D.

\( \\ \\ \)

\( \\ \\ \)

The discriminant of a quadratic equation is calculated as follows:

\( \sf D = b^2 - 4ac \)

\( \\ \)

Now, we have to determine the coefficients a, b, and c.

\( \sf x^2 - 4x + 4 = 0 \Longleftrightarrow \overbrace{\sf 1}^{a}x^2 + \underbrace{(\sf-4)}_{b} x + \overbrace{\sf 4}^{c} = 0 \)

\( \\ \)

Use these values to find the value of the discriminant:

\( \sf D = (-4)^2 - 4(1)(4) = 16 - 16 = \boxed{\sf 0} \)

\( \\ \)

Since D = 0, the system of equations has one real solution.

\( \\ \\ \\ \)

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Answer:

3x + 12

Step-by-step explanation:

5x + 6(x - 2) - 8(x - 3) ← distribute parenthesis

= 5x + 6x - 12 - 8x + 24 ← collect like terms

==(5x + 6x - 8x) + (- 12 + 24)

= 3x + 12

Answer:

x ≥ 2

Step-by-step explanation:

Distribute 8:

8 (3.5x - 2) ≥ 40

28x - 16 ≥ 40

Add 16:

28x ≥ 40 + 16

28x ≥ 56

Divide by 28:

x ≥ 56 ÷ 28

x ≥ 2

Answer:

x ≥ 28

Step-by-step explanation:

1.  8(3.5x-2) ≥ 40

2. 28x - 16 ≥ 40

     + 16   + 16

    28x  ≥  56

3.  x ≥ 28

Answer:

It would be c.

I hope that helps

Step-by-step explanation:

If you look at (0,0) you can see that if you go up two it will be right across second point.