The difference of the squares of two positive consecutive even integers is 76. find the integers. use the fact​ that, if x represents an even​ integer, then x+2 represents the next consecutive even integer.

Answer:  The required equation of the line is [tex] y=-\dfrac{5}{2}x-1.[/tex]

Step-by-step explanation:  We are given to find the equation of the line that is parallel to the following line and passes through the point (-2, 4) :

[tex]5x+2y=12~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that

the slope-intercept form of the equation of a straight line is given by

[tex]y=mx+c,[/tex]

where m is the slope of the line.

From equation (i), we have

[tex]5x+2y=12\\\\\Rightarrow 2y=-5x+12\\\\\Rightarrow y=-\dfrac{5}{2}x+6.[/tex]

So, the slope of line (i) is given by

[tex]m=-\dfrac{5}{2}.[/tex]

We know that the slopes of two parallel lines are equal. So, the slope of the new line will be

[tex]m=-\dfrac{5}{2}.[/tex]

Since the line passes through the point (-2, 4), so its equation will be

[tex]y-4=m(x-(-2))\\\\\\\Rightarrow  y-4=-\dfrac{5}{2}(x+2)\\\\\\\Rightarrow y-4=-\dfrac{5}{2}x-5+4\\\\\\\Rightarrow y=-\dfrac{5}{2}x-1.[/tex]

Thus, the required equation of the line is [tex] y=-\dfrac{5}{2}x-1.[/tex]

Using the Pythagorean theorem, we can calculate the distance between a small plane 20 miles north of an airport and a jet 64.5 miles west of the airport as 67.5 miles to the nearest tenth.

Given that a small plane is 20 miles due north of the airport and a jet is 64.5 miles west of the airport, the scenario forms a right-angled triangle with the legs representing the distances from the airport to each aircraft. To find the distance between the small plane and the jet, we can use the Pythagorean theorem which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (the legs).

The equation for the distance (d) between the two planes can be expressed as:

d² = north side² + west side²

d² = 202 + 64.52

d² = 400 + 4160.25

d² = 4560.25

d = √4560.25

d = 67.5 miles (rounded to the nearest tenth)

Thus, the distance between the small plane and the jet is 67.5 miles to the nearest tenth.

Answer:

25

Step-by-step explanation:

The baker's prediction had a 17.39% error.

To calculate the percent error of the baker's prediction, we use the formula:

Percent Error = (|Actual Value - Predicted Value| / Actual Value) * 100%

In this case, the Actual Value is the number of cupcakes actually sold, 115. The Predicted Value is the number the baker predicted to sell, 95.

So, the computation will be:

Percent Error = (|115 - 95| / 115) * 100%

Percent Error = (20 / 115) * 100

Percent Error = 0.1739 * 100%

Percent Error = 17.39%

Final answer:

The length of line CF is 20 units.

Explanation:

Let's analyze the given information step by step:

Since line EB is perpendicular to line BF, triangle EBF is a right triangle. Let's assume the length of line BF is x units. Using the area of a triangle formula, we have:

Area of triangle EBF = (1/2) * base * height

20 = (1/2) * x * 2

Simplifying the equation, we get:

20 = x

Therefore, the length of line BF (or CF) is 20 units.

Answer:

the person up is wrong

Step-by-step explanation:

i got it wrong on the test rn

Answer:

The number of solution is, 1 and the type of solution is, Integer solution.

Step-by-step explanation:

Given the equation:

[tex]8-4x=0[/tex]

Add 4x to both sides we have;

[tex]8 = 4x[/tex]

Divide both sides by 4 we have;

[tex]2 = x[/tex]

or

x = 2

Solution for this equation is, 2

Therefore, The number of solution is, 1 and the type of solution is, Integer solution.

The equation has a single real solution, x = 2.

The equation 8 − 4x = 0 can be solved as follows:

8 − 4x = 0

4x = 8

x = 2

The equation has one real solution, x = 2.

A real solution is a solution that is a number. The number 2 is a real number, so the equation has one real solution.

Here is a more detailed explanation of the solution:

We subtract 8 from both sides of the equation.

We divide both sides of the equation by -4.

We simplify both sides of the equation.

The answer is x = 2, which is a real number. So, the equation has one real solution.

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Given the segments of a quadrilateral, the steps show that for it to be closed, the expression 3y + 10x + 1 = 0 must hold. Additional information would be needed to find unique values for x and y.

Given the segments AB, BC, CD, and DA of a quadrilateral:

For a quadrilateral to be closed, the perimeter equations must be equal. Thus, we set up the equality:

AB + BC + CD + DA = 0

Substituting the given segment expressions:

(2y + 1) + (y + 1) + (7x - 3) + (3x) = 0

Simplifying this equation:

3y + 4 + 10x - 3 = 0

Combine like terms:

3y + 10x + 1 = 0

This represents a linear equation involving x and y.

Assuming the quadrilateral is closed, another equation or condition is needed to solve for x and y simultaneously. If additional geometric or numeric information is provided about the quadrilateral, it can help solve the system.

here is complete question-Find the values of x and y in ABCD. 9. AB=2y,BC=y+3,CD=5x-1,DA=2x+4 10. AB=2y+1,BC=y+1,CD=7x-3,DA=3x (6.3) Determine whether the quadrilateral must be a parallelogram.

Answer:

B. It is greater than -4  because 0.36*(7 5/8)  is less than 1/2 * 8

Step-by-step explanation:

Given the question:

Which statement about this product is true? 0.36*(-7 5/8)  

If you replace the multiplication:

0.36*(7 5/8)  

by

1/2*8 = 4

You will get a greater result because 1/2 ( or 0.5) is greater than 0.36 and 8 is greater than (7 5/8). Taking into account that the original multiplication involves a negative number, then:

0.36*(7 5/8) < 1/2*8

0.36*(-7 5/8) > 1/2*(-8)    (multiply by a negative number at both sides of the inequality change the sign)

In fact 0.36*(-7 5/8) = -2.745.

Answer:

true

Step-by-step explanation:

The answer is B or the purple one

Answer:

The image B with purple figures is correct.

Step-by-step explanation:

We are given the figure DEF and we are required to find the figure which is obtained after reflecting it.

Now, reflection of a figure means to flip the figure over a line.

In the green figure, the points D and E are interchanged which is not possible in reflection.

In the blue figure, there is no change.

In the purple figure, the triangle is flipped over the line DE and so it is the correct answer.

Hence, the purple figure is obtained after reflecting the figure DEF.

The ends of the graph of the function f(x) = 3x^5 + 6x will display the behavior described in option c. This is due to the highest power of x in the equation being an odd number and the coefficient being positive. As such, the left end of the graph will start down at a large negative and the right end will go upwards.

The behavior of the ends of the graph of the function f(x) = 3x^5 + 6x is determined by the highest power of x in the equation, which is 5 in this case. The coefficient of x^5 is positive, so as x approaches positive infinity, f(x) also approaches positive infinity. Conversely, as x approaches negative infinity, the value of f(x) would approach negative infinity. We can describe this behavior as the left end of the graph starting at a large negative and the right end going upwards. Thus, answer c. 'the left end will start down at a large negative and the right end will go upwards' is correct.

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Answer:  The required value of x is 32.

Step-by-step explanation:  We are given to find the length of the unknown side.

That is, x = ?

From the figure, we see a right-angled triangle with

length of the hypotenuse, h = 68 units,

length of the other two sides, a = 60 units and b = x.

Using Pythagoras theorem in the given right-angled triangle, we have

[tex]h^2=a^2+b^2\\\\\Rightarrow 68^2=60^2+x^2\\\\\Rightarrow x^2=68^2-60^2\\\\\Rightarrow x^2=4624-3600\\\\\Rightarrow x^2=1024\\\\\Rightarrow x=\pm32.[/tex]

Since x is the length of a side of the triangle, so it cannot be negative.

Therefore, x = 32 units.

Thus, the required value of x is 32.

The quadratic equation is y = x^2 - 8x + 16

From the question, we have:

x = 4

Since the graph only touches x = 4 and it does not cross it, then it means that the graph has a multiplicity of 2 at x = 4

The equation is then represented as:

y = (x - 4)^2

Expand

y = x^2 - 8x + 16

Hence, the quadratic equation is y = x^2 - 8x + 16

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Answer: b no because it is less then the deduction she would get from itemizing