solve for x -2x + 2 = x -13

Using the Pythagoras theorem, the longest leg has the length of 24 feet.

Given that,

A ladder of length (2x+6) feet is positioned x feet from a wall.

Height of the ladder = (2x + 6) feet

Distance of ladder from the wall = x feet

Height of the wall that the ladder is placed = (2x + 4) feet

These three lengths form s right triangle where (2x + 6) feet is the hypotenuse.

Longest leg is (2x + 4) feet

Using the Pythagoras theorem,

(2x + 6)² = (2x + 4)² + x²

4x² + 24x + 36 = 4x² + 16x + 16 + x²

4x² + 24x + 36 = 5x² + 16x + 16

x² - 8x - 20 = 0

(x - 10) (x + 2) = 0

x = 10 or x = -2

x = 2 is not possible.

So x = 10

Longest leg = 2x + 4 = 20 + 4 = 24 feet

Hence the length of the longest leg is 24 feet.

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The highest point for the quadratic function for the height of the object, h(t) = -16·t² + 224·t + 816, indicates that the interval over which the height of the object is increasing is; (-∞, 7]

The shape of the graph of a quadratic function is a parabola.

The function for the height of the object in question 3 is; h(t) = -16·t² + 224·t + 816

Where;

t = The time in seconds

The height of the object is increasing in the interval to the left of the highest point, which can be found as follows;

The x-coordinate of the highest point of the quadratic function, f(x) = a·x² + b·x + c is; x = -b/(2·a)

Therefore, the x-coordinates of the highest point of the object is; -224/(2 × (-16)) = 7

Therefore, the height of the object is increasing in the interval; -∞ < t ≤ 7

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Answer:

5.5 makes more sense.

Step-by-step explanation:

Step-by-step explanation:

y = 3.52x

This equation states that the total amount paid, y, is equal to 3.52 multiplied by the number of pounds of potatoes, x.

The class of the equation and the cross section equation are;

The equation is a hyperboloid of two sheets

The cross sections are;

Equation at z = 0 is; y²/8 - x²/8 = 1

Equation at y = -4 is; x²/8 + z² = 1

Equation at y = 0 is; x²/8 + z² = -1

Equation at y = 4 is; x²/8 + z² = 1

Equation at x = 0 is; y²/8 - z² = 1

An equation is a mathematical statement which indicates the equivalence two expressions by joining them with the '=' sign.

The equation can be presented as follows;

y² = x² + 8·z² + 8

y² - x² - 8·z² = 8

y²/8 - x²/8 - z² = 1

The above equation is the equation of an hyperboloid of two sheets, where;

a² = 8, b² = 1, and c² = 8

Please find attached the diagram of the surface, created with an online 3D graphing tool.

The equation for the cross section at z = 0, can be obtained by plugging in z = 0, into the equation as follows;

y²/8 - x²/8 - 0 = 1

y²/8 - x²/8 = 1

The above equation is the equation of an hyperbola in the xy plane

The equation for the cross section at y = -4, can be obtained by plugging in y = -4, into the equation as follows;

4²/8 - x²/8 - z² = 1

- x²/8 - z² = 1 - 4²/8 = -1

- x²/8 - z² = -1

x²/8 + z² = 1

The above is an equation of an ellipse in the xz plane

The equation for the cross section at y = 0, can be obtained by plugging in y = 0, into the equation as follows;

0²/8 - x²/8 - z² = 1

- x²/8 - z² = 1

Therefore; x²/8 + z² = -1

The equation for the cross section at y = 4, can be obtained by plugging in y = 4, into the equation as follows;

4²/8 - x²/8 - z² = 1

- x²/8 - z² = 1 - 2 = -1

x²/8 + z² = 1

The above equation is the equation of an ellipse in the xz plane

The equation for the cross section at x = 0, can be obtained by plugging in x = 0, into the equation as follows;

y²/8 - 0²/8 - z² = 1

y²/8 - z² = 1

The equation is the equation of an hyperbola in the yz plane

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Answer:

Median: 31

Mode: 31

Range: 67

Step-by-step explanation:

Median: To find the median, we first need to arrange the numbers in order from smallest to largest:

25, 29, 31, 31, 69, 80, 92

The middle number is 31, so the median is 31.

Mode: The mode is the number that appears most frequently in the set. In this case, the number 31 appears twice, which is more than any other number. So, the mode is 31.

Range: The range is the difference between the largest and smallest numbers in the set. The smallest number is 25 and the largest number is 92, so the range is:

92 - 25 = 67.

Therefore, the median is 31, the mode is 31, and the range is 67.

Answer:

The median of the given set of numbers is 31, the mode is 31, and the range is 67.

Step-by-step explanation:

To find the median, we need to first arrange the numbers in order from smallest to largest:

25, 29, 31, 31, 69, 80, 92

There are seven numbers in the list, which means the middle number will be the fourth number: 31.
Therefore, the median is 31.

To find the mode, we need to determine which number appears most frequently in the list.
In this case, the number 31 appears twice, which is more than any other number in the list.

Therefore, the mode is 31.

To find the range, we need to subtract the smallest number from the largest number. The smallest number is 25 and the largest number is 92, so the range is:

92 - 25 = 67

Therefore, the range is 67.

The Vertex is : (-6, -30)

The X-intercepts are : Approximately (-10.89, 0) and (-1.11, 0)

The Y-intercept is : (0, 6)

The Axis of symmetry is : x = -6

The functions Domain: is All real numbers

The Range is : All real numbers greater than or equal to -30.

To sketch the graph of the quadratic function \(f(x) = x^2 + 12x + 6,\) we can start by identifying the vertex, x-intercepts, y-intercept, axis of symmetry, domain, and range.

To find the vertex, we can use the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation in standard form\((ax^2 + bx + c).\)

In this case, a = 1, b = 12, and c = 6.

Applying the formula, we get x = -12/(2 \(\times\) 1) = -6.

To find the y-coordinate of the vertex, we substitute this x-value into the equation:\(f(-6) = (-6)^2 + 12(-6) + 6 = 36 - 72 + 6 = -30.\)

So, the vertex is (-6, -30).

To determine the x-intercepts, we set f(x) = 0 and solve for x. In this case, we need to solve the quadratic equation \(x^2 + 12x + 6 = 0.\)

Using factoring, completing the square, or the quadratic formula, we find that the solutions are not rational.

Let's approximate them using decimal values: x ≈ -10.89 and x ≈ -1.11. Therefore, the x-intercepts are approximately (-10.89, 0) and (-1.11, 0).

The y-intercept is obtained by substituting x = 0 into the equation: \(f(0) = 0^2 + 12(0) + 6 = 6.\)

Thus, the y-intercept is (0, 6).

The axis of symmetry is the vertical line that passes through the vertex. In this case, it is the line x = -6.

The domain of the function is all real numbers since there are no restrictions on the possible input values of x.

To determine the range, we can observe that the coefficient of the \(x^2\) term is positive (1), indicating that the parabola opens upward.

Therefore, the minimum point of the parabola occurs at the vertex, (-6, -30).

As a result, the range of the function is all real numbers greater than or equal to -30.

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Answer:

0.95p and 1 *0.95p

Step-by-step explanation:

Answer: 20

Step-by-step explanation: it is 20 because 2 negative numbers multiplied by each other will always be positive

1. The value of x is 9

2. The value of x is 8

To determine the value of the variables, we need to know the properties of a triangle.

These properties includes;

Now, from the information given, we have that;

<L = <Q

<M = <R

The side facing <L is 9

The side facing <Q is x

x = 9

2. The side facing <L is 6

The side facing <Q is 12

Then, x = 8

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Answer:

3/8 = 9/24

7/6 = 28/24

Step-by-step explanation:

The value of the test statistic is given as follows:

z = 4.47.

The equation to calculate the test statistic using the z-distribution is given as follows:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

In which:

The parameters for this problem are given as follows:

\(\overline{p} = 0.59, p = 0.5, n = 618\)

p = 0.5 as the most term means that we are testing if the proportion is either less than or greater than 0.5.

Then the test statistic is obtained as follows:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

\(z = \frac{0.59 - 0.5}{\sqrt{\frac{0.5(0.5)}{618}}}\)

z = 4.47.

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Answer:

w = 1/2

Step-by-step explanation:

One of the ways to solve problems using log is to use these two equations that use the same variables and plug in numbers.

log b (a) = c

b^c = a

By plugging in the numbers we get this:

log 16 (4) = w

16^w = 4

w = 1/2

Answer:

Castles made:    N         day 1

                           N - 4    day 2

                           N - 8     day 3

                           N - 12     day 4

                           N - 16      day 5

Total   5 N - 40 = 80

              N = 24  total  castles day 1

Total castles = 24 + 20 + 16 + 12 + 8 = 80

Answer:

Hi

Please mark brainliest ❣️

The assertion is true. Both 7√5 and √2 + 21 are irrational numbers because they cannot be expressed as fractions.

The assertion is true. Both 7√5 and √2 + 21 are irrational numbers.

An irrational number is defined as a number that cannot be expressed as a fraction of two integers and has an infinite non-repeating decimal representation.

In the case of 7√5, the square root of 5 is an irrational number because it cannot be expressed as a fraction. Multiplying it by 7 does not change its irrational nature.

Similarly, √2 is also an irrational number because the square root of 2 cannot be expressed as a fraction. Adding 21 to √2 does not alter its irrationality.

The reason provided, that every integer is a rational number, is not relevant to the given assertion. While it is true that every integer is a rational number because it can be expressed as a fraction (e.g., 3 can be written as 3/1), it does not contradict the fact that 7√5 and √2 + 21 are irrational numbers.

In conclusion, the assertion is valid, and both 7√5 and √2 + 21 are irrational numbers.

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The value x in the secant line using the Intersecting theorem is 4.

Intersecting secants theorem states that " If two secant line segments are drawn to a circle from an exterior point, then the product of the measures of one of secant line segment and its external secant line segment is the same or equal to the product of the measures of the other secant line segment and its external line secant segment.

From the figure:

First sectant line segment = ( x - 1 ) + 5

External line segment of the first secant line = 5

Second sectant line segment = ( x + 2 ) + 4

External line segment of the second secant line = 4

Using the Intersecting secants theorem:

5( ( x - 1 ) + 5 ) = 4( ( x + 2 ) + 4 )

Solve for x:

5( x - 1 + 5 ) = 4( x + 2 + 4 )

5( x + 4 ) = 4( x + 6 )

5x + 20 = 4x + 24

5x - 4x = 24 - 20

x = 4

Therefore, the value of x is 4.

Option C) 4 is the correct answer.

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Answer: A. 871.97 feet

Here given:

Using Sine Rule:

\(\sf sin(x) = \dfrac{opposite}{hypotenuse}\)

\(\rightarrow \sf sin(33) = \dfrac{height}{1601}\)

\(\rightarrow \sf height = 1601sin(33)\)

\(\rightarrow \sf height = 871.97 \ feet\)

Let's check

Now

Apply Pythagorean theorem

On solving we will get

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Answer:

It is the spot where sons raise meat.

Answer:

57,000

Step-by-step explanation:

Answer:

The answer is the 1st one (A) because it already is written in standard form.

Step-by-step explanation:

Answer:

each of the eight angles measures 45 degrees

Step-by-step explanation:

The sum of all exterior angles of any polygon always measures 360 degrees.

If it's 'regular' then all angles have the same measures.

If it's an octagon, then it has 8 sides.

360 divided by 8 = 45

Answer:

NO

Step-by-step explanation:

(4/5)^n will always be ≤ 1  for any positve n

The equation h ( n ) = 150 is false

No , the height of the ball cannot be 150 inches

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

h ( n ) = 120 x ( 4/5 )ⁿ

Now , substitute the value of h ( n ) = 150 , we get

150 = 120 ( 4/5 )ⁿ

Divide by 120 on both sides of the equation , we get

150 / 120 = ( 4/5 )ⁿ

On simplifying the equation , we get

5/4 = ( 4/5 )ⁿ

The equation is not true because we have a exponential decay function here. This height of the ball decreases with each bounce.

At bounce 0 the height of the ball is 120 inches, and then continuously decreases with a common factor of 4/5

Therefore , the value of h ( n ) can never be 150

Hence , the equation h ( n ) = 150 is false

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Answer:

The distance jogged by Karina is 3 km

Step-by-step explanation:

We are given that Karina runs east on 18th street for 2 km

So, She runs distance towards east = 2 km

Now we are given that turns right on Potrero Avenue, going south for 1 km

So, She runs the distance after turning right towards south = 1 km

So, total distance covered = 2 km + 1km

Total distance covered = 3 km

So,Distance jogged by Karina = 3 km

Hence The distance jogged by Karina is 3 km

The equation of the new path is y = -1/2x - 4

The equation is given as:

y = 2x - 7

A linear equation is represented as:

y = mx + c

Where m represents slope

This means that:

m = 2

Let the slope of the perpendicular equation be n.

The condition of perpendicular lines is

n = -1/m

So, we have:

n = -1/2

The equation of the new path is then calculated using:

y = n(x - x1) + y1

So, we have:

y= -1/2(x + 2) - 3

Expand

y = -1/2x - 4

Hence, the equation of the new path is y = -1/2x - 4

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Answer:

-8-495-18x

Step-by-step explanation:

-8-9(55)-9(2x)

-8-495-18x