What angle does a 3.8 m ladder make with the ground if it reaches 2.1 m up the wall? How far is the foot of the ladder from the wall? (Give your answers to the nearest degree and the 1 decimal place of the metre.)

If  a triangle has sides with lengths of 30 kilometers, 35 kilometers, and 45 kilometers. No it is not a right triangle.

We would be making use of converse of Pythagoras' theorem to determine whether the triangle is a right triangle.

In a situation were we have a right triangle the square on longest side will be the same with the sum of square of other sides

Longest side

45²  =  2025

Other side

30 ² + 35 ²

900 + 1,225

= 2125

Hence,

2025 ≠ 2125

Based on the above it is  not a right triangle because the longest side did not equate the other side.

Therefore it is not a right triangle.

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As 2125 ≠ 2025 therefore it didn't meet the requirements of Pythagoras' theorem, it is not a right-angle triangle.

This type of question makes a right-angled triangle that can be solved by Pythagoras's theorem.

In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.

Given, A triangle has sides with lengths of 30 kilometers, 35 kilometers, and 45 kilometers.

∴ 30² + 35² = 45².

900 + 1225 = 2025.

2125 ≠ 2025.

It is not a right-angle triangle because it didn't satisfy the property of Pythagoras's theorem.

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Answer:

C)

Step-by-step explanation:

elimination is not substitution.

therefore, A and B are out.

D does not work, because in the described way the x terms don't get different signs, and the addition does not eliminate any variable.

C brings both y terms to the same absolute value, and their signs are different, so the addition will eliminate the y terms leaving us with one equation in x that we can solve :

15x + 12y = 21

8x - 12y = 12

---------------------

23x 0 = 33

23x = 33

x = 33/23

Answer:

a is the right answer for you

Answer:

Yes.

Step-by-step explanation:

Replace x with 2 and y with 1 and see if the equation is true

x - 4y = -2

2 - 4(1) = -2

2 - 4 = -2

-2 = -2

The statement is true so the point is on the line.

The value of the function f(−2/3) will give the value 8/3.

A function is important to show the expression that's given.

Given: f(x) = 3x^2 −5x−2.

To find f(-2/3), we substitute x = -2/3  into the equation:

f(-2/3) = 3 x (-2/3)^2  - 5(-2/3) - 2

         = 3 x 4/9 + 10/3 -2

         = 12/9 + 10/3 - 2

         = (12 + 30 - 18) / 9

         = 24 /9

        = 8/3

Therefore, f(-2/3) evaluates to 8/3.

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Answer:1700

Step-by-step explanation:

We are asked to find an equivalent amount to 100 USD in french francs. Acording to the table, on tuesday, a dollar costs 4.3450 french francs, then we can find how many francs we got by multiplying 100 USD and 4.345, then we get:

Francs = 100×4.3450 = 434.50

Then, the answer is 434.5 french francs

Cyphon, this is the solution:

We have to multiply the following fractions:

7/12 * 4/3

7 * 4 / 12 * 3

28/36

Simplifying, we have:

7/9 (Dividing by 4 numerator and denominator)

We have to add the following fractions:

- 1/2 + 4/9

Let's find the lowest common denominator between 2 and 9, as follows:

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22

9, 18, 27, 36

The lowest common denominator is 18

Here is the graph for you!!

The y-intercept of the function y = 3.5x - 7 is ( 0, - 7 ).

A function is an association between inputs in which each input has a unique link to one or more outputs. Each function has a range, codomain, and domain.

Consider the function,

y = 3.5x - 7

The equation of a straight line is expressed in the slope-intercept form (a linear function). It takes the formula y = mx + b, where m is the slope, b is the y-intercept, and y and x serve as variables.

The value of y at x = 0 can be used to determine the y-intercept. The graph's intersection with the y-axis occurs at this location.

Then,

y = 3.5x - 7

y = 3.5( 0 ) - 7

y = - 7

The y-intercept of the function is ( 0, - 7).

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Answer:

30

Explanation:

To know the output value of the function, we need to replace x by -5 and calculated f(x). So:

Therefore, if the input x is -5, the output f(x) is 30

So, the answer is 30.

Answer:

23,180 pieces

Explanation:

The number of white paper used = 13,480 pieces

Since they used 7,880 fewer pieces of blue paper than white paper

The number of blue paper used = 13,480 - 7880 =5,600 pieces

They also used 1,500 fewer pieces of yellow paper than blue paper.

The number of yellow paper used = 5,600-1500 =4100 pieces

Therefore. the total number of pieces of paper

=13,480 + 5,600 + 4100

=23,180 pieces

Kadeem takes 0.5 hours to travel 25 miles, and Quinn 0.33 hours, so Kadeem takes longer.

Remember the relation:

Speed*time = distance.

Notice that if the distance is fixed, then for a longer speed the time needed will be smaller.

Here we know that:

Kadeem drives at a constant speed of 50mi/h

Quinn drives at a constant speed of 75 mi/h.

Replacing that in the equation:

Kadeem's case:

(50 mi/h)*t = 25mi

t = (25 mi)/(50 mi/h) = 0.5 hours.

Quinn's case:

t = (25mi)/(75 mi/h) = 0.33 hours.

So Kadeem takes longer.

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Answer:

48 push ups

Step-by-step explanation:

40 push ups in 5 days can be modelled with the fraction 40/5

you can simplify that to 8/1 after dividing both sides by 5

now set that equal to push ups over 6

but first you must declare a variable for push ups

let x = push ups

8/1 = x/6

multiply both sides by 6

48/1 = x

x = 48

that is your answer

48 push ups

To know how many reflections are made per day, a division is made between the days and the total number of reflections.

40 Flexions ➗ 5 days = 8 flexions a day.

Every day it has 8 flexions, in multiply the 6 days for the 8 flexions of each, then.

8 flexions (1 day) ✖ 6 days = 48 flexions.

Answer: 48 flexions = 6 days ✅.

By the distribution,6.3 minutes is the time limit that 75.8% of college students go over when looking for a parking space in the library parking lot.

Given that,

Finding a parking spot in the library parking lot takes college students an average of 7.0 minutes, with a standard deviation of 1 minute, according to a normal distribution.

Find the window of opportunity that 75.8% of college students miss when looking for a place in the library parking lot.

The following formula calculates the z-score of a measure X of a normally distributed variable with mean μ and standard deviationσ:

Z=(X-μ)/σ

The z-score calculates how far the measure deviates from the mean by standard deviation.

The p-value for this z-score, which is the percentile of X, can be obtained by looking at the z-score table.

The cut-off time is the 100th percentile minus 75.8th percentile, or X, for Z = -0.7, so:

Z=(X-μ)/σ

-0.7=(X-7)/1

-0.7=X-7

X=-0.7+7

X=6.3

Therefore, 6.3 minutes is the time limit that 75.8% of college students go over when looking for a parking space in the library parking lot.

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Answer:

  73 : 27

Step-by-step explanation:

You want the ratio of students that have a pet to students that don't have a pet, given that 73% of students have a pet.

If 73% of students have a pet, then the remaining 100% -73% = 27% of students do not have a pet.

The ratio of students who have a pet to students who don't have a pet is then ...

  (have a pet) : (don't have a pet) = 73% : 27% = 73 : 27

According to a recent survey, 73% of elementary school students have a pet, making the ratio of students with pets to those without pets 73:27.

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

You want the ratio of students that have a pet to students that don't have a pet, given that 73% of students have a pet.

If 73% of students have a pet, then the remaining 100% -73% = 27% of students do not have a pet.

The ratio of students who have a pet to students who don't have a pet is then,(have a pet) : (don't have a pet) = 73% : 27% = 73 : 27

A recent survey found that 73% of elementary school students own a pet, making the proportion of students who own pets to those who don't stand at 73:27.

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To give an entity the desired position, orientation, or shape starting from the current position, orientation, or shape, geometric transformations are required. Scaling, rotation, translation, and shear are the fundamental transformations. Projections and mappings are two additional crucial categories of transformation.

Y =- X is what kind of a transformation?

Y = X's reflection:

The x-coordinate and the y-coordinate switch positions when a point is reflected across the line y = x. Y = -x reflection: The x-coordinate and the y-coordinate switch places when you reflect a point across the line y = -x, and they are negated (the signs are changed).

The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse. The cross-sectional reflection of point (x, y)

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The correct option is option B that is "The graph of f(x) is shifted 17 units up". It is shifted 17 units up. By adding 17 to the equation, y increases by 17. If y increases by 17, the graph shifts up by 17.

In discrete mathematics, a graph is made up of vertices—a collection of points—and edges—the lines connecting those vertices. In addition to connected and disconnected graphs, weighted graphs, bipartite graphs, directed and undirected graphs, and simple graphs, there are many other types of graphs.

The process of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation. In particular, the modification of algebraic equations, it is a typical kind of algebraic problem.

It is shifted 17 units up.

By adding 17 to the equation, y increases by 17.

If y increases by 17, the graph shifts up by 17.

Option B, "The graph of f(x) is shifted 17 units up," is the answer. It is moved upward 17 units. Adding 17 to the formula causes y to rise by 17. The graph moves up 17 units if y rises by 17.

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The elk population in 2014 will be 19,700 ,A population is an identified grouping of objects with the purpose of analysis and data collection.

A population is an identified grouping of objects with the purpose of analysis and data collection. Examples include people and animals. It comprises of a related collection of species that live in a specific area and have the ability to interbreed.

The population increased by 12,700-12,000 = 700 between the two measures, however, it did so over a period of 1 year, from 2004 to 2003. Divide 700 elk by 1

The elk population in 2014 will be 19,700We must first establish the method

2014=700 should add 10 times then we will get the 2014th year population.

so the population of 2014th will 19700

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259 pieces of candy can be distributed in 80 bags to give 3 candy per bag and there will be 19 candies remaining

The concept for distributing the required candies is achieved by the mathematical operation called division.

Division is an inverse of multiplication. With division we can share and determine number of candy per bag

The question is solved by

= 259 ÷ 80

= 259 / 80

= 3 19/80

This means that there will be 3 candies per bag and after sharing among the nags there will be 19 candies remaining.

Putting this in decimal gives

= 3.2375 ≅ 3.24

In a situation where we are to count the candies if they are 3.25 pieces per bag the we multiply as follows

= 3.25 * 80

= 260

in this case the total number of candies should be 260

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-83843/21 is the partial fraction of Four thousand three hundred fifty seven divided by twenty one minus four thousand two hundred.

Two or more expressions with an Equal sign is called as Equation.

Four thousand three hundred fifty seven divided by twenty one minus four thousand two hundred.

4357/21 - 4200

Take LCM as 21.

4357-88200/21

-83843/21

=-3992.5

Hence -83843/21 is the partial fraction of Four thousand three hundred fifty seven divided by twenty one minus four thousand two hundred.

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Answer:

The equation in slope-intercept form is:

[tex]y=\frac{1}{3}x+3[/tex]

So the second option is the correct one.

Step-by-step explanation:

Step 1: Identify the gradient

The perpendicular line's equation is given as:

[tex]y=-3x+4[/tex]

This equation is in the form of:

[tex]y=mx+b[/tex]

Upon comparing the [tex]x[/tex] components of both equations, we get[tex]-3x=mx\\\text{Remove the}~ x~ \text{from both sides:}\\-3=m\\m=-3[/tex]

So, the gradient of this 'reference' equation is -3.

The equation we need to find is perpendicular to this 'reference' equation.

So, its gradient should be the negative reciprocal of the gradient of the 'reference' equation.

The negative reciprocal of -3 is:

[tex]-\frac{1}{(-3)}\\=\frac{1}{3}[/tex]

So, the gradient of our equation is [tex]\frac{1}{3}[/tex].

Step 2: Create the equation:

The equation crosses the x-axis at -9, which means its y-coordinate is 0 (at x-axis, y=0) ,so its coordinate is [tex](-9,0)[/tex].

The formula for an equation is:

[tex]y-y_{1}=m(x-x_{1})[/tex]

The coordinate [tex](x_{1},y_{1})[/tex] is [tex](-9,0)[/tex], and the gradient ([tex]m[/tex]) is [tex]\frac{1}{3}[/tex].

Substitute the values into the equation:

[tex]y-y_{1}=m(x-x_{1})\\y-0=\frac{1}{3}(x-(-9))\\\\\text{Simplify}\\y=\frac{1}{3}(x+9)[/tex]

[tex]\text{Simplify further}\\y=\frac{1}{3}x+3[/tex]

Since, the slope-intercept form is:

[tex]y=mx+b[/tex]

We already have our equation in the slope-intercept form.

The balance of the checks and cash (receipts and payments) is -$245.90.

The balance is the difference between receipts of cash and payments of checks and cash.

Using addition and subtraction operations, the balance is determined as follows:

32.96

121.03

24.70

Total checks = $178.69

22 one dollar bills = $22.00 (22 x $1)

5 ten dollar bills       $50.00 (5 x $10)

15.21 in coins              $15.21

Total cash payments = $87.21

$20 cash received

Total cash = $67.21

Balance   = -$245.90 [$20 - ($87.21 + $178.69)]

Thus, the balance of the checks and cash totals -$245.90, showing that payments outstripped receipts.

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How much is the balance between receipts and payments?

The age of the spear head is found to be 1625 years.

Let us recall that the age of the sample can be determined by the use of radiometric dating. Let us now define the variables;

The constant of the decay (k) =  0.0001

The amount of the sample originally present (No) = No

The amount of the sample at time t = 0.85No

t = The age of the sample

Given that;

N= Noe^-kt

N/No = e^-kt

0.85No/No = e^-0.0001t

0.85 = e^-0.0001t

ln0.85 = -0.0001t

t = ln0.85/ -0.0001

t = 1625 years

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Answer:

$8 an hour and also requires a 40-hour week

Step-by-step explanation:

the unit price for 1 lb of turky is $0.99

The cost of 14 lb of turkey = $13.86

let the cost of 1 lb of turkey = y

The unit price is the cost for 1lb of turkey:

14 lb = 13.86

1 lb = y

cross multiply:

14(y) = 1(13.86)

14y = 13.86

divide both sides by 14:

14y/14 = 13.86/14

y = 0.99

Hence, the unit price for 1 lb of turky is $0.99

Fencing of any rectangular region is basically represent perimeter of that rectangular region.

For most economical fencing, length L = 21.05 feet and width W = 13.301  feet.

Area of rectangular region is 280 square feet.

And length is L and width is W.

Area of rectangular region = L × W=280 square feet

W=280 / L

Since, The fence along three sides is to be made of material that costs 6 dollars per foot, and the material for the fourth side costs 14 dollars per foot.

Therefore, Total cost, C = 6(2L + W) + 13W = 12 L + 19 W

Total cost, C = 12 L+ 5,320 / L

To find most economical cost, differentiate above function and equate to zero.

C' = 12 - 5,320 / L²

simplifying the above equation, we get

⇒ 12 - 5,320 / L² = 0

⇒ L² = 5,320 / 12

L = 21.05 feet

Therefore, L = 21.05 feet

Substituting value of L in area equation.

We get, W = 13.301  feet.

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Answer:

an=7/2

Step-by-step explanation:

an=a(n-1)+15

given a1=8

multiply; a(n-1)

a(n-1)=an-a1

enter an-a1 in the equation

an=an-8+15

an=an+7

collect like terms;

an-an=(-7)

divide by negative both side

an-an/(-)=(-(-7)

2an=7

divide by 2 both side

2an/2=7/2

therefore the answer is an=7/2

The probability that you will be satisfied with 3 or more of the purchased products is 0.916

Given that,

The chance of being pleased with an internet purchase is 0.555. if you purchase 8 items online

Solution -

let  X denote the no of success of

Purchased product online

X ~ B(n,p)

n = 8

P= 0. 555

a = 1 - 0 .555 = 0.445

P ( X = x) = [tex]nc_{x} b^{x} a^{n-x}[/tex]

P ( X = x)= [tex]8c_{x} (0.555^{x} )(0.445)^{8-x[/tex]

P ( X>=3)= [tex]\lim_{3 \to 8} 8c_{x} (0.555^{x} )(0.445)^{8-x[/tex]

P ( X>=3)) = 0.91614

                 =0.916

Therefore we can conclude the probability that you will be satisfied with 3 or more of the purchased products is 0.916

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Answer:

r = 23.7

Step-by-step explanation:

17 = r - 6.7 ( add 6.7 to both sides )

23.7 = r