A limited-edition poster increases in value each year with an initial value of $18. After 1 year and an increase of 15% per

year, the poster is worth $20.70. Which equation can be used to find the value, y, after x years? (Round money values to

the nearest penny.)

- 10/1 151

Answer:

22.5

Step-by-step explanation:

9*.5*5=22.5

Answer: [tex]\frac{PQ}{PR} = \frac{DE}{DF} (because \frac{4}{6} =\frac{6}{9} )[/tex]

The triangles ΔPQR and ΔDEF are similar and PQ / PR = DE / DF

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be represented as ΔPQR

Let the second triangle be represented as ΔDEF

The measure of side PQ = 4 cm

The measure of side PR = 6 cm

And , the measure of side DE = 6 cm

The measure of side DF = 9 cm

So , the ratio of corresponding sides of similar triangles are in the same ratio

On simplifying , we get

PQ / PR = DE / DF

4/6 = 6/9

2/3 = 2/3

Hence , the triangles are similar

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Answer:

D.) subtract 3 from both sides

Step-by-step explanation:

-4.5x + 3 = 2 - 8.5x

8.5x - 4.5 x + 3 = 2

4x +3 = 2

next you would subtract 3 from each side

4x + 3 - 3 = 2 - 3

4x = -1

4x / 4 = -1 / 4

x = -0.25

Answer:

9.46 × 1012 kilometres or about 5.88 × 1012 (nearly six trillion miles)

Step-by-step explanation:

Answer:

(pq)/2

Step-by-step explanation:

p and q are the diagonals of the kite

Answer:

Area = (1/2) * (Diagonal_1)*(Diagonal_2)

where Diagonal_1 is one diagonal in the kite

and Diagonal_2 is 2nd diagonal in the kite

Step-by-step explanation:

The diagonals of a kite intersect at right angles and one diagonal bisects the other.

so you get two triangles, with a base length of (Diagonal 1)

the height_1 = a ,  height_2 = b

a + b = Diagonal_2

area of one triangle in Kite = (1/2)(Diagonal_1)*a

area of second triangle in Kite = (1/2)(Diagonal_1)*b

area of kite = area of triangle_1 + area of triangle_2

area of kite =  (1/2)(Diagonal_1)*a + (1/2)(Diagonal_1)*b

area of kite = (1/2)*(Diagonal_1)*(a + b)

Area of kite = (1/2) * (Diagonal 1)*(Diagonal2)

Answer:B

Step-by-step explanation:

The expression -1/2 + 5/4 represents a point on an numerate line approximately three-quarters of the way between 0 and 1, to the right of zero.

To represent the expression -1/2 + 5/4 on a numeral line, it is important first to understand the properties of fractions and their positioning on a numeral line. The fraction -1/2 is situated to the left side of the zero point. The fraction 5/4 is situated slightly beyond the whole number 1, given that it is greater than 1.

To visualize the sum, one can evaluate the fraction numerically, or equivalently, approximately 0.75 when converted to decimals. Since 0.75 is a positive value, it will be on the right side of 0 on the number line, but still within the range of the first whole number (1).

In conclusion, the expression -1/2 + 5/4 represents a point on a number line that is three-quarters of the way between 0 and 1, to the right of the 0, indicating a positive fraction when visualized on a number line.

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Answer:

The cost per print expressed as a slope is 7.125

Step-by-step explanation:

To calculate the cost per print, let’s envision that we have a graphical representation of cost of posters against the number of posters

We have the cost on the y-axis and the number of posters on the x axis

With the information given in the question, we shall be having two data points

Point 1 = (32,126)

point 2 = (48,240)

Now to find the slope of the line which is cost per print, we make use of both points in the slope equation.

Mathematically, slope m will be

m = y2-y1/x2-x1

Thus, we have;

m = (240-126)/(48-32)

m = 114/16

m = 7.125

The cost per print expressed as a slope is 7.125

Final answer:

To find the original cost before a 15% markup that results in an $85.10 selling price, divide the selling price by 1.15, which gives you $74.00.

Explanation:

The question is asking how to calculate the original cost of a product, given the selling price and the percent of markup. We can use the following formula to find the original cost (also known as the cost price):

Original Cost = Selling Price / (1 + Markup Percentage)

First, convert the percent of markup from a percentage to a decimal by dividing by 100:

15% / 100 = 0.15

Then apply the formula using the given selling price of $85.10:

Original Cost = $85.10 / (1 + 0.15)

Original Cost = $85.10 / 1.15

Original Cost = $74.00

Therefore, the original cost of the item before the 15% markup was applied is $74.00.

Answer:

The probability is 0.06681

Step-by-step explanation:

To calculate this, we need to calculate the standard score or z-score

Mathematically, the standard score can be calculated using the formula;

z-score = (x - mean)/SD

from the question, the mean is 514 and the standard deviation is 118

The z-score is thus = (691-514)/118 = 177/118 = 1.5

The probability we are trying to calculate is thus;

P(x ≥ 691) or P(z ≥ 1.5)

Using standard score table or calculator,

Recall, P( x < 691) = 1 - P( x ≥ 691)

Hence, P( x ≥ 691) = 1 - P( x < 691)

P( x ≥ 691) = 1 - 0.93319

= 0.06681

Final answer:

To find the probability of scoring 691 or greater on the SAT Math section, you calculate the Z-score using the given mean and standard deviation, then use this to determine the percentage of students scoring below this score, with a Z-score of 1.5 corresponding to approximately 6.68% scoring higher.

Explanation:

To determine the probability that a student scored 691 or greater on the SAT Math section, given the distribution has a mean of 514 and a standard deviation of 118, we first calculate the Z-score. The Z-score formula is Z = (X - μ) / σ, where X is the score of interest, μ is the mean, and σ is the standard deviation.

For a score of 691, the Z-score is:

Z = (691 - 514) / 118 = 177 / 118 ≈ 1.5

After calculating the Z-score, we look up this value in a standard normal distribution table or use a calculator with statistical functionalities to find the probability to the right of this Z-score. This gives us the probability of a student scoring 691 or higher on the SAT Math section.

However, without a Z-table or calculator at hand, we can approximate that a Z-score of 1.5 generally corresponds to being higher than approximately 93.32% of the distribution. Therefore, the probability of scoring 691 or greater is about 6.68% (100% - 93.32%).

Answer:

She has Rs 16,000 left with her

Step-by-step explanation:

In this question, we are concerned with calculating how much money is left with Rita after spending the fraction of her monthly income on the things given in the question.

Firstly, she spent 1/3 of this amount on books;

Amount spent on books is thus 32,000/3 = 10,666.67

she spent a quarter of the remainder on stationary items.

Amount spent on stationary items is 1/4 * (32,000 - 10,666.67)

= 1/4 * ( 21,333.33)

= 5,333.3325

The amount of money left with her is just simply calculated by subtracting the amount she has spent from the initial amount she had

Mathematically, that would be 32,000 - (10,666.67 + 5,333.325) = approximately Rs. 16,000

Answer:

-20

Step-by-step explanation:

Substitute a point into the equation

y = -10x+b

-320 = -10(30) + b

-320 = -300+b

Add 300 to each side

-320+300 =-300+300+b

-20 =b

Step-by-step explanation:

To get the Greates Common Factor (GCF) of 135000 and 54000 we need to factor each value first and then we choose all the copies of factors and multiply them:

135000:    2 2 2   3 3 3 5 5 5 5

54000:    2 2 2 2 3 3 3 5 5 5  

GCF:    2 2 2   3 3 3 5 5 5  

The Greates Common Factor (GCF) is:   2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 5 = 27000

Answer:

A, C, D, on Edge 2020

Step-by-step explanation:

The true statements about the circle are;

A line segment is known to be a kind of line that has two endpoints. It is said to have endpoints and some other points of the line found between them.

The angle intercepted on opposite side of the circle from an ARC is one that measure of half of the Arc.

Note that ∠CBA is half of the ARC CA.

∠CAB is given as 60°

So 60*2 will give you mArc C B = 120°. The same method is applicable to m∠COB = 120°

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Answer: the length of the needle is 8.49 inches.

Step-by-step explanation:

The diagram of the clear cube is shown in the attached photo. From the diagram, a right angle triangle ABC is formed.

BC represents the diagonal of a face of the cube.

AB represents the the side length of the clear cube.

AB = h represents the length of the needle

To determine AB, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

Therefore

AB² = 6² + 6² = 72

AB = √72

AB = 8.49

Answer:

41.6

Step-by-step explanation:

Answer:

A: definition of midpoint

B: angle BCA is congruent to angle DCA

Step-by-step explanation:

To prove ∆ACB ≅ ∆ACD, we use the Reflexive Property, the definition of a midpoint, and the Side-Angle-Side Congruence Postulate, based on the given that C is the midpoint of BD and ∠ACB and ∠ACD are right angles.

To prove that ∆ACB ≅ ∆ACD, given that C is the midpoint of BD in a triangle ABD with a line drawn from A to C creating right angles, we can use the two-column proof format.

By the Side-Angle-Side postulate, if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.

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Answer:

224 pages total

Step-by-step explanation:

To find how many total pages, you have to multiply the number of sections by the number of pages in each section. 14 sections times 16 pages per section equals a total of 224 total pages.

Answer:

-19

Step-by-step explanation:

If c = -4 and y = 3, replace c and y with their corresponding values in the expression, so that the expression will look like this: (-4) - (5 * 3).

Since multiplication comes before subtraction in PEMDAS, you would multiply 5 by 3, which gets you 15.

Now the expression is (-4) - (15). Then, you do the subtraction. -4 - 15 is equal to -19.

Does that help?

Final answer:

The expression c-5y evaluates to -19 when substituting c = -4 and y = 3.

Explanation:

To evaluate the expression c-5y when c = -4 and y = 3, we replace c with -4 and y with 3 in the expression. The value of the expression is -19, which is obtained by performing the arithmetic: (-4) - 5(3) = -4 - 15 = -19. Therefore, when c is -4 and y is 3, the expression c-5y yields -19.

This problem belongs to the topic of algebraic expressions, and this question demonstrates the importance of substitution to find the value of algebraic expression. This property is used has many applications in science and daily life.

Final answer:

The rate of speed for the slower boy is 3 km/h, while the rate of speed for the faster boy is 6 km/h.

Explanation:

The rate of speed for each of the two boys can be determined by using the formula:

Rate of speed = Distance / Time

Let's assume the rate of speed of the slower boy is 'x' km/h. Therefore, the rate of speed of the faster boy is '2x' km/h, as mentioned in the question.

For the slower boy: Distance = Speed * Time. Therefore, 3x = x * 3. Solving this equation, we get x = 0 which indicates that the slower boy is not moving.

For the faster boy: Distance = Speed * Time. Therefore, 3 * 2x = 6x.

According to the question, the total distance covered by both boys is 27 km in 3 hours. So, 6x + 3 * 2x = 27. Solving this equation, we get x = 3.

Therefore, the rate of speed for the slower boy is 3 km/h and the rate of speed for the faster boy is 6 km/h.

Answer:

Step-by-step explanation:

Greatest common factor of 4d and 8 is 4

4d + 8 = 4d + 4*2

          =4(d + 2)

Answer:

The volume of the pentagonal prism is 1446.25

Step-by-step explanation:

First of all we need to calculate the area of the pentagon

A = area

a =  apothem = 8.9

p = perimeter = 13 * 5 = 65

A = (a*p) / 2

A = (8.9 * 65) / 2

A = 578.5 / 2

A = 289.25

To calculate the volume of a pentagonal prism we have to use the following formula:

a = area =  289.25

v = volume

h = height  = 5

v = a * h

we replace the values that ​​we know        

v =   289.25 * 5

v = 1446.25

The volume of the pentagonal prism is 1446.25

ANSWER IS 60

EXPLAIN- 10/2= 5

5 TIMES 12= 60

Answer:

4044

Step-by-step explanation:

14 × (pi × d)

14 × 3.14 × 92

4044.32 feet

Donnie's average test score is 76 for all eight tests. The sum of his seven known test scores is 542. To find the missing score, subtracting this sum from the sum of all eight scores gives a missing test score of 66.

The correct answer is option B.

To find Donnie's score on the missing eighth test, we can use the fact that the average of all eight test scores is 76.

The sum of the eight test scores is 8 * 76 = 608 (since the average is calculated by summing all the scores and dividing by the number of scores).

Now, we know the sum of the seven test scores in his notebook:

71 + 92 + 87 + 75 + 64 + 70 + 83 = 542

To find the missing score, subtract the sum of the known scores from the sum of all eight scores:

608 - 542 = 66

So, Donnie's score on the missing eighth test is 66.

The correct answer is: B) 66

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Answer: No, it's not possible as every triangle is 180 degrees. These angles add to 220 degrees which is more than 180.

Step-by-step explanation:

This is backed by the Triangle Sum Theorem which states that the three interior angles of any triangle add up to 180 degrees.

It's impossible to form a triangle with angles measuring 90, 30, and 100 degrees because the sum of those angles exceeds 180 degrees, which violates the rule that the sum of all angles in a triangle must equal 180 degrees.

No, it is not possible to create a triangle with angle measures of 90 degrees, 30 degrees, and 100 degrees. This is because the sum of the angles in any triangle always equals 180 degrees. If you add up 90, 30, and 100, you get a sum of 220 degrees, which exceeds the 180-degree rule of triangles.

To understand this concept better, let's take a look at an example. In a right triangle, which is a triangle where one of the angles measures 90 degrees, the other two angles must add up to 90 degrees to satisfy the 180-degree rule. So, if we have a right triangle with one angle of 90 degrees and another angle of 30 degrees, the third angle would have to be 60 degrees (180 - 90 - 30), not 100 degrees.

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Answer:

2.4 hours

Step-by-step explanation:

Answer:

he worked for 6 hours and 30 min

Step-by-step explanation:

what you do is take 53.30 and divide it by 8.20

An equation is formed of two equal expressions. The number of hours Jaime worked last week is 6.5 hours.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given Jaime makes $8.20 per hour in his part-time job. He made $53.30 last week. Therefore, the number of hours he worked is,

$53.30 = n × $8.20

n = 6.5 hours

Hence, the number of hours Jaime worked last week is 6.5 hours.

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Answer:

sqrt(-8x+5)

Step-by-step explanation:

(5-8x)

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

sqrt(-8x+5)

We need to rationalize the denominator

(5-8x)               sqrt(-8x+5)

----------------- * ---------------

sqrt(-8x-5)         sqrt(-8x+5)

(5-8x)               sqrt(-8x+5)

----------------- * ---------------

(-8x+5)

The first term cancels

sqrt(-8x+5)

Answer:

Second option

Step-by-step explanation:

The radical represents the square root, i.e power ½

(5 - 8x) ÷ (5 - 8x)^½

(5 - 8x)^(1-½)

(5 - 8x)^½

(-8x + 5)^½ (just a rearrangement)