Frank has constructed a tent in the shape of a square pyramid.



The peak of the tent is at 30 feet and is at a horizontal distance of 20 feet from the left edge. The height of the tent varies at a rate of 1. 5 feet with the horizontal distance from the left edge.

The equation that models the height of the tent, h, in feet, with respect to the horizontal distance in feet from the left edge, d, is h = |d − | +. The height of the tent is 22. 5 feet at a horizontal distance of feet

Answer:

Step-by-step explanation:

26° + 100°

= 126°

360° - 126°

234°

The point (2, 3) lies in the first quadrant.

Quadrant

The axes of a two-dimensional Cartesian system divide the plane into four infinite regions, called quadrants, each bounded by two half-axes.

These are often numbered from 1st to 4th and denoted by Roman numerals: I (where the signs of the (x; y) coordinates are I (+; +), II (−; +), III (−; −), and IV (+; −).

Cartesian system

The Cartesian coordinate system uses a horizontal axis that is called the x-axis and a vertical axis called the y-axis. Equations for lines in this system will have both the x and y variable.

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To find the missing side length of the acute angled triangle apply the cosine law as follow:

a² = b² + c² - 2bccosA

b² = a² + c² - 2accosB

c² = b² + a² - 2abcosC

As given in the question,

Given triangle is acute angled triangle.

Let us consider the measure of two sides and its included angle of the acute angled triangle is given.

Let the triangle be ABC,

Side opposite to ∠A, ∠B , and ∠C are a , b, and c respectively.

Apply cosine law to find the measure of the missing side in the acute angled triangle:

a² = b² + c² - 2bccosA

b² = a² + c² - 2accosB

c² = b² + a² - 2abcosC

Therefore, to get the measure of the missing side length in the acute angled triangle apply cosine law.

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Answer:

35° and 100°

Step-by-step explanation:

The total angle of a triangle = 180°
The total angle of two angles = 180° - 45° = 135°
One part of the ratio = 135° : (20 + 7) = 5°
The smaller angle = 5° x 7  = 35°
The bigger angle = 5° x 20 = 100°

Answer:

35° and 100°

Step-by-step explanation:

the sum of the 3 angles in a triangle is 180°

the ratio of 2 angles is 7 : 20 = 7x : 20x ( x is a multiplier )

equate the sum to the 3 angles to 180 and solve for x

45 + 7x + 20x = 180

45 + 27x = 180 ( subtract 45 from both sides )

27x = 135 ( divide both sides by 27 )

x = 5

Then

7x = 7 × 5 = 35

20x = 20 × 5 = 100

the measure of the 2 angles is 35° and 100°

The length BC of the right triangle is 18 units.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The length BC of the right triangle can be found as follows:

Therefore, using proportion because triangle ABC is similar to triangle BDC.

x / 36 = 9 / x

cross multiply

x × x = 36 × 9

x² = 324

square root both sides of the equation

x = √324

x = 18 units

Therefore,

BC = 18 units

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Answer: This is a horizontal translation so, the equation is f(x) = (x + 5). Whenever you translate to the right it is negative

Step-by-step explanation:

It typically means that the person is being friendly and is in a good mood.The expression =] is often used as an emoticon to express friendliness, positivity, and happiness. It can be used as a stand-alone expression or as part of a longer sentence.

The expression =] is commonly used in text conversations as an emoticon to express friendliness, positivity, and happiness. It is typically used when a person wants to convey a feeling of warmth and good cheer. The expression can be used as a stand-alone expression or as part of a longer sentence. When used alone, it has a meaning similar to a smiley face and can be used to respond to a message in a positive way. When used as part of a longer sentence, it can be used to express a feeling of contentment. As an emoticon, it has no specific meaning, but it can be used to show that the person is in a positive and good mood. Using this expression can be a way to show that you are happy and in a friendly mood.

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On solving the provided question we can say that - her in the equation  14w + 3p = 70.50 and 10w+7p = 62.50 , w = 12; p = 18

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

[tex]14w + 3p = 70.50 \\[/tex]

10w+7p = 62.50 ,

[tex]w = 12\\[/tex]

p = 18

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He must purchase 3 packages of hot dogs and 2 packages of hot dog buns for a total of 24 hot dogs with buns if he doesn't want to have any leftover hot dogs or buns. You should be aware that students might respond with 24, which is the least common multiple of 8 and 12.

The hot dog buns most frequently used in the American region of New England and its cuisine are New England-style hot dog buns, also referred to as New England hot dog buns or top-loading hot dog buns.

As you can see, "hot dog" is a versatile word that can be used as a noun, verb, adjective, or even as an exclamation.

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For the polynomial 9, 3x², 8x; the degree is 2 and the leading coefficient is 3

An equation is used to show the relationship between numbers and variables.

Polynomial is an expression composed of variables, constants and exponents using mathematical operations such as addition, subtraction, multiplication and division

The degree is the highest exponent of variable for the polynomial. The polynomial with degree of 2 is known as a quadratic polynomial

Given the polynomial:

9, 3x², 8x

Writing in standard form is done by rearranging from highest exponent of variable to least. This is:

3x², 8x, 9

Hence the degree is 2 and the leading coefficient is 3

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Answer:

85+7.5v=160

7.5v=160-85

7.5v=75

V=75/7.5

V=10

Ryan would need to take 10 visits to get a free ticket.

Answer:

Step-by-step explanation:

1.change minutes to hours,45 minutes is [tex]\frac{3}{4}[/tex] hours

2.then use 390÷    [tex]\frac{3}{4}[/tex]=390·[tex]\frac{4}{3}[/tex]=130·4=520 nautical per hour

In order for a triangle to shrink in size but stay proportional to its original size, the scale factor, K, must be between zero and one.

What is scale factor?

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

In order for a triangle to shrink in size but stay proportional to its original size, the scale factor, K, must be between zero and 1.

The image is contracted if the scale factor is less than 1 (0< k <1).

The image is enlarged if the scale factor is more than 1 (k > 1).

The image remains the same if the scale factor is 1 (k = 1).

Hence, the scale factor k should be between 0 and 1.

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The pair of linear equations 3x + 2y = 5 and 2x + 3y = 7 has no solution.

To solve these equations, we will use the method of elimination.

We start by multiplying the first equation by 2:

6x + 4y = 10

Now we add both equations together:

6x + 4y + 2x + 3y = 10 + 7

Combining like terms, we have:

8x + 7y = 17

We can now solve for x by dividing both sides by 8:

x = 17/8

Now we can substitute this value of x into either of the original equations to solve for y:

3(17/8) + 2y = 5

51/8 + 2y = 5

2y = 5 - 51/8

2y = -41/8

y = -41/16

However, this value for y is not a real number, so there is no solution for the pair of linear equations.

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The final answer is 4x, which is the simplest form of expression.

What is the rational exponent?

A rational exponent is an exponent that is in the form of a ratio of two integers, such as a/b where a and b are integers and b is not equal to zero.

To rewrite the expression in simplest rational exponent form, we can first simplify the radicals and then combine any like terms. Here are the steps to simplify the given expression:

4√x* √x = 4 * 1 √x * √x = 4 * x^(1/2) * x^(1/2) = 4 * x^( (1/2)+(1/2) ) = 4 * x^(1)

x^(1) = x

So, the expression in simplest rational exponent form is 4x

x * 4x = 4x

Notice that 4 and x are in the same radical which means 4 is a coefficient of x.

Therefore, 4√x * √x can be written as 4x, which is in the simplest form.

hence, the final answer is 4x, which is the simplest form of expression.

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Answer:

1.

(a) 4y

(b) 5w

(c) 6a

(d) 3s

(e) 2n

(f) 3g

(g) 2y

(h) 0

2.

(a) -2u

(b) -w

(c) -3a

(d) -7y

3.

(a) 7a+3b

(b) 12y+4h

(c) 2g+10a

(d) 15m+10p

(e) 10e+4

(f) 12+5a

Step-by-step explanation:

Don't be intimidated by the "letter" variables. It is really just simple addition and subtraction. Examples:

For Q1=

y + y + y + y = 4y because there are 4 y's, and since we don't know the values of the y, this is the farthest we can simplify it.

For Q2=

4u - 6u = -2u. Since these two numbers have the same variable, this is just a simple subtraction problem. 4 - 6 = -2.

For Q3=

3a + 2b + 4a + b = 7a + 3b.

Look for the numbers with the same variable. 3a and 4a both have a's, so we add the two and get 7a. 2b and b (b is the same thing as 1b) both have b's, so we add them and would get 3b.

Therefore, the answer is 7a + 3b.

I hope this helped! Good luck with future endeavors!!

Step-by-step explanation:

attached the answers below, hope that helps...

Answer:

hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

Step-by-step explanation:

1.3338 is the likelihood, The probability of anything occurring is known as probability.

The probability of anything occurring is known as probability. To determine probability, divide the total number of possible outcomes by the number of possible ways an event could occur.

The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities.

Explanation:

Mean (m) = 25

The standard deviation is 13

Sample size (n) is 95.

Chance that x will fall between 22 and 27.

Zscore = x - mean / s / n

If x = 22, Zscore is equal to (22 - 25) / (13/95).

For x = 27, Zscore is equal to (27 - 25) / (13/95) / n = 13 / 95, which is 1.3338.

1.3338 is the likelihood.

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Answer:

Factor the numerator and denominator and then divide out any common factors.

Step-by-step explanation:

Tyler drove 40 miles in one hour.

To find how far Tyler drove in one hour, we need to divide the total distance he traveled (52 21/32 miles) by the total time it took him (1 2/3 hours). To do this, we first need to convert the time to a common denominator, which in this case is 32. We can convert 1 2/3 hours to 32/3 hours by multiplying the numerator and denominator of 2/3 by 32/32.

So, we have:

(52 21/32) miles / (32/3) hour = (52 21/32) miles * (3/32) hour

                                                = (52 21/32) * (3/32)

                                                = (52 213/3232)

                                                = (52 63/32) miles/hour

                                                = 40 miles/hour

So, Tyler drove 40 miles in one hour.

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65 seats in 20th row.

Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value. It is represented by the proportional symbol, ∝. In fact, the same symbol is used to represent inversely proportional, the matter of the fact that the other quantity is inverted here.

Given,

No. of seats in 3rd row = 31

No. of seats in 6th row = 37

Seats increase at a constant rate

Let k is the rate of increment.

Difference between no. of seats = k × difference between no. of rows

Difference of seats in 3rd and 6th rows = k difference between the no. of rows

37 - 31 = k ×(6-3)

6 = 3k

k = 2

Thus, we can determine

Difference between the no. of seats is twice the difference between the no. of rows.

Difference between 6th and 20th row = 14 rows

Hence the difference between number of seats = 2 × 14 = 28 seats.

No. of seats in 20th row = No. of seats in 6th row + 28 seats

No. of seats in 20th row = 37 + 28 = 65

Hence, there will be 65 seats in 20th row.

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You can ride in many places, so be sure to look for hazards that could cause injury or other risks while bicycling.

The number of miles you can cycle in a single day is unlimited. It depends on your level of fitness, your exercise regimen, and the distance you cycle. Starting out, 10 kilometres per day is OK.

If you're an experienced cyclist who can pedal 25–30 miles every day, 45 miles is a realistic limit.  You can ride a certain bike trail. By riding a bike to work, you can get in shape. If you've never rode a bike before, start out slowly. If you ride your bike for at least three miles every day, you might be able to travel further.

You may be able to make the most of your speed sensor’s accuracy, depending on how accurate it is. You need to know exactly how much effort you put in during your rides.

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The degree of the polynomial  [tex]2yA^2yA^32y^8[/tex] is 15

A polynomial's degree is the sum of the degrees of its monomials with non-zero coefficients. A term's degree is the sum of the exponents of the variables in it, and it is thus a non-negative integer.

The degree of a polynomial is the highest or largest power of a variable in a polynomial equation. The degree denotes the polynomial with the maximum exponential power (ignoring the coefficients).

Consider the following polynomial expression with two variables: [tex]x^3 + 6x^2y^4 + 3y^2+5[/tex]

The polynomial has a degree of 6.

This is because the exponent values of x and y in the second term of the algebraic formula, [tex]6x^2y^4[/tex], are 2 and 4, respectively. We get 6 when we sum the exponent values. As a result, the multivariable polynomial expression has a degree of 6.

As per question, polynomial is: [tex]2yA^2yA^32y^8[/tex]

The total sum of power is: 1+2+1+3+8=15

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Determine how many square centimeters make up a square meter in order to determine how long Marc will have brownies before they run out.

We must first determine the number of square centimeters in a square meter in order to determine how many days Marc has left of brownies before they run out. A square meter has 3.6 square meters in it.

Because of this, Marc has access to brownies for 3.6 days until they are finished.

Knowing the dimensions of a square or rectangle will allow you to compute its square meters. Also known as the shape's area, this term is used. Length times width equals m2, which is the formula used to calculate square meters. As an illustration, if your square is 3 meters long and 2 meters wide, 3 x 2 equals 6 meters2.

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The ∆ABX and ∆CDX formed after the mutual bisection of AC and BD each other at point X are congruent i.e ΔABX ≅ ΔCDX, by SAS congruance theorem.

SAS congruence theorem: "SAS " stands for "Side-Angle-Side". If there is two sides and the angle between these two sides are congruent to the corresponding sides and angle of another triangle, then the two triangles are said to be congruent. We have , A Quadrilateral ABCD, such that AC and BD bisect each other at point X. After bisection there is formed 4 triangles. We have to show ΔABX ≅ ΔCDX by SAS Congruance Rule. Now, as we know that bisect point divides the sides into two equal parts, i.e, AX = CX and DX = BX. So, in ΔABX and ΔCDX

As we see ∠AXB is angle in between to two sied AX and BX . Similarly, ∠CXD is in between CX and DX . So, by using SAS congruance theorem ∆ABX is congruent to ∆CDX i.e., ΔABX ≅ ΔCDX.

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The equations of the commissions are

From the question, we have the following parameters that can be used in our computation:

Also from the question, we have:

This means that:

Commission = Unit rate * Commission proportion * Number of pieces

Using the above as a guide, we have the following:

Sara: y = 25 * 60% * x

Ravi: y = 2000 * 25% * x

Evaluate

Sara: y = 15x

Ravi: y = 500x

See attachment for the graph of the commission equations

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For k=0 or k=3, the given equation will be a perfect square.

Note:  we are taking the equation to be: (4−k) X^2+(2k+4) x+8k+1=0

Taking,

(4−k) X2+(2k+4) x+8k+1=0

Here, a=4+k, b=2k+4, c=8k+1

The given equation will be a perfect square, When D= 0

We know, D = b^2−4ac [A perfect square trinomial is an expression that can be generated from the square of a binomial equation. If an equation has the formula ax^2 + bx + c and meets the requirement b^2 = 4ac, it is referred to as a perfect square trinomial. The formula for the perfect square has the following variations: ax2 + 2abx + b2 = (ax + b). When b^2 = 4ac, we know that an equation is a perfect square.]

b2−4ac=0

(2k+4)2−4(4−k) (8k+1) =0

4k2+16+16k−4(32k−8k2+4−k) =0

K2+4+4k−32k+8k2−4+k=0

9k2−27k = 0

K2−3k = 0

k(k−3) =0

k=0 or k=3

Hence for k=0 or k=3, the given equation will be a perfect square.

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In slope-intercept form, the equation of the line passing through the points (5.-4) and (-1,8) is y = -4x + 8 .

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter.

given

the points (5.-4) and (-1,8)

slope = [tex]m = \frac{y2 - y1}{x2 - x1}[/tex]

slope intercept form = y = mx + c

To find the equation of the line that passes through the points (5, -4) and (-1, 8),

The slope and the intercept by the slope intercept form = y = mx + c .

The slope is -4 and the intercept is 8.

In slope-intercept form, the equation of the line passing through the points (5.-4) and (-1,8) is y = -4x + 8 .

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