What is the probability of drawing a king or a queen?

Answer:

B) 6 times

Step-by-step explanation:

54/9=6

Answer:

x=90

Step-by-step explanation:

x/5=72/4

simplify 72/4 into 18

x/5=18

x=18*5

x=90

The reciprocal of x/5=72/4 is 5/x = 4/72.

Given,

Which of the following uses the reciprocal property to rewrite x/5 = 72/4?

A. 5/x = 4/72

B. x/4 = 5/72

C. x/5 = 72/4

We denote the reciprocal of a number M by 1/M.

Example: 1, 1/2, 2/3,

The reciprocal is:

1 = 1/1 = 1

1/2 = 1/(1/2) = 2

2/3 = 1/(2/3) = 3/2

We have,

x/5 = 72/4

If we apply reciprocal property here we get,

1/(x/5) = 1/(72/4)

5/x = 4/72

Thus the reciprocal of x/5=72/4 is 5/x = 4/72.

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13.23  miles

Step-by-step explanation:

The vector creates an inverted right-angled triangle. The westbound car will have covered 20 miles while the southbound car will ahve covered 15 miles in 30 mins;

40 miles /hr * ½ hr = 20 miles

30 miles/ hr * ½ hr = 15 miles

To find the hypotenuse (distance between the two cars), we shall use the formulae;

a² + b² = c²

20² + 15² = c²

c² = 20² – 15²

c² =  175

c = 13.23

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Answer:

B) y=1/2x-3/2

Step-by-step explanation:

y=2x+3

x=2y+3

2y=x-3

y=1/2x-3/2

Answer:

B

Step-by-step explanation:

EDGE 2020

Answer:

$20,001

Step-by-step explanation:

Let $x be the amount of dollars Lincoln needs to make in sales to earn more than $1500.

His boss pays him $500 for the week, plus a 5% commission on each vehicle he sells.

5% of $x is $0.05x, the Lincoln earns

[tex]\$(500+0.05x)[/tex] in total.

Hence,

[tex]500+0.05x>1,500[/tex]

Solve this inequality:

[tex]0.05x>1,500-500\\ \\0.05x>1,000\\ \\5x>100,000\\ \\x>20,000[/tex]

Lincoln needs to make in sales more than $20,000, so the minimum amount of dollars Lincoln needs to make in sales is $20,001

Answer:

there are 8 pigs because each pig has 4 legs. meanwhile, ducks technically by definition, only have 2 legs,wings do not count as legs.

Step-by-step explanation:

so 1 pig=4 legs.

8 pigs =32 legs

so 32+2x=36

To solve the problem, set up a system of equations using the number of pigs and ducks. Solve the system of equations to find the values of 'p' and 'd'. There are 8 pigs and 2 ducks in the farmhouse.

Let's assume the number of pigs is 'p' and the number of ducks is 'd'. Since each pig has 4 legs and each duck has 2 legs, we can set up the equation: 4p + 2d = 36 (since there are 36 legs in total). We also know that there are 10 animals in total, so we can set up another equation: p + d = 10. Now we have a system of equations which we can solve to find the values of 'p' and 'd'.

Multiplying the second equation by 2, we get 2p + 2d = 20. Subtracting this equation from the first equation, we get 4p + 2d - (2p + 2d) = 36 - 20, which simplifies to 2p = 16. Dividing both sides of the equation by 2, we find that p = 8. Substituting this value back into the second equation, we get 8 + d = 10, which means d = 2.

Therefore, there are 8 pigs and 2 ducks in the farmhouse.

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Answer: Yes

Step-by-step explanation: 144 is a perfect square. In other words, it's possible to find a whole number that can be multiplied by itself that gives us 144.

In this case, we multiply 12 by 12 or 12² to get 144 which means 144 is a perfect square. Also, it's on our perfect square list which I will attach below.

Answer:

Step-by-step explanation:its not a improper fraction

Answer:

1 and 2/9

Step-by-step explanation:

7 goes into 9 1 time and there are 2 left over so that 2 would be 2/9 so it's 1 whole and 2/9

To find kilometers per hour, we need to multiply 2 1/6 by 3, because it took Linley 1/3 hour to ride that far.

2 1/6 * 3 = 6 1/2

So, her average speed in kilometers per hour is 6 1/2 kph

Answer:

40 min

Step-by-step explanation:

1 x 48 + .20 .48

(1.20) (48)=  40 min

Answer:

I could do 1 and 3

1) 2x-3y=-2 ....1

-

2x+y=14......2

=-4y=-16

y=4

Substitute (y=4) into equation 1

2x-3 (4)=-2

2x-12=-2

2x=-2+12

2x=10

×=5

3) 5x+5y=20....1

-

-3x+5y=4......2

=8x=16

x=2

Substitute (x=2) into equation 1

5 (2)+5y=20

10+5y=20

5y=20-10

5y=10

y=2

Answer: (1) x = 5 , y = 4

(2) x = -3 and y = 0

(3) x = 2 and y = 2

Step-by-step explanation:

(1) 2x - 3y = -2  ................... equation 1

   2x + y = 14 ................ equation 2

solving the system of linear equation by elimination method. We need to decide the variable to eliminate first , in this case , since the coefficient of x are the same  and they have the same signs (+), we can eliminate the variable x first by subtracting equation 1 from equation 2, so we have

2x - 2x + y - (-3y ) = 14 - ( - 2)

4y = 16

divide through by 4

y = 4

substitute y = 4 into equation 1 , we have

2x - 3 (4) = -2

2x - 12 = -2

2x = -2 + 12

2x = 10

x = 5

Therefore :

x = 5 and y = 4

(2) x = -6y - 3 ....................... equation 1

    8x + 8y = -24 ....................... equation 2

Solving the system of linear equation by substitution method , substitute x = -6y - 3 into equation 2 , equation 2 becomes

8(-6y - 3 ) + 8y = -24

expanding , we have

-48y - 24 + 8y = -24

-40y - 24 = -24

Add 24 to both sides , we have

- 40y = -24 + 24

-40y = 0

divide through by -40

y = 0/-40

y = 0

substitute y = 0 into equation 1 , equation 1 then becomes

x = -6(0) - 3

x = -3

Therefore : x = -3 and y = 0

(3)  5x + 5y = 20 ........................ equation 1

    -3x + 5y = 4  ............................ equation 2

solving the system of linear equation by elimination method , we have to decide the variable to eliminate first , since the coefficient of y are the same and are both positive, we will eliminate y by subtracting equation 2 from equation 1 , we have

5x - (-3x) + 5y - 5y = 20 - 4

5x + 3x + 0 = 16

8x = 16

x = 2

substitute x = 2 into equation 1 , equation becomes

5(2) + 5y = 20

10 + 5y = 20

5y = 20 - 10

5y = 10

y = 2

Therefore : x = 2 and y = 2

Answer:

[tex] {x}^{2} + 2x - 15[/tex]

Step-by-step explanation:

[tex]x(x + 5) - 3(x + 5) \\ = \times {x}^{2} + 5x - 3x - 15 \\ = {x}^{2} + 2x - 15[/tex]

Final answer:

To expand and simplify (x - 3)(x + 5), we use the FOIL method, resulting in [tex]x^2 + 5x - 3x - 15[/tex]. Combining like terms, we get the simplified form [tex]x^2 + 2x - 15.[/tex]

Explanation:

To expand and simplify the expression (x - 3)(x + 5), we use the distributive property, also known as the FOIL method, which stands for First, Outer, Inner, and Last. This refers to the terms you multiply together in a binomial multiplication:

First: Multiply the first terms in each binomial: x* x = [tex]x^2[/tex]

Outer: Multiply the outer terms in the binomials: x *5 = 5x

Inner: Multiply the inner terms in the binomials: -3 * x = -3x

Last: Multiply the last terms in each binomial: -3 * 5 = -15

Combining these products gives us: [tex]x^2 + 5x - 3x - 15.[/tex] We then combine like terms, which in this case are 5x and -3x:

[tex]x^2 + 2x - 15.[/tex]

So, the expanded and simplified form of (x - 3)(x + 5) is [tex]x^2 + 2x - 15.[/tex]

Answer:

The graph of y + 1 = −3/5 (x − 4) would be a straight line. The graph figure is attached below.

Step-by-step explanation:

As the linear equation y + 1 = −3/5 (x − 4) is given.

Since y-y₁ = m (x - x₁) is the Point-slope form is the general form y-y₁=m(x-x₁) for linear equations.

Hence, from the linear equation we can determine the slop which is m = -3/5

Also, when we put x = 0 in the linear equation, we determine the y-intercept as follows:

                            y + 1 = −3/5 (x − 4)

                            y + 1 = -3/5(-4)      ∵x = 0

                            y = 12/5 - 1

                            y = 7/5

y-intercept: 7/5

Hence,

Table for some points can be made for x and values as:

0           7/5

1            4/5

The graph of y + 1 = −3/5 (x − 4) would be a straight line. The graph figure is attached below.

Keywords: graph, straight line

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Answer:

Measure of Angle 5 = 150 degree.

Step-by-step explanation:

Given line g and h are parallel lines.

Let angle measuring [tex]30\ degree[/tex] be a.

From figure we can see that [tex]\angle a\ and\ \angle 3[/tex] both are Linear Pair Postulate,

i.e. [tex]\angle\ a+\angle 3 =180\ degree[/tex]

So,

[tex]30\ degree +\angle 3 =180\ degree[/tex]

[tex]\angle 3 = 180-30[/tex]

[tex]\Therefore \angle 3=150\ degree[/tex]   ------------(equation 1)

Now, [tex]\angle\ a\ and\ \angle\ 4[/tex] are alternate interior angles, and alternate interior angles are equal.

i.e. [tex]\angle\ a = \angle 4[/tex]

Therefore  [tex]\angle\ 4 =30\ degree[/tex]  ------------(equation 2)

Now, [tex]\angle 4\ and\ \angle 7[/tex] both are Linear Pair Postulate,

i.e. [tex]\angle\ 4 +\angle\ 7 = 180\ degree[/tex]

[tex]30+\angle\ 7=180[/tex]    ------------------(from equation 2)

[tex]\angle\ 7 =180-30[/tex]

[tex]\therefore\ \angle\ 7 = 150\ degree[/tex] ---------(equation 3)

Now,  [tex]\angle\ 7\ and \angle\ 5[/tex] are vertically opposite angles, and vertically opposite angles are equal.

So,

[tex]\angle 7=\angle 5[/tex]

[tex]\therefore\ \angle 5=150\ \ degree[/tex] -----------------(from equation 3)

Answer:

x + 2 = 0 and y - 3 = 0

Step-by-step explanation:

We have to find the solution of the system of equations  

6x + 2y = - 6 ........... (1)

⇒ 12x + 4y = - 12 .......... (2) and  

3x - 4y = - 18 ........... (3)

Now, solving equations (2) and (3) we get,

15x = - 30

⇒ x = - 2

Hence, from equation (1) we get, 2y = - 6 - 6x = - 6 - 6(- 2) = 6

⇒ y = 3

Therefore, the solution of the given system of equations is (-2,3).

Now, x + 2 = 0 and y - 3 = 0 are another system of equations that have the same solutions. (Answer)

The graph of f(x) is stretched vertically by scale factor 3 and translated 2 units to the right to give the graph of 3f(x - 2)²

Step-by-step explanation:

Let us revise the vertical stretch and the horizontal translation

∵ f(x) = x²

∵ f(x) is multiplied by 3

- 3 is greater than 1, then the graph of f(x) is stretched vertically

  by scale factor 3

∴ The graph of f(x) is stretched vertically by scale factor 3

∵ x² is changed to (x - 2)²

- That means the graph of f(x) translated 2 units to the right

∴ The graph of f(x) is translated 2 units to the right

The graph of f(x) is stretched vertically by scale factor 3 and translated 2 units to the right to give the graph of 3f(x - 2)²

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1. Let x represent the missing angle.

The sum of angles in a triangle is 180°

65° + 57° +x =180

122° +x=180°

x=180-122

x=68°

2. Let y represent the missing angle.

Then

y+90°+40°=180°

y+130°=180°

y=180°-130°

y=50°

3. Let the missing angle be t, then

t+20°+130°=180°

t+150° =180°

t=180°-150°

t=30°

4. Let the missing angle be m, then

m+85°+50°=180°

m=180°-50°-85°

m=180-135°

m=45°

5. Let the missing angle be e, then by the exterior remote angle theorem:

137°=102° +e

137-102=e

e=35°

6. Let the unknown angle p, be the missing angle.

Then by vertical angle property and exterior angle property:

p=35° +100°

p=135°

7. Let g be the missing angle, then

g+20°+30°=180°

g+50°=180°

g=180°-50°

g=130°

8)

Let v be the missing angle:

By angle on straight line, and exterior angle theorem property,

g=(180-155)+60°

g=25°+60°

g=85°

Answer:

2 units

Question:

Calculate the distance between (3 + i) and (3 − i).

Step-by-step explanation:

This problem is equivalent to the problem:

"Calculate the distance between the points (3,1) and (3,-1)."

Since the [tex]x[/tex]-coordinates are the same, this is a vertical distance.

A vertical distance be be found by computing the positive difference of the [tex]y[/tex]-coordinates. In other words, we need only the find the distance between the numbers [tex]y=1[/tex] and [tex]y=-1[/tex] on a number line.

This distance is 1-(-1)=1+1=2 units.

Answer:

y = -2x + 3

Step-by-step explanation:

4x + 2y - 6 = 0

2y - 6 = -4x

2y = -4x + 6

y = -2x + 3

Answer:

The slope-intercept form is,

y = -2x + 3

Step-by-step explanation:

The given equation of the line is,

4x + 2y  - 6 = 0

Subtracting "(4x- 6)" from both sides of the above equation, we get

   4x + 2y - 6 - (4x - 6) = 0 - (4x - 6)

⇒ 4x + 2y - 6 - 4x + 6 = 0 - 4x + 6

⇒ 2y = -4x + 6

Now, dividing both sides by '2' of the above equation, we get

 2y ÷ 2 = (-4x + 6) ÷ 2

⇒y = -2x + 3

This is the required slope-intercept form of the given line.

Answer:

-5a - 4 is the expression equivalent

Following are the calculation to the given expression:

Given:

[tex]\bold{7a-8-12a+4}[/tex]

To find:

solve the expression=?

Solution:

[tex]\to \bold{7a-8-12a+4}\\\\\to \bold{-5a-4}\\\\[/tex]

Therefore, the final answer is "[tex]\bold{-5a-4}[/tex]".

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Answer: 21

Step-by-step explanation:

9  + 10 = 21

The expression simplifies to 81 over 16 by applying the exponent rules, particularly recognizing that any number to the power of 0 is 1 and when raising a power to a power, we multiply the exponents.

The student's question is asking to simplify the expression 3 to the power of 2 multiplied by 5 to the power of 0 whole over 4, the whole squared. To simplify this expression, we should apply the exponent rules.

Let's simplify step-by-step:

First, recognize that any number raised to the power of 0 is 1.

The expression now  simplifies to square of three, since anything multiplied by 1 remains unchanged.

Now, take the entire expression over 4 and square it as indicated.

Thus, the correct answer is 3 to the power of 4 multiplied by 1 squared over 4 squared equals 81 over 16.

Answer:

59°

Step-by-step explanation:

Since the triangle is isosceles then the base angles are congruent.

Subtract the vertex angle from 180° and divide the result by 2, that is

base angle = [tex]\frac{180-62}{2}[/tex] = 59°

Answer:

(0,3) (3,0)

Step-by-step explanation:

if your asking for y=-x+3

or y=x+3 is (0,3) (0,-3

Answer:

Step-by-step explanation:

A = L * W

A = 99

L = 2w + 7

now we sub

99 = (2w + 7)(w)

99 = 2w^2 + 7w

2w^2 + 7w - 99 = 0

(2w - 11)(w + 9) = 0

2w - 11 = 0

2w = 11

w = 11/2

w = 5 1/2 ft (or 5.5 ft) <==== width is 5 1/2 ft)

L = 2w + 7

L = 2(5.5) + 7

L = 11 + 7

L = 18 ft <====== length is 18 ft

Answer:

∠A= 112.5°, ∠B=67.5°, ∠C is 67.5° and ∠D 112.5°.

Step-by-step explanation:

Consider the provided information.

The sum of all interior angle of a polygon is: [tex](n-2)180[/tex]

Substitute n = 8.

[tex](8-2)180=1080[/tex]

Thus, the measure of each angle is: [tex]\frac{1080}{8}=135[/tex]

∠B and ∠C are congruent and their sum is 135°

∠B+∠C=135°

∠B=67.5°

Hence, the m angle B and m angle C is 67.5°.

The sum of all angles of a quadrilateral is 360°.

∠A+∠D+∠B+∠C=360°

∠A+∠D=360°-135°

∠A+∠D=225°

∠A and ∠D are congruent and their sum is 225°

∠A+∠D=225°

∠A=∠D=112.5°

Hence, the m angle A and m angle D is 112.5°.

Answer:

82q

Step-by-step explanation:

-2(-5)q+(-72)(-q)

10q+72q

82q

Hey there! :)

-2(-5)q + (-72)(-q)

Simplify!

10q + (72q)

Since both terms contain "q," we know that we can add them together.

Simply look at it this way: 10+72 , then add the q at the end of your answer.

10 + 72 = 82 --> add the q! Therefore, your final answer is 82q.

~Hope I helped! :)

Answer:

The value of [tex]a_{4}=15[/tex]

Step-by-step explanation:

Given that [tex]a_{1}=6[/tex] and [tex]a_{n}=a_{n-1}+3[/tex]

Given sequence is of the form arithmetic sequence

For arithmetic sequence the sequence is [tex]a_{1},a_{2},a_{3},...[/tex]

The nth term is of the form  [tex]a_{n}=a_{n-1}+d[/tex]

Here  [tex]a_{1}=6[/tex] and [tex]a_{n}=a_{n-1}+3[/tex]

from this the common differnce is 3.

Therefore d=3

To find  [tex]a_{2}[/tex], [tex]a_{3}[/tex] , [tex]a_{4}[/tex]

[tex]a_{n}=a_{n-1}+d[/tex]

put n=2 and d=3 we get

[tex]a_{2}=a_{2-1}+3[/tex]

[tex]a_{2}=a_{1}+3[/tex]

[tex]a_{2}=6+3[/tex]   (here  [tex]a_{1}=6[/tex] )

Therefore [tex]a_{2}=9[/tex]

[tex]a_{n}=a_{n-1}+d[/tex]

put n=3 and d=3 we get

[tex]a_{3}=a_{3-1}+3[/tex]

[tex]a_{3}=a_{2}+3[/tex]

[tex]a_{3}=9+3[/tex]   (here  [tex]a_{2}=9[/tex] )

Therefore [tex]a_{3}=12[/tex]

[tex]a_{n}=a_{n-1}+d[/tex]

put n=4 and d=3 we get

[tex]a_{4}=a_{4-1}+3[/tex]

[tex]a_{4}=a_{3}+3[/tex]

[tex]a_{4}=12+3[/tex]   (here  [tex]a_{3}=12[/tex] )

Therefore [tex]a_{4}=15[/tex]

Therefore the sequence is 6,9,12,15,...

Therefore the value of [tex]a_{4}=15[/tex]

Answer:

Step-by-step explanation:

39 cars every 3 hrs.......that means (39/3) = 13 cars every hr

and if its 13 cars every hr....in 7 hrs, there will be (7 * 13) = 91 cars <==

you can either do it that way....the unit rate way...OR

you can set it up as a proportion...

39 cars to 3 hrs = x cars to 7 hrs...

39 / 3 = x / 7....cross multiply

(3)(x)= (39)(7)

3x = 273

x = 273/3

x = 91 <====

either way, u get the correct answer

Answer:

3/5 0r 0.6

Step-by-step explanation:

A mod B = R

3/5 mod 6, because 3/5 < 6

so (3/5) / 6 = 0 ... R 3/5