Challenge Word Problems
1. A 747 Airplane la 762 Inohos tall. How fall to it in foot?
2. The river raft ride at the amusement park oan hold 12 riders at a
time. There are 527 people in line. How many times will the ride need
to run in order to get all 527 people through the ride?
3. One school bus can hold 46 students. There are 24 students in each
of the 5 fifth grade classes. How many buses will they need in order to
transport everyone to the zoo for a field trip?
4. Write and solve a word problem that requires long division AND has a
remainder.
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If a constant is required, it must be added in order to complete the square, which entails writing a quadratic in the shape of a squared bracket.

If a constant is required, it must be added in order to complete the square, which entails writing a quadratic in the shape of a squared bracket.

Finding the function's greatest or minimum value and its occurrence are two uses of the square that can be made.

Changing the equation so that the left side is a perfect square trinomial results in the completion of the square.

That's just a fancy way of saying that the method of factoring quadratic equations known as completing the square allows you to factor quadratic equations that previously couldn't be factored.

3x^2 + 9x - 4

3x^2 + 9x = 4

3(x^2 + 3x) = 4

Consequently, a = 3.

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Answer:

31

Step-by-step explanation: 0.62*50=31

Answer:

I'd say about 31 Kilometers. (Sorry if I'm wrong!)

The exponent form of given integer is equal to [tex]2^{5[/tex] with base 2 and exponent 5.

Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.

An exponent refers to the number of times a number is multiplied by itself.

We know from property of Exponents

[tex]a^m a^n= a^{m+n[/tex]

We have the number 32.

Then, the prime factorization of 32

32 = 2 x 2 x 2 x 2 x 2

     = [tex]2^{1+1+1+1+1[/tex]

     = [tex]2^{5[/tex]

So, the base is 2 and exponent is 5.

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Answer:

False

Step-by-step explanation:

To make this true the proportion would be 3

Answer:

The proportion is true

Step-by-step explanation:

3/5 = 0.6

3/5/2 = 0.6/2 = 0.3

1.8/6 = 0.3

So the proportion is true

a) The amount of the monthly mortgage payment is 843.86

b) The total amount of interest Ato Liku that will pay over the life of the mortgage is 104,000

c) The amount of the mortgage Ato Liku will have paid after 10 years is 101,263.20

a) To determine the amount of the monthly mortgage payment, we need to use the formula for the monthly mortgage payment (also known as the loan payment formula):

M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1]

where M is the monthly mortgage payment, P is the principal (the remaining balance after the down payment), i is the monthly interest rate (12%/12 = 1%), n is the number of payments (30 years x 12 months/year = 360 payments), and ^ denotes exponentiation.

P = 250,000 x (1-.20) = 200,000

n = 30 x 12 = 360

i = 0.12/12 = 0.01

M = 200,000 [ 0.01(1 + 0.01)^360 ] / [ (1 + 0.01)^360 - 1]

M = 843.86

b) To determine the total amount of interest Ato Liku will pay over the life of the mortgage, we can subtract the original loan amount (200,000) from the total amount of the payments over the life of the loan:

total interest = total payments - original loan amount

total payments = M x n = 843.86 x 360 = 304,000

total interest = 304,000 - 200,000 = 104,000

c) To determine the amount of the mortgage Ato Liku will have paid after 10 years, we need to multiply the monthly mortgage payment by the number of payments made after 10 years.

10 years x 12 months/year = 120 months

Mortgage paid after 10 years = 843.86 x 120 = 101,263.20

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Answer: D (x=-12)

Step-by-step explanation:

divide 4 on both sides of the equation. -48/4=-12

The probability of selecting a custard-filled donut followed by a lemon-filled donut is:

P(custard, lemon) = P(custard) * P(lemon | custard)

P(custard, lemon) = (2/3) * (5/23)

P(custard, lemon) = 10

What is the probability?

Probability is a measure of the likelihood that an event will occur. It is a number between 0 and 1, where 0 represents an impossible event, and 1 represents a certain event.

We can find the probability of selecting a custard-filled donut followed by a lemon-filled donut by multiplying the probability of selecting the first donut by the probability of selecting the second donut, given that the first donut was selected.

The probability of selecting a custard-filled donut is:

P(custard) = number of custard-filled donuts / total number of donuts

P(custard) = 16 / 24

P(custard) = 2/3

Given that a custard-filled donut was selected, the probability of selecting a lemon-filled donut next is:

P(lemon | custard) = number of lemon-filled donuts / total number of donuts remaining

P(lemon | custard) = 5 / (24-1) = 5/23

The probability of selecting a custard-filled donut followed by a lemon-filled donut is:

P(custard, lemon) = P(custard) * P(lemon | custard)

P(custard, lemon) = (2/3) * (5/23)

P(custard, lemon) = 10

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The naswer is X=<-5 Or X=-5,

A sentence having two inequality statements connected by the words "or" or "and" is referred to as a compound inequality.

We look at the graphs of each inequality, identify the integers that correspond to either graph, then add all those numbers up to determine the compound inequality's solution. We frequently use the union symbol,, to represent the union of the solutions presented in the graphs when writing the solution in interval notation.

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A pair of functions that are inverses of each other include the following: B. f(x) = 4x³ + 5 and g(x) = ∛[(x - 5)/4].

In order to determine the inverse of this function f(x) = -1 - 1/5x, we would interchange both the input value (x) and output value (y) as follows:

f(x) = y = ∛(x + 3) - 5

x = ∛(y + 3) - 5

x + 5 = ∛(y + 3)

Taking the cube of both sides of the function, we have:

(x + 5)³ = y + 3

g(x) = y = (x + 5)³ - 3 (Not an inverse of f(x)).

From the second answer option, we have the following:

f(x) = y = 4x³ + 5

x = 4y³ + 5

x - 5 = 4y³

Dividing both sides of the function by 4, we have the following:

y³ = (x - 5)/4

Taking the cube root of both sides of the function, we have:

g(x) = y = ∛[(x - 5)/4] (An inverse of f(x))

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Answer:

m = 5 and n = 6

Step-by-step explanation:

In a parallelogram, opposite sides of the figure are congruent (equal to each other).

This means that 3m - 7 = m + 3 and 2n + 12 = 4n

We can now solve for the variables

3m - 7 = m + 3

==> add 7 to both sides

3m = m + 10

==> subtract 2 from both sides

2m = 10

==> divide both sides by 2

m = 5

2n + 12 = 4n

==> subtract 2n from both sides

12 = 2n

==> divide both sides by 2

6 = n

Answer:

n=6,m=2

Step-by-step explanation:

4n=2n+12

2n =12

n=6

m+3=3m-1

4=2m

m=2

yes the length of the strawberry patch can be greater than 1 yard.

A rectangle is a quadrilateral with four sides and four right angles.

Given that Danah wants the area of her rectangular strawberry patch to be exactly 1 square yard.

We have to find out whether the length of the rectangular strawberry patch can have a value greater than 1.

Area of a rectangle = Length x Width.

The area of the rectangular strawberry patch is exactly 1 square yard.

Area  = 1 square yard

Length x Width = 1 square yard

To have the area of the rectangular strawberry patch be exactly 1 square yard.

We can have the following cases :

Case 1.

Length = 2 and Width = 0.5

Area = Length x Width = 2 x 0.5 = 1 square yard.

Case 2.

Length = 4 and width = 0.25

Area = Length x Width = 4 x 0.25 = 1 square yard.

Case 3.

Length = 8 and width = 0.125

Area = Length x Width = 8 x 0.125 = 1 square yard.

Case 4.

Length = 10 and width = 0.1

Area = Length x Width = 10 x 0.1 = 1 square yard.

We see that we can have the length as 2, 4, 8, and 20 in order to have an area of the rectangle as 1 square yard.

Hence, yes the length of the strawberry patch can be greater than 1 yard.

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The algebraic property used for the expansion of the algebraic expression is; Distributive Property.

There are different algebra properties such as Associative property, Identity Property, Inverse property, Distributive property, commutative property.

The examples of these algebra properties are;

1) Associative Property; a + ( b + c ) = ( a + b ) + c

a( b c ) = ( a b ) c

2) Commutative property; a + b = b + a

3) Identity Property;

a + 0 = a and a ⋅ 1 = a

4) Inverse Property;

a + ( − a ) = 0 and a ⋅ 1 a = 1

5) Distributive Property;
a ( b + c ) = a b + a c

We are given the expression;

15x - 20xy as 5x(3 - 4xy)

From the earlier properties explained, this is clearly an example of distributive property.

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The shortest length of wire is 74.9 feet.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.

Given:

A 170 ft tower is located on the side of a mountain that is inclined 19° to the horizontal.

A guy wire is to be attached to the top of the tower and anchored at a point 46 ft downhill from the base of the tower.

The visual representation of the phrase is given in the attached image.

Let b = 46 feet.

h = 70 feet.

And angle θ = 180 - 19 = 161°.

a = 46cos(161)

c = 46sin(161)

Then, the shortest length of the wire,

x = √{(h +c)²+(a)²}

x = √{(46 + 46sin (161))²+(46cos(161))²}

x = 74.9 feet

Therefore, the shortest length is 74.9 feet.

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Answer:200 bucks

Step-by-step explanation:

This is because the point (1,4) is on the line.

Plugging x = 1 into y = 4x leads to y = 4.

Plugging x = 3 into that equation leads to y = 12; which explains why the point (3,12) is also on the line.

The Difference between variables and constants is shwon below.

A fixed value that appears in algebraic expressions and equations is known as a constant. A constant has a fixed value and does not change over time.

Variables are concepts that evolve or change throughout time. Its value changes over time, unlike constants.

The Difference between variables and constants

On the other hand, a variable's value varies depending on the equation.

Variables have unique letter or symbol writing.

On the other hand, variables stand in for the unknowable values.

There is no set face value for a variable.

Now, Understanding variables is crucial since they serve as the fundamental building blocks of the data examined and evaluated in research projects. When doing descriptive research or interpreting the results of an experiment, researchers carefully examine and interpret the value(s) of each variable to understand how things relate to one another.

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Answer:

$8.35

Step-by-step explanation:

One pound of pecans would cost approximately $8.35, rounded to the nearest cent. To find this, divide the total cost by the number of pounds: $41.75 ÷ 5 pounds = $8.35 per pound.

Answer:

8.35

Step-by-step explanation:

divided 5 by 41.75. trust

The triangle's angle and side relationships, the triangle's angles, from smallest to greatest, would be ∠L, ∠M, ∠K.

When two triangle angles are not equal, their opposite sides' measurements are also not equal, with the longer side being opposite the larger angle.

The greatest side and angle in every triangle are on opposing sides. The smallest side and smallest angle of any triangle are in opposition to one another. The mid-sized side and mid-sized angle in every triangle are in opposition to one another.

The longest side of a triangle is located across from the largest angle. In a triangle, the longest side is located across from the one with the least angle.

As a result, given the triangle's angle and side relationships, the triangle's angles, from smallest to greatest, would be: C. ∠L, ∠M, ∠K.

The complete question is:

List the angles of the triangle in order from smallest to largest

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When a quadratic equation is graphed, a parabola is produced, whereas a linear equation results in a straight line.Consequently, (1, 3) and are the answers to the system of equations (-5, -3)

In the following respects, quadratic equations differ from linear equations:When a quadratic equation is graphed, a parabola is produced, whereas a linear equation results in a straight line.In contrast to the slope of a linear polynomial, a quadratic polynomial's slope is dynamic.

(1, 3) and are the answers to the system of equations (-5, -3)

Considering the subsequent features

Y=x^2+5x-3

Y-x=2; y = x + 2

The result of equating both outputs is

x^2+5x-3 = x + 2

x^2+5x-3 - x - 2 = 0

x^2 + 4x - 5 = 0

Formulation factorization

x^2 + 5x - x - 5=0

x(x+5) - 1(x+5) = 0

(x-1)(x+5) = 0

x = 1 and -5

Remember that y=x+2

y = 3 and -3

Consequently, (1, 3) and are the answers to the system of equations (-5, -3)

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If the price of Stock A at 9 A.M. was ​15.69$. The number of hours the prices of the two stocks be the​ same is: 3.125  hours.

Stock A = 15.69 + 0.05h

Stock B = 16.19 - 0.11

So equate Stock A and Stock B

15.69 + 0.05h = 16.19h - 0.11h

Combine like terms

0.11h + 0.05h = 16.19 -15.69

0.16h = 0.5

Divide both side by 0.16h

h = 0.5/0.16

h = 3.125 hours

Therefore the number of hours the prices of the two stocks be the​ same is: 3.125  hours.

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No because the bike order does not meet the restrictions of[tex]4c+6a \le 120 \ \text{ and } \ 4c+4a \le 100\\\\[/tex]

===================================================

Explanation:

c = number of child bikes

a = number of adult bikes

Each child bike takes 4 hours to build. This means 4c represents the total time spent building all c number of child bikes. Eg: if c = 2, then 4c = 4*2 = 8 hours is spent total building these two child bikes.

Meanwhile, each adult bike takes 6 hours to build. That means 6a represents the total time spent building these subset of bikes.

The expression 4c+6a is the total time spent building all of the bikes, child and adult.

The company has 120 hours of building time. The total time (4c+6a) cannot exceed this 120 hour ceiling.

This is how we arrive at [tex]4c+6a \le 120[/tex] which is one of the constraints or restrictions.

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

Now onto the testing side of things.

Each child bike takes 4 hours to test. That gives us 4c.

Each adult bike takes 4 hours to test. We get 4a.

4c+4a = total testing time for all of the bikes

[tex]4c+4a \le 100[/tex] is the second restriction we place, since we have at most 100 hours of testing time total. We cannot exceed this.

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

To summarize so far:

Let's see if we can build c = 20 child bikes and a = 6 adult bikes

Plug this pair of values into the first inequality

[tex]4c+6a \le 120\\\\4*20+6*6 \le 120\\\\80+36 \le 120\\\\116 \le 120[/tex]

The last inequality is true, which means the inequality [tex]4c+6a \le 120[/tex] is also true for the values c = 20 and a = 6.

So far it looks like we can build these number of bikes.

But we need to check the other inequality.

[tex]4c+4a \le 100\\\\4*20+4*6 \le 100\\\\80+24 \le 100\\\\104 \le 100\\\\[/tex]

We run into a problem. The last inequality is false, which means [tex]4c+4a \le 100[/tex] is false when c = 20 and a = 6 are plugged into it.

Meaning it is impossible to test 20 child bikes and 6 adult bikes in a week.

This is why   choice  A   is the final answer.

Answer:

the person above is correct

Step-by-step explanation:

All of your answers are correct so far.

4. Line L is y=-2x-3. Line M is y=-2/3x+1

5. The solution is x=-3, y=3

6. Point P represents the answer to the equations.

8. Inequalities:

Line L: y>-2x-3

Line M: y<-2/3x+1

9. -3, 3

a.  An inequality to represent how long the family should drive on the first day :

n ≥ 11.

b. the family should drive 11 hours.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

To get to the beach for vacation,

Cheng's family must drive at least 660 miles on the first day.

They are traveling at a constant speed of 60 miles per hour.

The total time  = 660 / 60 = 11 hours.

That means, the family should drive 11 hours.

An inequality to represent how long the family should drive on the first day :

n ≥ 11.

Therefore, inequality is n ≥ 11. And family should drive 11 hours.

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By the graph of function we say that,

⇒ The graph has a domain of {x | 0 < x < ∞} and an x - intercept of (1, 0).

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The function is,

⇒ f (x) = ln x

Now, When we draw the graph of function f(x) = ln x, we get;

The graph has a domain of {x | 0 < x < ∞}

And, The graph has an x - intercept at (1, 0).

Thus, The correct statement is,

⇒ The graph has a domain of {x | 0 < x < ∞} and an x - intercept of (1, 0).

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The perimeter of the triangle is  40.42 cm

The height of the triangle is 14 cm

A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

The length of the base is 9.5 cm

The total area of the triangle is 66.5 cm²

We know,

Area = (1/2)*base * height

⇒ 66.5 = (1/2)*9.5* h

⇒h = 14 cm

The height is 14 cm

By using Pythagoras theorem  

hypotenuse = √{(base)² + (height)²} = √{(9.5)² + (14)²}  = 16.92 cm

The hypotenuse is 16.92 cm

The perimeter of the triangle is height + base + hypotenuse = 14 + 9.5 + 16.92 = 40.42 cm

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The solution to the system of two equations is (x,y) = (10, -25.5).

An equation is a mathematical statement that two expressions are equal. It is written in the form of an equality sign, which is a line with two dots on either side. The expressions on either side of the equality sign represent the same value. Equations are used to solve problems, compare quantities, and describe relationships between variables. In addition, equations are often used to describe physical laws and scientific theories.

To solve the system of equations, one must first isolate the variables by subtracting one of the equations from the other. Subtracting equation 1 from equation 2 results in equation 2 having x terms on one side and y terms on the other.

3x + 4y = 19
-5x - 2y = -1

--------------------------------
-2x = -20

Now, solve for x by dividing both sides by -2.

x = 10

Next, substitute x = 10 into equation 1 and solve for y.

5x + 2y = −1
5(10) + 2y = -1
50 + 2y = -1
2y = -51
y = -25.5

Therefore, the solution to the system of two equations is (x,y) = (10, -25.5).

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The independent variable is the cause of change of dependent variable.

What is Algebraic expression?

Algebraic expressions are the concept of expressing numbers using letters or alphabets with out specifying their actual values. The basics of algebra taught us a way to explicit an unknown fee using letters which includes x, y, z, etc. those letters are referred to as here as variables. An algebraic expression may be a aggregate of both variables and constants. Any cost that is located earlier than and improved by way of a variable is a coefficient.

Given ,

To identify the given independent variable,

that is the amount of money , m , earned if t raffle tickets are sold.

So,

The more t , the more m .

that means if t increases , m increases

and if t decreases , m decreases.

and here t causes m increases.

Hence, The independent variable is the cause of change of dependent variable.

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Answer:

16 degrees

Step-by-step explanation:

90-74=16. Because the whole is 90 degrees, So you subtract it from the 74 degrees and you get your answer