which of the following describes a compound
- a single atom
- a particle that is smaller than at atom
- two or more types of atoms chemically bonded together
- two unrelated atoms that are not chemically bonded ​

Answer:

QR = 19

SR = 24

PT = 21

SQ = 20

m∠QRS = 74°

m∠PQS = 49°

m∠RPS = 39°

m∠PSQ = 57°

Step-by-step explanation:

Attached is the complete question:

By definition, a parallelogram is a quadrilateral, which means it has 4 sides where the opposite pairs are parallel to each other. These pair of sides are congruent.

With that we can assume the following:

PQ ≅ SR

PS ≅ QR

m∠PQR ≅ m∠ PSR

m∠QRS ≅ m∠ QPS

The given states that:

PQ ≅ SR

PS ≅ QR

then:

PQ = 24

PS = 19

So we know that:

QR = 19

SR = 24

When it comes to the angles, we have the following theorems:

Opposite angles (Opposite edges) are congruent

Consecutive angles are supplementary, or they sum up to 180°

We are given the following angles:

m∠PQR = 106°

m∠QSR = 49°

m∠PRS = 35°

Based on the theorems we know the following:

m∠PQR ≅ m∠PSR

m∠PQR + m∠QRS = 180°

Then:

m∠PQR + m∠QRS = 180°

106° + m∠QRS = 180°

m∠QRS = 180° - 106°

m∠QRS = 74°

In addition, m∠PSR = 106° and m∠QSR = 49° then when we add it to m∠PSQ it should be equal to m∠PSR

m∠QSR + m∠PSQ = m∠PSR

49° + m∠PSQ = 106°

m∠PSQ = 106° - 49°

m∠PSQ = 57°

Now notice that a parallelogram when you cut them in half, it makes two congruent triangles. All angles in a triangle sum up to 180° so we can assume that:

m∠PSR + m∠PRS + m∠RPS = 180°

So:

106° + 35° + m∠RPS = 180°

141° + m∠RPS = 180°

m∠RPS = 180° - 141°

m∠RPS = 39°

Following the same logic:

m∠QPS ≅ m∠QRS

m∠QPS  = 74°

m∠QPS + m∠PSQ + m∠PQS = 180°

74° + 57° + m∠PQS = 180°

131° + m∠PQS = 180°

m∠PQS = 180° - 131°

m∠PQS = 49°

For this case we must simplify the following expression:

[tex]\frac {3- \frac {2} {a}} {5+ \frac {3} {a}}[/tex]

So, we have:

[tex]\frac {\frac {3a-2} {a}} {\frac {5a + 3} {a}} =[/tex]

We apply double C:

[tex]\frac {a (3a-2)} {a (5a + 3)} =[/tex]

We simplify:

[tex]\frac {3a-2} {5a + 3}[/tex]

Answer:

The simplified expression is:

[tex]\frac {3a-2} {5a + 3}[/tex]

Answer:

701 revolutions

Step-by-step explanation:

Given: Length= 2.5 m

            Radius= 1.5 m

            Area covered by roller= 16500 m²

Now, finding the Lateral surface area of cylinder to know area covered by roller in one revolution of cylindrical roller.

Remember; Lateral surface area of an object is the measurement of the area of all sides excluding area of base and its top.

Formula; Lateral surface area of cylinder= [tex]2\pi rh[/tex]

Considering, π= 3.14

⇒ lateral surface area of cylinder= [tex]2\times 3.14\times 1.5\times 2.5[/tex]

⇒ lateral surface area of cylinder= [tex]23.55 \ m^{2}[/tex]

∴ Area covered by cylindrical roller in one revolution is 23.55 m²

Next finding total number of revolution to cover 16500 m² area.

Total number of revolution= [tex]\frac{16500}{23.55} = 700.6369 \approx 701[/tex]

Hence, Cyindrical roller make 701 revolution to cover 16500 m² area.

The number of revolutions a cylindrical roller makes can be determined by first finding the area it covers in one revolution (using the formula for the surface area of a cylinder) and then dividing the total area covered by this. The formula to calculate the surface area of a cylinder is 2πrh, where r is the radius and h is the length of the cylinder.

First, we need to find the surface area of the roller. The surface area of a cylinder can be calculated using the formula: 2πrh, where r is the radius and h is the height (or in this case, the length of the roller). Here, r = 1.5m and h = 2.5m, so the surface area that the roller covers in one revolution is 2π(1.5m)(2.5m) = 11.25π m².

The roller covers an area of 16500 m², so to find out how many revolutions it makes, we divide the total area by the area covered in one revolution. That is, 16500m² / 11.25π m². After carrying out the division, we get the number of revolutions the roller makes. This will give us the desired answer.

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Answer:

(x/2)*4=3

= x*4/2=3

2x=3

x=1.5

Check:

4*(1.5)/2

=6/2

=3

Answer:

DC = 4.5

Step-by-step explanation:

Since DC is on AC it is a segment bisector.

This divides AC exactly in half.

AC = 9 / 2  = 4.5

DC = 4.5

Final answer:

The answer is 64 green marbles.

Explanation:

To find out how many green marbles are there, we can set up an equation based on the given information. Let G represent the number of green marbles and R represent the number of red marbles. We know that the total number of marbles is 77, so we have the equation G + R = 77. We are also given that the number of green marbles is 1 less than 5 times the number of red marbles, which can be written as G = 5R - 1.

We can solve this system of equations by substituting the second equation into the first equation:

5R - 1 + R = 77

6R = 78

R = 13

Substituting the value of R back into the second equation, we can find the number of green marbles:

G = 5(13) - 1 = 64

Therefore, there are 64 green marbles in the bag.

The expression (4r+6)÷2 can be used to represent the number of females on a team if r is used to represent the number of female team members. Otherwise, it represents what the variable r represents.

The expression (4r+6)÷2 represents an algebraic equation where r is a variable. If r is representing the number of female team members in a sport, then the value for r can be inserted into the equation to find the total. For instance if r=5, representing 5 female team members, the equation would then be (4*5+6) ÷2 = (20+6) ÷ 2 = 26 ÷ 2 = 13.

However, it's important to note that this equation does not inherently represent the number of females on a team. The value it represents is dependent on what the variable r is representing. If r represents something different, then the result would represent that different thing. Thus, the equation can only represent the number of females on a team if r is used to represent that.

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Answer:

2 3

4 5

(2x+3)(4x-5)

Step-by-step explanation:

Ur welcome

Answer:

[tex]r=4\\ \\s=3\\ \\t=-1[/tex]

Step-by-step explanation:

Given the system of three linear equations:

[tex]\left\{\begin{array}{l}-6r+5s+2t=-11\\ \\-2r+s+4t=-9\\ \\4r-5s+5t=-4\end{array}\right.[/tex]

Cheange the positions of the first and the second equations:

[tex]\left\{\begin{array}{l}-2r+s+4t=-9\\ \\-6r+5s+2t=-11\\ \\4r-5s+5t=-4\end{array}\right.[/tex]

Multiply the first equation by -3 and add it to the second equation and then multiply the first equation by 2 and add it to the third equation:

[tex]\left\{\begin{array}{r}-2r+s+4t=-9\\ \\2s-10t=16\\ \\-3s+13t=-22\end{array}\right.[/tex]

Multiply the second equation by 3, the third equation by 2 and add them:

[tex]\left\{\begin{array}{r}-2r+s+4t=-9\\ \\2s-10t=16\\ \\-4t=4\end{array}\right.[/tex]

From the third equation,

[tex]t=-1[/tex]

Substitute it into the second equation:

[tex]2s-10\cdot (-1)=16\\ \\2s+10=16\\ \\2s=6\\ \\s=3[/tex]

Substitute [tex]t=-1[/tex] and [tex]s=3[/tex] into the first equation:

[tex]-2r+3+4\cdot (-1)=-9\\ \\-2r+3-4=-9\\ \\-2r-1=-9\\ \\-2r=-9+1\\ \\-2r=-8\\ \\2r=8\\ \\r=4[/tex]

Hence,

[tex]r=4\\ \\s=3\\ \\t=-1[/tex]

Answer:

9.01 maybe my math might be wrong

Step-by-step explanation:

Answer:

In total it would be $10.71

Step-by-step explanation:

Turn the percent into a decimal, 6% into 0.06. Then multiply that with 8.50.

8.50×0.06= 0.51

Now, turn 20% into a decimal and multiply that with 8.50.

8.50×0.20= 1.70

Then, add 0.51 and 1.70 to 8.50.

0.51+1.70+8.50= 10.71

x + y = 12

Equation 2: Difference:

x - y = 4

Solution:

x + y = 12

x - y = 4

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

Add the two equations together:

2x = 16

Divide both sides by 2:

x = 8

Solve for y:

Use equation 1 substituting for x:

x + y = 12

8 + y = 12

Subtract 8 from both sides:

y = 4

Answer:

one number is 8 and the other number is 4.

8 + 4 = 12

8 - 4 = 4

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The numbers are 8 and 4.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Let the two numbers be M and N.

Now,

The sum is 12 and their difference is 4.

This can be written as,

M + N = 12 _____(1)

M - N = 4 _______(2)

From (1) we get,

M = 12 - N ______(3)

Putting (3) in (2) we get,

M - N = 4

12 - N - N = 4

12 - 2N = 4

Add 2N on both sides.

12 = 4 + 2N

Subtract 4 on both sides.

12 - 4 = 2N

8 = 2N

Divide 2 on both sides.

N = 8/2

N = 4

Now,

Put N = 4 on (3).

M = 12 - 4

M = 8

We can cross-check.

M + N = 12

8 + 4 = 12

12 = 12

M - N = 4

8 - 4 = 4

4 = 4

Proved.

Thus,

The numbers are 8 and 4.

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Answer:

0

Step-by-step explanation:

Answer:

$500

Step-by-step explanation:

We are given;

We are supposed to determine the amount spent on food;

Therefore;

Amount on gas and hotel room = 3/5 × $2500

                                                     = $ 1500

Thus;

Remaining amount = $2500 - $1500

                                = $1000

But;

1/2 of the remainder was spent for the food

Thus;

Amount on food = 1/2 × $1000

                           = $500

Hence, the family spent $500 on food

Answer:

Therefore the coordinates of C is

C(4,9).

Step-by-step explanation:

Given:

Point A , B , and C are Collinear.

i.e A-B-C is a Straight Line

AB : BC = 1 : 1

i.e B is the Mid Point of AC.

And Point A , B and C lie on the Same Line

point A( x₁ , y₁) ≡ ( 0 ,-9)

point B( x , y) ≡ (2 , 0)

To Find:

point C( x₂ , y₂) ≡ ?

Solution:

B is the Mid Point of AC. Hence by Mid point Formula,

[tex]Mid\ point(AC)=(\dfrac{x_{1}+x_{2} }{2}, \dfrac{y_{1}+y_{2} }{2})[/tex]

Substituting the values we get

[tex]B(2,0)=(\dfrac{0+x_{2} }{2}, \dfrac{-9+y_{2} }{2})[/tex]

Substituting x and y value we get

[tex]2=\dfrac{0+x_{2} }{2}\\and\\0=\dfrac{-9+y_{2} }{2}[/tex]

[tex]x_{2}=4\\and\\y_{2}=9[/tex]

Therefore the coordinates of C is

C(4,9).

Answer:

Simplified: 10x-55

Step-by-step explanation:

Distribute the five into the parenthesis..

(5)2x- (5)11

Then, multiply.

10x-55

10x-55 is the simplified version by the distributive property.

Answer:

10x - 55

Step-by-step explanation:

5(2x-11)

5*2x=10x

5*11

10x-55

Answer:

the ratio of part time workers to total workers are 12/30

Answer:

number of sodas sold = 105

number of hot dogs sold = 61

Step-by-step explanation:

i) Let the number of sodas sold be = x

ii) Let the number of hot dogs sold be = y

iii) It is given that the total number of hot dogs and sodas sold = 166

Therefore we can say that x + y = 166

iv) It also given that the number of sodas sold was 44 more than the number of hot dogs sold

Therefore we can say that x = y + 44

v) Substituting the value of x from iv) in the equation in iii) we get

    (y + 44) + y  = 166 ⇒    2y + 44 = 166    ⇒   2y = 122  ∴ y = 61

   Therefore the number of hot dogs sold = 61

vi) Substituting the value of y from v) in iv) we get

            x = y + 44    ⇒    x = 61 + 44   ∴ x = 105

     Therefore the number of sodas sold = 105

Answer: -1

Step-by-step explanation:

i^42

(i^2)^21 ( NOTE i^2 = -1 )

(-1)^21

-1 ( -1^odd number is -1 )

x + 5y = -9

8x - 10y = 28

Set y equal

-2y - 10y = 18

8x - 10y = 28

Subtract from one another

-10x = -10

Divide

x = 1

Plug x in one of the equations and solve

x + 5y = -9

1 + 5y = -9

5y = -10

y = -2

Answer

(1,-2)

Hope this helps! ;)

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}x+5y=-9\\8x-10y=28&\text{divide both sides by 2}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}x+5y=-9\\4x-5y=14\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad5x=5\qquad\text{divide both sides by 5}\\.\qquad\boxed{x=1}\\\\\text{Put it to the first equation}\\\\1+5y=-9\qquad\text{subtract 1 from both sides}\\5y=-10\qquad\text{divide both sides by 5}\\\boxed{y=-2}[/tex]

Answer:

A Factor can be explained as combination of the numerator and denominator by which the demo is decided by the numerator

Answer:

factor a number means to break it up into numbers that can be multiplied together to get the original number. EXAMPLES: 6 = 3 x 2 so, factors of 6 are 3 and 2 9 = 3 x 3 so, factors of 9 are 3 and 3 Sometimes, numbers can be factored into different combinations.

Step-by-step explanation:

Answer:

B. 2 x 40 x pi

Step-by-step explanation:

the other answer lead me to the correct answer. I just chose this option on TTM and it was correct.

An expression that can be used to find the circumference of the skating rink, in feet is: (B) 2 ⋅ 40 ⋅ π

The formula to find the Circumference of a Circle is:

C = 2πr

Where:

C is Circumference

r is radius

We are given that the radius is: r = 40 ft

Thus the circumference is:

C = 2 * 40 * π

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Answer:

[tex]5s^2 +13s-10[/tex]

Step-by-step explanation:

Given the expression

[tex]5s(3+s)-(2s+10)[/tex]

First, use distributive property:

[tex]5s(3+s)=5s\cdot 3+5s\cdot s=15s+5s^2\\ \\-(2s+10)=(-1)\cdot (2s+10)=(-1)\cdot 2s+(-1)\cdot 10=-2s-10[/tex]

Now, the given expression is equivalent to the following expression:

[tex]15s+5s^2-2s-10[/tex]

Rewrite this expression using commutative property:

[tex]5s^2+15s-2s-10\\ \\=5s^2 +13s-10 \ [\text{Add the like terms}][/tex]

The given equation is y + 2 = 4(x - 1)

The equation of the parallel line in the slope-intercept form is y = 4x - 7

Step-by-step explanation:

Parallel lines have

The slope-intercept form of the equation of a line is y = mx + b, where m is the slope of the line and b is the y-intercept

∵ The equation of the given line is y + 2 = 4(x - 1)

- Change its form to slope-intercept form to find its slope

∵ y + 2 = 4(x) - 4(1)

∴ y + 2 = 4x - 4

- Subtract 2 from both sides

∴ y = 4x - 6

- Compare it with the slope-intercept form to find m

∵ the slope-intercept form is y = mx + b

∴ m = 4

∵ The parallel lines have same slopes

∴ The slope of the parallel line is 4

- Substitute it in the form of the equation

∴ The equation of the parallel line is y = 4x + b

- To find b substitute x and y in the equation by the

   coordinates of a point on the line

∵ The parallel line passes through point (1 , -3)

∴ x = 1 and y = -3

∵ -3 = 4(1) + b

∴ -3 = 4 + b

- Subtract 4 from both sides

∴ -7 = b

∴ The equation of the parallel line is y = 4x + (-7)

∴ The equation of the parallel line is y = 4x - 7

The equation of the parallel line in the slope-intercept form is y = 4x - 7

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Answer:

X + 12x +35+3x + 15=16x+50

Step-by-step explanation:

6.9

323.6/4=6.885

Round to the nearest tenth=6.9

Answer:

Step-by-step explanation:

Answer:

= 8a/b + 6b/a

look at the phot below for more details.

:)

Answer:

It has 2 solutions

Step-by-step explanation:

Solution 1

-17(y - 2) = -17y + 64 - 17(y - 2)

Solution 2

-17y + 64 - 17(y - 2) = -17y + 64

-17(y - 2) = -17y + 64

-17y  + 34 = -17y + 64

-17y + 17y = 64 - 34

0 = 30 (incorrect)

this system has NO SOLUTIONS

Ricky jogged 6 miles on tuesday and 6 miles on friday

Solution:

Given that,

Rick jogged the same distance on tuesday and friday

Let "x" be the distance jooged on each tuesday and friday

He also jogged for 8 miles on sunday

Total of 20 miles for the week

Therefore, we frame a equation as,

total distance jogged = miles jogged on tuesday + miles jogged on friday + miles jogged on sunday

20 = x + x + 8

20 = 2x + 8

2x = 20 - 8

2x = 12

x = 6

Thus Ricky jogged 6 miles on tuesday and 6 miles on friday

Final answer:

Rick jogged 6 miles each day on Tuesday and Friday. This was found by solving the equation 2x + 8 = 20, where 2x represents the total distance for Tuesday and Friday, and 8 miles is the distance for Sunday.

Explanation:

Rick jogged the same distance on Tuesday and Friday, and 8 miles on Sunday for a total of 20 miles for the week. Since Rick jogged the same distance on both Tuesday and Friday, we can let the distance he jogged on each of those days be represented by the variable x. The total distance jogged over these three days (Tuesday, Friday, and Sunday) can be represented by the equation 2x + 8 = 20.

To solve for x, first subtract 8 from both sides of the equation to isolate the variable:

2x + 8 - 8 = 20 - 8

2x = 12

Then, divide both sides by 2 to get the value of x:

2x / 2 = 12 / 2

x = 6

The distance Rick jogged on Tuesday and Friday was therefore 6 miles each day.

Answer:

3/8

Step-by-step explanation:

The product of the fraction numbers 5/4 and 3/10 in the simplified form will be 3/8.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The fraction numbers are given below.

5/4 and 3/10

Then the product of the fraction numbers 5/4 and 3/10 is given as,

⇒ 5/4 x 3/10

⇒ 15 / 40

⇒ 3/8

The product of the fraction numbers 5/4 and 3/10 in the simplified form will be 3/8.

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