Please help me simplify these expressions

Answer:

The answer is 48.

Step-by-step explanation:

The formula for discriminant, D = b² - 4ac. Then you have to substitute the following values into the formula :

[tex]D = {b}^{2} - 4ac[/tex]

[tex]let \: a = 2 \\ let \: b = \sqrt{32} \\ let \: c = - 2[/tex]

[tex]D = {( \sqrt{32} )}^{2} - 4(2)( - 2)[/tex]

[tex]D = 32 + 16[/tex]

[tex]D = 48[/tex]

Answer:

On the y-axis line

Step-by-step explanation:

Given the location (a,b) of the point P on the coordinated plane.

If a=0

Then the location of P on the x-axis is at x=0

Since b is not equal to zero, b could be positive or negative.

Therefore, the point P could be located on the positive y-axis or the negative y-axis,

It must be exactly on the line.

Answer: The answer is D: 1 (Vote me brainliest)

Answer:

y=1

Step-by-step explanation:

0.3y-0.3=0.4-0.4y

+0.4y

0.7y-0.3=0.4

               +0.3

0.7y=0.7

        -----

        0.7

y=1

Answer:

4x - 3y = 0

Step-by-step explanation:

The angle between the radius and the tangent at P is right

The equation of a line in slope- intercept form is

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

Rearrange 4y + 3x = 25 into this form

Subtract 3x from both sides

4y = - 3x + 25 ( divide all terms by 4 )

y = - [tex]\frac{3}{4}[/tex] x + [tex]\frac{25}{4}[/tex] ← in slope- intercept form

with slope m = - [tex]\frac{3}{4}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{3}{4} }[/tex] = [tex]\frac{4}{3}[/tex] , thus

y = [tex]\frac{4}{3}[/tex] x + c ← is the partial equation

To find c substitute P(3, 4) into the partial equation

4 = 4 + c ⇒ c = 4 - 4 = 0

y = [tex]\frac{4}{3}[/tex] x ← equation of radius in slope- intercept form

Multiply through by 3

3y = 4x ( subtract 3y from both sides )

4x - 3y = 0 ← equation of radius in standard form

Answer:

47=4.7

1000= 100.0

Answer:

The line AB, with A(Ax, Ay), B(Bx, By) and midpoint M(Mx, My) satisfying:

Ax + Bx = 2Mx

Ay + By = 2My

=>

2 + Bx = 2*1

5 + By = 2*2

=> Bx = 0

=> By = -1

=> B(0, -1)

Hope this helps!

:)

Answer:

B(3, 8 )

Step-by-step explanation:

Using the midpoint formula

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then midpoint is

[ [tex]\frac{1}{2}[/tex](x₁ + x₂ ), [tex]\frac{1}{2}[/tex](y₁ + y₂ ) ]

let the coordinates of B = (x, y ), then

[tex]\frac{1}{2}[/tex](1 + x) = 2 ( multiply both sides by 2 )

1 + x = 4 ( subtract 1 from both sides )

x = 3

and

[tex]\frac{1}{2}[/tex] (2 + y) = 5 ( multiply both sides by 2 )

2 + y = 10 ( subtract 2 from both sides )

y = 8

Thus

coordinates of B = (3, 8 )

Answer:

The rational number representing the average change in the volume of water each day is:

[tex]\frac{0.875 liters}{1 day}[/tex]

Step-by-step explanation:

Rational numbers are those that can be represented as the quotient of two integers. That is, rational numbers can be represented by a fraction [tex]\frac{a}{b}[/tex], where a is the numerator and b is the denominator that must be other than zero. To express the set of these numbers, mathematicians use a capital Q.

In this case we know that Finn's pool leaked a total 3.5 L in 4 days, so the rate can be written as:

[tex]\frac{3.5 liters}{4 days}[/tex]

Now you must make this division or quotient, where the denominator will be 1 because you must know the number of liters drained per day:

[tex]\frac{3.5 liters}{4 days}=\frac{0.875 liters}{1 day}[/tex]

So the rational number representing the average change in the volume of water each day is:

[tex]\frac{0.875 liters}{1 day}[/tex]

Answer:

Step-by-step explanation:

If two variables, x and y have a direct variation, it means that an increase in x would lead to a corresponding increase in y. A decrease on x would lead to a corresponding decrease in y.

Therefore, we would compare the scenarios to determine which is not a direct variation. The correct option is

d) Time taken will be less if number of workers are increased to complete the same work.​

The rest are direct variation scenarios

The margin of error would be 1 / √n, where n is the number of students asked.

Margin of error = 1/√501 = 0.0446

Multiply by 100 to change to a percent:

0.446 x 100 = 4.46%

Rounding may be off slighly, so it looks like b would be the correct answer.

Answer:

lresaputa es la C  

Step-by-step explanation:

Answer:

5,500

Step-by-step explanation:

2,500 + 3,000:

2000 + 3000 + 500

5000 + 500

5500

Easy!

Answer:

Option C.

Step-by-step explanation:

Kurt started for the school at 07:35 and ends at 08:25.

Time taken by Kurt to reach the school

= 08:25 - 07:35

= (07 hours + 85 minutes) - (07 hours + 35 minutes) [Since 08 hours + 25 minutes = 07 hours + (60 + 25)minutes]

= 85 minutes - 35 minutes

= 50 minutes

Time taken by Drew to reach the school

= 08:30 - 07:55

= (07 hours + 90 minutes) - (07 hours + 55 minutes) [Since 08 hours + 30 minutes = 07 hours + (60 + 30)minutes]

= 90 minutes - 55 minutes

= 35 minutes

Difference in the time taken by Kurt and Drew = 50 - 35 = 15 minutes.

Therefore, Drew is 15 minutes faster than Kurt.

Option C. is the answer.

Answer:

8,181 ft^2

Step-by-step explanation:

Area of the parking lot = Area of the whole structure - Area of the building

The building is a square of 12cm by 12cm

which is 72ft by 72ft since 1 cm is 6 ft

its area is thus 72 * 72 = 5,184 ft^2

The structure measures 16.5 cm by 22.5 cm

Multiplying the sides by 6, we have 99 ft by 135 ft

So its area is 99 * 135 = 13,365 ft^2

The area of the parking lot = 13,365 - 5,184 =

8,181 ft^2

Answer:

Let the first trip be x

Second trip is 2x-4

Third trip is 2(2x-4)

Fourth trip is 3x + 18

x + (2x-4) + 2(2x-4)+3x+18 = 426

x + 2x -4 + 4x - 8 + 3x + 18 = 426

10x + 6 = 426

10x = 426-6

x = 420/10 = 42 km

Second trip was

2x-4 = 2(42)-4 = 84-4 = 80 km

Third trip was

2 * 80 = 160 km

Fourth trip was

3(42) + 18 = 144 km

Answer:

Step-by-step explanation:

Given : QP║RT and QR║US

To prove: ∠1 ≅ ∠5

                Statements                   Reasons

1).   QP║RT                           1). Given

2). QR║US                           2). Given

3). ∠1 ≅ ∠2                           3). Alternate angles

    ∠2 ≅ ∠5                          

4). ∠1 ≅ ∠5                           4). Transitive property

Reasons for third step,

PQ║RT and QR is a transverse therefore, ∠1 and ∠2 will be alternate angles.

Similarly, QR║US and RT is a transverse therefore, ∠2 and ∠5 will be the alternate angles.

Answer:

The answer is "[tex]\bold{6\sqrt(2)i+2\sqrt(2)j)}[/tex]"

Step-by-step explanation:

Given:

[tex]w=3\sqrt(2)i+\sqrt(2)j[/tex]

To Find:

2w=?

Solution:

[tex]\Rightarrow 2w= 2\times w\\\\\Rightarrow 2w= 2\times (3\sqrt(2)i+\sqrt(2)j)\\\\\Rightarrow 2w= 6\sqrt(2)i+2\sqrt(2)j)\\[/tex]

Answer:

WE need the numbers

Step-by-step explanation:

a

Answer:

a)3

b)3

c)?

Step-by-step explanation:

Answer: c( 320 gallons/34 miles or d( 320 miles/34 gallons

hope it helps..

Answer:

Step-by-step explanation:

Given the following explicit formula, we are to calculate the first four (4) terms of the sequence.

1)  f(n) = 9+8n

When n = 1

f(1) = 9+8(1)

f(1) = 17

when n = 2

f(2) = 9+8(2)

= 9+16

= 25

When n = 3

f(3) = 9+8(3)

f(3) = 33

when n = 4

f(4) = 9+8(4)

= 41

= 25

The first four terms are 17, 25, 33 and 41

2) f(n) = 8(n+1)-13

When n = 1

f(1) = 8(2)-13

f(1) = 3

when n = 2

f(2) =  8(3)-13

= 24-13

= 11

When n = 3

f(3) =  8(4)-13

f(3) = 32-13

= 19

when n = 4

f(4) =  8(5)-13

= 40-13

= 27

The first four terms are 3, 11, 19 and 27

3) f(n) = 65-9n

When n = 1

f(1) = 65-9(1)

f(1) = 56

when n = 2

f(2) = 65-9(2)

= 65-18

= 47

When n = 3

f(3) = 65-9(3)

f(3) = 65-27

= 38

when n = 4

f(4) = 65-9(4)

= 65-36

= 29

The first four terms are 56, 47, 38 and 29

Answer:

No.

Step-by-step explanation:

It is because a line is said to be perpendicular to another line if the two lines intersect at a right angle or at 90° and the two lines in the graph does not intersect at 90° angle..

mark brianliest if my answer suit your question..

Answer:

1:4 or 25% or 1/4

Step-by-step explanation

There are 60 minutes in an hour and 60 divided by 15 is four. So basically, 15 minutes is 1/4 of an hour, 25% of an hour, and 1:4 of an hour.

Answer: (1) Measure of angle K = x degrees

(12) Measure of angle L = (5x) degrees

(3) Measure of angle k + Measure of angle L + Measure of angle N = 180 degrees

Step-by-step explanation: First of all, what we have is a triangle, and one of the properties of a triangle is all three angles add up to 180 degrees. This simply means that the addition of angles K and L and N would be equal to 180 degrees.

The question states that angle K is represented as x degrees, and angle L is 5 times the measure of angle K. Therefore, if K is x degrees, then L is 5 times x, which becomes 5x degrees. Also, angle N is given as 16 degrees less than 8 times the measure of angle K (x degrees). Eight times the measure of angle K is given as 8x. Sixteen degrees less than 8x would now become, 8x - 16 (degrees). Therefore, the angles have been derived as;

Angle K = x degrees

Angle L = 5x degrees

Angle N = 8x - 16 degrees

Having known that one of the properties of any triangle is all angles adding up to 180 degrees, we can now derive the following equation;

x + 5x + 8x - 16 = 180

14 x - 16 = 180

Add 16 to both sides of the equation

14x = 196

Divide both sides of the equation by 14

x = 14

Therefore, angle K = 14 degrees (x), angle L = 70 degrees (5x) and angle N = 96 degrees (8x - 16)

*14 + 70 + 96 = 180*

Answer:

145

Step-by-step explanation:

Answer:

" Expected Payoff " ⇒ $ 1.56 ; Type in 1.56

Step-by-step explanation:

Consider the steps below;

[tex]Tickets That Can Be Entered - 1 Ticket,\\Total Tickets Entered - 1000 Tickets,\\\\Proportion - 1 / 1000,\\Money One ( First Ticket ) = 820 Dollars,\\Money One ( Second Ticket ) = 740 Dollars,\\\\Proportionality ( First ) - 1 / 1000 = x / 820,\\Proportionality ( Second ) - 1 / 1000 = x / 740\\\\1 / 1000 = x / 820,\\1000 * x = 820,\\x = 820 / 1000,\\x = 0.82,\\\\1 / 1000 = x / 740,\\1000 * x = 740,\\x = 740 / 1000,\\x = 0.74\\\\Conclusion ; " Expected Payoff " = 0.82 + 0.74 = 1.56[/tex]

Solution; " Expected Payoff " ⇒ $ 1.56

Answer:

C. (1,-1)

Step-by-step explanation:

Lines are intersecting each other at point (1, - 1).

Hence, the system of equations graphed here would be (1, - 1)

Answer:

(a-b)^3 = [tex]\left(a-b\right)^3=a^3-3a^2b+3ab^2-b^3[/tex]

Step-by-step explanation:

(a-b)^3 = (a-b)(a-b)(a-b)

According to the perfect cube formula (a-b)^3 = [tex]\left(a-b\right)^3=a^3-3a^2b+3ab^2-b^3[/tex]

And there you have it! The perfect cube formula already solved your equation!

Group 'em together

a b − a + 1 − b

a b − a = a ( b − 1 )

Notice that there will be a 1 as without it it'll simply be  ab

1 − b = 1 ( 1 − b )

Notice that it doesn't match with the upper one... so we'll change the signs

1 ( 1 − b ) = − 1 ( b− 1 )

(try to multiply them now!!

Jot them down in one expression

a ( b − 1 ) − 1 ( b − 1 )

You get!!!!!!

( a − 1 ) ( b − 1 )