Trevor and Marissa together have 26 t-shirts to sell. If marissa has 6 fewer t shirts than trever, how many t shirts does Trevor have

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.

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:

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:

86%

Step-by-step explanation:

77% students are good students after 10 students join the school.

Percentage is a part of the whole number. It is denoted by % sign.

1 %= 1/100.

Given that,

The number of sophomores in the school = 100

Also, the percentage of good students = 85%

So, number of good students = 100x85/100 = 85

If 10 students join the group,

Then total number of students = 100+10 =110

Percentage of good students = 85 x 100/110

= 77.181

= 77%(round to whole number)

The percentage of good students is 77% in school.

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Answer:

The correct answer is option C, 228 feet

Step-by-step explanation:

As per Newton’s third law of motion:

V2 – U2 = 2 x a x S

Where V = final velocity

U = Initial Vlocity

a = acceleration (-ve)

S= distance travelled

V= 0 mph

U= 55 mph = 80.6667 ft /sec

0 – (80.6667 ft /sec)2 = 2 x (-g/2) x S

S = (80.6667 ft /sec)2 /(32.2 feet per second per second x0.5)

S = 202.1 feet

So the most nearest option is option C

Answer:

Correct choice is B

Step-by-step explanation:

The exponential regression model can be written as exponential function

[tex]y=a\cdot b^x.[/tex]

Then

[tex]5,000=a\cdot b^0=a,\\ \\5,510=a\cdot b^2\Rightarrow 5,510=5,000\cdot b^2,\\ \\b^2=\dfrac{5,510}{5,000}=\dfrac{551}{500}\Rightarrow b\approx 1.05.[/tex]

Thus,

[tex]y=5,000\cdot (1.05)^x.[/tex]

When [tex]x=12,[/tex] you get

[tex]y(12)=5,000\cdot (1.05)^{12}\approx \$8,980.[/tex]

Answer:

-7.77778

If you use google it will help u

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

[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:

5x + 2x = -7  

3y - 4y = -6

Step-by-step explanation:

Given the matrix, we can multiply across the constant matrix and down the  variable matrix

5x +2y = -7

3x -4y = -6

Answer: (C)

Step-by-step explanation:

When multiplying matrices:

Row 1 x Column 1 = the value in Row 1 Column 1

Row 2 x Column 1 = the value in Row 2 Column 1

Combine the two equations to get:

[tex]\left \{ {{5x + 2y = -7} \atop {3x - 4y = -6}} \right[/tex]

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 :)

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.

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.

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.

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

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:

-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)

Answer:

Step-by-step explanation:

It is the first one because a parabola cannot go sideways from a funtion because there are more than one y values for each x value

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:

y=8+6t

Step-by-step explanation:

Answer:

[tex]F(t)=6t+8[/tex].

Step-by-step explanation:

Let t represent number of hours.

We have been given that Carolina charges $6 for each hour of work. So amount charged for t hours of work would be [tex]6t[/tex].

Let us find initial cost by subtracting charges for 4 hours from 32 as:

[tex]\text{Initial cost}=32-4\times 6[/tex]

[tex]\text{Initial cost}=32-24[/tex]

[tex]\text{Initial cost}=8[/tex]

The total cost for t hours of work would be initial cost plus cost per hour: [tex]6t+8[/tex].

Our required function would be [tex]F(t)=6t+8[/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."

To find 5% of 220 files, convert the percentage to a decimal (5/100 = 0.05) and multiply it by 220. The result is 11, meaning 5% of 220 files is 11 files.

To calculate 5% of 220 files, you need to use the concept of percentage from basic mathematics. Here's a step-by-step explanation:

Understand that 'percent' means 'per hundred'. So, 5% can be expressed as 5/100.

Multiply the percentage (in this case, 5/100) by the total number of files (which is 220).

Perform the calculation: (5/100) times 220 = 0.05 times 220 = 11.

Therefore, 5% of 220 files is 11 files.

Answer:

B: (x + 2)(x - 3)^2

Step-by-step explanation:

This is only going to have 3 roots. One of them is (x - 3)

D does not look right. So let's solve it using synthetic division.

3 || 1    - 4      -3       18

            3       -3      -18

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

     1     -1       -6        0

So what you have is a quadratic

The answer is B

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]

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:

44

Step-by-step explanation:

diet : regular = 8:4

=> 88:44

Answer:

Step-by-step explanation:

General Remark

Let's start with the long way.

Each day 1 traditional candle (shamash) is lit along with a number of candles representing that day of Chanukah. I'm taking it that a new Shamash candle must be used each day.

Total Candles = 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 44

Givens

Formula

Sum = (a + L)*n/2

Solution

If this is wrong can you tell me what assumption I'm making that  is incorrect.

Answer: Your answer is Hanukkah

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:

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