Jillian’s school is selling tickets for a play. The tickets cost $10.50 for adults and $3.75 for students. The ticket sales for opening night totaled $2071.50. The equation 10.50a+3.75b=2071.50, where a is the number of adult tickets sold and b is the number of student tickets sold, can be used to find the number of adult and student tickets. If 82 students attended, how may adult tickets were sold?]

Answer:

A. (1,2)

B. (3,1)

C.(4,4)

D. (6,6)

E. (8,4)

Step-by-step explanation:

Answer:

Answer:

A. (1,2)

B. (3,1)

C.(4,4)

D. (6,6)

E. (8,4)

Step-by-step explanation:

Answer:

132 m².

Step-by-step explanation:

What's the surface area of each lateral face of this pyramid?

Each lateral face of this pyramid is a triangle, with

The base of this pyramid is a square. As a result, all four lateral sides are congruent. The area of each of these triangle is thus

[tex]\displaystyle \frac{1}{2}\times \text{Base}\times \text{Height} = \rm \frac{1}{2} \times 6 \times 8 = 24\; m^{2}[/tex].

The base of this pyramid is a square. The length of a side of this square is 6 meters. The area of the base will be

[tex]\text{Side}^{2} = \rm 6^{2} = 36\; m^{2}[/tex].

Put the five faces together to get the total surface area of this square pyramid:

[tex]\rm 4\times 24 + 36 = 132\; m^{2}[/tex].

Answer :

[tex]\frac{7}{15}[/tex]×[tex]\frac{2}{15}[/tex] = [tex]\frac{14}{225}[/tex]

Step-by-step explanation:

P([tex]Event_{1}[/tex]) = choosing yellow marble from paper bag = [tex]\frac{favourable outcomes}{possible outcomes}[/tex] = [tex]\frac{7}{15}[/tex]

P([tex]Event_{2}[/tex]) = choosing yellow marble from cloth bag = [tex]\frac{favourable outcomes}{possible outcomes}[/tex] = [tex]\frac{2}{15}[/tex]

∵ Resultant outcome is dependent upon both the events and both events are independent from each other, so we can apply intersection rule [ P(A∩B)=P(A)×P(B) ] here

∴ Probability ( Both marbles are yellow) = P([tex]Event_{1}[/tex]) × P([tex]Event_{2}[/tex]) = [tex]\frac{7}{15}[/tex] × [tex]\frac{2}{15}[/tex]

The probability that Tim will draw a yellow marble from both bags is found by multiplying the probability of drawing a yellow marble from each bag, giving a result of 14/225 or approximately 0.0622.

The question is asking to find the probability of Tim drawing two yellow marbles, one from each bag, so this is a question about probability.

We know that there are 7 yellow marbles out of 15 in the paper bag, so the probability of drawing a yellow marble from this bag is 7/15. In the cloth bag, there are 2 yellow marbles out of 15, making the probability of drawing a yellow marble from this bag 2/15.

To find the overall probability that both marbles Tim draws are yellow, we multiply the two independent probabilities: (7/15) × (2/15) = 14/225.

So the probability that Tim will draw a yellow marble from both bags is 14/225, or approximately 0.0622 when expressed as a decimal.

Answer:

A

Step-by-step explanation:

Degree: that's the power on the x term. 2

Coefficient on the x term. That is             3

Constant term. That has no x                   -4

The minus is included.

The answer is A

Answer:

C

Step-by-step explanation:

You have a vertex of (-2,2) since -b/(2a)=-12/(2*3)=-12/6=-2

and then plug it in for the y-coordinate 3(-2)^2+12(-2)+14=2

So you have a vertex of (-2,2).

The parabola is open up since 3 is positive.

So far it looks like the choice is C because it is the only one that says the vertex is (-2,2) and it does have that it is open up.

Let' s look at (-3,5) and (-1,5).

So if we plug in -3 into 3x^2+12x+14 we get 3(-3)^2+12(-3)+14=5 check mark

what about x=-1?  3(-1)^2+12(-1)+14=5

Bingo! C checks out!

Answer:

V = (π/4)s³

Step-by-step explanation:

The volume of a cylinder can be found using the formula ...

V = πr²h

In this problem, we have r=s/2 and h=s. Filling in these values, the volume is ...

V = π(s/2)²·s = (π/4)s³

Answer:

Its A

Step-by-step explanation:

V= 1/4 pi S^3

Answer:

f(x)=4x

Step-by-step explanation:

In order to make the graph of f(x)= 4x we will find out few coordinates first and then plot them on the graph. In order to find the coordinates we will find the values of f(x) for random values of x .

Let us see:

x=1 ; f(x) = 4(1) = 4

x=2 ; f(x) = 4(2)=8

x=0 ; f(x) = 4(0)=0

x=-1 ; f(x)= 4(-1) = -4

x=-2 ; f(x)=4(-2)= -8

Hence our coordinates are

(-2,-8) ; (-1,-4) ; (0,0) ; (1,4) ; (2,8)

Now we plot those coordinates on x - y plane and join them to make our line. Please see the graph in the attachment.

Answer:

  B) 504

Step-by-step explanation:

They should expect 30% of 40 out of every 300 of the 12,600, so ...

  0.30 × 40/300 × 12,600 = 504

About 504 residents might be expected to join.

To estimate the number of residents that Muscles can expect to join its new branch, multiply the total number of residents within driving distance by the percentage of respondents who would actually join the gym. Muscles can expect about 1,680 residents to join its new branch.

To estimate the number of residents that Muscles can expect to join its new branch, we can multiply the total number of residents within driving distance by the percentage of respondents who would actually join the gym.

First, we need to calculate the percentage of respondents who would join the gym:

Percentage = (Number of respondents who would join the gym / Total number of respondents) * 100

Percentage = (40 / 300) * 100 = 13.33%

Next, we multiply the estimated percentage by the total number of residents within driving distance:

Number of residents who would join the gym = (Percentage / 100) * Total number of residents within driving distance

Number of residents who would join the gym = (13.33 / 100) * 12,600 = 1,678.5

Therefore, Muscles can expect about 1,680 residents to join its new branch.

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Answer:

59

Step-by-step explanation:

Let c and b represent the scores of Colin and Brian respectively.  Then

c + b = 59.  Since brian scored 59 more points than Colin, that means c = 0 and b = 59.  Their combined score is 0 + 59 = 59.

For this case we have that the area of the kite is given by the area of two triangles, the triangles share the same base of 3 + 3 = 6 meters and one has height of 2m and the other height of 4m.

So, the total area is given by:

[tex]A = \frac {1} {2} * 6 * 2 + \frac {1} {2} * 6 * 4\\A = \frac {1} {2} 12+ \frac {1} {2} *24\\A = 6 + 12\\A = 18[/tex]

Thus, the area of the kite is [tex]18m ^ 2[/tex]

ANswer:

[tex]18m ^ 2[/tex]

Answer:

A. -19

Step-by-step explanation:

There are lots of ways to get there. One of them is to realize that the average rate of change between two adjacent numbers is the negative of their sum. -(9+10) = -19.

__

Another is to extend the table:

6 to 7 : -13

7 to 8 : -15

8 10 9 : -17

9 to 10 : -19

__

Yet another is to write an equation for the function, and compute the average rate of change:

f(x) = -x^2 -1

average rate of change from 9 to 10 = (f(10) -f(9))/(10 -9) = (-101 -(-82))/(10 -9) = -19

Answer:

A. -19

Step-by-step explanation:

Answer: 3.6 hours

Step-by-step explanation:

Given : The time taken by Blake to paint the room : [tex]t_1=9\text{ hours}[/tex]

The time taken by Ned to paint the room : [tex]t_2=6\text{ hours}[/tex]

Then , the time taken (T) by both of them to paint the room if they work together is given by :-

[tex]\dfrac{1}{T}=\dfrac{1}{t_1}+\dfrac{1}{t_2}\\\\\Rightarrow\ \dfrac{1}{T}=\dfrac{1}{9}+\dfrac{1}{6}\\\\\Rightarrow\dfrac{1}{T}=\dfrac{5}{18}\\\\\Rightarrow\ T=\dfrac{18}{5}=3.6\text{ hours}[/tex]

Hence, it will take 3.6 hours to the two companies if they working together .

For a system of linear equations to have a solution, it means that they would cross over at some point, thus if we are looking for a system of linear equations that do not have a solution (ie. they do not cross over), we are looking for two parallel lines.

Now for two lines to be parallel, they must have the same gradient. Thus, we must find the value of a for which both the equations have the same gradient. In order to do this, we should first write both equations in the form y = mx + c, where m is the gradient and c the y-intercept.

1) Equation 1:

(1/2)x - (2/3)y = 7

(3/4)x - y = 21/2 (Multiply both sides by 3/2)

(3/4)x = 21/2 + y (Add y to both sides)

(3/4)x - 21/2 = y (Subtract 21/2 from both sides)

Thus, the first equation may be written as y = (3/4)x - 21/2

2) Equation 2:

ax - 8y = -1

(a/8)x - y = -1/8 (Divide both sides by 8)

(a/8)x = -1/8 + y (Add y to both sides)

(a/8)x + 1/8 = y (Add 1/8 to both sides)

Thus, the second equation may be written as y = (a/8)x + 1/8

Now that we know the equations of the two lines, we can compare their gradients.

Equation 1: m = 3/4

Equation 2: m = a/8

Remember, for the two lines to be parallel, their gradients must be the same. Thus, we must equate the two gradients above to find the value of a:

3/4 = a/8

24/4 = a (Multiply both sides by 8)

6 = a

Therefor, if the system of linear equations has no solution, and a is a constant, the value of a is 6 (answer D).

Answer:

Part 21) The distance from Football Field to the Park is [tex]10.95\ miles[/tex]

Part 22)

a) The value of a is [tex]20\ units[/tex]

b) The value of b is [tex]20.10\ units[/tex]

Step-by-step explanation:

Part 21)

Let

A -----> Football Field

B -----> Park

C -----> Home

D -----> Library

x -----> the distance from Football Field to the Park

In the right triangle ABD

[tex]cos(A)=10/x[/tex] -----> equation A

In the right triangle ABC

[tex]cos(A)=x/12[/tex] ----> equation B

equate equation A and equation B

[tex]10/x=x/12[/tex]

solve for x

[tex]x^{2}=120\\ \\x=10.95\ miles[/tex]

Part 22)

see the attached figure with letter to better understand the problem

step 1

Find the value of a

In the right triangle ABD

[tex]tan(ABD)=a/200[/tex] ----> equation A

In the right triangle ADC

[tex]tan(DAC)=2/a[/tex] ----> equation B

remember that angle ABD is congruent with angle DAC

therefore

equate equation A and equation B

[tex]a/200=2/a[/tex]

solve for a

[tex]a^{2}=400\\ \\a=20\ units[/tex]

step 2

Find the value of b

In the right triangle ADC

Applying the Pythagoras Theorem

[tex]b^{2}=a^{2}+2^{2}[/tex]

substitute the value of a

[tex]b^{2}=20^{2}+2^{2}[/tex]

[tex]b^{2}=404[/tex]

[tex]b=20.10\ units[/tex]

Answer:

6π ft

Step-by-step explanation:

I believe you meant CIRCUMFERENCE, the distance around the outer edge of this circle.  The appropriate formula for the circumference is C = 2πr, where r is the radius.  In the illustration we see that line segment PA has length 3 ft.  Thus, the circumference of this circle is C = 2π(3 ft) = 6π ft (the next to last answer choice).

Answer:

=6π ft

Step-by-step explanation:

The circumference of a circle is calculated using the formula C=2πr where r is the radius and C the circumference of the circle.

In the circle provided r= 3ft

C= 2π × (3ft)

=6π ft

We do not use the approximate value of pi as the question demands us to leave pi unsolved.

First, lets focus on finding out the other two legs of the large triangle.

To do this, we use Pythagoras' Theorem.

So the left leg = √(16² + x²)

So the right leg = √(9² + x²)

Notice, the larger triangle is also a right angled triangle, that means the sum of the two legs squared = hypotenuse squared.

Since we have just worked out the two legs, we can substitute them into:

a² + b² = c²

(√(16² + x²) )²  +  (√(9² + x²) )² = (16 + 9)²

Notice that the power of two cancels out with the squareroots so we get:

(16² + x² ) + (9² + x² ) = (25)²     (simplify and collect like terms)

256 + x² + 81 + x² = 625    

337 + 2x² = 625     (subtract 337 from both sides to isolate the x )

2x² = 288                    (divide both sides by 2)

x² = 144                        (square root both sides)

x = √144

x = 12

_______________________________________

Answer:

x = 12

_______________________________________

Note: if you have any questions, please ask and I will be more than happy to help and give further explanations!

I can confirm that the other person is right, the answer is 12.

Answer:

The initial position was 35.1 m

Step-by-step explanation:

Let

x -----> the initial position

we know that

The linear equation that represent this problem is equal to

x+18.4=53.5

Solve for x

Subtract 18.4 both sides

x=53.5-18.4

x=35.1 m

Answer: se necesitan 4 medidas de B para obtener una de D

Step-by-step explanation:

Las medidas serán entendidas como unidades de.. (A , B o C)

Entonces, de esta manera

1A + 1C = 5B

1A + 1B = 1 C

1B + 1C = 1D

Para lograr el cometido debo combinar las 3 relaciones de cambio de tal manera que se cancelen totalmente las partes A y C utilizando los multiplicadores adecuados

Entonces,

Uso 5 unidades de B para conseguir una de A y una de C

5B = 1A + 1C

Con esa A y otra de B obtengo otra C

1A + 1B = 1C

Por último con esas dos unidades de C y dos unidades mas de B consigo 2 de D

2B+ 2C = 2D

En total utilicé 5 + 1 + 2 = 8 unidades de B para obtener 2 de D

Entonces para obtener una de D necesitaría 4 unidades de B

Answer:

Perimeter = 20 units

x = 120°

Step-by-step explanation:

We are given a triangle ABC with known side lengths for all three sides and an inscribed circle.

We are to find the perimeter of triangle ABC and the value of x.

Perimeter of triangle ABC = 2 + 2 + 5 + 5 + 3 + 3 = 20 units

The kite shape at the end is a quadrilateral which has a sum of angles of 360 degrees.

Two out of four angles are right angles and one is 60 so we can find the value of x.

x = 360 - (90 + 90 + 60) = 120°

Answer:

6.  20                      8.  120

Step-by-step explanation:

add the side measurements up of the triangle:

2+5+2+3+3+5=7+5+8=20

That shape where the x is a quadrilateral so is't interior angles must add to 360 so you have 90+90+60+x=360

Solving:  230+x=360

So x=360-240=120

Answer:

last choice

Step-by-step explanation:

Let's look at (8,-2)

We are moving this point 7 units right and 2 units down so that becomes

(15,-4)

But you are also reflecting it across y-axis so the x becomes opposite and y stays the same so you have the final image point after the transformations is (-15,-4).

So it can only be choice D, the last choice.

Answer:

Im positive the answer is A: x^3-3x+2

Answer:

a     x^3-3x+2

Step-by-step explanation:

f(x) = -3x+2

g(x)= x^3

(f+g)(x)= -3x+2+x^3

          = x^3-3x+2

Answer:

Step-by-step explanation:

try using the equation of y=mx+b

Answer:

Discriminant D = -4 , no real solution

Step-by-step explanation:

Here our equation is

[tex]x^{2}-4x+5=0[/tex]

Discriminant (D)= [tex]b^2-4ac[/tex]

where

a = coefficient of term containing [tex]x^{2}[/tex]

b= coefficient of the term containing [tex]x[/tex]

c is the constant term

hence

a=1 , b =-4 and c=5

Hence

[tex]D=b^2-4ac\\D=(-4)^2-4*1*5\\D=16-20\\D=-4\\[/tex]

Hence D is less than 0 , therefore we do not have any real solution to this quadratic equation.

Answer:

b on edge-The discriminant is −4, so the equation has no real solutions.

Step-by-step explanation:

Without a given equation or inequality to work with, it is impossible to determine the value of 'x' based on the presented information.

The provided question seems to be missing some key elements that would offer us enough information to determine the value of x. In mathematics, to find the value of a variable, such as x, you generally need some form of an equation or inequality where x is a part of and other elements present in the equation give indirect details about x. This could include clues as to its relationships with other values, or boundaries for its possible amount. Without an equation, it is impossible to ascertain the value of x based on the given question.

This reasoning is based on the fundamental principles of algebra, a branch of mathematics. For example, if given an equation like '3x + 2 = 8', we could apply algebraic principles to solve for x. However, in this case, no such equation has been provided, and so we cannot calculate the value of x. Thus, there is not enough information provided.

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Answer:

Given the function f(x) = 3x + 1, evaluation of f(a + 1) gives:  

C. 3a + 4

Step-by-step explanation:

Given function:

f(x) = 3x + 1

We have to find f(a+1).

For this purpose, we will take x = a+1 and

substitute it in the function f(x) = 3x+1:

f(x) = 3x + 1

f(a+1) = 3(a+1) +1

f(a+1) = 3(a) + 3(1) +1

f(a+1) = 3a+3+1

f(a+1) = 3a + 4

So the function f(a+1) is equal to option C. 3a + 4.

the answer is

3a + 4

Answer:

914 and 916

Step-by-step explanation:

let the first integer be x

The next largest consecutive even integer is hence x+2

given that the 2 integers add up to 1830,

x + (x+2) = 1830

2x + 2 = 1830

2x = 1828

x = 914

Hence the first number is 914

the second number is 914 + 2 = 916

Check Answer:

914 + 916 = 1830 (verified)

[tex]2n+2n+2=1830\\4n=1828\\n=457\\\\2n=914\\2n+2=916[/tex]

914 and 916

Answer:

(x+1)^2+(y-7)^2=8

Step-by-step explanation:

You should try the next one and I can check work or tell you if it is right.  

The diameter length can be found be computing the distance that (-3,5) is to (1,9) which is sqrt(4^2+4^2)=sqrt(32).

The radius is half the diameter so it is sqrt(32)/2.

The center of the circle is the midpoint of a diameter. So compute the (Average of x, average of y)=(-1,7)

So plug into (x-h)^2+(y-k)^2=r^2 we get

(x+1)^2+(y-7)^2=32/4

simplifying gives

(x+1)^2+(y-7)^2=8

(I had to type this twice; my cat jump on my keyboard)

ANSWER

[tex]{(x + 1)}^{2} + {(y - 7)}^{2} = 8[/tex]

EXPLANATION

The given circle has P(-3,5) and Q(1,9) as its diameter.

The center can be obtained using the midpoint rule.

[tex]( \frac{ - 3 + 1}{2} , \frac{5 + 9}{2} )[/tex]

[tex]( - 1,7)[/tex]

The radius is obtained using the distance formula,

[tex]r = \sqrt{( - 1 - - 3 )^{2} + {(7 - 5)}^{2} } [/tex]

[tex]r = \sqrt{( 2)^{2} + {(2)}^{2} } = \sqrt{8} [/tex]

The equation is given by

[tex] {(x - h)}^{2} + {(y - h)}^{2} = {r}^{2} [/tex]

We substitute the center and radius to get:

[tex]{(x - - 1)}^{2} + {(y - 7)}^{2} = { (\sqrt{8}) }^{2} [/tex]

[tex]{(x + 1)}^{2} + {(y - 7)}^{2} = 8[/tex]

Answer:

  (B) only I and II

Step-by-step explanation:

An odd relation is symmetrical about the origin. All of the relations are odd.

An even relation is symmetrical about the y-axis. Only the first two relations are even.

_____

The graph shows the first relation is that of a circle. It is symmetrical about its center at the origin and about any diameter, including the y-axis.

The second relation is a degenerate hyperbola. It graphs as the pair of lines y=x and y=-x. It is symmetrical about both the origin and the y-axis. (It also has other lines of symmetry.)

The third relation is a line with slope -1 (represented by dots). It is symmetrical about the origin, but not the y-axis. It is only an odd relation.

Answer:

80 per hour

Step-by-step explanation:

because every hour it goes up 80 every time

The speed of the car is 80 km/h.

Speed exists as the time rate at which an object exists moving along a path, while velocity exists as the rate and direction of an object's movement. Put another way, speed exists as a scalar value, while velocity is a vector.

Speed exists the rate at which an object’s position changes, measured in meters per second.

The speed of the car is 80 km/h.

Therefore, 80 km/h stands as the correct answer.

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