The ratio of dogs to cats in the shelter is 10 to 8. If there are 20 cats, how many dogs are in the shelter?

If a student has some 1 bills and 5 bills in his wallet and he has a total of 15 bills that are worth 47, then the number of 1 bills he has is equal to 7 and the number of 5 bills he has is equal to 8.

The number of bills of each type can be calculated by forming a system of equations.

Consider x to be the number of 1 bills and y to be the number of 5 bills.

The first equation can be given as,

x + y = 15

The second equation can be given as,

x + 5y = 47

The two equations can be solved by using the substitution method:

By rearranging the first equation the value of x can be calculated to be,

x + y = 15

x = 15 - y

Putting this value of x in the second equation,

x + 5y = 47

15 - y + 5y = 47

4y = 47 - 15

4y = 32

y = 32 ÷ 4

y = 8

The value of x can be determined by putting y = 8 in the first equation,

x + y = 15

x + 8 = 15

x = 15 - 8

x = 7

Hence, the number of 1 bills and 5 bills are equal to 7 and 8 respectively.

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The coordinates of the centroid of Δ ABC is y = -1/3x + 2.

The slope of the line is the rise-to-run ratio or the rise divided by the run. It expresses the slope of a line in the coordinate plane. Finding the slope of a line is similar to determining the slope between two points.

The midpoint D of AC is (-3+4/2, 3-3/2) or (1/2, 0).

Note that DB is a line that connects the vertex B and D, the midpoint of AC.

The slope of the line DB is ((5-0)/(2-1/2)) or 10/3.

The equation of DB is

y - 5 = 10/3 (x - 2)

simplifying the above equation, we get

y - 5 = 10x/3 - 20/3

y - 5 + 5 = 10x/3 - 20/3 + 5

y = 10x/3 - 5/3

Use the same method to find the equation of the line between point A and the midpoint of BC.

Therefore, the coordinates of the centroid of Δ ABC is y = -1/3x + 2.

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The ball hits the surface at 43.5° and bounces back at 43.5°.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given that When a ball is bounced on a smooth surface, the angles formed by the path of the ball are congruent.

If the path of a ball forms a 53 angle with the floor, find  the angle with the floor, x

Let the angle with the floor, x

Using, to find x, setup the equation:

x+ 53 +x=180

2x+ 53 =180

2x = 127

x= 43.5°

Therefore, the ball hits the surface at 43.5° and bounces back at 43.5°.

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Answer:

70 miles per hour

Step-by-step explanation:

take 875mi and divide by how long it took: 12.5 hours

Answer:

I'm pretty sure the answer is E

The vector PQ is given by the addition of the components of the two vectors i.e. →PQ = →Q + →P

Vector is a quantity having magnitude as well as direction and is used to denote the mathematical and geometrical direction of the given quantity.

For example : Velocity, Displacement etc.  

Let us first assume that,

P(x,y,z) and Q(u,v,w)

Now, we need to find the vector PQ

→PQ = →Q + →P

= (ui + vj + wk ) + (xi + yj + zk)

= (ui + xi ) +(vj  + yj) + (wk +zk)

= (u+x) i + (v + y) j + (w + z)k

= →PQ

For example : Let P(1,2,1) and Q ( -1, -2,4)

Then,  →PQ = →Q + →P

= (1i + 2j + 1k ) + (-1i + (-2)j + 4k)

=  (1-1) i + (2 -2) j + (1 + 4)k

= oi+0j +5j

= 5j

Hence, the vector PQ is given by the addition of the components of the two vectors.

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The area of the figure is 289 square unit

The area of a rectangle can be calculated by multiplying the length and the width of the shape.

Given that

But the length and the width have two equal opposite sides. The shape is a square

20 - x = 3x + 8

20 - 8 = 3x + x

12 = 4x

x = 12/4

x = 3

L = 20 - 3 = 17

B = 3(3) + 8

B = 9 + 8

B = 17

A = 17 x 17

A = 289 square unit

Therefore, the area of the figure is 289 square unit

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Answer:

[tex]1 - 5q + 5q + 16 \\ = 17[/tex]

The expression is simplified to s = -5/ 4

Algebraic expressions are expressions composed of terms, variables, constants, factors and coefficients.

They are also made up of mathematical operations such as addition, subtraction, multiplication, division, etc

Given the expression;

42 = 14{ 4 + 4/ 5s}

Divide both sides by 14

42/14  = 14{ 4 + 4/ 5s}/14

3 = 4 + 4/ 5s

3 =   20 + 4s/5

cross multply

15 = 20 + 4s

collect like terms

15 - 20 = 4s

-5 = 4s

Make 's' the subject

s = -5/ 4

Thus, the expression is simplified to s = -5/ 4

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Answer: 36

Step-by-step explanation:

XZ=XY+YZ

48=12+YZ

48-12=12-12+YZ

YZ=48-12

YZ=36

The fabric that she cannot use is the softballs.

A proper fraction is a non-integer that is made up of a numerator that is smaller in value than the denominator. A mixed fraction is a fraction that is made up of an integer and a proper fraction. An example of a mixed fraction is 1 7/8.

The first step is to determine the total amount of fabric needed for the 4 friends : 1 7/8 x 4

15/8 x 4 = 60 /8 = 7 1/2 yards

The second step is to convert the mixed fractions to decimals, by dividing the numerator by the denominator and adding the integer.

7 1/2 = 7.5

73/5 = 7.6

The fabric that cannot be used as the fabrics that are less than 7.5 yards.

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Answer:

well done .....I hope it's helpful

Answer:

x | y

-2. -2

-1. 2

0. 6

1. 10

2. 14

how many numbers do we have between each number on Y? 4

Step 1

this you have to use this data to make your function

f(x)=4X

Always you have to use the spaces times X

Step 2

We have to calculate what do we need to satisfy the function, in this case we have to add 6

f(x)=4x+6

The numbers that makes the inequality s ≤ 6 true include:

Inequality graphs are graphs made to represent inequality equations.

the equation s ≤ 6 is interpreted to be the value of s that is less than or equal to 6.

From the interpretation, any value from 6 downwards is the correct answer. Hence we have the correct numbers listed as:

Other numbers above 6 are wring and do not fit in

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The probability of getting an Ace is 1/13.

Probability of an event = number of favorable outcomes for the event/number of all possible products.

First, let's calculate the number of all possible outcomes. Randomly picking the cards could result in each of the 52 being selected. So, there are 52 possible outcomes.

But if you want an Ace in your desired event, you have four options—ace of Spades, Ace of Clubs, Ace of Hearts, and Ace of Diamonds. Therefore, the number of favorable outcomes for Aces = 4.

Therefore,

The probability of getting an Ace with a deck of 52 cards = 4/52 = 1/13.

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The product of the smallest and largest integer is 672

Represent the smallest even integer with x.

So, the other even integers are x + 2 and x + 4

The sum is represented as

x + x + 2 + x + 4 = 18 + 5/2x

Evaluate the like terms

3x + 6 = 18 + 5/2x

Evaluate the like terms

1/2x = 12

Multiply by 2

x = 24

The largest integer is x + 4

So, we have

x + 4 = 24 + 4

x + 4 = 28

The product of the smallest and largest integer is

Product = 24 * 28

Evaluate

Product = 672

Hence, the product of the smallest and largest integer is 672

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7/10 is 17th term of sequence a₁₆ = 1/5, d= 1/2.

Given the 16th term and the common difference, we add the common difference from the 16th term to determine the 17th term:

a₁₇ =  a₁₆ + d

    =  1/5 + 1/2

    = 7/10

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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In mathematics, an inequality is a relation which makes a non-equal comparison between the two numbers or other mathematical expressions. Inequalities have no solution are X>X, -4+X>-2+X.

An inequality compares two values, showing if one is less than, greater than, or simply not equal to the another value.

Inequalities are governed by following properties. All of these properties also hold if all of non-strict inequalities (≤ and ≥) are replaced by their corresponding strict inequalities (< and >) and — in case of applying a function — monotonic functions are limited to the strictly monotonic functions.

From the above equations, the inequalities having no solutions are,

X>X

-4+X>-2+X

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The approximate circumference of the path Round to the nearest hundredth is 93.12 feet.

A circle's outside boundary is called the circumference and can be measured, or calculated, by using

Circumference = 2πr

where r is the radius of circle.

Now it is given that,

circumference of pond = 68 feet

⇒ 2πr = 68

⇒ r = 34/π

⇒ r = 10.82 feet

Now it is also given that, The outer edge of the path is going to be 4 feet from the pond all the way around

⇒ Radius of path, R = r + 4

⇒ Radius of path, R = 10.82 + 4  

⇒ R = 14.828

So,circumference of the path = 2πR

⇒ circumference of the path = 2π*14.828 = 93.119 feet

⇒ circumference of the path Round to the nearest hundredth = 93.12 feet

Thus, the approximate circumference of the path Round to the nearest hundredth is 93.12 feet.

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Answer:

Step-by-step explanation:

Answer:

Yes, that means the whole fraction is negative.

Also for future note, if the negative is on the top or bottom, the fraction will still be negative. Unless it says to simplify.

Hope this helps!

Answer:

7

Step-by-step explanation:

5x + 3 = 38

5x + 3 - 3 = 38 - 3

5x = 35

5x ÷ 5 = 35 ÷ 5

x = 7

Answer:

[tex]81x {}^{6} - 108 { \times }^{5} + 54 { \times }^{4} - 12 { \times }^{3} + { \times }^{2} [/tex]

He estimates that he will stand 6 feet 9 inches tall when he is 20 years old. His prediction is correct.

Given: Growth per year = 3 inches

Height at 15 yrs of age = 5'6''

Height at 20 yrs of age = 6'9''(predicted)

We know that Jesse grows 3 inches every year.

In 5 years(15yrs - 20yrs) his growth = 5 × 3 = 15 inches.

At 15 years(present) height = 5'6''

At 20 years (future) height = 5'6'' + 15'' = 6'9'' (since, 1ft = 12 inches)

Thus, Jesse's prediction is correct

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Answer:

base : 7 units

height : 4 units