A ladder is 6 m long. How much farther up a wall does the ladder reach when the base of the ladder is 2 m from the wall than when it is 3 m from the wall? Round to the nearest tenth of a meter.

Answers

Answer 1

ANSWER

0.5m UP

EXPLANATION

Given:

Determine the value of x at 3m using Pythagorean Theorem

$\begin{gathered} Hyp^2\text{ = Opp + Adj}^2 \\ 6^2\text{ = x}^2\text{ + 3}^2 \\ x^2\text{ = 36 - 9} \\ x\text{ = }\sqrt{27} \\ x\text{ = 5.2} \end{gathered}$

Determine the value of x at 2m using Pythagorean Theorem

$\begin{gathered} Hyp^2\text{ = Opp}^2\text{ + Adj}^2 \\ 6^2\text{ = x}^2\text{ + 2}^2 \\ x^2\text{ = 36 -4} \\ x\text{ = }\sqrt{32} \\ x\text{ = 5.7} \end{gathered}$

The Difference

5.7 - 5.2 = 0.5 m

Hence, the ladder reach 0.5m farther up when the base of the ladder is 2 m from the wall than when it is 3 m from the wall

A Ladder Is 6 M Long. How Much Farther Up A Wall Does The Ladder Reach When The Base Of The Ladder Is

Related Questions

The revenue, in dollars. of a company that produces video game systems can be modeled by the expression 52 +
2t - 80. The cost in dollars, of producing the video game systems can be modeled by 5.22 -+ 100, where x is the
number of video game systems sold. If profit is the difference between the revenue and the cost, what expression
represents the profit?
Profit can be modeled by the polynomial expression
If 1,000 video game systems are sold, the company's profit is $

Answers

Answer:

1). Profit = 3x - 180

2) Profit of selling 1000 video games = $2820

Step-by-step explanation:

Expression for the revenue = 5x² + 2x - 80

Expression for the production cost of the video games = 5x² - x + 100

Since, profit is the difference between the revenue and the cost,

Expression for the profit will be,

Profit = Revenue - Cost

= (5x² + 2x - 80) - (5x² - x + 100)

= 5x² + 2x - 80 - 5x² + x - 100

= 3x - 180

Here, x = Number of video games sold

If number of video games sold = 1000

Profit = (3×1000) - 180

= 3000 - 180

= $2820

An airplane is flying at a constant speed of 500 mph at a bearing of 45° north of west. A 40 mph wind is blowing due south. What are the plane's actual speed and direction? Draw a diagram and show your work to justify your answer. Round the speed to the nearest tenth and the direction to the nearest degree. (5 points)

Answers

Answer:I’m pretty sure I got this one right too

Step-by-step explanation:

An airplane is flying at a constant speed of 500 mph at a bearing of 45 north of west. A 40 mph wind

The actual speed of the airplane is 472.56 mph in the direction of 41.57° north of west.

What are the x and y-components of a vector?

"In a two-dimensional coordinate system, any vector can be broken into x -component and y -component according to axis."

We can assume, east as the positive x- axis and north as the positive y-axis, respectively.

Similarly, west as the negative x- and south as the negative y-axis, respectively.

Therefore, the x- and y-components of the speeds.

Now, for the airplane:

x-component: - 500 × cos(45°) mph = - 353.55 mph

y-component: 500 × sin(45°) mph = 353.55 mph

For the wind:

y-component: -40 mph

Therefore, sum of the x-components = -353.55 mph

Similarly, sum of the y-components = (353.55 - 40) mph = 313.55 mph

Now, the actual speed =

$\sqrt{(-353.55)^{2} + (313.55)^{2}}$ mph

= $\sqrt{223313.6}$ mph

= 472.56 mph

Now, the direction of the airplane is:

tan(Ф) = $\frac{313.55}{- 353.55}$

⇒ Ф = tan⁻¹( $\frac{313.55}{- 353.55}$)

⇒ Ф = - 41.57°

The actual speed of the airplane is 472.56 mph in the direction of 41.57° north of west.

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how do you know that 2 to the power of 3 x 3 is not a common multiple

Answers

Answer:

512

Step-by-step explanation:

A common multiple is defined as a whole number, a shared multiple of each set of numbers. The multiples common to two or more numbers are called the common multiples of those numbers.

OML I just gave u the answer do I need to put this in simple terms for you since u don't understand - 2 to the power of 3 x 3 is 512 and that is not a whole number a common multiple is defined as a whole number and for 512 to be an integer it has to be a whole number. UNDERSTAND NOW???

pls i need help asap Solve the equation shown for x. 4(–x + 4) = 12 Enter your answer in the box. x =

Answers

Answer: 15

Step-by-step explanation:

casue

Answer:

x = 1

Lemme know if you need the steps.

Please mark brainliest if possible :)

Determine the value of x. Round to the tenths place. 30/4 65/x

Answers

wow that's really hard... :) greetings from South Korea My name is Naoyoung nei The abbreviation of Nanda is Naoyoung nei And the name DA is the name of my father and mother

HAVE A NICE DAY
WILL GIVE BRAINLST :)

Answers

Answer:

1. A

2. C

Step-by-step explanation:

Two sisters, Jenny and Jada, are saving money for summer vacation. Their mom gets them started by giving the two sisters, Jenny and Jada, $25. Each sister will put part of the pay from their after-school job in the account each week. Jenny will deposit $8 per week. Jada will each deposit $5 per week.
1. Make a table for the total savings for each sister.
2. Graph each sister’s savings on the same set of axes.
3. Find the slope and y-intercept of the graph of each sister.
4. Model each sister’s savings plan using an equation in the form y = mx + b.
5. How much will each sister have after 3 weeks? After 7 weeks?

6. Who will have more money saved? Explain how you know?

Answers

Answer:

Step-by-step explanation:

This problem requires the use of the Pythagorean Theorem to find the lengths of the sides of a piece of property in the shape of a right triangle

Example:

Taylor finds a piece of property in the shape of a right triangle. She finds that the longer leg is 10 m shorter than twice the length of the shorter leg and the hypotenuse is 20 m longer than the longer leg. Find the lengths of the sides of the triangular lot.

Hi, please let me know if this is correct, please tell me if I’m wrong, thx (:

Answers

Answer:

It's correct!

Step-by-step explanation:

20.9/10000=0.00209

pls mark me as brainliest!

50 points. use rotation tool in top right to flip upright.

Answers

Answer:

(a) 56%

(b) 28%

Step-by-step explanation:

Hope this helps! :)

Product of 5604 and 81

Answers

Answer:

Solving vertically

Step-by-step explanation:

5604*1=5604

5604*8=40000+4800+32=44832

44832*10+5604=453924

The value of the product of 5604 and 81 is 453924 and this can be determined by using the arithmetic operations.

Given :

Number 1 - 5604

Number 2 - 81

The following steps can be used to determine the product of 5604 and 81:

Step 1 - Write the expression.

$=5604\times 81$

Step 2 - Now, split 81 in 9$\times$9 in the above expression.

$=5604\times 9 \times 9$

Step 3 - Now, write 5604 as $1401\times 4$ in the above expression.

$=1401\times 4 \times 9 \times 9$

Step 4 - Multiply 4 by 9 in the above expression.

$=1401\times 36\times 9$

Step 5 - Multiply 36 by 4 in the above expression.

$=1401\times 324$

Step 6 - Multiply 1401 by 324 in the above expression.

= 453924

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Over the next 17 months you have to read at least 68 books. You have to read x books per month.
The inequality 17x2 68 represents this situation. Solve the inequality to find the number of books
you have to read per month.

Answers

Answer:

You have to read 4 or more books per month.

Step-by-step explanation:

Given that:

Number of months to read the books = 17 months

Number of books to read = 68 at least

Number of books per month = x

The inequality for the situation is;

$17x\geq 68$

Dividing both sides by 17

$\frac{17x}{17}\geq \frac{68}{17}$

x ≥ 4

Hence,

You have to read 4 or more books per month.

an improper fraction is equal to or greater than _____________

Answers

Answer:

an improper fraction is equal to or greater than 1

Step-by-step explanation:

An improper fraction is a fraction in which the numerator is greater than the denominator. Thus, an improper fraction is always greater than 1.

Find the value of x if 27:x = 36:48

Answers

Answer:

x = 36

Step-by-step explanation:

27 : x = 36 : 48

27 * 48 = 36 * x

1296 = 36x

x = 36

Answer:The value of x=36

adVGIKCGHJGFVBJCJVHOZASUZDHNISHNOWDFYIHFSRNY PLS NO DOWNLOAD FILES

Answers

Answer:

891.46

Step-by-step explanation:

"Nearest hundreth" refers to the second decimal place. You can remember this by knowing that 100 has two zeroes and a decimal place in the nearest hundredth has two numbers after the decimal.

We know that the answer is 891.46 because original decimal was .456. 6 is greater than 4, so it can be rounded to 10. The 1 is brought to the 5, making it 6. The 0 is not written. 0 is never included at the end of a decimal place.

When camping alone, Mr. Adams uses all of the water in the storage barrel I. 12 days. If mrs. Adams caps with him, they use all the water in 8 days. In how many days will mrs. Adams use the water if she camps alone?

Answers

Answer:

24 days

Explanation:

for Mr.Adams

12 days ---> 1 barrel of water

1 days ---> 1/12 barrel of water

8 days ---> [(1/12)*8] = 8/12 barrel of water

For Mrs Adams in 8 days:

she uses: 1 - 8/12 = 4/12

If she camps alone:

she uses 4/12 in 8 days

to use full:

(4/12)*3 barrels in (8*3) days

1 barrels in 24 days

She can therefore use 24 days if she camps alone.

Mrs. Adams will use the water for 24 days.

Data;

Mr. Adams = 12 daysMr. Adam + Mrs. Adam = 8 days

Fractions

To solve this problem, we have to know the fraction or proportion of water mrs. adam will use.

let mr. adam be represented by and mrs adam be represented by y

$1/x + 1/ y = 1/8\\x= 12\\1/12 + 1/y = 1/8\\1/y = 1/8 - 1/12\\1/y = 1/24\\y = 24$

From the calculations above, Mrs. Adams will use the water for 24 days.

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Learn more about fractions and proportions here;

i need help on this question

Answers

Answer: B I think...

Step-by-step explanation: Sorry if im wrong

Answer:

Step-by-step explanation:

Average rate per hour = 18 / 3 or 6

if we want to find how many miles the hot air balloon will travel in 3/4 of an hour we multiply average distance by time

So our answer = 3/4 * 6

3/4 * 6 = 4.5

Therefore in 3/4 hour the hot air balloon will have traveled 4.5 miles.

Unions, intersections, and complements involving 2 sets
Sets B and C are subsets of the universal set U.
These sets are defined as follows.
U={f, k, m, s, x, y, z)
B={k, s, y}'
C={s,z}
(a) B'UC' = 1
(b) B'nc =

Answers

Intersection of B'∩C = {k, y}

To find the intersection of B' and C, we need to first find the complement of set B (B') and then find the intersection between B' and C.

1. Complement of set B (B'):

The complement of set B (B') consists of all elements in the universal set U that are not in set B. From the given information, set B is defined as {k, s, y}', which means it contains all elements in U except for k, s, and y. Therefore, the complement of set B is {f, m, x, z}.

2. Intersection between B' and C:

Now, we need to find the intersection between B' (complement of B) and set C. From the given information, set C is defined as {s, z}. To find the intersection, we need to identify the common elements between B' and C.

The elements present in both B' and C are k and y. Therefore, the intersection of B' and C is {k, y}.

So, the answer to (b) is B'∩C = {k, y}.

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50 points.
Daisy is a botanist who works for a garden that many tourists visit. The function f(s) = 3s + 30 represents the number of flowers that bloomed, where s is the number of seeds she planted. The function s(w) = 12w represents the number of seeds she plants per week, where w represents the number of weeks.

Part A: Write a composite function that represents how many flowers Daisy can expect to bloom over a certain number of weeks.

Part B: What are the units of measurement for the composite function in Part A?

Part C: Evaluate the composite function in Part A for 36 weeks.

Answers

From the situation described in this problem, it is found that:

A. The composite function is: f(s(w)) = 36w + 30.

B. The unit of measurement of the composite function is: flowers.

C. After 36 weeks, Daisy can expect to bloom 1326 flowers.

Composite function

For a composite function, the output of the inner function serves as the input of the outer function.

In the context of this problem, the functions are given as follows:

f(s) = 3s + 30.s(w) = 12w.

Hence the composite function that represents how many flowers Daisy can expect to bloom over a certain number of weeks is:

f(s(w)) = f(12w) = 3(12w) + 30 = 36w + 30.

The unit of measurement of the composite function is the unit of the outer function, which is flowers.

After 36 weeks, the number of flowers that Daisy can expect to bloom is given as follows:

f(s(36)) = 36(36) + 30 = 1326 flowers.

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please help// geometry question... i will post the other picture for this question it will be under “geometry question pt.2”

Answers

Answer:

a) E

b) line segment AB

Step-by-step explanation:

a) E

b) line segment AB (It's AB with the line over it - no arrowheads)

Answer:

a)e

b)a

c)e

Step-by-step explanation:

144-120x+25x² help me

Answers

Answer:

$144 - 120x + 25 {x}^{2} \\ 144 - 95 {x}^{3} $

Is it SSS, SAS, ASA, AAS, or HL?

Answers

Triangle ABC is congruent to triangle DEF based on the SAS congruence theorem.

What is the SAS Theorem?

The SAS theorem is a triangle congruence theorem that states that two triangles are congruent if they have two pairs of congruent sides that are corresponding to each other, and a pair of congruent included angles.

Triangles ABC and DEF have:

A pair of congruent included angles - ∠DEF ≅ ∠ABCTwo pairs of congruent sides - AB ≅ DE and CB ≅ FE

Therefore, they are congruent by SAS.

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Solve by Factoring:
2x^2 - x - 3 = 0

Answers

Answer:

x = 3/2 or x = -1

Step-by-step explanation:

2x² - x - 3 = 0

2*(-3) = -6

Factors of -6:

(-1, 6), (1, -6), (-2, 3), (2, -3)

We need to find a pair that adds up to the co-eff of x which is (-1)

Factors :(2,-3)

2 - 3 = -1

so, 2x² - x - 3 = 0 can be written as:

2x² + 2x - 3x - 3 = 0

⇒ 2x(x + 1) -3(x + 1) = 0

⇒ (2x - 3)(x + 1) = 0

⇒ 2x - 3 = 0 or

x + 1 = 0

⇒ 2x = 3 or x = -1

⇒ x = 3/2 or x = -1

Solve for x and y !!!!!!!!!!!

Answers

Answer:

x=12; y=138.

Step-by-step explanation:

1. 4x+(3x+6)=90 - to calculate 'x';

3x+6+y=180 - then to calculate 'y';

2. 7x+6=90; ⇒ x=12;

3. 3*12+6+y=180; ⇒ y=138°.

Math Problem 30 points please help

Answers

Answer: One solution

Step-by-step explanation:

Answer:

Step-by-step explanation:

they intersect at 1 point

g the gatewat arch in st louis is 630ft high and has a 630-ft bas its shape can be mdoeled by the parabolo y

Answers

The height of the Arch at any given horizontal distance from the base can be calculated by plugging the distance into the equation and solving for y.

The Gateway Arch in St. Louis is a 630-ft tall monument modeled after a parabola, which is a type of curved line that opens up on both sides. The parabola can be expressed in mathematical terms by the equation y = x^2. In this equation, y is the height of the Arch and x is the horizontal distance from the base. The base of the Arch is also 630-ft.

To calculate the height of the Arch at any given horizontal distance from the base, we can plug the distance into the equation and solve for y. For example, if we wanted to calculate the height of the Arch at a horizontal distance of 200-ft from the base, we would plug this value into the equation and solve for y:

y = (200)^2

y = 40000

Therefore, the height of the Arch at 200-ft from the base is 40000-ft. This same equation can be used to calculate the height of the Arch at any horizontal distance from the base.

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Complete question:

What is the height of the Gateway Arch in St. Louis?

A t-shirt requires 1 3/8 yards of material. How many t-shirts can be made from 41 1/4 yards of material?

Answers

Applying the knowledge of fractions, the number of t-shirts that can be made is: 30 t-shirts.

How to Divide Fractions?

In the problem given, we have the following information:

Material needed for one t-shirt = 1 3/8 yards

We want to find how many 1 3/4 we would find in 41 1/4.

Applying the knowledge of fraction, we are to divide 41 1/4 by 1 3/8. Convert both mixed fractions to improper fractions then divide:

41 1/4 ÷ 1 3/8

165/4 ÷ 11/8

165/4 × 8/11

15/1 × 2/1

= (15 × 2)/(1 × 1)

= 30/1

= 30.

Therefore, applying the knowledge of fractions, the number of t-shirts that can be made is: 30 t-shirts.

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The National Assessment of Educational Progress (NAEP) is a nationwide assessment of students’ proficiency in nine subjects: mathematics, reading, writing, science, the arts, civics, economics, geography, and U.S. history. The main NAEP assessments are conducted annually on samples of students from grades 4, 8, and 12.
In 2002, the reading scores for female students had a mean of 269 with a standard deviation of 33. Assume that these scores are normally distributed with the given mean and standard deviation.
Identify the scores that are three standard deviationsabove and below the mean of the population. For this example, the limits will be 269 ± (33)(3). The lower limit is . The upper limit is . The probability that a female student will have a score between these limits is .
A score of 302 is above the mean. As a result, the percentage of female students with scores below 302 is .
You can infer that 97.72% of the female students have scores above .

Answers

"97.72% of the female students have scores above," seems to be a misinterpretation as the correct statement is that approximately 99.72% of the female students have scores between the lower and upper limits

To calculate the scores that are three standard deviations above and below the mean, we use the formula:

Lower limit = Mean - (Standard Deviation * 3)

Upper limit = Mean + (Standard Deviation * 3)

Given:

Mean = 269

Standard Deviation = 33

Using the formula, we can calculate the limits:

Lower limit = 269 - (33 * 3) = 269 - 99 = 170

Upper limit = 269 + (33 * 3) = 269 + 99 = 368

Therefore, the lower limit is 170 and the upper limit is 368.

To calculate the probability that a female student will have a score between these limits, we need to find the area under the normal distribution curve between the lower and upper limits. This can be calculated using a standard normal distribution table or calculator.

Since the distribution is assumed to be normal, approximately 99.72% of the scores will fall within three standard deviations from the mean. Therefore, the probability that a female student will have a score between these limits is approximately 99.72%.

For a score of 302, which is above the mean of 269, we can calculate the percentage of female students with scores below 302:

Percentage = (1 - Probability) * 100

= (1 - 0.9972) * 100

= 0.0028 * 100

= 0.28%

Therefore, approximately 0.28% of the female students have scores below 302.

It's important to note that the value mentioned, "97.72% of the female students have scores above," seems to be a misinterpretation as the correct statement is that approximately 99.72% of the female students have scores between the lower and upper limits

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Identify the range of the function shown in the graph.

Answers

Answer:

Step-by-step explanation:

The range is all values of y. Y goes from -1 to 1. Please mark brainliest.

Answer:

see below

Step-by-step explanation:

The domain of the function is the possible x values

The domain is all real values since x can be any number

The range of the function is the possible y value

The values of y go from -1 to 1 so

-1 ≤y≤1

Which of the following is a trinomial with a constant term?
OA. x³ + 11x² + x
OB. -x+y¹0
OC. x+4y+7
OD. y5

Which of the following is a trinomial with a constant term?OA. x + 11x + xOB. -x+y0OC. x+4y+7OD. y5

Answers

Answer:

Step-by-step explanation:

A trinomial has 3 terms, so eliminate B and D.

A constant term is a term that is not dependent on a variable, so the answer is C. (7 is a constant term)

Owen receives $10 and puts it into his saving account. He adds $0.50 to the account each day for a number of day, d, after that. He writes the expression 10+ 0.5(d-1) to find the amount of money in his account after d days. Which statement about his expression is true?

Answers

The true expression about the account is D.) It is the sum of the initial amount and the additional amount after d days.

What does the expression 10+0.5(d−1) represent in Owen's savings account?

The answer is D because it represents the sum of the initial amount and the additional amount after d days. The initial amount is $10 and Owen adds $0.50 to the account each day for a number of days, represented by d.

By subtracting 1 from d, the expression ensures that on the first day (when d=1), only the initial $10 is counted. On each subsequent day, the additional amount of $0.50 is added to the total. Therefore, the expression 10+0.5(d−1) gives the amount of money in Owen's account after d days.