Right triangle STD has a longer leg measuring exactly 3√5 cm. The altitude from right angle T to hypotenuse
SD cuts the hypotenuse into two segments where the shorter part is 1 less than the longer part. Find the exact
length of each part of the hypotenuse, SU and UD, the exact length of altitude TU and the exact length of ST.

The solution set of the inequality -x - 8 < 16 is graphed in the number line at the end of the answer.

Here we want to see which number line represents the solution set of the inequality:

-x - 8 < 16

First, let's solve the inequality by isolating x, then we will get:

-x - 8 < 16

-8 - 16 < x

-24 < x

That is the inequality solved, the graph of this will be an open circle at x = -24 and then a line that goes to the right, like in the image posted at the end of this answer.

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Answer:

the missing value of the side length is 19.04

Anderson traveled 15 mph to go to the restaurant and 12 mph to get home. Anderson went at 15 mph for 3 hours and at 12 mph for 6 hours. if the entire trip took 9 hours.

    The given speed Anderson, the total time taken, and asked to find the time traveled at each speed:

         Speed, [tex]S_1[/tex] = 15 mph

         Speed, [tex]S_2[/tex] = 12 mph

         Total time, [tex]t[/tex] = 9 hours

         Time traveled with speed 1,

         [tex]t_1[/tex] Time traveled with speed 2, [tex]t_2[/tex]

To solve the given problem, let's use the following formula:

         Total   [tex]t[/tex] (time) = [tex]t_1[/tex] ( time 1) + [tex]t_2[/tex] (time 2)

   Now, time 1 can be represented as

          [tex]t_1[/tex] (time 1) = [tex]d[/tex] (distance) /  [tex]S_1[/tex] (speed 1)

Similarly, time 2 can be represented as:

           [tex]t_2[/tex] (time 2) = [tex]d[/tex] (distance) /  [tex]S_2[/tex] (speed 2)

 Here, we need to find the time traveled at each speed. Let's use these equations to solve the given problem.

      Time traveled with speed 1, [tex]t_1[/tex]  = [tex]d[/tex] /  [tex]S_1[/tex]

      Time traveled with speed 2,  [tex]t_2[/tex] = [tex]d[/tex] /  [tex]S_2[/tex]

As we know the total time, we can find the value of d in terms of [tex]t[/tex].

        So, [tex]d[/tex] =  [tex]S_1[/tex] * [tex]t_1[/tex]  =  [tex]S_2[/tex]  *  [tex]t_2[/tex]

     From the above equation, we can write: [tex]t_1[/tex]  /  [tex]t_2[/tex] =  [tex]S_2[/tex]  /  [tex]S_1[/tex] [tex]t_2[/tex]

                                                                                    =  [tex]t[/tex]  - [tex]t_1[/tex]

     Substitute the value of  [tex]t_2[/tex]  in equation(1):

           [tex]t_1[/tex]  / ([tex]t[/tex] - [tex]t_1[/tex] ) =  [tex]S_2[/tex]  / [tex]S_1[/tex][tex]t_1[/tex]  [tex]S_1[/tex]

                            = ([tex]t[/tex] - [tex]t_1[/tex] ) [tex]S_2[/tex] .[tex]t_1[/tex] . [tex]S_1[/tex] + [tex]t_1[/tex]  [tex]S_2[/tex]

                            = [tex]tS_1[/tex][tex]t_1[/tex]  

                            = [tex]tS_1[/tex] / ( [tex]S_1[/tex] +  [tex]S_2[/tex] ) [tex]t_2[/tex]  

                            =  [tex]t[/tex]  - [tex]t_1[/tex]  

                            = [tex]tS_2[/tex] / ( [tex]S_1[/tex] +  [tex]S_2[/tex] )

   Therefore, Anderson traveled at 15 mph for 3 hours Anderson traveled at 12 mph for 6 hours.

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Answer:

22: 2

23: -7

25: 6

26: 3

Let me know if this helped by clicking the help button or if not please comment with issues and I'll get right back to you!

Step-by-step explanation:

For 22: 2 * 2 * 2 = 8, therefore, 2

For 23:  -7 * -7 * -7 = -343. This results in a negative number because there is is an odd number of negative numbers (follows the odd-even negative rule).

For 25: Multiply both sides of the equation by -1/2 to get z^3 = 216. The cube root of 216 is 6

For 26: Add 11 to both sides to get 2h^3 = 54. Divide both sides by 2 to get h^3 = 27. Cube root of 27 is 3.

Let me know if this helped by clicking the help button or if not please comment with issues and I'll get right back to you!

The system of linear inequalities to model the number of hours that you could work at each location in a week is:

x ≥ 4

x + y ≤ 15

What is system of linear inequality?

A system of linear inequalities is a set of two or more linear inequalities with the same variables. It describes a region in the coordinate plane that satisfies all of the inequalities in the system.

In this case, we are trying to model the number of hours that someone could work at two different jobs.

The first inequality given is that the person must work at least 4 hours per week at the trampoline park. Let x be the number of hours worked at the trampoline park. This can be represented as:

x ≥ 4

The second inequality given is that the total number of hours worked at both jobs cannot be greater than 15. Let y be the number of hours worked at the landscaping company. Then, the total number of hours worked can be represented as:

x + y ≤ 15

Together, these two inequalities form a system of linear inequalities that model the possible number of hours that the person can work at each job in a given week.

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Patrick's goal will reached by 30.7 hours

The inequality is 163 + (10x) > 470

Let's use x to represent the number of hours it will take to reach Patrick's goal.

First step: The total number of chandeliers made must be greater than 470.

163 + (10x) > 470

Second step: Solve for x by isolating it on one side of the inequality.

10x > 307

x > 30.7

Therefore, it will take more than 30.7 hours to reach Patrick's goal of making greater than 470 chandeliers.

The inequality can be written as: 163 + (10x) > 470

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The inequality "w < 30" describes the weeks for which Halimah will put money in the bank instead of buying an oud. It means she must save for less than 30 weeks to have less than $300 saved.

Let's assume the number of weeks Halimah saves money is represented by the variable "w".

Halimah saves $10 per week, so the total amount of money she saves after "w" weeks is:

Total amount saved = $10 x w

According to the problem, Halimah will put the money in the bank instead of buying an oud if she saves less than $300. Therefore, the inequality that describes the number of weeks for which Halimah will put money in the bank is:

$10 x w < $300

Simplifying the inequality:

w < 30

Therefore, the inequality that describes the number of weeks for which Halimah will put money in the bank is "w < 30".

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Complete question:

Halimah saves $10 per week for w weeks to buy an oud. If she saves less than $300, she will put the money in the bank instead of buying an oud.

What inequality describes the number of weeks for which Halimah will put money in the bank?

Harold therefore walks an average distance of 10 metres when moving from one location to another.

All the points in a plane that are equally spaced from a fixed point known as the centre make up a circle, which is a geometric form. The radius of a circle is the separation between any two points on the circle and its centre. A circle's diameter is defined as a line segment whose endpoints are on the circle and which goes through the centre of the circle. Circles are helpful in many areas of mathematics and science due to a number of significant characteristics.

given

A circle with a dimension of 100 metres has a circumference of d, where d is the diameter. As a result, this circle's diameter is:

C = d = (100) = 100 m

Harold will walk from one spot to the next after completing 1/6

of the circle's circumference because the circle's circumference has six points that are all equally spaced apart. As a result, Harold travels the following distance between each location:

Distance equals 1/6 * C * 1/6 * 100 * (50/3) metres.

b) The average of the distances between each location, which we just discovered to be (50/3) metres, represents the average distance that Harold covers when moving from one place to another. The circle has six evenly distributed points, so the average distance travelled by Harold is:

(Total distance travelled) / Mean distance (Number of segments)

Total distance travelled equals the distance between two adjacent locations on the circle, which is C/2, or (1/2) 100 metres, or 50 metres.

Segment count equals number of marks - 1 (i.e., 6 - 1 = 5).

The average distance Harold travels while strolling is as follows:

Typical distance is calculated as (Total distance travelled) / (Number of segments), which equals (50) / 5 = 10 metres.

Harold therefore walks an average distance of 10 metres when moving from one location to another.

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Answer: why is it wrong

Step-by-step explanation:i said so

Answer:

Step-by-step explanation:

Here's a graph of a line with a negative slope:

| /

| /

| /

| /

|/

------->

The line descends from left to right.

To draw the slope triangles, we can choose any two points on the line and draw a triangle with one vertex at each point. Let's choose the points (0, 4) and (3, 0):

| /

| /

| / T1

| /

|/

----/-------

/|

/ |

/ |

/ |

T2

The height of the first triangle, T1, is the difference between the y-coordinates of the two points: 4 - 0 = 4. The base of T1 is the difference between the x-coordinates: 3 - 0 = 3. So the rise/run ratio for T1 is 4/3.

The height of the second triangle, T2, is the difference between the y-coordinates of the two points: 0 - 4 = -4. Note that because the slope of the line is negative, the height of the triangle is negative as well. The base of T2 is the difference between the x-coordinates: 3 - 0 = 3. So the rise/run ratio for T2 is (-4)/3, which simplifies to -1.33.

The slope of the line is defined as rise divided by run. In this case, the rise is -4 (because the line is descending) and the run is 3. So the slope is (-4)/3, which is approximately -1.33. We can see that the simplified ratio of the rise/run of each triangle is indeed equivalent to the slope of the line.

Answer:

y - (-4) = 6(x - 3)

y - 2 = -3(x - 4)

y - (-7) = 1(x - (-2))

y - 0 = -1(x - 4)

Bytaking the quotient between the probabilities we can see that Getting a 17 is three times more likely to get a 18.

If you toss 3 dices with 6 sides each, then the total number of combinations is:

6*6*6 = 216

Now, the outcomes that add up to 18 are:

dice 1, dice 2, dice 3, sum:

6            6         6       , 18

The outcomes that add up to 17 are:

dice 1, dice 2, dice 3, sum:

5           6         6       , 17

6            5         6       , 17

6            6         5       , 17

So the probabilities are:

P(18) = 1/216

P(17) = 3/16

The quotient gives:

P(17)/P(18) = 3

Getting a 17 is 3 times more likely to get a 18.

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Therefore , the solution of the given problem of function comes out to be even though the two functions' maximum numbers are different, their final behavior is the same.

On the midterm exam, there will be inquiries about design, mathematics, each topic, and both actual and hypothetical locations. a summary of the connections between various components that work together to produce the same outcome. A service is made up of many unique parts that work together to produce unique outcomes for each input. Each post also has a particular location, that could be the enclave, an area, or even something completely different.

Here,

When x = 2, the maximum value of function f is 6, and

when x = -2, the highest value of function g is 3.

Both functions result in the same action in the end.

Both functions move closer to positive infinity as x gets closer to positive or negative infinity.

This is due to the positive quadratic component that dominates the behavior of the leading term in both functions as x increases in magnitude.

As a result, even though the two functions' maximum numbers are different, their final behavior is the same.

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Keith took a four question test and got 1 and a half questions wrong. His final score is 2.5 out of 4, or 62.5%.

To calculate Keith's final score, you need to divide the number of correct answers by the total number of questions. In this case, Keith answered 2.5 out of 4 questions correctly. Therefore, his final score is 2.5 divided by 4, which equals 0.625. This is equal to 62.5%.
To summarize, Keith took a four question test and got 1 and a half questions wrong, giving him a final score of 62.5%.

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Therefore, the equation of the function in slope-intercept form is: y = 24x - 18.

An equation is a mathematical statement that asserts the equality of two expressions, often containing variables. It typically consists of two expressions separated by an equal sign. The expressions on either side of the equal sign may contain constants, variables, operators (such as +, -, ×, ÷), and functions.

Here,

We can use the two given points to find the slope and y-intercept of the function, and then write the equation of the function in slope-intercept form y = mx + b.

The slope of the function can be found using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (1, 6) and (x2, y2) = (3, 54):

m = (54 - 6) / (3 - 1) = 24

So the slope of the function is 24.

To find the y-intercept, we can use one of the two given points and the slope of the function:

y = mx + b

6 = 24(1) + b

b = -18

So the y-intercept of the function is -18.

Therefore, the equation of the function in slope-intercept form is:

y = 24x - 18

Any equation in this form with the same slope and y-intercept will represent the same function passing through the given points.

For example, y = 24x - 18, y = 24x - 20, and y = 24x - 16 are all equations that could represent the function passing through the points (1, 6) and (3, 54).

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Answer:c 4.2 cups

Step-by-step explanation:

just do 63 divided 15

Work Shown:

1 km = 1000 m

5*(1 km) = 5*(1000 m)

5 km = 5000 m

Step-by-step explanation:

let x= m

1 km=1000m

5km= x.m

1km.x/1km=5000.km/1km

x=5000m

therefore 5km=5000m

The center of a dilation is a fixed point in the plane about which all points are expanded or contractedAnswer:

Step-by-step explanation:

The base-10 expansion after calculations, of 123 comes up as -: 123 = 1 x 10^2 + 2 x 10^1 + 3 x 10^0.

The given statement is about finding the last digit of the base-b expansion of an integer n, and a base b. We can find the last digit of the base-b expansion of n by performing the division algorithm to find n = qb + r. The remainder r is the last digit. By repeating the process with q instead of n, we find the next digit, and so on.

That means we can determine all the digits one by one by repeating this process. Let's take an example: Suppose we need to find the last digit of 123 in base 10. We can use the division algorithm to find 123 = 12 x 10 + 3. Here, the remainder 3 is the last digit. Now, to find the second-last digit, we repeat the process with q=12 instead of n=123.

That is, 12 = 1 x 10 + 2. Here, the remainder 2 is the second-last digit. Finally, to find the third-last digit, we repeat the process with q=1 instead of n=12. That is, 1 = 0 x 10 + 1. Here, the remainder 1 is the third-last digit.

Therefore, the base-10 expansion of 123 is 123 = 1 x 10^2 + 2 x 10^1 + 3 x 10^0.

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After answering the presented question, we can conclude that equation Therefore, the height of the plane after 6 minutes of descending is 19,500 feet.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

h(t) = 32,000 - 2,250t

h(6) = 32,000 - 2,250(6) = 19,500 feet

Therefore, the height of the plane after 6 minutes of descending is 19,500 feet.

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To the nearest tenth, the length of each side of the equilateral triangle is roughly [tex]10(\sqrt{(3) - 1)[/tex].

An equilateral triangle has the following three characteristics: identical lengths on all three sides. The three angles are identical. Three symmetry lines may be seen in the figure.

All of the triangle's sides are equal in length since it is equilateral. Call this length "s" for short.

The distance from vertex A to side x, measured in altitude, is equal to the length of side x. Call the intersection of the altitude and side x "P" for short.

The length of AP is [tex](s/2) * \sqrt{}[/tex] because we know that the altitude from vertex A creates a triangle with sides of 30-60-90. (3).

Since side BP is half the length of side AB, we also know that its length is (s/2).

As a result, x's length equals the product of AP and BP:

x = AP + BP

= (s/2) * [tex]\sqrt{(3) + (s/2)[/tex]

= [tex](s/2)(\sqrt{(3) + 1)[/tex]

We are told that x equals 10. We may put the formula we discovered for x equal to 10 and do the following calculation to find s:

[tex](s/2)(\sqrt{(3) + 1)[/tex] = 10

The result of multiplying both sides by two is:

[tex]s(\sqrt{(3) + 1) = 20[/tex]

When you divide both sides by [tex](\sqrt{(3) + 1)[/tex], you get:

[tex]s = 20/(\sqrt{3) + 1)[/tex]

The result of multiplying the numerator and denominator by the conjugate of [tex](\sqrt{(3) + 1), (\sqrt{(3) - 1)[/tex], is as follows:

s = [tex]20(\sqrt{3) - 1)/(3 - 1)[/tex]

= [tex]10(\sqrt{(3) - 1[/tex]

As a result, to the nearest tenth, the length of each side of the equilateral triangle is about [tex]10(\sqrt{(3) - 1[/tex].

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Symmetrical balance, also known as bilateral symmetry, is a type of balance in which two halves are mirror images of each other. This type of balance can be found in both visual art and in nature.

In visual art, symmetrical balance is achieved when similar shapes, colors, lines, and textures are repeated on either side of a vertical axis. This creates an even distribution of visual elements and creates a sense of harmony and equilibrium. In nature, symmetrical balance is created when there is a symmetrical arrangement of organs and features in plants and animals.

Symmetrical balance is often used to create a sense of order and balance in visual works of art, as well as to emphasize the balance of nature in landscapes. It can also be used to convey a sense of unity and tranquility, as the repetition of similar elements creates an overall feeling of calmness and symmetry. Symmetrical balance is an important element in many types of artwork, and it is used in all kinds of visual art, including paintings, photographs, sculptures, and more.

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Answer:

(2x - 1) (4x + 3)

Step-by-step explanation:

8x² + 2x - 3

= 8x² - 4x + 6x - 3

= 4x (2x - 1) + 3 (2x - 1)

= (2x - 1) (4x + 3)

So, the factor is (2x - 1) (4x + 3)

The tree from which the wood was obtained died 13,729 years ago, considering the exponetial function that models the situation.

The standard definition of an exponential function is given by the equation presented as follows:

[tex]A(t) = A(0)b^{\frac{t}{n}}[/tex]

The parameters of the exponential function with format above are given as follows:

The half-life of carbon-14 is 5,730 years, hence the parameters b and n have the values given as follows:

b = 0.5, n = 5730.

Then the exponential function for the amount of the substance after t years is given as follows:

[tex]A(t) = A(0)(0.5)^{\frac{t}{5730}}[/tex]

19% of the substance remained, hence the time is obtained as follows:

[tex]0.19A(0) = A(0)(0.5)^{\frac{t}{5730}}[/tex]

[tex](0.5)^{\frac{t}{5730}} = 0.19[/tex]

t = 5730 x log(0.19)/log(0.5)

t = 13,729 years.

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Total volume of the shape is 124 cm³

A cuboid is a three-dimensional solid shape that has six rectangular faces or sides, where each face meets at a right angle with its adjacent faces.

The formula for the volume of a cuboid is:

Volume = Length x Width x Height

So, the Volume of first cuboid = 3 × 4 × 5 = 60 cm³

and the Volume of second cuboid = 2 × 4 × 8 = 64 cm³

Total volume of the shape = Volume of first cuboid + Volume of second cuboid

Total volume of the shape = 60 cm³ + 64 cm³

Total volume of the shape = 124 cm³

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The area of the equilateral triangle is 36√3 square units

What is area of the equilateral triangle?

Area of an equilateral triangle is equal to(√3/4)a², where an is the length of the triangle's side.

In an equilateral triangle, the center, the centroid, and the circumcenter coincide.

The distance between the center and a vertex is 6cm, which is also the radius of the circumcircle.

The side length is [tex]6(3)^{1/2}[/tex], which is twice the length of the radius.

So, the radius of the circumcircle is 6 cm, and the length of each side of the equilateral triangle is 12 cm.

The area of an equilateral triangle with side length s is given by:

A = (s² * √3) / 4

Substituting s = 12, we get:

A = (12² * √3) / 4

= 36√3

Therefore, the area of the equilateral triangle is 36√3 square units.

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If you know 63 people have swim suits on and 43 have sunglasses, 32 people have swim suits on but not sunglasses.

To find out how many people have swim suits on but not sunglasses, we can use the principle of inclusion-exclusion.

We know that there are 75 people in the park, and 63 of them have swim suits on. We also know that 43 people have sunglasses. However, some people have both swim suits and sunglasses. Let's denote the number of people who have both by x. Then we can use the formula:

total = swim suits + sunglasses - both

Substituting in the given values, we get:

75 = 63 + 43 - x

Simplifying, we get:

x = 31

Therefore, 31 people have both swim suits and sunglasses, and the number of people who have swim suits on but not sunglasses is:

63 - 31 = 32

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the answer is 207 Remainder 1