the regular price of any souvenir at a gift shop is x dollars. During a sale today, if a customer purchases one souvenir at its regular price, the price of each additional souvenir will be 0.3x less than the regular price. if carmen purchases 10 souvenirs today, and x=$30, what does carmen pay

The solutions to the equation x² - 18x + 81 = 4 by completing the square are x = 9 + 2i and x = 9 - 2i.None of the answer choices A, B, C, or D are correct.

An equation is a mathematical statement that shows the equality between two expressions, often containing variables and mathematical operations.

To solve the equation x² - 18x + 81 = 4 by completing the square, we can follow these steps:

x² - 18x + 77 = 0

Divide both sides by the coefficient of x² to make the coefficient 1:

x² - 18x + (81/1) = -77/1

x² - 18x + 81 = -77

Add the square of half the coefficient of x to both sides of the equation:

x² - 18x + (9)² = -77 + (9)²

x² - 18x + 81 = -4

(x - 9)² = -4

x - 9 = ±√(-4)

x - 9 = ±2i (where i is the imaginary unit)

x = 9 ±2i

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Answer:

[tex]x-1/x^2 +5x+4[/tex] = no real value

Step-by-step explanation:

Step 1 : Multiply through by x^2

[tex]x^{2} -1 +5x^{3}+ 4x^{2}[/tex]

Step 2 : Collect like terms

[tex]5x^{3}+5x^{2} -1\geq 0[/tex]

Step 3 : Ignore the sign and solve for x

[tex]5x^{3} +5x^{2} -1 = 0\\x =0.380609458\\x= 0.4(2dp)[/tex]

Step 4 : Input back into the equation

Step 5: This shows that  x-1/x^2 +5x+4 has no real values.

The solution of this expression is 37

To solve this, first calculate the operations in parentheses.
Then perform the other operations, following the order of resolution

[tex]\begin{array}{l}\sf (6 + 3)2-17\times 3 + 70\\\sf 9\times 2-51+ 70\\\sf 18-51+ 70\\\sf 88-51\\\therefore \bf 37\end{array}[/tex]

For this expression, the result is 37

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The total of the first four terms is thus 8/3.

The outcome of adding two or even more numbers or phrases is known as the sum in mathematics. The sum is a method of bringing things together as a result. To put it another way, adding any number of numbers together results in a previous result or total.

The sum of a Fibonacci sequence that has the initial component a = 1 and the general ratio r = 5/3 is determined using the formula you gave.

We enter these numbers into the formula to determine the sum of the initial n terms:

S(n) = [tex]a(1-r^n)/(1-r)[/tex]

S(n) = [tex]1(1-(5/3)^n)/(1-5/3)[/tex]

S(n) = [tex]3/2(1-(5/3)^n)[/tex]

So, we add n to this formula to get the sum of the initial n terms of a given sequence:

S(n) = [tex]3/2(1-(5/3)^n)[/tex]

For instance, we replace n = 4 to get the sum of the initial four terms:

S(4) = [tex]3/2(1-(5/3)^4)[/tex]

S(4) = 3/2(1-625/81)

S(4) = 3/2(144/81)

S(4) = 72/27

S(4) = 8/3

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The total of the first four terms is thus 8/3.

The outcome of adding two or even more numbers or phrases is known as the sum in mathematics. The sum is a method of bringing things together as a result. To put it another way, adding any number of numbers together results in a previous result or total.

The sum of a Fibonacci sequence that has the initial component a = 1 and the general ratio r = 5/3 is determined using the formula you gave.

We enter these numbers into the formula to determine the sum of the initial n terms:

S(n) = [tex]a(1-r^{n} )/(1-r)[/tex]

S(n) = [tex]1(1-(5/3)^{n} /(1-5/3)[/tex]

S(n) = [tex]3/2(1-(5/3)^{n} )[/tex]

So, we add n to this formula to get the sum of the initial n terms of a given sequence:

S(n) = 3/2(1 - [tex](5/3)^{n}[/tex] )

For instance, we replace n = 4 to get the sum of the initial four terms:

S(4) = [tex]3/2(1-(5/3)^{4} )[/tex]

S(4) = 3/2(1-625/81)

S(4) = 3/2(144/81)

S(4) = 72/27

S(4) = 8/3

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complete ques is:

Find the sum of the first n terms ( 1,2,3,4,5.......n)

using the formula:

a(1-r^n)/1-r

1, 5/3, 25/9, 125/27, 625/81

so hmmm 25% of that 300,000 is going as a downpayment, so he need the loan for the remaining 75% of that hmmm

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{75\% of 300000}}{\left( \cfrac{75}{100} \right)300000}\implies 225000[/tex]

so for that much, so since he'll be making monthly payments, the compounding period will be monthly, now, we're assuming the payments are at the end of each month.

[tex]~~~~~~~~~~~~\underset{\textit{payments at the end of the period}}{\textit{Payments of an ordinary annuity}} \\\\ pmt=A\left[ \cfrac{\frac{r}{n}}{\left( 1+\frac{r}{n} \right)^{nt}-1} \right][/tex]

[tex]\begin{cases} A=\textit{accumulated amount}\dotfill &225000\\ pmt=\textit{periodic payments}\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &25 \end{cases}[/tex]

[tex]pmt=225000\left[ \cfrac{\frac{0.02}{12}}{\left( 1+\frac{0.02}{12} \right)^{12 \cdot 25}-1} \right] \\\\\\ pmt=225000\left[ \cfrac{\frac{1}{600}}{\left( \frac{601}{600} \right)^{300}-1} \right]\implies pmt\approx 578.67[/tex]

The area of the shaded sector is equal to: A. 415π/2 ft².

Mathematically, the area of a sector can be calculated by using this formula:

Area of sector = θπr²/360

Where:

Substituting the given parameters into the area of a sector formula, we have the following;

Area of sector = 332(π/180) × (15)²/2

Area of sector = 74,700π/180 × 1/2

Area of sector = 415π/2 ft²

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Answer: To find the points where the circle intersects the line x=1, we substitute x=1 in the equation of the circle:

2(1)² + 2y² - 5(1) + 7y - 36 = 0

Simplifying, we get:

2y² + 7y - 31 = 0

We can solve this quadratic equation by using the quadratic formula:

y = (-7 ± √(7² - 4(2)(-31))) / (2(2))

y = (-7 ± √225) / 4

y = (-7 ± 15) / 4

So the two possible values of y are:

y = 2 or y = -8/2 = -4

Therefore, the points where the circle intersects the line x=1 are (1, 2) and (1, -4).

Step-by-step explanation:

Answer:  What an entrepreneur really is, though, is someone who runs their own business and takes a risk to do it.

Step-by-step explanation:

Based on division operation, the number of boxes of papers that the back of Nico's truck can stack in is 224.

Division operation is one of the four basic mathematical operations, including addition, subtraction, and multiplication.

Division operation involves the dividend divided by the divisor to produce a result known as the quotient.

In this situation, the volume of Nico's truck is determined as the dividend. The volume of each box of paper is determined as the divisor.

The result of the division operation is the quotient showing the number of boxes the truck can contain.

The length of Nico's truck = 7 feet

The width of Nico's truck = 4 feet

The height of Nico's truck = 8 feet

The volume that Nico's tuck can contain = 224 cubic feet (7 × 4 × 8)

= 224 feet³

The length of each box = 1 foot

The width of each box = 1 foot

The height of each box = 1 foot

The volume of each box of papers = 1 feet³ (1 × 1 × 1)

The number of boxes the truck can contain = 224 boxes (224/1)

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The cοrrect respοnse is that mοney cοllects interest and mοney is safe and insured.

The fee yοu spend tο bοrrοw the mοney οr the fee yοu pay tο lend the mοney is called interest. Interest is frequently calculated as a yearly percentage οf the amοunt bοrrοwed. This percentage represents the lοan's interest rate.

Interest equals P, R, and T is the fundamental interest fοrmula. P is the initial value (the beginning balance). Rate οf Interest, R (usually per year, expressed as a decimal). T is the sum οf all time frames (generally οne-year time periοds).

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It can be estimated that approximately 3,042 people in attendance would prefer ketchup on a hot dog.

Thus, the correct answer is 3,042.

To determine how many people in attendance would prefer ketchup on a hot dog based on the data from the sample, we need to calculate the proportion of people who prefer ketchup and apply it to the total attendance.

The sample indicates that out of 150 people surveyed:

54 people prefer ketchup

36 people prefer relish

60 people prefer chili

To find the proportion of people who prefer ketchup, we divide the number of people who prefer ketchup by the total number of people surveyed:

Proportion of people who prefer ketchup = 54 / 150 = 0.36

Now, to estimate the number of people in attendance who would prefer ketchup on a hot dog, we multiply the proportion calculated above by the total attendance:

Estimated number of people who prefer ketchup = 0.36 [tex]\times[/tex] 8,450 = 3,042

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Alternatively, if we want to solve for r in terms of h, we can rearrange the equation as follows: r = h - 35

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Let h be the height of the railing from the ground and let r be the height of the ramp from the ground.

We are given that the railing is 35 inches above the ramp, which means that the total height of the railing from the ground is h = r + 35.

So the equation that represents the situation is:

h = r + 35

Therefore, Alternatively, if we want to solve for r in terms of h, we can rearrange the equation as follows: r = h - 35

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The perihelion is the point in a planet's orbit where it is closest to the sun.

The equation for the orbit of a planet around the sun depends on various factors, such as the shape of the orbit, the mass of the planet, and the gravitational force between the planet and the sun. Kepler's laws of planetary motion provide a framework for understanding the motion of planets in orbit, and the equations used to describe these orbits are generally based on these laws. The specific equation for the orbit of planet A would depend on the specific parameters of that planet's orbit.

Answer:

The equilibrium price is $250.

The equilibrium quantity is 26 units.

Step-by-step explanation:

To find the equilibrium price, we need to find the price at which the quantity demanded equals the quantity supplied. This occurs when q (quantity demanded) equals q (quantity supplied).

So, we can set the two equations for q equal to each other:

(380-p)/5 = (p-172)/3

To solve for p, we can cross-multiply and simplify:

3(380-p) = 5(p-172)

1140 - 3p = 5p - 860

1140 + 860 = 8p

2000 = 8p

p = 250

Therefore, the equilibrium price is $250. We can plug this value back into either equation for q to find the equilibrium quantity.

Using q = (380-p)/5, we get:

q = (380-250)/5 = 26

So the equilibrium quantity is 26 units.

Answers:

Increasing:  [tex](-1.5, 2)[/tex]

Decreasing:  [tex](-\infty,-1.5) \cup (2,\infty)[/tex]

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

Explanation:

A function curve is considered increasing when moving uphill as you move to the right.

We're going uphill on the interval [tex]-1.5 < \text{x} < 2[/tex] which translates to the interval notation [tex](-1.5, 2)[/tex]. Be sure not to confuse this with ordered pair notation which unfortunately looks identical. The curved parenthesis are used to exclude each endpoint.

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

When moving to the right, we go downhill on two separate regions:

The first portion translates to the interval notation [tex](-\infty,-1.5)[/tex]

The second portion translates to [tex](2,\infty)[/tex]

We glue those regions together with a union symbol to get [tex](-\infty,-1.5) \cup (2,\infty)[/tex]

The union symbol basically means "or" when it comes to interval notation. So we are decreasing on the interval [tex](-\infty,-1.5)[/tex] or decreasing on the interval [tex](2,\infty)[/tex]

The value of the expression is between 7/9 and 8, since 7/9 < 56/9 < 8. So the correct option is D.

Algebraic expressions can represent real-world situations, formulas, and equations. They are commonly used in algebra, which is a branch of mathematics that deals with symbols and the rules for manipulating these symbols.

Algebraic expressions are important tools in solving equations and real-world problems that involve variables and unknowns. They are also used in calculus, physics, engineering, and other fields that require mathematical modeling and analysis.

The value of the expression 8×7/9 can be simplified using the order of operations (PEMDAS) as follows:

8×7/9 = (8×7)/9 = 56/9

Therefore, the value of the expression is between 7/9 and 8, since:

7/9 < 56/9 < 8

So the correct statement is: D) between 7/9 and 8.

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Answer: We have the equation:

24,816,000 = x / 10^5

To solve for x, we can multiply both sides by 10^5:

24,816,000 * 10^5 = x

Using a calculator or long multiplication, we can simplify this to:

2,481,600,000,000 = x

Therefore, 24,816,000 is equal to 2,481,600,000,000 divided by 10 to the fifth power.

Step-by-step explanation:

Answer:

x = 10

Step-by-step explanation:

A trapezoid is a quadrilateral with one pair of parallel sides.

The median of a trapezoid connects the midpoint of the non-parallel sides.

IJ is the median of the trapezoid. I is the midpoint of EH, and J is the midpoint of GF.

Also, the median of a trapezoid is also parallel to the parallel sides. IJ║ HG║ EF.

(The proof of this is extensive and requires drawing additional lines such as HJ and extending EF further until HJ and EF intersect at another point, Y. It is given as the other diagram. You also need prior knowledge of the midsegment of a triangle.)

The measure of the midsegment of a trapezoid, by definition, is also equal to the average of the measure of the parallel segments.

In the figure,

[tex]IJ=\dfrac{(HG+EF)}{2}[/tex]

Substituting the values we have, HG = 8, EF = 12 gives us:

[tex]IJ=\dfrac{(HG+EF)}{2}[/tex]

[tex]IJ=\dfrac{(8+12)}{2}[/tex]

[tex]IJ=\dfrac{20}{2}[/tex]

[tex]IJ=10[/tex]

IJ is 10 units.

The length of AB which is the missing length side of the similar triangles would be = 28 cm.

To calculate the missing length of the triangle = AB , the scale factor should be determined.

The scale factor that exists between two similar object shows the number of times the original object can be found in the new formed one.

The scale factor = dimensions of new object/ dimensions of original object.

A side of original = EF =22cm

A side of the new triangle = BC = 44

Scale factor = 44/22 = 2

Therefore the missing length of the new triangle = 14×2 = 28cm

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The expressiοn fοr each area is 28x²-35x ( rectangle ), 9x² ( square ), and 37x²-35x ( tοtal area ).

A sοlid οbject's surface area is a measurement οf the οverall space that the οbject's surface takes up. The tοtal area includes bοth the Carpet Area and Exclusive Areas as well as all οther lands within the Prοperty's perimeter bοrders.

Here, we have

Given: Helena wants tο change the figure shοwn intο twο οr mοre figures sο she can mοre easily find the area.

The figure is cοmpοsed οf a square and a rectangle. See the attached image.

Therefοre, yοu shοuld sum the area οf these geοmetric figures fοr determining the area οf the irregular figure.

Area οf the rectangle = bh.

The figure shοws that the sides fοr this rectangle are equal tο 4x-5 and (4x+3x). Then,

b = length οf the base= 4x-5

h = height = 4x+3x = 7x

A rectangle = bh = (4x-5)*7x = 28x²-35x

Area οf the square =  l². The figure shοws that the sides fοr this square are equal tο 3x

l = length οf the side= 3x

Thus,  A square = l² = (3x)² =9x²

We have tο find an expressiοn fοr the tοtal area οf the figure.

A tοtal= A rectangle+ A square

A tοtal= 28x²-35x+9x²

A tοtal= 37x²-35x

Hence, The expressiοn fοr each area is 28x²-35x ( rectangle ), 9x² ( square ), and 37x²-35x ( tοtal area ).

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Answer:

Step-by-step explanation:

To write the equation of the line that passes through the points (3, -4) and (7, 6), we can follow these steps:

Step 1: Find the slope of the line

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:

slope = (y2 - y1) / (x2 - x1)

Plugging in the given values, we get:

slope = (6 - (-4)) / (7 - 3)

slope = 10 / 4

slope = 5 / 2

Step 2: Use point-slope form to write the equation of the line

Point-slope form of a line with slope m passing through a point (x1, y1) is given by:

y - y1 = m(x - x1)

We can use either of the given points to write the equation. Let's use (3, -4):

y - (-4) = (5/2)(x - 3)

Simplifying this equation, we get:

y + 4 = (5/2)x - (15/2)

Subtracting 4 from both sides, we get:

y = (5/2)x - (23/2)

This is the equation of the line in point-slope form.

Step 3: Simplify the equation if it is not in point-slope form

The equation we obtained in step 2 is already in point-slope form, so we do not need to simplify it any further.

Note: If the line was horizontal (i.e., it had zero slope), then its equation would be y = constant, where the constant is the y-coordinate of any point on the line. If the line was vertical (i.e., its slope was undefined), then its equation would be x = constant, where the constant is the x-coordinate of any point on the line.

Answer:

K150

Step-by-step explanation:

10 x K2.00 = K20.00

20 x K5.00 = K100.00

10 x K3.00= K30.00

20+100+30= K150

Answer:

Let's call the height of the antenna "h".

First, we can use the angle of elevation of 38^{\circ} ∘ to find the height of point A above the ground.

tan(38^{\circ}) = \frac{h}{21}

h = 21 \cdot tan(38^{\circ})

h \approx 15.6

So point A is approximately 15.6 meters above the ground.

Next, we can use the angle of elevation of 46^{\circ} ∘ to find the height of point B above the ground.

tan(46^{\circ}) = \frac{h}{d}

h = d \cdot tan(46^{\circ})

We can find the value of "d" using the Pythagorean theorem.

d^2 = 21^2 + 15.6^2

d \approx 25.7

So the distance from point A to point B is approximately 25.7 meters.

Finally, we can use the height of point A and the distance from point A to point B to find the height of point B (the height of the antenna).

h = d \cdot tan(46^{\circ})

h \approx 25.7 \cdot tan(46^{\circ})

h \approx 23.2

Therefore, the height of the antenna is approximately 23.2 meters.

Step-by-step explanation:

the scenario creates 2 right-angled triangles.

both have the same first leg : the horizontal distance from Avani's eyes to the building (21 m).

and both have a right angle (90°) at the point, where the horizontal distance meets the building.

the difference is now the second leg : the height of the building (starting at 1.66 m above ground), and the height of the building plus the height of the antenna (again starting at 1.66 m above ground).

another difference is the length of the line of sight (from Avani to AA, and from Avani to BB).

driving these differences is the difference in the angle at Avani (38° vs. 46°).

now, remember the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

a, b, c are the sides of the triangle, A, B, C are the corresponding opposite angles of the triangle.

and remember : the sum of all angles in a triangle is always 180°.

what is the plan ?

we need to calculate the second leg of the larger triangle, and then the second leg of the smaller triangle and subtract that from the second leg of the larger triangle.

in other words :

(building + antenna) - building = antenna

so, we start with the larger triangle (up to BB).

the angle at Avani is 46°.

the angle at the building is 90°.

the angle at BB is then

180 - 90 - 46 = 44°.

21/sin(44) = (building + antenna)/sin(46)

(building + antenna) = 21×sin(46)/sin(44) =

= 21.74613659... m

now, for the smaller triangle (up to AA).

the angle at Avani is 38°.

the angle at the building is 90°.

the angle at AA is then

180 - 90 - 38 = 52°.

21/sin(52) = building/sin(38)

building = 21×sin(38)/sin(52) = 16.40699816... m

the height of the antenna is then again

(building + antenna) - building = 5.339138433... m

≈ 5.3 m

The volume of the two cuboid added together will be 192 cm³.

what exactly is a cuboid?

A cuboid, also known as a rectangular prism, is a three-dimensional solid shape that has six rectangular faces. It is a type of polyhedron, a geometric figure with flat faces and straight edges.

A cuboid has three pairs of congruent and parallel faces, with each pair being congruent to the other. These pairs of opposite faces are known as bases, and the other four faces are called lateral faces. The lateral faces are also rectangles and are perpendicular to the bases.

Now,

As Volume of the cuboid= L*B*H

where l=length, B=Breadth and H=Height

and volume of the figure =volume of 2 cuboids

=8*4*3+10*3*4

=72+120

=192 cm³

Hence,

           The volume of the two cuboid added together will be 192 cm³.

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Answer:

The correct answer is g(x) = (x+4)2+3

Step-by-step explanation:

The graph is sifted 3 units up and 4 units left.

Answer:same

Step-by-step explanation:because I said so

Answer: To find the perimeter of the door on a scale drawing, we need to first determine the dimensions of the door on the scale drawing.

If the actual height of the door is 7 centimeters, then the height on the scale drawing will be:

7 cm ÷ 3.5 = 2 cm

Similarly, if the actual width of the door is 3 centimeters, then the width on the scale drawing will be:

3 cm ÷ 3.5 = 0.857 cm

Now we can use these dimensions to find the perimeter on the scale drawing:

Perimeter = 2 × (height + width) = 2 × (2 cm + 0.857 cm) = 2 × 2.857 cm = 5.714 cm

Therefore, the perimeter of the door on the scale drawing is 5.714 centimeters.

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