Parallel to y=−3/2x+1, through (0, -4)

According to the characteristics of ticket sales and the resulting system of linear equations we find that 122 children bought each one a ticket on Sunday.

In this question we have a word problem, whose information must be translated into algebraic expressions to find a solution. Let be x and y the number of children and adults that went to the movie theatre, respectively.

We need two linear equations, one for the number of people assisting to the theatre and another for the total sales:

x - 4 · y = 0     (1)

6.30 · x + 9.50 · y = 1063.20     (2)

By algebraic procedures the solution to this system is: x = 122.559, y = 30.639. Since the number of tickets sold are integers, then we truncate each result: x = 122, y = 30.

According to the characteristics of ticket sales and the resulting system of linear equations we find that 122 children bought each one a ticket on Sunday.

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Answer:

a = - 2

Step-by-step explanation:

calculate the slope of the 2 given points and equate to 0.75

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (4, a ) and (x₂, y₂ ) = (8, 1 )

m = [tex]\frac{1-a}{8-4}[/tex] = [tex]\frac{1-a}{4}[/tex]

then equating

[tex]\frac{1-a}{4}[/tex] = 0.75 ( multiply both sides by 4 to clear the fraction )

1 - a = 3 ( subtract 1 from both sides )

- a = 2 ( multiply both sides by - 1 )

a = - 2

Using the given information, the value of x is -66

From the question, we are to determine the value of x

In the given diagram,

∠UYV and ∠WYX are vertically opposite angles

By vertical opposite angles theorem,

∠UYV = ∠WYX

∴ 56° = (-x - 10)°

56° = -x° - 10°

56° + 10° = -x°

66° = -x°

∴ x = -66

Hence, the value of x is -66.

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Answer:

[tex]x= 4[/tex]

Step-by-step explanation:

[tex]~~~~~~\log_ 6 10 + \log_6 x = \log_6 (40)\\\\\implies \log_6(10x) = \log_ 6 (40)~~~~~~~~~~~~~~~~~~~~~;[\log_b(mn) = \log_b m + \log_b n]\\\\\implies 10x = 40\\\\\implies x = \dfrac{40}{10}\\\\\implies x = 4[/tex]

Answer:

35

Step-by-step explanation:

All you need to do is substitute!

(3x2)^2-1

6^2-1

36-1

= 35

Hope this helps!!

A. The Area of one triangular face would be 320 ft². B. The total surface area, in square feet, of the square pyramid is 2,304 ft².

The Area of one triangular face can be calculated as;

A = area of triangle = ½ x b x h

Where,

b = 32 ft

h = 20 ft

A = ½ x 32 x 20 = 16 x 20

A = 320 ft²

Area of 1 triangular face = 320 ft²

B.

Total surface area = area of the 4 triangular faces + area of the base of the square pyramid

T.S.A = 4(320) + (s²)

Where,

s = 32 ft

T.S.A = 4(320) + (32²)

T.S.A = 1,280 + 1,024

= 2,304 ft²

A. The Area of one triangular face would be 320 ft². B. The total surface area, in square feet, of the square pyramid is 2,304 ft².

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Two angles are said to be complementary angles if their sum is 90 degrees. Then ∠I ≅ ∠H is proved, below.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Two angles are said to be complementary angles if their sum is 90 degrees.

∠G and ∠H are complementary angles and ∠G and ∠I are complementary angles.

Then show that ∠I ≅ ∠H

∠G + ∠H = 90°  ...1

∠G + ∠I = 90°  ...2

Then from equation 1 and 2, we ahve

∠G + ∠I = ∠G + ∠H

        ∠I = ∠H

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Answer:

The question is not included in your sentence.

The equation for the given parabola is; x = ¹/₁₂(y - 3)² - 2

From the graph, we see that;

Focus = (1, 3)

Directrix; x = -5

General form of equation of a parabola is;

(y - k)² = 4p(x - h)

where;

focus is (h + p, k)

directrix is x = h - p

Thus;

(1, 3) = (h + p, k)

h + p = 1  -----(1)

k = 3

Similarly;

h - p = -5   -----(2)

Add eq 1 to eq 2 to get;

2h = -4

h = -2

-2 - p = -5

p = 3

Thus, equation of the parabola is;

(y - 3)² = 4(3)(x - (-2))

(y - 3)² = 12(x + 2)

divide both sides by 12 to get;

¹/₁₂(y - 3)² = x + 2

x = ¹/₁₂(y - 3)² - 2

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Answer:

x = 7

Step-by-step explanation:

5x - 1 = 34

First, take -1 to the right side.

5x = 34 + 1

5x = 35

Divide both sides by 5.

x = 7

Step-by-step explanation:

please mark me as brainlest

Answer:

See the image.

Step-by-step explanation:

Constant balance in a bank account signifies that the balance in the account remains constant throughout time.

That is, it did not rise or diminish with time.

As a result, the graph of such a circumstance is a horizontal line parallel to the Time period axis.

Answer:

The straight line.

Step-by-step explanation:

Answer: 168cm^2

Step-by-step explanation:

lets split this into two shapes:

a rectangle and a triangle

Formulas:

rect: b * h

Tri: (b*h)/2

Solve:

12 * 10 = 120

(12*8)/2 = 48

120 + 48 =

168cm^2

Answer:

x = -7

Step-by-step explanation:

The whole line is 12

the whole line is also   x + 14  and  x + 12

  so make them equal:

      x+14     +      x +12     = 12  

       2x   + 26   = 12        now subtract 26 from both sides

               2x = - 14           now divide both sides by 2

                 x = -7

Answer:x = -7

Step-by-step explanation:

The whole line is 12

the whole line is also   x + 14  and  x + 12

 so make them equal:

     x+14     +      x +12     = 12  

      2x   + 26   = 12        now subtract 26 from both sides

              2x = - 14           now divide both sides by 2

                x = -7

Answer:

2 (x minus 6) = negative 35 is equivelant to 2 x = negative 23

Step-by-step explanation:

You need to work out the options you are given and see which statement comes out to be true. In this case the question is not as relevant.

Answer:

c

Step-by-step explanation:

Note: You will need to write the degree symbol for the arguments of these trigonometric functions.

As sin(x)=cos(90-x), this means sin10 = cos80 and cos75=15.

So,

LHS = (cos80)(sec80)(sin15)(cosec15)

LHS = (cos 80)(1/cos 80)(sin 15)(1/sin 15)

LHS = 1

Therefore, the identity is true.

Answer:

Step-by-step explanation:

MA²=MX²+AX²

=20²+21²

=400+441

=841

MA=√841=29

Answer:

29

Step-by-step explanation:

Applying Pythagorean Theorem :

⇒ MA² = MX² + AX²

⇒ MA² = 20² + 21²

⇒ MA² = 400 + 441

⇒ MA = √841

⇒ MA = 29

Answer:

Go to Betty's Breakables, if the price is below $37.50.

The advice that I will give my friend in the purchase of crystal candlestick is to Go to Betty's Breakables if the price is above $25.00.

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them. Factors can be found using either division or multiplication.

Given:

Betty's Breakables is offering a 40% discount whereas Annie Attic is offering a $10 discount.

The discount at Betty's Breakables

=  $10 ($25 x 40%) when the price is, let's say, $25.00.

As a result, the cost drops to $15. This is true even if my friend uses his $10 discount at Annie Attic.

However, if the price is higher—say let's $30—more gain is realized.

Betty's Breakables is offering a $12 discount at this price. The savings at Annie Attic will still be $10.

Thus, if the candlestick costs more than $25, it will be less expensive for my friend to visit Betty's Breakable.

On the other hand, if the cost is less than $25, Annie Attic will provide a better deal.

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∠SPQ and ∠HIj are congruent corresponding angles, therefore, the equation that must be true is: C. IJ = PQ

From the image given, the angles formed along the transversal, ∠SPQ and ∠HIj are corresponding angles and they are congruent to each other.

Also, since they are congruent and the arcs are also congruent, therefore, the equation that must be true is:

C. IJ = PQ

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Answer:

C. IJ = PQ

Step-by-step explanation:

The equation that models the distance of the crank's handle to the ground in terms of the bucket's distance from the bottom of the well will be y = x + 0.5y + 0.4 = 1.5

From the information given, the well. the crank's handle is at its farthest point from the ground, 1.5 m. the handle is 0.5 m away from the middle of the crank. one full turn of the crank raises the bucket 0.4 m.

Therefore, the equation will be:

y = x + (0.5 × y) + 0.4 = 1.5

y = x + 0.5y + 0.4 = 1.5

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Step-by-step explanation:

u have to use your branly

Answer:

(x+3)^2 + (y-5)^2 = 4

Step-by-step explanation:

the center point gives you the how much you have to subtract from the x and y and the radius squared is the last part.

Answer:

c is the correct option as √ is 1/2×5=5/2.

This is my personal opinion.

Answer:

what the guy above me said

Step-by-step explanation:

its what he said c

Answer:

  55°

Step-by-step explanation:

When the protractor is aligned with 0 on the inner scale, the angle is measured using the inner scale.

__

The measure of the angle shown is 55°.

The fine detail of the angle value is found on the outer scale. That scale shows the 125 mark being covered by the black arrow, so the angle measure is 180-125 = 55°.

The greatest common factor is 3x^5.

We have given the following monomials

48x^5

39x^6

The greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.

To the greatest common divisor 3x^5

Therefore the greatest common factor is 3x^5.

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D option is correct answer.

Answer:

lt the no s be x, x+1 and x+2 then x+(x+1)+(x+2)=72

x+x+x+1+2=72

3x + 3 = 72

3x = 72 - 3

3x = 69 (dividing both sides by "3")

we get x = 23

so the numbers are 23, 24 and 25

Answer:

11/15

Step-by-step explanation:

create a proportion

2 1/5 = 11/5

1/3 times 11/5 = 11/15

One possible answer: {1, 2, 5, 12, 14, 16, 20}  

See figure 1 below

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

Another possible answer:  {1, 1, 5, 12, 15, 16, 20}

See figure 2 below

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

Another possible answer:  {1, 1, 1, 12, 15, 20, 20}

See figure 3 below

Infinitely many answers are possible. You only need to pick one as what you'll show to your teacher.

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

Explanation:

Let A,B,C,D,E,F,G be the 7 unknown numbers. We'll have the numbers go from smallest to largest. Though as you'll see later, through some shuffling around, we can have repeats. For now, we'll have A through G be distinct values.

The median is 12, and we have an odd number of values here. This tells us that D = 12 must be the case since D is right in the middle.

The set is now A,B,C, 12, E, F, G

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

Recall the process to find the arithmetic mean is to

We're given a mean of 10 which tells us,

mean = (sum of the values)/(number of values)

10 = (A+B+C+12+E+F+G)/(7)

(A+B+C+12+E+F+G)/(7) = 10

A+B+C+12+E+F+G = 10*7

A+B+C+12+E+F+G = 70

A+B+C+E+F+G = 70-12

A+B+C+E+F+G = 58

Unfortunately at this point we don't have enough info to find the solutions to A,B,C,E,F,G. There are infinitely many ways to solve this.

But we do know that A,B,C are less than 12 while E,F,G are larger than 12.

Let's pick at random 5 values to assign to A,B,C,E, and F. The remaining value G will be solved for.

The random numbers I'll pick are:

So,

A+B+C+E+F+G = 58

1+2+5+14+16+G = 58

38+G = 58

G = 58-38

G = 20

So the set

{A,B,C,D,E,F,G} = {1, 2, 5, 12, 14, 16, 20}

has D = 12 in the middle as the median

Also, the values add up to 1+2+5+12+14+16+20 = 70 and it leads to the arithmetic mean of 70/7 = 10

This confirms the set {1, 2, 5, 12, 14, 16, 20} fits the description. It is one possible answer (out of infinitely many).

How do we make the dot plot? Well we draw out a number line, and then place a dot above each number mentioned. We'll have a dot above 1, then above 2, then 5, then 12, and so on. Refer to figure 1 below.

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

If you want, you can stop here since the dot plot and data set are already done. Read on if you want to see how to generate other possible solutions.

Admittedly, the dot plot is rather boring. It's just a flat horizontal set of dots. But we can add a bit of variety.

If we had repeated numbers, then the dots would stack up.

We'll need to keep the 12 anchored where it is. That will not change.

The other values around it can change, but do so carefully. Let's change the "2" into a "1".

So we go from {1, 2, 5, 12, 14, 16, 20} to {1, 1, 5, 12, 14, 16, 20}. There's a problem though: the arithmetic mean is not 10 anymore.

The drop from 2 to 1 is -1. So we need to have a +1 to exactly one of the other values (not the 12) to balance things out. Let's say we add 1 to 14 to get 15

So the set {1, 1, 5, 12, 14, 16, 20} changes to {1, 1, 5, 12, 15, 16, 20} which is another possible answer.

Refer to figure 2 for the dot plot of this. We have exactly one stack of dots (2 units high) over the "1". Every other dot is on its own.

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

Now let's say we wanted to form two stacks.

Starting from {1, 1, 5, 12, 15, 16, 20} we can subtract 4 from 5 to get 5-4 = 1

So we can change the "5" into "1" to get {1, 1, 1, 12, 15, 16, 20}

Then add 4 to another value, let's say the 16 to get 16+4 = 20. This is to balance out the -4 earlier.

Therefore we have {1, 1, 1, 12, 15, 20, 20} as another possible answer

Now we have two stacks. The left most stack has 3 items, and the right most has 2 items. The 12 and 15 are separate dots.

Refer to figure 3 for the dot plot.

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

This process of shuffling around pebbles so to speak can be done an infinite number of ways. Feel free to get creative to try out different sets and different dot plots.

Make sure that whatever you end up going with, the 12 stays in the middle and the values add up to 70.

Answer:

0

Step-by-step explanation: