Solve the following system of equations using the elimination method. x – y = 11 2x + y = 19 Question 5 options: A) (–3,9) B) (10,–1) C) (–9,6) D) (–10,2)

The value of x in this equation is found to be 8±4√7.

What is Pythagoras theorem?

The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC2 = AB2 + AC2 in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized.

Here given in the question that one side of the wall 5 feet

So as it is a rectangular bedroom it can be split into 2 right-angled triangles.

So the hypotenuse of the triangle is 13 feet

Now using the Pythagoras theorem we can find out the length of the other wall

b²=h²-p²

(x-4)²+(x+6)² = (x+10)²

x²+16-8x+x²+36+12x = x²+100+20x

x²-16x-48=0

x= 8±4√7.

Hence The value of x in this equation is found to be 8±4√7.

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Answer:

Step-by-step explanation:

sin(0) = 0/2

sin(30) = 1/2

sin(45) = \(\sqrt{2}\)/2

sin(60) = \(\sqrt{3}\)/2

sin(90) = \(\sqrt{4}\)/2

cos(90) = 0/2

cos(60) = 1/2

cos(45) = \(\sqrt{2}\)/2

cos(30) = \(\sqrt{3}\)/2

cos(0) = \(\sqrt{4}\)/2

notice that sin and cos repeat,   but in reverse

the answer for your questions is in there.  

The angle in degrees is 873.1843.

Let the measure of the angle be θ in degrees. Therefore, the measure of the same angle in gradians is (θ × π/180).

According to the given information, the number of degrees of a certain angle added to the number of gradians of the same angle is 152.(θ) + (θ × π/180) = 152.

Simplifying the above equation, we get:(θ) + (θ/180 × π) = 152.

Multiplying both sides of the equation by 180/π, we get:

θ + θ = (152 × 180)/π2θ = (152 × 180)/πθ = (152 × 180)/(3.14)θ = 873.1843

Thus, the angle in degrees is 873.1843.

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25% of the students in the seminar are shorter than 65 inches.

To find the percentage of students who are shorter than 65 inches, we first need to find the number of students whose height is less than 65 inches:

There are three students who are shorter than 65 inches: 62, 60, and 58.

Therefore, the percentage of students who are shorter than 65 inches is:

(3 students / 12 students) × 100% = 25%

Note that the value given for 1% × 5 does not appear to be relevant to this question, and is not necessary for the calculation of the percentage of students who are shorter than 65 inches.

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a. The table beside the graph should be completed as follows;

b. The table beside the graph should be completed as follows;

Based on the diagram, we can logically deduce that the graph of the first quadratic function is an upward parabola because the coefficient of x² has a positive value. Also, the value of "a" is greater than zero (0) with the x-intercept (roots) being (-5, 0) and (-1, 0) while the y-intercept is (0, 4).

Additionally, the vertex is given by the ordered pair (-3, -4) and it has a minimum value of -4.

Part b.

Based on the diagram, we can logically deduce that the graph of the second quadratic function is a downward parabola because the coefficient of x² has a negative value. Also, the value of "a" is less than zero (0) with the x-intercept (roots) being (-2, 0) and (4, 0) while the y-intercept is (0, 8).

In conclusion, the vertex is given by the ordered pair (1, 9) and it has a maximum value of 9.

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Answer: The quotient is 3y² + 2y - 1.

Step-by-step explanation:

You can use long division to solve this expression by setting the dividend under the roof and the divisor outside as you would normally do when dividing numbers.

1) Look at the first term of the dividend, 15y³, and the first term of the divisor, 5y. Determine what value multiplied by 5y would give you 15y³. The answer is 3y², and given the number, you multiply it by the WHOLE divisor.

3y²(5y + 6) = 15y³ + 18y² <-- subtract this from the dividend.

2) Continue this process and make sure to drag down the next term for each new value you form after subtracting. Keep in mind of any negative values! When you reach up to -5y, determine what value multiplied by 5y would give you the value of -5y, which would be -1.

3) You should be left with a remainder of 0, leaving you with a quotient of 3y² + 2y - 1.

Let x represent Mikhail's age.

Since Gabrielle is 8 years older than Mikhail, it means that Gabrielle's age is

x + 8

If the sum of their ages is 104, it means that

x + x + 8 = 104

2x = 104 - 8

2x = 96

x = 96/2

x = 48

Mikhail's age is 48

Answer:

44

Step-by-step explanation:

1×5² + 3×5¹ +4×5⁰

25+15+4

44

Answer:

2/19

Step-by-step explanation:

i just took the test and no one helped me i got is wrong but when you go back to review it it tells you the answer hope im not too late

Answer: 20, 40, 60, 80, 100,....

Step-by-step explanation:

Given that :

It is possible to create teams of 4 for a relay race with no student leftover

Also,

It is possible to create teams of 5 for dodgeball with no student left over from the same class

To deduce the possible number of students in the class, then the number of students should be a multiple of both 4 and 5

Multiples of 4 include = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100,....

Multiples of 5 : 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100,....

Multiples common to both 4 and 5 : 20, 40, 60, 80, 100,....

By calculating this average, we can approximate the slope of the tangent line to the curve at P (16, 7).

To find the slope of the secant line PQ, we need to calculate the difference in y-coordinates (change in y) divided by the difference in x-coordinates (change in x) between the points P and Q.

For x = 16.1:

Coordinates of Q: (16.1, √(16.1) + 3)

Slope of PQ = (y-coordinate of Q - y-coordinate of P) / (x-coordinate of Q - x-coordinate of P)

Slope of PQ = (√(16.1) + 3 - 7) / (16.1 - 16)

Slope of PQ = (√(16.1) - 4) / 0.1

Similarly, we can find the slope of PQ for the other given values of x:

For x = 16.01: Slope of PQ = (√(16.01) - 4) / 0.01

For x = 15.9: Slope of PQ = (√(15.9) - 4) / (-0.1)

For x = 15.99: Slope of PQ = (√(15.99) - 4) / (-0.01)

Based on the given values, we can observe that as x approaches 16, the values of the slopes of PQ get closer to a certain value. This suggests that the slope of the secant line PQ tends to converge to a specific value as x approaches 16.

Therefore, we can infer that the slope of the tangent line to the curve at P (16, 7) is the limit of the slopes of PQ as x approaches 16. To get an estimate of the slope of the tangent line, we can take the average of the slopes of PQ for x = 16.1 and x = 15.9:

Slope of the tangent line at P ≈ (slope of PQ for x = 16.1 + slope of PQ for x = 15.9) / 2.

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Note that the parameters of the graph a and graph b are given below.

Graph A - y=2(x-1)²

See graph attached.

Graph B - y = 1/2x² + 3

Vertex: The vertex of the function is (0, 3).

Axis of symmetry: The axis of symmetry is the vertical line passing through the vertex, which is x = 0.

Y-intercept: The y-intercept is the point where the graph intersects the y-axis. It is (0, 3).

Minimum or maximum: The coefficient of x² is positive, which means the parabola opens upwards, and therefore the function has a minimum value. The minimum value is 3.

Solutions: To find the solutions or roots of the quadratic equation, we need to set y or f(x) equal to zero and solve for x.

0 = 1/2 x² + 3

Subtracting 3 from both sides, we get:

-3 = 1/2 x²

Multiplying both sides by -2, we get:

6 = -x²

Taking the square root of both sides, we get:

x = ±√(-6)

Since the square root of a negative number is not a real number, the function has no real roots.

Minimum or maximum value: The minimum value of the function is 3.

Range: The range of the function is y ≥ 3, because the function has a minimum value of 3.

Domain: The domain of the function is all real numbers, because there are no restrictions on the values of x for which the function is defined.

Stretch/Shrink/Standard: The coefficient of x^2 is positive and less than 1, which means that the graph of the function is narrower than the graph of y = x². This is an example of a standard quadratic function that has been vertically compressed by a factor of 1/2.

See graph attached.


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Answer:

9:0

Step-by-step explanation:

how do u expect me to explain it

None of the given answer options (-10, 10, 16, ¾/1) correspond to the correct slope of -1/2.

To find the slope of the red line given that it is perpendicular to the green line with a slope of 2, we can use the property that perpendicular lines have slopes that are negative reciprocals of each other.

The slope of the green line is 2. To find the slope of the red line, we take the negative reciprocal of 2. The negative reciprocal is obtained by taking the reciprocal (flipping the fraction) and changing the sign.

Reciprocal of 2: 1/2

Negative reciprocal: -1/2

Therefore, the slope of the red line is -1/2.

However, none of the given answer options (-10, 10, 16, ¾/1) correspond to the correct slope of -1/2.

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The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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Answer:

12 and 6

Step-by-step explanation:

Let the numbers be x and y

Sum of two numbers is 18.

 ⇒ x + y = 18  ----------------(II)

\(\sf \text{Reciprocal of x = $\dfrac{1}{x}$}\\\\ \text{Reciprocal of y =$\dfrac{1}{y}$}\)

Sum of reciprocals is 1/4

       \(\sf \dfrac{1}{x}+\dfrac{1}{y}=\dfrac{1}{4}\\\\ \dfrac{1*y}{x*y}+\dfrac{1*x}{y*x}=\dfrac{1}{4}\\\\\dfrac{y}{xy}+\dfrac{x}{xy}=\dfrac{1}{4}\\\)

            \(\sf \dfrac{x +y}{xy}=\dfrac{1}{4}\)

Plugin (x +y = 18)

               \(\dfrac{18}{xy}=\dfrac{1}{4}\\\\\)

Cross multiply,

           18*4   = 1*(xy)

              xy   = 72

                 \(x = \dfrac{72}{y}\)

Substitute x value in equation (I)

            \(\dfrac{72}{y}+y=18\\\\\text{Multiply the entire equation by y}\\\\\\ 72 + y^2=18y\\\)

        y² - 18y + 72 = 0

 y² - 12y - 6y + 72 = 0

y(y -12) - 6(y - 12) = 0

       (y - 12)(y -6 ) = 0

y - 12 = 0              ; y - 6 = 0

    y = 12              ; y = 6

Answer:

0.12 Miles

Step-by-step explanation:

Given:

Joakin = 0.3 Miles from Keith

Layla lives 0.4 times as far as Joakim

Solution:

If Joakin lives 0.3 miles from keith and Layla lives 0.4 times as far from keith as Joakim that mean to multiply 0.3 by 0.4.

0.3 x 0.4 = 0.12

Hence, Layla live 0.12 Miles from Keith.

Answer:

a convex polygon is a simple polygon in which each of the interior angles measure less than 180-degrees

Answer:

ik only 1 of them and i dont even know if this is correct...

a) A

\( \sf{\red{ANSWER \: \: :}}\)

x = 18 1/3

\( \sf{\purple{EXPLANATION \: \: :}}\)

x - 20 + 2x = 35

- 20 + 3x = 35

3x = 35 + 20

3x = 55

x = 55/3

x = 18 1/3

The expression using exponents we can rewrite as \(a^2 . c^2\) .

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Answer:

the solution to the system of equations is (x, y) = (3, -2).

Step-by-step explanation:

y = -2x + 4 (Equation 1)

y = x - 5 (Equation 2)

To solve for x, we can equate the right sides of the equations:

-2x + 4 = x - 5

Now, we can solve for x:

-2x - x = -5 - 4

-3x = -9

x = (-9) / (-3)

x = 3

Substituting the value of x back into Equation 2, we can solve for y:

y = 3 - 5

y = -2

Answer:

No

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x + 1 ← is in slope- intercept form

with slope m = 3

Calculate the slope using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (2,4) and (x₂, y₂ ) = (4, 12) ← 2 ordered pairs from the table

m = \(\frac{12-4}{4-2}\) = \(\frac{8}{2}\) = 4

Parallel lines have equal slopes

The slope of these 2 lines are not equal , thus not parallel

The length of the fence must be 618cm

The volume that it can hold is 1,909,620 cm³

First, the fence is just equal to the circumference of the cylinder, remember that the circumfernce of a circle of diameter D is:

C = П*D

Here we use П = 3, then:

C = П*206cm

C = 3*206cm = 618cm

Now the volume, for a cylinder of diameter D and height H, the volume is:

V = П*(D/2)²*H

Replacing the values that we know we will get:

V = 3*(206cm/2)²*60cm = 1,909,620 cm³

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The paycheck of the salesperson at the clothing store for two weeks will amount to c. $890.

The paycheck can be computed by working out the base salary, overtime pay if any, and the sales commission separately and adding up these.

Some deductions (withholding taxes and insurance) are made to the gross pay to arrive at the paycheck, which is known as the net pay.

Base salary = $10.00 per hour

Overtime pay = 1.5 of the base salary per hour

Work week = 40 hours

Commission on total sales = 3%

Sales for a month = $3,000

Commission on $3,000 sales = $900 ($3,000 x 3%)

Base salary for two weeks = $800 ($10 x 40 x 2)

Paycheck = $890 ($800 + $900)

Thus, the paycheck of the salesperson at the clothing store for two weeks will amount to c. $890.

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Answer:

Step-by-step explanation:

8ab = 4a × (2b)

12a² = 4a × (3a)

Then

LCM(8ab , 12a²) = 4a × (2b) × (3a)

                          = (4×2×3) × (a×a×b)

                          = (24) × (a²×b)

                          = 24a²b

The length of side AB  of this rectangle is 5 units

The cooridnates of the rectangle are given as:

A(-8, -6), B(-3,-6), C(-3, -4), and D(-8, -4).

The length of side AB is calculated as;

AB = √(x1 - x2)^2 + (y1 - y2)^2

This gives

AB = √(-8 + 3)^2 + (-6 + 6)^2

Evaluate

AB = 5

Hence, the length of side AB  of this rectangle is 5 units

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Complete question

Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(-8, -6), B(-3,-6), C(-3, -4), and D(-8, -4).

Given these coordinates, what is the length of side AB of this rectangle?

The amount of money each student will pay, excluding taxes and tip,  $23.534

Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.

Numerator is a number which lies on the top side, it indicates the number of equal parts taken and denominator is on the bottom side, it indicates the equal parts of the whole number.

Given that,

3 Coffee 5.85

1 Diet Bev. – lg. 3.38

1 Sparkling Water 2.50

3 Ranch Chicken Sandwich 44.97

1 Classic Burger 12.95

1 Thai Stir-fry Special 11.50

2 Club Sandwich 22.98

Subtotal 104.13

Tax (13%) 13.54

Total 117.67

The receipt is for lunch for five students. Each student will pay 1/5 of the bill

The amount of money each student will pay = ?

⇒  1/5x117.67

⇒   23.534

Therefore, the amount each student will pay, $23.534

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