The price of a watch was increased by 20% to 198. What was the price before the increase?

Answer:

[tex]\large\boxed{x=\dfrac{4a^2+3a}{9-2a}}[/tex]

Step-by-step explanation:

[tex]\dfrac{3x-a}{x+2a}=\dfrac{2a}{3}\qquad\text{cross multiply}\\\\(3)(3x-a)=(2a)(x+2a)\qquad\text{use the distributive property}\\\\(3)(3x)+(3)(-a)=(2a)(x)+(2a)(2a)\\\\9x-3a=2ax+4a^2\qquad\text{add}\ 3a\ \text{to both sides}\\\\9x=2ax+4a^2+3a\qquad\text{subtract}\ 2ax\ \text{from both sides}\\\\9x-2ax=4a^2+3a\qquad\text{distributive}\\\\(9-2a)x=4a^2+3a\qquad\text{divide both sides by}\ (9-2a)\neq0\\\\x=\dfrac{4a^2+3a}{9-2a}[/tex]

I could be wrong but

area=172.1

Area of the pentagon after rounding to the nearest tenth is 172.5 cm²

Given: a regular pentagon with sides measuring 10 cm and apothem measuring 6.9 cm

To find: area of the pentagon

We know that the area of a regular pentagon can be found by the formula:

[tex]\text{area}= \frac{1}{2} \times \text{perimeter of pentagon} \times \text{apothem}[/tex]

Before putting the values in the formula, we need to find the perimeter of the pentagon. It can be found by fining the sum of all of its side as follows:

[tex]\text{perimeter} = 10+10+10+10+10 = 5 \times 10 = 50[/tex] cm

Now we can put the values in the formula for area as follows:

[tex]\text{area}= \frac{1}{2} \times 50 \times 6.9\\[/tex]

[tex]\text{area}= 172.5[/tex] cm²

As the area is already rounded off to the nearest tenth we do not need to perform any additional calculations

So, area of the given pentagon is 172.5 cm².

the length of DE is 9/2 units and m<CAB is 45

The measurements of DE and angle CAB in the given triangle ABC are 4.5 units and 45° respectively.

A triangle is a polygon with three angles and sides.

Given that, a right triangle ABC, right-angled at B,  

Here D and E are midpoints of AB and BC, and also AB = AC, CB = 9 units.

We need to find the measurements of DE and angle CAB in the given triangle ABC,

Since, the two sides are equal in the triangle then it is a right-isosceles triangle,

In a right-isosceles triangle, the two acutes angles are measured 45°

Therefore, ∠ CAB = ∠ ACB = 45°

Hence, ∠ CAB = 45°

Now, using the midpoint theorem, we will get. CB = 2DE

Therefore,

9 = 2DE

DE = 4.5 units

Hence, the measurements of DE and angle CAB in the given triangle ABC are 4.5 units and 45° respectively.

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Answer:

8

Step-by-step explanation:

The question is on number of subsets

Number of subset is given by 2^n

n=3 in our question, A,B,C

2^n = 2^3 =8

They are; { }, A, B, C, AB, AC, BC, ABC

Answer:

8

Step-by-step explanation:

Answer:

The product of x and y is 8[tex]8[/tex]

Step-by-step explanation:

If [tex]\log_{5\sqrt{5}}125=x[/tex], then the exponential form is:

[tex]125=(5\sqrt{5})^x[/tex]

[tex]\implies 5^3=(5)^{\frac{3x}{2}}[/tex]

[tex]\implies 3=\frac{3x}{2}[/tex]

[tex]\implies 6=3x[/tex]

[tex]\implies x=\frac{6}{3}=2[/tex]

Also  if, [tex]\log_{2\sqrt{2}}64=y[/tex], then the exponential form is:

[tex]64=(2\sqrt{2})^y[/tex]

[tex]\implies 2^6=(2)^{\frac{3y}{2}}[/tex]

[tex]\implies 6=\frac{3y}{2}[/tex]

[tex]\implies 12=3y[/tex]

[tex]\implies y=4[/tex]

The product of x and y is [tex]xy=2\times 4=8[/tex]

Gradient= -3/2 Equation: Y=mx+c Y=2 , X=8

So you substitute the numbers in

2=(-3/2) x 2 + c (then you backtrack to solve for c which is the y intercept)

2=-3+c

5=c So the equation should be Y=-3/2x+5

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - [tex]\frac{3}{2}[/tex], thus

y = - [tex]\frac{3}{2}[/tex] x + c ← is the partial equation

To find c substitute (8, 2) into the partial equation

2 = - 12 + c ⇒ c = 2 + 12 = 14

y = - [tex]\frac{3}{2}[/tex] x + 14 ← equation in point- slope form

Answer:

The t-shirt cost $23.33.

Step-by-step explanation:

Answer:

$140

Step-by-step explanation:

If x was the amount of money Mr. Green had remaining, and y was the amount of money Mrs. Green had remaining, then:

x / y = 3 / 2

And, since they spent the same amount of money:

200 - x = 180 - y

We can solve this system of equations through substitution.

x = 3/2 y

200 - 3/2 y = 180 - y

20 = 1/2 y

y = 40

So Mrs. Green had $40 remaining.  Since she started with $180, she must have spent $140.  So that was the cost of the shirt.  Let's check our answer by seeing how much Mr. Green had remaining and how it compares.

$200 - $140 = $60

$60 / $40 = 3 / 2

Yep, it checks out.

Answer:

(i) 16 cm.

(ii) 37 pieces in total.

Step-by-step explanation:

Through determining each lengths factors, it can be determined that every ribbon can be equally divided into 16 cm. long ribbons, so we already have our first answer. A 160 cm. long ribbon divided into 16 cm. long pieces will create 10 ribbons from that one piece; the 192 cm. long ribbon cut into the same 16 cm. lengths will equal 12 pieces of equal length; and the 240 cm. long ribbon will divide its 16 cm. lengths into 15 pieces of equal length. So the 10 pieces, plus the 12 pieces, plus the 15 pieces, will equal 37 total pieces, each 16 cm. in length.  

Final answer:

This answer explains how to find the largest length of pieces and total number of pieces cut from different ribbon lengths. Therefore, the largest piece length is 16 cm. and  Total number of pieces of ribbons cut  is 37.

Explanation:

(i) Largest possible length of each piece of ribbons: To find the largest piece length, we need to determine the greatest common divisor (GCD) of the ribbon lengths. The GCD of 160, 192, and 240 is 16. Therefore, the largest piece length is 16 cm.

(ii) Total number of pieces of ribbons cut: To find the total number of pieces, divide each ribbon length by the largest piece length. For 160 cm, it gives 10 pieces. For 192 cm, it gives 12 pieces, and for 240 cm, it gives 15 pieces. Adding these, the total number of pieces is 37.

Answer:

The points corresponding to P=(3,4) and Q=(6,7), so the answer is D.

Step-by-step explanation:

Ok, in mathematics, given two sets X and Y, the collection of all the ordered pairs (X, Y), formed with a first element in X and a second element in Y, is called the Cartesian product of X and Y. The Cartesian product of sets allows define relationships and functions. In this case, it is a function that contains two points, denoted P and Q. Given, the ordered pair of each, first read the one corresponding to the X axis  and then to the Y axis.

For P: you read X and you see that it is on 3 (between 2 and 4), and then the Y axis is on 4 (between 3 and 5).

For Q: you read X and you see that it is on 6 (between 5 and 7) and then the Y axis is on 7 (between 6 and 8)

[tex]

48=5t-7 \\

55=5t\Longrightarrow t=\frac{55}{5}=\boxed{11}

[/tex]

Answer:

Step-by-step explanation:

11

Answer:

22/25

Step-by-step explanation:

The overlap between the 61% and the 75% is the 48%, which means that 13% of the people are married and have no kids (61-48=13)

The 75% includes the people who have one or more kids, and the people who have one or more kids and are married.

Now all we have to do is 13% + 75% = 88% = 22/25

Using Venn probabilities, it is found that there is a 0.88 = 88% probability that a person in a survey is married or has a child.

In a Venn probability, two non-independent events are related with each other, as are their probabilities.

The "or probability" is given by:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

In this question, the events are:

The probabilities are given by:

[tex]P(A) = 0.61, P(B) = 0.75, P(A \cap B) = 0.48[/tex]

Hence:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

[tex]P(A \cup B) = 0.61 + 0.75 - 0.48[/tex]

[tex]P(A \cup B) = 0.88[/tex]

0.88 = 88% probability that a person in a survey is married or has a child.

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Answer: -8 square root of 3 (choice a)

Step-by-step explanation:

You have to find 2 numbers that multiply to 48 and in the same time, 1 of these numbers is a perfect square. In this case, the numbers are 16 and 3. So -2√16*3

Then since 16 is. A perfect square, and the square root is 4, you take out the 4 and multiply it by -2 so that is -8 and now you are left with -8√3. Hopefully that helped.

ANSWER

[tex] - 8 \sqrt{3} [/tex]

EXPLANATION

We want to simplify:

[tex] - 2 \sqrt{48} [/tex]

Remove the perfect square under the radical sign.

[tex] - 2 \sqrt{16 \times 3} [/tex]

Split the radical sign for the factors under it.

[tex] - 2 \sqrt{16} \times \sqrt{3} [/tex]

Simplify:

[tex] - 2 \times 4\times \sqrt{3} [/tex]

This finally gives us:

[tex] - 8 \sqrt{3} [/tex]

The first choice is correct.

Answer:

The answer is A. 70 in^2

Step-by-step explanation:

trust me it is right :) hope this helps! I JUST TOOK THE TEST

ANSWER

A. 70 in^2

EXPLANATION

The area of a tra-pezoid is

[tex] = \frac{1}{2} (sum \: of \: parallel \: sides) \times height[/tex]

Substitute the side lengths into the formula to obtain,

[tex] = \frac{1}{2} (8 + 14) \times 7[/tex]

Simplify the parenthesis

[tex] = \frac{1}{2} (20) \times 7[/tex]

Cancel out the common factors,

=10×7

Simplify

[tex] = 70 {in}^{2} [/tex]

The correct answer is A

Answer:

the inter-quartile range will increase

Step-by-step explanation:

The initial data-set was;

20,32,32,45,50

Adding a new value 78 will have several effects;

The mean of the new set of values will increase since 78 is mostly likely to be an outlier.

The median of the new data set will increase. The median of the old data set is 32 while that of the new data set will be 38.5

The mode is the most frequent observation. Both the new and the old sets of values will have a mode of 32. The mode will therefore remain the same.

The inter-quartile range just like the range will increase

Answer:277.50

Step-by-step explanation:you do this than u do that

Answer: Option 'D' is correct.

Step-by-step explanation:

Since we have given that

On 1st June, amount in piggy bank = $2.00

On 2nd June, amount in piggy bank = $2.50

On 3rd June, amount in piggy bank = $3.00

So, it forms an arithmetic sequence:

Here, a = $2

d = 0.50

n = 30 days

So, Sum of 30 terms would be

[tex]S_{30}=\dfrac{30}{2}(2\times 2+(30-1)0.5)\\\\S_{30}=15(4+29\times 0.50)\\\\S_{30}=15(4+14.5)\\\\S_{30}=15(18.5)\\\\S_{30}=\$277.50[/tex]

Hence, Option 'D' is correct.

Answer:

204,160,000

Step-by-step explanation:

Assuming the sample is a good representation of the people from the United States.

Since there were 1,000 surveyed... and 638 of them were wearing glasses,  that makes a proportion of 638 out of  1,000 people, or 63,8 / 100 people... so 63.8%... or 0.638

So, if we assume that the US population is of 320 million, how many people does that make wearing glasses.... we just have to multiply 320M by 0.638

G = 320,000,000 * 0.638 = 204,160,000

Answer:

39.68 million[

Step-by-step explanation:

Remember that the sample is 1000 people.

Of those 1000 people we know that 762 wear corrective lenses. 124 of these people wear contact lenses.

The probability that a randomly selected person will wear contact lenses is:

[tex]P = \frac{124}{1000}\\\\P = 0.124[/tex]

Then, the expected number of people who wear contact lenses is:

[tex]N = 320 * P[/tex]

Where N is given in units of millions.

[tex]N = 320 * 0.124[/tex]

[tex]N = 39.68\ million[/tex]

Answer:

[tex]\large\boxed{5(x+y)-3\left(\dfrac{y}{x}\right)=5x+5y-\dfrac{3y}{x}}[/tex]

Step-by-step explanation:

[tex]5(x+y)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=5x+5x\\\\3\left(\dfrac{y}{x}\right)=\dfrac{3y}{x}\\\\5(x+y)-3\left(\dfrac{y}{x}\right)=5x+5y-\dfrac{3y}{x}[/tex]

Answer:

Square

Step-by-step explanation:

Well, the options they have given you to choose from are a pentagon, a quadrilateral and a square. Let's first take a look at these options and eliminate which ones can't be possible. The first option, a pentagon, can be eliminated from the possibilities because a pentagon has five sides and figure ABCD has only four sides. The second option, quadrilateral, is true because a quadrilateral has four sides and so does figure ABCD. But, if you look at the third option, a square, this is the best way out of all the options to classify this figure because there are three things ALL squares must have:

- four sides

- all right angles

- all the sides MUST be equal

Knowing this, taking a look at the picture, you will see that there are indeed four right angles, four sides AND all congruent sides, proven by the four triangles inside the square. The answer isn't quadrilateral because, although that may be true, there are MANY types of quadrilaterals, trapezoids, rectangles, rhombuses and so on, each having different properties and characteristics. Therefore, the third option, SQUARE is the right answer.

HOPE THIS HELPED! Please contact me if you have any further questions about this topic and feel free to ask any more questions you need! :)

The perimeter of tile which is 3 by 3 would be 12. If each side is 3 and the tile is a square which has four sides we can do 3 x 4 to determine the perimeter of the tile. To determine perimeter just add up all the sides. In this case since it’s a square you are able to multiply. 3 x 4 or 3 + 3 + 3 + 3 = 12

Answer:

The answer is 12

Step-by-step explanation:

Because it is lol and i just got it right

Answer:

Step-by-step explanation:

In the form ...

  ax^2 +bx +c = 0

the sum of the roots is -b/a. Here, that is -k/3. You want that value to be 3, so we have ...

  -k/3 = 3

  k = -9

__

The solution can be found by completing the square. We choose to start by making the leading coefficient be 1.

  x^2 -3x +4/3 = 0

  (x^2 -3x +9/4) + (4/3 -9/4) = 0 . . . . . . . add and subtract (3/2)^2

  (x -3/2)^2 = 11/12 . . . . . . . . . . . . . . . . . . add 11/12, write as square

  x = 3/2 ± √(11/12) = (9±√33)/6 . . . . . . . .simplify

(a): 18

(b): $792

Step-by-step explanation:

A: 900 - 576 = 324. 324/18 = 18.

18 * 18 = 324. 324 + 576 = 900.

B: 6 * 18 = 108. 900 - 108 = 792

Answer:

d) 18

Step-by-step explanation:

The question is on graphing linear functions

Given the table of values of x and y, plot the graph and observe the gradient of -2 and the y-intercept at (0,-5) as shown on the attached graph with blue color.

Use the given function y=7x+13 to formulate a table of values of x with corresponding values of y

x     y

-3   -8

0      13

1       20

With the above values, plot the graph of y=7x+13 and obtain the y-intercept at (0,13) as shown in the red line graph attached.

To find the distance between the y-intercepts of the two graphs we apply the expression for distance between two points;

[tex]D=\sqrt{(X2-X1)^2 +(Y2-Y1)^2 \\\\[/tex][/tex]

points are (0,-5) and (0,13)

D=√ (0-0)² + (13--5)²

D=√(18)²

D=18 units

The y-intercepts of the two functions y = 7x + 13 and y = 3x + 9 are 13 and 9 respectively. The distance between the y-intercepts is the absolute difference between them, which is 4, a result not listed among the options.

Firstly, we need to find the equation that fits the values in the table. With the given x and y values, applying a method such as 'point-slope,' we calculate the slope (m) and y-intercept (b). We find the equation is y = 3x + 9.

Then, we determine the y-intercepts of both functions. For the function y = 7x + 13, the y-intercept is 13 (the constant term). For the function y = 3x + 9, the y-intercept is 9.

The distance between the y-intercepts of the two functions is simply the absolute difference between them, which equals |13 - 9| = 4. However, none of the options a), b), c), or d) are identical to this value. There might be a mistake in the question.

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Answer:

x is greater than 5, so x could be anything more than 5.

Step-by-step explanation:

Hope my answer has helped you!

Answer:

The temperatures were more consistent in Springville

Step-by-step explanation:

This question is on consistency of data

Generally, consistency of a data set is measured by determining the range, the variance or the standard deviation.In this case, we will use the standard deviation.

A small standard deviation means higher consistence.A lower standard deviation  will mean easy to predict a value because most of the values are closer to the average value.When the variations are less, a better analysis can be performed on a set of data.

Temperatures were more consistent in Springville that had a standard variation of 4F compared to Dakota that had a standard deviation of 6.8F

Answer:

13 min 40 sec

Step-by-step explanation:

656 copies *(1 min/48 copies)= 656 /48 min = 13  32/48 min = 13 2/3 min

2/3 min = 2/3 min * 60 sec/1 min = 40 sec

13 2/3 min = 13 min 40 sec

Answer:

Step-by-step explanation:

The sum of the two shorter sides must be greater than the longest side.

5 + 8 = 13

13 is not greater than 14, so the three segments cannot form a triangle.

Answer: No

Step-by-step explanation:

A triangle can be formed only if the sum of 2 sides of the triangle is bigger than the length of the third side of this triangle.

In this case we have AB = 5, BC = 8 and AC = 14.

AB + AC > BC → 5 + 14 > 8 →1 9 > 8 ok!

AB + BC > AC → 5 + 8 > 14 → 13 > 14 false!

BC + AC > AB → 8 + 14 > 5 → 22 > 8 ok!

As we have that AB + BC > AC FALSE, this segments cannot form a triangle.

Answer:

1112

Step-by-step explanation:

For this case we have that by definition, a flat angle is the space included in an intersection between two straight lines whose opening measures 180 degrees.

Now, according to the figure we have that from V to S there are 180 degrees, like this:

[tex]5x + 25x + 30 = 180[/tex]

We add similar terms:

[tex]30x + 30 = 180[/tex]

Subtracting 30 from both sides of the equation:

[tex]30x = 150[/tex]

Divide by 30 on both sides of the equation:

[tex]x = \frac {150} {30}\\x = 5[/tex]

Answer:

[tex]x = 5[/tex]

Answer:

Step-by-step explanation:

y=5+2(3+4x) - Multiply parenthesis by 2

0=5+6+8x - Add the numbers

0=11+8x - Move variable to left

-8x=11 - Divide both sides by -8

x=-1.375

Answer:

1000 runners

Step-by-step explanation:

Take total number of runners to be -----------x

90% of x managed to complete the marathon= 90/100 × x =0.9x

30% of those who completed the marathon were men= 30% × 0.9x

=0.3×0.9x= 0.27x

=270 men completed the marathon; this means

0.27x=270--------------------------------find x by dividing both sides by 0.27

x= 270/0.27

x=1000 runners

Answer:

1000

Step-by-step explanation:

Given : In a marathon 90% runner were managed to complete it and 30% were men.

To Find: If 270 men completed it how many total runner began the marathon.

Solution:

Let x be the number of total runners

Now we are given that 90% runner were managed to complete it

So, number of runners managed to complete = [tex]90\% \times x =\frac{90}{100}x=0.9x[/tex]

Now we are given that out of 90% , 30% were men

So, Numbers of men runners = [tex]30\% \times 0.9x=\frac{30}{100} \times 0.9x =0.27x[/tex]

Now we are given that 270 men completed it

So, [tex]0.27x=270[/tex]

[tex]x=\frac{270}{0.27}[/tex]

[tex]x=1000/tex]

Hence 1000 runners began the marathon.