Susan is attending a talk at her son's school. There are 8 rows of 10 chairs where 54 parents are sitting.
Susan notices that every parent is either sitting on their own or next to just one other person.
What is the largest possible number of adjacent empty chairs in a single row at that talk?

Its neither of the above(maybe you type something wrong?)

The total cost is

$(3 x 3 + 4 x 2)

Answer:

Integers are 48, 49, 50

Step-by-step explanation:

x+(x+1)+(x+2) = 147

3x + 3 = 147

3x = 147-3

x = 144 / 3 = 48

Answer:

1/3 y  +5

Step-by-step explanation:

five more than one-third y

1/3 y  +5

Answer:

5+1/3y

Step-by-step explanation:

Hope it helps

Answer:

-2<x<2

Step-by-step explanation:

its wrong but ur from britain luv innit xxx

Answer:

Sorry your mouse is blocking the fx equation. Is it x squared? I can't help you if I can't see what the equation is I'm sorry

Step-by-step explanation:

Answer:

x-14

Step-by-step explanation:

The binomial which is a factor of this trinomial is (x- 14).

An algebraic expression with three terms is called a trinomial.

Examples of a trinomial expression: x + y + z is a trinomial in three variables x, y and z.

Given:

p(x) = x²-16x + 28

If x+ a is factor of any polynomial p(x) then x= -a satisfy the polynomial.

factorizing p(x)

x²-16x + 28

= x²-14x + 2x + 28

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

= (x- 14)(x+ 2)

Hence, the binomial is (x- 14).

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Answer:

Step-by-step explanation:

The length of the base is 3 feet and the height of the triangle is 6 feet.

Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees. The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the triangle in a two-dimensional plane is called the area of the triangle.

Given that the height of a triangle is 3 feet greater than the base. The area of the triangle is 54 square feet.

The dimensions of the triangle will be calculated as,

A = (1/2)  x b x h

A = (1/2) x b x ( b + 3 )

54 = ( 1 / 2 ) x ( b² + 3b )

108 =  ( b² + 3b )

( b² + 3b - 108) = 0

( b² + 12b -3b -108 ) = 0

(b - 3 ) ( b+ 12 ) = 0

b = 3 and b = -12 ignore negative value.

The height will be calculated as,

h = b + 3

h = 3 + 3

h = 6 feet

Therefore, the length of the base is 3 feet and the height of the triangle is 6 feet.

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Answer:

vertex is (2,-25) Y-intercept is -21

Step-by-step explanation:

Answer: EDMENTUM USERS!

I got this correct on the tutorial. Hope this helps!

Step-by-step explanation:

Answer:

0.08 minutes for a kilometer.

Step-by-step explanation:

If the track is 25 kilometers, and he runs 25 kilometers in 2 minutes, he runs a kilometer in 2÷25 minutes or 0.08 minutes which is 4.8 seconds.

I'm pretty sure the track isn't 25 kilometer or he can't run a lap in 2 minutes. But if so, the answer is 0.08 minutes.

Answer:

1. x = 32°

2. x = 28°

3. x = 15°

4. x = 30°

5. x = 40°

6. x = 20°

Step-by-step explanation:

All the angles should add up to 90° as they are complementary.

Answer:

3s+15

Step-by-step explanation:

let 's' be the length of the shortest side

-> twice as long as the length of the shortest side =2s

->length of the longest side to be three more than twice as long as the length of the shortest side = 2s + 3

-> the third side= 12 feet

p = s + 12 + 2s+3

p= 3s+15

Answer:

m∠D = 46°

m∠F = 44°

Step-by-step explanation:

cos D =base/hypo

cosD =23.5/33.8 = 0.695

so and D = 45.97°

thus angle F = 180-(90+45.97) =44.03°

Using relations in a right triangle, it is found that:

The relations in a right triangle are given as follows:

In this problem:

Hence:

[tex]\sin{D} = \frac{24.3}{33.8}[/tex]

[tex]D = \sin^{-1}{\left(\frac{24.3}{33.8}\right)}[/tex]

[tex]D = 46^\circ[/tex]

[tex]\sin{F} = \frac{23.5}{33.8}[/tex]

[tex]F = \sin^{-1}{\left(\frac{23.5}{33.8}\right)}[/tex]

[tex]F = 44^\circ[/tex]

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===========================================================

Explanation:

Check out the diagram below for a visual.

The line x = 2 is a vertical line in which every point on this line has x coordinate 2. Two points on this line are (2,0) and (2,1).

The point (-2,4) is 4 units away in the horizontal direction from the line x = 2. Basically we start at (-2,4) and move 4 units to the right to arrive at (2,4). Move 4 more units to arrive at (6,4).

In short: we reflect (-2,4) over the line x = 2 and it lands on (6,4)

We see that choice C must be the answer as no other answer choices have (6,4). So if you are pressed for time, you can stop here.

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

Let's keep going for the sake of completeness

We'll follow the same steps for the point (-1,5).

Move 3  units to the right to go from (-1,5) to (2,5). The goal again is to reach the vertical line x = 2

Then move another 3 units to the right to arrive at (5,5)

(-1,5) reflects over x = 2 to land on (5,5).

Answer: No

Step-by-step explanation:

Because there is more than one 3 in the following ordered pair. If you make this a table it will be easier.

Answer:

No

Step-by-step explanation:

It would be yes only if the output (y-value) has values one time.

There are double 2s in the output so therefore your answer would be no

Hope this helps!

Answer:

( fraction negative 1 over 4, fraction 1 and 3 over 4 )

Step-by-step explanation:

Answer:

1st one will be it!

Step-by-step explanation:

Answer:

0.35

Step-by-step explanation:

This probability distribution is shown below:

Pitch                   1            2        3          4         5

Frequency         15         20      40        15        10

Probability         0.15     0.2      0.4      0.15      0.1

The probability that the pitcher will throw fewer than 3 pitches to a batter = P(X < 3)

X  is the number of pitches thrown. Therefore:

P(X < 3) = P(X = 1) or P(X = 2)

The additive rule pf probability states that if two events X and Y are dependent events, the probability of X or Y occurring is the sum of their individual probability.

P(X < 3) = P(X = 1) or P(X = 2) = P(X = 1) + P(X = 2) = 0.15 + 0.2 = 0.35

The probability that the pitcher will throw fewer than 3 pitches to a batter = 0.35

Answer:

.35

Step-by-step explanation:

Answer:

70 degrees

Step-by-step explanation:

We want to determine an angle [tex]\theta$ such that $0.3<\cos \theta<0.5[/tex]

If [tex]0.3<\cos \theta<0.5,$ then:[/tex]

[tex]\arccos 0.3< \theta<\arccos 0.5[/tex]

[tex]60^\circ<\theta<72.53^\circ[/tex]

Therefore, any angle greater than 60 degrees but less than 72.54 degrees will give a cosine value of the required range.

Example:

[tex]\cos 70^\circ =0.342[/tex]

Answer:

4 ²/3

Step-by-step explanation:

( 5+2) ×( 6-4) / ( 2+1 )

= (7)×(2) / 3

= 4 ²/3

Answer:

The height of the flag staff is 73 m

Step-by-step explanation:

Let H₁ be the height of the building.

Since the angle of elevation of the top of the tower is 45° from a point 100 m away from the base of the tower,

From tan45° = H₁/100

H₁ = 100tan45° = 100 m

Let H₂ be the height of the building plus flag staff.

Since the angle of elevation of the top of the flag staff is 60° from the same point 100 m away from the base of the tower,

From tan60° = H₂/100

H₂ = 100tan60°

= 100√3

= 100 × 1.73

= 173 m.

So, the height of the flag staff is h = H₂ - H₁

= 173 m - 100 m

= 73 m.

So, the height of the flag staff is 73 m

The -3 is not in the exponent

Explanation:

The parent function is [tex]f(x) = 2^x[/tex]. Plugging in x = 0 leads to y = 1. So the point (0,1) is on the f(x) curve. Going from (0,1) to (0,-2) is a vertical shift of 3 units downward. To represent this shift, we tack on a "-3" at the end of the f(x) function.

[tex]g(x) = f(x) - 3\\\\g(x) = 2^x - 3[/tex]

You could look at other points as well, but I find working with x = 0 is easiest.

As a check, plugging x = 0 into g(x) leads to...

[tex]g(x) = 2^x - 3\\\\g(0) = 2^0 - 3\\\\g(0) = 1 - 3\\\\g(0) = -2[/tex]

This confirms our answer.

Answer:

Step-by-step explanation:

If Marios share is 3 parts and is £96, then

Find one part = 96/3 = 32

So,

Rachel receives = 32 x 4 = £128

Sanjay receives = 32 x 9 = £288

Hope this helps

Answer:

0

Step-by-step explanation:

The lines are parallel, they will never intersect

Answer:

no solution ( 0)

Step-by-step explanation:

If the lines have the same slope by different y intercepts, the lines are parallel

They will never intersect, so they have no solution

Answer:

  a) h(t) = -16t^2 +41t +37

  b) see attached (3.270 seconds)

  c) (41+√4049)/32 seconds

  d) 1.28125 seconds; 63.265625 feet

  e) [1.5, 2]: -15; [2, 2.5]: -31; [2.5, 3]: -47

Step-by-step explanation:

a) The formula and initial values are given. Putting those values into the formula, we get ...

  h(t) = -16t^2 +41t +37

__

b) The graph is attached. It shows the t-intercept to be about 3.270 seconds.

__

c) Using the quadratic formula, we can find the landing time as ...

  [tex]t=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-41\pm\sqrt{41^2-4(-16)(37)}}{2(-16)}\\\\=\dfrac{41\pm\sqrt{4049}}{32}\qquad\text{only $t>0$ is useful}[/tex]

The exact landing time is (41+√4049)/32 seconds.

__

d) The highest point is at t=-b/(2a) = -41/(2(-16)) = 41/32 seconds.

The value of the function at that point is ...

  h(41/32) = (-16(41/32) +41)(41/32) +37 = 41^2/64 +37 = 4049/64

The maximum height is 4049/64 = 63.265625 feet.

__

e) For a quadratic function, that average rate of change on an interval is the derivative at the midpoint of the interval. Here, the derivative is ...

  h'(t) = -32t +41 . . . in feet per second

Then the average rates of change are ...

  arc[1.5, 2] = h'(1.75) = -32·1.75 +41 = -15 ft/s

  arc[2, 2.5] = h'(2.25) = -32(2.25) +41 = -31 ft/s

  arc[2.5, 3] = h'(2.75) = -32(2.75) +41 = -47 ft/s

These are the average velocity of the water balloon over the given interval(s) in ft/s. Negative indicates downward.

Answer:

(a) h(t) = -16t² + 41t + 37

(b) About 3.3 s

[tex]\large \boxed{\text{(c) }\dfrac{41+ \sqrt{4049}}{32}\text{ s}}[/tex]

(d) -15 ft/s; -31 ft/s; -47 ft/s

Step-by-step explanation:

(a) The function

h(t) = -16t² + v₀t + s₀

 v₀ = 41 ft·s⁻¹

 s₀ = 37 ft

The function is

h(t) = -16t² + 41t + 37

(b) The graph

See Fig. 1.

It looks like the water balloon lands after about 3.3 s.

(c) Time of landing

h = -16t² + 41t + 37

a = -16; b = 41; c = 37

We can use the quadratic formula to solve the equation:

[tex]h = \dfrac{-b\pm\sqrt{b^2 - 4ac}}{2a} = \dfrac{-b\pm\sqrt{D}}{2a}[/tex]

(i) Evaluate the discriminant D

D = b² - 4ac = 41² - 4(-16) × 37 = 1681 + 2368  = 4049

(ii) Solve for t

[tex]\begin{array}{rcl}h& = & \dfrac{-b\pm\sqrt{D}}{2a}\\\\ & = & \dfrac{-41\pm\sqrt{4049}}{2(-16)}\\\\ & = & \dfrac{41\pm\sqrt{4049}}{32}\\\\t = \dfrac{41- \sqrt{4049}}{32}&\qquad& t = \dfrac{41+ \sqrt{4049}}{32}\\\\\end{array}\\[/tex]

[tex]\text{The water balloon will land after $\large \boxed{\mathbf{\dfrac{41+ \sqrt{4049}}{32}}\textbf{ s}} $}[/tex]

(d) Time and maximum height

(i) Time

The axis of symmetry (time of maximum height) is at t = -b/(2a)

[tex]t = \dfrac{-41}{2(-16)} = \dfrac{41}{32} = \textbf{1.281 s}[/tex]

(ii) Maximum height

The vertex is at y = h(1.281) = h(t) = -16(1.281)² + 41(1.281) + 37  = 63.27 ft

(e) Average rate of change

(i) Arc{1.5,2}

h(1.5) = 62.5

  h(2) = 55

m = (h₂ - h₁)/(t₂ - t₁) = (55 - 62.5)/(2 - 1.5) = -7.5/0.5 = -15 ft/s

The water balloon has started to fall after it has reached peak height, so it is not going very fast

(ii) Arc{2,2.5}

h(2.5) =39.5

m = (39.5 - 55)/(2 - 1.5) = -15.5/0.5 = -31 ft/s

The balloon is in mid-fall, so gravity has caused it to speed up.

(iii) Arc{2.5,3}

h(3) = 16

m = (16 - 39.5)/(2 - 1.5) = -23.5/0.5 = -47 ft/s

The balloon is about to hit the ground, so it is falling at almost its maximum velocity.

Fig. 2 shows the height of the balloon at the above times.

Answer:

28ft.

Step-by-step explanation:

If [tex]s[/tex] equals 7 and the perimeter equals 4 times [tex]s[/tex], then the perimeter would be 4 times 7.

Answer:

segments shown in the coordinate plane are congruent?

A(-2, 3) B(5, 7) C (3, -3) D (-3,-5) E (-3, 10)

00

00

-10 8 6 4 2

2 4 6 8 10

y = -8x + 5

y - 9 = -2(x+1)

y - 9 = -2x - 2

y = -2x +7

y + 2 = 6(x+10)

y + 2 = 6x + 60

y = 6x + 58

The linear function has the steepest slope is y = -8x + 5

A)y = -8x + 5

B) y – 9 = -2(x+1)

⇒y – 9 = -2x - 2

⇒y = -2x +7

C) y=7x-3

D) y + 2 = 6(x+10)

⇒y + 2 = 6x + 60

⇒y = 6x + 58

Steepest slope is determined by the greatest value of gradient(m).

Therefore, The linear function has the steepest slope is y = -8x + 5

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Answer:

D

Step-by-step explanation:

The measure of an inscribed angle is half the measure of its intercepted arc, that is

∠ GHI = 0.5 × arc GI = 0.5 × 80° = 40° → D