Jonathan collects postcards and stamps. The number of postcards in his collection is 12 more than the number of stamps. He has 39 postcards in all. If Jonathan has x stamps, which equation represents this situation and how many stamps does he have?

Answer:

x = 2 , y = 4

Step-by-step explanation:

If a quadrilateral has diagonals which bisect each other, then it is a parallelogram.

From the parallelogram we see:

2x = y

y = 2x

Substitute y = 2x in 2(y) - 2 = 6, gives:

2(2x) - 2 = 6

4x = 6 +2

x =2

Substitute x = 2 in y = 2x, gives:

y = 2(2)

y = 4

So x = 2 , y = 4

Answer:

x = 5

Step-by-step explanation:

5x + 7/2 = 3/2x - 14

like terms together;

5x - 3/2x = -14 - 7/2

7/2x = 35/2

divide both sides by the reciprocal of the fraction next to the unknown

divide by 2/7

x = 5

Answer:

[tex]256cm^2[/tex]

Step-by-step explanation:

Calculate the area of the two triangles first: 6 * 16 = 96

Then the rectangle: 10 * 16 = 160

160 + 96 = 256

Answer:

Step-by-step explanation:

Answer:

√b/a

Step-by-step explanation:

Answer:

n = ± [tex]\sqrt{\frac{b}{a} }[/tex]

Step-by-step explanation:

Given

an² = b ( divide both sides by a )

n² = [tex]\frac{b}{a}[/tex] ( take the square root of both sides )

n = ± [tex]\sqrt{\frac{b}{a} }[/tex]

Answer:

tanθ=2√2

Step-by-step explanation:

cosθ= 1/3, and θ is acute;

cos²θ=1/9

sin²θ+cos²θ=1

sin²θ=1-cos²θ=1-1/9=8/9

=> sinθ=√(8/9)=2√2 /3

tanθ=sinθ/cosθ

tanθ=(2√2 /3)/(1/3)=2√2

tanθ=2√2

Answer:

-24

Step-by-step explanation:

1/8(5y+64)=1/4(20+2y)

Multiplying both sides of the equation...

1/8(5y)+1/8(64)=1/4(20)+1/4(2y)

1/8(5y)+(64/8)=(20/4)+(2y/4)

1/8(5y)+8=5+y/2

1/8(5y)+8=5+1/2(y)

Now multiplying through by the least common multiple, which is 8

8×1/8(5y)+8×8=8×5+8×1/2(y)

1×1(5y)+64=40+4×1(y)

Simplifying both sides...

5y+64=40+4(y)

5y+64=40+4y

By grouping like terms...

5y-4y=40-64

1(y)= -24

y= -24

hope this was helpful

Answer:

If I do not like art class, then I do not like painting.

Step-by-step explanation:

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Step-by-step explanation:

Answer:

Commutative property

Step-by-step explanation:

This is an example of the commutative property as its states that it is applicable in multiplication and addition where 2 numbers can switch places and give the same result in both situations.

(4)(2) = 8

(2)(4) = 8

Answer:

Paco contributed = 360pesos

Juan contributed = 504pesos

Question:

Two brothers gathered their money to buy a gift for their dad. Between them they gathered 864, which amount each contributed if Paco gave 5 pesos for every 7 that Juan gave.

Step-by-step explanation:

Let the common factor between each brother = p

Paco gave = 5×common factor = 5p

Juan gave = 7×common factor = 7p

Total money contributed by both brothers = 864

Total money contributed by both brothers = 5p + 7p

5p + 7p = 864

12p = 864

p = 864/12

p = 72

Paco contributed = 5p = 5×72 = 360pesos

Juan contributed = 7p = 7×72 = 504pesos

Answer:

45 miles

Step-by-step explanation:

5 miles = 8 km

72 km = 9 * 8 km

Since 8 km = 5 miles, replace 8 km with 5 miles

72 km = 9 * 8 km = 9 * 5 miles = 45 miles

Answer:

It is 4 cavities

Step-by-step explanation:

The interquartile range (IQR) of the data in the dot plot is 4

From the question, we are to determine the interquartile range (IQR) of the data

From the diagram, we can produce the data set

0, 0, 0, 1, 1, 3, 3, 4, 7, 7

Now, we will determine the interquartile range of this data set.

The interquartile range is the difference in value between the upper quartile and lower quartile.

The upper quartile (Q3), is the value under which 75% of data points are found when arranged in increasing order.

The lower quartile (Q1), is the value under which 25% of data points are found when they are arranged in increasing order.

∴ IQR = Q3 - Q1

From the data set

0, 0, 0, 1, 1, 3, 3, 4, 7, 7

Upper quartile (Q3) = 4

and

Lower quartile (Q1) = 0

∴ Interquartile range (IQR) = 4 - 0

IQR = 4

Hence, the interquartile range (IQR) of the data in the dot plot is 4

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Answer:

Step-by-step explanation:

AP = 8, 24 , 40....

a = 8 , d =16 , n =98 , An = ?

an= a +(n-1)d

an = 8+97*16

an=8+1552

an=1560

hope it helps you..

The 98th term of the arithmetic sequence ( 8, 24, 40, . . . ) is 1560 ( One thousand five hundred and sixty ).

An arithmetic sequence is simply a sequence of numbers in which the difference between the consecutive terms is constant.

The nth term is an arithmetic sequence is expressed as;

aₙ = a₁ + ( n - 1 )d

Where aₙ is the nth term, a₁ is the first term in the sequence and d is the the common difference between terms.

Given the data in the question;

We substitute our given values into the expression above.

aₙ = a₁ + ( n - 1 )d

a₉₈ = 8 + ( 98 - 1 )16

a₉₈ = 8 + ( 97 )16

a₉₈ = 8 + 1552

a₉₈ = 1560

Therefore, the 98th term of the arithmetic sequence ( 8, 24, 40, . . . ) is 1560 ( One thousand five hundred and sixty ).

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Answer:

21°

Step-by-step explanation:

Supplementary is defined as two angles whose sum is 180. These angles must therefore be on a straight line cut by a transversal and must be less than 180 by themselves.

If one angle is 159, then we can simply subtract it from 180 to get the other angle.

A more algebraic way is to set up the equation, 159 + x = 180. Subtract 159 from 180 to find x.

The Measure of supplementary angle is 21⁰.

The pair of angles that always add up to 180 degrees are referred to as supplementary angles. The term "supplements of each other" refers to these two angles. The Latin words "Supplere" and "Plere" are the source of the word "supplementary." "Supplere" means "supply," while "Plere" means "fill." Thus, "something when supplied to complete a thing" is the definition of "supplementary."

Given an angle 159⁰

and according to supplementary angles property,

when sum of two angles is 180⁰ are supplementary

∠A + ∠B = 180⁰ (angles are supplementary)

Let the another angle be x

159 + x = 180

x = 180 - 159

x = 21⁰

Hence the supplementary angle is 21⁰.

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Answer:

Step-by-step explanation:

2m

______

2

______ X 0m X 0

1

= 0

Answer: 187.5 tons of cement

Step-by-step explanation:

From the question, Sadie's Road Paving Company used 750 tons of cement to pave 4 miles of roadway. To calculate the number of cement on average that the company use per mile, we divide 750 tons of cement by 4 miles. This will be:

= 750 tons of cement/4

= 187.5 tons of cement

The company used 187.5 tons of cement per mile.

Answer: The company used 187.5 tons per mile.

Step-by-step explanation:

Hi, to answer this question we simply have to divide the amount of cement used (750 tons) by the miles that the company pavemented (4 miles):

Mathematically speaking:

750 t / 4 m = 187.5 tons per mile

The company used 187.5 tons per mile.

Feel free to ask for more if needed or if you did not understand something.

Answer:

B= 55°

Step-by-step explanation:

A+B+C= 180°

90°+B+35°=180°

B= 55°

Answer:

1600

Step-by-step explanation:

40x40

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Find the area of the big rectangle first:

14 x 11 = 154

Fine the area of the small rectangle:

5 x 3 = 15

Use πr^2

π(4)^2 = 16π

Divide this by 4 as it is only a quarter of the circle:

16π / 4 = 4π

Add all the values together:

4π + 154 + 15 = 181.5663709

Round this off as needed.

To 2 d.p. it is 181.57 in^2

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Answer:

The numerator of the fraction is -360

Step-by-step explanation:

a=180(n-2)/n

Solve for n

a=180(n-2)/n

Open parenthesis

a=180n-360/n

Cross product

an=180n-360

Collect like terms

an-180n=-360

Factorise

n(a-180)=-360

Make n the subject of the formula

n=-360/(a-180)

The numerator of the fraction is -360

The denominator is (a-180)

Answer:

-360

Step-by-step explanation:

Answer:

-45

Step-by-step explanation:

Answer:

9,11

Step-by-step explanation:

let the numbers be x, x+2 (since consecutive odd integers have a difference of 2)

therefore;

x(x+2)= 99

x²+2x=99

I usually solve the sum like this,

we need to find the nearest square number ( number smaller than the number on the R.H.S)

here, it is 81, whose square root is 9. therefore the solution is 9

verification:

(9)²+2*9=99

81+18=99

99=99

hence, 9 is the solution. therefore the positive odd consecutive integers are  

x=9

x+2=9+2= 11

verification:

9*11=99

99=99

L.H.S=R.H.S

Answer:

6m

Step-by-step explanation:

the side of first square = 3 m

area of first square = 3^2= 9 m^2

let the side of second square = x m

since diagonal of first square = x m as per the question

in a square each angle is 90 degree

therefore by applying pythagorus theorem ,

diagonal ^2 = side^2 + side ^2

diagonal^2 = 3^2+3^2=9+9

DIAGONAL= square root of 18

diagonal= 3[tex]\sqrt{2}[/tex] m = side of second square

therefore in second square ,

one angle is 90  degree , therefore by applying pythagorue theorem

diaqonal^2 = side ^2 + side ^2 = (3[tex]\sqrt{2}[/tex])^2 + ( 3[tex]\sqrt{2}[/tex])^2

diagonal ^2 = 18 + 18

diagonal = square root of 36

therefore diagonal of second square is 6m

hope it helps you... please mark me as the brainliest..

Answer:

6m explained it all hope it helps

Answer:

yes

Step-by-step explanation:

Using the Pythagorean Theorem, we should get 20² + 99² = 101² and we need to check if this is a true statement.

400 + 9801 = 10201

10201 = 10201 so yes, it is.

Answer:

9.5

Step-by-step explanation:

Answer:

Therefore the sum of three odd numbers is always an odd number. Hence Proved. Let the number is 15,13 and 3 then 15=2*7+1 13=2*6+1 3=2*1+1 where 1,6 and 7 now 15+13+3=2*7+1+2*6+1+281+11 =2(7+6+1)+3 =2*14+3(24 is our 'm') and 2*14≠30. OR 15+13+3≠30

Step-by-step explanation:

The question is that you cannot get 30 by adding any three odd numbers because addition of 3 odd numbers always give another odd number and hence 30 which is an even number cannot be achieved. 2n-1 where n is a natural number.

Answer:

The ticket is bought for 28 students.

Step-by-step explanation:

It is given that the teacher is going to buy museum ticket for each students.

Total money spent = $182

Price of each ticket = $6.50

Let total number of tickets bought = [tex]x[/tex]

We know that to find the total amount of money spent on ticket, we can add price of each ticket (i.e. $6.50) [tex]x[/tex] number of times.

OR

In other words, simply multiply the number of tickets with price of each ticket to find the total money spent.

Total money spent = [tex]x \times 6.50[/tex]

We know that total money spent is $182.

[tex]\Rightarrow x \times 6.50 = 182\\\Rightarrow x = \dfrac{182}{6.50}\\\Rightarrow x = 28[/tex]

The ticket is bought for 28 students

Answer:

2 minutes 10 seconds!!!!!

Answer:

4 amperes

Step-by-step explanation:

I graphed the function on the graph below to find the maximum value of c.