An airplane flies at a speed of 474 miles per hour. How many miles does the plane fly on 5 hours?

Change the mixed numbers to the impropert fractions:

[tex]4\dfrac{2}{3}=\dfrac{4\cdot3+2}{3}=\dfrac{14}{3}\\\\11\dfrac{1}{4}=\dfrac{11\cdot4+1}{4}=\dfrac{45}{4}[/tex]

[tex]4\dfrac{2}{3}\cdot11\dfrac{1}{4}=\dfrac{14}{3}\cdot\dfrac{45}{4}=\dfrac{7}{1}\cdot\dfrac{15}{2}=\dfrac{105}{2}=52\dfrac{1}{2}\to\boxed{D.}[/tex]

So firstly, we need to isolate the x terms onto one side. To do this, subtract 48 on both sides of the equation:

[tex]2x^2-20x=-48[/tex]

Next, divide both sides by 2:

[tex]x^2-10x=-24[/tex]

Next, we are gonna make the left side of the equation a perfect square. To find the constant of this soon-to-be perfect square, divide the x coefficient by 2 and then square the quotient. Add the result onto both sides of the equation:

[tex]-10 \div 2=-5\\(-5)^2=25\\\\x^2-10x+25=1[/tex]

Now, factor the left side:

[tex](x-5)^2=1[/tex]

Next, square root both sides of the equation:

[tex]x-5=\pm 1[/tex]

Next, add 5 to both sides of the equation:

[tex]x=5\pm 1[/tex]

Lastly, solve the left side twice -- once with the plus sign and once with the minus sign.

[tex]x=6,4[/tex]

In short, x = 6 and 4

Answer: x = 4   x = 6

Step-by-step explanation:

2x² - 20x + 48 = 0

2x² - 20 x + _____ = -48 + ______      subtracted 48 from both sides

2(x² - 10x + _____ ) = 2(-24 + _____ )   factored out 2 from both sides

x² - 10x + _____  = -24 + _____          divided both sides by 2

x² - 10x + 25  = -24 +25          added 25 to both sides

       ↓        ↑            ↑

     [tex]\dfrac{-10}{2}=(-5)^2[/tex]     [tex]\bigg(\dfrac{b}{2}\bigg)^2[/tex] makes a perfect square

(x - 5)² = 1             simplified

[tex]\sqrt{(x-5)^2} =\sqrt{1}[/tex]    took square root of both sides

x - 5 = ± 1             simplified

x - 5 = 1       x - 5 = -1     split into two separate equations

   x = 6           x = 4       solved for x

Answer:

224 stamps.

Step-by-step explanation:

We have been given that Becki put 14 stamps on each page.

To find the total number of stamps that Becki put in the book we will multiply the number of stamps put on each page by the number of completely filled pages.

[tex]\text{The total number of stamps in the book}=14\times 16[/tex]

[tex]\text{The total number of stamps in the book}=224[/tex]

Therefore, Becki put 224 stamps in the book.

To find out how many stamps Becki added to her collection, we multiply the number of stamps per page, which is 14, by the number of filled pages, which is 16, resulting in a total of 224 stamps.

To determine how many stamps Becki put into her stamp collection book, we need to calculate the total number of stamps populated over the completely filled pages. She placed 14 stamps on each page and filled 16 pages. The total number of stamps is the product of the number of stamps on each page and the number of pages filled.

The formula we will use is:

Total stamps = Number of stamps per page x Number of filled pages

Substituting the given values:

Total stamps = 14 stamps/page x 16 pages = 224 stamps

Therefore, Becki put 224 stamps in her stamp collection book.

By definition, i = sqrt(-1) because it is used to solve the equation x^2+1 = 0 or x^2 = -1, which has no real number solutions.

Since i is imaginary or complex, then so is 2i

You can express it as 2i = 0+2i to be in the form a+bi with a = 0 as the real part and b = 2 as the imaginary component.

The question involves creating and analyzing scientific models, collaborating in groups to build and refine these models based on experimental evidence, and engaging in critical thinking about their accuracy and limitations.

The question involves students creating and analyzing models that represent certain scientific situations. Creating a model is a fundamental part of scientific inquiry as it helps in visualizing and understanding complex concepts. Students are tasked with exchanging and labeling pictures or drawings of their models, which aids in the development of the communication of scientific ideas. They then apply their models to specific situations, test these models, and note the outcomes to assess the accuracy and limitations of the models they have built. This process involves critical thinking, collaboration, and application of scientific knowledge.

Moreover, students are required to modify their models based on experimental evidence and discussions about the limitations of their models. When building models of atoms, for example, students must consider basic ratios, an understanding of atomic structure, and the unique characteristics of the element they are representing.

The complete question is:Drag one model next to each situation. The correct model for each group represents that situation

Answer:

-7.77778

If you use google it will help u

Answer:

B

Step-by-step explanation:

Because the angles make up the interior parts of the triangle without the extra endings

Answer: The answer would be B

Answer:

1-x represents the percent of the original price being paid.

Step-by-step explanation:

The expression 24(1−x) gives the discounted price of a pair of shorts, where x is the percent of the discount written in decimal form.

For example , 10% is the discount percentage

1 - 10% = 90% will be the percentage of original price to be paid

Here x represents the percent of the discount

so 1-x represents the percent of the original price being paid.

Answer:

percent of original price being paid

Step-by-step explanation:

Answer:

Vertical angle property

Step-by-step explanation:

We are given that e is parallel to f and g is a transversal. Using the alternate interior angles property, ∠4=∠5 which is given.

Since, g is a transversal of the two parallel lines e and f, then ∠1=∠4 and ∠8=∠5 by the vertical opposite angle property.

Hence, ∠1≅∠8 by the transitive angle property.

Answer:

verticle angles theorem

Step-by-step explanation:

hope this helps :)

Answer:

an elephant can run 25 miles per hour

Step-by-step explanation:

60 minutes x 60 seconds = 3,600 seconds in an hour

3600 / 36 = 100

100 x .25 = 25 miles an hour

The degree of this polynomial is 9

Answer:

Answer in image

Step-by-step explanation:

Answer in image

Answer: 1.1 seconds

Step-by-step explanation:

leap = 4t²  ; leap = 4 ft 11 inches, find t

[tex]4\frac{11}{12} = 4t^2[/tex]

[tex]\frac{59}{12} = 4t^2[/tex]

[tex]\frac{59}{48} = t^2[/tex]

[tex]\sqrt{\frac{59}{12}} = \sqrt{t^2}[/tex]

[tex]\sqrt{1.23} = t[/tex]

1.1 = t

Answer:

The answer is C. AAA is not a congruency postulate because the side lengths may be different sizes although the angles are the same.

triangles ABC and DEF are congruent by the Side-Side-Side (SSS) postulate.

In other words, if two triangles have all three corresponding sides equal, then the triangles are congruent.

So the answer to the question is B. Congruent - SSS.

If triangles ABC and DEF are congruent, and if so, to name the postulate that applies.

The triangles are congruent because they have the same side lengths and angles. This can be seen from the following:

AD = BE (given)

∠ADB=∠BED (vertical angles)

AB = EF (given)

∠ABD=∠EBD (corresponding angles when  AD ∥ EF  )

BC = DF  (given)

Therefore, triangles ABC and DEF are congruent by the Side-Side-Side (SSS) postulate

Answer:

A) 0-37000-80049-9

Step-by-step explanation:

For a standard  bar code, it consists of a five digit manufacturer number and a five digit product number.  Check digits are a single digit computed from the other characters in the string of numbers. Check digits are on the far right.

Add the odd number digits: 0+7+0+8+0+9 = 24.

Multiply the result by 3: 24 × 3 = 72.

Add the even number digits: 3+0+0+0+4 =7.

Add the two results together: 72 + 07 = 79.

The last digit is 9

Answer:b

Step-by-step explanation: USA test prep

Answer:

x = 5

Step-by-step explanation:

720 = 2^4 × 3^2 × 5

√720 = 2^2 × 3 × √5

√(720×5) = 2^2 × 3 × 5

Answer:

39 feet

Step-by-step explanation:

Since the triangle is right we can use the tan ratio to find BC

tan 30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{68}[/tex]

multiply both sides by 68

68 tan 30° = BC ⇒ BC ≈ 39 feet ( to nearest foot )

Answer:

5 months

Step-by-step explanation:

The taxpayer can only deduct the first five months of the qualifying child. May is the fifth month. On June 1st, the qualifying child is going to be 14 years old. Therefore he cannot be included in work-related expenses as specified in the Publication 503 - Main Content from the IRS. Please see the Working-Related Expenses, Indent (b) which is as follows:

(b) The parent of your qualifying person if your qualifying person is your child and under age 13.

let's recall the pythagorean identity that sin²(θ) + cos²(θ) = 1.

[tex]\bf \cfrac{sin(x)}{1-cos(x)}-\cfrac{1-cos(x)}{sin(x)}=2cot(x) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{sin(x)}{1-cos(x)}-\cfrac{1-cos(x)}{sin(x)}\implies \cfrac{[sin(x)]^2-[1-cos(x)]^2}{sin[1-cos(x)]} \\\\\\ \cfrac{[sin^2(x)]-[1^2-2cos(x)+cos^2(x)]}{sin[1-cos(x)]}\implies \cfrac{sin^2(x)-1+2cos(x)-cos^2(x)}{sin[1-cos(x)]} \\\\\\ \cfrac{sin^2(x)-[\underline{sin^2(x)+cos^2(x)}]+2cos(x)-cos^2(x)}{sin[1-cos(x)]} \\\\\\ \cfrac{sin^2(x)-sin^2(x)-cos^2(x)+2cos(x)-cos^2(x)}{sin[1-cos(x)]}[/tex]

[tex]\bf \cfrac{-2cos^2(x)+2cos(x)}{sin[1-cos(x)]}\implies \cfrac{2cos(x)[-cos(x)+1]}{sin[1-cos(x)]}\implies \cfrac{2cos(x)[\underline{1-cos(x)}]}{sin[\underline{1-cos(x)}]} \\\\\\ \cfrac{2cos(x)}{sin(x)}\implies 2\cdot \cfrac{cos(x)}{sin(x)}\implies 2cot(x)[/tex]

Answer:

The correct answer is D. This statement describes Confucius.

Step-by-step explanation:

Confucius was a Chinese philosopher, whose teachings had a great influence in China, Korea, Japan and Vietnam.  According to tradition, he was born in the city of Qufu, in the Kingdom of Lu, now part of Shandong Province. He is said to have become Minister of Justice in Lu's kingdom. After being forced to resign, he toured the small kingdoms of northeast and central China, explaining his ideas about governance.  

He emphasizes his philosophy of morality, right social relationships, justice and honesty, both in personal life and in government. During the Han Dynasty period in China, his teachings became the official philosophy of the state. His teachings were introduced to Europe by the Jesuit Matteo Ricci, the first to Latinize his name as "Confucius."

Answer: D.

Step-by-step explanation:

52,165 + 49,872 = 102,037

Answer:

$3.6

Step-by-step explanation:

We are told that the pie store is having a 20% off sale on all of its pies. The pie you want regularly costs $18.

To find the amount saved with the discount let us find 20% of 18.

[tex]\text{The amount saved with discount}=\frac{20}{100}\times 18[/tex]

[tex]\text{The amount saved with discount}=0.20\times 18[/tex]

[tex]\text{The amount saved with discount}=3.6[/tex]

Therefore, the amount saved with the discount is $3.6.

Identity to verify:

[tex]\dfrac{\cot x}{1+\csc x}=\dfrac{\csc x-1}{\cot x}[/tex]

Recall that

[tex]\cos^2x+\sin^2x=1[/tex]

Divide both sides by [tex]\sin^2x[/tex] and we get

[tex]\cot^2x+1=\csc^2x[/tex]

or

[tex]\cot^2x=\csc^2x-1=(\csc x-1)(\csc x+1)[/tex]

So if we multiply the numerator and denominator of

[tex]\dfrac{\cot x}{1+\csc x}[/tex]

by [tex]\csc x-1[/tex], we get

[tex]\dfrac{\cot x(\csc x-1)}{(1+\csc x)(\csc x-1)}=\dfrac{\cot x(\csc x-1)}{\csc^2x-1}=\dfrac{\cot x(\csc x-1)}{\cot^2x}[/tex]

Then as long as [tex]\cot x\neq0[/tex], we can cancel terms to end up with

[tex]\dfrac{\csc x-1}{\cot x}[/tex]

and establish the identity.

You solve the substitution method to solve a system of equality by expressing one variable in terms of the other using one equation, and then plugging this expression in the other(s).

In this case, the first equation gives us a way to express n in terms of m. So, we can replace every occurrence of n in the second equation with the given formula.

The result is

[tex] 14m+2n=-8 \iff 14m+2(-7m-4)=-8 \iff 14m-14m-8=-8 \iff -8=-8 [/tex]

So, the second equation turned to be an equality, i.e. an equation where both sides are the same.

This implies that the system has infinitely many solutions, because every couple [tex] (n,m) [/tex] such that [tex] n=-7m-4 [/tex] is a solution to the system, because it satisfies both equations: the first is trivially satisfied, whereas the second is an identity, and as such is satisfied by any value of the variable.

Answer:

Exactly 12 years it will take for these trees to be the same height

Step-by-step explanation:

Slope intercept form: An equation of line is in the form of [tex]y = mx+b[/tex] where m is the slope or unit rate and b is the y-intercepts.

Let x represents the time in years and y represents the height of the tree.

Use conversion:

1 ft = 12 inches

As per the given statement:

Type A is 8 feet tall and grows at a rate of 3 inches per year.

⇒unit rate per year = 3 inches = [tex]\frac{1}{4}[/tex] ft

Then, we have;

[tex]y =\frac{1}{4}x + 8[/tex]                      ......[1]

Similarly for;

Type B  is 7 feet tall and grows at a rate of 4 inches per year.

⇒unit rate per year = 4 inches = [tex]\frac{1}{3}[/tex] ft

then;

[tex]y =\frac{1}{3}x + 7[/tex]                   .....[2]

To find after how many years it will take for these trees to be the same height.

Since, trees to be the same height;

⇒equate [1] and [2], to solve for x;

[tex]\frac{1}{4}x + 8 = \frac{1}{3}x +7[/tex]

Subtract 7 from both sides we get;

[tex]\frac{1}{4}x + 8-7= \frac{1}{3}x +7-7[/tex]

Simplify:

[tex]\frac{1}{4}x + 1= \frac{1}{3}x[/tex]

Subtract [tex]\frac{1}{4}x[/tex] from both sides we get;

[tex]1= \frac{1}{3}x-\frac{1}{4}x[/tex]

Simplify:

[tex]1 = \frac{x}{12}[/tex]

Multiply both sides by 12 we get;

x = 12

Therefore, exactly it will take for these trees to be the same height is, 12 years

Answer:

Step-by-step explanation:

Start with (1,2) . One of the pairs has to begin with a 1. Look around to see which set of points has a 1 for the x value.

B and C do. So all you have gotten rid of is A and D.  D looks like it might work, but it really does not. It has - 1 as it's starting point. The point must start with 1.

The next step is to find the distance between the 2 given points. The y value for the two points already on the graph is the same so they do not contribute anything to the distance. -3 and 1 are 4 units apart.

1 and ? must also be 4 units apart. Only D does. 1 and -3 are the x values 2 and 6 are the y values. The answer is B

Answer:

44

Step-by-step explanation:

diet : regular = 8:4

=> 88:44

Answer:

-9sqrt(5)

Step-by-step explanation:

-2 sqrt20 - sqrt125

Lets simplify the square roots

sqrt(ab) = sqrt(a)sqrt(b)

-2 sqrt(4) sqrt(5) - sqrt(25) sqrt(5)

-2 *2sqrt(5) - 5sqrt(5)

-4sqrt(5) -5sqrt(5)

-9sqrt(5)

[tex]\displaystyle\bf\\\text{\bf kinetic energy}=\frac{mv^2}{2}=\frac{54\times3^2}{2}=27\times9=\boxed{\bf243~J} \\\\\text{\bf Correct answer: D.}[/tex]

Answer:

The answer would be be D.243 j

Step-by-step explanation:

Answer:

6x^2 +81x - 17

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

7x-15

Step-by-step explanation:

We cannot solve for x since this is  an expression

((6x+9) (x+12) -sqrt(49+76) ^2

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

(49+7x) -64

Lets simplify the numerator

((6x+9) (x+12) -sqrt(49+76) ^2

Simplify what is inside the last parentheses

((6x+9) (x+12) -sqrt(125) ^2

Squaring a square root leaves the original number

((6x+9) (x+12) -(125)

FOIL the first two terms

First 6x*x = 6x^2

Outer:  6x*12 = 72x

Inner: 9x

Last : 9*12 = 108

Add them together

6x^2 +72x+9x+108 = 6x^2 +81x+108

Subtract the 125

6x^2 +81x+108-125

6x^2 +81x - 17

Now lets simplify the denominator

(49+7x) -64

49+7x-64

7x-15

6x^2 +81x - 17

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

7x-15

Answer:

ds/dt =8  when t =1.5

Step-by-step explanation:

s = t^2 + 5t - 8

We want to find ds/dt

ds/dt = 2t +5

evaluated when t=1.5

ds/dt = 2(1.5) +5

ds/dt = 3+5

ds/dt =8  when t =1.5

Replace t with 1.5 seconds and solve for s:

s = 1.5^2 + 5(1.5) -8

s = 2.25+7.5-8

s= 9.75 -8

s = 1.75

Rate of change is S/t

Rate of change = 1.75 / 1.5

Rate of change of s = 1.17