Some History teachers at Dayton High School are purchasing tickets for students and their adult chaperones to go on a field trip to a nearby museum. For her class, Mrs. Gruber bought 25 student tickets and 28 adult tickets, which cost a total of $984. Mr. Ellison spent $900, getting 25 student tickets and 25 adult tickets. What is the price for each type of ticket?

Answer:

The value of x in this equation is -4.

Step-by-step explanation:

2(4x - 6) = 4(3x - 7)

Distribute 2 to (4x - 6) and distribute 4 to (3x - 7)

8x - 12 = 12x - 28

Subtract 12x form both sides of the equation.

-4x - 12 = -28

Add 12 to both sides of equation.

-4x = 16

Divide -4 on both sides of the equation.

x = -4

The value of x is -4.

Answer:

x=4

Step-by-step explanation:

Starting with 2(4x-6) you apply the distributive law: a(b-c) = ab - ac

a =2,  b=4x, c=6

2(4x-6) = 2*4x-2*6 Then multiply the numbers 2*4

8x-2*6 = multiply 2*6

8x-12

Then for 4(3x-7) you apply the distributive law.

a =4, b=3x, c=7

4*3x-4*7 multiply 4*3

12x-4*7 multiply 4*7

12x-28

Then the equation would be 8x-12 = 12x-28. Add 12 to both sides.

8x=12x-16 Subtract 12x to both sides

-4x=-16 divide both sides by -4

then you'll get Positive 4 as your x.

Answer: 34

Step-by-step explanation: B=10 S1=12 S2=12. Add them up

Answer:

I'm assuming the sides are 12 and the bottom 10 so your perimeter is 34

If you count the boxes the line of the triangle takes up, its 12 and the bottom is 10

Sides: 12

bottom: 10

If you add them up:

12 + 12 + 10 = 34

Answer:

2.556818 miles

Step-by-step explanation:

Answer:

Step-by-step explanation:

This problem is on the mensuration of flat shapes, a circular shape.

the problem also requires that we find the perimeter of the circular track

the expression for the perimeter of a circle is given as

[tex]C= 2\pi r[/tex]

Given

diameter of the circular track = 75 meters

radius of circular track = d/2 = 75/2= 37.5 meters

Substituting our data into the expression for perimeter we have

[tex]C= 2*3.142 *37.5\\\\C= 235.65[/tex]

Approximately the length is 235 meters.

Answer:

b

Step-by-step explanation:

Answer: Answer is in the step.

Step-by-step explanation:

The student made a mistake by identifying the maximum point by the x coordinate value of the vertex. Minimum or maximum points are determine using the y coordinate value.The student can determine the difference between a maximum and minimum by identifying the y coordinate of the vertex.

Direct variation uses the equation y = kx, where I is the constant of variation.

1. Is not a direct variation because the line is curving so the change in x is not constant.

2 and 3 Are straight lines, so Show direct variation. You can find 2 points on each line and calculate the slope which would be a constant variation.

Answer:

[tex]\Large \boxed{\mathrm{Water}}[/tex]

Step-by-step explanation:

Hydrogen and oxygen are elements that form the compound known as water.

Water comes pouring out, it drips, it dribbles, and it comes from a spout.

Answer:

Water

Step-by-step explanation:

Most of the water in our world is a combination of "ordinary" hydrogen atoms with "ordinary" oxygen atoms, but there are actually three different istopes (atomic varieties) of hydrogen and each of those can combine with oxygen to give a different kind of water.

If deuterium (hydrogen whose atoms contain one neutron and one proton instead of just one proton by itself) combines with oxygen, we get something called heavy water, which is about 10% heavier than normal water.

Similarly, tritium (hydrogen with two neutrons and one proton) can combine with oxygen to make something called super heavy water.

Water comes pouring out it drips and it dribbles and it comes from a spout​.

so you divide the rational number if the decimal on both sides if one is greater and the other less than the number that's greater should have the greater sign. but, if theres a number that's less then you should put the less than sign and if both numbers are the same number you should put the equal sign

Answer:

21

Step-by-step explanation:

Use PEMDAS

P ---> Parenthesis

E ----> Exponents

M & D -------> Multiplication & Division

A & S ------> Addition & Subtraction

5 + 4*(8 - 6)² = 5 + 4*(2)²

                     = 5 + 4*4

                     = 5 + 16

                     = 21

Answer:add 3

Step-by-step explanation:

Answer:

x^2 +14x+49

Step-by-step explanation:

Area = length * width

        = ( x+7) * ( x+7)

       FOIL

    first: x^2

    outer: 7x

   inner: 7x

    last: 7*7 = 49

Add them together

x^2 +7x+7x + 49

Combine like terms

x^2 +14x+49

Answer:

1/7

Step-by-step explanation:

If one child was born on a Monday, then we don't have to consider that when solving the question, as it asks if both children were born on a Monday.

Thus, we only need to find the probability that the second child is born on a Monday. Since there are 7 days in a week and equally likely that the child is born on any day, then the probability of the child being born on a Monday would be 1/7.

Answer:

f(-9) = 279

Step-by-step explanation:

f(x) = 4x^2 + 7x + 18

f(-9) = 4(-9)^2 +7(-9) + 18

       = 4(81) - 63 + 18

       = 324 - 63 + 18

       = 279

Answer:

75 miles squared

Step-by-step explanation:

First we have to convert 1 inch = 5 miles to square miles as that is what we are trying to get

So, 1 inch squared = 25 miles squared

To get 75 miles squared, we multiply both sides by 3.

So 3 * 1 inch squared = 3 * 25 miles squared

Gets us 3 inch squared = 75 miles squared

Full question :

A man buys a certain number of oranges at 20 for Rs. 60 and an equal number at 30 for Rs. 60. He mixes them and sells them at 25 for Rs. 60. What is the gain or loss percent?

Answer:

4% loss(percentage loss on cost price)

Step-by-step explanation:

we will be employing algebra in solving this problem :

20 oranges at 60 Rs=60Rs/20 per orange=3Rs per orange

Say x oranges bought at 3Rs per orange=3Rsx

Equal number of oranges at 30 oranges for 60 Rs=60Rs/30 per orange=2Rs per orange

Say x oranges bought at 3Rs per orange=2Rsx

Total Cost Price = 3Rsx + 2Rsx = 5Rsx

He then sells all oranges at 25 for 60 Rs

Therefore price per orange=60/25=12/5Rs

since he sold x+x oranges(from the above calculations)

Total selling price=total oranges *12/5Rs=2x oranges*12/5Rs=24x/5Rs

Profit or loss=24x/5-5x=-x/5

therefore we have a loss =-x/5

Percentage of loss(on cost price)

=x/5÷5x∗100=

=1/25∗100=4%

Answer: True

Step-by-step explanation: The altitude of an isosceles triangle can be drawn from the vertex angle and be proven to be a median

Answer:

x = -1, 2

Step-by-step explanation:

Step 1: Write out equation

(x - 2)(3x + 3) = 0

Step 2: Solve each individual root

x - 2 = 0

x = 2

3x + 3 = 0

3x = -3

x = -1

Step 3: Arrange from least to greatest

-1 < 2

So x = -1, 2

Answer:

x = -1    x = 2

Step-by-step explanation:

(x-2)(3x+3)=0

Using the zero product property

x-2 =0    3x+3 =0

x=2       3x = -3

             x = -3/3

             x = -1

hope this helps! Its the answer key to something almost exact

The size of the crowd that is 10 feet deep on ONE side of the street along a 1-mile section of a parade route is 25344 option (A) 25344 is correct.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

12 people fit comfortably in a 5 by 5 feet area.

Let x be the size of a crowd that is 10 feet deep on ONE side of the street along a 1-mile section of a parade route.

The fractions:

12/25 = x/(5280×10)

After cross multiplication:

25x = 633600

x = 633600/25

x = 25344

Thus, the size of the crowd that is 10 feet deep on ONE side of the street along a 1-mile section of a parade route is 25344 option (A) 25344 is correct.

Learn more about the fraction here:

brainly.com/question/1301963

#SPJ2

Answer:

f (x,y) = sin (x,y)  & points = (1,0)

Maximum  rate of change in f at given point & direction = 1

Step-by-step explanation:

The function & points are not given,

Considering them as general example : f (x,y) = sin (x,y) & points = (1,0)

Maximum rate of change in f (x,y) happens in direction of ∇ f (1,0)

∇  f (x,y) =  [ df / dx ,  df/ dy ]

= [ y cos (xy) , x cos (xy) ]

∇ f (1,0)  = [ 0, cos (0) ] = (0,1)

Magnitude at (1,0) = ∇ f (1,0)  = √ 0^2 + 1^2  = 1

Answer:

4 hours 7 minutes

Step-by-step explanation:

Since Trevon takes 10 hours to clean the attic, he cleans 1/10, 10% or .1 of the attic per hour. Since Cody takes 7 hours to clean the attic, he cleans 1/7, 14.3% or .143 of the attic per hour.

Together, that means they clean .1 + .143 of the attic per hour. That's an hourly rate of:

.1 + .143 = .243

The portion of the attic they clean in x hours is .243x. We'd like to know how long it will take them to clean 100% or 1 of the attic. So:

.243x = 1   Divide each side by .243

x = 1/.243

x ≈ 4.115

Let's convert .115 to minutes by multiplying by 60

.115 * 60 = 6.9 round to 7 for 7 minutes

It will take them around 4 hours 7 minutes to clean the attic.

Answer:

The answer is

Step-by-step explanation:

To solve the radicals make sure that they both have the same radical

That's

Simplify 3√28 in order to combine the radicals

We have

So we now have

Using the rules of surds

That's

Simplify the expression

We have

We have the final answer as

Hope this helps you

Answer:

Step-by-step explanation:

[tex]4\sqrt{7}+3\sqrt{28}=4\sqrt{7}+3\sqrt{2*2*7}\\\\\\ =4\sqrt{7}+3*2\sqrt{7}\\\\\\= 4\sqrt{7}+6\sqrt{7}\\\\\\=(4+6)\sqrt{7}\\\\\\ =10\sqrt{7}[/tex]

Answer:

17

Step-by-step explanation:

3x + 2y = 3(3) + 2(4) = 9 + 8 = 17

Answer:

[tex]\huge\boxed{17}[/tex]

Step-by-step explanation:

[tex]3x+2y\\\\\text{When: }\boxed{x=3; y=4}\\\\3(3)+2(4)\\\\3*3+2*4\\\\9+8\\\\\boxed{17}[/tex]

Answer:

7

Step-by-step explanation:

Prime factors of 4732:

As we see if we remove 7 from the factors list, we get the perfect square of 2²×13²= 26²

So the number by which 4732 should be divided is 7

Answer:

Step-by-step explanation:

[tex]3+11t-9u\\t = 9\\u =11\\\\3+11(9) -9(11)\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:11\left(9\right)\::\quad 99\\=3+99-9\left(11\right)\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:9\left(11\right)\::\quad 99\\=3+99-99\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:3+99-99\:\\:\quad 3[/tex]

Answer:

[tex] - 19[/tex]

Step-by-step explanation:

[tex]3 + 11t - 9u = 3 + 11(9) - 9(11) = 3 + 99 - 121 = - 19[/tex]

Answer:

1. 5040

2. 20

Step-by-step explanation:

1. using the formula for permutation

nPr=n!/(n-r)!

10P4 = 10!/(10-4)!

=10*9*8*7*6!/6!

then we are left with

=10*9*8*7

=5040

2.using the formula for combination

nCr=n!/(n-r)!r!

6C3=6!/(6-3)!3!

=6*5*4*3!/3!3!

=6*5*4/3*2*1

=20

Answer:

see below (I hope this helps!)

Step-by-step explanation:

T = WP [ M² - (M - S)² ]

T = WP [ M² - (M² - 2MS + S²) ]

T = WP (2MS - S²)

T = 2WPMS - WPS²

T + WPS² = 2WPMS

M = (T + WPS²) / (2WPS)

Answer:

only (12) has a linear pair

Step-by-step explanation:

Recall that for two angles to be called a "Linear Pair", they need to satisfy several conditions:

1) The two lines must intersect at a shared point (i.e common vertex)

2) The two angles must be adjacent (i.e immediately next to one another)

3) The two angles must add up to 180 degrees.

In our case,

in (9), the angles are not adjacent and  they do not add up to 180 deg, so this is NOT a linear pair

in (10), the angles are not adjacent and they do not add up to 180 deg, so this is NOT a linear pair

in (11), the lines do not intersect at a shared point(they do not have a common vertex). Plus we cannot be 100% sure that they add up to 180 deg. Hence this is not a linear pari

in (12), we can see that the angles satisfy all 3 conditions above. This is a linear pair.