Marilyn buys pens that cost $12 per dozen. What is the cost of one pen?
$12.00
$24.00
$1.00
$1.20

Answer:

6610

Step-by-step explanation:

We have tan(X) = opposite/ adjacent

tan(QBP) = PQ/BQ

tan(35) = PQ/BQ    ---eq(1)

tan(QAP) = PQ/AQ

tan(20) = \(\frac{PQ}{AB +BQ}\)

\(=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}\)

230*tan(20) + PQ*tan(20)*tan(35) = PQ

⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)

⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]

\(PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}\)

\(= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4\)

PQ = 110.4

≈110

Height above sea level = 6500 + PQ

6500 + 110

= 6610

Answer:

  x = 8

Step-by-step explanation:

The angle with the expression in it is complementary to the 30° angle, so is 60°. Then we have ...

  4 +7x = 60

  7x = 56 . . . . . . subtact 4

  x = 8 . . . . . . . . .divide by 7

We can label the point (75, 50) as the optimal solution for the banquet, as it represents the maximum number of guests that can be invited while staying within the constraints.

What is banquet?

A banquet is a large formal meal that usually involves multiple courses and is served to a group of people on special occasions such as weddings, awards ceremonies, or fundraising events. Banquets often include speeches, presentations, and entertainment, and are typically held in a large venue such as a hotel ballroom, banquet hall, or conference center. Banquets can be hosted for a variety of purposes, such as to honor a special guest, celebrate an achievement, or raise money for a charitable cause.

To create a graph showing the solution region of the system of inequalities representing the constraints of the situation, we can use custom relationships to define the variables and constraints.

Let's define the variables:

Let x be the number of adult guests.

Let y be the number of student guests.

Now, let's write the system of inequalities representing the constraints of the situation:

The total number of guests cannot exceed 125: x + y ≤ 125

The cost of hosting the banquet cannot exceed $3375: 45x + 15y ≤ 3375

To graph this system of inequalities, we can plot the boundary lines of each inequality and shade the region that satisfies all the constraints.

The boundary lines of each inequality are:

x + y = 125 (the line that connects the points (0, 125) and (125, 0))

45x + 15y = 3375 (the line that connects the points (0, 225) and (75, 0))

To find the viable combinations of guests that satisfy all the constraints, we need to shade the region that is below the line x + y = 125 and to the left of the line 45x + 15y = 3375.

The resulting graph should look like this:

The point where the two lines intersect, (75, 50), represents the maximum number of adult guests (75) and the maximum number of student guests (50) that can be invited to the banquet while staying within the budget and venue capacity. Any point within the shaded region represents a viable combination of guests.

We can label the point (75, 50) as the optimal solution for the banquet, as it represents the maximum number of guests that can be invited while staying within the constraints.

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Answer:

Es el acronimo de la (Contraloría General de la República

Step-by-step explanation:

Espero ayudarte suerte

Significado de SGR. El significado de la sigla SGR es el acrónimo de Sociedades de Garantía Recíproca. El significado de la sigla SGR es el acrónimo de sociedad de garantía recíproca y pertenece a la categoría Europa. El significado de la sigla SGR es el acrónimo de Sociedad de Garantías Recíprocas.

Answer:

To solve this I would multiply both sides by 3

Step-by-step explanation:

i would use the multiplication property of equality

The property that justifies that action x/3=12 is a linear question using reciprocal law.

A linear equation has one or two variables.

explanation:-

x/3= 12

x = 12*3 ( using reciprocal)

hence x = 36

solving this we will get the valve of Y if x is given.

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Answer:

Step-by-step explanation:

\(\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}\)

Answer:

4/21

Step-by-step explanation:

first you need to make them both fractions, not mixed numbers. so it would be 2/5 divided by 21/10. then you flip the second number so you can multiply it : 2/5 * 10/21. 5 and 10 are divisible by 5 so you can cross 5 out and make a 1 and cross 10 out and make a 2: 2/1 * 2/21. then multiply and you get 4/21!

hope this helps!

Answer:

The answer to this problem is just 6t.

Answer:

The answer is not reasonable.

The error that Clayton made was that he accidentally added all of the products that had a saved price tag on it, he did not find the difference between the old price and the new, sales price.

Step-by-step explanation:

Hope this helps :) Mark me brainliest if anyone else answers this question.

Answer:

13 minutes and 30 seconds

Step-by-step explanation:

Okay so first you would divide 128 by 576. But since it takes her 3 minutes just to type 128 words you have to multiply 4.5 times 3. It will take her 13.5 minutes to type 576 words or 13 minutes and 30 seconds.

Step-by-step explanation:

points on the line: (4, -2) & (-5, 3)

gradient of the line = -5/9

general equation for all straight lines: y = mx + c

substitute one coordinate and the gradient into the equation. 3 = (-5/9)(-5) + c

therefore, c = 2/9

so the general equation is y = (-5/9)x + 2/9

Answer:

increases

Step-by-step explanation:

Since the lines goes up as the variable F increases( F is the horizontal variable), C will increase

Answer:

The line increases because u can obviously see the line going up...

Step-by-step explanation:

Answer:

hi wyd

Step-by-step explanation:

I want to know how u did this summer 1 time ok

The length of one side of the equilateral triangle in terms of x is 6x.

To find the length of one side of the equilateral triangle in terms of x, we need to consider the perimeter of both the rectangle and the equilateral triangle.

The perimeter of a rectangle is given by the formula:

Perimeter of rectangle = 2(length + width)

In this case, the length of the rectangle is 7x cm, and the width is 2x cm. Substituting these values into the formula, we have:

Perimeter of rectangle = 2(7x + 2x) = 2(9x) = 18x

We are told that the equilateral triangle has the same perimeter as the rectangle.

Since an equilateral triangle has all sides equal, the perimeter can be calculated by multiplying the length of one side by 3.

Therefore, we have:

Perimeter of equilateral triangle = 3(side length)

Since the perimeter of the equilateral triangle is equal to the perimeter of the rectangle (18x), we can set up the equation:

3(side length) = 18x

Dividing both sides of the equation by 3, we get:

side length = 6x

Hence, the length of one side of the equilateral triangle in terms of x is 6x.

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The complete question may be like: A rectangle measures 2x cm by 7x cm. An equilateral triangle has the same perimeter as the rectangle. What is the length of one side of the triangle in terms of x?

Let be "w" the number of people who won something in the raffle.

Answer:

The value of 9x+2 when x=3 is 29

Step-by-step explanation:

Algebraic Expressions

We are given the expression

9x + 2

And it's required to evaluate the expression when the value of x is 3.

It can be done by substituting x by 3:

9*3 + 2

=27 + 2

=29

The value of 9x+2 when x=3 is 29

Answer:

y=-5

Step-by-step explanation:

-10/2=2y/2

-5=y

y=-5

Answer:

y = - 5

Step-by-step explanation:

You have yo divided the numbers

Cancel terms that are in both the numerator and denominator

Move the variable to the left

Answer:

1/8 of a pound

Step-by-step explanation:

Gina's bag of gumdrops : 1/4 of a pound

Gina's + sister's bag of gumdrops : 3/8 of a pound

To find how much her sister's gumdrops weighed, you will have to subtract fractions.

Equation : 3/8 - 1/4 or 3/8 - 2/8

To subtract, you need to make sure the denominators are the same.

1 × 2

-------  =  2/8

4 × 2

Now, you can subtract. Subtract the numerators.

3/8 - 2/8 = 1/8

So, Gina's sister's red gumdrops weigh 1/8 of a pound.

Hope this helped !

Gina's sister's red gumdrops weigh 1/8 of a pound.

Let's use an equation to find the weight of Gina's sister's red gumdrops.

Let x be the weight of Gina's sister's red gumdrops in pounds.

According to the information given:

Gina's bag of black gumdrops weighs 1/4 pound.

Gina pays for both her gumdrops and her sister's red gumdrops, totaling 3/8 pound of gumdrops.

Weight of Gina's gumdrops (black gumdrops) + Weight of sister's gumdrops (red gumdrops) = Total weight of gumdrops purchased

1/4 + x = 3/8

Solve for x

x = 3/8 - 1/4

To subtract fractions, we need a common denominator, which is 8:

x = (3/8) - (2/8)

x = 1/8

Therefore, Gina's sister's red gumdrops weigh 1/8 of a pound.

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The start of the account = $104.23

The cost of 5 coffees = 5 * $5.23 = $26.15

The cost of the comic books = 7 * $6.99 = $48.93

The cost of groceries and delivery = $65.89 + $7.5 + $5 = $78.39

The cost of tickets for the next week = $120

So, the total costs = 26.15 + 48.93 + 78.39 + 120 = 273.47

So, the amount of money need to deposit = 273.47 - 104.23 = $169.24

The shape is a triangular prism with a triangular base, base area of 24in², height of 5in and volume of 40in³

The given solid is a triangular prism since its base figure is triangular in nature.

Since the base is a triangle, the area of the base is expressed as:

Area = 1/2 * base * height

Area of base = 1/2 * 6 * 8

Area of base = 24 square inches

The height of the solid is 5 inches and the required volume is calculated as:

Volume = BH/3

Volume = 24*5/3

Volume = 40 cubic inches

The shape is a triangular prism with a triangular base, base area of 24in², height of 5in and volume of 40in³

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Answer:

4

Step-by-step explanation:

This is wanting you to put a numerator that will make this fraction bigger then 2/4.

2/4 is greater then 1/6, so that won't work

2/4 is greater then 2/6, so that won't work either

2/4 is equal to 3/6 because they reduce to 1/2, so it won't work

2/4 is less then 4/6, this will work

any number bigger then 3 can be put in the ? spot

Answer:

n = 2m

Step-by-step explanation:

n being the number of movies

and m being the months

Answer:

Step-by-step explanation:

idek bro idek

Answer:

25

Step-by-step explanation:

l x w = h

25 x 7.2 = 180

Roman should invest $18,223.97 in order to withdraw $22450.15 in exactly 3.7 years from now if interest rate is 5.65 % compounded monthly.

First, convert R as a percent to r as a decimal

r = R/100

r = 5.65/100

r = 0.0565 per year,

Then, solve the equation for P

P = A / (1 + r/n)^(nt)

P = 22,450.15 / (1 + 0.0565/12)^{(12)(3.7)}

P = 22,450.15 / (1 + 0.0047)(44.4)

P = $18,223.97

The principal investment required to get a total amount of $22,450.15 from compound interest at a rate of 5.65% per year compounded 12 times per year over 3.7 years is $18,223.97.

Therefore, Roman should invest $18,223.97 in order to withdraw $22450.15 in exactly 3.7 years from now if interest rate is 5.65 % compounded monthly.

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a) Angle of line of sightFrom a point O in the school compound, Adeolu is 100 m away on a bearing N 35° E and Ibrahim is 80 m away on a bearing S 55° E. (a) How far apart are both boys? (b) (c) What is the bearing of Adeolu from point O, in three-figure bearings? What is the bearing of Ibrahim from point O, in three-figure bearings?The angle of the line of sight of Adeolu from the point O is given by:α = 90 - 35α = 55°.The angle of the line of sight of Ibrahim from the point O is given by:β = 90 - 55β = 35°.a) By using the Sine Rule, we can determine the distance between Adeolu and Ibrahim as follows:$

\frac{100}{sin55^{\circ}} = \frac{80}{sin35^{\circ}

100 sin 35° = 80 sin 55°=57.73 mT

herefore, both boys are 57.73 m apart. b) The bearing of Adeolu from the point O can be determined as follows:OAN is a right-angled triangle with α = 55° and OA = 100. Therefore, the sine function is used to determine the side opposite the angle in order to determine AN.

Thus:$$sin55^{\circ} = \frac{AN}{100}$$AN = 80.71 m.

To find the bearing, OAD is used as a reference angle. Since α = 55°, the bearing is 055°.

Therefore, the bearing of Adeolu from the point O is N55°E. c) Similarly, the bearing of Ibrahim from the point O can be determined as follows:OBS is a right-angled triangle with β = 35° and OB = 80. Therefore, the sine function is used to determine the side opposite the angle in order to determine BS.

Thus:$$sin35^{\circ} = \frac{BS}{80}$$BS = 46.40 m.

To find the bearing, OCD is used as a reference angle. Since β = 35°, the bearing is 035°.Therefore, the bearing of Ibrahim from the point O is S35°E. A boy walks 5 km due North and then 4 km due East. (a) Find the bearing of his current posi- tion from the starting point.

(b) How far is the boy now from the start- ing point?The boy's position is 5 km North and 4 km East from his starting position. The Pythagorean Theorem is used to determine the distance between the two points, which are joined to form a right-angled triangle. Thus

:$$c^2 = a^2 + b^2$$

where c is the hypotenuse, and a and b are the other two sides of the triangle. Therefore, the distance between the starting position and the boy's current position is:$$

c^2 = 5^2 + 4^2$$$$c^2 = 25 + 16$$$$c^2 = 41$$$$c = \sqrt{41} = 6.4 km$$

Therefore, the boy is 6.4 km from his starting point. (a) The bearing of the boy's current position from the starting point is given by the tangent function.

Thus:$$\tan{\theta} = \frac{opposite}{adjacent}$$$$\tan{\theta} = \frac{5}{4}$$$$\theta = \tan^{-1}{\left(\frac{5}{4}\right)}$$$$\theta = 51.34^{\circ}$$

Therefore, the bearing of the boy's current position from the starting point is N51°E.

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The term that should be added to the expression to make the expression perfect square trinomial is 169/4. The expression then becomes : (y - 13/2)²

What is meant by a perfect square trinomial?

By multiplying a binomial by another binomial, perfect square trinomials—algebraic equations with three terms—are created. A number can be multiplied by itself to produce a perfect square. Algebraic expressions known as binomials are made up of simply two words, each of which is separated by either a positive (+) or a negative (-) sign. Similar to polynomials, trinomials are three-term algebraic expressions.

A perfect square trinomial expression can be created by taking the binomial equation's square. If and only if a trinomial satisfying the criterion b² = 4ac has the form ax² + bx + c, it is said to be a perfect square.

Given expression y² - 13y + ?

Comparing with the general equation

a = 1

b = -13

For perfect square trinomial

b² = 4ac

(-13)² = 4 * 1 * c

169 = 4c

c = 169/4

So the expression becomes,

y² - 13y + 169/4 = (y - 13/2)²

Therefore the term that should be added to the expression to make the expression perfect square trinomial is 169/4.

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Answer:

Angle sum Theorem says that the sum of the measures of the interior angles of a triangle is 180 degrees. ... This creates alternate interior angles that are congruent. Sum of two interior angles equals the opposite exterior angle...33 + 87 = yy = 120°

Step-by-step explanation:

Answer:

\(\displaystyle A=\frac{20}{3}\)

Step-by-step explanation:

\(\displaystyle A=\int^2_{-2}(|x|-(x^2-2))\,dx\\\\A=2\int^2_0(x-(x^2-2))\,dx\\\\A=2\int^2_0(-x^2+x+2)\,dx\\\\A=2\biggr(-\frac{x^3}{3}+\frac{x^2}{2}+2x\biggr)\biggr|^2_0\\\\A=2\biggr(-\frac{2^3}{3}+\frac{2^2}{2}+2(2)\biggr)\\\\A=2\biggr(-\frac{8}{3}+2+4\biggr)\\\\A=2\biggr(-\frac{8}{3}+6\biggr)\\\\A=2\biggr(\frac{10}{3}\biggr)\\\\A=\frac{20}{3}\)

Bounds depend on whether you use -x or +x instead of |x|, but you double regardless. See the attached graph for a visual.